| Cellular materials refer to the combination of a matrix material and a large number of open or closed holes,which have a certain cellular structure.Metal foams are a kind of cellular material with metal as the matrix,which have various excellent mechanical properties such as high specific strength and high specific stiffness that traditional metals do not have.Therefore,metal foams are widely used in aerospace,transportation,military,construction and other industrial fields.Metal foams are often subjected to complex loads in practical engineering applications,so understanding the yield behavior and constitutive relationship of metal foams under multiaxial loading is very important to guide the design of metal foam parts.Most of the existing 3D constitutive models for metal foams are based on the isotropic assumption,among which the Deshpande-Fleck model has a simple form and is widely used in various finite element software.The Deshpande-Fleck model simplifies the yield-hardening stage of metal foams,which has been controversial.Moreover,the Deshpande-Fleck model adopts the associated flow rule applicable to traditional metals,and it is still questionable whether the plastic flow rule of metal foams is associated.In addition,in recent years,researchers have found that metal foams have anisotropic yield characteristics and tensile-compression asymmetry.However,there are few three-dimensional anisotropic constitutive models suitable for metal foams,and they are all phenomenological in nature.As a result,these models rely heavily on the support of a large amount of experimental data,which reduces the applicability.The current anisotropic yield criteria focus on describing the mechanical behavior under compressive stress state,and cannot characterize the tensile-compression asymmetry of metal foams.In view of the above problems about predicting the yield behavior of metal foams through constitutive model,the simulation and experimental study of the metal foams are carried out in this paper,and the constitutive behavior of the metal foams under the assumption of isotropy and anisotropy is explored.The summary is as follows:Using Beizer curve and surface algorithms,the traditional Voronoi 2D and 3D models,which are widely used in finite element simulation of metal foams,are optimized respectively.A geometric model of metal foams based on fourth-order Bezier curves and biquartic Bezier surfaces is established.In the process of establishing the optimization model,a dimensionless shape parameter—filling degree is introduced,and the functional relationship between the relative density and filling degree is defined.The method of adjusting the filling degree to obtain the specified relative density geometric model is realized through algorithm programming.The internal mesostructure of the optimized model is highly consistent with the real metal foams,and can restore the typical deformation history of metal foams under compressive load.The uniaxial compression experiments of aluminum foam material are carried out,and the experimental results are compared with the simulation results of the optimization model to verify the accuracy of the model.Based on this optimization model,the follow-up study on the constitutive relationship of foam metal is carried out.Modifications of variable plastic Poisson’s ratio and variable ellipticity are carried out for the isotropic Deshpande-Fleck foam constitutive model based on the non-associated flow rule.The plastic Poisson’s ratio,which characterizes the compressibility of foam materials,is measured by DIC experimental equipment,and it is found that the plastic Poisson’s ratio is a variable value and is affected by both plastic strain and relative density.The coupling function relationship of plastic Poisson’s ratio on plastic strain and relative density is established.The finite element multiaxial compression simulation experiments are carried out with the proposed optimized geometric model,including uniaxial,biaxial and triaxial loading cases.The ellipticity is obtained by fitting the loading results by the ellipse standard equation.It is found that the ellipticity is more convergent when the equivalent plastic strain is adopted as the independent variable.It is also found that the ellipticity is independent of the relative density and is only related to the equivalent plastic strain,and the fitting equation of the ellipticity with respect to the strain is also defined in this paper.Based on varying plastic Poisson’s ratio and varying ellipticity,a modified Deshpande-Fleck model is proposed.By means of numerical calculation,the modified Deshpande-Fleck foam constitutive model is verified by simulation and experiment.The original Deshpande-Fleck model uses fixed-value plastic Poisson’s ratio and fixed-value ellipticity,while the modified model uses variable parameters.Two models are used to make predictions for proportional loading and non-proportional loading cases,and the predicted results are compared with the simulation and experimental loading results,respectively.It is found that the prediction results of the modified Deshpande-Fleck model are better than the initial model regardless of the loading cases.Then,on the basis of the non-associated flow rule,through a control experiment,the influence mechanism of plastic Poisson’s ratio and ellipticity on the prediction accuracy of the modified model is analyzed,and it is found that the two parameters must take variable values at the same time to ensure the prediction accuracy.Aiming at the anisotropic yield characteristics of metal foams,based on the normalization idea and the strain energy density equation,a yield criterion for metal foams considering anisotropy is proposed,and the tensile-compression asymmetry is characterized.The criterion contains a scalar form of characteristic stress-strain relationship,which can describe the mechanical response of metal foams under any stress state through a single curve,avoiding the drawback of fitting criterion parameters through a large number of experiments.In addition,the criterion can characterize the tension-compression asymmetry by considering the firstorder mean stress term.It has been verified that the yield criterion can accurately describe the strength anisotropy of metal foams.The flow rule and hardening law suitable for the subsequent yield stage of metal foams are established,and an anisotropic plastic constitutive model is established based on the proposed anisotropic yield criterion.The subsequent yield evolution characteristics of metal foams are analyzed,and it is found that the subsequent yield surface approximately evolves in a self-similar form,and the associated flow law and flow potential function are defined based on this feature.Then,the coupling relationship between the hardening modulus and plastic strain,stress path and relative density is studied,and the hardening modulus is expressed by a fitting function.An anisotropic plastic constitutive model suitable for foam metals is constructed,and the accuracy of the model is verified by simulation experiments using the mesoscopic finite element model.Finally,the model is realized by ABAQUS VUMAT subroutine,and the influence of anisotropic characteristics on the service performance of foam metal sandwich panel composite structure is quantitatively analyzed through three-point bending simulation experiment,which provides guidance for the design of foam metal composite structure parts. |
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