论文标题

基于应变梯度可塑性的裂纹尖端场和断裂抗性参数

Crack tip fields and fracture resistance parameters based on strain gradient plasticity

论文作者

Shlyannikov, V., Martínez-Pañeda, E., Tumanov, A., Tartygasheva, A.

论文摘要

分析和数值研究了应变梯度可塑性固体的裂纹尖端力学。基于泰勒的脱位模型的基于一阶机理的应变梯度(MSG)可塑性理论通过用户子例程在商业有限元包ANSYS中采用并实现。考虑了两个边界值问题,一个单个边缘张力标本和一个双轴负载的板。首先,表征了裂纹尖端字段。与错位硬化机制相关的应变梯度效应相对于常规可塑性提高了裂纹尖端应力。进行了一项参数研究,并量化了常规可塑性预测的差异。此外,研究了裂纹尖端溶液的渐近性。数值结果表明,一阶MSG理论所预测的奇异性顺序与线性弹性固体相等或更高。另外,裂纹尖端场似乎没有可分离的解决方案。此外,与在MSG可塑性的高阶版本中显示的内容相反,奇异性顺序对塑料材料特性具有敏感性。其次,采用分析方法和数值方法来制定应变梯度可塑性的新振幅因子。推导并用于表征非线性振幅因子。获得了分析应力强度因子的封闭形式方程。通过分解裂纹尖端应力场的数值解决方案也得出了振幅因子。非线性振幅因子溶液是在材料长度尺度L和应变硬化指数N范围内确定的。鉴定了应变梯度相关性的域,为应用一阶MSG可塑性用于裂缝和损伤评估树立了基础。

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.

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