Theoretical Model Of Elastoplastic Proportional Superposition Of Metal Material And Application Of Ball Indentation And Ball Deformation

Stress vs.strain relations,yield strength and tensile strength are fundamental relationships and properties for material mechanical behavior,which are usually obtained through conventional uniaxial tensile tests.However,it is impossible to perform standard tensile tests on in-service structures and small-volume materials,so it has the increasing importance of testing by small sample including micro-destructive miniature indentation testing.This paper assumes that constitutive relations of materials meet with Ramberg-Osgood power law,and there exists proportion superposition between the pure elastic strain energy and pure plastic strain energy in the deformation process.The theoretical and experimental methods are studied based on the median energy density equivalence.The main research contents are as follows:(1)A semi analytical model of the relationship between strain energy U_e or pure elastic displacement h_e with load P and material constant E under pure elastic condition and between strain energy(U_p)or pure plastic displacement(h _P)with load and material constant(K and N)under pure plastic condition is established through introduce new and unified characteristic strain energy U~*and characteristic load P~*in pure elastic and pure plastic conditions.A semi analytical model for the relationship between strain energy(U)or elastic-plastic displacement(h)and load with material constants(E,K and N)is established by introducing elastic-plastic scale factorsλ_e andλ_P.In view of the parameters contained in the model,a method to determine the model parameters by finite element analysis of a small amount of materials is proposed.(2)A proportional superposition-based elastoplastic model was developed to describe the relationships between the displacement and the load during the ball indentation.Furthermore,a new test method of ball indentation based on elastoplastic proportional superposition was developed to obtain the constitutive relationships of R-O law materials.For 80 types of hypothetical material constitutive relationship,the load–displacement curves predicted using displacement load model of ball indentation were found to agree closely with the finite element analysis(FEA)results.Moreover,the load displacement curve calculated by FEA is used as the test simulation curve,and the stress vs.strain curves predicted using the BI-EPS method were in better agreement with those obtained by FEA.Additionally,ball indentation was performed on eleven types of metal materials including 5 types of aluminum alloys and 6 types of steels.The test results showed that the stress vs.strain relationships,elastic modulus and the tensile strength values predicted using the proposed BI-EPS method agreed well with the results obtained using conventional uniaxial tensile tests.(3)The finite element analysis of 32 types of hypothetical materials was carried out based on the spherical indentation method(Kwon method)which is based on the empirical equation of stress and strain,and the multi-stage loading and unloading tests of 4 types of metal materials(2 types of aluminum alloy and 2 types of steel)were completed.Evaluate the method combined with the ball indentation test method based on the elastoplastic proportional superposition.The results of finite element analysis and test show that the empirical indentation method represented by Kwon method has a great limitation on material adaptability,and the stress-strain relationship has a large degree of deviation for materials with high yield strength and large strain range.In addition,the test efficiency is low because it needs to be loaded and unloaded many times.The BI-EPS method proposed in this paper adopts single loading,and the experimental efficiency and the prediction accuracy of stress-strain relationship are high.(4)In order to solve the problem of how to obtain the mechanical properties of microspheres in nuclear power engineering,a proportional superposition-based elastoplastic model was developed to describe the relationships between the displacement and the load during the ball compression based on the theoretical model method mentioned above.Furthermore,a new test method of ball compression based on elastoplastic proportional superposition was developed to obtain the stress vs.strain relationships of materials.For 25types of hypothetical material constitutive relationship,the load displacement curves predicted by the displacement load model of ball compression are in good agreement with the FEA results.Moreover,the load displacement curve calculated by FEA is used as the test simulation curve,and the stress vs.strain curves predicted using the method were in better agreement with those obtained by FEA.