In this study, we present a Finite Difference Method (FDM)-based stress integration algorithm for Crystal Plasticity Finite Element Method (CPFEM). It addresses the complexity of computing the first derivative of resolved shear stress in the Euler backward stress integration algorithm with Newton-Raphson method. The proposed FDM-based model was verified by evaluating its accuracy, convergence and computational efficiency through single-element simulations. The developed FDM-based model can be easily applied to various constitutive models for CPFEM, overcoming the problem of deriving complex derivative regardless of constitutive models. Additionally, the proposed FDM-based model was validated with the reduced texture approach using AA 2090-T3. Specific parameters including crystallographic orientations were calibrated and the plastic anisotropy was successfully described. In addition, the earing profiles were compared using various stress integration methods. As a result, the proposed FDM-based model can be used as an alternative to the Euler backward method using analytic derivatives with the compatible accuracy, convergence, computational efficiency along with easy implementation within the CPFEM framework.

在本研究中，我们提出了一种基于有限差分法 (FDM) 的晶体塑性有限元法 (CPFEM) 应力积分算法。它解决了使用牛顿-拉夫森方法的欧拉后向应力积分算法中计算解析剪应力的一阶导数的复杂性。通过单元模拟评估其准确性、收敛性和计算效率，验证了所提出的基于 FDM 的模型。所开发的基于 FDM 的模型可以轻松应用于 CPFEM 的各种本构模型，克服了无论本构模型如何导出复杂导数的问题。此外，所提出的基于 FDM 的模型通过使用 AA 2090-T3 的简化纹理方法进行了验证。校准了包括晶体取向在内的具体参数，并成功描述了塑性各向异性。此外，还使用各种应力积分方法对耳廓进行了比较。因此，所提出的基于 FDM 的模型可以用作使用解析导数的欧拉后向方法的替代方案，具有兼容的精度、收敛性、计算效率以及在 CPFEM 框架内易于实现的优点。