This work presents a fast Fourier transform (FFT) based method that can be used to model interface decohesion. The inability of an FFT solver to deal with sharp interfaces discards the use of conventional cohesive zones to model the interfacial mechanical behaviour within this framework. This limitation is overcome by approximating sharp interfaces (e.g. grain/phase boundaries) with an interphase. Within the interphase, the background plastic constitutive behaviour is inherited from the respective adjacent grains. The anisotropic kinematics of the decohesion process is modelled using a damage deformation gradient that is constructed by mapping the opening strains (in normal and tangential modes) to the associated projection tensors. The degradation (damage) of the interfacial opening resistances is modelled via a dimensionless nonlocal damage variable that prevents localisation of damage within the interphase. This nonlocal variable results from the solution of a gradient damage based regularisation equation within the interphase subdomain. The damage field is constrained to the interphase region by applying a relatively large penalisation on the damage gradients inside the interphase. The extent of nonlocality ensures that the damage is largely uniform in the direction perpendicular to the interphase, thus making its thickness the theoretical lengthscale for dissipation. To achieve model predictions that are objective with respect to the interphase thickness, scaling relations of the model parameters are proposed. The numerical performance is shown for a uniform opening case and then for a propagating crack. Finally, an application to an artificial polycrystal is shown.

中文翻译：

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一种基于 FFT 的频谱求解器，用于使用梯度损伤方法进行界面去内聚建模

这项工作提出了一种基于快速傅立叶变换 (FFT) 的方法，该方法可用于模拟界面去内聚。FFT 求解器无法处理尖锐的界面，因此放弃使用传统的内聚区来模拟该框架内的界面力学行为。通过用中间相逼近尖锐的界面（例如晶粒/相界）可以克服这种限制。在界面内，背景塑性本构行为是从相应的相邻晶粒继承的。脱聚过程的各向异性运动学使用损伤变形梯度进行建模，该梯度是通过将开口应变（在法向和切向模式下）映射到相关投影张量而构建的。界面开口电阻的退化（损坏）通过无量纲的非局部损坏变量进行建模，该变量可防止界面内损坏的局部化。该非局部变量源自相间子域内基于梯度损伤的正则化方程的解。通过对界面内的损伤梯度施加相对较大的惩罚，损伤场被限制在界面区域。非局部性的范围确保损伤在垂直于界面的方向上基本均匀，从而使其厚度成为耗散的理论长度尺度。为了实现相对于相间厚度的客观模型预测，提出了模型参数的比例关系。数值性能显示为均匀开口情况，然后是扩展裂纹。最后，展示了人造多晶的应用。