Cohesive models for damage evolution in laminated composites

A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models.     

An energy based damage model for thin laminated composites

The present paper outlines an unconventional energy based composite damage model capable of modelling woven and unidirectional composite materials. The damage model has been implemented into the LLNL-DYNA3D and LS-DYNA3D finite element codes for shell elements (plane stress), relevant to tensile, compressive and shear damage failure modes. The damage model uses five damage variables assigned to tensile, compressive and shear damage at a laminae level. The evolution of damage in each mode is controlled via a series of damage-strain equations, thus allowing the total energy dissipated for each damage mode to be controlled during a dynamic or impact event.The materials under investigation were a uni-directional (UD) carbon-epoxy and a woven carbon epoxy composite. Recent experimental test results from the CEC HICAS project have also been used to verify the behaviour of the model at elevated strain rates. Experimental data for the 0° and 90° tensile response indicates effectively rate independent, while matrix dominated modes, such as the shear response is highly rate dependent.The 0° and 90° tensile response and the tensile shear response have been modelled at a coupon level, including relevant strain rate effects, with the proposed damage model. Results show very good agreement with the available coupon experimental data. Suggestions are also presented for additional non-standard experimental tests to derive the material model parameters.A follow on paper describes the results of a series of simulations using the proposed material model on a number of experimental plate impact tests performed on the CEC HICAS project.     

单向复合材料横向裂纹黏弹性损伤演化模型

建立一个考虑基体黏弹性的纤维增强聚合物单向复合材料在产生横向裂纹时的损伤演化模型,有效地预测了单向复合材料横向拉伸行为。假设呈现威布尔分布的缺陷会在变形的驱动下演化为损伤,并以此为基础建立了单向复合材料横向损伤演化模型。通过此模型,时间-温度叠加原理（TTSP）得到了更具有物理基础的解释。最后,通过具体例子阐述了此模型的应用,并通过试验对模型预测结果进行了验证。本模型有效地预测了单向复合材料横向拉伸行为。由于单向复合材料横向性能存在脆性,此模型还无法准确预测失效和强度。      

Crack initiation in laminated metal-intermetallic composites

Several mechanisms have been proposed to describe crack initiation and propagation in ductile-brittle composites. This experimental study shows that the failure of metal intermetallic (metal-aluminides) composites was initiated by cracking initiation in the intermetallic layers. For metal layers that allowed shear deformation, crack initiation in adjacent intermetallic layers resulted from shear bands propagating from a crack tip in the intermetallic layer through the metal layer and producing stress concentration points at the interfaces of adjacent intermetallic layers. For metal layers that did not support shear deformation, crack initiation in the intermetallic layers resulted from the continued build up of stresses within the intermetallic layers, resulting in a relatively uniform distribution of cracks within the individual intermetallic layers. Prior to failure, lateral constraints produce lateral cracks in the intermetallic layers. The final fracture features of both failure mechanisms were similar for both metal-intermetallic systems.     

Generalized effective stiffness theory for nonelastic laminated composites

Effective stiffness theory of the Nth order is derived for the modeling of the 3-dimensional dynamic motion of a laminated medium made of elastic-viscoplastic work-hardening constituents. The resulting theory represents the composite as a higher order homogeneous continuum with microstructure, whose motion is governed by higher order displacements and stresses. The derivation is systematic and can be applied to other types of nonelastic laminated media to the desired degree of accuracy.     

A damage model for ductile crack initiation and propagation

Damage-induced ductile crack initiation and propagation is modeled using a constitutive law with asymmetrical contraction of the yield surface and tip remeshing combined with a nonlocal strain technique. In practice, this means that the void fraction depends on a nonlocal strain. Finite strain plasticity is used with smoothing of the complementarity condition. The prototype constitutive laws take into account pressure sensitivity and the Lode angle effect in the fracture strain. Two plane idealizations are tested: plane stress and plane strain. Thickness variation in the former is included by imposing a null out-of-plane normal stress component. In plane strain, pressure unknowns and bubble enrichment are adopted to avoid locking and ensure stability of the equilibrium equations. This approach allows the representation of some 3D effects, such as necking. The nonlocal approach is applied to the strains so that the void fraction value evolves up to one and this is verified numerically. Three verification examples are proposed and one validation example is shown, illustrating the excellent results of the proposed method. One of the verification examples includes both crack propagation in the continuum and rigid particle decohesion based on the same model.     

A model for anisotropic viscoelastic damage in composites

A model for continuous damage combined with viscoelasticity is proposed. The starting point is the formulation connecting the elastic properties to the tensor of damage variables. A hardening law associated with the damage process is identified from available experimental information and the rate-type constitutive equations are derived. This elastic damage formulation is used to formulate an internal variable approximation to viscoelastic damage in the form of a non-linear Kelvin chain. Elastic and viscoelastic equations are implemented into a finite element procedure. The code is verified by comparison with closed-form solutions in simplified configurations, and validated by fitting results of experimental creep tests.     

A damage model for knitted fabric composites

A progressive damage model is presented for the prediction of the overall non-linear tensile behaviour of knitted fabric composites. The model is an extension of a recently developed inclusion method for textile composites, taking into account the major damage modes of knitted fabric composites simultaneously. Matrix non-linearities, playing an important role in the behaviour of knitted fabric composites, are implemented using the secant stiffness method. Whereas, non-linearities can be attributed to different sources, depending upon the resin toughness, only some limited yielding was currently investigated. Yarn/matrix debonding, predominantly responsible for the knee behaviour of knitted fabric composites, is investigated using a simple interfacial failure criterion. A selective degradation scheme based upon a finite set of interfacial damage state variables is employed in the reduction of the inclusion stiffness. Finally, a Hoffman criterion is used for yarn failure. The model was used to simulate the tensile behaviour of knitted fabric E-glass/epoxy composites, showing the ability to predict the material response with reasonable accuracy in the region before ultimate failure.     

A computational strategy for the localization and fracture of laminated composites. Part 1. Development of a localization criterion adapted to model damage evolution time-delay

A criterion of instability and localization adapted for modeling the damage evolution with delay effect on a homogeneous laminate composite T300/914 beam is proposed. In the one-dimensional case, the results obtained have revealed the existence of a simultaneous rupture zone in the entire structure. A solution based on treatment provision regulating the use of meso-modeling calculations in composite structures is proposed. The calculation results using this approach provide correct bursting time prediction of specimens with rigidity malfunctions.     

A mechanistic approach to damage in short-fiber composites based on micromechanical and continuum damage mechanics descriptions

A micro-macro mechanistic approach to matrix cracking in randomly oriented short-fiber composites is developed in this paper. At the micro-scale, the virgin and reduced elastic properties of the reference aligned fiber composite are determined using micromechanical models [Proc. Roy Soc. Lond. A241 (1957) 376; Acta Metall. 21 (1973) 571; Mech. Mater. 2 (1983) 123], and are then distributed over all possible orientations in order to compute the stiffness of the random fiber composite containing random matrix microcracks. After that the macroscopic response is obtained by means of a continuum damage mechanics formulation, which extends the thermodynamics based approach in [Comp. Sci. Technol. 46 (1993) 29] to randomly oriented short-fiber composites. Damage accumulations leading to initiation and propagation of a macroscopic crack are modeled using a vanishing element technique. The model is validated against the published experimental data and results [Comp. Sci. Technol 55 (1995) 171]. Finally, its practical application is illustrated through the damage analysis of a random glass/epoxy composite plate containing a central hole and under tensile loading.     

Hygrothermal effects on structural stiffness and structural damping of laminated composites

In this paper the hygrothermal effects on structural stiffness and damping of laminated composites are investigated. Since the hygrothermal influence on properties of composite materials is primarily matrix dominated, we first determine experimentally the effects of temperature and moisture on the storage modulus, Poisson's ratio and material damping of the epoxy matrix. With the experimentally determined properties of the epoxy material, we then determine the complex moduli (E _L ^* ,E _T ^* ,G _LT ^* andv _LT ^* ) of unidirectional glass-epoxy and graphite-epoxy composites. The structural stiffness (extensional and flexural) and damping of symmetric angle-ply laminates of glass-epoxy and graphite-epoxy are then investigated both analytically and experimentally for temperatues of 20° C and 80° C, respectively. Three moisture contents which are the dry, saturated and a non-uniform moisture gradient states corresponding to each temperature case are considered. Numerical and limited experimental results show that the effects of moisture on the real part ofA ₁₁ ^* ,A ₆₆ ^* ,D ₁₁ ^* andD ₆₆ ^* at room temperature, 20° C, are negligible for all the considered cases. But as temperature increases, the moisture and temperature combined influence induces significant changes in the complex stiffnessA ₁₁ ^* A ₆₆ ^* ,D ₁₁ ^* , andD ₆₆ ^* especially for the matrix dominated terms.     

A stochastic damage accumulation model for crack initiation in high-cycle fatigue

A stochastic damage accumulation model for crack initiation in high-cycle fatigue is proposed. It is assumed that the fatigue damage is accumulated in the form of dislocations under the repeated stress and that the slip band crack is initiated when the strain energy due to a local pile-up of dislocations exceeds a critical value. The size of an initiating crack is the cell size, derived from a probabilistic argument and its depth is determined in relation to the stored dislocation energy. Our theoretical results are compared with the experimental data from a low-carbon steel S20C in order to examine the consistency of our model.     

Progressive damage and failure modeling in notched laminated fiber reinforced composites

A novel progressive damage and failure model for fiber reinforced laminated composites is presented in this work. The model uses the thermodynamically based Schapery Theory (ST) to model progressive microdamage in the matrix phase. Matrix failure is not governed with a matrix failure criterion, but rather matrix failure occurs naturally through the evolution of microdamage. A maximum strain criterion is used to dictate tensile failure in the fiber direction, while compressive failure is automatically accounted for by allowing local fiber rotations and tracking the evolution of rotation. The results of this model are compared to a previously developed model that used ST at the lamina level to calculate matrix microdamage, but used the Generalized Method of Cells to resolve the lamina level strains into constituent level stresses and strains and determines constituent failure by evaluating failure criteria at the micro, fiber/matrix level. Results for global load versus displacement and local strain from both models are compared to experimental data for notched laminates loaded in uniaxial tension. The results show remarkable agreement qualitatively, and in many cases the quantitative agreement is good. Accurate damage contours and failure paths are predicted.     

Analysis of matrix damage evolution in laminated composite plates

A new model has been developed to investigate matrix cracking in laminated fibrous composite structures. The model can predict matrix cracking and its effect on stiffness reduction. It can also compute the load transfer from the cracked matrix to surrounding fibers. The model is based on the micromechanical concept of the fiber and matrix as well as the matrix material degradation concept as matrix cracking progressed. The micromechanical concept uses a rectangular cell geometry representing a fiber and its surrounding matrix while the material degradation concept uses an empirical expression of a Weibull type function. Two material constants are required for matrix cracking. The constants were obtained from an experiment on matrix cracking. With those constants, the present model predicts the matrix cracking in other cases. The predicted solutions were comparable to the experimental data.     

A constitutive model of particulate-reinforced composites taking account of particle size effects and damage evolution

This paper deals with a constitutive model of particulate-reinforced composites which can describe the evolution of debonding damage, matrix plasticity and particle size effects on deformation and damage. An incremental damage model of particulate-reinforced composites based on the Mori–Tanaka’s mean field concept has been extended to consider the particle size effects by using the Nan–Clarke’s simple method. The particle size effect on deformation is realized by introducing dislocation plasticity for stress–strain relation of in situ matrix in composites, and the particle size effect on damage is described by a critical energy criterion for particle–matrix interfacial debonding. For composites containing particles of various sizes, the effects of particle size distribution is incorporated into the model. Influence of debonding damage, particle size and particle volume fraction on overall stress–strain response of composites is discussed based on numerical results.     

A new numerical modeling for laminated composites

Recently, with increasing interest in the performance of fiber reinforced laminated composites, various behaviors of these materials have been simulated by the finite element method (FEM). However, conventional models are not good enough to simulate behaviors of laminated composites. The main reason is that the laminated composite is modeled by assuming it to be a homogeneous object though it has a heterogeneous nature. In this paper, the new numerical modeling for laminated composites was proposed. In order to check the validity of the proposed model, elementary simulations were performed and compared with theoretical results. Moreover the application of the proposed model to the laminated composites with interlaminar delamination was discussed.     

Experimental observations and finite element modelling of damage initiation and evolution in carbon/epoxy non-crimp fabric composites

Damage in carbon/epoxy non-crimp stitched fabric (NCF) reinforced composites, produced by the resin transfer moulding (RTM) process is described. Formation of the stitching loop results in a certain disturbance of the uniform placement of the fibres. These deviations in fibre placement produce resin-rich zones that can influence the mechanical behaviour of the composite part. Tensile tests on quadriaxial (45°/90°-45°/0°)_s laminates are performed accompanied by acoustic emission (AE) registration and X-ray imaging. Early initiation of damage (matrix cracking) in plies with different fibre orientation has been detected. Damage sites correlate with the resin-rich zones created by the stitching. Finite element (FE) analysis is carried out to develop a model that describes damage of the NCF composites. Numerical multi-level FE homogenization is performed to obtain effective elastic orthotropic properties of NCF composite at micro (unit cell of unidirectional tow) and meso (fabric unit cell) levels. A hierarchical sequence of FE models of different scales is created to analyze in detail the 3D stress state of the NCF composite (meso unit cell). A multi-level submodeling approach is applied during FE analysis. Zones of matrix-dominated damage are predicted. A comparison of non-destructive testing results with computational model is performed. Fracture mechanics parameters of matrix crack are computed and cracks growth stability is studied.     

Study of damage evolution in composites using damage mechanics and micromechanics

A numerical modeling technique was presented to simulate, predict and evaluate progressive damage or failure in a composite structure subjected to an external loading. To this end, a micro/macromechanical approach was proposed along with damage mechanics at the microlevel. The micro/ macromechanical model utilized both the macromechanical analysis and the micromechanical analysis in tandem. The continuum damage mechanics was applied to the microlevel stresses-strains in order to predict damage evolution in a composite structure from the initiation of damage through to complete failure of the structure. Crack initiation and growth in a particulate composite with stress concentration was simulated using the proposed technique, and the results were compared to experimental data. The comparison showed a very good agreement.