On The Macroscopic Strength Criterion And Elastoplastic Constitutive Law Of Nanoporous Metallic Materials

Nanoporous metallic materials have outstanding advantages such as high specific surface area,light weight and high strength,shock resistance and energy absorption,heat and moisture resistance,and noise reduction,and have the great application potential.Most of the existing studies try to deduce the strength criterion of nanoporous metallic materials with a Gurtin–Murdoch type surface mechanical model from a single scale.However,previous studies have shown that the Gurtin–Murdoch surface mechanics model only considers the effects of nanopore surface tension and surface tensile stress,while ignoring the effect of surface bending moments.In addition,in the production process of nanoporous metallic materials,nanoscopic and micro-scopic pores coexist.Therefore,it is necessary to extend the macroscopic strength criterion of single-scale nanoporous metallic materials to multi-scale macroscopic strength criterion and elastoplastic constitutive law in order to better meet the needs of design and production.Based on the above research background,this dissertation takes nanoporous metallic ma-terials as the research object to study the macroscopic strength criterion and elastoplastic con-stitutive law of nanoporous metallic materials from the perspectives of Steigmann–Ogden type surface plasticity and surface elastic response.Then,based on the Steigmann–Ogden surface elastic mechanics model for the coexistence of nanoscopic and microscopic pores in the pro-duction and service process of nanoporous metallic materials,Gurson and Eshelby two types of microscopic matrix velocity fields are used,respectively.The macroscopic strength criterion of two-scale nanoporous metallic materials is studied and the corresponding power-law hardening elastoplastic constitutive law is solved based on the time-evolution iterative method.The main research contents and conclusions of this dissertation can be divided into the following aspects.1)First,this dissertation derives a macroscopic strength criterion that takes into account the elastic response of the cavity surface.Based on the Mori–Tanaka model and the Steigmann–Ogden cavity surface elastic mechanics model,the displacement fields that determine the equivalent bulk modulus and equivalent shear modulus of nano-representative volume element are established respectively.The variational method is used to obtain the expression of the equivalent stress of the nano-matrix under the minimum elastic poten-tial energy.Then the implicit macro-strength criterion of the single-scale nanoporous metallic material is derived based on the elastic limit state.(2)Secondly,a macroscopic strength criterion for single-scale nanoporous metallic materials considering the plastic response of the pore surface is deduced.Based on the Gurson velocity field,equivalent strain rate,surface strain rate,and rate of curvature change,the limit analysis of spherical representative volume element under arbitrary strain rate loads is performed.The surface effect of pores is introduced into the macroscopic strength criterion through the Steigmann–Ogden type surface plastic mechanics model.In addition to the matrix plastic dissipation power rate included in the classical solution,the surface plastic dissipation power rate due to surface tension,surface tensile stress and surface bending moment is also considered.On this basis,a parametric macroscopic strength criterion for single-scale nanoporous metallic materials is obtained.(3)Thirdly,this dissertation deduces the macroscopic strength criterion of two-scale nanoporous metallic materials based on Gurson velocity field.It is assumed that the nanoporous metallic material contains both microscopic and nanoscale pores,where the microscopic matrix satisfies a strength criterion that can account for the elastic response of the pore surface.Based on the Gurson microscopic velocity field,the plastic dissipation power rate of the microscopic representative volume element in the limit state is obtained.Due to the compressibility of the microscopic matrix,the minimum dissipation power rate principle should be used to determine the expansion rate of the microscopic matrix.Through the conjugate relationship between the macroscopic stress and the macroscopic strain rate,the implicit macroscopic strength criterion of the two-scale nanoporous metallic material is obtained.(4)Then,this dissertation deduces a two-scale strength criterion for nanoporous metallic ma-terials based on the Eshelby velocity field.It is assumed that the velocity field of the mi-croscopic matrix is the Eshelby velocity field.According to the geometric relationship,the microscopic strain rate is obtained by using the microscopic velocity field.After-wards,the microscopic plastic dissipation power rate of the matrix is derived through the limit state.According to the conjugation relation of dissipation power rate,the implicit macroscopic strength criterion of two-scale nanoporous metallic materials is obtained.(5)Finally,the macroscopic elastoplastic constitutive laws of the above four types of nanoporous metallic materials are also studied.It is assumed that the yield strength of the nanoma-trix satisfies the law of power function enhancement.Firstly,the variation law of each parameter with the elastoplastic strain rate of the macroscopic strength criterion of four kinds of materials is established.Then the time iterative numerical method is used to ob-tain the specific value of each parameter at each moment.The macroscopic stress at each moment is then solved based on the derived strength criterion.Finally,the constitutive law between macroscopic stress and macroscopic elastoplastic strain is obtained.Based on the theoretical derivation and numerical iterative solution method,this disserta-tion also quantitatively analyzes the influence of different surface effect parameters and porosity on the macroscopic strength criterion and elastoplastic constitutive law of nanoporous metal-lic materials.The parametric analysis results show that the surface tension only increases the macroscopic mean stress.The surface tensile strength increases both the macroscopic equiva-lent stress and the macroscopic mean stress of the nanoporous metallic material,the surface bulk modulus increases both,and the surface shear modulus only increases the macroscopic equiv-alent stress.On the other hand,the introduction of surface bending strength only increases the macroscopic equivalent stress.Since the Gurson velocity field only considers the effect of cavity expansion and ignores the deviatoric strain of the cavity,the macroscopic yield surface based on the Eshelby velocity field has the same macroscopic mean stress and a smaller macro-scopic equivalent stress compared with the Gurson velocity field.In this dissertation,the macro-scopic strength criterion and elastoplastic constitutive law of four types of nanoporous metallic materials are systematically solved,and all surface mechanical parameters,microscopic and nanoscopic porosity are analyzed in detail.The research results in this dissertation can make up for the lack of theoretical support in the field of nanoporous metallic materials,and can also provide theoretical reference for the design and manufacture of nanoporous metallic materials.