热力学位错理论中的平均化：一般宏观均匀应力与应变状态
Averaging in thermodynamic dislocation theory: general macroscopically uniform stress and strain states
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- Institute for Advanced Study in Technology, Ton Duc Thang University（Ton Duc Thang大学先进技术研究院）
- Faculty of Civil Engineering, Ton Duc Thang University（Ton Duc Thang大学土木工程学院）
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中文总结 AI 辅助
将热力学位错理论的平均化方法推广至任意宏观均匀应力应变状态，推导出相关$J_2$流动理论，并用一组铜参数统一描述拉伸、压缩和扭转实验。
中文摘要 AI 辅助
为轴向对称拉伸或压缩下的多晶棒材开发的平均化程序被扩展到任意宏观均匀的应力与应变状态。从晶粒取向的等概率假设出发，平均分解剪应力和平均分解弹性及塑性剪应变被定义为所有滑移系取向上的均方根平均值。两个各向同性取向平均的精确恒等式表明，平均分解剪应力与冯·米塞斯等效应力成正比，并且由塑性滑移率与作用于其上的分解剪应力成正比的假设得到的宏观塑性流动方向为应力偏量。其结果是相关的$J_2$流动理论，其硬化规律并非拟合得到，而是遵循热激活位错脱钉动力学以及热力学位错理论中位错密度和有效无序温度随时间的演化方程，从而可以跟踪任意加载路径。对于扭转，该理论直接给出棒材和管材的扭矩-扭转角关系，无需经典地简化为剪应力-应变曲线。铜的参数由霍普金森杆拉伸、室温和高温下的动态压缩以及多个扭转速率下的扭矩-扭转角记录联合识别。一组材料参数（与先前仅压缩识别一致）描述了从室温到$1173$\,K、从$10$到$2300$\,s$^{-1}$的拉伸、压缩和扭转，在142个数据点上均方根误差为6\%；Johnson和Cook注意到的拉伸-扭转差异可追溯至其扭转试样的初始位错状态。
英文摘要
The averaging procedure, developed for polycrystalline bars under axially symmetric tension or compression, is extended to arbitrary macroscopically uniform stress and strain states. Starting from the equal probability hypothesis for grain orientations, the mean resolved shear stress and the mean resolved elastic and plastic shear strains are defined as root-mean-square averages over all slip-system orientations. Two exact identities for isotropic orientation averages show that the mean resolved shear stress is proportional to the von Mises equivalent stress, and that the direction of macroscopic plastic flow, obtained from the hypothesis that the plastic slip rate on a system is proportional to the resolved shear stress acting on it, is the stress deviator. The result is an associated $J_2$ flow theory whose hardening law is not fitted but follows from the kinetics of thermally activated dislocation depinning and the evolution equations for the dislocation density and the effective disorder temperature of thermodynamic dislocation theory, written as rates with respect to time so that arbitrary loading paths can be followed. For torsion the theory yields the torque--twist relation of bars and tubes without the classical reductions to a shear stress--strain curve. The parameters for copper are identified jointly from Hopkinson-bar tension, dynamic compression at room and elevated temperatures, and torque--twist records at several twist rates. One set of material parameters, consistent with the earlier compression-only identification, describes tension, compression and torsion from room temperature to $1173$\,K and from $10$ to $2300$\,s$^{-1}$ to $6$\,\% rms over 142 data points; the tension--torsion discrepancy noted by Johnson and Cook is traced to the initial dislocation state of their torsion specimens.
