Overall moduli and natural frequencies of composite laminates containing multiple interlaminar transverse cracks

In this paper, the overall tensile modulus of a composite laminate containing embedded multiple interlaminar transverse cracks is studied. The modulus is calculated based upon an energy method and the crack opening displacement which is obtained by solving a boundary-value problem. Numerical computation is applied to fibre-reinforced composite laminates following the theoretical analysis. The theoretical prediction is compared with the experimental data, and good agreement is found. The solution is then used to examine the natural frequencies of two representative cross-ply beams with multiple matrix cracks in some of the outer transverse layers. The difference between the natural frequencies of the intact and the damaged cross-ply beams is presented. It is found that for a graphite/epoxy composite, the multiple transverse cracks only have a minor influence on the frequency, whereas for a glass/epoxy composite, the multiple cracks may have a significant influence on the frequency when the cracks reach the saturation level in a relatively large area of a beam.     

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

Experimental evidence of crack tip shielding mechanisms in quasi-brittle materials

To gain insight into the shielding processes in quasi-brittle materials, in situ crack propagation and crack profile measurements were performed inside the scanning electron microscope (SEM). Crack tip shielding phenomena were studied in monolithic alumina and in SiC fibre-reinforced alumina matrix composites as a function of fibre coatings. The crack in the fibre-reinforced composite samples is bridged by a row of fibres which contains a fibre area fraction of 10%. The applied stress intensity factor necessary to extend the crack in the composite materials increased 25% for the gold coated fibre-reinforced alumina matrix composites and 13% for the polymer-coated fibre-reinforced composites, compared to the monolithic samples. Crack extension in the monolithic samples and in the fibre-reinforced composites occurred after the crack opening displacements close to the crack tip approached the critical crack tip profile corresponding to the intrinsic toughness of alumina. A hypothesis on the effect of closure stresses on crack profile shape and net toughness has been developed. Furthermore, crack profiles revealed that grain bridging in the vicinity of the fibres was operative in the fibre-reinforced composites at stress intensity factors far exceeding the critical stress intensity factor of the monolithic matrix material. The additional grain bridging in the vicinity of the fibres has never been reported and can only be revealed through crack profile measurements. This revised version was published online in November 2006 with corrections to the Cover Date.     

复合材料层板损伤过程的刚度分析

本文对典型铺设的[0₂/±45₂/90₂]_s碳/环氧复合材料层板中的典型损伤状态进行了实验观察,测定出损伤对层板刚度引起的下降率.建立了横向裂纹扩展、分层伴以横向裂纹扩展的三维有限元分析模型,计算出对层板刚度引起的下降率,并与实验值进行了比较.结果表明,横向裂纹和分层是层板的主要损伤型式,分层损伤扩展是一个主导性的稳定的损伤扩展过程,是导致刚度下降的主要因素.     

Fracture mechanics and optimization — a useful tool for fibre-reinforced composite design

This paper will demonstrate the application of fracture mechanics and optimization techniques for the optimum design of fibre-reinforced composite laminates (FRC). First, a boundary-value problem of a cracked composite laminate is solved within the framework of linear elastic fracture mechanics (LEFM). The solution relates the stress intensity factor at a crack tip and the crack-induced interfacial stresses to the laminate configuration. These results are then used in two types of the optimum design of fibre-reinforced composite laminates. In the first type of optimum design, namely a crack-insensitive design of the laminate, the crack driving force and interfacial principal tensile stress are both minimized by using single- and multicriterion optimization techniques. The second type of optimum design involves in situ strength design of multidirectional angle-ply laminates. In this case, a set of in situ strength parameters are proposed based on theoretical analysis and experimental observations. This optimization problem is a min {max} one and non-differentiable. A proper treatment of the non-differentiability is introduced and the min {max} optimization problem is converted into a differentiable single-criterion one using the bound-formulation technique. All the optimization problems are solved by non-linear mathematical programming. The results show that optimization can greatly enhance the load carrying capacity of the laminates.     

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.     

Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model to estimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loads varied with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracture toughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, the fracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantly at cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.     

Micromechanics characterization of sublaminate damage

A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.     

Determination of fracture stress and strain of highly oriented short fibre-reinforced composites using a fracture mechanics-based iterative finite-element method

For a tensile test specimen made of a short fibre-reinforced composite with the fibres oriented in the direction of force, a model was developed to describe the onset and propagation of microcracks, which finally lead to macroscopic failure of the specimen. The crack propagation theory used is based on a standard fracture mechanics method and was applied to the microstructure of the specimen by the finite element method. The results appear qualitatively correct. The micromechanical method applied gives a deeper insight into the fracture processes within short fibre-reinforced composites.     

Random fatigue life prediction of carbon fibre-reinforced composite laminate based on hybrid time-frequency domain method

To evaluate fatigue life of composite laminate with hole under random loading, a random fatigue life prediction model is established by hybrid time-frequency domain method in this paper. Firstly, dynamic response of composite laminate is obtained from FE model in frequency domain. Secondly, root mean square of stress of six stress components of critical damage point in frequency domain are transferred to stresses in time domain. At last, 3D Tsai–Hill static failure criterion is adopted to convert the multiaxial stress into the uniaxial equivalent stress. Fatigue life is predicted by equivalent stress fatigue life code. The method is validated with the random vibration fatigue test of carbon fibre-reinforced composite laminate. Numerical results are compared with random fatigue experiments which show good agreement with numerical results.     

Simulation of Low Velocity Impact Induced Inter- and Intra-Laminar Damage of Composite Beams Based on XFEM

In this paper, the Inter-Fiber Fracture (IFF) criterion of Puck failure theory based on the eXtended Finite Element Method (XFEM) was implemented in ABAQUS code to predict the intra-laminar crack initiation of unidirectional (UD) composite laminate. The transverse crack path in the matrix can be simulated accurately by the presented method. After the crack initiation, the propagation of the crack is simulated by Cohesive Zoom Model (CZM), in which the displacement discontinuities and stress concentration caused by matrix crack is introduced into the finite element (FE) model. Combined with the usage of the enriched element interface, which can be used to simulate the inter-laminar delamination crack, the Low Velocity Impact (LVI) induced damage of UD composite laminate beam with a typical stacking of composite laminates [0₅/90₃]_S is studied. A complete crack initiation and propagation process was simulated and the numerical results obtained by the XFEM are consistent with the experimental results.     

Fatigue behaviour of carbon fibre-reinforced aluminium laminates

A new hybrid composite (CARALL), consisting of thin layers of carbon fibre/ epoxy prepreg sandwiched between aluminium sheets, has been developed. It is shown that this class of materials offers higher modulus, higher tensile strength and lower density than 2024-T3 alloy in the longitudinal direction. Under tension-tension fatigue loading, the hybrid laminates showed superior fatigue crack propagation resistance in the longitudinal direction, which may be attributed to the bridging effect imposed by the intact fibres in the crack wake. It has also been shown that the effectiveness of fatigue crack growth reduction increases with the thickness of the carbon fibre/epoxy layer. The resistance to fatigue crack propagation can be further improved by introducing compressive residual stresses in the aluminium layer by postcure stretching the laminate in the plastic region of the aluminium alloy.     

Experimental fatigue crack growth analysis and modelling in part‐through circumferentially pre‐cracked pipes under pure bending load

In the present work, an attempt has been made to study the fatigue crack growth in a part‐through circumferentially notched pipe specimen. It has been observed that under four‐point bend cyclic load, the crack propagates in a transverse plane in the radial direction initially followed by propagation in the circumferential direction. The crack extension in the circumferential direction resulted crack growth retardation in the radial direction. This behaviour of the fatigue crack growth has been modelled, and a fatigue life prediction methodology based on an exponential model has been applied for prediction of fatigue crack growth.     

Elastoplastic modelling of subsurface crack growth in rail/wheel contact problems

Propagation of small subsurface cracks subjected to shear under repeated rolling contact load is studied. An analytical crack model (Dugdale) with plastic strips at the two crack tips is employed. Compressive stresses promoting crack closure and friction between crack faces are considered. The triaxial stress state is used in the yield criterion. A damage criterion is suggested based on experimental LCF data. In a numerical study, critical crack lengths are found below which propagation of an existing crack should be effectively suppressed.     

Stress intensity factor for a three-layered plate with a crack in the center layer

The objective of this study is to model the laminated composite as a multilayered plate each layer being made of a different material. With a crack in the mid-layer of the laminate, the stresses can vary in all three space coordinate directions and the problem is recognized as a three-dimensional one. A laminate plate theory is developed by application of the minimum complementary energy theorem in variational calculus such that the qualitative three-dimensional character of the crack edge stresses is retained while approximations are made in a quantitative sense on the stress intensity factor.Numerical values of the stress intensity factors for different construction of the laminate are reported and compared with the same size plate made of a single homogeneous material. When the modulus of elasticity of the middle layer which contains the crack is lower than that of the outer layers, the load transmission to the crack site as measured by the stress intensity factor can be reduced significantly. The present model assumes failure by crack propagation in only one layer of the laminate. Other possible modes of failure such as cohesive and/or adhesive fracture in laminated structures have yet to be explored.     

Compressive strength of unidirectional and crossply carbon fibre/PEEK composites

The commonly accepted production methods of composite systems generally result in departure of the plies properties from transverse isotropy due to stresses acting during fibre—matrix bond formation. This anisotropy coupled with the composite structure affects compressive loading; the ultimate stresses as well as the direction, in- or out-of-plane, of kink propagation. A unidirectional and a crossply carbon fibre/PEEK composites were compression tested at ambient and elevated temperature as well as exposed to various chemical environments. Significant disruptions in fibre—matrix interface in the crossply composite were indicated. The compression tests showed that failure occurred through in-plane and out-of-plane fibre bucking and kinking in the unidirectional and crossply composites, respectively. Failure of the longitudinal plies in the crossply laminate occurred at significantly higher compression stress than for the unidirectional composite. Compressive failure mechanisms in unidirectional and multi-directional laminates are considered.     

Thermal expansion characteristics of PEEK composites

The thermal expansion behaviour of several fibre-reinforced PEEK composites is assessed. It is shown that thermal expansion behaviour is consistent, and changes in a predictable manner with changes in fibre type. Using a composite manufactured such that no interfacial bonding took place, it is demonstrated that compressive forces caused by differential thermal contraction of fibre and matrix are sufficiently large to dominate behaviour in a direction parallel to the fibres. This suggests that PEEK composites should be resistant to changes in thermal expansion behaviour with repeated thermal cycling, and such resistance is demonstrated for AS4/PEEK (APC-2/AS4). It is shown that conventional models for predicting laminate response from unidirectional composite properties are valid for such materials, but it is also shown that the common analytical models for calculating transverse fibre behaviour from composite properties are inaccurate.     

Interactions between propagating cracks and bioinspired self-healing vascules embedded in glass fibre reinforced composites

This study considers the embedment of a bioinspired vasculature within a composite structure that is capable of delivering functional agents from an external reservoir to regions of internal damage. Breach of the vascules, by propagating cracks, is a crucial pre-requisite for such a self-healing system to be activated. Two segregated vascule fabrication techniques are demonstrated, and their interactions with propagating Mode I and II cracks determined. The vascule fabrication route adopted played a significant role on the resulting laminate morphology which in-turn dictated the crack-vascule interactions. Embedment of the vascules did not lower the Mode I or II fracture toughness of the host laminate, with vascules orientated transverse to the crack propagation direction leading to significant increases in G_I and G_II through crack arrest. Large resin pockets were found to redirect the crack around the vascules under Mode II conditions, therefore, it is recommended to avoid this configuration for self-healing applications.