The Theory Based On Mean-value Energy Equivalence And The Small Specimen Testing Methods For Materials

The relationships among the uniaxial stress-strain relationship parameters,strength,hardness and the elastoplastic deformation response are the basis for structural integrity analysis and material testing.It is of great significance for engineering safety evaluation.On one hand,for the mechanical problems under axis symmetry,plane stress and plane strain,people have long been able to obtain very limited elastoplastic solutions under certain assumptions for engineering analysis.On the other hand,due to the coexistence of the development needs of key projects such as nuclear power,aviation,and aerospace and the inevitable harsh environmental factors such as high temperature,high pressure,and irradiation,to acquire accurate basic mechanical properties by small specimen testing methods(SSTM)based on millimeter or micron deformation zone is critical for structural safety design and evaluation.For SSTM such as indentation,ring compression and small punch test etc.,it is difficult to achieve universality and reliability for them with different sized specimens and different materials based on existing empirical formulas or numerical equations from finite element analysis(FEA).Thus,to establish the analytical or semi-analytical relationship between the mechanical properties of materials and the elastoplastic deformation responses is particularly critical.In this paper,the energy equivalence theory for material deformation,the elastoplastic deformation response law of the experimental structural component and the SSTM and its application are systematically studied.Main tasks include:1.For the monotonic-loaded experimental structural components(SCs)with materials meet isotropic and power-law or linear-law constitutive relation,the mean-value energy equivalence principle is proposed innovatively,i.e.,the external force of the constructor is equal to the energy of the deformation domain.The energy density of the density median point RVE(Representative Volume Element)and the effective deformation domain volume,and the complex stress state energy density of the RVE at median point is equivalent to its energy density of the uniaxial equivalent stress and strain state;2.It is assumed that the equivalent strain of the RVE at median point and the volume of effective deformation region are respectively in power-law relationship with the unidirectional load or the load-line displacement.A unified elastoplstic semi-analytical model correlating energy,materials paramters(such as Young’s modulus,stress hardening exponent and strength coefficient),load-displacement response and geometric dimensions is proposed to describe more than 10 kinds SCs based on mean-value energy equivalence.The loaded component is calculated by finite element method.The numerical verification by FEA is carried out within power-law hardening materials,and the results show that the model has wide universality and accuracy;3.Based on the unified elastoplastic semi-analytical model of load-displacement relationship,for indentation and ring compression with different geometric dimensions,new small specimen test methods for obtaining the equivalent stress-strain relation and tensile strength of materials are developed.The forward and reverse verifications of the new methods were carried out by numerical analysis.The experiments of spherical indentation,dual conical indentation and ring compression were carried out to verify the feasibility and accuracy of the new methods.For the materials in RO(Ramberg-Osgood)law,unified semi-analytical models for K_I factor,compliance and J-integral with mode-I cracked SCs are respectively established.Based on the elastoplastic semi-analytical load-displacement model of indentation,conversion relationships among Brinell,Rockwell,Vickers hardness and tensile strength are proposed.