A Method For Determining Non-equibiaxial Residual Stress By Instrumented Spherical Indentation Based On The Asymmetry Of Residual Impression

The existing of residual stresses in structures or components has significant effects on the mechanical properties,such as fatigue and brittle fracture.At present,the commonly used residual stress test methods are mechanical and physical methods,which are applicable to specific conditions.Compared with traditional testing technology,instrumented indentation has some advantages,such as micro-zone,micro-destructive,material and stress adaptability.According to the application scale,residual stress analysis methods can be divided into two types:equi-biaxial residual stress and non-equibiaxial residual stress,and all have their defects.These methods some are limited to equi-biaxial stresses,and the other has problems that the analytical parameter cannot be measured or not easy to measure.This paper aims at developing an practical non-equibiaxial residual stress analysis method which is based on the asymmetry of residual impression.The present work is summarized as follows.（1）Analysis tools.In order to determine the elastic-plastic state of the material at different relative indentation depths,some basic relationships are derived.The derivation of these relationships is conducive to determining the critical indentation conditions of the material.To facilitate the application of non-equibiaxial residual stresses,a three-dimensional simulation model was established,at the same time,the basis of the model parameter were given.Finally,we verified the reliability of the model by analytical results.（2）Analytical parameter.The asymmetry of residual impression was selected as the analytical parameter,and the dimensionless relationship between the asymmetry and the indentation variable is established by means of dimensional analysis.The logarithm of the asymmetry of the spherical indentation is found by finite element simulation.And the simulation results showed that the asymmetric of impression is approximately linear with the equi-biaxial residual stress,the shear residual stress is related to the intercept in the linear relationship.Finally,the stability and sensitivity of this relationship are tested numerically.（3）Analytical method.We decomposed the work for solving general stresses into two parts,and formed analysis methods through relational equations.Creating this analysis method requires three steps:Firstly,establish the relationship between the asymmetry of residual impression and the shear stress;secondly,based on the previous work,establish the relationship between the relative load and the equi-biaxial residual stress;Finally,combine the two equations to form the analysis method which is suitable for solving general stress.（4）Numerical verification.Numerical verification had been divided into stability analysis and sensitivity analysis.The stability analysis:First we introduced a relative error of±5%to the εy,n,（F-F₀）/F₀,σ^R,and λ.When εy introduced errors,the calculation of the shear stress can be controlled within 8%,equi-biaxial stress can be controlled within 3%;when n introduced errors,both calculation deviation can be controlled within 5%;when（F-F₀）/F₀ introduced errors,shear stress can be controlled within 7%,equi-biaxial stress can be controlled within 5%;when λ introduced errors,shear stress can be controlled within 10%,and the equi-biaxial stress was not affected by it.Afterσ^R introduced errors,shear stress can be controlled within 8%.The sensitivity analysis:In the process of establishing this analysis method,due to different problems,sensitivity of the analysis method cannot be obtained,but the results of the two relationships can be referred to.This paper proposed a new method for analyzing non-equibiaxial residual stresses based on the asymmetry of residual impression.The measurable indentation parameter are convenient,reliable and sensitive.At the same time,the stability of the analytical method is high and the error transmission is weak.