Microstructure damage related to stress–strain curve for grain composites

Mathematical model of micro-heterogeneous medium with random deformation and strength properties of microstructure is developed assuming that the tensor of macroscopic deformations is known for the structure. Green–Somigliana tensor is used to obtain the formulas for random stress distribution in microstructure elements. The probability of the stress exceeding the ultimate strength in an element determines the probability of fracture in this element and the relative micro-damage. The correlation functions of stochastic microstructure ultimate strength condition are calculated for various types of stress. Normal distribution is used to calculate the damage. The distribution density can be adjusted through the stress moments to the fourth order.Micro-fractions change the composite’s macro modules of elasticity. Therefore, changes the relationship between stress and strain. Setting an increment step on the macro-strain axis, the stress–strain curve is plotted taking into account changes in composite properties. Stress–strain curves are obtained for different types of load.The increase of the factor of safety corresponds with the reduction of microstructure damage permitted in the design. Critical microstructure damage also depends on the dispersion of the microstructure properties. It is shown that the microstructure properties of composite significantly influence the behavior of materials under load and the shape of stress–strain curve. Findings are compared with experiment data.     

Accelerated aging of unidirectional hybrid composites under the long-term elevated temperature and moisture concentration

Despite their high performances, composites with polymer matrix are very sensible to the increase in temperature and moisture concentration. During long years of services, both phenomena cause a critical transient hygrothermal transverse stresses, particularly at first-ply; i.e. at two edges of the composite plates. Therefore, significant degradation of hygrothermal characteristics and ultimate strengths of materials are occurred. To get an explicit relation between the durability and the damage probability of the composite, quadratic failure criterion in stress space is used. This criterion enables us to find a direct relation between transient hygrothermal stresses produced by the increase in temperature and moisture concentration and the ultimate strengths. It is necessary to calculate the strength ratio R from initial to saturation time for each condition imposed of temperature and moisture concentration. The strength ratio gives a point of view on the damage probability of the composite plates, where the rupture occurs if R = 1. In order to limit the consequences of simultaneous effects of temperature and moisture concentration, unidirectional hybrid composites in graphite epoxy was proposed. To reach this aim, hygrothermal transverse stresses are calculated through the thickness of unidirectional hybrid plate. Finally, the strength ratio was evaluated along of the plate with a gradual increase in temperature and moisture concentration.     

含弧形裂纹复合陶瓷强度的尺度效应

认为含弧形裂纹复合陶瓷由随机方向的三相胞元与有效介质构成,用细观力学的方法研究了复合陶瓷的损伤失效和强度。首先确定三相胞元的外载应变,再依据复合陶瓷在损伤过程中的细观应力场和广义热力学力,计算出三相胞元内基体和颗粒的损伤等效应力,当基体和颗粒的损伤等效应力分别等于两者的极限应力时,得到基体和颗粒的破坏应力。然后,根据混合型应力强度因子计算弧形裂纹扩展时的能量释放率,进而得到界面的破坏应力。最后综合考虑基体、颗粒和和界面损伤影响,获得含弧形裂纹复合陶瓷的宏观强度及其尺度效应。     

Deformation and long-term damage of particulate composites under thermal loads

A theory of long-term damage of particulate composite materials under thermal load is proposed. The damage of the composite components is modeled by randomly dispersed micropores. The failure criterion for a single microvolume is determined by its stress-rupture strength, which, in turn, is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the ultimate strength according to the Schleicher–Nadai criterion. The damage (porosity) balance equation is derived for an arbitrary time, taking the thermal effect into account. Algorithms for calculating microdamage and macrostresses as functions of time are developed     

ROBUST OPTIMUM DESIGN OF LAMINATED COMPOSITE PLATES

A last-ply failure (LPF) analysis method for laminated composite plates is incorpo- rated into the ?nite element code-ANSYS, and a robust optimum design method is presented. The composite structure is analyzed by considering both in-plane and out-…     

材料强度对层板抗弹性能和损伤特性的影响

根据纤维增强复合材料宏细观结构特征,基于ABAQUS软件平台,建立了层合板高速冲击损伤三维有限元分析模型。该模型在复合材料层间引入界面单元模拟层间分层,采用三维粘弹性本构,结合Hashin失效准则模拟单层板面内损伤.利用该模型,深入研究了复合材料层板的抗弹性能和损伤特性,数值分析结果与实验结果吻合良好,证明了该方法的合理有效性。通过数值分析,详细探讨了材料强度参数对层板抗弹性能和损伤特性的影响规律,获得了一些有价值的结论。     

含孔复合材料层合板静拉伸三维逐渐损伤分析

针对面内静拉伸纤维增强复合材料含中孔层合板，发展了参数化三维逐渐损伤模型. 该模型 可以模拟含中孔层合板损伤起始、发展及最终结构破坏整个过程，并能较好地预测含中孔层 合板的破坏模式和破坏强度. 采用所发展的模型和有限元三维逐渐损伤分析技术即应力分 析、失效判定准则及损伤过程中材料性能退化等，对其他文献所提供的9种不同类型含中孔层合板进行了损伤扩展分析及强度预测，同时对层合板的损伤基本机理、类型及其相互关联作用进行了探讨，计算结果与文献实验结果非常吻合.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

角铺设复合材料层合板内部脱层破坏的研究

在面内剪切外载作用下，角铺设复合材料层板板最终的宏观破坏模式是脱层，然而从细观角度来看，宏观的脱层破坏可以对应不同的细观损伤过程，以破坏面的形貌为例，有些破坏面的形貌为例，有些破坏面主要由裸露的纤维和纤维迹组成，而有些破坏面则主要由矩齿形基体材料组成。不同的过程对应着不同的力学性能、诸如脱层强度、韧性等、本文从细观角度研究了脱层破坏过程，并就铺设角、界面强度、基体开裂强度对该过程的影响进行了讨论。     

On some composite failure criteria based on the averaging method

The construction of an anisotropic criterion for composite failure is based on the use of the averaging method and micromechanical criteria for each of the components. The averaging method permits calculating not only the effective properties of a composite using the solutions of a local problem on the periodicity cell but also the stresses and strains in each composite. Using the superposition method and studying the composite brittle failure, we can calculate the stress distribution for an arbitrary radial (simple) macroloading as the linear combination of six basic problems on the periodicity cell. The limit load for an effective material is obtained from the condition that some of the composite components starts to fail. For given trajectories, the limit loads depend on the geometry of elastic properties and mainly on the ratio of ultimate strengths for different components of the composite.     

短柱型复合材料加筋壁板轴向压缩破坏分析方法研究

复合材料加筋结构可作为航空结构中的承力部件,其损伤与破坏对航空器的结构安全和服役性能至关重要.本文通过试验和数值仿真手段研究了短柱型复合材料结构压缩失效机理和极限承载力.通过短柱型单加筋板的轴向压缩破坏试验,分析梳理出界面脱粘和材料压溃两种典型失效形式;分别建立加筋板壳单元模型和实体单元模型,引入内聚力模型和Hashi...     

An experimental and analytical investigation of the rail shear-test method as applied to composite materials

This report presents the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test. The effects of nonuniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates are shown. A two-dimensional linearly elastic finite-element model was used to analytically determine how various geometric parameters influenced the magnitude and distribution of inplane normal and shear stresses in a tensile-rail-shear specimen. Rail shear tests were conducted at room temperature and 589 K (600°F) on selected graphite-polyimide composite laminates using two titanium rail configurations. The analysis and test methods are discussed, and the results of the effects of the various parameters on shear modulus and ultimate strength are presented.     

A percolation-type fracture criterion for composites with randomly oriented fibres

A fracture model is built up for a solid composed of brittle fibres randomly oriented in the matrix volume. The fracture process includes a stable growth of microcracks caused by fibre breaking under the load and formation of an infinite cluster of the microcracks. Both upper and lower bounds for ultimate stress in a fibre system are found as functions of the fibre volume fraction. The calculation of the ultimate stresses are performed by using the percolation theory and the theory of branching processes. At the present stage of the theory under consideration, only two types of the microcracks are appraised, namely that of a delamination type which corresponds to a weak fibre/matrix interface, and that of a penny shape which corresponds to a strong fibre/matrix interface. A particular solid contains only one type of the microcracks. In both cases, non-linear dependencies of the ultimate composite strength on fibre volume fraction are obtained.     

Strong flow criteria based on microstructure deformation

The dynamics of fluid systems which consist of a suspended material in a Newtonian continuous phase is investigated theoretically. Criteria are derived to predict conditions under which the strength of a flow, i.e. a measure of the form and magnitude of the velocity gradient tensor, is sufficient to induce significant deformation and/or orientation of the fluid microstructure, that is, the elements which collectively comprise the suspended phase. The development relies upon the choice of a model to describe the microstructure, and the form of the criteria reflects this choice. Once the choice is made, however, the detailed material properties of a particular fluid system enter only as parameters in the resulting equations, and thus, the results encompass a large class of systems, including particulate suspensions and macromolecular solutions. Two microstructure models are investigated here. When the microstructure is characterized by a vector, the flow strengths of all linear flows are displayed in a single figure from which the strength of a particular flow can be evaluated directly. A comparison is then made for selected flows between these results and those for the case where an irreducible second order tensor is employed to describe the microstructure. A significant difference between the two models derives from the fact that the “volume” of the microstructure must be conserved in the second-order tensor case. The criteria are finally used to predict the degree of macromolecular stretching in a model turbulent flow and the breakup of immiscible liquid drops in simple shear flow. A comparison between the flow strength predictions and experimental data yields good qualitative agreement in the latter case.     

冻土破坏过程的微裂纹损伤区的计算分析

对冻土破坏过程进行了试验研究，冻土破坏的过程是微裂纹损伤与临界串接的演化过程，确认了冻土微裂纹损伤区的存在，并分别用莫尔准则和最大拉应力准则建立了微裂纹损伤区计算模式。将微裂纹损伤区按缺陷处理并简化为当量裂纹，进行了裂纹尺寸的定量计算，结果表明其尺寸与冻土中初始裂纹尺寸相当，将计算结果与观测结果相比较，误差不超过10％。     

杆系结构静强度和疲劳失效机理及可靠性分析

根据疲劳载荷造成的疲劳累积损伤对结构极限承载力的影响情况,讨论了结构系统承载能力的可靠度计算方法,分析了结构系统中每一个单元在静载和疲劳载荷作用下的两种失效模式,并考虑了二者之间的相关性对该单元可靠性的影响,具体分析了结构系统在这两种载荷作用下的失效机理,给出了在这两种载荷作用下结构系统的可靠性分析方法. 算例表明,在不同的使用年限内,静载和疲劳载荷对结构系统可靠性的影响是不同的;在结构系统主要失效路径中既有单元静强度失效又有单元疲劳失效,这是符合结构系统使用真实情况的.     

New Statement of the elasticity problem for a layer

The problem on the equilibrium of an inhomogeneous anisotropic elastic layer is considered. The classical statement of the problem in displacements consists of three partial differential equations with variable coefficients for the three displacements and of three boundary conditions posed at each point of the boundary surface. Sometimes, instead of the statement in displacements, it is convenient to use the classical statement of the problem in stresses [1] or the new statement of the problem in stresses proposed by B. E. Pobedrya [2]. In the case of the problem in stresses, it is necessary to find six components of the stress tensor, which are functions of three coordinates. The choice of the statement of the problem depends on the researcher and, of course, on the specific problem. The fact that there are several statements of the problem makes for a wider choice of the method for solving the problem. In the present paper, for a layer with plane boundary surfaces, we propose a new statement of the problem, which, in contrast to the other two statements indicated above, can be called a mixed statement. The problem for a layer in the new statement consists of a system of three partial differential equations for the three components of the displacement vector of the midplane points. The system is coupled with three integro-differential equations for the three longitudinal components of the stress tensor. Thus, in the new statement, just as in the other statements in stresses, one should find six functions. In the new statement, three of these functions (the displacements of the midplane points) are functions of two coordinates, and the other three functions (the longitudinal components of the stress tensor) are functions of three coordinates. It is shown that all equations in the new statement are the Euler equations for the Reissner functional with additional constraints. After the problem is solved in the new statement, three components of the displacement vector and three transverse components of the stress tensor are determined at each point of the layer. The new statement of the problem can be used to construct various engineering theories of plates made of composite materials.     

A DAMAGE CONSTITUTIVE MODEL OF ROCK WITH CONSIDERATION OF RESIDUAL STRENGTH

基于岩石微元强度服从Weibull分布规律,引入损伤变量修正因子,建立了考虑残余强度影响的岩石损伤本构模型.运用多元函数求极值的方法,推导了含修正系数的模型参数\(m\)和\(F_{0}\)的理论表达式;对模型修正因子的选取进行了讨论分析. 结果表明：本文修正模型的实质是增加了一个含有修正系数的线性项;修正系数 \(\delta \)主要反映岩石的残余强度特征,选取合适的 \(\delta \) 值可以提高修正后本构模型的准确性.     

Assessment of composite failure and ultimate strength without experiment on composite

This paper attempts to estimate the ultimate strength of a laminated composite only based on its con- stituent properties measured independently. Three important issues involved have been systematically addressed, i.e., stress calculation for the constituent fiber and matrix materials, failure detection for the lamina and laminate upon the internal stresses in their constituents, and input data determination of the constituents from monolithic measurements. There are three important factors to influence the accuracy of the strength prediction. One is the stress concentration factor （SCF） in the matrix. Another is matrix plasticity. The third is thermal residual stresses in the constituents. It is these three factors, however, that have not been sufficiently well realized in the composite community. One can easily find out the elastic and strength parameters of a great many laminae and laminates in the current literature. Unfortunately, necessary information to determine the SCF, the matrix plasticity, and the thermal residual stresses of the composites is rare or incomplete. A useful design methodology is demonstrated in the paper.     

Nonlinear viscoelastic multi-scale repetitive unit cell model of 3D woven composites with damage evolution

Three-dimensional (3D) textile composites have great potential applications to aircrafts and high speed vehicles because of the high strength/weight ratios and the capabilities of manufacturing complex, net-shape preforms. This paper reports the nonlinear viscoelastic responses and damage mechanisms of one kind of 3D textile composites, named as 3D orthogonal woven composite (3DOWC) under quasi-static tensile loading based on a micro/meso-scale repetitive unit cells (RUCs) model. In the RUCs model, the resin is described with a nonlinear viscoelastic material and the fibers/tows with an elastic material. The damage initiation and propagation in resin are simulated by the post-damage constitutive models with maximum principal theory failure criteria. The fibers/tows impregnated with resin are defined by elastic transverse-isotropic material model with ultimate strengths failure of ‘expanded smeared crack’ both along and perpendicular to fibers/tows axis direction. The engineering parameters and ultimate strengths of homogenized fibers/tows filled with matrix in meso-RUCs model are transferred from the numerical analysis of the micro-RUCs. The results are compared with experimental and theoretical values of RUC deformation and damage initiation and propagation under monotonic axial loading. The methodology of establishing the nonlinear visco-elastic multi-scale model of 3D textile composites without introducing the real fabric architecture in finite element analyses is explained. With the multi-scale RUCs model, the mechanical behaviors of other kinds of 3D textile composites can also be predicted.