In this paper, an anisotropic ductile fracture is studied using a phase-field model. This model is on the basis of the energy principle in which a scalar field is added as a phase-field variable to determine the probability paths of cracks. Therefore, the system of equations, included for the displacement and phase field, is obtained and solved in a nonlinear finite element procedure through a user element subroutine in ABAQUS commercial software. The effect of anisotropy on cracks’ paths for an anisotropic fracture is assessed according to the Hill criterion for ductile materials. Moreover, an implicit integration algorithm for an anisotropy model combined with a phase field is shown for the plane strain state. The proposed model can also be used for the combination of various constitutive models along with an anisotropy such as the anisotropic rate-dependent (visco-Hill) and the anisotropic rate-independent (elasto-Hill). Furthermore, the threshold parameter is introduced to examine the plastic deformation influence on cracks initiation and propagation in this study. Finally, the influence of the anisotropy on the responses of different specimens in various fracture processes is interrogated. The accuracy of the suggested model is demonstrated by juxtaposing the achieved and given experimental and numerical results in the way that it can be able to simulate the anisotropy effects on the gradual evolution of cracks from ductile to brittle.

本文利用相场模型研究了各向异性延性断裂。该模型基于能量原理，其中将标量场作为相场变量添加，以确定裂纹的概率路径。因此，通过ABAQUS商业软件中的用户元素子例程，通过非线性有限元程序获得并求解了包括位移和相场在内的方程组。根据韧性材料的希尔准则，评估各向异性对各向异性断裂裂纹路径的影响。此外，针对平面应变状态，展示了一种各向异性模型与相场相结合的隐式积分算法。所提出的模型还可以用于各种本构模型以及各向异性的组合，例如各向异性的速率依赖性（粘滞山丘）和各向异性的速率依赖性（弹性山丘）。此外，引入阈值参数以检查塑性变形对裂纹萌生和扩展的影响。最后，研究了各向异性对不同断裂过程中不同试样响应的影响。通过并置获得的和给出的实验和数值结果来证明所建议模型的准确性，该模型可以模拟各向异性对裂纹从延性到脆性逐渐演化的影响。引入阈值参数来研究塑性变形对裂纹萌生和扩展的影响。最后，研究了各向异性对不同断裂过程中不同试样响应的影响。通过并置已获得的实验结果和给定的实验结果以及数值结果，表明该模型的准确性，从而可以模拟各向异性对裂纹从延性到脆性逐渐演化的影响。引入阈值参数来研究塑性变形对裂纹萌生和扩展的影响。最后，研究了各向异性对不同断裂过程中不同试样响应的影响。通过并置已获得的实验结果和给定的实验结果以及数值结果，表明该模型的准确性，从而可以模拟各向异性对裂纹从延性到脆性逐渐演化的影响。