The paper reports the development of an implicit numerical scheme for plane stress cyclic elasto-plasticity, capable of integrating a wide range of hardening rules, and simulating multi-axial ratcheting in metal structural components. Constitutive relations account for von Mises yielding in combination with mixed hardening. Emphasis is given to the kinematic hardening part, which is described with an advanced multiple back-stress model suitable for multi-axial material ratcheting simulation. The constitutive equations are integrated implicitly, and the accuracy of the algorithm is assessed via iso-error maps. Two main novelties of the algorithm refer to the incremental update of the internal variables through the solution of a single scalar equation, and the explicit formulation of the consistent tangent moduli. The numerical scheme is implemented within the finite element environment as an external material subroutine, and its computational efficiency is demonstrated through the simulation of large-scale experiments on pipe elbows. Using the proposed computational framework, two kinematic hardening rules are employed to simulate the elbow response with emphasis on local strain amplitude and accumulation (“ratcheting”). The good comparison between numerical and experimental results demonstrates the computational efficiency of the numerical scheme and highlights some key issues concerning multi-axial ratcheting simulation.

本文报道了一种平面应力循环弹塑性隐式数值方案的开发，该方案能够集成广泛的硬化规则，并模拟金属结构部件中的多轴棘轮。本构关系说明了von Mises与混合硬化相结合的屈服。重点介绍了运动硬化部分，并通过适用于多轴材料棘轮模拟的高级多重背应力模型进行了描述。本构方程被隐式积分，并且通过等误差图评估算法的准确性。该算法的两个主要新颖之处在于通过单个标量方程的解和内部切线模量的显式表示来实现内部变量的增量更新。该数值方案是在有限元环境中作为外部材料子例程实现的，并且通过对弯头进行大规模实验的模拟证明了其计算效率。使用提出的计算框架，采用了两个运动强化规则来模拟弯头响应，重点是局部应变幅度和累积（“棘轮”）。数值与实验结果之间的良好对比证明了数值方案的计算效率，并突出了与多轴棘轮仿真有关的一些关键问题。使用两个运动学硬化规则来模拟肘部响应，重点是局部应变幅度和累积（“棘轮”）。数值与实验结果之间的良好对比证明了数值方案的计算效率，并突出了与多轴棘轮仿真有关的一些关键问题。使用两个运动学硬化规则来模拟肘部响应，重点是局部应变幅度和累积（“棘轮”）。数值与实验结果之间的良好对比证明了数值方案的计算效率，并突出了与多轴棘轮仿真有关的一些关键问题。