For many materials, plastic deformations under cyclic loadings differ from monotonic loading. Cyclic plastic zone with considering the strain hardening effects becomes complicated during unloading step. In this research, the effects of nonlinear kinematic and isotropic hardening behaviours on the cyclic plastic reaction around the crack tip for different conditions are investigated. For study of various hardening characteristics, as‐received and annealed copper are tested under same symmetric cyclic loadings. The results indicate considerable isotropic hardening behaviour in annealed material. A Chaboche nonlinear hardening model was used to determine the hardening parameters. The cyclic plastic zone around the crack tip in C(T) specimen was measured by back stresses. The cyclic plastic zones are specified via variations of the back stresses in a cycle. The cyclic plastic zones predicted by Chaboche model are smaller than those for Irwin model because of the hardening effects. Also, Irwin model for prediction of the cyclic plastic zone size is modified with considering the cyclic plastic effects. According to the results, the cyclic plastic zone around the crack tip is almost constant in the same load range, and load ratio (R) has a slight effect on this zone. Whereas, for constant load range, cyclic J‐integral (∆J) is different for various R values. For studying of the fatigue crack growth, two parameters of ∆J and cyclic plastic zone area were evaluated. These parameters can apply in fracture mechanics especially in elastic–plastic conditions with considering the cyclic plastic responses.

中文翻译：

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基于Chaboche模型的运动学各向同性硬化材料中基于循环塑性区和循环J积分的疲劳裂纹扩展确定

对于许多材料，循环载荷下的塑性变形不同于单调载荷。考虑到应变硬化效应的循环塑性区在卸载步骤中变得复杂。在这项研究中，研究了非线性运动学和各向同性硬化行为对不同条件下裂纹尖端周围循环塑性反应的影响。为了研究各种硬化特性，在相同的对称循环载荷下测试了接收和退火的铜。结果表明在退火材料中相当大的各向同性硬化行为。Chaboche非线性硬化模型用于确定硬化参数。C（T）试样中裂纹尖端周围的环状塑性区是通过反应力测量的。通过循环中背应力的变化来指定循环塑料区域。由于硬化作用，Chaboche模型预测的循环塑性区小于Irwin模型的循环塑性区。此外，考虑到循环塑性效应，对用于预测循环塑性区大小的欧文模型进行了修改。根据结果​​，在相同载荷范围内，裂纹尖端周围的循环塑性区几乎恒定，载荷比为R）对该区域有轻微影响。而对于恒定的负载范围，不同的R值的循环J积分（∆J）是不同的。为了研究疲劳裂纹扩展，评估了∆J和循环塑性区面积这两个参数。考虑到循环塑性响应，这些参数可以应用于断裂力学，特别是在弹塑性条件下。