Residual stress plays an important role in the mechanical performance of engineering structures. In this paper, the indentation of pre-stressed strain hardening materials by a rigid sphere is simulated through the finite element method. It is shown that the mean contact pressure in the post-yield regime keeps continuously increasing with the indentation proceeding. Compared to the case without residual stress, compressive residual stress tends to increase the mean contact pressure at a given indentation depth, while tensile stress has an inverse effect. To quantitatively indicate the influence of residual stress, a nominal contact pressure is defined, which obtains its maximum value at a critical depth. The dependences of the maximum nominal pressure and the critical indentation depth on the residual stress and the material properties are determined explicitly through large numbers of simulations. Inspired by the nominal pressure deviation stemmed from residual stress, a new approach is proposed for measuring residual stress through spherical indentation tests.

中文翻译：

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等双轴残余应力对应变硬化材料球面压痕的影响

残余应力对工程结构的力学性能起着重要作用。本文通过有限元方法模拟了刚性球对预应力应变硬化材料的压痕。结果表明，后屈服状态下的平均接触压力随着压痕的进行而不断增加。与没有残余应力的情况相比，压缩残余应力倾向于增加给定压痕深度处的平均接触压力，而拉伸应力具有相反的效果。为了定量地表示残余应力的影响，定义了一个标称接触压力，它在临界深度处获得最大值。最大公称压力和临界压痕深度对残余应力和材料特性的依赖性是通过大量模拟明确确定的。受残余应力引起的公称压力偏差的启发，提出了一种通过球形压痕测试测量残余应力的新方法。