约束剪切中的非二次应变梯度塑性理论及尺寸效应

IF 2.6 4区 工程技术 Q2 MECHANICS
M. Kuroda, A. Needleman
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引用次数: 1

摘要

将先前提出的应变梯度塑性理论扩展为在指数为N+1的自由能表达式中包含塑性应变梯度的非二次幂律函数。N的值在N=1到N=0之间变化。分析了刚性边界之间金属层的一个简单剪切问题。考虑了塑性变形的两个阶段。在阶段I中,将边界处的塑性应变取为零。当在边界处获得指定大小的塑性应变梯度时,阶段I结束。在第二阶段,边界处的塑性应变梯度的大小固定在指定值。当N=0时,不能在边界处指定临界塑性应变梯度,因为塑性应变斜率在边界处是无限的。N=0的理论预测在初始屈服后立即出现恒定的平台应力,并且平台应力对层厚度的依赖性可以拟合实验观察到的平台应力值。然而,当N=0时,在初始屈服应力和平台应力之间出现应力间隙。对于该范围内的任何N值,0<N=1和阶段II的理论也可以再现实验观察到的平台应力对层厚度的依赖性,在边界处具有适当的临界塑性应变梯度值。0本文章由计算机程序翻译,如有差异,请以英文原文为准。
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Non-quadratic strain gradient plasticity theory and size effects in constrained shear
A previously proposed strain gradient plasticity theory is extended to incorporate a non-quadratic power law function of the plastic strain gradient in the free energy expression with an exponent of N + 1. The values of N are taken to vary from N = 1 to N = 0. A simple shear problem of a metal layer between rigid boundaries is analyzed. Two stages of plastic deformation are considered. In stage I, the plastic strain is taken to be zero at the boundaries. Stage I ends when a specified magnitude of the plastic strain gradient is attained at the boundaries. In stage II, the magnitude of the plastic strain gradient at the boundaries is fixed at the specified value. With N = 0, a critical plastic strain gradient cannot be specified at the boundaries because the plastic strain gradient is infinite at the boundaries. The theory with N = 0 predicts a constant plateau stress immediately after initial yield, and the dependence of the plateau stress on the layer thickness can fit experimentally observed plateau stress values. However, with N = 0, a stress gap occurs between the initial yield stress and the plateau stress. The theory with 0 < N = 1 and with stage II also can reproduce the experimentally observed dependence of the plateau stress on the layer thickness for any value of N in that range, with an appropriate value of critical plastic strain gradient at the boundaries. The solution for 0 < N = 1 includes that for N = 0 as a limiting case.
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来源期刊
Journal of Applied Mechanics-Transactions of the Asme
CiteScore
4.80
自引率
3.80%
发文量
95
审稿时长
5.8 months
期刊介绍: All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation
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