Finite-Element-Simulation der nichtlinearen Verformung von Carbon/Carbon-Verbundwerkstoffen

The mechanical properties of a 2D continuous fiber reinforced Carbon/Carbon-composite are described with a macroscopic model. The chosen material is representative for ceramic matrix composites which are damage tolerant because of a porous and weak matrix and not because of a weak fiber matrix interphase. Occurring damage of the matrix and inelastic deformation of the composite are modeled and the corresponding equations are included to the finite-element-program MARC in order to calculate the stress-strain behavior dependent on different angles between loading direction and fiber orientation. Thus, the behavior in tensile, shear and mixed tensile-shear loading can be predicted.     

金属芯压电纤维/聚合物复合材料压电-黏弹-塑性行为的细观力学模型

为了表征金属芯压电纤维增强聚合物基（MPF/PM）复合材料非线性、时变的压电-黏弹-塑性行为,基于变分渐近理论建立MPF/PM增量形式的细观力学模型。首先分别导出聚合物和MPF增量型本构方程,基于汉密尔顿扩展原理推导出MPF/PM压电-黏弹-塑性变分原理的能量泛函。考虑材料的时变和非线性特征,建立与求解瞬时有效机-电耦合矩阵有关的增量过程,并通过有限元技术实现模型的数值模拟。利用构建模型研究了不同铝芯体积分数、电场变化率和加载条件对MPF/PM有效全局应力-应变和单轴纵向拉伸性能的影响。结果表明,构建的模型能准确模拟MPF/PM多场耦合作用下的非线性、时变行为,为该新型智能材料的实际工程应用奠定理论基础。     

Local and overall flow in composites predicted by micromechanics

Rate-dependent inelastic flow in metal matrix composites subjected to multiaxial stress states is quantified by flow surfaces, which are geometrically analogous to yield surfaces. The definition of flow is important because the most meaningful definition from a theoretical viewpoint, dissipation, is not measurable in the laboratory. Inelastic power is measurable, but differs from the dissipation due to residual stresses and evolution of the material state. Since experiments are necessary for development and validation of models, both definitions are important and considered here. The relationship between local flow in the matrix and overall flow of the composite is explored using finite element and generalized method of cells micromechanical analyses. The loci of flow surfaces in the axial–transverse and transverse–transverse stress planes are plotted. At the threshold, the overall flow surface is the intersection of all the local flow surfaces. Beyond the threshold, the intersection of all the local flow surfaces is smaller than the overall flow surface and differences between the dissipation and inelastic power are notable. Most importantly, the directions of the overall inelastic strain rate vectors are generally not normal to the overall surface of constant dissipation after the material state has begun to evolve. Thus, an associative macroscale continuum model will be, at best, approximate. Interestingly, local flow surfaces beyond the threshold are not necessarily convex when plotted in the overall stress plane. This is due to the existence of residual stresses. In addition, the generalized method of cells was found to accurately estimate the inner and outer envelopes of the local flow surface cluster with a surprisingly small number of subcells.     

An inelastic micro/macro theory for hybrid smart/metal composites

Motivated by the emerging concept of including metal phases within piezoelectric and other smart structures and materials, this paper presents a micro/macro theory for determining the coupled thermo-electro-magneto-elasto-plastic behavior of arbitrary composite laminates. The approach involves two models capable of analyzing geometries that include inelastic materials. The first is the electro-magnetic generalized method of cells (EMGMC) (Micromechanical Prediction of the Effective Behavior of Fully Coupled Electro-Magneto-Thermo-Elastic Multiphase Composites, 2000. [1]) micromechanics model. EMGMC has been reformulated to improve its computational efficiency and has been extended to admit arbitrary anisotropic local material behavior (in terms of the thermal response, mechanical response, electric response, magnetic response, as well as the coupling behavior) and inelasticity. The second model is classical lamination theory, which has also been extended for arbitrary anisotropic material behavior and electro-magnetic and inelastic effects. The end result is a coupled theory that employs EMGMC to provide the homogenized behavior of the composite plies that constitute the thermo-electro-magneto-elasto-plastic laminate. Sample results, which address the inelastic response of a hybrid smart/metal matrix composite laminate, are presented.     

Analytical Models for Sliding Interfaces Associated with Fibre Fractures or Matrix Cracks

Analytical stress transfer models are described that enable estimates to be made of the stress and displacement fields that are associated with fibre fractures or matrix cracks in unidirectional fibre reinforced composites. The models represent a clear improvement on popular shear-lag based methodologies. The model takes account of thermal residual stresses, and is based on simplifying assumptions that the axial stress in the fibre is independent of the radial coordinate, and similarly for the matrix. A representation for both the stress and displacement fields is derived that satisfies exactly the equilibrium equations, the required interface continuity equations for displacement and tractions, and all stress-strain equations except for the one that relates to axial deformation. In addition, the representation is such that the Reissner energy functional has a stationary value provided that averaged axial stress-strain relations for the fibre and matrix are satisfied. The improved representation is fully consistent with variational mechanics and provides both the stress and displacement distributions in the fibre and the matrix. For isolated or interacting fibre fractures or matrix cracks, interface sliding is considered where two types of condition are investigated. Firstly, it is assumed that the shear stress is uniform within the sliding region, and a small transition zone is included in the model in order that essential zero traction conditions can be satisfied on the crack surfaces. Secondly, it is assumed that stress transfer in the sliding region is controlled by Coulomb friction. Illustrative predictions are made for an example polymer composite, although the methodology presented is equally applicable to other types of composite (e.g. metal and ceramic matrix composites).     

On the mechanics of microballon-reinforced metal matrix composites

The elastic/plastic response of ceramic microballon-reinforced metal matrix composites subject to uniaxial loading are examined using finite element analysis. The microballoons are assumed to be spherical and their morphology characterized by the ratio of wall thickness, t, to radius, R. The key parameters investigated are the relative wall thickness, t/R, the modulus ratio (matrix/ceramic) and the yield and hardening characteristics of the matrix. The emphasis of the study is on the overall stress-strain response of the composite, the development of matrix plasticity and the development of stress within the microbaloon.     

Thermo-mechanical fatigue modeling of advanced metal matrix composites in the presence of microstructural details

An analytical model developed for predicting the inelastic response of metal matrix composites subjected to axisymmetric loading is employed to investigate the behavior of SiC---Ti composites under thermo-mechanical fatigue loading. The model is based on the concentric cylinder assemblage consisting of arbitrary numbers of elastic or inelastic sublayers with isotropic, transversely isotropic, or orthotropic, temperature-dependent properties. In the present work, the inelastic response of the titanium matrix is modeled by the Bodner-Partom unified viscoplastic theory. These features of the model allow the investigation of microstructural effects (such as the layered morphology of the SCS-6 fiber, including the weak carbon coating, and matrix microstructure) and rate-dependent response of the matrix on the fatigue behavior.

In this paper, we employ the predictions of the multiple concentric cylinder model to study the effects of the layered morphology of the SCS-6 SiC fiber and two-phase microstructure of the Ti-15-3 matrix on the response of a SiC---Ti composite under thermo-mechanical fatigue loading. It is shown that ignoring the microstructure can lead to significant errors in the predictions of the internal stress and inelastic strain distributions.     

Dynamic buckling of metal matrix composite plates and shells under cylindrical bending

A micro-to-macro analysis is offered to investigate the dynamic response and buckling of metal matrix composite cylindrical shells and plates under cylindrical bending. The micromechanical analysis relies on the elastic fibers and inelastic matrix material properties, and provides the bulk behavior of the metal matrix composite at room and elevated temperatures. The macromechanical analysis employs the classical and higher order plate theories in conjunction with a spatial finite difference and temporal Runge-Kutta integrations to provide the dynamic response of the structure. The effects of the metallic matrix inelasticity, material rate sensitivity, shear deformation, fiber orientation, and initial geometrical imperfection on the behavior of the metal matrix composite structures are studied.     

Multiscale design of three-dimensional nonlinear composites using an interface-enriched generalized finite element method

A computational framework is developed to model and optimize the nonlinear multiscale response of three-dimensional particulate composites using an interface-enriched generalized finite element method. The material nonlinearities are associated with interfacial debonding of inclusions from a surrounding matrix which is modeled using C⁻¹ continuous enrichment functions and a cohesive failure model. Analytic material and shape sensitivities of the homogenized constitutive response are derived and used to drive a nonlinear inverse homogenization problem using gradient-based optimization methods. Spherical and ellipsoidal particulate microstructures are designed to match a component of the homogenized stress-strain response to a desired constructed macroscopic stress-strain behavior.     

Fatigue and stress rupture of silicon carbide fibre-reinforced glass-ceramics

Fatigue and stress-rupture testing of unidirectional Nicalon-type silicon carbide fibre-reinforced lithium aluminosilicate glass-ceramic matrix composites is described. Tensile fatigue testing was performed at 22°C on two different composite systems to contrast the behaviour under applied stresses above and below the levels necessary to cause matrix cracking. The higher strength of the two composites was then also tested in flexural fatigue and constant-load stress rupture at 22, 600 and 900° C in air. It is shown that the level of tensile stress at which composite inelastic stress-strain behaviour begins is an important factor in the control of overall composite performance, and that properties at elevated temperature are significantly different to those at room temperature.     

Fiber interactions and effective elasto-plastic properties of short-fiber composites

The fiber–fiber or fiber–matrix interactions and effective elasto-plastic properties of aligned short-fiber-reinforced metal matrix composite are studied by using a micromechanical model and the finite element method. The fiber is assumed to be elastic and the matrix to be elasto-viscoplastic continuum. The local elasto-plastic stress fields of a unit cell in composite are examined in order to understand the mechanism of inelastic deformations and interactions between fibers or between fiber and matrix. Effective elasto-plastic properties of B/Al composites are predicted by the domain average method. It is shown that present predictions are in agreement with the experimental data for the B/Al system.     

A specialized finite element for the study of woven composites

 A specialized finite element is developed for the study of woven composites. The element utilizes an asymptotic displacement expansion comprised of the homogenized displacements and the local micro-displacements associated with the woven unit-cell elasto-statics. Basic trigonometric functions first developed in [1], are employed as solutions to the local woven unit-cell problem under a general state of in-plane loading. The formulation also incorporates robust unit-cell geometry models for both polymer and ceramic matrix woven systems. As a result, the element can be used to predict not only the macroscopic homogeneous elastic response but also the microscopic elastic response of a finite geometry of a woven composite subjected to a general in-plane as well as transverse bending loading. The element performance is demonstrated by solving the finite geometry uni-axial tension problem and via near-tip studies for a crack under mode-I, mode-II, and mixed mode fracture conditions. In each case, the specialized element predictions are compared to known solutions for a corresponding cracked orthotropic material subjected to the same macroscopic loading conditions as well as the approximate solutions obtained using the well established 4-noded isoparametric plane elasticity element. Received 27 November 2000     

A mechanistic analysis of the correlation between overall strength and indentation hardness in discontinuously reinforced aluminum

It is well established that the indentation hardness of metallic alloys shows a reasonable correlation with their yield strength or ultimate strength. Experiments illustrate that such a unique correlation is nonexistent for discontinuously reinforced metal matrix composites, even when the indentation size is much greater than the reinforcement size. For aluminum alloys reinforced with silicon carbide particles, the same composite yield strength and tensile strength with different reinforcement fractions do not lead to similar hardness, or vice versa. Finite element analyses are carried out to rationalize the experimental findings. The modeling utilizes a two-dimensional plane-strain formulation. Discrete particles are included in the material model, and the overall stress-strain response and the indentation response are numerically simulated. The results confirm the lack of unique correspondence between the composite hardness and strength. The alteration of local heterogeneity in the composite is found to affect the indentation response. Effects of the geometrical arrangement of particles and thermal residual stresses on the indentation response are also investigated numerically.     

Finite difference solution of steady state creep deformations in a short fiber composite in presence of fiber/matrix debonding

A finite difference technique is developed to predict the second stage creep displacement rates and stress analysis of a short fiber metal matrix composite subjecting to a constant axial load through a micromechanical approach. The technique is capable to take into account the presence of interfacial debonding as one of the main factors affecting the creep performance of short fiber composites. The exponential law is adopted to describe the matrix creep behavior. Also, a model for prediction of interfacial debonding at fiber/matrix interface is developed using a stress based method. The obtained results could greatly help to better understand the flow pattern of matrix material and the load transfer mechanism between fiber and matrix with and without the presence of interfacial debond. The predicted strain rate by the proposed approach exhibits good agreement with the experimental results.     

Micromechanically Established Constitutive Equations for Multiphase Materials with Viscoelastic–Viscoplastic Phases

A model for viscoelastic–viscoplastic solids is incorporated in a micromechanical analysis of composites with periodic microstructures in order to establish closed-form coupled constitutive relations for viscoelastic–viscoplastic multiphase materials. This is achieved by employing the homogenization technique for the establishment of concentration tensors that relate the local elastic and inelastic fields to the externally applied loading. The resulting constitutive equations are sufficiently general such that viscoelastic, viscoplastic and perfectly elastic phases are obtained as special cases by a proper selection of the material parameters the phase. Results show that the viscoelastic and viscoplastic mechanisms have significant effect on the global stress-strain, relaxation and creep behavior of the composite, and that its response is strongly rate-dependent in the reversible and irreversible regimes.     

The mechanical properties of the matrix in continouos-fibre 6061 aluminum-alloy metal-matrix composites

Various factors affecting the matrix properties of metal-matrix composites have been investigated by a series of experiments on the unreinforced matrix material. The effect of the rate of cooling from the fabrication temperature to room temperature is studied by comparing the stress-strain behaviour of quenched and air-cooled specimens. During cooling, fibres constrain the contraction of the matrix owing to the difference in thermal-expansion coefficients of the two materials. The effect of this constrains was simulated by clamping aluminum specimens to a steel plate during heat treatment. It was found that the main effect of the constraint was to produce strain-hardening and a much sharper yield point. The strain-hardened stress-strain curve can be predicted in terms of the material's room-temperature stress-strain curve if the temperature change and the coefficients of thermal expansion of the fibre and matrix are known. Subsequent ageing of the matrix was also examined. The presence of rseidual stress does not affect the amount of age-hardening. However, the effect of prior plastic deformation reduces the amount of precipitation-hardening. Creep of the matrix during cooling appears to be negligible, but some relaxation of residual stress in the matrix material may subsequently occur at room temperature.     

Mechanical properties of a self-healing fibre reinforced epoxy composites

Inspired by biological systems in which damage triggers an autonomic healing response, a polymer composite material that can heal itself when cracked has been developed. In this work, compression and tensile properties of a self-healed fibre reinforced epoxy composites were investigated. Microencapsulated epoxy and mercaptan healing agents were incorporated into a glass fibre reinforced epoxy matrix to produce a polymer composite capable of self-healing. The self-repair microcapsules in the epoxy resin would break as a result of microcrack expansion in the matrix, and letting out the strong repair agent to recover the mechanical strength with a relative healing efficiency of up to 140% which is a ratio of healed property value to initial property value or healing efficiency up to 119% if using the healed strength with the damaged strength.     

金属基复合材料微屈服行为的力学分析与试验

本文采用细观力学计算、有限元分析和试验测试等方法,定量研究了短纤维增强金属基复合材料微屈服过程中应力应变分布和微屈服规律,结果表明不同短纤维分布朝向、体积比的Al2O3-SiO2(sf)/Al-Si复合材料微屈服行为符合Brown-Lukens关系,在增强体短纤维附近存在较大应力集中,晶粒直径、位错密度等材料参数对等效应力影响不大,对等效塑性应变有显著影响,同时分析了增强体短纤维的体积含量和短纤维分布状态对材料微屈服强度的影响。     

Numerical modelling of failure of cement concrete using a unit cell approach

In this paper, a unit cell based approach is followed, where a unit cell consisting of one aggregate surrounded by mortar matrix is used for numerical simulation of mechanical response of cement concrete. Unit cell approach is a simple mathematical approximation that helps us to simplify the simulation of mechanical response of multi-phase composites. To model the failure of matrix, brittle cracking model is used, where the entire fracture zone is represented by a band of micro cracked material. Current study involves; (a) failure analysis of the concrete unit cell when it is subjected to tensile loads, and (b) parametric study of variation of peak strength with shape and volume fraction of aggregate. In this study, circular and square aggregates at various orientations are modelled. The simulation results predict that the peak tensile stresses are not very sensitive to the volume fraction of aggregates, when the unit cell is subjected to tensile loads. This paper effectively demonstrates the power of unit cell model in simulating the nonlinear mechanical response of cement concrete when it is subjected to tensile loading.