{"title":"通过对多晶体平均滑移距离的概率分析,计算应变硬化过程中的晶粒尺寸效应。","authors":"Rafael Schouwenaars","doi":"10.1016/j.ijplas.2024.104012","DOIUrl":null,"url":null,"abstract":"<div><p>Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size <span><math><mrow><mo>(</mo><msub><mi>d</mi><mi>g</mi></msub><mo>)</mo><mspace></mspace></mrow></math></span>causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include <span><math><msub><mi>d</mi><mi>g</mi></msub></math></span>. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of <span><math><mrow><msub><mi>d</mi><mi>g</mi></msub><mspace></mspace></mrow></math></span>to good approximation, for <span><math><mrow><msub><mi>d</mi><mi>g</mi></msub><mo>></mo><mn>1</mn><mrow><mi>μ</mi><mi>m</mi></mrow></mrow></math></span>. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-<span><math><mrow><mi>μ</mi><mi>m</mi></mrow></math></span> range.</p></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":null,"pages":null},"PeriodicalIF":9.4000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals\",\"authors\":\"Rafael Schouwenaars\",\"doi\":\"10.1016/j.ijplas.2024.104012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size <span><math><mrow><mo>(</mo><msub><mi>d</mi><mi>g</mi></msub><mo>)</mo><mspace></mspace></mrow></math></span>causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include <span><math><msub><mi>d</mi><mi>g</mi></msub></math></span>. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of <span><math><mrow><msub><mi>d</mi><mi>g</mi></msub><mspace></mspace></mrow></math></span>to good approximation, for <span><math><mrow><msub><mi>d</mi><mi>g</mi></msub><mo>></mo><mn>1</mn><mrow><mi>μ</mi><mi>m</mi></mrow></mrow></math></span>. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-<span><math><mrow><mi>μ</mi><mi>m</mi></mrow></math></span> range.</p></div>\",\"PeriodicalId\":340,\"journal\":{\"name\":\"International Journal of Plasticity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":9.4000,\"publicationDate\":\"2024-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Plasticity\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0749641924001396\",\"RegionNum\":1,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Plasticity","FirstCategoryId":"88","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0749641924001396","RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals
Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include . Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of to good approximation, for . Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub- range.
期刊介绍:
International Journal of Plasticity aims to present original research encompassing all facets of plastic deformation, damage, and fracture behavior in both isotropic and anisotropic solids. This includes exploring the thermodynamics of plasticity and fracture, continuum theory, and macroscopic as well as microscopic phenomena.
Topics of interest span the plastic behavior of single crystals and polycrystalline metals, ceramics, rocks, soils, composites, nanocrystalline and microelectronics materials, shape memory alloys, ferroelectric ceramics, thin films, and polymers. Additionally, the journal covers plasticity aspects of failure and fracture mechanics. Contributions involving significant experimental, numerical, or theoretical advancements that enhance the understanding of the plastic behavior of solids are particularly valued. Papers addressing the modeling of finite nonlinear elastic deformation, bearing similarities to the modeling of plastic deformation, are also welcomed.