| Isotropic non-dense metallic materials,such as foam metals,porous metals,and lattice metals,are mainly affected by multiaxial loads in engineering applications.Therefore,the mechanical behavior and constitutive relationships of non-dense metals under multiaxial loads have been extensively studied,including initial yield surface and subsequent yield surface.However,there are still many controversies in the current mainstream theoretical models,such as the unclear physical meaning of ellipticity,the inadequate equivalent stress and equivalent strain equations,and the inconsistent shape of subsequent yield surfaces.Due to the difficulty in conducting multiaxial loading experiments,existing theoretical models and subsequent yield surface equations have not been fully validated in the entire permissible loading space.To address these controversies,this paper proposed a new plastic flow theoretical model based on the fundamental assumptions of isotropic non-dense metallic materials and established simulation test models with different meso-structures and relative densities.By conducting multiaxial static and dynamic simulation tests covering the entire permissible loading space,the validity of the new plastic flow theoretical model was verified.Finally,this paper analyzed and discussed the shape and strain rate effect of subsequent yield surfaces.The main research content of this paper includes:(1)Based on the two basic assumptions of isotropic non-dense metals,we extended the plastic flexibility rate equation of dense metals to the plastic volumetric flexibility rate equation and the plastic distortion flexibility rate equation for non-dense metals.We constructed the extended Prandtl-Reuss equations applicable to isotropic non-dense metals.Through closure analysis of this equation group,we pointed out the basic conditions for improving constitutive equations.Based on the extended Prandtl-Reuss equations,we derived a new expression for plastic dissipation power and define equivalent stress and equivalent plastic strain rate intuitively based on two equivalent forms of the expression.Through equation analogy,we clarified the physical meaning of ellipticity in the Deshpande-Fleck model(D-F model): the square of ellipticity is the ratio of plastic volumetric flexibility rate and plastic distortion flexibility rate.To ensure the closure of the constitutive equation group,we proposed two constitutive equations that need to be obtained from material tests,the relation equation of equivalent stress and equivalent strain and the equation of plastic volumetric flexibility rate.We designed an extreme deformation condition: compressing the non-dense metal to fully dense state to theoretically validate our new plastic flow theoretical model.The result shows our model adapts the equivalent stress,equivalent plastic strain,and constitutive equations seamlessly to deformation from non-dense to dense state.(2)To comprehensively validate the rationality of the plastic flow theoretical model,we establish two simulation test models with different meso-structures and relative densities: a uniform spherical cell model and a Voronoi meso-structure model.We verified the reliability of the models by conducting uniaxial and biaxial loading experiments and isotropic verification.Then,we conducted static multiaxial loading numerical simulation tests covering the entire permissible principal strain space for the two simulation test models,obtaining up to 31 sets of triaxial stress-strain simulation test data.The data not only well validates our theoretical model but also will be beneficial to the mechanical study of non-dense metals under multiaxial loadings.(3)By applying simulation test data,parameter optimization was carried out for the quasi-static models under different loading conditions,and based on the same optimization parameters,the equivalent stress-strain relationships under each loading ratio were obtained for both the uniform spherical cell model and the Voronoi meso-structure model.The consistency of the equivalent stress and equivalent strain relationships under different loading conditions for both models is relatively good and can be described uniformly using the constitutive equation proposed in this paper.Compared with the D-F model and Zhu-Zheng model,the result calculated by our theoretical model in this paper has better consistency.(4)Using the same equivalent plastic strain as the criterion for the subsequent yield surface,the shape of the subsequent yield surface in the principal strain space is presented.By rotating the principal strain coordinate system,a coordinate system directly related to the volumetric strain,Mises strain,and Lode parameter was established.It was found that different yield surfaces can be well described by the standard equation of the ellipsoid in this coordinate system.By analyzing the ratio of the three principal axes of different ellipsoids,it was concluded that the subsequent yield surfaces of non-dense metals do not exhibit self-similarity.(5)To investigate the strain rate effect of non-dense metal materials(without considering the strain rate effect of the matrix metal),we conducted multiaxial dynamic numerical simulation tests with the maximum axial nominal strain rate as the control index.The research results showed that regardless of the different stages of loading conditions or different maximum nominal strain rate loading conditions,the equivalent plastic strain rate of the material was different.That is,there is rarely a constant strain rate deformation for non-dense metal materials during dynamic deformation.After dividing the test data into different ranges of equivalent plastic strain rates,we analyzed the relationship between equivalent stress and equivalent plastic strain,as well as the subsequent yield surface.We found that with the increase of equivalent plastic strain rate,non-dense metal materials exhibited a "weak" strengthening effect on equivalent stress and the relationship between equivalent plastic strain,as well as the subsequent yield surface. |
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