Research On The Nonlinear Constitutive Relationship Of2D C/SiC Composites

Carbon fiber reinforced silicon carbide (C/SiC) composites have attractive properties such asgood endurance to high-temperature, excellent oxidation resistance capacity, enhancedfracture toughness etc., and for these reasons they have become important candidate materialsto be used in the hot sections of aircrafts and spacecrafts, which have increasing requirementson the structural weight and extreme temperatures. In last two decades, a number of structuralapplications of these materials have been reported. However, the wide usage is restrained dueto their high fabrication costs. It becomes important for researchers to develop constitutivemodels and implement them in the finite element (FE) code, which would cut down the costby reducing the test number, and moreover, optimize the structural design. Under mechanicalloadings, multiple energy dissipation mechanisms including matrix microcracking, interfacedebonding and sliding, fiber breakage and pull-out would prevent brittle rupture of thematerial and result in remarkable nonlinear macroscopic stress-strain relationships. As aconsequence, the traditional elastic analysis method is no longer adequate for their structuraldesign, and it is necessary to eastblish appropriate nonlinear constitutive models for thesecomposites. However, research in this field is far from mature. In the published literature,some material models have neglected factors such as the damage evolution law in thecomplex stress state, and some theorectical models are too complicated for finite elementimplementation. In view of these deficiencies, this paper is aimed at developing a moresuitable macroscopic constitutive model for C/SiC composites.The plain-woven C/SiC composite was studied in the present paper. The mechanicalbehaviors of this material (which include the stress-strain relationships, evolution laws of thedamage and inelastic strain, microscopic damage and fracture modes) in simple and planestress states were firstly studied through a systematic experimental investigation, and thenthree different macroscopic nonlinear constitutive models were successively developed basedon the experimental observations and implemented in the FE code.The main contents and conclusions of this paper were listed as follows:(1)0°on-axis and15°,30°,45°off-axis plates and Iosipescu shear specimens were designedand fabricated, and in-plane mechanical tests were performed on them. The incrementalloading-unloading test method, strain and acoustic emission measurement as well as thescanning electronic microscopy were applied during or after the tests. The stress-strain curvesof the material subjected to different proportional loading conditions were obtained, and thedamage and inelastic strain evolution laws as well as the microscopic damage modes were analyzed. The experiment results reveal that multiple damage modes are generated in thematerial during tension or shear loadings, resulting in stiffness degradation, inelasticdeformation and, consequently, the nonlinear stress-strain relationships at the macroscale.Moreover, the damage evolution rate is accelerated due to the observable damage couplingeffect under combined biaxial tension and shear loadings. Comparatively, the damage level ismuch lower under the compression loading, and the normal compression stresses show anobvious impediment effect on shear damage evolution. Besides, the damage deactivationeffect caused by the compression stress is observed from the tension-compression test results,indicating the remarkable unilateral mechanical behaviors of this material. The axialanisotropy of the modulus and strength of the off-axis tension and compression specimensfurther reveal that this material belongs to the fiber-dominant composite.(2) A phenomenological nonlinear constitutive model was firstly developed based on thenonlinear characteristics of the material’s tensile and shear stress-strain curves at themacroscale. In which polynomial functions were applied to describe the nonlinearstress-strain relationships during the monotonic tension and shear loadings, and logisticfunctions were used to simulate the relation between the unloading modulus and the strain ofthe unloading point. Meanwhile, different tensile and compressive behaviors as well as thedamage deactivation effect after the load reversal from tension to compression werepreliminarily considered. The model was implemented in the FE software (ABAQUS)through a user-defined material subroutine (UMAT). Mechanical responses of simple-loadedunnotched plates and two open-hole tension specimens were simulated and then comparedwith the experiment results. The comparison results verify that the model can well predict theloading/unloading mechanical behaviors of the components subjected to relatively simpleloadings.(3) An elasto-plastic damage model was proposed based on the continuum damage mechanics(CDM) and plasticity theories. In this model the variation of material’s compliancecoefficients was selected as a measurement of the damage state, and accordingly a set ofscalar damage variables were introduced. Then a complementary elastic strain energy densityfunction was proposed based on the damage characteristics of the material, and an elastic lawfor the damaged material was deduced. A thermodynamically consistent damage evolutionlaw was established, in which the damage coupling effect under the combined tension andshear stress states and the impediment effect of the compression stress on the shear damageevolution were considered. In addition, the generalized plasticity theory was applied todescribe the inelastic strain evolution of the C/SiC composite, where the isotropic hardening law and the associated plastic flow rule were adopted. A yield function was built in the spaceof effective stresses, and an evolution law of effective inelastic strains was deduced. Finally,the model was implemented in the user-defined subroutine and validated through severalnumerical examples. The simulation results show that the model can moderately simulate thenonlinear stress-strain relationships of the material and components in simple and plane stressstates, and the main advantages and shortcomings of this material model were discussed.(4) A modified elasto-plastic damage model was developed still in the theoretical frameworkof CDM and plasticity. In the new model, the degradation ratio of the elastic modulus waschosen as the damage variable, and a new thermodynamic potential function was proposedtaking into account the damage, unilateral and damage deactivation behaviors of the material.Different damage deactivation rates during the unaxial and biaxial compression loadings werealso considered. Besides, the plasticity theory based on the effective stresses was applied todescribe the initiation and evolution of inelastic tensile and shear strains. The backward Eulerimplicit integration algorithm and the consistent tangential stiffness matrix were built uponthe consitutive model, which allows better integration of the model into the FE software. Themechanical behaviors of on-and off-axis plates under different loading conditions and anotched45°off-axis tension plate were simulated in the ABAQUS software in order tovalidate the material model. The comparison between the simulation and experiment resultsreveals that this modified material model can more precisely predict the nonlinear mechanicalresponses of the2D C/SiC composite components than the previous models.