【作者】 李俊；

【导师】 矫桂琼；

【作者基本信息】 西北工业大学 ， 力学， 2014， 博士

【摘要】 C/SiC陶瓷基复合材料具有耐高温、抗氧化和高断裂韧性等优异性能，可满足航空航天器的热端部件对于减重、提高使用温度等方面的要求，已成为重要的热结构备选材料之一，近二十年来已经出现了大量的结构应用实例。由于该材料仍然有制备成本较高的缺点，为其建立本构模型并结合有限元分析，有助于减少试验，降低制造成本，辅助结构的优化设计。由于在机械载荷的作用下，该材料内部存在基体开裂、界面脱粘和滑移、纤维断裂和拔出等多种能量耗散机制，能够防止材料发生脆性断裂，相应的其应力-应变关系亦表现出显著的非线性特征。传统的线弹性分析方法已不再适用，有必要为其建立合适的非线性本构模型，而目前针对该材料的相关研究有所欠缺。现有的一些本构模型中，没有考虑多种因素，如复杂应力状态下的损伤演化规律；有的理论模型过于复杂，难以实现有限元应用。本文将针对这些问题，为该材料发展相对完善的宏观非线性本构模型。本文以二维编织C/SiC复合材料为研究对象，首先对该材料在简单和平面应力状态下的力学行为（包括应力-应变关系、损伤和非弹性应变的演化特性、损伤和失效模式等）进行了较为系统的试验研究；在此基础上，先后为其建立了三个不同的宏观非线性本构模型，并分别实现了理论模型的有限元编程与应用。本文的主要研究内容和结果如下：(1)设计并制备了0°、15°、30°和45°四组不同偏轴角度平板以及Iosipescu面内剪切试件，进行了面内力学试验。试验中采用加卸载试验方法，结合应变测量、扫描电镜观察和声发射技术，获取了材料在不同比例加载条件下的宏观应力-应变曲线，并分析了宏观损伤演化规律，以及微细观损伤模式。试验结果表明，拉、剪加载时材料内部产生多种微观损伤模式，材料的刚度折减并形成非弹性应变，应力-应变曲线表现出显著的非线性。拉剪平面应力状态下，存在显著的损伤耦合效应，损伤演化加速。相比之下，压缩加载时材料的损伤水平较低，压剪平面应力状态下，压应力分量对剪切损伤的演化形成阻碍作用；此外，拉-压加卸载试验结果发现，压缩加载阶段已有的损伤逐步钝化，材料具有显著的单边力学特性。偏轴拉、压试件模量和强度的轴向各向异性表明，该材料仍属于纤维控制复合材料。(2)根据材料的拉伸和剪切应力-应变曲线的非线性特征，首先为其建立了一个唯象的宏观非线性本构模型。其中采用了多项式和逻辑函数，依次描述拉、剪单调加载时材料的非线性应力-应变关系，以及卸载模量与卸载点应变之间的关系。同时，初步考虑了材料在拉、压加载条件下不同的力学响应，以及拉压应力状态转换时，材料的损伤钝化效应。将模型编写成材料子程序（UMAT），与ABAQUS有限元软件连接。通过对简单加载平板和两组带孔板的拉伸力学响应进行了模拟，验证了该模型能够较好地预测承载状态相对简单的构件的加、卸载力学行为。(3)基于连续介质损伤力学（CDM）和塑性力学理论，建立了一个弹塑性损伤本构模型。模型中以材料柔度的变化作为损伤的度量，引入了一组标量型损伤变量，并根据材料的损伤特性建立了弹性应变余能表达式，推导了含损伤材料的弹性本构方程。同时，建立了符合热力学定律的损伤演化法则，其中考虑了拉剪平面应力状态下损伤的耦合效应，以及压缩应力对剪切损伤演化的阻碍作用。另外，将塑性理论应用于描述C/SiC材料的非弹性应变演化过程，采用了各向同性强化和关联流动性假设，在有效应力空间上建立了屈服函数，推导了有效非弹性应变的演化法则。通过有限元编程以及算例验证表明，该本构模型能够较好地模拟简单、平面应力状态下材料和构件的非线性应力-应变关系。文中对该模型的优缺点进行了分析讨论。(4)同样基于CDM和塑性力学的理论框架，对前一个弹塑性损伤本构模型进行了改进。新的模型中以弹性模量的退化程度作为损伤因子，提出了一个新的热力学势能函数表达式，使得本构方程中能够描述材料的损伤、单边效应和损伤钝化力学行为，并考虑了单、双轴压缩应力状态下损伤钝化速率不同的因素。同时，仍然采用了基于有效应力的塑性理论，以描述拉伸和剪切非弹性应变的起始和演化。在该本构模型的基础上，建立了向后欧拉隐式积分算法，并推导了一致性切线刚度矩阵，更好地实现了理论模型与有限元软件的结合。在ABAQUS有限元软件中，对不同加载条件下正轴和偏轴平板、含缺口45°偏轴拉伸平板的力学响应进行了模拟。计算与试验结果的对比表明，该材料模型能够更准确地模拟二维C/SiC复合材料构件的非线性力学响应。更多还原

【Abstract】 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.更多还原