应变梯度塑性中Ⅰ型和II型应力强度因子及位错密度行为
Mode I and Mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity
摘要：
在这项研究中，我们使用的机制为基础的应变梯度塑性理论来评估裂纹尖端位错密度的行为和耦合效应的材料塑性特性和非线性振幅因子的固有材料长度。两个平面经典的应力-应变状态，即平面应变和平面应力，无论是在纯模式I和纯模式II加载条件下进行检查。本构关系是基于泰勒的位错模型，这使得获得洞察的作用，增加位错密度与大梯度的塑性应变裂纹附近。使用用户子程序的商业有限元（FE）软件包中实现的材料模型，和非线性应力强度因子（SIF）作为固有材料长度的函数进行评估，表征梯度效应变得显着的规模。作为位错密度分布的有限元计算的结果，断裂模式和应力-应变状态的影响被确定。在纯模式I中，几何上必要的位错（GND）密度相对于钝裂纹尖端对称地定位。相反，在纯模式II下，GND密度变得集中在裂纹尖端的钝化和尖锐的部分。在这种情况下，断裂萌生被证明是可能发生附近的裂纹尖端的钝化区域，在那里的应力三轴度和GND密度是在它们的最大值。讨论了位错密度的平衡态与内禀材料长度的关系以及塑性应力强度因子与加工硬化指数的关系。
英文摘要：
In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress-strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor's dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIF) are evaluated as a function of the intrinsic material length, characterising the scale at which gradient effects become significant. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress-strain state are determined. In pure mode I, the geometrically necessary dislocation (GND) density is located symmetrically with respect to the blunted crack tip. On the contrary, under pure mode II, the GND density becomes concentrated in the blunted and sharp parts of the crack tip. In this case, fracture initiation is shown to be likely to occur near the blunted region of the crack tip, where both the stress triaxiality and the GND density are at their maximum. The relation between the equilibrium state of dislocation densities and the intrinsic material length as well as the plastic SIF as a function of the work hardening exponent is discussed.
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