Due to its superior modelling capabilities, there is an increasing interest in distortion gradient plasticity theory, where the role of the plastic spin is accounted for in the free energy and the dissipation. In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye’s tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. A generalised J-integral is defined and employed to determine the power of the singularity. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic $r^{-1/2}$ stress singularity. This finding is verified by detailed finite element analyses using a new numerical framework, which builds upon a viscoplastic constitutive law that enables capturing both rate-dependent and rate-independent behaviour in a computationally efficient manner. Numerical analysis is used to gain further insight into the stress elevation predicted by distortion gradient plasticity, relative to conventional J₂ plasticity, and the influence of the plastic spin under both mode I and mixed-mode fracture conditions. It is found that Nye’s tensor contributions have a weaker effect in elevating the stresses in the plastic region, while predicting the same asymptotic behaviour as constitutive choices based on the plastic strain gradient tensor. A minor sensitivity to χ, the parameter governing the dissipation due to the plastic spin, is observed. Finally, distortion gradient plasticity and suitable higher order boundary conditions are used to appropriately model the phenomenon of brittle failure along elastic-plastic material interfaces. We reproduce paradigmatic experiments on niobium-sapphire interfaces and show that the combination of strain gradient hardening and dislocation blockage leads to interface crack tip stresses that are larger than the theoretical lattice strength, rationalising cleavage in the presence of plasticity at bi-material interfaces.

由于其出色的建模能力，人们对畸变梯度可塑性理论的兴趣日益浓厚，在该理论中，塑料自旋的作用是在自由能和耗散中占的比例。在这项工作中，使用变形梯度可塑性来深入了解裂纹尖端之前的材料变形。这也构成了以Nye张量为主要运动学变量的梯度可塑性理论的首次断裂力学分析。首先，对裂纹尖端场的渐近性质进行了分析研究。广义J-integral被定义并用于确定奇异性的幂。我们表明存在一个内部弹性区域，靠近裂纹尖端，其中弹性应变主导塑性应变，柯西应力遵循线性弹性${\mathrm{[R}}^{-\mathrm{1个}/2}$应力奇点。该发现通过使用新的数值框架进行的详细有限元分析得到了证实，该数值框架建立在粘塑性本构关系的基础上，该定律能够以计算有效的方式捕获速率相关和速率无关的行为。数值分析用于进一步了解变形梯度可塑性相对于常规J ₂塑性所预测的应力升高，以及在模式I和混合模式断裂条件下塑性自旋的影响。已发现，Nye的张量贡献在提高塑性区域的应力方面效果较弱，同时根据塑性应变梯度张量预测与本构选择相同的渐近行为。对χ的敏感性较小观察到了控制由于塑料自旋引起的耗散的参数。最后，使用变形梯度可塑性和合适的高阶边界条件对沿弹塑性材料界面的脆性破坏现象进行适当建模。我们在铌-蓝宝石界面上重现了范式实验，并显示出应变梯度硬化和位错阻塞的组合会导致界面裂纹尖端应力大于理论晶格强度，从而在双材料界面存在塑性的情况下使劈裂合理化。