The crack tip mechanics of strain gradient plasticity solids is investigated analytically and numerically. A first-order mechanism-based strain gradient (MSG) plasticity theory based on Taylor's dislocation model is adopted and implemented in the commercial finite element package ANSYS by means of a user subroutine. Two boundary value problems are considered, a single edge tension specimen and a biaxially loaded plate. First, crack tip fields are characterized. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. A parametric study is conducted and differences with conventional plasticity predictions are quantified. Moreover, the asymptotic nature of the crack tip solution is investigated. The numerical results reveal that the singularity order predicted by the first-order MSG theory is equal or higher to that of linear elastic solids. Also, the crack tip field appears not to have a separable solution. Moreover, contrarily to what has been shown in the higher order version of MSG plasticity, the singularity order exhibits sensitivity to the plastic material properties. Secondly, analytical and numerical approaches are employed to formulate novel amplitude factors for strain gradient plasticity. A generalized J-integral is derived and used to characterize a nonlinear amplitude factor. A closed-form equation for the analytical stress intensity factor is obtained. Amplitude factors are also derived by decomposing the numerical solution for the crack tip stress field. Nonlinear amplitude factor solutions are determined across a wide range of values for the material length scale l and the strain hardening exponent N. The domains of strain gradient relevance are identified, setting the basis for the application of first-order MSG plasticity for fracture and damage assessment.

中文翻译：

---

基于应变梯度塑性的裂纹尖端场和断裂阻力参数

应变梯度塑性固体的裂纹尖端力学分析和数值研究。采用基于泰勒位错模型的一阶机制应变梯度（MSG）塑性理论，并通过用户子程序在商业有限元包ANSYS中实现。考虑了两个边界值问题，单边拉伸试样和双轴加载板。首先，对裂纹尖端场进行表征。与位错硬化机制相关的应变梯度效应相对于常规塑性提高了裂纹尖端应力。进行参数研究并量化与传统塑性预测的差异。此外，研究了裂纹尖端解的渐近性质。数值结果表明，一阶MSG理论预测的奇点阶数等于或高于线弹性固体的奇点阶数。此外，裂纹尖端场似乎没有可分离的解决方案。此外，与 MSG 可塑性的高阶版本中所显示的相反，奇异阶表现出对塑性材料特性的敏感性。其次，采用解析和数值方法来制定应变梯度塑性的新振幅因子。导出了广义 J 积分并用于表征非线性幅度因子。获得解析应力强度因子的封闭形式方程。振幅因子也可以通过分解裂纹尖端应力场的数值解来推导出来。