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.     

On the transverse cracking and stiffness degradation of aged angle-ply laminates

A modified shear lag analysis, taking into account the concept of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in aged angle-ply laminated composites. The results of this paper represent well the dependence of the degradation of elastic properties on the cracks density, hygrothermal conditions and the fibre orientation of the outer layers.     

Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.     

Modelling of chip separation in machining unidirectional FRP composites by stiffness degradation concept

Progressive failure of unidirectional glass fiber-reinforced polymer composites (FRP) was studied using finite element analysis in orthogonal machining. Chip formation process and damage modes such as matrix cracking, fiber–matrix debonding and fiber breaking were modelled by degrading the material properties. Damage analysis was carried out using Hashin, Maximum stress and Hoffman failure criteria. After damage was detected, selective stiffness degradation was applied to the workpiece material. The objective of this study is to better understand the chip formation process and to analyse the cutting-induced damage from initiation stage until complete chip formation. The effect of the fiber orientation on cutting forces and sub-surface damage was investigated with different failure criteria. The results were addressed in terms of cutting forces evolution and damage progression in the composite structure during machining. It was demonstrated that the use of the stiffness degradation concept with the appropriate failure criterion responds potentially in a predictable fashion to changes in chip formation process for machining of FRPs.     

Matrix fatigue cracking in fiber composites

A model is developed for fatigue growth of matrix cracks in metals reinforced with aligned continuous elastic fibers. The mechanics of elastic cracks bridged by frictionally constrained fibers is used to develop the model, which provides estimates of the tip value of the stress intensity factor amplitude, ΔK_TIP. It is found that when the applied load amplitude is held fixed during fatigue crack growth, ΔK_TIP, and thus the rate of growth approach an asymptotic value independent of crack length. The residual strength after fatigue crack growth is also discussed. In some cases, the residual strength is unaffected by prior fatigue growth. But, in another regime, the matrix crack length allows fibers to begin breaking before the matrix crack grows. The strength is then inversely proportional to the square root of fatigue crack length.     

Strength and stiffness parameters for composites

This short paper proposes the adoption of a convention for reporting and specifying strength and stiffness properties of composites which offers some advantages by comparison with BS4994, currently under revision.     

Characterization of stiffness degradation caused by fatigue damage in textile composites using circumferential plate acoustic waves

The aim of this paper is to show the possibility of fatigue damage characterization in GFRP-tube-like components by using circumferential plate waves. For that purpose, fatigue tests with different loading directions have been conducted and the stiffness degradation has been monitored. After a preset number of loading cycles, non-destructive ultrasonic tests using circumferential plate waves were performed. The correlation between damage induced amplitude changes of the plate waves and stiffness degradation in non-crimped fabric composites is discussed. The results indicate that the technique is applicable to fatigue damage assessment in complex-shaped components of composite materials and is relevant to a wide field of applications.     

Restrained shrinkage cracking in fibre-reinforced cementitious composites

The influence of seven types of fibres on restrained shrinkage cracking in Portland cement pastes and mortars is investigated at various fibre volume fractions. Linear specimens with one-dimensional restraint were subjected to a drying environment soon after casting. Fibres belonging to two major categories-macro (large) and micro (fine)-were investigated. These two categories of fibres were found to result in distinctly different cracking patterns due, in part, to their different reinforcing mechanisms. An attempt is made to relate the observed cracking patterns with the perceptible micromechanical processes. A ‘fibre efficiency factor’ is proposed which appears to be an appropriate basis for grading the fibres.     

Matrix cracking and interface debonding in fiber-reinforced cement-matrix composites

The processes of matrix cracking and interface debonding were studied using the high sensitivity Moire interferometry technique. The experiments were conducted with continuous steel fiber reinforced cementitious composites subjected to uniaxial tension. The initiation and propagation of cracking and debonding were observed during the tests with the specimens of different fiber-volume ratios. Based on the experiments, the fiber stress, the interface slip, the interface shear stress, and the matrix strain distribution were calculated. It was shown that interfacial frictional shear stresses were not constant either along the whole interface or at different loading levels. The strain localization was observed in the matrix where it was bonded to the fiber. The average contribution of the matrix was greater for the composites with the higher fiber-volume ratio.     

Stress-corrosion cracking and its propagation in aligned short-fibre composites

Stress-corrosion tests are conducted on aligned short-fibre composites to assess their performance in both air and 1 N H₂SO₄ environments. The materials used are 3 mm E-glass, AS4 carbon, and their hybrid fibre reinforced epoxy composites. Several crack propagation models are developed to describe different cracking behaviour; the observed composite fracture modes verify these proposed models. Pre-immersion has significant effects onK _l-t _f and crack arrest of hybrid composites. A comparison of theoretical and experimentalK _l-t _f curves indicates good agreement of time to failure. The present research has quantified the susceptibility of these composites to environmental attack.     

Fatigue life prediction of nanoparticle/fibrous polymeric composites based on the micromechanical and normalized stiffness degradation approaches

In this paper, a new model based on the micromechanical and normalized stiffness degradation approaches is established. It has been assumed that during the fatigue condition, only material properties of composites (fiber and matrix) were degraded and nanofillers remain intact under different states of stress. A normalized stiffness degradation model was proposed for laminated fibrous composites reinforced with nanoparticles to derive a novel model to predict the stiffness reduction. The developed model is capable of predicting the fatigue life of nanoparticle-filled fibrous composites based on the experimental data of fibrous composites without nanofillers. The new fatigue model is verified by applying it to different experimental data provided by different researchers. The obtained results by the new fatigue model are in very good agreement with the experimental data of nano-silica glass/epoxy composites under constant cyclic stress amplitude fatigue and also for silica/epoxy nanocomposites in various states of stress with negligible error.     

The full-cell cracking mode in unidirectional brittle-matrix composites

In this work we consider the issues associated with predicting the initiation of matrix cracking within a unidirectional brittle-matrix composite (BMC). The analysis is accomplished as a case study for a restrictive, though important, class of composites consisting of silicon carbide fibres and a glass-ceramic matrix. A newly-derived axisymmetric variational model is employed to predict the stress field and energy release rates in a composite having a single damaged cell (or randomly located non-interacting cells) in which an annular matrix crack is introduced. Propagation of this crack to the fibre/matrix interface generates what we call the full-cell cracking mode. Strength and toughness properties of the matrix material are assumed to infer the potential for growth of the annular crack as well as its influence on the interface stresses and plausible scenarios governing the behaviour of secondary flaws. In turn, the synergistic influence of the latter flaws on the original annular crack is predicted. Since fibre spacing seems to be of paramount importance in real composites, a model of a composite having a non-uniform fibre distribution is also developed. The work includes a study of crack deflection at the fibre/matrix interface and comments are made regarding the perceived need for poor bonding in these materials. Also noted are the key parameters that need to be determined by experiment to quantify the failure prediction.     

Some factors controlling transverse cracking in cross-plied composites

Journal of Materials Science -     

Stochastic dynamics with fatigue-induced stiffness degradation

This article deals with stochastic dynamics coupled with simultaneous evolution of degradation of the system properties. We provide a general formulations and interpretations of various response-degradation problems associated with randomly vibrating systems and then an efficient analysis of vibratory systems with fatigue-induced stiffness degradation is presented. First, an approach to the random vibration problem with empirical characterization of stiffness degradation is sketched out and then the efficient sequential method for a coupled analysis of the response-degradation is presented in detail including numerical illustration of the results.     

Correlation between resin material variables and transverse cracking in composites

In this paper, the correlation between the resin material variables and the transverse cracking in composites is established. A theoretical model based on the fracture mechanics principle is built to describe thein situ failure process of transverse cracking. The central concept of the model is that the fracture is controlled by the plastic zone developed at the crack tip. Based on an approximate crack tip stress distribution, a quantitative representation is found to relate the laminate transverse cracking fracture toughness,G _c(comp), to certain resin properties: fracture toughness,G _c(resin), yield stress, _y, Young's modulus,E, and residual stress build-up, _R.G _c(comp) values of several fibre-glass/epoxy laminate systems were measured using the double torsion technique. The experimental results are found to be interpreted reasonably well by the theory. As a result, a clear picture of transverse cracking emerges. It seems that _y ²/E plays a more dominant role thanG _c(resin) in controllingG _c(comp). The residual stress _R can weaken the laminate significantly when its level is high. It is also shown that the failure model discussed here can be readily applied to laminate delamination failure as well as adhesive bond fracture.     

Simulating cracking and failure in multilayer composites: Multiple failure

Summary A model has been devised for the failure in a layered composite with long-time static loading. Each layer is considered as reinforced in one direction by continuous fibers with any cross section. Damage accumulation is accompanied by changes in the elastic and strength characteristics for each layer and for the composite as a whole.The model has been used in a scheme for forecasting the working life of a layered composite on long-time static loading on the assumption that the damage accumulates uniformly in each layer.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 44–50, May–June, 1991.     

Distributed damage in composites,theory and verification

A model that accounts for the effect of structural changes, resulting from the application of loads, in composite materials is developed. Such changes are incorporated in the theory through a tensor form of a damage variable. The model extends the theory of elasticity and it accounts for certain important properties observed in composite materials. The parameters involved in the theory are identified and determined from available experimental data. Back prediction of test results, for two different composite materials, verifies the theory.     

Matrix cracking initiated by fibre breaks in model composites

Fracture of resin in a composite material can be initiated by a tensile break in a fibre. This process has been investigated for a simple model composite, consisting of two inextensible rods placed along the axis of a cylindrical elastic block and touching in the centre. The rods represent a broken fibre. Energy release rates,G, were calculated by finite element methods for a circular crack growing outwards from the point where the rod ends separated as they were pulled apart. Results are compared with experimental observations on cracking of a silicone rubber cylinder containing two steel rods. It was found that a crack grew outwards under increasing load until its radius reached a certain size, approximately half-way to the surface of the resin cylinder. At this point,G reached a minimum value and then increased. Simultaneously, the crack accelerated and the sample broke. Forces required to propagate the crack were successfully predicted by linear elastic fracture mechanics at all stages of crack growth and for a wide range of fibre and sample radii. In particular, good agreement was obtained with the maximum force that the model system could support, i.e. the breaking load. When the sample was surrounded by a rigid tube, representing neighbouring fibres surrounding the broken one, growth of a crack required an increasing load at all stages. The sample finally fractured when the broken fibre pulled out with resin still attached to it. Application of these results to unidirectional fibre-reinforced materials is discussed.