Simulation of perforation and penetration in metal matrix composite materials using coupled viscoplastic damage model

In the first part of the two companion papers, theoretical formulation of the multiscale micromechanical constitutive model that couples the anisotropic damage mechanism with the viscoplastic deformation is presented. In the second part of these companion papers the numerical simulation of the computational aspects of the theory are elaborated. The perforation and penetration problem of metal matrix composites (MMCs) due to high impact loading is simulated. In this sense, the computational aspects of the developed theory are elaborated here. First, the verification of the developed model is performed through its numerical implementation in order to test the model predictions of the material characteristic tests. This encompasses uniaxial monotonic loading and unloading under different strain rates, uniaxial cyclic loading, and uniaxial loading and relaxation. The verified material routine of the developed model is then implemented in the explicit finite element code ABAQUS via the user defined subroutine VUMAT at each integration point in order to analyze the projectile impact and penetration into laminated composite plates.     

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.     

On the dynamic response of metal matrix composite panels to uniform temperature loading

Thermal dynamic response of antisymmetrically laminated metal matrix composite flat and curved panels subjected to uniform time-dependent temperature field is studied. Temperature dependence of both elastic and viscoplastic properties of the metallic matrix is taken into account. The structural analysis is combined with a micromechanical approach which is employed to establish the instantaneous thermo-inelastic constitutive law of the composite at every point of the structure at each time increment. Results are presented for SiC/Al panels. The effects of boundary conditions, panel curvature and inelastic behavior of the metallic matrix on the thermally induced vibrations are illustrated. The thermal dynamic buckling behavior of flat and curved panels is studied.     

Multiscale finite element modeling of failure process of composite laminates

A multiscale nonlinear finite element modeling technique is developed in this paper to predict the progressive failure process for composite laminates. A micromechanical elastic–plastic bridging constitutive model, which considers the nonlinear material properties of the constituent fiber and matrix materials and their interaction and the damage and failure in fibrous composites at the fiber and matrix level, is proposed to represent the material behavior of fiber-reinforced composite laminates. The micromechanics constitutive model is employed in the macroscale finite element analysis of structural behavior especially progressive failure process of the fiber-reinforced composites based on a 4-node 24-DOF shear-locking free rectangular composite plate element.     

纤维增强复合材料层板高速冲击损伤数值模拟

推导了复合材料应变率相关三维本构关系, 并将其用于复合材料层板高速冲击损伤的数值模拟。该模型在复合材料层间引入界面单元模拟层间分层, 结合三维Hashin失效准则进行单层板面内损伤识别, 引入材料刚度退化, 采用非线性有限元方法, 研究了复合材料层板高速冲击的破坏过程及层板的损伤特性。数值分析结果表明, 剩余速度预报结果与实验结果吻合较好, 层板的主要损伤形式是层间分层、 基体微裂纹和纤维断裂, 减小弹体直径、 增大铺层角度和层板厚度能够有效降低层板损伤面积。      

Multi-scales modelling of dynamic behaviour for discontinuous fibre SMC composites

The requirements of passive security, notably in the transport industry, impose to maximize the dissipation of the energy and to minimize the decelerations undergone by a vehicle and thus passengers due to violent shocks (crash). This paper aims at establishing efficient expected answers towards the preoccupations mainly emanating from transport industry. Currently, the behaviour laws implemented in the dynamic explicit schemes (RADIOSS, PAM-CRASH and LS-DYNA) do not integrate sufficiently the physical aspects in the material degradation, mainly the damage process, their kinetics, the variability and especially the heterogeneity of the composite materials microstructure. This paper deals with the development of a multi-scale predictive model coupling specific experimental methodologies and the micromechanical formulation of damage mechanisms in order to build constitutive laws for discontinuous fibre reinforced composites materials. The developed micromechanical modelling is based on an experimental methodology conducted over a range of strain rates from quasi static to 250 s⁻¹. The latter has enabled identifying local probabilistic damage criterion formulated through the Weibull’s statistical integrating the strain rate effect and describing the progressive interfacial debonding under rapid loading. The developed model has been validated to predict the stiffness reduction and the overall elastic visco-damage behaviour for SMC composite material. The model simulations agree well with high speed tensile tests and confirm that the damage threshold and kinetic in the SMC are mainly strain rate sensitive.     

Micromechanical approach to damage mechanics of composite materials with fabric tensors

The purpose of this study is to apply continuum damage mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of damage mechanics for composite materials will be developed using fabric tensors. The introduction of fabric tensors into the analysis of damage of composite materials will allow for an enhanced and better understood physical meaning of damage. The micromechanical approach will be used here to relate the damage effect through fabric tensors to the behavior of composite materials. In this approach, damage mechanics is introduced separately to the constituents of the composite material through different constituents’ damage effect tensors. The damaged properties of the composite system as a whole can then be obtained by proper homogenization of the damaged properties of the constituents.

The derivation of a generalized formulation of damage evolution will be shown here in a mathematically consistent manner that is based on sound thermodynamic principles. Numerical examples will be presented to show applicability. In addition, damage evolution for the one-dimensional tension case is also illustrated.     

A computational approach to the investigation of impact damage evolution in discontinuously reinforced fiber composites

 A micromechanical damage constitutive model for discontinuous fiber-reinforced composites is developed to perform impact simulation. Progressive interfacial fiber debonding and a crack-weakened model are considered in accordance with a statistical function to describe the varying probability of damage. Emanating from a constitutive damage model for aligned fiber-reinforced composites, a micromechanical damage constitutive model for randomly oriented, discontinuous fiber-reinforced composites is developed. The constitutive damage model is then implemented into a finite element program DYNA3D to simulate the dynamic behavior and the progressive damage of composites. Finally, numerical simulations for a biaxial loading test and a four-point bend impact test of composite specimens are performed to validate the computational model and investigate impact damage evolution in discontinuous fiber-reinforced composite structures. Furthermore, in order to address the influence of Weibull parameter S _o on the damage evolution in composites, parametric analysis is carried out. Received 29 April 2000     

不同形状弹体高速冲击下复合材料层板损伤分析

根据纤维增强复合材料宏细观结构,基于纤维的线弹性假设和基体的粘弹性假设,推导了单向复合材料粘弹性损伤本构关系。在此基础上,结合Hashin失效准则进行单层板面内损伤识别,通过界面单元模拟层间分层损伤,采用非线性有限元方法,建立了复合材料层板高速冲击损伤有限元分析模型。利用该模型,深入研究了不同形状弹体高速冲击下复合材料层板的弹道性能和损伤特性,探讨了相关参数对冲击损伤的影响规律,获得了一些有价值的结论。     

Progressive damage and nonlinear analysis of pultruded composite structures

This study combines a simple damage modeling approach with micromechanical models for the progressive damage analysis of pultruded composite materials and structures. Two micromodels are used to generate the nonlinear effective response of a pultruded composite system made up from two alternating layers reinforced with roving and continuous filaments mat (CFM). The layers have E-glass fiber and vinylester matrix constituents. The proposed constitutive and damage framework is integrated within a finite element (FE) code for a general nonlinear analysis of pultruded composite structures using layered shell or plate elements. The micromechanical models are implemented at the through-thickness Gaussian integration points of the pultruded cross-section. A layer-wise damage analysis approach is proposed. The Tsai–Wu failure criterion is calibrated separately for the CFM and roving layers using ultimate stress values from off-axis pultruded coupons under uniaxial loading. Once a failure is detected in one of the layers, the micromodel of that layer is no longer used. Instead, an elastic degrading material model is activated for the failed layer to simulate the post-ultimate response. Damage variables for in-plane modes of failure are considered in the effective anisotropic strain energy density of the layer. The degraded secant stiffness is used in the FE analysis. Examples of progressive damage analysis are carried out for notched plates under compression and tension, and a single-bolted connection under tension. Good agreement is shown when comparing the experimental results and the FE models that incorporate the combined micromechanical and damage models.     

Micromechanical modelling of the transverse damage behaviour in fibre reinforced composites

A micromechanics damage model is presented which examines the effect of fibre-matrix debonding and thermal residual stress on the transverse damage behaviour of a unidirectional carbon fibre reinforced epoxy composite. It is found that for a weak fibre-matrix interface, the presence of thermal residual stress can induce damage prior to mechanical loading. However, for a strong fibre-matrix interface the presence of thermal residual stress is effective in suppressing fibre-matrix debonding and improving overall transverse strength by approximately 7%. The micromechanical model is subjected to a multiple loading cycle (i.e. tension-compression-tension), where it is shown to provide novel insight into the microscopic damage accumulation that forms prior to ultimate failure, clearly highlighting the different roles that fibre-matrix debonding and matrix plasticity play in forming the macroscopic response of the composite. Such information is vital to the development of accurate continuum damage models, which often smear these effects using non-physical material parameters.     

A constitutive model for self-reinforced ductile polymer composites

Self-reinforced polymer composites are gaining increasing interest due to their higher ductility compared to traditional glass and carbon fibre composites. Here we consider a class of PET composites comprising woven PET fibres in a PET matrix. While there is a significant literature on the development of these materials and their mechanical properties, little progress has been reported on constitutive models for these composites. Here we report the development of an anisotropic visco-plastic constitutive model for PET composites that captures the measured anisotropy, tension/compression asymmetry and ductility. This model is implemented in a commercial finite element package and shown to capture the measured response of PET composite plates and beams in different orientations to a high degree of accuracy.     

纤维增强复合材料层板高速倾斜冲击损伤数值模拟

根据复合材料三维黏弹性本构关系, 建立了纤维增强复合材料层板高速倾斜冲击损伤的数值分析模型。该模型在复合材料层间引入界面单元模拟层间分层, 结合三维Hashin失效准则进行单层板面内损伤识别, 引入材料刚度折减方案, 采用非线性有限元方法, 研究高速倾斜冲击下复合材料层板的破坏过程和损伤特性。研究结果表明: 层板的主要损伤形式是层间分层、 基体微裂纹和纤维断裂; 冲击速度不变而入射角度增大时, 剩余速度减小, 层板损伤面积在一定入射角度范围内有明显变化; 入射角度不变而冲击速度增大时, 剩余速度增大, 层板损伤面积在一定速度范围内也有明显变化。     

Effects of interphase properties in unidirectional fiber reinforced composite materials

A micromechanical study has been performed to investigate the mechanical properties of unidirectional fiber reinforced composite materials under transverse tensile loading. In particular, the effects of different properties of interphase within the representative volume element (RVE) on both the transverse effective properties and damage behavior of the composites have been studied. In order to evaluate the effects of interphase properties on the mechanical behaviors of unidirectional fiber reinforced composites considering random distribution of fibers, the interphase is represented by pre-inserted cohesive element layer between matrix and fiber with tension and shear softening constitutive laws. Results indicate a strong dependence of the RVE transverse effective properties on the interphase properties. Furthermore, both the damage initiation and its evolution are also clearly influenced by the interphase properties.     

Micromechanical modeling of the progressive failure in short glass–fiber reinforced thermoplastics – First Pseudo-Grain Damage model

This paper presents a new micromechanical damage model, called “First Pseudo-Grain Damage” (FPGD) model, to predict the overall elasto-plastic behavior and damage evolution in short fiber reinforced thermoplastic materials typically produced by injection molding. The model combines mean-field homogenization theory with a continuum damage model, leading to a semi-analytical estimate of the composite incremental response that is convenient for the large scale simulation of composite structures. Each representative volume element (RVE) of the composite is decomposed into a set of pseudo-grains (PGs), which are two-phase composites with aligned fibers of the same aspect ratio. The PGs are homogenized individually according to a nonlinear Mori–Tanaka scheme. Then, a self-consistent scheme is applied to the aggregate of homogenized PGs. An anisotropic damage model is used at the PG level which enables accommodating arbitrary multiaxial and non-monotonic loading histories. Damage evolution inside PGs progressively affects the overall stiffness and strength of the RVE up to total failure. An evaluation of the proposed model against experimental data is conducted for short glass–fiber reinforced polyamide 6,6 (PA6,6). It is shown that the model yields satisfactory predictions of the response under uniaxial tension on samples with different fiber contents and under various loading directions relative to the main injection flow direction.     

Ultrasonic evaluation of fatigue damage in metal matrix composites

This paper describes an experimental nondestructive technique for fatigue damage assessment in metal matrix composites by measuring ultrasonic phase velocity and attenuation. A [0/90] SiC/Ti---15V---3Cr---3Al---3Sn metal matrix composite is considered as a model system. Cyclic loading at 50 and 70% of the ultimate sample strength were used until failure. The ultrasonic phase velocities and attenuations were measured periodically and found to be very sensitive to fatigue damage. The fatigue-induced changes in the composite elastic constants were calculated from the measured ultrasonic velocity data. For samples heat treated prior to fatigue (815°C) above the matrix β transus (about 760°C), the dominant damage mechanism is debonding of the fiber/matrix interface. We found that when samples were fatigued for less than 50% of the lifetime, the reduction of the composite moduli was linearly dependent on the number of fatigue cycles, which is explained by extension of interfacial partial debonds. This was supported by micromechanical analysis based on a partial disbond model. The rate of decrease in the composite moduli in the second half of the fatigue life was found to be lower, which may serve as a basis for estimation of the remaining fatigue life of the composite from ultrasonic velocity and attenuation measurements. The attenuation data was obtained in directions perpendicular to the fiber. A single-fiber scattering model has been used to explain the effect of the fiber/matrix interface on attenuation. Good correlation between attenuation and moduli measurements was observed.     

Micromechanical analysis of stress relaxation response of fiber-reinforced polymers

The paper describes a micromechanical method to determine the stress relaxation response of polymer composites consisting of linearly viscoelastic matrices and transversely isotropic elastic fibers. A representative unit cell is subjected to some prescribed axial and shear loadings to study and quantify the time-dependent behavior of composite materials. Closed-form analytical expressions are derived describing the anisotropic viscoelastic response of composite materials as functions of matrix and fiber properties. The present analytical expressions are employed to determine the stress relaxation behavior of a graphite/epoxy composite and the results are compared with the finite element analysis of the micromechanical model. Very good correlation between analytical expressions and numerical results is illustrated for the linearly anisotropic viscoelastic response of composite materials.     

纤维增强复合材料本构模型研究进展

本文对纤维增强复合材料的本构模型最新研究成果进行简要阐述和归纳,并结合实例进行了相关数值模拟计算。文中阐述的复合材料为纤维增强树脂复合材料、纤维增强金属基复合材料和纤维编织复合材料。目前,关于纤维增强金属基复合材料的研究较少,大多数研究集中在纤维增强树脂复合材料和纤维编织复合材料。许多学者在经典弹性本构模型和连续介质力学基础上,推导出了一些弹塑性、粘弹性和考虑损伤的非线性本构模型。通过实例计算结果表明,考虑损伤导致刚度退化的复合材料弹塑性本构模型计算得到的拉伸应力应变曲线与测试结果基本一致。本文通过对复合材料本构模型的最新研究成果的归纳和数值模拟实例计算,为后续研究工作提供借鉴,推动其在实际工程中的应用。