When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during crack propagation. As such, the study of crack front deformations is key to rationalize the effective failure properties of micro-structured solids and interfaces. Yet, the impact of a localized dissipation in a finite region behind the crack front, called the process zone, has often been overlooked. In this work, we derive the equation ruling 3D coplanar crack propagation in heterogeneous cohesive materials where the opening of the crack is resisted by some traction in its wake. We show that the presence of a process zone results in two competing effects on the deformation of crack fronts: (i) it makes the front more compliant to small-wavelength perturbations, and (ii) it smooths out local fluctuations of strength and process zone size, from which emerge heterogeneities of fracture energy. Their respective influence on front deformations is shown to strongly impact the stability of perturbed crack fronts, as well as their stationary shapes when interacting with arrays of tough obstacles. Overall, our theory provides a unified framework to predict the variety of front profiles observed in experiments, even when the small-scale yielding hypothesis of linear elastic fracture mechanics breaks down.

当裂纹与材料异质性相互作用时，其前端会发生扭曲并采用复杂的曲折构型，这让人联想到裂纹扩展过程中遇到的能量屏障。因此，裂纹前沿变形的研究是合理化微结构固体和界面的有效失效特性的关键。然而，裂纹前沿后面的有限区域（称为过程区）的局部耗散的影响经常被忽视。在这项工作中，我们推导出了支配异质粘性材料中3D 共面裂纹扩展的方程，其中裂纹的开口受到其尾迹的一些牵引力的抵抗。我们表明，一个过程区的存在会导致两个竞争对裂纹前沿变形的影响：（i）它使前沿更符合小波长扰动，（ii）它消除了强度和过程区尺寸的局部波动，由此出现了断裂能量的不均匀性。它们各自对前沿变形的影响被证明会强烈影响受扰动裂纹前沿的稳定性，以及它们在与坚硬障碍物阵列相互作用时的静止形状。总体而言，我们的理论提供了一个统一的框架来预测实验中观察到的各种前沿剖面，即使线弹性断裂力学的小规模屈服假设失效。