In this study, a strain-pattern-based method was proposed to simultaneously determine the uniaxial tensile residual stress and flow property from a single-cycle spherical indentation test. The variation of the plastic zone radius (at the specimen surface) with uniaxial tensile residual stress was analytically investigated by the expanding cavity model. The analysis proved that the circular plastic boundary will be elliptical under the action of uniaxial residual stress (with a shrunken plastic zone radius along the loading direction and an extended plastic zone radius vertical to the loading direction), and this difference can be used to calibrate the magnitude of the residual stress. The analytical result was verified and modified through finite element calculations, after which a set of regression functions for Holloman hardening metals was established for load compensation, proportional limit correction, and hardening exponent calculation. The effectiveness of the method was verified through finite element calculations of spherical indentation tests on 16 Holloman hardening and 6 metals used in engineering applications at different residual stress levels. The verification proved that maximum errors for strength and residual stress calculations are about 10% and 15%, respectively, and the potential of the new proposed method was validated.

中文翻译：

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一种用于同时测定单轴拉伸残余应力和流动特性的基于应变模式的球形压痕方法

在这项研究中，提出了一种基于应变模式的方法，以从单循环球形压痕测试中同时确定单轴拉伸残余应力和流动特性。通过扩展腔模型分析研究了塑性区半径（在试样表面）随单轴拉伸残余应力的变化。分析证明圆形塑性边界在单轴残余应力的作用下将呈椭圆形（沿加载方向收缩塑性区半径，垂直于加载方向延伸塑性区半径），该差异可用于标定残余应力的大小。分析结果通过有限元计算得到验证和修正，之后建立了一套霍洛曼硬化金属的回归函数，用于载荷补偿、比例极限修正和硬化指数计算。通过对 16 种霍洛曼硬化和 6 种工程应用中不同残余应力水平的金属进行球形压痕试验的有限元计算，验证了该方法的有效性。验证证明强度和残余应力计算的最大误差分别约为 10% 和 15%，并且验证了新方法的潜力。通过对 16 种霍洛曼硬化和 6 种工程应用中不同残余应力水平的金属进行球形压痕试验的有限元计算，验证了该方法的有效性。验证证明强度和残余应力计算的最大误差分别约为 10% 和 15%，并且验证了新方法的潜力。通过对 16 种霍洛曼硬化和 6 种工程应用中不同残余应力水平的金属进行球形压痕试验的有限元计算，验证了该方法的有效性。验证证明强度和残余应力计算的最大误差分别约为 10% 和 15%，并且验证了新方法的潜力。