Characterizations Of Initial Yield Surface And Failure Surface Of Metallic Foams In The Principal-stress Space And The Principal-strain Space

As a versatile structural material with excellent energy absorption characteristics,metallic foams usually work with complex stress state in the engineering applications.Therefore,it is necessary to study the initial yield surface and the failure surface of metallic foams in quasi-static and dynamic loadings.However,the difficulty of multi-axial tension loading leads to the very small number of data points under multi-axial loadings in the experiments.It is unreasonable to characterize the initial yield surface and the failure surface only with several data points.This is the main reason for the controversy about the initial yield surface and the failure surface of metallic foams.Therefore,it is necessary to use a sufficient number of data points that almost cover the entire permissible area to fit the initial yield surface and the failure surface directly in the principal-stress/strain space.In this study,aluminum foam models composed of Voronoi structures are built based on the results of uniaxial compression,uniaxial tension and biaxial tensile tests.By presetting the triaxial ratio of initial force loading,data points covering the whole permissible area of the principal-stress space and the principal-strain space can be obtained to characterize the initial yield surface and the failure surface.The main contents of this paper are as follows:(1)The initial yield criterion and the failure criterion of metallic foams under multi-axial loading are proposed,respectively.The criteria are the methods to determine the data points on the initial yield surface and the failure surface.However,many studies usually regarded the stress or strain in one loading direction as the sign of initial yield moment or failure moment under multi-axial loading,ignoring the contributions in the other loading directions.In the study of yield surface,an initial yield criterion based on the plastic dissipation energy of matrix material is proposed.In addition,a failure criterion based on the failed elements of metallic foam is also proposed to solve the key problem of determining the failure state of the foam under multi-axial loadings.(2)Characterize the initial yield surface in the principal-stress space and the principal-strain space when the metallic foam is under multi-axial quasi-static loadings.The initial yield points are arranged orderly along different Lode angles in the principal-stress/strain space.However,the distribution of stress yield points is discrete because of the influence of plastic flow.Therefore,it is better to characterize the global yield surface of metallic foams in the principal-strain space than in the principal-stress space.Yield points in the principal stress/strain space constitute an ellipsoidal intial yield surface,which can also be characterized on the(?_m,?_e)stress plane and on the(?_m,?_e)strain plane.The asymmetry of tension and compression increased with relative density but was eliminated when using two parameters to normal-ize the strain yield surfaces.The normalized strain yield surface of metallic foams was independent of relative density,and the surface could be characterized by a unified elliptic equation on the(?_m,?_e)plane.(3)Characterize the failure surface in the principal-stress space and the principal-strain space when the metallic foam is under multi-axial quasi-static loadings.Failure points are arranged orderly along different Lode angles in the principal stress/strain space and form an ellipsoidal failure surface in the permissible region.Similar to the initial yield surface,an elliptic equation can be used to characterize the failure surface on the(?_m,?_e)plane,the shape of which increases with the increase of the relative density of the metallic foam.Metallic foams under multi-axial compression will be compressed until dense without failure,which results in a“missing area”occurring in the global topology of the failure surface.The boundaries of the stress missing area and the strain missing area were determined analytically and had good agreement with critical points from the numerical results.(4)Characterize the failure surface of metallic foam under multi-axial dynamic loadings.In the multi-axial tensile loading conditions with medium strain rate,the cell walls of the foam exhibit local failed characteristics.Due to stress concentration,the connections between cell pores are destroyed first.And the stress wave cannot be fully propagating inside the foam,resulting in the decrease of the stress at the fixed end when the strain rate increases.According to the mechanism of microstructural failure,the shape of the failure surface of foam metal expands with the increase of strain rate.An elliptic equation with the parameters of strain rate is used to characterize the failure surface on the(?_m,?_e)stress plane.This equation of failure surface is independent of the relative density and is also applicable to the situation of quasi-static multi-axial loading.