Behaviour up to rupture of woven ply laminate structures under static loading conditions

A general model based on continuum damage mechanics (CDM) and a non-local ply scale criterion were developed to describe the failure of carbon woven ply laminated structures. This non-local criterion is based on mean quantities over a fracture characteristic volume (FCV) corresponding to a cylinder with a circular area and a given ply thickness. The nonlinear behaviour and the non-local criterion were implemented in the finite element code ABAQUS. This paper presents new comparisons between the results of experimental data and simulations performed on plates with notches and saw cuts. The results show the efficiency of this approach, even for structures with very high stress gradients. A simplified approach based on the FCV and the Tsai criterion is also presented here and the results obtained with this method are then compared with the experimental data.     

A generalized damage model for woven ply laminates under static and fatigue loading conditions

A generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loading is developed in this paper. The damage, consisting of small cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. The model presented here describes the evolution of the damage up to failure of the first ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model is extended to cover a broad range of plies, from quasi-unidirectional to balanced woven plies. A continuum damage approach (CDM) is then used to define the behaviour of the two virtual unidirectional plies under static and fatigue loading conditions. The model is applied here to an unbalanced woven ply with glass reinforcement and the results of the simulations are compared with experimental data.     

A Higher Order Synergistic Damage Model for Prediction of Stiffness Changes due to Ply Cracking in Composite Laminates

A non-linear damage model is developed for the prediction of stiffness degradation in composite laminates due to transverse matrix cracking. The model follows the framework of a recently developed synergistic damage mechanics (SDM) approach which combines the strengths of micro-damage mechanics and continuum damage mechanics (CDM) through the so-called constraint parameters. A common limitation of the current CDM and SDM models has been the tendency to over-predict stiffness changes at high crack densities due to linearity inherent in their stiffness-damage relationships. The present paper extends this SDM approach by including higher order damage terms in the characterization of ply cracking damage inside the material. Following the SDM procedure, predictions are aided by suitable micromechanical computations of crack opening displacements. A nonlinear SDM model is developed and applied for multiple classes of composite laminate layups. Stiffness predictions for damaged laminates using the developed model are compared with the experimental data for cross-ply ([0m/90n]s), angle-ply ([±θm/90n]s), off-axis ([0/±θ4/01/2]s) and quasi-isotropic ([0/90/±45]s) laminates. A comparison with current linear damage models showcases the usefulness of the proposed nonlinear SDM approach.     

Predicting evolution of ply cracks in composite laminates subjected to biaxial loading

An energy-based model is developed to predict the evolution of sub-critical matrix crack density in symmetric multidirectional composite laminates for the case of multiaxial loading. A finite element-based numerical scheme is also developed to evaluate the critical strain energy release rate, G_Ic, associated with matrix micro-cracking, a parameter that previously required fitting with experimental data. Furthermore, the prediction scheme is improved to account for the statistical variation of G_Ic within the material volume by using a two-parameter Weibull distribution. The variation of G_Ic with increasing crack density is also accounted for based on reported experimental evidence. The simulated results for carbon/epoxy and glass/epoxy cross-ply laminates demonstrate the ability of the improved model to predict the evolution of multidirectional ply cracking. By integrating this damage evolution model with the synergistic damage mechanics approach for stiffness degradation, the stress-strain response of the studied laminates is predicted. Finally, biaxial stress envelopes for ply crack initiation and pre-determined stiffness degradation levels are predicted to serve as representative examples of stiffness-based design and failure criterion.     

Current research into modelling of shock damage to large scale composite panels

This study aims to model the damage incurred to large woven roving E-glass/vinyl-ester composite panels subjected to shock loads, with particular emphasis on developing an effective, simple to use delamination model. An energy criterion for failure is applied at resin-rich layers, which are modelled in between every ply. The finite element program Abaqus/Explicit together with a user material subroutine (VUMAT) is used to simulate both large and small scale impact tests. The resin-rich layers are modelled as non-linear elastic and matrix and fibre damage is modelled at the woven plies using Hashin’s 2D stress-based failure criteria with a once-only degradation of the material properties.     

Finite Element Computation of Woven Ply Laminated Composite Structures up to Rupture

For unidirectional ply laminates, the great diversity of the damage mechanisms and their patterns of evolution make it extremely difficult to estimate the strength margins. In the case of woven ply laminates, the number of damage mechanisms is fairly small (no transverse rupture occurs and the material has a greater resistance to delamination) and the behaviour of the material is fairly simple to model up to rupture. In this study, a numerical model for woven ply laminated composite structures up to rupture is developed. The implementation is performed in a Euler Backward scheme and the consistent tangent stiffness matrix is calculated. Comparison with some experiments on structures are made and the model predicts these experiments well.     

Numerical derivation of pressure–impulse diagrams for prediction of RC column damage to blast loads

Pressure–impulse (P–I) diagrams are commonly used in the preliminary design or assessment of protective structures to establish safe response limits for given blast-loading scenarios. Current practice in generating the pressure–impulse diagram for structure components is primarily based on the simplified single degree of freedom (SDOF) model. The damage criterion is usually defined in terms of deformation or displacement response. Under blast loads, structures usually respond at their local modes, the equivalent SDOF system derived using the fundamental structure response mode might not be suitable. Moreover, structure is often damaged owing to brittle shear failure. In this case, the deformation-based damage criterion might not be able to give an accurate indication of local damage of a structural component. In this paper, a new damage criterion for RC column is defined based on the residual axial load-carrying capacity. A numerical method to generate pressure–impulse diagram for RC column is proposed. Parametric studies are carried out to investigate the effects of column dimension, concrete strength, longitudinal and transverse reinforcement ratio on the pressure–impulse diagram. Based on the numerical results, analytical formulae to predict the pressure–impulse diagram for RC column are derived. A case study shows that the proposed analytical formulae can be easily used to generate pressure–impulse diagram for RC columns accurately. The results are also compared with those obtained from the SDOF approach. It is shown that the proposed method gives better prediction of pressure–impulse diagram than the SDOF approach.     

Prediction of local hygroscopic stresses for composite structures – Analytical and numerical micro-mechanical approaches

The aim of this article is to propose an analytical micro-mechanical self-consistent approach dedicated to mechanical states prediction in both the fiber and the matrix of composite structures submitted to a transient hygroscopic load. The time and space dependent macroscopic stresses, at ply scale, are determined by using continuum mechanics formalism. The reliability of the new approach is checked, for carbon–epoxy composites, through a comparison between the local stress states calculated in both the resin and fiber according to the new closed-form solutions and the equivalent numerical model.     

Damage behaviour of laminated composites during fatigue loading

This study deals with the modelling of damage evolution in the carbon/epoxy laminated composites under static and fatigue loading. A cumulative damage model is developed on the basis of damage evolution due to static and fatigue during cyclic loading. A continuum damage mechanics (CDM)‐based damage model coupling with the micromechanics has been utilized to predict the fatigue behaviour of laminate composites. A multicriterion approach has been introduced to predict the damage behaviour in the longitudinal, transverse, and shear direction at the ply scale. Extensive experimental results on T300/EPL1012 carbon/epoxy laminates are prepared to characterize under static and fatigue loading and to evaluate the proposed model in different conditions. The obtained results show that at the beginning of the cyclic loading, the damage grows suddenly and increases until final failure, which justifies the proposed method is able to predict the evolution of the damage due to static and fatigue loading separately during cyclic loading. The obtained results show that considering damage due to static loading leads to more accurate results, particularly in low‐cycle fatigue.     

A Modeling Approach Across Length Scales for Progressive Failure Analysis of Woven Composites

This paper presents a multiscale modeling approach for the progressive failure analysis of carbon-fiber-reinforced woven composite materials. Hierarchical models of woven composites at three different length scales (micro, meso, and macro) were developed according to their unique geometrical and material characteristics. A novel strategy of two-way information transfer is developed for the multiscale analysis of woven composites. In this strategy, the macroscopic effective material properties are obtained from property homogenizations at micro and meso scales and the stresses at three length scales are computed with stress amplification method from macroscale to microscale. By means of the two-way information transfer, the micro, meso and macro structural characterizations of composites are carried out so that the micromechanisms of damage and their interactions are successfully investigated in a single macro model. In addition, both the nucleation and growth of damages are tracked during the progressive failure analysis. A continuum damage mechanics (CDM) method is used for post-failure modeling. The material stiffness, tensile strength and damage patterns of an open-hole woven composite laminate are predicted with the proposed multiscale method. The predictions are in good agreement with the experimental results.     

平面编织复合材料层合板低速冲击后的拉伸性能

对两种不同铺层形式的平面编织复合材料层合板低速冲击后拉伸性能进行了实验研究,在此基础上建立了有限元损伤扩展仿真模拟。在所建立的有限元模型中,将低速冲击损伤等效为形状规则的软化夹杂,并针对两种铺层形式采用不同的损伤判据和模量衰减准则。研究结果表明:该有限元模拟结果与实验结果符合,说明该模型能够准确地预测低速冲击后平面编织复合材料层合板的损伤扩展规律和剩余拉伸强度;不同铺层形式的平面编织复合材料层合板在低速冲击后拉伸的损伤扩展规律不同;它们的冲击后拉伸强度降均>50%,在复合材料结构设计中应该受到重视。      

Interlaminar and intralaminar reinforcement of composite laminates with aligned carbon nanotubes

Three-dimensional reinforcement of woven advanced polymer–matrix composites using aligned carbon nanotubes (CNTs) is explored experimentally and theoretically. Radially-aligned CNTs grown in situ on the surface of fibers in a woven cloth provide significant three-dimensional reinforcement, as measured by Mode I interlaminar fracture testing and tension-bearing experiments. Aligned CNTs bridge the ply interfaces giving enhancement in both initiation and steady-state toughness, improving the already tough system by 76% in steady state (more than 1.5 kJ/m² increase). CNT pull-out on the crack faces is the observed toughening mechanism, and an analytical model is correlated to the experimental fracture data. In the plane of the laminate, aligned CNTs enhance the tension-bearing response with increases of: 19% in bearing stiffness, 9% in critical strength, and 5% in ultimate strength accompanied by a clear change in failure mode from shear-out failure (matrix dominated) without CNTs to tensile fracture (fiber dominated) with CNTs.     

Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its influence on creep

A model to predict time-dependent evolution of simultaneous transverse cracking developed in multiple plies during creep loading and its effects on creep of multidirectional polymer matrix composite laminates is presented. The stress states in the intact regions of the plies are determined using the lamination theory during an incremental change in time. The stored elastic energy, determined using this stress state, is compared with a critical stored elastic energy value for damage to determine if a ply would fracture after the increment. If fracture is predicted, variational analysis is used to determine the perturbation in ply stresses due to cracking. This procedure is repeated to determine the crack evolution and creep strain. Model predictions compared well with experimental results for a [±θ_m/90_n]_s laminate.     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。      

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.     

A phenomenologically based damage model for textile composites with crimped reinforcement

A phenomenological damage model for textile composites with woven or braided reinforcement is presented and verified in this paper. Essential mechanical questions are clarified with regard to the dominant damage mechanisms and the definition of representative equivalent layers. Using the framework of continuum damage mechanics, damage is defined as the change of the tensor of elasticity. The initiation of damage is described using novel failure criteria based on the Failure-Mode-Concept. Damage variables and associated evolution laws are introduced to describe the subsequent degradation of the material stiffness. The capability of the proposed model is shown for woven thermoplastic composites made of hybrid glass–polypropylene yarns.     

Experimental investigation of three-dimensional woven composites

This paper summarizes an extensive experimental study of composites reinforced with three-dimensional woven preforms subjected to tensile, compressive and in-plane shear loading. Three innovative three-dimensional woven architectures were examined that utilize large 12 K and 24 K IM7 carbon tows, including two ply to ply angle interlock architectures and one orthogonal architecture. Additionally, a two-dimensional quasi-isotropic woven material was evaluated for comparison. Loads were applied in both the warp and the weft directions for tensile and compressive loading. Digital image correlation was used to investigate full field strains leading up to quasi-static failure. Experimental results including ultimate strengths and moduli are analyzed alongside representative failure modes. The orthogonal woven material was found to have both greater strength and modulus in tension and compression, though a ply to ply woven architecture was found to outperform the remaining three-dimensional architectures. Recommendations are made for improving the manufacturing processes of certain three-dimensional woven architectures.     

Nonuniform transformation field analysis of elastic–viscoplastic composites

To exactly describe the macroscopic behaviour of composites with non linear dissipative constituents, it is necessary to take an infinitely large number of internal variables into account. Simplifying assumptions are usually adopted to reduce this number. A new method has been proposed [Michel JC, Suquet P. Nonuniform transformation field analysis. Int J Solids Struct 2003;40:6937–55], based on the transformation fields approach [Dvorak G. Transformation field analysis of inelastic composite materials. Proc Roy Soc Lond A 1992;437:311–27], but not taking transformation fields to be necessarily uniform. The interest of this new method has been shown in the case of composites with elastic–plastic constituents. Here we deal with composites having elastic–viscoplastic and porous elastic–viscoplastic constituents. In the latter case, the viscoplastic strain has a dilatational part.