Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase field fracture poor convergence is found or, in the case of using staggered algorithms, leads to the presence of jumps in the evolution of the cracks. In this work, a novel method is proposed to perform micromechanical simulations with phase field fracture imposing monotonic increases of crack length and allowing the use of monolithic implementations, being able to resolve all the snap-backs during the unstable propagation phases. The method is derived for FFT based solvers in order to exploit its very high numerical performance n micromechanical problems, but an equivalent method is also developed for Finite Elements (FE) showing the equivalence of both implementations. It is shown that the stress-strain curves and the crack paths obtained using the crack control method are superposed in stable propagation regimes to those obtained using strain control with a staggered scheme. J-integral calculations confirm that during the propagation process in the crack control method, the energy release rate remains constant and equal to an effective fracture energy that has been determined as function of the discretization for FFT simulations. Finally, to show the potential of the method, the technique is applied to simulate crack propagation through the microstructure of composites and porous materials providing an estimation of the effective fracture toughness.

翻译：在微观层面模拟裂纹扩展对于理解微观结构对断裂过程的影响至关重要。然而，微观扩展往往不稳定，使用相场断裂模型时会出现收敛困难，而在采用交错算法时则会导致裂纹演化过程中出现跳跃现象。本研究提出了一种新颖方法，用于执行相场断裂的微观力学模拟，该方法强制裂纹长度单调递增，并允许采用整体式实现方案，能够解析不稳定扩展阶段的所有回跳现象。该方法专为基于FFT的求解器设计，以充分发挥其在微观力学问题中极高的数值性能，同时我们也为有限元法开发了等效方法，证明两种实现方案的等价性。研究表明，在稳定扩展阶段，采用裂纹控制方法获得的应力-应变曲线和裂纹路径与使用交错算法的应变控制方法所得结果完全吻合。J积分计算证实，在裂纹控制方法的扩展过程中，能量释放率保持恒定，且等于通过离散化参数确定的FFT模拟有效断裂能。最后，为展示该方法的应用潜力，我们将该技术应用于模拟复合材料和多孔材料微观结构中的裂纹扩展，从而实现对有效断裂韧性的定量评估。