On modelling of damage evolution in textile composites on meso-level via property degradation approach

The continuous damage mechanics (CDM) approach is a popular tool for modelling of damage evolution in textile composites on the meso-level. It is based on the assumption that a material with defects can be replaced by a fictitious material with no defects but with degraded elastic constants. In such way the presence of defects is only reflected in the material elastic properties and damage evolution is recorded through the loss of these properties. The CDM approach incorporated into finite element analysis often predicts unphysically wide damage zones and in some cases failure across yarns – findings that are not supported by experimental data. The current work is geared toward identifying the source of inconsistencies between experiment and modelling by revisiting basic assumptions of CDM. A test problem is proposed to illustrate a break down of the CDM approach where a single crack-like defect in a yarn is modelled as an inhomogeneity with elastic constants reduced according to Murakami–Ohno model. It is shown that CDM in combination with local stress analysis of failure may predict a different direction of damage evolution as well as an incorrect failure mode in comparison with the crack problem. We also investigate whether the Murakami–Ohno model adopted for calculation of properties of a fictitious inhomogeneity contributes to the unphysical results. For this we compare contributions of a crack and an inhomogeneity into material elastic response. A new property degradation procedure is suggested (referred here as an effective elastic response model) where the size of an inhomogeneity and properties of the surrounding material are taken into account.     

Automatic differentiation of micromechanics incremental schemes for coupled fields composite materials: Effective properties and their sensitivities

A modeling approach based on automatic differentiation and micromechanics incremental schemes for coupled fields composite materials is presented in this work. In the multi-sites framework, the micromechanics incremental schemes presented herein are able to account for the anisotropic behavior of the constituents, the morphological and the topological textures and the strong contrast between the properties of the individual phases of these composite materials. By applying automatic differentiation to these micromechanics incremental schemes, the first order and high order sensitivities of the effective material properties can be easily computed in the same analysis. An application on three-phase magneto-electro-elastic composite material is presented in the framework of mono-site micromechanics to show the effectiveness of this composite materials modeling approach. The details on the implementation of this modeling approach in the multi-sites framework will be discussed in a future work. The composite materials modeling methodology reported here may be used for material microstructure sensitive design in material by design strategies.     

Mechanics of textile composites: Micro-geometry

Textile fabric geometry determines textile composite properties. Textile process mechanics determines fabric geometry. In previous papers, the authors proposed a digital element model to generate textile composite geometry by simulating the textile process. The greatest difficulty encountered with its employment in engineering practice is efficiency. A full scale fiber-based digital element analysis would consume huge computational resources. Two advances are developed in this paper to overcome the problem of efficiency. An improved contact-element formulation is developed first. The new formulation improves accuracy. As such, it permits a coarse digital element mesh. Then, a static relaxation algorithm to determine fabric micro-geometry is established to replace step-by-step textile process simulation. Employing the modified contact element formulation in the static relaxation approach, the required computer resource is only 1–2% of the resource required by the original process. Two critical issues with regards to the digital element mesh are also examined: yarn discretization and initial yarn cross-section shape. Fabric geometries derived from digital element analysis are compared to experimental results.     

Damage in MMCs using the GMC: theoretical formulation

In this work the incorporation of damage in the material behavior is investigated. Damage is incorporated into the generalized cells model (GMC), and applied to metal-matrix composites (MMCs). The local incremental damage model of Voyiadjis and Park is used here in order to account for damage in each subcell separately. The resulting micromechanical analysis establishes elasto-plastic constitutive equations that govern the overall behavior of the damaged composite. The elasto-plastic constitutive model is first derived in the undamaged configuration for each constituent of the metal-matrix composite. The plasticity model used here is based on the existence of a yield surface and flow rule. The relationships are then transformed for each constituent to the damaged configuration by applying the local incremental constituent damage tensors. The overall damaged quantities are then obtained by applying the local damage concentration factors obtained by employing the rate of displacement and traction continuity conditions at the interface between subcells and between neighboring repeating cells in the generalized cells model. Examples are solved numerically in order to explore the physical interpretation of the proposed theory for a unit cell composite element.     

Thermodynamically consistent coupled viscoplastic damage model for perforation and penetration in metal matrix composite materials

Accurate modeling and efficient analysis of the metal matrix composite materials failure mechanism during high velocity impact conditions is still the ultimate goal for many researchers. The objective is to develop a micromechanical constitutive model that can effectively simulate the high impact damage problem of the metal matrix composite materials. Therefore in this paper, a multiscale micromechanical constitutive model that couples the anisotropic damage mechanism with the viscoplastic deformation is presented here as a solution to this situation. This coupled viscoplastic damage model is formulated based on thermodynamic laws. Nonlinear continuum mechanics is used for this heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic damage. It includes the strong directional effect of the fiber on the evolution of the back stress and the development of the viscoplastic strain in the material behavior for high velocity impact damage related problems.     

Interlaminar and intralaminar durability characterization of wet layup carbon/epoxy used in external strengthening

Carbon fibers in unidirectional fabric form are increasingly being used as a means of strengthening deteriorating and understrength concrete components and systems through application as externally bonded reinforcement. The use of wet layup process under ambient conditions makes these composites susceptible to moisture and environment-related deterioration. In addition since the composite is formed in the field, often in overhead or vertical configurations, by sequential placement of fabric layers, it is critical, for the assessment of materials integrity, to characterize damage mechanisms and durability of interlaminar and intralaminar performance characteristics. It is shown that aqueous exposure, as well as freeze–thaw, results in significant fiber–matrix debonding, and this causes deterioration in short-beam-shear and in-plane shear characteristics. Changes in interlaminar properties are seen to be correlated with moisture uptake. It is also seen that fracture toughness, in the short-term, is enhanced by some of these exposures due to plasticization and flexibilizing of the matrix, which assists in the blunting of crack front progression. However, when accompanied by chemical degradation, such as with immersion in alkali solution, and embrittlement caused by low temperature exposure, G_IC values are seen to deteriorate as well. The data provides a crucial set of material characteristics for consideration side-by-side with fiber dominated characteristics (such as tensile strength and modulus, which are the only ones considered conventionally in rehabilitation design), since the matrix dominated properties will often be the critical links in determining service life.     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

含损伤复合材料的湿热弹性响应

依据不可逆热力学理论, 未引入任何附加假设, 建立了湿热弹性各向异性损伤复合材料的一般理论。应用建立损伤本构方程的本构泛函展开法, 推导出湿热弹性损伤材料全部本构方程的一般形式, 其中包括比自由能密度表达式、 应力-应变关系、 熵密度方程、 损伤应变能释放率表达式、 吸湿对偶力表达式、 湿-热-固-损伤耦合的热传导方程和损伤演化方程。研究表明, 在本构方程中含有若干损伤效应函数, 表征损伤对材料宏观力学性能与湿、 热性能的影响, 其具体形式可由细观力学解确定, 从而使连续损伤力学与细观损伤力学有机结合在一起。最后, 从细观力学与实验观测两个角度, 举例说明损伤效应函数与系数张量的确定方法, 为分析变温变湿环境下复合材料的损伤问题提供重要的理论依据。      

Analysis of knitted fabric reinforced composites: Part I. Fibre orientation distribution

The fibre orientation distributions in different types of warp knitted fabric are studied. The fibre orientations are represented by orientation tensors. This allows for the production of second- and fourth-order approximations of the orientation distribution function, which contain the relevant part of the orientation distribution for second- and fourth-order tensorial properties, respectively. Also, the symmetry that is present in the knitted fabrics can be analysed with the help of orientation tensors. It is shown that all the knitted fabrics are ‘almost' monoclinic. Determination of the ‘nearly' on-axis coordinate system is of interest for the data reduction of tensile test data.     

Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach

The subject of this paper is numerical prediction of bird strike induced damage in real aeronautical structures using highly detailed finite element models and modern numerical approaches. Due to the complexity of today’s aeronautical structures, numerical damage prediction methods have to be able to take into account various failure and degradation models of different materials. A continuum damage mechanics approach has been employed to simulate failure initiation and damage evolution in unidirectional composite laminates. Hashin’s failure initiation criteria have been employed in order to be able to distinct between four ply failure modes. The problem of soft body impacts has been tackled by applying the Coupled Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. This improvement in impactor deformation modelling resulted in a more realistic behaviour of bird material during impact. Numerical geometrical and material nonlinear transient dynamic analyses have been performed using Abaqus/Explicit. The main focus of the work presented in this paper is the application of the damage prediction procedure in damage assessment of bird impact on a typical large airliner inboard flap structure. Due to the high cost of gas-gun testing of aircraft components, experimental testing on the real flap structure could not have been performed. In order to evaluate the accuracy of the presented method, the bird and composite damage model have been validated against experimental data available in the literature.     

Modelling of composite sheet forming: a review

The use of composite materials in sheet forming applications is gaining popularity with the rise of consumer demands and specific mechanical properties. In addition to unidirectional (UD) fibres, the use of textile reinforcements such as woven fabric and knitted fabric has been shown to be feasible in recent years. This paper gives a survey on the modelling of composite sheet forming for both UD fibre and textile composites. Two broad approaches are reviewed here—the mapping approach and the mechanics approach. Mapping approaches for UD fibre composites, woven fabric composites and knitted fabric composites are elucidated on the basis of their fibre geometry. For the mechanics approach both the viscous fluid models and elastic solid models, as a means of describing the constitutive properties, are reviewed. Various updating methods for modelling large deformation found in sheet forming are then described. Finally, a guideline for the choice of modelling techniques for various types of fibre/fabric reinforcements and suggestions for future work are given.     

Characterization of fatigue damage in long fiber epoxy composite laminates

A study of damage characterization of a GFRC laminate is presented here. Forty fatigue tests were executed and S–N curves traced. Two parameters were chosen to monitor damage evolution during each test: stiffness and dissipated energy per cycle. Moreover, the presence of three zones in graphs of processed data can be observed and it is evident that the most important structural transformations take place only in the very final part of life. Adopting a continuum mechanics approach, the degradation through the whole life in composite is evaluated and it is shown that the two parameters are strictly related to damage state of composite material. A method for predicting the remaining life in a GFRC is here proposed.     

Analysis of fatigue damage evolution and associated anisotropic elastic property degradation in random short-fiber composite

A theoretical analysis of cyclic fatigue damage and associated anisotropic property degradation in a random short-fiber composite is presented. The fatigue damage takes various forms of microcracking, originated from microscopic stress concentrators in the highly heterogeneous material system. A probabilistic treatment of the microcracks is introduced to evaluate the statistical nature of the microscopic fatigue damage. Damage evolution and accumulation are analyzed through the development of probabilistic density functions of microcrack length and orientation during the cyclic loading history. Constitutive equations for the damaged fiber composite are then derived on the basis of a self-consistent mechanics scheme in conjunction with a three-dimensional elliptic crack theory and the microcrack density functions. Cyclic fatigue degradation and associated damage-induced anisotropy of composite material properties are determined and checked against experiments. The tensorial nature of material damage and composite stiffness changes during fatigue are evaluated explicitly. A power-law relationship between the rate of damage growth and the fatigue loading cycle is obtained. The rate of fatigue damage growth is found to decrease exponentially with load cycles—a phenomenon unique to the random short-fiber composite. This study provides a comprehensive analytical treatment of the homogeneous fatigue damage problem for random short-fiber composites. The fundamental mechanics and mechanisms of fatigue damage evolution and associated anisotropic property degradation of the composite are elucidated.     

基于单胞解析模型的复合材料层合板渐进损伤数值分析

基于单胞解析模型,建立一种从复合材料细观组分到宏观层合板的渐进损伤分析模型。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该矩阵将细观组分材料的弹性和损伤性能传递到宏观复合材料中。该模型只需给出纤维和基体的材料属性及纤维体积含量无需层合板的弹性和强度参数,通过组分材料的损伤失效判据确定其是否损伤,如果发生损伤则用损伤因子折算成相应的刚度衰减。通过用户材料子程序UMAT 及VUMAT将单胞解析模型以及损伤理论嵌入到有限元软件ABAQUS 中,对开孔复合材料层合板的渐进损伤过程进行模拟,预测了层合板强度。结果表明:预报的强度与试验值吻合较好,验证了该方法的有效性。     

Quantification of uncertainty modelling in stochastic analysis of FRP composites

The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process.     

Effective moduli of multi-scale composites

The effective moduli of a multi-scale composite are evaluated by a bottom-up (hierarchical) modeling approach. We focus on a two-scale structure in which the small scale includes a platelet array inside a matrix, and the large scale contains fibers inside a composite matrix. We demonstrate that the principal moduli of the multi-scale composite can be fine-tuned by the platelet arrangement and orientation. As a case study, we consider the phenomenon of fiber micro-buckling within the multi-scale composite. It is found that the compressive micro-buckling strength can be considerably increased for specific platelet orientations. The multi-scale design approach presented here can be used to generate novel families of composite materials with tunable mechanical properties.     

Strength prediction in CFRP woven laminate bolted double-lap joints under quasi-static loading using XFEM

The current paper is concerned with modelling damage and fracture in woven fabric composite double-lap bolted joints that fail by net-tension. A 3-D finite element model is used, which incorporates bolt clamp-up, to model a range of CFRP bolted joints, which were also tested experimentally. The effects of laminate lay-up, joint geometry, hole size and bolt clamp-up torque were considered. An Extended Finite Element (XFEM) approach is used to simulate damage growth, with traction–separation parameters that are based on previously reported, independent experimental measurements for the strength and toughness of the woven fabric materials under investigation. Good agreement between the predicted and measured bearing stress at failure was obtained.