Study On The Failure Surface Of Gradient Metallic Foams Under Triaxial Loading

Metallic foams offer significant performance gains in light,stiff structures,for efficient absorption of energy.In practical applications,metallic foams are usually subjected to multi-axial loading and exhibit failure behaviors.Lacking of failure data of metallic foams under multiaxial loading,the characterization of failure surface is still controversial and effects of meso-structural irregularities on failure surface are unclear.Hence,a constitutive law describing the failure behavior of gradient metallic foams is essential.Numerical simulations under triaxial loading were conducted to investigate properties of the failure surface based on 3D Voronoi models with gradient distribution of size irregularity.Failure surfaces of gradient metallic foams were characterized in principal stress space and strain space,and effects of the gradient parameter were discussed in detail.The main contents of this paper are as followings:(1)A theoretical method was proposed to characterize stress-strain data of gradient metallic foams in stress hardening region under uniaxial compressive loading.The stress hardening region is caused by the nonlinear spatial distribution of relative density of foams with gradient size irregularity.In stress hardening region,local deformations are observed obviously,and foams’ structures are compressed layer by layer in the gradient direction from larger cells to smaller cells.Based on these mechanisms,a theoretical method is proposed to well characterize the stress-strain data of gradient foam in the stress hardening region.(2)Properties were investigated including deformations,loaddisplacement data and energy absorption characteristics of gradient foams with different gradient combination scheme of shape irregularity under different impact velocities.Results show that the impact velocity has a significant effect on the properties of the shape irregularity gradient combination model when impact velocity varies in specific ranges,and the combination model with the shape irregularity gradient from small to large along the impact direction has the best energy absorption capacity.(3)Numerical simulations under triaxial loading were carried out to study the failure properties of foams with gradient distribution of size irregularity.Three kinds of failure deformations were observed: the tensile breaking mode,the buckling mode and the mixed.The initial failure criterion is recommended for metallic foam with shape irregularity gradient under triaxial loading: the first peak moment of the normal stress of each direction,von Mises equivalent stress and mean stress.This criterion is suitable for both isotropic and anisotropic foams under complex loadings.(4)The properties of failure surface of gradient foams were analyzed both in the stress(or strain)plane and the principal stress(or strain)space respectively.In von Mises equivalent stress and mean stress plane,the failure surface including the principal stress in the gradient direction is smaller than that in the non-gradient direction.Considering both the asymmetric of failure surface in tensile and compressive state and the anisotropic in different direction,the failure surface were normalized by uniaxial tensile failure stress and axial compressive failure stress of three directions respectively.The normalized failure surface is approximately parabola in the stress plane,and effects of anisotropy of gradient foams could be eliminated.The normalized failure surface is almost independent of the gradient parameter of gradient foams.The normalized failure surface approximates an ellipsoid in principal stress space,and the Lode angle has a little influence on it.The failure surface characterization of the anisotropic gradient foams could not be well characterized in the strain plane or in the principal strain space.