Analysis Of The Low Cycle Fatigue Behaviour Of Ductile Metals Based On Inhomogeneous Deformations At Grain Scale

Due to the inner structure inhomogeneity,metals under the reciprocating loading are always facing stress and strain localization issues,which may cause the formation and evolution of microcracks.From this point of view,we may discripe the mechanism of fatigue.Two main aspects are discussed in this paper,(1)Elastic-plastic constitutive relations to discripe the deformations under cycle loading were applied.In other to know how materials fatigue,we need to know how they deform first.From the perspective of micro-structure evolution,even in high cycle fatigue issues,the formation of fatigue source is strongly related to the accumulation of micro-plasticity.Hense,constitutive relations which can be used in cycle loading are important and worthy of studying.(2)Methodology which can predict strain amptitude vurses fatigue curves was established.Classical fatigue predicting models are always based on experience.In other to understand the basic character of fatigue,a series of experiments need to be done to fit the character lines.Such descriptions are based on interpolation function fitting.In this paper,a new methodology is adopted though which we can know the basic character of fatigue with one single fatigue test.The research in this paper mainly makes the following progress:1.The Chaboche cyclic plastic constitutive equation with AF type back stress andthe implicit integral formula of crystal plastic constitutive equation with AF type back stress were derived and successfully compiled into the material subroutine UMAT for preparation.2.Combined with the fatigue test data of polycrystalline copper,the macroscopic Chaboche model was adopted to describe the cyclic plastic properties of the grains,and the mechanical response differences caused by random orientation of the grains were characterized by the model parameters of random distribution.On this basis,polycrystalline RVE was used to simulate the macroscopic behavior and mesoscopic non-uniform deformation and difference changes of polycrystalline copper under the strain cycle.It was found that :(a)the distribution of stress and strain at the grain scale of material caused by material heterogeneity was uneven.With the increase of cycle number,the deformation becomes more and more uneven.(b)the results of numerical simulation are all similar to the models constructed by inhomogenizing different parameters(c)As long as the inhomogeneity description of the material is considered in the RVE,the inhomogeneity or localization of the strain of the material after the cycle can be simulated,even the macroscopic constitutive relationship without the information of the material meso-structure.(d)Since the macroscopic constitutive relation cannot simulate the deformation mechanism of the meso-structure,the simulation in the late fatigue life is weak.In spite of this,the early data can be revised to become a good fatigue indicator parameter(FIP).3.In combination with the low-cycle uniaxial fatigue experiment of Q235 steel,crystal plastic RVE is used as the material model reflecting the characteristics of polycrystalline.In addition,the relationship between the deformation inhomogeneity and fatigue is further discussed.Then by referring to the simulation of cyclic loading in the actual process the evolution of inhomogeneity of deformation of grain size in the cyclic process is analyzed.Finally,the prediction ability of different fatigue indicator parameters FIP on fatigue life is tested.The following conclusions are obtained:(a)It isreasonable and effective to use the statistical standard deviation of loading axial strain and the first principal strain to characterize the non-uniform deformation of the material and as the FIP.(b)Under the same loading condition,the development of axial strain statistical standard deviation and the first principal strain statistical standard deviation are roughly the same,and the predicted fatigue life of the two is close to each other.4.Crystal plastic RVE is adopted as the polycrystalline material model.By referring to the simulation of graded cyclic loading in the actual process,the uneven deformation evolution of material grain scale in the variable amplitude cycling process is analyzed,and the life of Q235 structural steel's thin-walled circular tube specimen under the two-stage variable strain amplitude fatigue test is predicted by the new method.The conclusions are as follows :(a)In the variable amplitude loading test,it is still reasonable and effective to use the statistical standard deviation of axial strain and the first principal strain to represent the non-uniform deformation of the material as the FIP.(b)In the absence of some standard experiments(such as quoting the experimental data of others),we can calculate the ? when materials failure by establishing the loading mode of RVE with full-course simulation experiment,so as to roughly estimate the FIP limits ?.(c)Crystal plastic RVE was used to study the impact of material cycle history on damage accumulation.It was found that Miner linear damage accumulation model has limits,that is,the damage accumulation of material is not strictly linear,and the speed of damage accumulation was related to the previous damage history.