Computational Study of Precipitation Hardening Process Effects on Mechanical Performance of Al-Zn-Mg Alloy: Molecular Dynamics Simulation

Computational Study of Precipitation Hardening Process Effects on Mechanical Performance of Al-Zn-Mg Alloy: Molecular Dynamics Simulation | 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 Computational Study of Precipitation Hardening Process Effects on Mechanical Performance of Al-Zn-Mg Alloy: Molecular Dynamics Simulation Roozbeh Sabetvand This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4679291/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The precipitation hardening is a heat treatment process used to increase the strength and hardness of certain alloys. The atomic analysis of this procedure can be presented valuable hints in actual applications. In current research, we used molecular dynamics (MD) method to introduce the temperature of precipitation hardening process effects on mechanical performance of Al-Zn-Mg alloy. Our MD research done in 2 main steps. Firstly, the equilibrium phase of modeled alloy reported by temperature and total energy convergence. After equilibrium phase detection, the mechanical properties of samples introduced by structural expansion process. MD results indicated the mechanical performance of Al-Zn-Mg alloy improved appreciably by using precipitation hardening process rather to pure aluminum sample. Furthermore, simulations outputs predicted the 473 K is appropriate temperature in precipitation hardening process of designed alloy. The ultimate strength and Young’s modulus of Al-Zn-Mg alloy increased to 348.98 MPa and 69.46 GPa (respectively) in optimum condition which should be supposed in mechanical applications. Atomic and Molecular Physics Al-Zn-Mg alloy Precipitation hardening process Mechanical performance Temperature effect Molecular dynamics Atomic modeling 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 1. Introduction Alloys play a crucial role in various industries, ranging from aerospace and automotive to construction and electronics [ 1 , 2 ]. These materials composed of two or more metallic elements; offer enhanced mechanical properties compared to pure metals. By carefully selecting alloying elements and controlling the microstructure through heat treatments, engineers can tailor the mechanical properties to meet specific application requirements [ 3 , 4 ]. Several mechanical properties are commonly evaluated to assess the performance of alloys such as strength, ductility, hardness, toughness, and fatigue resistance. Understanding these properties of alloys enables the design and production of components that can withstand the demands of various industries. The improvement of alloy’s mechanical properties is needed in today industry. The precipitation hardening process is a widely used process in the field of metallurgy to enhance the mechanical properties of alloys [ 5 , 6 ]. This process involves a series of heat treatments that result in the formation of fine precipitates within the alloy matrix, thereby increasing its strength and hardness. Precipitation hardening is commonly employed in various industries, including aerospace, automotive, and defense, where high-performance materials are required [ 7 ]. The precipitation hardening process typically consists of three processes: solution procedure, quenching step, and aging phase. Each step plays a crucial role in achieving the desired material properties. Several factors influence the precipitation hardening process and its outcome. Two important factors are alloy composition and aging temperature. The composition of the alloy plays a crucial role in determining its response to precipitation hardening. Elements such as copper, aluminum, titanium, and nickel are commonly inserted into sample to promote the stabilization of precipitates. Also, the temperature and duration of the aging process significantly affect the size, distribution, and composition of the precipitates. Higher aging temperatures generally result in larger precipitates with lower strength, while longer aging times can lead to averaging and reduced mechanical properties. Recently, a lot of research has been done in the field of precipitation hardening and its effect on the mechanical behavior of alloys. Between various alloys, the Al-Zn-Mg alloy attracts more scientists’ attention [ 8 – 10 ]. Chemingui et al. [ 11 ] studied the structure evolution of 7020 alloy via differential scanning calorimetry and XRD methods. Their outputs indicated the creation of hardening phase GP zones, intermediate hardening and stability phases. Their numerical outputs are in acceptable consistency and validate the successive precipitation/dissolution procedure. In other work, Chinh et al. [ 12 ] described the influence of Cu element on the mechanical and precipitation behavior of the Al at % Zn-2.1% and Mg-2.4% mixture structure (alloy). They used DSC, TEM and 3DAPFIM approaches to describe mechanical performance of alloy. They indicated the clustering of solute particles and defects during or immediately after aqueous environment quenching plays a remarkable effect in the nucleation of intermediate phase precipitates in one-step aging and the addition of copper atoms to ternary Al–Zn–Mg mixture caused the variations also in the initial clustering procedure. Nie et al. [ 13 ] developed a numerical approach for simulating double-peak precipitation hardening kinetics in Al-Zn-Mg mixture sample with the creation of various types of precipitates at target temperatures based on optimized Langer-Schwartz method. The systematic and quantitative results in this work shows the calculated hardness outputs of double peaks with inserting a shape dependent factor in the growth equation for growth and coarsening common agree appropriate with the calculated ones. Zhang et al. [ 14 ] introduced the mechanical performance of Al-Zn-Mg mixture structure by using the multi-stage aging methods. The microstructures of aged samples were identified with SEM and TEM methods. Their reported outputs described the appreciable ratio of GP zones and some part of unstable regions were created during T = 363.15 K aging at the 3 stage aging, which consumed effectively solid solubility. Also, they concluded the intergranular equilibrium η phase is beneficial to pin the evolution of dislocation, which avoids fracture process caused by accumulation of particle-base defects around the large 2 phase and on the grain region boundaries. By studying previous reports, we concluded the atom-base study on temperature of precipitation hardening process effect on mechanical performance of Al-Zn-Mg alloys doesn’t reported. It is expected that the atomic analysis of the precipitation hardening process of Al-Zn-Mg alloy can provide suitable hints for the design of effective mechanical alloy. So, we used the molecular dynamics (MD) approach to simulate precipitation hardening process of target alloy in various temperatures for the first time [ 15 , 16 ]. Our MD simulations done in two main steps include equilibrium and mechanical description of ideal Al-Zn-Mg mixture structure (alloy). In equilibrium phase, the temperature and total energy calculation done to equilibrium phase detection. Next, the deformation settings implemented to sample and mechanical performance of them reported by stress-strain curve estimation. These simulation phases done by using large scale atomic/molecular massively parallel simulator (LAMMPS) [ 17 – 19 ]. 2. MD Simulation Details The MD formalism is a powerful tool in studying the mechanical performance of alloys. It is a computational approach that simulates the behavior of atoms and molecules in a system over time, allowing for the prediction of mechanical outputs (parameters) such as strength, ductility, and fracture toughness [ 20 ]. At its core, MD formalism is based on classical mechanics and statistical thermodynamics. It involves solving the equations of motion for each atom in a system, taking into account the interatomic forces that govern their behavior [ 21 ]. This allows for the simulation of the system's dynamics over time, providing insight into its mechanical properties as below equation [ 22 ], $${F_i}=\sum\limits_{{i \ne j}} {{F_{ij}}={m_i}\frac{{{d^2}{r_i}}}{{d{t^2}}}={m_i}\frac{{d{v_i}}}{{dt}}}$$ 1 To solve this equation, force field of modeled system is important parameter [ 23 ]. In current research, to define atomic interactions, the modified embedded-atom method (MEAM) implemented [ 24 ]. The MEAM force field defined as Eq. ( 2 ), $$E=\sum _{i}\{{F}_{i}\left({\rho }_{i}\right)+\frac{1}{2}\sum _{i\ne j}{\phi }_{ij}\left({r}_{ij}\right)\}$$ 2 Here, F is the embedding energy parameter and describes the electron density ρ parameter in modeled sample, and φ introduced the pair interaction inside sample. The last parameter is calculated for various neighbors’ parties which located inside cutoff radius of center particle. Force field implementing inside box, Newton’s evolution equation fulfilled and various particles displacement in defined condition predicted. Technically, integrate of the Newton’s formalism is calculated by the velocity Varlet method as equations ( 3 ) and ( 4 ) [ 25 , 26 ], $$r\left( {t+\Delta t} \right)=r\left( t \right)+v\left( t \right)\Delta t+\frac{1}{2}a\left( t \right)\Delta {t^2}+O\left( {\Delta {t^4}} \right)$$ 3 $$v\left( {t+\Delta t} \right)=v\left( t \right)+\frac{{a\left( t \right)+a\left( {t+\Delta t} \right)}}{2}\Delta t+O\left( {\Delta {t^2}} \right)$$ 4 Where, r(t + Δt)/v(t + Δt) parameters are the coordinate and velocity of various atoms in t + Δt time of simulations, respectively. Currently, described computational method used to estimate the hardening process effects on mechanical performance of Al-Zn-Mg alloy. For this, MD simulations divided into 2 main phases as below, Equilibrium Phase – In the first step, the extra stress of model Al-Zn-Mg alloy eliminated by using the NVE ensemble for 1 ns. Next, the temperature of system changed from target value (773 K) to 298 K by implementing NVT ensemble (with 1 fs time step and 0.1 fs for temperature damping ratio). MD simulation done for 10 ns in this step. Computationally, the MD box size set to 120×340×340 Å 3 by using periodic boundary condition [ 27 ]. Our atomic representation of modeled Al-Zn-Mg alloy with 31850 atoms depicted in Fig. 1 . In this sample, modeled alloy consists of 92%Al- 5.5%|Zn- 2.5% Mg. Mechanical Evolution Phase – Secondary, the mechanical test settings implemented to equilibrated alloys. This setting caused the structural expansion of models with 0.1 fs − 1 ratio. In this step, the Nose-Hoover thermostat controlled the temperature of allies in expansion procedure [ 28 , 29 ]. Our used MD settings in our numerical research presented in Table 1 . Table 1 The MD method parameters value in atomic/mechanical description of Al-Zn-Mg alloy. MD Simulation Parameter Parameter Setting Computational Box Length 120×340×340 Å 3 Number of Atoms 31850 Boundary Setting PBC Barostat/Thermostat Nose-Hoover Temperature of Initial Condition 773 K Time Step 1 fs Temperature Damping Ratio 0.1 fs Simulation Total Time 20 ns 3. MD Simulation Outputs and Description 3.1 Equilibrium Step of Al-Zn-Mg Alloy The physical stability of designed Al-Zn-Mg alloy is important parameter for actual applications of them. To analyze this stability, the equilibrium phase of modeled samples estimated with MD simulations. Technically, the target alloy temperature changed from 773 K to 298 K in 6 computational cycles. Also, temperature of hardening process set to 423 K, 473 K, and 523 K for various designed alloys. Finally, the alloy equilibrated at 298 K for 10 ns. The temperature and total energy variation of sample by simulation time passing depicted in Fig. 2 . As seen from this MD output, the temperature of systems converged to 298 K after 10 ns. This outputs indicated the simulation time is sufficient to equilibrium phase detection in current phase. Physically, this thermal performance of various prepared Al-Zn-Mg alloys arises from atomic mobility convergence by MD time steps passing. Furthermore, the numeric convergence can be detected for total energy of various modeled alloys. Numerically, this energy converged to -3.047, -3.048, and − 3.051 eV in the final time step of current simulations. The negative value of total energy shows the average interatomic adsorptive interaction between various atoms inside alloy. Also, the negative value of total energy arises from appropriate MD settings in structures as reported in previous researches [ 30 – 32 ]. Between various equilibrated alloys, the sample with 473 K for precipitation hardening process haze maximum physical stability. The maximum value of interaction energy in this sample caused the high stability of them. To more structural analysis of samples, the atomic representation of them depicted in Fig. 3 . In this figure, the structural unity of various samples which arises from potential energy and modeling process settings, can be detected. The radial distribution function (RDF) of them more described the physical stability of Al-Zn-Mg alloys in defined condition. Computationally, the RDF is a parameter used to describe the distribution of particles in a system of atoms or molecules [ 33 ]. It measures the probability of finding a particle at a given distance from another particle. In atomic structures, the RDF is often used to analyze the packing and ordering of atoms in a material. It can provide information about the structure, stability, and properties of the material. MD outputs for RDF of designed Al-Zn-Mg alloys after equilibrium phase detection shown in Fig. 4 . As reported before, the numerous peaks in RDF results predicted the phase state and structural unity of alloys [ 34 ]. 3.2 Mechanical Evolution of Designed Alloys 3.2.1 Mechanical Behavior of Pure Al Sample In the first phase of current computational step, the mechanical evolution of pure aluminum matrix evaluated by using MD approach. The mechanical evolution of this sample in 298 K depicted in Fig. 5 . This figure predicted the physical stability of sample by MD time steps passing and structural expansion. To numerical analysis of this procedure, the stress-strain curve of Al matrix calculated. Figure 6 shows stress-strain outputs of them. This MD results consistent with previous report and validated our computational method [ 35 , 36 ]. Numerically, the ultimate strength and Young’s modulus of this sample reached to 290.10 MPa and 54.75 GPa, respectively. From these results, we concluded our MD settings are appropriate to numeric study of Al-based atomic structures mechanical performance. After equilibrium phase detection in model alloys, the structural expansion settings implemented to them. The time evolution of Al-Zn-Mg alloy in our designed mechanical test depicted in Fig. 7 . Physically, the negative value of total energy inside samples caused the amplitude of atomic fluctuations converged to constant value and structural unity don’t disrupted in various steps of MD simulation. The stress-strain output for this process depicted in Fig. 8 . From this curve which calculated for Al-Zn-Mg alloy with 423 K value for precipitation hardening process, we concluded the mechanical performance of designed alloy improved appreciably rather to pure Al matrix. Numerically, the ultimate strength and Young’s modulus of structure reached to 319.58 MPa and 62.93 GPa, respectively (see Fig. 8 ). As reported before, the precipitation hardening process temperature affected the structural behavior of prepared alloys. So, we expected this parameter changes, converted the numeric mechanical outputs of Al-Zn-Mg alloy. In this step, the mechanical test settings implemented to alloys which prepared by 473 K and 523 K. The snapshot of expanded alloys by using 473 K and 523 K values for precipitation hardening process temperature shown in Fig. 9 . This graphical output indicated our designed alloys in these operate temperatures can be used in actual applications. Furthermore, the stress-strain curves of samples predicted the 473 K is appropriate for using as precipitation hardening process temperature in Al-Zn-Mg alloy production procedure. Numerically, the ultimate strength and Young’s modulus of sample increased to 348.98 MPa and 69.46 GPa for this mixture structure as shown in Fig. 10 . To more emphasize on precipitation hardening process temperature, the changes of ultimate strength and Young’s modulus of designed alloys presented in Fig. 11 and Table 2 . MD outputs in this section predicted the ultimate strength changes from 319.58 to 348.98 MPa in various designed alloys. Ultimate strength refers to the maximum amount of stress a material, such as an alloy, can withstand before it breaks or fractures. So, we expected 473 K is appropriate value in alloy preparing process. Furthermore, the Young’s modulus changes can be highlighted the mechanical performance of various samples in current research. This mechanical parameter is a measure of the stiffness or rigidity of a material, including alloys. It quantifies the material's ability to deform elastically when subjected to an external force. Numerically, Young’s modulus changes between 62.79 and 69.46 GPa in current research. In the final step of current research, the structural evolution of samples described with dislocation analysis of them. The atomic dislocation in alloys refers to the presence of defects or irregularities in the arrangement of atoms within the crystal lattice structure of the alloy. These dislocations occur when atoms are displaced from their ideal lattice positions, leading to localized regions of strain and distortion. Figure 12 depicted the atomic dislocation in various modeled alloys. As shown in this figure, by using 473 K in alloy designing process, the dislocation intensity decreased and described procedure caused this alloy has optimum mechanical performance. From MD outputs, we concluded the hardening process temperature changed the atomic arrangement inside Al-Zn-Mg alloys. By this structural evolution, the interatomic force changed and potential energy of them converged to various values. Finally, this procedure affected the mechanical performance of Al-Zn-Mg alloys which should be supposed in actual applications. Table 2 The ultimate strength and Young’s modulus changes of Al-Zn-Mg alloys in various precipitation hardening process temperature. Precipitation Hardening Process Temperature (K) Ultimate Strength (MPa) Young’s Modulus (GPa) Pure Aluminum 290.10 54.75 423 319.58 62.93 473 348.98 69.46 523 329.18 62.79 4. Conclusion The mechanical performance of alloys refers to their ability to resist deformation, fracture, and failure when subjected to external forces. Atom-base analysis of mechanical performance of these structures is important for effective mechanical designing samples. Currently, the computer simulations used to describe mechanical performance of Al-Zn-Mg alloy. For this, molecular dynamics method implemented to designed sample with LAMMPS package. molecular dynamics outputs in equilibrium simulation predicted the structural stability of Al-Zn-Mg alloy with total energy convergence to negative value. After this computational phase, the equilibrated sample expanded by 0.1 fs -1 value for strain rate. Numerically, mechanical outputs predicted the 290.10 MPa and 54.75 GPa for ultimate strength and Young’s modulus parameters of pure Aluminum sample, respectively. Furthermore, our simulation indicated the mechanical behavior of designed alloy can be improved by precipitation hardening process set on 473 K. By this production condition, the ultimate strength and Young’s modulus of Al-Zn-Mg alloy increased to 348.98 MPa and 69.46 GPa, respectively. This mechanical evolution arise from atomic dislocation minimize in optimum mechanical sample. 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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-4679291","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":322141942,"identity":"62b04cdc-c69b-4044-8d0a-477c3d0f070d","order_by":0,"name":"Roozbeh Sabetvand","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYJACZiht+ABI8PARqcUARBuDSB42UrSYSYBIglrMG9gffi6o+JPYP7t5W+XXHDsZNgbmh49u4NEic4DHWHrGGYPEGXeOld2W3ZYMdBibsXEOHi0SDDwM0rxtBsYMN3LMbktuYwZq4WGTxq+F/fFv3n8GxvJALcWS2+qJ0cJgJs3bYCBnANTC+HHbYSK0MPOYWc84ZixneCOtWJpx23EeNmZCfmFvf3y7oEaOR+5G8saPP7dV2/OzNz98jE8LPOrBbB50EYKA8QcpqkfBKBgFo2DEAADecj0lYHhxpgAAAABJRU5ErkJggg==","orcid":"","institution":"Amirkabir University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Roozbeh","middleName":"","lastName":"Sabetvand","suffix":""}],"badges":[],"createdAt":"2024-07-03 09:34:57","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4679291/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4679291/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59643447,"identity":"acc045a5-e9fd-478d-a6d6-d895300c0eba","added_by":"auto","created_at":"2024-07-04 08:20:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":285348,"visible":true,"origin":"","legend":"\u003cp\u003eThe atomic representation of Al-Zn-Mg alloy in the first step of current research from (a) side and (b) perspective views. In these snap shots, the pink, blue, and yellow spheres represents Al, Mg, and Zn atoms.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/9aa93ff066d0cd09893778a0.png"},{"id":59643438,"identity":"e0c97660-c7aa-4789-98de-4b5150d988e7","added_by":"auto","created_at":"2024-07-04 08:20:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":29763,"visible":true,"origin":"","legend":"\u003cp\u003ea) Temperature and b) total energy variation of various designed Al-Zn-Mg alloys as a function of simulation time.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/6ac8282a11e34ae4176a2ef5.png"},{"id":59644252,"identity":"e06b1fee-9b94-467d-8707-685894efe714","added_by":"auto","created_at":"2024-07-04 08:28:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":459860,"visible":true,"origin":"","legend":"\u003cp\u003eThe atomic representation of equilibrated Al-Zn-Mg alloy by using (a) 423, (b) 473, and (c) 523 K values for temperature of precipitation hardening process.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/d5cd3a24d562574df22caf24.png"},{"id":59643440,"identity":"1d2234d4-4307-4831-8a68-fb3899d69c0c","added_by":"auto","created_at":"2024-07-04 08:20:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":35874,"visible":true,"origin":"","legend":"\u003cp\u003eThe RDF of Al-Zn-Mg alloy by using 423, 473, and 523 K values for temperature of precipitation hardening process after equilibrium phase occur.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/e2a1072f9ca8244b7cabdfae.png"},{"id":59644254,"identity":"92f1530d-f2eb-4410-a0c2-618e36768aea","added_by":"auto","created_at":"2024-07-04 08:28:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":237735,"visible":true,"origin":"","legend":"\u003cp\u003eThe mechanical evolution of pure aluminum matrix in validation process phase of current research.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/0bf343a73af57b40d3608db2.png"},{"id":59644255,"identity":"d9ce1192-8ffe-49f0-9965-2457332c740c","added_by":"auto","created_at":"2024-07-04 08:28:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":19232,"visible":true,"origin":"","legend":"\u003cp\u003eThe calculated stress-strain curve for pure aluminum sample at 298 K by using MD approach.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/9814e61e7daf22b9f6e521a3.png"},{"id":59643448,"identity":"eac0b807-afb3-407b-b968-778f25428164","added_by":"auto","created_at":"2024-07-04 08:20:29","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":399100,"visible":true,"origin":"","legend":"\u003cp\u003eThe mechanical evolution of designed Al-Zn-Mg alloy by setting precipitation hardening process temperature at 423 K.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/65b1ff0ca63ae5d12b74ced5.png"},{"id":59643443,"identity":"d723b5f5-bc88-46e3-a1f6-2c13d3b24959","added_by":"auto","created_at":"2024-07-04 08:20:29","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":24135,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Stress-strain and (b) Young’s modulus outputs of designed Al-Zn-Mg alloy by setting precipitation hardening process temperature at 423 K.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/fa553d35da991207c0cd74a8.png"},{"id":59643450,"identity":"9f0c23a3-bcab-4830-af8a-cfad3c4a3223","added_by":"auto","created_at":"2024-07-04 08:20:31","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":314727,"visible":true,"origin":"","legend":"\u003cp\u003eThe atomic representation of expanded Al-Zn-Mg alloy by setting precipitation hardening process temperature at (a) 423, (b) 473, and (c) 523 K.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/73cb73cca7ceffb288abffc4.png"},{"id":59643446,"identity":"7f5c1860-a13f-45c7-a3af-c0e8dfcf4595","added_by":"auto","created_at":"2024-07-04 08:20:29","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":38249,"visible":true,"origin":"","legend":"\u003cp\u003eThe (a) stress-strain and (b) Young’s modulus outputs of designed Al-Zn-Mg alloy by precipitation hardening process temperature changes from 423 to 523 K.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/052004bb60c51b915e2a7da1.png"},{"id":59643439,"identity":"408126f3-23c2-4428-88c2-e8139e0f07cf","added_by":"auto","created_at":"2024-07-04 08:20:28","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":24481,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Ultimate strength and (b) Young’s modulus changes of Al-Zn-Mg alloy by precipitation hardening process temperature variation.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/f146c51fa165039f0bb63e39.png"},{"id":59644253,"identity":"d2bc746d-6e45-4626-a03b-1a2808349325","added_by":"auto","created_at":"2024-07-04 08:28:29","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":857288,"visible":true,"origin":"","legend":"\u003cp\u003eThe atomic dislocation of expanded Al-Zn-Mg alloy by setting precipitation hardening process temperature at (a) 423, (b) 473, and (c) 523 K. In these figures, the location route highlighted with green line. Also, atoms in new crystal structure depicted by red color.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/d76580bc9b5ee0021c28fa69.png"},{"id":59645000,"identity":"fff1cb2b-15ff-4912-864e-01f932a5e3bd","added_by":"auto","created_at":"2024-07-04 08:36:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2998188,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4679291/v1/c4c6547d-2078-45e0-8c77-7db382af04b6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eComputational Study of Precipitation Hardening Process Effects on Mechanical Performance of Al-Zn-Mg Alloy: Molecular Dynamics Simulation\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAlloys play a crucial role in various industries, ranging from aerospace and automotive to construction and electronics [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. These materials composed of two or more metallic elements; offer enhanced mechanical properties compared to pure metals. By carefully selecting alloying elements and controlling the microstructure through heat treatments, engineers can tailor the mechanical properties to meet specific application requirements [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Several mechanical properties are commonly evaluated to assess the performance of alloys such as strength, ductility, hardness, toughness, and fatigue resistance. Understanding these properties of alloys enables the design and production of components that can withstand the demands of various industries.\u003c/p\u003e \u003cp\u003eThe improvement of alloy\u0026rsquo;s mechanical properties is needed in today industry. The precipitation hardening process is a widely used process in the field of metallurgy to enhance the mechanical properties of alloys [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. This process involves a series of heat treatments that result in the formation of fine precipitates within the alloy matrix, thereby increasing its strength and hardness. Precipitation hardening is commonly employed in various industries, including aerospace, automotive, and defense, where high-performance materials are required [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The precipitation hardening process typically consists of three processes: solution procedure, quenching step, and aging phase. Each step plays a crucial role in achieving the desired material properties. Several factors influence the precipitation hardening process and its outcome. Two important factors are alloy composition and aging temperature. The composition of the alloy plays a crucial role in determining its response to precipitation hardening. Elements such as copper, aluminum, titanium, and nickel are commonly inserted into sample to promote the stabilization of precipitates. Also, the temperature and duration of the aging process significantly affect the size, distribution, and composition of the precipitates. Higher aging temperatures generally result in larger precipitates with lower strength, while longer aging times can lead to averaging and reduced mechanical properties.\u003c/p\u003e \u003cp\u003eRecently, a lot of research has been done in the field of precipitation hardening and its effect on the mechanical behavior of alloys. Between various alloys, the Al-Zn-Mg alloy attracts more scientists\u0026rsquo; attention [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Chemingui et al. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] studied the structure evolution of 7020 alloy via differential scanning calorimetry and XRD methods. Their outputs indicated the creation of hardening phase GP zones, intermediate hardening and stability phases. Their numerical outputs are in acceptable consistency and validate the successive precipitation/dissolution procedure. In other work, Chinh et al. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] described the influence of Cu element on the mechanical and precipitation behavior of the Al at % Zn-2.1% and Mg-2.4% mixture structure (alloy). They used DSC, TEM and 3DAPFIM approaches to describe mechanical performance of alloy. They indicated the clustering of solute particles and defects during or immediately after aqueous environment quenching plays a remarkable effect in the nucleation of intermediate phase precipitates in one-step aging and the addition of copper atoms to ternary Al\u0026ndash;Zn\u0026ndash;Mg mixture caused the variations also in the initial clustering procedure. Nie et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] developed a numerical approach for simulating double-peak precipitation hardening kinetics in Al-Zn-Mg mixture sample with the creation of various types of precipitates at target temperatures based on optimized Langer-Schwartz method. The systematic and quantitative results in this work shows the calculated hardness outputs of double peaks with inserting a shape dependent factor in the growth equation for growth and coarsening common agree appropriate with the calculated ones. Zhang et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] introduced the mechanical performance of Al-Zn-Mg mixture structure by using the multi-stage aging methods. The microstructures of aged samples were identified with SEM and TEM methods. Their reported outputs described the appreciable ratio of GP zones and some part of unstable regions were created during T\u0026thinsp;=\u0026thinsp;363.15 K aging at the 3 stage aging, which consumed effectively solid solubility. Also, they concluded the intergranular equilibrium η phase is beneficial to pin the evolution of dislocation, which avoids fracture process caused by accumulation of particle-base defects around the large 2 phase and on the grain region boundaries.\u003c/p\u003e \u003cp\u003eBy studying previous reports, we concluded the atom-base study on temperature of precipitation hardening process effect on mechanical performance of Al-Zn-Mg alloys doesn\u0026rsquo;t reported. It is expected that the atomic analysis of the precipitation hardening process of Al-Zn-Mg alloy can provide suitable hints for the design of effective mechanical alloy. So, we used the molecular dynamics (MD) approach to simulate precipitation hardening process of target alloy in various temperatures for the first time [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Our MD simulations done in two main steps include equilibrium and mechanical description of ideal Al-Zn-Mg mixture structure (alloy). In equilibrium phase, the temperature and total energy calculation done to equilibrium phase detection. Next, the deformation settings implemented to sample and mechanical performance of them reported by stress-strain curve estimation. These simulation phases done by using large scale atomic/molecular massively parallel simulator (LAMMPS) [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. MD Simulation Details","content":"\u003cp\u003eThe MD formalism is a powerful tool in studying the mechanical performance of alloys. It is a computational approach that simulates the behavior of atoms and molecules in a system over time, allowing for the prediction of mechanical outputs (parameters) such as strength, ductility, and fracture toughness [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. At its core, MD formalism is based on classical mechanics and statistical thermodynamics. It involves solving the equations of motion for each atom in a system, taking into account the interatomic forces that govern their behavior [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. This allows for the simulation of the system's dynamics over time, providing insight into its mechanical properties as below equation [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e],\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${F_i}=\\sum\\limits_{{i \\ne j}} {{F_{ij}}={m_i}\\frac{{{d^2}{r_i}}}{{d{t^2}}}={m_i}\\frac{{d{v_i}}}{{dt}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTo solve this equation, force field of modeled system is important parameter [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. In current research, to define atomic interactions, the modified embedded-atom method (MEAM) implemented [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The MEAM force field defined as Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e),\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$E=\\sum _{i}\\{{F}_{i}\\left({\\rho }_{i}\\right)+\\frac{1}{2}\\sum _{i\\ne j}{\\phi }_{ij}\\left({r}_{ij}\\right)\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, F is the embedding energy parameter and describes the electron density ρ parameter in modeled sample, and φ introduced the pair interaction inside sample. The last parameter is calculated for various neighbors\u0026rsquo; parties which located inside cutoff radius of center particle. Force field implementing inside box, Newton\u0026rsquo;s evolution equation fulfilled and various particles displacement in defined condition predicted. Technically, integrate of the Newton\u0026rsquo;s formalism is calculated by the velocity Varlet method as equations (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e],\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$r\\left( {t+\\Delta t} \\right)=r\\left( t \\right)+v\\left( t \\right)\\Delta t+\\frac{1}{2}a\\left( t \\right)\\Delta {t^2}+O\\left( {\\Delta {t^4}} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$v\\left( {t+\\Delta t} \\right)=v\\left( t \\right)+\\frac{{a\\left( t \\right)+a\\left( {t+\\Delta t} \\right)}}{2}\\Delta t+O\\left( {\\Delta {t^2}} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, r(t\u0026thinsp;+\u0026thinsp;Δt)/v(t\u0026thinsp;+\u0026thinsp;Δt) parameters are the coordinate and velocity of various atoms in t\u0026thinsp;+\u0026thinsp;Δt time of simulations, respectively. Currently, described computational method used to estimate the hardening process effects on mechanical performance of Al-Zn-Mg alloy. For this, MD simulations divided into 2 main phases as below,\u003c/p\u003e \u003cp\u003e \u003cb\u003eEquilibrium Phase \u0026ndash;\u003c/b\u003e In the first step, the extra stress of model Al-Zn-Mg alloy eliminated by using the NVE ensemble for 1 ns. Next, the temperature of system changed from target value (773 K) to 298 K by implementing NVT ensemble (with 1 fs time step and 0.1 fs for temperature damping ratio). MD simulation done for 10 ns in this step. Computationally, the MD box size set to 120\u0026times;340\u0026times;340 \u0026Aring;\u003csup\u003e3\u003c/sup\u003e by using periodic boundary condition [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Our atomic representation of modeled Al-Zn-Mg alloy with 31850 atoms depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In this sample, modeled alloy consists of 92%Al- 5.5%|Zn- 2.5% Mg.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMechanical Evolution Phase \u0026ndash;\u003c/b\u003e Secondary, the mechanical test settings implemented to equilibrated alloys. This setting caused the structural expansion of models with 0.1 fs\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e ratio. In this step, the Nose-Hoover thermostat controlled the temperature of allies in expansion procedure [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Our used MD settings in our numerical research presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \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 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe MD method parameters value in atomic/mechanical description of Al-Zn-Mg alloy.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMD Simulation Parameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter Setting\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComputational Box Length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e120\u0026times;340\u0026times;340 \u0026Aring;\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of Atoms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e31850\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBoundary Setting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePBC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBarostat/Thermostat\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNose-Hoover\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature of Initial Condition\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e773 K\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime Step\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 fs\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature Damping Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1 fs\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulation Total Time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 ns\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"3. MD Simulation Outputs and Description","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Equilibrium Step of Al-Zn-Mg Alloy\u003c/h2\u003e \u003cp\u003eThe physical stability of designed Al-Zn-Mg alloy is important parameter for actual applications of them. To analyze this stability, the equilibrium phase of modeled samples estimated with MD simulations. Technically, the target alloy temperature changed from 773 K to 298 K in 6 computational cycles. Also, temperature of hardening process set to 423 K, 473 K, and 523 K for various designed alloys. Finally, the alloy equilibrated at 298 K for 10 ns. The temperature and total energy variation of sample by simulation time passing depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. As seen from this MD output, the temperature of systems converged to 298 K after 10 ns. This outputs indicated the simulation time is sufficient to equilibrium phase detection in current phase. Physically, this thermal performance of various prepared Al-Zn-Mg alloys arises from atomic mobility convergence by MD time steps passing. Furthermore, the numeric convergence can be detected for total energy of various modeled alloys. Numerically, this energy converged to -3.047, -3.048, and \u0026minus;\u0026thinsp;3.051 eV in the final time step of current simulations. The negative value of total energy shows the average interatomic adsorptive interaction between various atoms inside alloy. Also, the negative value of total energy arises from appropriate MD settings in structures as reported in previous researches [\u003cspan additionalcitationids=\"CR31\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBetween various equilibrated alloys, the sample with 473 K for precipitation hardening process haze maximum physical stability. The maximum value of interaction energy in this sample caused the high stability of them. To more structural analysis of samples, the atomic representation of them depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In this figure, the structural unity of various samples which arises from potential energy and modeling process settings, can be detected. The radial distribution function (RDF) of them more described the physical stability of Al-Zn-Mg alloys in defined condition. Computationally, the RDF is a parameter used to describe the distribution of particles in a system of atoms or molecules [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. It measures the probability of finding a particle at a given distance from another particle. In atomic structures, the RDF is often used to analyze the packing and ordering of atoms in a material. It can provide information about the structure, stability, and properties of the material. MD outputs for RDF of designed Al-Zn-Mg alloys after equilibrium phase detection shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As reported before, the numerous peaks in RDF results predicted the phase state and structural unity of alloys [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Mechanical Evolution of Designed Alloys\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Mechanical Behavior of Pure Al Sample\u003c/h2\u003e \u003cp\u003eIn the first phase of current computational step, the mechanical evolution of pure aluminum matrix evaluated by using MD approach. The mechanical evolution of this sample in 298 K depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. This figure predicted the physical stability of sample by MD time steps passing and structural expansion. To numerical analysis of this procedure, the stress-strain curve of Al matrix calculated. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows stress-strain outputs of them. This MD results consistent with previous report and validated our computational method [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Numerically, the ultimate strength and Young\u0026rsquo;s modulus of this sample reached to 290.10 MPa and 54.75 GPa, respectively. From these results, we concluded our MD settings are appropriate to numeric study of Al-based atomic structures mechanical performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter equilibrium phase detection in model alloys, the structural expansion settings implemented to them. The time evolution of Al-Zn-Mg alloy in our designed mechanical test depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Physically, the negative value of total energy inside samples caused the amplitude of atomic fluctuations converged to constant value and structural unity don\u0026rsquo;t disrupted in various steps of MD simulation. The stress-strain output for this process depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. From this curve which calculated for Al-Zn-Mg alloy with 423 K value for precipitation hardening process, we concluded the mechanical performance of designed alloy improved appreciably rather to pure Al matrix. Numerically, the ultimate strength and Young\u0026rsquo;s modulus of structure reached to 319.58 MPa and 62.93 GPa, respectively (see Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAs reported before, the precipitation hardening process temperature affected the structural behavior of prepared alloys. So, we expected this parameter changes, converted the numeric mechanical outputs of Al-Zn-Mg alloy. In this step, the mechanical test settings implemented to alloys which prepared by 473 K and 523 K. The snapshot of expanded alloys by using 473 K and 523 K values for precipitation hardening process temperature shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. This graphical output indicated our designed alloys in these operate temperatures can be used in actual applications. Furthermore, the stress-strain curves of samples predicted the 473 K is appropriate for using as precipitation hardening process temperature in Al-Zn-Mg alloy production procedure. Numerically, the ultimate strength and Young\u0026rsquo;s modulus of sample increased to 348.98 MPa and 69.46 GPa for this mixture structure as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTo more emphasize on precipitation hardening process temperature, the changes of ultimate strength and Young\u0026rsquo;s modulus of designed alloys presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. MD outputs in this section predicted the ultimate strength changes from 319.58 to 348.98 MPa in various designed alloys. Ultimate strength refers to the maximum amount of stress a material, such as an alloy, can withstand before it breaks or fractures. So, we expected 473 K is appropriate value in alloy preparing process. Furthermore, the Young\u0026rsquo;s modulus changes can be highlighted the mechanical performance of various samples in current research. This mechanical parameter is a measure of the stiffness or rigidity of a material, including alloys. It quantifies the material's ability to deform elastically when subjected to an external force. Numerically, Young\u0026rsquo;s modulus changes between 62.79 and 69.46 GPa in current research. In the final step of current research, the structural evolution of samples described with dislocation analysis of them. The atomic dislocation in alloys refers to the presence of defects or irregularities in the arrangement of atoms within the crystal lattice structure of the alloy. These dislocations occur when atoms are displaced from their ideal lattice positions, leading to localized regions of strain and distortion. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e depicted the atomic dislocation in various modeled alloys. As shown in this figure, by using 473 K in alloy designing process, the dislocation intensity decreased and described procedure caused this alloy has optimum mechanical performance. From MD outputs, we concluded the hardening process temperature changed the atomic arrangement inside Al-Zn-Mg alloys. By this structural evolution, the interatomic force changed and potential energy of them converged to various values. Finally, this procedure affected the mechanical performance of Al-Zn-Mg alloys which should be supposed in actual applications.\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 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe ultimate strength and Young\u0026rsquo;s modulus changes of Al-Zn-Mg alloys in various precipitation hardening process temperature.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePrecipitation Hardening Process Temperature (K)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUltimate Strength (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYoung\u0026rsquo;s Modulus (GPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePure Aluminum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e290.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e423\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e319.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.93\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\u003e348.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e69.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e329.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.79\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 \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThe mechanical performance of alloys refers to their ability to resist deformation, fracture, and failure when subjected to external forces. Atom-base analysis of mechanical performance of these structures is important for effective mechanical designing samples. Currently, the computer simulations used to describe mechanical performance of Al-Zn-Mg alloy. For this, molecular dynamics method implemented to designed sample with LAMMPS package. molecular dynamics outputs in equilibrium simulation predicted the structural stability of Al-Zn-Mg alloy with total energy convergence to negative value. After this computational phase, the equilibrated sample expanded by 0.1 fs\u003csup\u003e-1\u003c/sup\u003e value for strain rate. Numerically, mechanical outputs predicted the 290.10 MPa and 54.75 GPa for ultimate strength and Young\u0026rsquo;s modulus parameters of pure Aluminum sample, respectively. Furthermore, our simulation indicated the mechanical behavior of designed alloy can be improved by precipitation hardening process set on 473 K. By this production condition, the ultimate strength and Young\u0026rsquo;s modulus of Al-Zn-Mg alloy increased to 348.98 MPa and 69.46 GPa, respectively. This mechanical evolution arise from atomic dislocation minimize in optimum mechanical sample. So, we expected by controlling the temperature of precipitation hardening process, the mechanical performance of Al-Zn-Mg alloy manipulated for various actual cases.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCallister, W.D. \u0026quot;Materials Science and Engineering: An Introduction\u0026quot; 2007, 7th edition, John Wiley and Sons, Inc. New York, Section 4.3 and Chapter 9.\u003c/li\u003e\n\u003cli\u003eVerhoeven, John D. (2007). Steel Metallurgy for the Non-metallurgist. ASM International. p. 56. ISBN 978-1-61503-056-9. Archived from the original on 2016-05-05.\u003c/li\u003e\n\u003cli\u003eDavis, Joseph R. (1993) ASM Specialty Handbook: Aluminum and Aluminum Alloys. ASM International. p. 211. ISBN 978-0-87170-496-2.\u003c/li\u003e\n\u003cli\u003eRoberts, George Adam; Krauss, George; Kennedy, Richard and Kennedy, Richard L. (1998) Tool steels Archived 2016-04-24 at the Wayback Machine. ASM International. pp. 2\u0026ndash;3. ISBN 0-87170-599-0.\u003c/li\u003e\n\u003cli\u003eGlerum, Jennifer; Kenel, Christoph; Sun, Tao; Dunand, David (2020). \u0026quot;Synthesis of precipitation-strengthened Al-Sc, Al-Zr and Al-Sc-Zr alloys via selective laser melting of elemental powder blends\u0026quot;. Additive Manufacturing. 36: 101461. doi:10.1016/j.addma.2020.101461. S2CID 225632137.\u003c/li\u003e\n\u003cli\u003eAboulkhair, N.T.; Tuck, C.; Ashcroft, I.; et, al. (2015). \u0026quot;. On the Precipitation Hardening of Selective Laser Melted AlSi10Mg\u0026quot;. Metall Mater Trans A. 46 (8): 3337\u0026ndash;3341. Bibcode:2015MMTA...46.3337A. doi:10.1007/s11661-015-2980-7. S2CID 53535935.\u003c/li\u003e\n\u003cli\u003eRakhmonov, Jovid; Weiss, David; Dunand, David (July 2022). \u0026quot;Solidification microstructure, aging evolution and creep resistance of laser powder-bed fused Al-7Ce-8Mg (wt%)\u0026quot;. Additive Manufacturing. 55: 102862. doi:10.1016/j.addma.2022.102862. S2CID 248486205.\u003c/li\u003e\n\u003cli\u003eL.K Berg; J Gj\u0026oslash;nnes; V Hansen; X.Z Li; M Knutson-Wedel; G Waterloo; D Schryvers; L.R Wallenberg (2001). GP-zones in Al\u0026ndash;Zn\u0026ndash;Mg alloys and their role in artificial aging. , 49(17), 3443\u0026ndash;3451. doi:10.1016/s1359-6454(01)00251-8.\u003c/li\u003e\n\u003cli\u003eJ.C. Werenskiold; A.; Y. Br\u0026eacute;chet (2000). Characterization and modeling of precipitation kinetics in an Al\u0026ndash;Zn\u0026ndash;Mg alloy. , 293(1-2), 267\u0026ndash;274. doi:10.1016/s0921-5093(00)01247-8.\u003c/li\u003e\n\u003cli\u003eL\u0026ouml;ffler, H., Kov\u0026aacute;cs, I. \u0026amp; Lendvai, J. Decomposition processes in Al-Zn-Mg alloys. J Mater Sci 18, 2215\u0026ndash;2240 (1983). https://doi.org/10.1007/BF00541825.\u003c/li\u003e\n\u003cli\u003eChemingui, M., Ameur, R., Optasanu, V. et al. DSC analysis of phase transformations during precipitation hardening in Al\u0026ndash;Zn\u0026ndash;Mg alloy (7020). J Therm Anal Calorim 136, 1887\u0026ndash;1894 (2019). https://doi.org/10.1007/s10973-018-7856-9.\u003c/li\u003e\n\u003cli\u003eN.Q. Chinh; J. Lendvai; D.H. Ping; K. Hono (2004). 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Failure characteristics of strength-equivalent aluminium and steel plates in impact conditions. 10.1201/b15120-25.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Amirkabir University of Technology","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Al-Zn-Mg alloy, Precipitation hardening process, Mechanical performance, Temperature effect, Molecular dynamics, Atomic modeling","lastPublishedDoi":"10.21203/rs.3.rs-4679291/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4679291/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe precipitation hardening is a heat treatment process used to increase the strength and hardness of certain alloys. The atomic analysis of this procedure can be presented valuable hints in actual applications. In current research, we used molecular dynamics (MD) method to introduce the temperature of precipitation hardening process effects on mechanical performance of Al-Zn-Mg alloy. Our MD research done in 2 main steps. Firstly, the equilibrium phase of modeled alloy reported by temperature and total energy convergence. After equilibrium phase detection, the mechanical properties of samples introduced by structural expansion process. MD results indicated the mechanical performance of Al-Zn-Mg alloy improved appreciably by using precipitation hardening process rather to pure aluminum sample. Furthermore, simulations outputs predicted the 473 K is appropriate temperature in precipitation hardening process of designed alloy. The ultimate strength and Young\u0026rsquo;s modulus of Al-Zn-Mg alloy increased to 348.98 MPa and 69.46 GPa (respectively) in optimum condition which should be supposed in mechanical applications.\u003c/p\u003e","manuscriptTitle":"Computational Study of Precipitation Hardening Process Effects on Mechanical Performance of Al-Zn-Mg Alloy: Molecular Dynamics Simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-04 08:20:23","doi":"10.21203/rs.3.rs-4679291/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"394de320-9b63-4e77-9c56-a72751584c83","owner":[],"postedDate":"July 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":34063153,"name":"Atomic and Molecular Physics"}],"tags":[],"updatedAt":"2024-07-04T08:20:23+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-04 08:20:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4679291","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4679291","identity":"rs-4679291","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}