Analysis Of Two-scale Elastic-Plastic Deformation And Fatigue Life Prediction For Metal Under Spectrum Loading

Metallic components are the key load-carrying part of aircraft.Fatigue damage and fracture due to the complicated loading conditions and stress status is the primary failure mode for metallic parts.In general,the fatigue life of crack initiation takes about 80%of the whole fatigue life.At present,though the engineering method for the fatigue life estimation is convenient,the predicted result is often with low precision,which significantly affects the reliability and safety of aircraft.Based on this,it is quite necessary to study the theories of constitutive equation,fatigue damage accumulation and reliability prediction of fatigue life.In this paper,based on the elastic-plastic mechanics and cyclic constitutive model,the theory of macro-meso inclusion is used to improve the numerical method of two-scale elastic-plastic cyclic stress strain relation.Considering the variable load spectrum in practice,the two-scale fatigue damage model is developed to take the loading sequence into account.The main works in this paper are listed as follow.1)Investigation of nonlinear cyclic macro elastic-plastic constitutive model.To improve the accuracy of fatigue life prediction and to reveal the mechanism of loading sequence effect,a nonlinearelastic-plastic constitutive model is founded through the research of metal cyclic deformation orderliness.This model is based on the elastic-plastic constitutive theory and the kinematic and isotropic hardening effects are taken into account using multi-exponential functions.The nonlinear mixed-hardening-coefficient function is defined and changes with the equivalent plastic strain.The tension-unload-compress tests of 2A12-T4 aluminium are conducted to fit the function form,which is more approximated to the metal hardening feature.Based the boundary coordination rule,the reverse transition curve is designed using the similar model of tension curve.This constitutive model can characterize the cyclic hardening and loading sequence effect quantitatively and reflect the nonlinear feature of elastic-plastic curve.The comparison with 2A12-T4 aluminium low cycle fatigue deformation curve was in a good agreement with test data,which show the nationality and accuracy of the model.2)Numerical algorithm of nonlinear cyclic macro elastic-plastic constitutive model.For the purpose of realizing the numerical computations of combined hardening and combined proportion function,UMAT subroutine for ABAQUS is used to define the material nonlinearityand update the Jacobian matrix.The accuracy and robust of the multimode UMAT program are verified by comparing the results between the exponential constitutive model and ABAQUS.The characteristics of cyclic stress strain relation of aluminum alloy under the load-controlled mode and displacement-controlled mode is experimentally investigated to validate the accuracy of the combined hardening constitutive model.The variations of the macro cyclic stress strain curve under constant amplitude,different stress ratio and high-low loading sequence are presented.3)Investigation of nonlinear cyclic meso elastic-plastic constitutive modelbased on two-scale theory.In order to solve high cycle fatigue damage accumulation problem,based on the Elshelby-Kroner localization law,the macro-meso two-scale theory is introduced to develop the elastic-plastic stress-strain relation and the meso cyclic elasticplastic combined constitutive model under the variable loading conditions.The single exponential function is used to determine the meso kinematic hardening and isotropic hardening with the discrete-changed mixed-hardening-coefficient to improve the calculation efficiency.Combined with the weaken yield surface and mixed-hardening-coefficient,the meso elastic-plastic stress strain curve can be fitted while R>0.The method to determine the parameters in the model of initial meso yield strength is presented and the numerical method for meso stress strain calculation is given to consider the loading sequence.4)Numerical algorithm of nonlinear cyclic meso elastic-plastic constitutive model.In order to solve the lacking of automatic high cycle faigue elastic-plastic calculation problem,based on the incremental method and Newton iteration,FORTRAN language is used to write a subroutine NonMiHard.for for the numerical computation of the meso constitutive equation.The meso elastic plastic stress strain curves under the plane stress and 3D stress state are computed,and the example validates the effectiveness of the model.The meso cyclic elastic-plastic stress strain curves are given by combination of Hardmacro.for and NonMiHard.for.5)Investigation of fatigue damage evolution and life estimation modelunder spectrum loading.The basic theory of damage mechanics is summarized.The laws of thermodynamics are based on to derive the constitutive relation with damage variable.The dissipation potential function is used to obtain the damage evolution equation,which meets the self-consistent of thermodynamic.The failure criterion of damage evaluation is described.Theunreasonable items of Lemaitre's damage evolution equation are revised,such as the plastic strain damage threshold.The macro and meso damage are normalized and a unified damage evolution model is developed for the low and high cycle fatigue evaluation.This model can take account of the material nonliearity,the kinematic and isotropic hardening effects,loading sequence effect and compress loading effect,which can improve the accuracy of fatigue life prediction.The model coefficents are given through minium error optimization of constant amplitude fatigue tests.6)Experimental verification of nonlinear cyclic elastic-plastic constitutive model and fatigue life estimation method under spectrum loading.The 2A12-T4 aluminium tests of smooth bar and single-hole plate under constant amplitude loading,high-low and block spectrum loading are designed and conducted.Based on the FEM,two-scale model,and the developed damage evolution model,the macro meso elastic plastic stress strain,fatigue damage accumulation and fatigue life prediction of 2A12-T4aluminum alloy are studied.Compared with the test data of smooth barwith fatgue life from 10~2 to 10~6,the maximum error is 23.92%and the minimum error is-5.81%which show that the theoretical result is in good agreement with the experimental result,validating the accuracy of the current model.The applicability and feasibility of the model are also confirmed by experiments under the high-low loading sequence and the block spectrum with maximum error of-34%.The present research gives insight into accurate fatigue life prediction of aircraft in practical engineering.