Contrastive analysis of temperature and stress field distribution in cladding layer by Gaussian and Hollow-Ring laser modes

Contrastive analysis of temperature and stress field distribution in cladding layer by Gaussian and Hollow-Ring laser modes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Contrastive analysis of temperature and stress field distribution in cladding layer by Gaussian and Hollow-Ring laser modes Gangxian Zhu, Guangqi Li, Lifang Wang, Shihong Shi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1761335/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Jul, 2023 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 5 You are reading this latest preprint version Abstract The Gaussian laser mode can be converted into a hollow-ring laser mode through beam conversion system, realizing the conversion of circular and solid spot into a hollow-ring spot, which changes the energy distribution form of the laser spot. In order to study effects of the Gaussian and hollow-ring laser modes on temperature and stress fields in cladding layers, the numerical simulation and experimental investigation were performed. The results showed that molten pool experienced once temperature peak and generated sharp temperature change under the Gaussian laser, while the molten pool experienced twice temperature peaks and temperature changed relatively gentle when used the hollow-ring laser. Comparing with the Gaussian laser, the maximum temperature gradient along the depth of cladding layer decreased by 72.3% from 1.79×10 6 ℃/m to 4.95×10 5 ℃/m and the maximum residual stress decreased from 272MPa to 251MPa under hollow-ring laser. Meanwhile, the simulation results were validated by experiments with the same process. Further more, the sample microstructure were studied from the experiment. The microstructure was finer and more uniform using hollow-ring laser. This paper can provide guidance and advantage for laser cladding and direct metal deposition based on the hollow-ring mode, and broad the application of laser field. Laser cladding Hollow-ring laser Residual stress Numerical simulation Defocusing amount Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1 Introduction Laser cladding is an advanced surface strengthening technology that uses a high-energy density laser as a heat source to rapidly melt the metal powder and form a metallurgical combination with the substrate with extremely low dilution after cooling[ 1 ]. Laser cladding has many advantages, such as little deformation of substrate, high hardness, well abrasion resistance, high corrosion resistance and oxidation resistance[ 3 ] and has broad application prospects in fields of aerospace, automotive, medical, nuclear and shipping[ 7 ] During laser cladding process, local heat input will inevitably lead to an uneven temperature field and a large temperature gradient. After cooling, it is easy to generate residual stress in cladding layers. High residual stress has an undesirable effect on the crack sensitivity, deformation of substrate, yield strength, ultimate strength and fatigue strength, as well as the life expectancy of materials[ 12 ], which affects the mechanical properties of formed parts in turn[ 17 ]. Therefore, how to solve the residual stress problem has become a hot issue in the field of laser cladding. At present, numerical simulation combining experimental investigation is Corresponding author. E-mail address: [email protected] ; Gangxian Zhu and Guangqi Li have contributed equally to this work. mostly used to study and predict the residual stress distribution of cladding layer under Gaussian laser source[ 19 ]. Sun et al. built the 3D finite element model to simulate the temperature and stress field distribution in the process of laser cladding nicked-base alloys, the results showed that a large temperature gradient was generated near the heat source, which easily caused high residual stress. And the cladding layer cracked along the vertical sirection.[ 21 ]. Wang et al.[ 22 ] performed numerical simulation and experimental research on the effects of process parameters on residual stress during laser deposition forming and the results showed that the residual stress on the top surface of the cladding layer decreased with scanning speed and preheating temperature increasing. Haider et al.[ 23 ] studied the effect of scanning path on residual stress and the results showed that the residual stress was the largest with adopting partitioned scanning strategy. Wang et al.[ 24 ] analyzed the effects of laser process parameters and different scanning strategies on the residual stress of the cladding layer, and concluded that the formation of the internal stress of the cladding layer was mainly due to unevenness heat input. Heigel et al. [ 25 ] adopted the thermal-mechanical coupling finite element method to study the stress evolution rule of TC4 titanium alloy during laser deposition, the results showed that large temperature gradient caused high residual stress and plastic deformation. Yan et al.[ 26 ] explored the effect of process parameters on the deformation of cladding layer 316L stainless steel powder and the results showed that laser power and powder feeding rate had a greater effect on the deformation of the cladding layer. Reducing the powder feeding rate and laser power could effectively reduce the temperature gradient distribution, which reduced residual stress and deformation of the cladding layer. Krzyzanowski et al.[ 27 ]studied the transient thermal and stress distributions with a numerical model during laser cladding, they found the crack susceptibility was reduced by the preheated base plate. Wang et al.[ 28 ]studied the influence of process parameters on thermal behavior during laser cladding of TI-6Al-4V metal powder by finite element method and concluded that the increasing laser power could increase the cooling rate and crack tendency of cladding layer. Mugwagwa et al.[ 29 ]researched the influence of laser power and scanning speed on the deformation of parts during laser cladding forming. The results showed that the deformation amount increased with the increase of the scanning speed, and the laser power had no significant effect on the deformation amount. Liu et al.[ 30 ]discussed the effects of process parameters on thermal stress in a single-track cladding layer with wide-spot laser beam by numerical simulation. The results showed that the laser power and scanning speed directly affected the solidification rate, temperature gradient and cooling rate of the molten pool. Stress increased with increasing of laser power and decreased with increasing of scanning speed. Most of the above literatures focus on the Gaussian laser spot. The high energy is concentrated in the center of the spot, while the energy at the edge is low. Such energy distribution is easily to cause large temperature gradient in cladding. In addition, the adhering powder defects is often produced on both edges of the cladding layer with Gaussian laser spot in actual cladding process, which reduces the powder utilization rate. In order to solve the above defects caused by Gaussian laser spot, the research group invented a laser cladding nozzle device based on "hollow beam and internal powder feeding" cladding process[ 31 ]. The laser spot transformed from solid spot to hollow-ring spot by beam conversion system, and the energy distribution is more uniform, which can improve poor metallurgical bonding defect and enhance powder utilization rate[ 32 ]. Although much research on the temperature and stress field of Gaussian laser spot has been performed, the temperature and stress distribution with a hollow-ring laser spot has not been studied. On account of different energy distributions, it is valuable to explore the temperature and stress fields with hollow-ring laser and broad the application of laser field. 2 Mechanism Of Hollow-ring Laser Cladding 2.1 Generation principle of hollow-ring laser spot According to the coaxial nozzle device developed by our research group, the mechanism of hollow-ring spot is shown in Fig. 1 . The powder feeding system consists of a powder feeder and a specially designed coaxial nozzle device[ 34 ],which makes the laser beam be split by a cone mirror and then focused by another ring mirror. Subsequently, the parallel beam is transferred into an internal hollow beam. By this method, the way of external-side powder feeding is transferred to inside-beam powder feeding and the laser beam is guided to the worktable through an optical fiber and focused by an optical system with a 192mm focal length to focus a hollow-ring laser spot. The powder tube is wrapped inside by the laser beam and drops vertically into the molten pool to avoid powder shunting, realizing the concentricity of the powder spot and the laser spot, the coaxiality of the powder flow and the laser beam, which greatly improves the utilization rate of metal powder. 2.2 Mathematical model of hollow-ring laser energy Hollow-ring laser has a "Gaussian-like" energy distribution and the energy density satisfie[ 35 ]: $${q}_{z}\left(x,y\right)=\frac{\eta \cdot 2\cdot P}{\pi \left({R}_{0}^{2}+2{R}_{0}z\text{cot}\phi \right)}\text{e}\text{x}\text{p}(-\frac{2{\left(\sqrt{{x}^{2}+{y}^{2}}-\left(z\text{cot}\phi +\xi {R}_{0}\right)\right)}^{2}}{{R}_{0}^{2}})$$ 1 $${ R}_{A}=z{cot}\phi$$ 2 \({R}_{B}=z{cot}\phi\) + \({R}_{0 }\) (3) Where: \(P\) —laser power, W. \(\eta\) —laser absorption efficiency. \({R}_{0}\) —radius at focal position, mm. \(z\) —defocusing amount, mm. \(\phi\) —the angle between the laser beam and the horizontal direction,°. ξ—energy peak position coefficient, ξ∈[0 ~ 1]. \({R}_{A}\) —inner radius of ring spot, mm. \({R}_{B}\) —outer radius of ring spot, mm. According to the formula, the energy distribution of the hollow-ring laser is related to the laser defocusing amount and the position of the energy peak. The energy values are obtained separately by taking different defocusing amounts and energy peak positions coeffcient. Considering the hollow-ring laser head structure used in the experiment, the energy peak is located in the middle of the ring region, so ξ is taken as 0.5 in this paper. In addition, the energy density satisfies the Gaussian energy distribution when z = 0 according to formula 10. As shown in the Fig. 2 , the energy of the hollow-ring laser spot is concentrated in the ring region and the central region presents low energe, which is contrary to the Gaussian energy distribution. 3 Finite Element Model Theory During laser cladding process, the melting and solidification of the molten pool are completed in an instant. The actual size of cladding layer is small, and the size of the molten pool is basically stable. To simplify the model calculation, the model is made the following assumptions[ 36 ]: (1) The materials are all isotropic; (2) The ambient temperature is 25℃ (3) Both the cladding layer and the substrate are rectangular, ignoring subtle details such as rounded corners of the model; (4) The flow effect inside the molten pool is ignored; (5) Metal powder and substrate will not cause vaporization during cladding process; (6) The heat radiation effect is not considered separately and is equivalent coupled to convection heat transfer. 3.1 Thermal analysis 3.1.1 Governing equation Laser cladding process is a typical transient heat transfer process. The transient heat source control equation satisfies the first law of thermodynamics and the Fourier heat equation[ 37 ]: $$\rho c\frac{\partial T}{\partial t}=k\left(\frac{{\partial }^{2}T}{\partial {x}^{2}}+\frac{{\partial }^{2}T}{\partial {y}^{2}}+\frac{{\partial }^{2}T}{\partial {z}^{2}}\right)+{Q}_{laser}$$ 4 Where ρ (kg \(\cdot\) m −3 ) is the material density, k (W \(\cdot\) m −1 \(\cdot K\) −1 ) and c (J \(\cdot\) kg −1 \(\cdot\) K −1 ) respectively represent the thermal conductivity and specific heat capacity of the material, \({Q}_{laser}\) (W \(\cdot\) m 2 ) represents the input laser energy. 3.1.2 Initial and boundary conditions When the cladding process is not performed, the substrate has a uniform room temperature, which is the initial temperature. $$T\left(x,y,z,t=0\right)={T}_{0}$$ 5 \({T}_{0}\) stands for room temperature and the default value is 25°C. During laser cladding process, the heat conversion mainly includes: the heat absorbed by the metal powder, the heat lost and radiated by the convective heat exchange between the workpiece and the surrounding environment. According to the law of conservation of energy, the boundary conditions are: - \(k\frac{\partial T}{\partial n}\) = \(h(T-{T}_{0})\) (6) In the formula, \(T\) \(\text{a}\text{n}\text{d} {T}_{0}\) represent the boundary temperature and the room temperature, respectively, and h represents the comprehensive coefficient considering the effects of convection and radiation. The formula for calculating the comprehensive coefficient is as follows[ 38 ]: $$h=24.1\times {10}^{-4}\epsilon {T}^{1.61 }$$ 7 where ε is the surface emissivity. The top surface is set to: - \(k\frac{\partial T}{\partial n}\) = \({Q}_{laser}-{h}_{1}\left(T-{T}_{0}\right)-\sigma \epsilon \left({T}^{4}-{T}_{0}^{4}\right)\) (8) Where \({h}_{1}\) =100 W \(\cdot\) (m 2 \(\cdot \text{K}\) ) −1 represents the convection coefficient between the molten pool and the surrounding environment, \(\sigma\) = 5.67×10 − 8 W \(\cdot\) (m 2 \(\cdot\) K 4 ) −1 represents the Stefan Boltzmann constant. The boundary conditions at the bottom of the substrate are: - \(k\frac{\partial T}{\partial n}\) = \({h}_{2}\left(T-{T}_{0}\right)\) (9) Where \({ h}_{2}\) represents the convection coefficient between the substrate bottom and the worktable, \({h}_{2}\) =30 W \(\cdot\) (m 2 \(\cdot\) K) −1 [ 39 ]. The rest of surfaces are set to the following boundary conditions: - \(k\frac{\partial T}{\partial n}\) = \({h}_{3}\left(T-{T}_{0}\right)\) (10) where \({h}_{2}\) is the natural convection coefficient, \({h}_{3}\) =15 W \(\cdot\) (m 2 \(\cdot\) K) −1 [ 37 ] 3.2 Mechanical analysis A thermal-elastic-plastic model is adopted to simulate the stress field. The total strain increment includes the following[ 41 ]: $$\varDelta \epsilon =\varDelta {\epsilon }^{e}+\varDelta {\epsilon }^{p}+\varDelta {\epsilon }^{T}+\varDelta {\epsilon }^{\varDelta V}+\varDelta {\epsilon }^{\text{Tr}p}$$ 11 Where \(\varDelta {\epsilon }^{e}、\varDelta {\epsilon }^{p} \text{a}\text{n}\text{d} \varDelta {\epsilon }^{T}\) represent the elastic strain increment, plastic strain increment and thermal strain increment respectively, \(\varDelta {\epsilon }^{\varDelta V}\) represents volumetric strain increment and \(\varDelta {\epsilon }^{\text{Tr}p}\) represents strain increment caused by phase change. In stress field analysis, the initial boundary conditions are: $$\sigma （x,y,z,0）=0, \epsilon \left(x,y,z,0\right)=0$$ 12 Two sides of the substrate are subject to displacement constraints, which is in line with the fixture fixing in the actual cladding process. 3.3 Element birth and death The birth and death technology in ANSYS is used to achieve the energy loading of the laser beam. The so-called "death" means that the stiffness matrix of the element is multiplied by an infinitesimal default value to make it infinitely close to 0 when no laser energy is loaded on the corresponding element. Before simulation, all elements built in cladding layers are killed. Therefore, in the laser scanning process, the deactivated element does not participate in the heat transfer process. During the simulation, the elements are activated to participate in the heat conduction process when the laser energy is loaded on the corresponding element. 3.4 Geometric Modeling and Meshing Figure 3 (a) shows the finite element model. The size of the cladding layer is 42mm×42mm×0.6mm and the size of the substrate is 60mm×60mm×6mm. A gradient mesh is chosen to simplify the model and improve the calculation accuracy, that is the laser irradiation region and the heat affected zone is more finely divided in the cladding layer whereas the substrate away from the cladding layer is sparsely divided[ 42 ]. The cladding layer grid size is 0.3mm×0.3mm×0.1mm. Node B is located on the upper surface of the cladding layer and the section P 1 -P 2 is the vertical plane of X-Y plane. On the section P 1 -P 2, path1 is along the cladding layer depth, as shown in Fig. 3 (b). 3.5 Thermo physical Properties of 316L The substrate material and cladding material are 316L stainless steel. The chemical composition is shown in Table 1: Table 1 Chemical composition of 316L powder wt.% Material C Si Mn P S Ni Cr Mo 316L 0.03 1.00 2.00 0.035 0.03 13.5 17 2.5 Combing literature[ 44 ]with interpolation method, the thermophysical parameters of the 316L stainless steel material at different temperatures are obtained. as shown in Table 2 and Table 3 . Where \({\rho }\) -density, T-Celsius, c-specific heat capacity, \({\kappa }\) -thermal conductivity, E-elastic modulus, \({{\alpha }}_{\text{l}}\) -thermal expansion coefficient, \({\upsilon }\) -Poisson's ratio, σ -yield stress, and \({\text{E}}^{{\prime }}\) -Tangent modulus of the material. Table 2 Thermo-physical parameters of 316L stainless steel T/(K) c/(J \(\cdot\) kg \(\cdot\) K − 1 ) \({\kappa }\) /(W•m − 1 •K − 1 ) \({\rho }\) /(kg•m − 3 ) 293 477 13.31 7966 373 487 14.68 7937 473 528 16.33 7898 573 529 17.93 7857 673 550 19.47 7814 773 571 20.96 7769 873 592 22.38 7724 973 613 23.76 7677 1073 634 25.07 7630 1173 655 26.33 7583 1273 676 27.53 7535 1373 698 28.67 7486 1473 719 29.76 7436 1693 765 31.95 7320 1733 765 32 7320 Table 3 Mechanical properties of 316L stainless steel T/(K) E/(Pa) \({{\alpha }}_{\text{l}}\) /(K − 1 ) \({\upsilon }\) \({\sigma }\) /(Pa) \({\text{E}}^{{\prime }}\) /(Pa) 293 2.21 \(\cdot\) 10 11 15.24 \(\cdot\) 10 − 6 0.267 0.278 \(\cdot\) 10 9 2.21 \(\cdot\) 10 10 473 1.96 \(\cdot\) 10 11 16.43 \(\cdot\) 10 − 6 0.290 0.193 \(\cdot\) 10 9 1.96 \(\cdot\) 10 10 673 1.86 \(\cdot\) 10 11 17.44 \(\cdot\) 10 − 6 0.322 0.154 \(\cdot\) 10 9 1.86 \(\cdot\) 10 10 873 1.71 \(\cdot\) 10 11 18.21 \(\cdot\) 10 − 6 0.296 0.141 \(\cdot\) 10 9 1.71 \(\cdot\) 10 10 1073 1.32 \(\cdot\) 10 11 18.83 \(\cdot\) 10 − 6 0.262 0.130 \(\cdot\) 10 9 1.32 \(\cdot\) 10 10 1173 1.17 \(\cdot\) 10 11 19.11 \(\cdot\) 10 − 6 0.240 0.086 \(\cdot\) 10 9 1.17 \(\cdot\) 10 10 1273 1.01 \(\cdot\) 10 11 19.38 \(\cdot\) 10 − 6 0.229 0.045 \(\cdot\) 10 9 1.01 \(\cdot\) 10 10 1373 0.81 \(\cdot\) 10 11 19.66 \(\cdot\) 10 − 6 0.223 0.022 \(\cdot\) 10 9 0.81 \(\cdot\) 10 10 1473 0.35 \(\cdot\) 10 11 19.95 \(\cdot\) 10 − 6 0.223 0.013 \(\cdot\) 10 9 0.35 \(\cdot\) 10 10 1693 0.02 \(\cdot\) 10 11 20.7 \(\cdot\) 10 − 6 0.223 0.003 \(\cdot\) 10 9 0.02 \(\cdot\) 10 10 1733 0.02 \(\cdot\) 10 11 20.7 \(\cdot\) 10 − 6 0.223 0.003 \(\cdot\) 10 9 0.02 \(\cdot\) 10 10 4 Results And Discussion The solid70 element has 8 nodes and 8 temperature degrees of freedom, which can achieve uniform heat flow in three directions, it is often used in the process of three-dimensional transient thermal analysis. While the solid45 element has 8 nodes and 24 displacement degrees of freedom with large deformation and large strain capacity and it is used as a three-dimensional structural field analysis. So solid70 was adopted as the element type in the temperature field simulation process. The thermal analysis element type solid70 was converted to the structural element type solid45 and all boundary conditions were deleted in the thermal analysis simulation. By loading the temperature data, the results of transient stress, strain and displacement could be obtained. The numerical simulation process parameters were shown in Table 4 . Table 4 Laser cladding process parameters Power, P(W) Scanning speed, V(mm/s) Defocus amount, z(mm) Laser absorptivity, A Feeding rate, v(g/min) Ambient temperature, T 0 (℃) 1100 6 0/-3 0.4 8 25 4.1 Analysis of temperature field results 4.1.1 Temperature distribution Figure 4 shows the temperature field distribution of Gausssian laser spot with z = 0mm and the hollow-ring laser spot with z=-3mm at B positon, respectively. According to Fig. 4 (a), the shape of the spot is circular and solid. The high energy is distributed in the central region of the spot and temperature reaches 2386.53℃. While z=-3mm, the spot shape presents "crescent" and the high energy is distributed in ring region that temperature is up to 1940℃, as shown in Fig. 4 (b). Figure 5 illustrates the temperature distribution of P 1 -P 2 section when the spot center is located at B position. It can be seen from Fig. 5 (a) that the high temperature region concentrates in the middle of the cladding layer and the temperature on both sides is relatively low. On the contrary, high temperature region is concentrated on both sides of the cladding layer, and the temperature in the middle region is lower, as shown in Fig. 5 (b). 4.1.2 Characteristics of temperature curve Figure 6 (a) shows the temperature change curve of node B with time under different defocusing amounts. According to Fig. 6 , node B experiences one temperature peak during the cladding process and the temperature changes relatively drastic when z = 0mm, which reflected that the laser cladding is a transient process of rapid heat and cooling. While z=-3mm, node B experiences two temperature peak and the latter temperature peak is higher than the previous one during the cladding process, which is related to the energy distribution of the hollow laser. By comparing the temperature change curves of the two energy distributions, the temperature change is relatively gentle when z=-3mm, which is conductive to reduce the temperature gradient. 4.1.3 Characteristics of temperature gradient The temperature gradient distributions on path1 under different defocusing amounts are illustrated in Fig. 7 . As shown in Fig. 7 , the temperature gradient distribution on path1 first increases and then decreases. That is, the temperature gradient is large in the cladding layer and reaches the maximum at the joint surface between the cladding layer and the substrate and then drops rapidly as it goes deep into the substrate region. The maximum temperature gradient reaches 1.78×10 6 ℃/m when z = 0mm. While z=-3mm, the maximum temperature gradient is only 4.95×10 5 ℃/m, which is 72.3% lower than that z = 0mm. Thus the temperature gradient of the cladding layer can be significantly reduced when z=-3mm, which is benefical to reduce the internal stress of the cladding layer. 4.2 Analysis of stress field results 4.2.1 Residual Stress distribution Figure 8 shows the residual stress distributions in X, Y, Z directions and Von-Mises when z=-3mm. The X direction residual stress distribution is symmetrical at both ends of the joint surface and maximum residual stress value reaches 236 MPa, whereas the cladding layer presents low stress state. The residual stress in Y direction of the cladding layer is tensile stress, and the high residual stress is distributed on the upper surface of the cladding layer and the maximum value reaches 273MPa, the region away from the cladding layer is compressive stress. The overall residual stress in Z direction is low and the cladding layer presents compressive stress. The equivalent stress distribution presents “dumbbell” shape, the maximum stress is distributed at the beginning of the cladding and the maximum value reaches 299MPa. The above analysis showed that the residual stress in Y direction was the largest and was the main stress[ 46 ]. Therefore, the residual stress in Y direction is mainly studied in this paper. 4.2.2 Stress distribution on the path Figure 9 illustrates the Y direction residual stress distribution on cladding layer along path1 under different defocusing amounts. According to Fig. 9 , the Y direction residual stress distribution tendency of cladding layer on path1 is consistent under different defocusing amounts. The residual stress first increases and then decreases with the increase of the cladding layer depth and reaches maximum value at 1/4 position from the joint surface. The comparison shows that the residual stress is larger when z = 0mm than z=-3mm. This can be interpreted as the concentration of laser energy at the focal point and the cladding layer absorbs more energy when z = 0mm, resulting in large temperature gradient. Therefore, the residual stress of cladding layer can be reduced when z=-3mm, which is conductive to reduce crack tendency, and it proves the superiority of hollow laser cladding process and the rationality of energy distribution. 5 Experiment Procedure Figure 10 shows the experimental setup applied for the laser cladding process. The system includes: IPG YLS-2000-TR high Power fiber laser, GTV PF2/2M powder feeder, 6-axis KUKA robot, powder feeding system, tilting rotary table and gas system. 5.1 Experimental results and analysis 5.1.1 Laser energy distribution test This paper adopted Beam Monitor laser analysis meter to measure the energy density distribution of hollow laser spot and the test results are shown in Fig. 11 According to the test data from Fig. 11 (a), the energy of the hollow laser at the focal point(z = 0) presents a Gaussian distribution. But the energy shows two Gaussian-like energy distribution on both sides of the center line and there is no energy distribution near the center line when z=-3mm, as shown in Fig. 11 (b), which is consistent with the temperature field analysis results. 5.1.2 Residual stress test results In this paper, single-track laser cladding experiments were carried out with process parameters which were consistent with numerical simulation, and the samples were as shown in Fig. 12 (a). The X-350A stress tester was adopted to measure the residual stress of the sample. In order to otain the residual stress in depth of cladding layer, the surface of cladding layer was stripped and polished electrolytically using saturated \(\text{N}{\text{H}}_{4}\text{C}\text{l}\) -solution. The measurement points were five along depth direction of the cladding layer as shown in Fig. 12 (b). The residual stress test results in Y direction were shown in Fig. 13 . According to the Fig. 13 , the residual stress measured in the experiment showed a tendency which was firstly increasing and then decreasing with the depth growth. The overall stress presented tesile stress and the maximum residual stress appeared at 1/4 position away from the joint surface, which was consistent with the simulation and verified the correctness of the numerical simulation. Meanwhile, some differences existed between numerical simulation and experiment results. The main reasons were as follows: on the one hand,the model assumption was simplified and the finite element mesh couldn’t be meshed thinly, which leaded to calculation deviation. On the other hand, part of residual stress would be released during the stripping process in the experiment, which affected the accuracy of the measurement. 5.1.3 Microstructure analysis The microstructure of the component determines the mechanical properties and performance. The optical examination was carried out on samples with defocusing amount of z = 0 and z=-3mm. The microstructure was examined in the adjacent region of the top, middle and bottom, respectively, as shown in Fig. 14 . Figure 14 Microstructure of samples with different defcusing amounts at different positions As can be seen from Fig. 14 , no pores and microcracks were observed in the cross-section. It can be identified that the microstructure shows a mixture of dendrite and cellular structures. The difference is that the finest microstructure is shown on the top. The microstructure at the bottom is dendrite structures, because the deposited layers at the bottom are close to the substrate and the temperature gradient is more than the middle and top. Therefore, it is suggested that the difference of the microstructure resulted from the different molten pool temperature gradients. Comparing with the Gaussian laser, the microstructure was finer and more uniform using hollow-ring laser. 6 Conclusion In order to discuss the influence of the Gaussian and hollow-ring laser modes on temperature and stress fields in cladding layers, a 3D finite element method is established and experimental verification is performed with the same process parameters. The conclusions are as below. (1) The temperature of node on the cladding changed sharply and the temperature gradient was large when z = 0mm, while the temperature distribution was more uniform and the temperature gradient was smaller when z=-3 mm. (2) The residual stress in Y direction of the cladding layer was largest and the residual stress was higher when z = 0mm. Residual stress level could be effectively reduced when z=-3mm, which was benifical to reduce the cracking tendency of cladding. (3) Through the microstructure analysis and comparison, the grain size difference between the top, middle and bottom of the cladding was smaller than z = 0mm, which proved the uniformity and rationality when z=-3mm. Declarations Funding The work was financially supported by the National Key Research Program of China through Grant No.2016YFB1100300. Ethics approval Not applicable. Consent to participate Not applicable. Consent for publication Not applicable. Conflict of interest The authors declare no competing interests. References EI Cheikh H, Courant B, Branchu S, Hascoët JY, Guillén R (2012) Analysis and prediction of single laser tracks geometrical characteristics in coaxial laser cladding process. Opt Lasers Eng 50(3):413–422 Zeng C, Tian W, Liao WH, Hua L (2016) Microstructure and porosity evaluation in laser-cladding deposited Ni-based coatings. Surf Coat Technol 294:122–130 Weng F, Chen CZ, Yu HJ (2014) Research status of laser cladding on titanium and its alloys: A review. 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Int J Heat Mass Transfer 64:352–360 Sun ST, Fu HG, Chen SY, Ping XL, Wang KM, Guo XY, Lin J, Lei YP (2019) A numerical-experimental investigation of heat distribution, stress field and crack susceptibility in Ni60A coatings. Opt Laser Technol 117:175–185 Wang H (2014) Effect of process parameters on residual stress distribution during direct laser metal deposition. Adv Mater Res 989/994:49–54 Ali H, Ghabeigi H, Mumtaz K (2018) Effect of scanning strategies on residual stress and mechanical properties of selective laser melted Ti-6Al-4V. Mater Sci Eng 712:175–187 Wang LF, Jiang XH, Zhu YH, Zhu XG, Sun J, Yan B (2018) An approach to predict the residual stress and distortion during the selective laser melting of AlSi10Mg parts. Int J Adv Manuf Tech 97(9/12):1–12 Heigel JC, Michaleris P, Reutzel EW (2015) Thermo-mechanical model development and validation of directed energy deposition additive manufacturing of Ti-6Al-4V. 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Northwestern Polytechnical University Press, Xi an Cite Share Download PDF Status: Published Journal Publication published 17 Jul, 2023 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Major Revisions Needed 30 Oct, 2022 Reviewers agreed at journal 23 Jun, 2022 Reviewers invited by journal 23 Jun, 2022 Editor assigned by journal 22 Jun, 2022 First submitted to journal 20 Jun, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1761335","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":115737193,"identity":"ce9f6617-593d-4c61-b1ac-b2ba0e6e3d62","order_by":0,"name":"Gangxian Zhu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYHACNgaGCiB1AIh5iNdyhmQtjG2kaJGPSH/2mHdeXWLf8QOMD962McibE9JieOZAujHvtsOJM88kMBvObWMw3NlASEt7wzFp3m0HEjccSGCT5m1jSDA4QEhLM2ObNO+cusQN5x+w/yZKizx7M9DwBubEDTcS2JiJ0mLAc4xNcs6xw8YzbzxslpxzTsJwA0FbZqQ/k3hTUyfbdz754Ic3ZTbyhG1BKGBsABISBNSDbGkgrGYUjIJRMApGOgAA339BZ5qusyAAAAAASUVORK5CYII=","orcid":"","institution":"Soochow University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Gangxian","middleName":"","lastName":"Zhu","suffix":""},{"id":115737194,"identity":"9b6b863a-751b-4de7-8438-08cce02cb9b2","order_by":1,"name":"Guangqi Li","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Guangqi","middleName":"","lastName":"Li","suffix":""},{"id":115737195,"identity":"45c7ea52-5113-432b-be2d-9cb3785c8701","order_by":2,"name":"Lifang Wang","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Lifang","middleName":"","lastName":"Wang","suffix":""},{"id":115737196,"identity":"a7dcf14d-afc6-448a-92ce-f7a8c9c3b337","order_by":3,"name":"Shihong Shi","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Shihong","middleName":"","lastName":"Shi","suffix":""}],"badges":[],"createdAt":"2022-06-15 13:05:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1761335/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1761335/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-023-11809-z","type":"published","date":"2023-07-17T21:42:40+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":23450588,"identity":"9acc1416-dddc-4ece-a710-631b2ec6ea54","added_by":"auto","created_at":"2022-07-05 14:04:14","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":31338,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of hollow-ring spot generation\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/a77ae47269227b268899fad6.jpg"},{"id":23452789,"identity":"68ff2950-778e-4b40-917b-887576da26a4","added_by":"auto","created_at":"2022-07-05 14:14:14","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":39933,"visible":true,"origin":"","legend":"\u003cp\u003eEnergy distribution of hollow-ring laser spot (a) three-dimension energy diagram (b) spot contour diagram\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/792ce47d48391fa931d9e5f6.jpg"},{"id":23453582,"identity":"2ea05c03-c16f-4a09-ba81-afd3afa9c2f2","added_by":"auto","created_at":"2022-07-05 14:19:14","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":31775,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic diagram of finite element geometric model (b) Schematic diagram of path establishment\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/060642842342b002b8d0b26d.jpg"},{"id":23451501,"identity":"5c61cb7d-3726-43b7-bd83-a6d6abe4467d","added_by":"auto","created_at":"2022-07-05 14:09:14","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":24079,"visible":true,"origin":"","legend":"\u003cp\u003e\tTemperature distribution with different defocusing amounts (a) z=0mm (b)z=-3mm\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/3f43fa89015818cdab5093ab.jpg"},{"id":23450589,"identity":"f38b2f41-ee10-4559-a3d7-cd2164be240f","added_by":"auto","created_at":"2022-07-05 14:04:14","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":31092,"visible":true,"origin":"","legend":"\u003cp\u003eThe temperature distribution of section P\u003csub\u003e1\u003c/sub\u003e-P\u003csub\u003e2\u003c/sub\u003e with different defocusing amounts (a)z=0 (b)z=-3mm\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/807675862d014fce8dc8049a.jpg"},{"id":23450592,"identity":"4daf5522-11c5-4ae5-99ef-cdfcad8b16e5","added_by":"auto","created_at":"2022-07-05 14:04:14","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":23866,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature change curve of node B under different defocusing amounts.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/d4a7d21af8e338dea4f15bc0.jpg"},{"id":23451504,"identity":"120a027e-4b0f-4b58-b701-dea753dc45b2","added_by":"auto","created_at":"2022-07-05 14:09:14","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":24479,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature gradient distribution on path1 under different defocusing amounts\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/34736c8df915b5f46de7eb76.jpg"},{"id":23451505,"identity":"4586d1ef-d98e-420d-8dc6-e395e5d444dc","added_by":"auto","created_at":"2022-07-05 14:09:14","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":62887,"visible":true,"origin":"","legend":"\u003cp\u003eResidual stress distribution in different directions (a) X-Direction stress (b) Y-Direction stress (c) Z-Direction stress (d) equivalent stress\u0026nbsp;\u0026nbsp;\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/4ded8c1901c1e1728db6b93e.jpg"},{"id":23450595,"identity":"9dcc2c42-41ee-439f-bc02-c46aac25be46","added_by":"auto","created_at":"2022-07-05 14:04:14","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":24589,"visible":true,"origin":"","legend":"\u003cp\u003e\tY direction stress distribution on Path 1 under different defocusing amounts\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/f5129f616cd8925422ce059e.jpg"},{"id":23452790,"identity":"60f45f45-51cb-4254-ab68-81cac4f07c5b","added_by":"auto","created_at":"2022-07-05 14:14:14","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":35037,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the experimental setup\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/94cca7454bcf6626ec6492e7.jpg"},{"id":23451509,"identity":"4069b3b7-f10f-4281-8391-127fcbea4e78","added_by":"auto","created_at":"2022-07-05 14:09:14","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":42036,"visible":true,"origin":"","legend":"\u003cp\u003eEnergy density distribution with different defocusing amount (a) z=0 (b)z=-3mm\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/0fdfdd8474daa51e244799da.jpg"},{"id":23453605,"identity":"097f86bc-b803-472e-87ad-ef973e6ee6f3","added_by":"auto","created_at":"2022-07-05 14:19:14","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":36776,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Single-track laser cladding samples with different defocusing amounts (b) schematic diagram of residual stress test point on cladding layer\u0026nbsp;\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/06835cb1872505c4b30c944a.jpg"},{"id":23453597,"identity":"b7e795c2-d2fa-49ff-bac9-fb94f98f5dad","added_by":"auto","created_at":"2022-07-05 14:19:14","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":40341,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of experimental results and simulation results\u0026nbsp;\u003c/p\u003e","description":"","filename":"13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/b559bf750c1d0b5bb43e5908.jpg"},{"id":23450601,"identity":"e449ee01-424e-4944-b09a-b3785f7d4423","added_by":"auto","created_at":"2022-07-05 14:04:14","extension":"jpg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":85473,"visible":true,"origin":"","legend":"\u003cp\u003eMicrostructure of samples with different defcusing amounts at different positions\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"14.jpg","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/5ad0eba025b5cd7362c17092.jpg"},{"id":44736193,"identity":"a72911ec-2178-47b8-8e95-ef06ef9dc0c2","added_by":"auto","created_at":"2023-10-16 22:29:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":921898,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1761335/v1/0fbd9e0b-f2d2-48c0-8bab-cc6eed315c33.pdf"}],"financialInterests":"","formattedTitle":"Contrastive analysis of temperature and stress field distribution in cladding layer by Gaussian and Hollow-Ring laser modes","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eLaser cladding is an advanced surface strengthening technology that uses a high-energy density laser as a heat source to rapidly melt the metal powder and form a metallurgical combination with the substrate with extremely low dilution after cooling[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Laser cladding has many advantages, such as little deformation of substrate, high hardness, well abrasion resistance, high corrosion resistance and oxidation resistance[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] and has broad application prospects in fields of aerospace, automotive, medical, nuclear and shipping[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] During laser cladding process, local heat input will inevitably lead to an uneven temperature field and a large temperature gradient. After cooling, it is easy to generate residual stress in cladding layers. High residual stress has an undesirable effect on the crack sensitivity, deformation of substrate, yield strength, ultimate strength and fatigue strength, as well as the life expectancy of materials[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], which affects the mechanical properties of formed parts in turn[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Therefore, how to solve the residual stress problem has become a hot issue in the field of laser cladding. At present, numerical simulation combining experimental investigation is\u003c/p\u003e \u003cp\u003e Corresponding author. E-mail address:[email protected]; Gangxian Zhu and Guangqi Li have contributed equally to this work.\u003c/p\u003e \u003cp\u003emostly used to study and predict the residual stress distribution of cladding layer under Gaussian laser source[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSun et al. built the 3D finite element model to simulate the temperature and stress field distribution in the process of laser cladding nicked-base alloys, the results showed that a large temperature gradient was generated near the heat source, which easily caused high residual stress. And the cladding layer cracked along the vertical sirection.[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Wang et al.[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] performed numerical simulation and experimental research on the effects of process parameters on residual stress during laser deposition forming and the results showed that the residual stress on the top surface of the cladding layer decreased with scanning speed and preheating temperature increasing. Haider et al.[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] studied the effect of scanning path on residual stress and the results showed that the residual stress was the largest with adopting partitioned scanning strategy. Wang et al.[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] analyzed the effects of laser process parameters and different scanning strategies on the residual stress of the cladding layer, and concluded that the formation of the internal stress of the cladding layer was mainly due to unevenness heat input. Heigel et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] adopted the thermal-mechanical coupling finite element method to study the stress evolution rule of TC4 titanium alloy during laser deposition, the results showed that large temperature gradient caused high residual stress and plastic deformation. Yan et al.[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] explored the effect of process parameters on the deformation of cladding layer 316L stainless steel powder and the results showed that laser power and powder feeding rate had a greater effect on the deformation of the cladding layer. Reducing the powder feeding rate and laser power could effectively reduce the temperature gradient distribution, which reduced residual stress and deformation of the cladding layer. Krzyzanowski et al.[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]studied the transient thermal and stress distributions with a numerical model during laser cladding, they found the crack susceptibility was reduced by the preheated base plate.\u003c/p\u003e \u003cp\u003eWang et al.[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]studied the influence of process parameters on thermal behavior during laser cladding of TI-6Al-4V metal powder by finite element method and concluded that the increasing laser power could increase the cooling rate and crack tendency of cladding layer. Mugwagwa et al.[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]researched the influence of laser power and scanning speed on the deformation of parts during laser cladding forming. The results showed that the deformation amount increased with the increase of the scanning speed, and the laser power had no significant effect on the deformation amount. Liu et al.[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]discussed the effects of process parameters on thermal stress in a single-track cladding layer with wide-spot laser beam by numerical simulation. The results showed that the laser power and scanning speed directly affected the solidification rate, temperature gradient and cooling rate of the molten pool. Stress increased with increasing of laser power and decreased with increasing of scanning speed.\u003c/p\u003e \u003cp\u003eMost of the above literatures focus on the Gaussian laser spot. The high energy is concentrated in the center of the spot, while the energy at the edge is low. Such energy distribution is easily to cause large temperature gradient in cladding. In addition, the adhering powder defects is often produced on both edges of the cladding layer with Gaussian laser spot in actual cladding process, which reduces the powder utilization rate. In order to solve the above defects caused by Gaussian laser spot, the research group invented a laser cladding nozzle device based on \"hollow beam and internal powder feeding\" cladding process[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The laser spot transformed from solid spot to hollow-ring spot by beam conversion system, and the energy distribution is more uniform, which can improve poor metallurgical bonding defect and enhance powder utilization rate[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Although much research on the temperature and stress field of Gaussian laser spot has been performed, the temperature and stress distribution with a hollow-ring laser spot has not been studied. On account of different energy distributions, it is valuable to explore the temperature and stress fields with hollow-ring laser and broad the application of laser field.\u003c/p\u003e"},{"header":"2 Mechanism Of Hollow-ring Laser Cladding","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Generation principle of hollow-ring laser spot\u003c/h2\u003e \u003cp\u003eAccording to the coaxial nozzle device developed by our research group, the mechanism of hollow-ring spot is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe powder feeding system consists of a powder feeder and a specially designed coaxial nozzle device[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e],which makes the laser beam be split by a cone mirror and then focused by another ring mirror. Subsequently, the parallel beam is transferred into an internal hollow beam. By this method, the way of external-side powder feeding is transferred to inside-beam powder feeding and the laser beam is guided to the worktable through an optical fiber and focused by an optical system with a 192mm focal length to focus a hollow-ring laser spot. The powder tube is wrapped inside by the laser beam and drops vertically into the molten pool to avoid powder shunting, realizing the concentricity of the powder spot and the laser spot, the coaxiality of the powder flow and the laser beam, which greatly improves the utilization rate of metal powder.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Mathematical model of hollow-ring laser energy\u003c/h2\u003e \u003cp\u003eHollow-ring laser has a \"Gaussian-like\" energy distribution and the energy density satisfie[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${q}_{z}\\left(x,y\\right)=\\frac{\\eta \\cdot 2\\cdot P}{\\pi \\left({R}_{0}^{2}+2{R}_{0}z\\text{cot}\\phi \\right)}\\text{e}\\text{x}\\text{p}(-\\frac{2{\\left(\\sqrt{{x}^{2}+{y}^{2}}-\\left(z\\text{cot}\\phi +\\xi {R}_{0}\\right)\\right)}^{2}}{{R}_{0}^{2}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${ R}_{A}=z{cot}\\phi$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({R}_{B}=z{cot}\\phi\\)\u003c/span\u003e \u003c/span\u003e+\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{0 }\\)\u003c/span\u003e\u003c/span\u003e (3)\u003c/p\u003e \u003cp\u003eWhere:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\)\u003c/span\u003e\u003c/span\u003e\u0026mdash;laser power, W.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\eta\\)\u003c/span\u003e \u003c/span\u003e\u0026mdash;laser absorption efficiency.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({R}_{0}\\)\u003c/span\u003e \u003c/span\u003e\u0026mdash;radius at focal position, mm.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(z\\)\u003c/span\u003e \u003c/span\u003e\u0026mdash;defocusing amount, mm.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\phi\\)\u003c/span\u003e \u003c/span\u003e\u0026mdash;the angle between the laser beam and the horizontal direction,\u0026deg;.\u003c/p\u003e \u003cp\u003eξ\u0026mdash;energy peak position coefficient, ξ\u0026isin;[0\u0026thinsp;~\u0026thinsp;1].\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({R}_{A}\\)\u003c/span\u003e \u003c/span\u003e\u0026mdash;inner radius of ring spot, mm.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({R}_{B}\\)\u003c/span\u003e \u003c/span\u003e\u0026mdash;outer radius of ring spot, mm.\u003c/p\u003e \u003cp\u003eAccording to the formula, the energy distribution of the hollow-ring laser is related to the laser defocusing amount and the position of the energy peak. The energy values are obtained separately by taking different defocusing amounts and energy peak positions coeffcient. Considering the hollow-ring laser head structure used in the experiment, the energy peak is located in the middle of the ring region, so ξ is taken as 0.5 in this paper. In addition, the energy density satisfies the Gaussian energy distribution when z\u0026thinsp;=\u0026thinsp;0 according to formula 10.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cp\u003eAs shown in the Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the energy of the hollow-ring laser spot is concentrated in the ring region and the central region presents low energe, which is contrary to the Gaussian energy distribution.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Finite Element Model Theory","content":"\u003cp\u003eDuring laser cladding process, the melting and solidification of the molten pool are completed in an instant. The actual size of cladding layer is small, and the size of the molten pool is basically stable. To simplify the model calculation, the model is made the following assumptions[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]:\u003c/p\u003e \u003cp\u003e(1) The materials are all isotropic;\u003c/p\u003e \u003cp\u003e(2) The ambient temperature is 25℃\u003c/p\u003e \u003cp\u003e(3) Both the cladding layer and the substrate are rectangular, ignoring subtle details such as rounded corners of the model;\u003c/p\u003e \u003cp\u003e(4) The flow effect inside the molten pool is ignored;\u003c/p\u003e \u003cp\u003e(5) Metal powder and substrate will not cause vaporization during cladding process;\u003c/p\u003e \u003cp\u003e(6) The heat radiation effect is not considered separately and is equivalent coupled to convection heat transfer.\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Thermal analysis\u003c/h2\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 Governing equation\u003c/h2\u003e \u003cp\u003eLaser cladding process is a typical transient heat transfer process. The transient heat source control equation satisfies the first law of thermodynamics and the Fourier heat equation[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\rho c\\frac{\\partial T}{\\partial t}=k\\left(\\frac{{\\partial }^{2}T}{\\partial {x}^{2}}+\\frac{{\\partial }^{2}T}{\\partial {y}^{2}}+\\frac{{\\partial }^{2}T}{\\partial {z}^{2}}\\right)+{Q}_{laser}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eρ\u003c/em\u003e (kg\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003em\u003csup\u003e\u0026minus;3\u003c/sup\u003e) is the material density, \u003cem\u003ek\u003c/em\u003e (W\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003em\u003csup\u003e\u0026minus;1\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot K\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003e\u0026minus;1\u003c/sup\u003e) and c (J\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003ekg\u003csup\u003e\u0026minus;1\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003eK\u003c/em\u003e\u003csup\u003e\u0026minus;1\u003c/sup\u003e) respectively represent the thermal conductivity and specific heat capacity of the material, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{laser}\\)\u003c/span\u003e\u003c/span\u003e(W\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003em\u003csup\u003e2\u003c/sup\u003e) represents the input laser energy.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 Initial and boundary conditions\u003c/h2\u003e \u003cp\u003eWhen the cladding process is not performed, the substrate has a uniform room temperature, which is the initial temperature.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$T\\left(x,y,z,t=0\\right)={T}_{0}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({T}_{0}\\)\u003c/span\u003e \u003c/span\u003e stands for room temperature and the default value is 25\u0026deg;C.\u003c/p\u003e \u003cp\u003eDuring laser cladding process, the heat conversion mainly includes: the heat absorbed by the metal powder, the heat lost and radiated by the convective heat exchange between the workpiece and the surrounding environment. According to the law of conservation of energy, the boundary conditions are:\u003c/p\u003e \u003cp\u003e-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\frac{\\partial T}{\\partial n}\\)\u003c/span\u003e\u003c/span\u003e=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(h(T-{T}_{0})\\)\u003c/span\u003e\u003c/span\u003e (6)\u003c/p\u003e \u003cp\u003eIn the formula, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(T\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{a}\\text{n}\\text{d} {T}_{0}\\)\u003c/span\u003e\u003c/span\u003e represent the boundary temperature and the room temperature, respectively, and h represents the comprehensive coefficient considering the effects of convection and radiation. The formula for calculating the comprehensive coefficient is as follows[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$h=24.1\\times {10}^{-4}\\epsilon {T}^{1.61 }$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003ewhere ε is the surface emissivity.\u003c/p\u003e \u003cp\u003eThe top surface is set to:\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\frac{\\partial T}{\\partial n}\\)\u003c/span\u003e\u003c/span\u003e=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{laser}-{h}_{1}\\left(T-{T}_{0}\\right)-\\sigma \\epsilon \\left({T}^{4}-{T}_{0}^{4}\\right)\\)\u003c/span\u003e\u003c/span\u003e(8)\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{1}\\)\u003c/span\u003e\u003c/span\u003e=100 W\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e(m\u003csup\u003e2\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot \\text{K}\\)\u003c/span\u003e\u003c/span\u003e)\u003csup\u003e\u0026minus;1\u003c/sup\u003erepresents the convection coefficient between the molten pool and the surrounding environment, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e= 5.67\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003eW\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e(m\u003csup\u003e2\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003eK\u003csup\u003e4\u003c/sup\u003e)\u003csup\u003e\u0026minus;1\u003c/sup\u003erepresents the Stefan Boltzmann constant.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe boundary conditions at the bottom of the substrate are:\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\frac{\\partial T}{\\partial n}\\)\u003c/span\u003e\u003c/span\u003e=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{2}\\left(T-{T}_{0}\\right)\\)\u003c/span\u003e\u003c/span\u003e(9)\u003c/p\u003e \u003cp\u003eWhere\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ h}_{2}\\)\u003c/span\u003e\u003c/span\u003e represents the convection coefficient between the substrate bottom and the worktable, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{2}\\)\u003c/span\u003e\u003c/span\u003e=30 W\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e(m\u003csup\u003e2\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003eK)\u003csup\u003e\u0026minus;1\u003c/sup\u003e[\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe rest of surfaces are set to the following boundary conditions:\u003c/p\u003e \u003cp\u003e-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\frac{\\partial T}{\\partial n}\\)\u003c/span\u003e\u003c/span\u003e=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{3}\\left(T-{T}_{0}\\right)\\)\u003c/span\u003e\u003c/span\u003e(10)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{2}\\)\u003c/span\u003e\u003c/span\u003e is the natural convection coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({h}_{3}\\)\u003c/span\u003e\u003c/span\u003e=15 W\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e(m\u003csup\u003e2\u003c/sup\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003eK)\u003csup\u003e\u0026minus;1\u003c/sup\u003e[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Mechanical analysis\u003c/h2\u003e \u003cp\u003eA thermal-elastic-plastic model is adopted to simulate the stress field. The total strain increment includes the following[\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\varDelta \\epsilon =\\varDelta {\\epsilon }^{e}+\\varDelta {\\epsilon }^{p}+\\varDelta {\\epsilon }^{T}+\\varDelta {\\epsilon }^{\\varDelta V}+\\varDelta {\\epsilon }^{\\text{Tr}p}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {\\epsilon }^{e}、\\varDelta {\\epsilon }^{p} \\text{a}\\text{n}\\text{d} \\varDelta {\\epsilon }^{T}\\)\u003c/span\u003e\u003c/span\u003e represent the elastic strain increment, plastic strain increment and thermal strain increment respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {\\epsilon }^{\\varDelta V}\\)\u003c/span\u003e\u003c/span\u003e represents volumetric strain increment and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta {\\epsilon }^{\\text{Tr}p}\\)\u003c/span\u003e\u003c/span\u003e represents strain increment caused by phase change.\u003c/p\u003e \u003cp\u003eIn stress field analysis, the initial boundary conditions are:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\sigma （x,y,z,0）=0, \\epsilon \\left(x,y,z,0\\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTwo sides of the substrate are subject to displacement constraints, which is in line with the fixture fixing in the actual cladding process.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Element birth and death\u003c/h2\u003e \u003cp\u003eThe birth and death technology in ANSYS is used to achieve the energy loading of the laser beam. The so-called \"death\" means that the stiffness matrix of the element is multiplied by an infinitesimal default value to make it infinitely close to 0 when no laser energy is loaded on the corresponding element. Before simulation, all elements built in cladding layers are killed. Therefore, in the laser scanning process, the deactivated element does not participate in the heat transfer process. During the simulation, the elements are activated to participate in the heat conduction process when the laser energy is loaded on the corresponding element.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Geometric Modeling and Meshing\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) shows the finite element model. The size of the cladding layer is 42mm\u0026times;42mm\u0026times;0.6mm and the size of the substrate is 60mm\u0026times;60mm\u0026times;6mm. A gradient mesh is chosen to simplify the model and improve the calculation accuracy, that is the laser irradiation region and the heat affected zone is more finely divided in the cladding layer whereas the substrate away from the cladding layer is sparsely divided[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. The cladding layer grid size is 0.3mm\u0026times;0.3mm\u0026times;0.1mm. Node B is located on the upper surface of the cladding layer and the section P\u003csub\u003e1\u003c/sub\u003e-P\u003csub\u003e2\u003c/sub\u003e is the vertical plane of X-Y plane. On the section P\u003csub\u003e1\u003c/sub\u003e-P\u003csub\u003e2,\u003c/sub\u003e path1 is along the cladding layer depth, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Thermo physical Properties of 316L\u003c/h2\u003e \u003cp\u003eThe substrate material and cladding material are 316L stainless steel. The chemical composition is shown in Table\u0026nbsp;1:\u003c/p\u003e \u003cp\u003e \u003cb\u003eTable\u0026nbsp;1\u003c/b\u003e Chemical composition of 316L powder\u003c/p\u003e \u003cp\u003ewt.%\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSi\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMn\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNi\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCr\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMo\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e316L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e13.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eCombing literature[\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]with interpolation method, the thermophysical parameters of the 316L stainless steel material at different temperatures are obtained. as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }\\)\u003c/span\u003e\u003c/span\u003e-density, T-Celsius, c-specific heat capacity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa }\\)\u003c/span\u003e\u003c/span\u003e-thermal conductivity, E-elastic modulus, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\alpha }}_{\\text{l}}\\)\u003c/span\u003e\u003c/span\u003e-thermal expansion coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\upsilon }\\)\u003c/span\u003e\u003c/span\u003e-Poisson's ratio, \u003cem\u003eσ\u003c/em\u003e-yield stress, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{E}}^{{\\prime }}\\)\u003c/span\u003e\u003c/span\u003e-Tangent modulus of the material.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThermo-physical parameters of 316L stainless steel\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT/(K)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ec/(J\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003ekg\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003eK\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa }\\)\u003c/span\u003e\u003c/span\u003e/(W\u0026bull;m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u0026bull;K\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }\\)\u003c/span\u003e\u003c/span\u003e/(kg\u0026bull;m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e293\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7966\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e487\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7937\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e528\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7898\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e573\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e529\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e17.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7857\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7814\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e773\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7769\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e873\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e592\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e22.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7724\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e973\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e613\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7677\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e634\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7630\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e655\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e26.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7583\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e27.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7535\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e698\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7486\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e719\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7436\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1693\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e765\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e31.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7320\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1733\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e765\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7320\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMechanical properties of 316L stainless steel\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT/(K)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE/(Pa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\alpha }}_{\\text{l}}\\)\u003c/span\u003e\u003c/span\u003e/(K\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\upsilon }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }\\)\u003c/span\u003e\u003c/span\u003e/(Pa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{E}}^{{\\prime }}\\)\u003c/span\u003e\u003c/span\u003e/(Pa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e293\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.21\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e15.24\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.278\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.21\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.96\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e16.43\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.290\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.193\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.96\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.86\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e17.44\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.322\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.154\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.86\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e873\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.71\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e18.21\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.141\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.71\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.32\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e18.83\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.262\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.130\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.32\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.17\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e19.11\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.086\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.17\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.01\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e19.38\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.229\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.045\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.01\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.81\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e19.66\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.022\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.81\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.35\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e19.95\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.013\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.35\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1693\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.02\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e20.7\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.003\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.02\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1733\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.02\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c3\"\u003e \u003cp\u003e20.7\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.003\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.02\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Results And Discussion","content":"\u003cp\u003eThe solid70 element has 8 nodes and 8 temperature degrees of freedom, which can achieve uniform heat flow in three directions, it is often used in the process of three-dimensional transient thermal analysis. While the solid45 element has 8 nodes and 24 displacement degrees of freedom with large deformation and large strain capacity and it is used as a three-dimensional structural field analysis. So solid70 was adopted as the element type in the temperature field simulation process. The thermal analysis element type solid70 was converted to the structural element type solid45 and all boundary conditions were deleted in the thermal analysis simulation. By loading the temperature data, the results of transient stress, strain and displacement could be obtained. The numerical simulation process parameters were shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLaser cladding process parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePower, P(W)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScanning speed, V(mm/s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDefocus amount, z(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLaser absorptivity, A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFeeding rate, v(g/min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAmbient temperature, T\u003csub\u003e0\u003c/sub\u003e(℃)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0/-3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Analysis of temperature field results\u003c/h2\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e4.1.1 Temperature distribution\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the temperature field distribution of Gausssian laser spot with z\u0026thinsp;=\u0026thinsp;0mm and the hollow-ring laser spot with z=-3mm at B positon, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a), the shape of the spot is circular and solid. The high energy is distributed in the central region of the spot and temperature reaches 2386.53℃. While z=-3mm, the spot shape presents \"crescent\" and the high energy is distributed in ring region that temperature is up to 1940℃, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b).\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the temperature distribution of P\u003csub\u003e1\u003c/sub\u003e-P\u003csub\u003e2\u003c/sub\u003e section when the spot center is located at B position.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a) that the high temperature region concentrates in the middle of the cladding layer and the temperature on both sides is relatively low. On the contrary, high temperature region is concentrated on both sides of the cladding layer, and the temperature in the middle region is lower, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e4.1.2 Characteristics of temperature curve\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) shows the temperature change curve of node B with time under different defocusing amounts.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, node B experiences one temperature peak during the cladding process and the temperature changes relatively drastic when z\u0026thinsp;=\u0026thinsp;0mm, which reflected that the laser cladding is a transient process of rapid heat and cooling. While z=-3mm, node B experiences two temperature peak and the latter temperature peak is higher than the previous one during the cladding process, which is related to the energy distribution of the hollow laser. By comparing the temperature change curves of the two energy distributions, the temperature change is relatively gentle when z=-3mm, which is conductive to reduce the temperature gradient.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e4.1.3 Characteristics of temperature gradient\u003c/h2\u003e \u003cp\u003eThe temperature gradient distributions on path1 under different defocusing amounts are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the temperature gradient distribution on path1 first increases and then decreases. That is, the temperature gradient is large in the cladding layer and reaches the maximum at the joint surface between the cladding layer and the substrate and then drops rapidly as it goes deep into the substrate region.\u003c/p\u003e \u003cp\u003eThe maximum temperature gradient reaches 1.78\u0026times;10\u003csup\u003e6\u003c/sup\u003e℃/m when z\u0026thinsp;=\u0026thinsp;0mm. While z=-3mm, the maximum temperature gradient is only 4.95\u0026times;10\u003csup\u003e5\u003c/sup\u003e℃/m, which is 72.3% lower than that z\u0026thinsp;=\u0026thinsp;0mm. Thus the temperature gradient of the cladding layer can be significantly reduced when z=-3mm, which is benefical to reduce the internal stress of the cladding layer.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Analysis of stress field results\u003c/h2\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e4.2.1 Residual Stress distribution\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the residual stress distributions in X, Y, Z directions and Von-Mises when z=-3mm. The X direction residual stress distribution is symmetrical at both ends of the joint surface and maximum residual stress value reaches 236 MPa, whereas the cladding layer presents low stress state. The residual stress in Y direction of the cladding layer is tensile stress, and the high residual stress is distributed on the upper surface of the cladding layer and the maximum value reaches 273MPa, the region away from the cladding layer is compressive stress. The overall residual stress in Z direction is low and the cladding layer presents compressive stress. The equivalent stress distribution presents \u0026ldquo;dumbbell\u0026rdquo; shape, the maximum stress is distributed at the beginning of the cladding and the maximum value reaches 299MPa.\u003c/p\u003e \u003cp\u003eThe above analysis showed that the residual stress in Y direction was the largest and was the main stress[\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Therefore, the residual stress in Y direction is mainly studied in this paper.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2 Stress distribution on the path\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e illustrates the Y direction residual stress distribution on cladding layer along path1 under different defocusing amounts.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the Y direction residual stress distribution tendency of cladding layer on path1 is consistent under different defocusing amounts. The residual stress first increases and then decreases with the increase of the cladding layer depth and reaches maximum value at 1/4 position from the joint surface. The comparison shows that the residual stress is larger when z\u0026thinsp;=\u0026thinsp;0mm than z=-3mm. This can be interpreted as the concentration of laser energy at the focal point and the cladding layer absorbs more energy when z\u0026thinsp;=\u0026thinsp;0mm, resulting in large temperature gradient.\u003c/p\u003e \u003cp\u003eTherefore, the residual stress of cladding layer can be reduced when z=-3mm, which is conductive to reduce crack tendency, and it proves the superiority of hollow laser cladding process and the rationality of energy distribution.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5 Experiment Procedure","content":"\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the experimental setup applied for the laser cladding process. The system includes: IPG YLS-2000-TR high Power fiber laser, GTV PF2/2M powder feeder, 6-axis KUKA robot, powder feeding system, tilting rotary table and gas system.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Experimental results and analysis\u003c/h2\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003e5.1.1 Laser energy distribution test\u003c/h2\u003e \u003cp\u003eThis paper adopted Beam Monitor laser analysis meter to measure the energy density distribution of hollow laser spot and the test results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the test data from Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a), the energy of the hollow laser at the focal point(z\u0026thinsp;=\u0026thinsp;0) presents a Gaussian distribution. But the energy shows two Gaussian-like energy distribution on both sides of the center line and there is no energy distribution near the center line when z=-3mm, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(b), which is consistent with the temperature field analysis results.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section3\"\u003e \u003ch2\u003e5.1.2 Residual stress test results\u003c/h2\u003e \u003cp\u003eIn this paper, single-track laser cladding experiments were carried out with process parameters which were consistent with numerical simulation, and the samples were as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(a). The X-350A stress tester was adopted to measure the residual stress of the sample. In order to otain the residual stress in depth of cladding layer, the surface of cladding layer was stripped and polished electrolytically using saturated \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{N}{\\text{H}}_{4}\\text{C}\\text{l}\\)\u003c/span\u003e\u003c/span\u003e-solution. The measurement points were five along depth direction of the cladding layer as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(b).\u003c/p\u003e \u003cp\u003eThe residual stress test results in Y direction were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, the residual stress measured in the experiment showed a tendency which was firstly increasing and then decreasing with the depth growth. The overall stress presented tesile stress and the maximum residual stress appeared at 1/4 position away from the joint surface, which was consistent with the simulation and verified the correctness of the numerical simulation. Meanwhile, some differences existed between numerical simulation and experiment results. The main reasons were as follows: on the one hand,the model assumption was simplified and the finite element mesh couldn\u0026rsquo;t be meshed thinly, which leaded to calculation deviation. On the other hand, part of residual stress would be released during the stripping process in the experiment, which affected the accuracy of the measurement.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section3\"\u003e \u003ch2\u003e5.1.3 Microstructure analysis\u003c/h2\u003e \u003cp\u003eThe microstructure of the component determines the mechanical properties and performance. The optical examination was carried out on samples with defocusing amount of z\u0026thinsp;=\u0026thinsp;0 and z=-3mm. The microstructure was examined in the adjacent region of the top, middle and bottom, respectively, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e14\u003c/span\u003e Microstructure of samples with different defcusing amounts at different positions\u003c/p\u003e \u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e14\u003c/span\u003e, no pores and microcracks were observed in the cross-section. It can be identified that the microstructure shows a mixture of dendrite and cellular structures. The difference is that the finest microstructure is shown on the top. The microstructure at the bottom is dendrite structures, because the deposited layers at the bottom are close to the substrate and the temperature gradient is more than the middle and top. Therefore, it is suggested that the difference of the microstructure resulted from the different molten pool temperature gradients. Comparing with the Gaussian laser, the microstructure was finer and more uniform using hollow-ring laser.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"6 Conclusion","content":"\u003cp\u003eIn order to discuss the influence of the Gaussian and hollow-ring laser modes on temperature and stress fields in cladding layers, a 3D finite element method is established and experimental verification is performed with the same process parameters. The conclusions are as below.\u003c/p\u003e \u003cp\u003e(1) The temperature of node on the cladding changed sharply and the temperature gradient was large when z\u0026thinsp;=\u0026thinsp;0mm, while the temperature distribution was more uniform and the temperature gradient was smaller when z=-3 mm.\u003c/p\u003e \u003cp\u003e(2) The residual stress in Y direction of the cladding layer was largest and the residual stress was higher when z\u0026thinsp;=\u0026thinsp;0mm. Residual stress level could be effectively reduced when z=-3mm, which was benifical to reduce the cracking tendency of cladding.\u003c/p\u003e \u003cp\u003e(3) Through the microstructure analysis and comparison, the grain size difference between the top, middle and bottom of the cladding was smaller than z\u0026thinsp;=\u0026thinsp;0mm, which proved the uniformity and rationality when z=-3mm.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe work was financially supported by the National Key Research Program of China through Grant No.2016YFB1100300.\u003c/p\u003e\n\u003cp\u003eEthics approval Not applicable.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConsent to participate Not applicable.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConsent for publication Not applicable.\u003c/p\u003e\n\u003cp\u003eConflict of interest The authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eEI Cheikh H, Courant B, Branchu S, Hasco\u0026euml;t JY, Guill\u0026eacute;n R (2012) Analysis and prediction of single laser tracks geometrical characteristics in coaxial laser cladding process. 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Northwestern Polytechnical University Press, Xi an\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Laser cladding, Hollow-ring laser, Residual stress, Numerical simulation, Defocusing amount","lastPublishedDoi":"10.21203/rs.3.rs-1761335/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1761335/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Gaussian laser mode can be converted into a hollow-ring laser mode through beam conversion system, realizing the conversion of circular and solid spot into a hollow-ring spot, which changes the energy distribution form of the laser spot. In order to study effects of the Gaussian and hollow-ring laser modes on temperature and stress fields in cladding layers, the numerical simulation and experimental investigation were performed. The results showed that molten pool experienced once temperature peak and generated sharp temperature change under the Gaussian laser, while the molten pool experienced twice temperature peaks and temperature changed relatively gentle when used the hollow-ring laser. Comparing with the Gaussian laser, the maximum temperature gradient along the depth of cladding layer decreased by 72.3% from 1.79\u0026times;10\u003csup\u003e6\u003c/sup\u003e℃/m to 4.95\u0026times;10\u003csup\u003e5\u003c/sup\u003e℃/m and the maximum residual stress decreased from 272MPa to 251MPa under hollow-ring laser. Meanwhile, the simulation results were validated by experiments with the same process. Further more, the sample microstructure were studied from the experiment. The microstructure was finer and more uniform using hollow-ring laser. This paper can provide guidance and advantage for laser cladding and direct metal deposition based on the hollow-ring mode, and broad the application of laser field.\u003c/p\u003e","manuscriptTitle":"Contrastive analysis of temperature and stress field distribution in cladding layer by Gaussian and Hollow-Ring laser modes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-07-05 14:04:12","doi":"10.21203/rs.3.rs-1761335/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2022-10-30T23:30:35+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2022-06-23T16:37:42+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-06-23T06:10:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-06-22T07:50:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2022-06-21T02:17:56+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f92bce38-72dc-4d60-8dcb-cd0c6e73409a","owner":[],"postedDate":"July 5th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T22:18:59+00:00","versionOfRecord":{"articleIdentity":"rs-1761335","link":"https://doi.org/10.1007/s00170-023-11809-z","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2023-07-17 21:42:40","publishedOnDateReadable":"July 17th, 2023"},"versionCreatedAt":"2022-07-05 14:04:12","video":"","vorDoi":"10.1007/s00170-023-11809-z","vorDoiUrl":"https://doi.org/10.1007/s00170-023-11809-z","workflowStages":[]},"version":"v1","identity":"rs-1761335","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1761335","identity":"rs-1761335","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}