Stiffness and fracture analysis of laminated composites with off-axis ply matrix cracking

Matrix cracks parallel to the fibres in the off-axis plies is the first intralaminar damage mode observed in laminated composites subjected to static or fatigue in-plane tensile loading. They reduce laminate stiffness and strength and trigger development of other damage modes, such as delaminations. This paper is concerned with theoretical modelling of unbalanced symmetric laminates with off-axis ply cracks. Closed-form analytical expressions are derived for Mode I, Mode II and the total strain energy release rates associated with off-axis ply cracking in [0/θ]_s laminates. Stiffness reduction due to matrix cracking is also predicted analytically using the Equivalent Constraint Model (ECM) of the damaged laminate. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

A novel statistical model for predicting matrix cracking in high temperature polymer composite laminates

This paper studied the progressive matrix cracking in high temperature polymer composite laminates that could be used for next generation high speed transport airframe structures and aircraft engine components exposed to elevated temperatures. Damage mechanisms of matrix cracking were identified by X-ray radiography at room temperature and in-test photography technique at high temperature. It was found that the non-deterministic scenario is always involved in the procedure of transverse matrix cracking. Monte Carlo simulations using experimentally obtained materials properties were applied to simulate the multiple transverse cracking and compared with the experiment data. Finally, a novel statistical model combining Weibull theory with shear lag model was proposed to predict the matrix cracking based upon the previously obtained probability density function of crack spacing. It is shown that the predictions of this statistical model agree well with the experimental results and can be used to have an in-depth understanding of the random matrix cracking problem in composite laminates.     

Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates

Specimens of 90° cross-ply glass-reinforced epoxy resins were tested in tension parallel to the direction of reinforcement in the outer plies. The thickness of the inner ply was varied and cracking constraint was observed at small thicknesses. At large inner-ply thicknesses the specimens showed uniform transverse cracking, and at very low inner-ply thicknesses this transverse cracking could be suppressed completely prior to total specimen failure. Fracture toughness values were determined on transverse unidirectional laminates of the same volume fraction. It was found that the cracking constraint observed can be accounted for, using the theory of Aveston and Kelly.     

Interaction between matrix cracking and edge delamination in composite laminates

Matrix cracking and edge delamination are two main damage modes in continuous-fibre composite laminates. They are often investigated separately, and so the interaction between two damage modes has not yet been revealed. In this paper, a simple parallel-spring model is introduced to model the longitudinal stiffness reduction due to matrix cracking and edge delamination together. The energy release rate of edge delamination eliminating the matrix crack effect and the energy release rate of matrix cracking in the presence of edge delamination are then obtained. Experimental materials include carbon- and glass-fibre-reinforced bismaleimide composite laminates under static tension. The growth of matrix cracks and edge delaminations was recorded by means of NDT techniques. Results show that matrix cracks may initiate before or after edge lamination. This depends on the laminate layup, and especially on the thickness of the 90° plies. Edge delamination may also induce matrix cracking. Matrix cracking has a significant effect on the stiffness reduction in GRP laminates. The present model can predict the stiffness reduction in a laminate containing both matrix cracks and edge delaminations. The mixed-mode delamination fracture toughness obtained from the present model shows up to 50% differences compared with O'Brien's model for GRP laminates. However, matrix cracking has a small effect on the mixed-mode interlaminar fracture toughness of the CFRP laminates.     

复合材料层合板基体裂纹的协同损伤演化模型

首先,为研究复合材料层合板在准静态载荷下的基体裂纹演化特征,提出了一个基于能量的协同损伤演化模型。然后,通过模型对损伤进行了多尺度分析:从微观角度,采用三维有限元方法求得裂纹表面位移;从宏观角度,结合裂纹表面位移,推导了萌生基体裂纹的能量释放率。最后,根据裂纹萌生准则对基体裂纹的演化过程进行预测。模型考虑了演化过程中损伤的相互影响、残余应力、基体材料非线性、材料初始损伤分布及损伤演化的不均匀性。根据演化分析流程计算了[±θ/904]s铺层玻璃纤维复合材料的基体裂纹演化过程。结果表明:这一模型能够准确地预测准静态载荷下复合材料层合板基体裂纹的损伤演化规律。     

Multi-directional stiffness degradation induced by matrix cracking in composite laminates

A model was developed for predicting the stiffness degradation of fiber reinforced plastics (FRP), with ply configuration [0_m/±θ_n]_S, induced by matrix cracking under in-plane tension. The model assumes that the cracks in off-axis plies are uniformly distributed and a damage variable D is defined. Based on the theory of fracture mechanics, the elastic moduli of cracked matrix are obtained and indicated by the damage variable D, then the reduction of elastic moduli of laminates caused by the matrix cracks was studied. Comparison with experimental values for the glass/epoxy [90₃/0]_S, [0/90]_S and [0/±45]_S laminates shows good agreement with the theoretical prediction given by the presented model.     

Analysis of first ply failure in composite laminates

The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking. It is found that cracks may propagate in two directions on planes which are parallel to the fiber axis and perpendicular to the midplane of the ply. In general, crack propagation in the direction of the fiber axis controls the strength of thin plies, while cracking in the direction perpendicular to the fiber axis determines the strength of thick plies. The theory relates ply thickness, crack geometry and ply toughness to ply strength. It predicts a significant increase in strength with decreasing ply thickness in constrained thin plies. The strength of thick plies is found to be constant, but it may be reduced by preexisting damage. Results are illustrated by comparison with experimental data.     

A simplified analysis of transverse ply cracking in cross-ply laminates

This paper presents a method of analyzing transverse crack initiation and multiplication in symmetric cross-ply laminates. The method is based on the concept of a through-the-thickness inherent flaw and the energy balance principle. With a second-order polynomial assumed for the crack opening displacement, the perturbed stress field due to the presence of ply cracks is determined from the equilibrium conditions. The energy released as a result of ply cracking is then calculated and used to predict the increase in crack density. Based on an experimental correlation of the analytical result, a resistance curve is proposed to be used as a measure of the resistance to crack multiplication. The resistance to crack multiplication is shown to increase with the increasing crack density.     

Characterization and analysis of carbon fibre-reinforced polymer composite laminates with embedded circular vasculature

A study of the influence of embedded circular hollow vascules on structural performance of a fibre-reinforced polymer (FRP) composite laminate is presented. Incorporating such vascules will lead to multi-functional composites by bestowing functions such as self-healing and active thermal management. However, the presence of off-axis vascules leads to localized disruption to the fibre architecture, i.e. resin-rich pockets, which are regarded as internal defects and may cause stress concentrations within the structure. Engineering approaches for creating these simple vascule geometries in conventional FRP laminates are proposed and demonstrated. This study includes development of a manufacturing method for forming vascules, microscopic characterization of their effect on the laminate, finite element (FE) analysis of crack initiation and failure under load, and validation of the FE results via mechanical testing observed using high-speed photography. The failure behaviour predicted by FE modelling is in good agreement with experimental results. The reduction in compressive strength owing to the embedding of circular vascules ranges from 13 to 70 per cent, which correlates with vascule dimension.     

The effect of explosives on polymer matrix composite laminates

Small explosive charges were placed on the surface or stood off from carbon fibre and glass fibre laminates. Surface charges produced circular holes surrounded by a delaminated area. The holes increased in size with increased explosive amount. For charges stood off the amount of damage was a function of impulse as well as peak pressure. Damage associated with the attachment of the laminate occurred at lower peak pressures (0.5 MPa) than previously reported. The extent of damage was less for adhesively bonded laminates than for clamped laminates. Damage was in the form of fibre breakage as well as interply delamination.     

On cross-ply cracking in glass and carbon fibre-reinforced epoxy laminates

The transverse tensile strength (or fracture strain) of unidirectional fibre-reinforced materials is an important mechanical property. The transverse fracture strain of a single ply in an angle-ply laminate, however, is not an independent mechanical property as it is influenced by its thickness and neighbouring plies. The present investigation describes the phenomenon of multiple fracture of glass and carbon fibre-reinforced epoxy 90° plies. Based on the model that a 90° ply consists of elements all of which can break, the applicability of Weibull statistics in describing the fracture strain is investigated.     

Stiffness properties of composite laminates with matrix cracking and interior delamination

Two modes of damage in composite laminates are considered: the intralaminar damage (matrix cracking) and the interlaminar damage (interior delamination). Using a vectorial representation of damage as internal variables in a phenomenological theory, relationships between the overall stiffness properties and the intensity of damage in the individual modes are determined. These relationships show that the intralaminar damage reduces all elastic moduli for a general orientation of the damage entities (cracks) and changes the initial orthotropic symmetry of a laminate. The interlaminar damage, however, does not change the symmetry but reduces the moduli. Predictions of the elastic moduli changes are compared with experimental results, showing excellent agreement.     

In‐plane progressive matrix cracking analysis of symmetric cross‐ply laminates with holes

Most of the previously performed damage analyses in composite laminates have been restricted to model the plain laminates without geometry discontinuities. In this study, a micromechanical damage model is combined with the finite element formulation and is implemented in the integration points to perform progressive damage analyses of composite laminates. A micromechanical damage model based on the stress transfer method is used to find the degradation of mechanical properties of composite laminates. Crack density is also used as an only state variable representing the damage in each Gauss point of every layer of the laminate. The strain energy and critical energy release rate criterion is also used to predict the damage initiation and evolution in each layer. A finite element discretization is used in conjunction with the user element definition capability of ABAQUS commercial software. To verify the developed procedure, a single element is analysed, and the obtained results are compared with available results in the literature. Progressive damage analyses are also performed for several symmetric cross‐ply laminates with and without geometry discontinuity subjected to matrix cracking damage mechanism under in‐plane loading conditions. The obtained mechanical response and variations of matrix crack density versus the applied load are also discussed.     

Activation theory for creep of matrix resin and carbon fibre-reinforced polymer composite

Activation theory used in metals and polymers has been used to model creep of unidirectional composite and resin matrix, using the concept of internal stress. The model fits the experimental creep curves very well for a range of materials. The results obtained for a brittle epoxy and its carbon fibre-reinforced composite with two fibre orientations are reported. The model parameters, such as internal stress, activation volume and activation energy, have been measured experimentally and compared with model-fit values, and their influence on creep is discussed. Finally, an approach to predict the creep rupture of unidirectional composites using internal stress is presented.     

Fracture and fatigue of a Nicalon/CAS continuous fibre-reinforced glass-ceramic matrix composite

The fracture and fatigue behaviour of Nicalon/CAS continuous fibre-reinforced glass-ceramic matrix composite was studied at temperatures of up to 1000°C in both air and vacuum. Using chevron-notched test-pieces in bending, high nominal toughness values are measured at ambient temperature and at 1000°C in vacuum. In contrast, toughness values obtained in air decrease progressively with test temperature increase from 600 to 1000°C, and at 1000°C they are reduced by a factor of three from their values at ambient temperature. Marked changes in micromechanisms of crack growth under cyclic loading are also observed in air as the test temperature is increased: multiple cracking occurs at ambient temperature, while dominant Mode I cracks can be produced at 1000°C. A further study has been carried out in air on plane-sided test-pieces at a temperature at 1000°C, under both monotonic and cyclic loading. At ambient temperature, effects of cyclic loading have been deduced, while crack growth at 1000°C in air appears to be dominated by static loading with little effect of cyclic loading. These subcritical crack growth and toughness observations are consistent with changes that occur in the fibre/matrix interfaces at elevated temperatures in air reported in the literature.     

The behaviour of cross-ply hybrid matrix composite laminates: Part 2: Modelling

In Part 1 of this work experimental data were presented for the initiation and propagation of damage in hybrid matrix and uniform matrix laminates. The data showed that during the extension of cross-ply laminates, either constrained (stable) matrix cracking or brittle (unstable) matrix cracking occurs in the transverse plies, with the transverse ply thickness and level of urethane in the transverse ply determining which type of cracking is observed. In the present paper the stable cracking behaviour is modelled using a shear-lag stress analysis combined with an energy balance and the unstable cracking behaviour is discussed in terms of a statistical distribution of transverse ply strengths.     

复合材料层板冲击剪切实验技术研究

基于HOPKINSON杆冲击剪切试验技术、复合材料层板的材料性能及应用特点的分析,对“杆-管”冲击剪切动态力学性能实验技术进行了改进优化,解决了输入杆跳动、同轴调节困难、结果分散大等实验技术问题。根据输入杆、输出管和复合材料试样的匹配分析,确立了输入杆、试样和输出管针对动态冲击剪切实验的约束尺寸条件。通过有限元数值分析,研究了预置剪切间隙对冲击剪切的影响,研究认为0.2mm～0.3mm间隙设计对Ф14.5mm输入杆冲击 2mm～4mm层板试样的冲剪试验是合适的。冲击剪切实验数据表明,加载率对玻纤增强复合材料层板的动态剪切力学性能影响明显。     

Modelling low-speed drop-weight impact on composite laminates

The impact responses of typical laminates are investigated numerically in this research. Delamination responses among plies and fibre and/or matrix damage responses within plies are simulated to understand the behaviours of laminates under different impaction conditions. Damage resistance of a laminate is highly dependent upon several factors including geometry, thickness, stiffness, mass, and impact energies (impact velocities), which are here considered by the finite element (FE) method. Three groups of composite laminates are simulated and the numerical results in general are in good agreement with corresponding experiments. Models containing different stacking sequences and impact energies are built to study their influence on impact responses and demonstrate that clustered (or nearly clustered) plies in the laminate can effectively reduce the degree of interface damage. Models containing different indenters and plate shapes are also built to systematically study their influence on the low-speed drop-weight behaviour of composite laminates. Suggestions are proposed for designing impact tests for particular purposes.