This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the crack propagates throughout the material and the evolution of the effective toughness as a function of the layer angle. We first study three idealized situations, where only one property among fracture toughness, Young's modulus and yield strength is heterogeneous whereas the others are uniform. We observe that in the case of toughness and strength heterogeneity, the material exhibits anomalous isotropy: the effective toughness is equal to the largest of the point-wise values for any layer angle except when the layers are parallel to the macroscopic direction of propagation. As the layer angle decreases, the crack propagates along the brittle-to-tough interfaces, whereas it goes straight when the layers have different yield strength but uniform toughness. We find that smooth deflections in the crack path do not induce any overall toughening and that the effective toughness is not proportional to either the cumulated fracture energy or the cumulated plastic work. In the case of elastic heterogeneity, the material is anisotropic in the sense of the effective toughness, as the latter varies as a function of the layer angle. Four toughening mechanisms are active: stress fluctuations, crack renucleation, plastic dissipation and plastic blunting. Finally, we consider a layered medium comprised of compliant-tough-weak and stiff-brittle-strong phases, as it is the case for many structural composites. We observe a transition from an interface-dominated to a plasticity-dominated failure regime, as the phase constituents become more ductile. The material is anisotropic in the sense of the effective toughness.

中文翻译：

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塑性对有效断裂韧性各向异性的影响

本文研究了塑性对有效断裂韧性的影响。分层材料被视为建模系统。弹塑性相场模型和冲浪边界条件用于研究裂纹如何在整个材料中传播以及作为层角函数的有效韧性的演变。我们首先研究了三种理想化的情况，其中断裂韧性、杨氏模量和屈服强度中只有一个属性是异质的，而其他属性是均匀的。我们观察到，在韧性和强度不均匀的情况下，材料表现出异常的各向同性：有效韧性等于任何层角度的最大点值，除非层平行于宏观传播方向。随着层角减小，裂纹沿脆韧界面扩展，而当层具有不同的屈服强度但韧性一致时，裂纹会直线传播。我们发现裂纹路径中的平滑偏转不会引起任何整体增韧，并且有效韧性与累积断裂能或累积塑性功不成正比。在弹性异质性的情况下，材料在有效韧性的意义上是各向异性的，因为后者作为层角的函数而变化。四种增韧机制处于活动状态：应力波动、裂纹再成核、塑性耗散和塑性钝化。最后，我们考虑由柔顺-坚韧-弱相和硬-脆-强相组成的层状介质，就像许多结构复合材料一样。我们观察到从界面主导到塑性主导失效状态的转变，因为相成分变得更具延展性。该材料在有效韧性意义上是各向异性的。