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 °.     

Onset of free-edge delamination in composite laminates under tensile loading

Edge delamination onset on composite laminates has been investigated for a carbon/epoxy T800/914 composite material. On the edge of laminates, out-of-plane stresses arise, even up to material's failure. Layer thickness is also known as well to influence delamination onset stress. Making use of a conventional model (that is to say assuming plies homogeneity, elastic linear behaviour, plane interlaminar surface and interface's infinite stiffness) and of a local stress tensor correction near the edge, allows, thanks to an asymptotic method, an efficient calculation of the full stress tensor. A stress criterion has then been studied. Criterion parameters assessment, from test results, has been focused on, based on conjugate gradient method and experimental thickness effect. Edge Delamination Tests have been performed on several specimens of various layups. Interlaminar shear, tension, as well as shear and tension combination have been investigated. Acoustic emission was used to detect delamination onset. As expected, these tests have exhibited layer thickness influence on onset stress. Shear parameter assessment shows good agreement between theory and experimental results. A single set of parameters is necessary to predict delamination for different layups. But experimental testing for both tensile and mixed mode has shown that failure may not be interlaminar, as expected, but intralaminar.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

Fatigue delamination growth in woven glass/epoxy composite laminates under mixed-mode II/III loading conditions at cryogenic temperatures

We investigate the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode II/III fatigue loading. Fatigue delamination tests were conducted with six-point bending plate (6PBP) specimens at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), and the delamination growth rate data for various mixed-mode ratios of Modes II and III were obtained. The energy release rate was evaluated using the three-dimensional finite element method. In addition, the fatigue delamination growth mechanisms were characterized by scanning electron microscopic observations of the specimen fracture surfaces.     

Fatigue crack propagation under non-proportional mixed mode loading

Under non-proportional mixed I+II loading, two kinds of stable crack propagation may be distinguished. An existing precrack will either kink, mode I controlled (tensile mode), or will propagate, coplanarly mode II controlled (shear mode). Shear mode growth will occur if the effective mode II range exceeds the material-specific threshold ΔK_{II th sm} and in addition to that, the ΔK_II-value on the starter crack is larger than the ΔK¹_I (Δϕ)-range on the infinitesimally short additional crack. Examination under the scanning electron microscope showed that flaws are not the reason for the mode II controlled crack propagation and support the criteria introduced. If the crack opening is large enough, the crack propagation rate is higher for shear-stress controlled crack growth than for normal-stress controlled crack extension, the deviation angle of which is well predictable via the MTS criterion due to Erdogan and Sih [On the crack extension in plates under plane loading and transverse shear. J Basic Engng 1963;85:519–25].     

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.     

Fatigue life prediction of woven composite laminates with initial delamination

An engineering approach for fatigue life prediction of fibre‐reinforced polymer composite materials is highly desirable for industries due to the complexity in damage mechanisms and their interactions. This paper presents a fatigue‐driven residual strength model considering the effect of initial delamination size and stress ratio. Static and constant amplitude fatigue tests of woven composite specimens with delamination diameters of 0, 4 and 6 mm were carried out to determine the model parameters. Good agreement with experimental results has been achieved when the modified residual strength model has been applied for fatigue life prediction of the woven composite laminate with an initial delamination diameter of 8 mm under constant amplitude load and block fatigue load. It has been demonstrated that the residual strength degradation‐based model can effectively reflect the load sequence effect on fatigue damage and hence provide more accurate fatigue life prediction than the traditional linear damage accumulation models.     

Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth

A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension–compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0_n, ?_m]_s with severed central plies [?], and of stacking order [0₂, +45, 0₂, ?45, 0, 90]_s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.     

Fatigue crack growth in fibre metal laminates under selective variable-amplitude loading

To extend the predictive capability of existing crack growth models for fibre metal laminates under constant amplitude fatigue loading to variable-amplitude loading, further research on variable-amplitude fatigue mechanisms in fibre metal laminates is necessary. In response to this need, an experimental study into the effects of multiple overloads, underloads and various block-loading sequences on crack growth in the fibre metal laminate Glare was investigated. Crack growth retardation effects were observed in the tests; however, the magnitude of these effects was lower than seen in monolithic aluminium because of fibre bridging. As a result, predictions of the observed behaviour were attempted using an existing constant-amplitude fatigue crack growth model for Glare in combination with a linear damage accumulation law.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

Temperature effects on mixed mode I/II delamination under quasi-static and fatigue loading of a carbon/epoxy composite

This paper addresses the effect of temperature on the mixed-mode interlaminar fracture toughness and fatigue delamination growth rate of a carbon-fibre/epoxy material, namely IM7/8552. Quasi-static and fatigue characterisation tests were carried out at −50 °C, 20 °C, 50 °C and 80 °C, using asymmetric cut-ply coupons. The experimental results show that temperature may have an accelerating or delaying effect on delamination growth, depending on the loading regime, i.e. either quasi-static or fatigue. Fractographic examinations were also carried out in order to assist the interpretation of the experimental data. A semi-empirical equation is introduced to describe the experimentally observed fatigue delamination growth rates at elevated temperatures.     

Bridging effect on mode I fatigue delamination behavior in composite laminates

This paper discusses the bridging effect of fibres on mode I fatigue delamination growth in unidirectional and multidirectional polymer composite laminates based on a series of double cantilever beam (DCB) tests. From the results, there is sufficient evidence that fibre bridging can decrease the crack growth rate da/dN significantly, and using only one fatigue resistance curve to determine the delamination behavior in composite materials with large-scale fibre bridging may be inadequate. The bridging created in fatigue delamination is different from that of quasi-static delamination at the same crack length. So it is incorrect to use the resistance curve (R-curve) from quasi-static delamination tests to normalize fatigue delamination results.     

Strength reduction and delamination growth in thin and thick composite plates under compressive loading

In this paper, the coupled local-global buckling behavior in laminated composite plates with elliptic delaminations and the associated mechanisms of delamination growth under compressive loads are critically examined. The J-integral technique is used for delamination growth prediction in terms of pointwise energy release rate distribution along the delamination edge. A Multi-plate model, in conjunction with a 3-noded quasi-conforming shell element, is used to model the delaminated plates. The incremental equilibrium equations are set up based on total Lagrangian formulation. The solution strategy incorporates Gauss elimination in a cycle of Newton-Raphson iterations and is augmented with automated arc-length controled load incrementation and equilibrium iterations; and with automated post-buckling path tracing based on a linearised asymptotic solution. The effects of structural parameters such as delamination thickness, size and shape, on the post-buckling behavior and on the delamination growth are critically examined.This work was supported by the FAA to the Center of Excellence for Computational Modeling of Aircraft Structures at Georgia Institute of Technology, and in part by a grant from ONR.     

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF₃/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30)₃/90₂]_s and [(±45)₂/O₂/90₂]_s. Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.     

Fatigue crack growth rates under sequential mixed-mode I and II loading cycles

One common mode of failure that occurs in rolling bodies such as gears, bearings and rails is due to the fatigue process. Several research workers suggest that rolling contact fatigue cracks are subjected to mixed mode I and II loading cycles. It is believed that the correct modelling of loading cycles can help us to study the mechanics of crack growth because fatigue comprises a major safety consideration in the design process. Experiments have been performed under nonproportional mixed-mode I and II loading cycles with fixed degrees of overlap, so that coplanar cracks were produced. Three empirical crack propagation laws have been established which are related to both mode I and mode II effective stress intensity factor ranges.     

Matrix failure in composite laminates under compressive loading

The failure envelope of the matrix in composite laminates under compressive loads has not received much attention in literature. There are very little to no experimental results to show a suitable failure envelope for this constituent found in composites. With increasing popularity in the use of micromechanical analysis to predict progressive damage of composite structures which requires the use of individual failure criteria for the fibre and matrix, it is important that matrix behaviour under compression is modelled correctly.In this study, off-axis compression tests under uniaxial compression loading are used to promote matrix failure. Through the use of micromechanical analysis involving Representative Volume Elements, the authors were able to extract the principal stresses on the matrix at failure. The results indicated that hydrostatic stresses play an important role in the failure of the matrix. Thus, Drucker–Prager failure criterion is recommended when modelling compressive matrix failure in composite structures.     

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6

Fatigue crack initiation and growth characteristics under mixed mode loading have been investigated on aluminum alloys 2017-T3 and 7075-T6, using a newly developed apparatus for mixed mode loading tests. In 2017-T3, the fatigue crack initiation and growth characteristics from a precrack under mixed mode loading are divided into three regions—shear mode growth, tensile mode growth and no growth—on the ΔK_I-ΔK_II plane. The shear mode growth is observed in the region expressed approximately by ΔK_II > 3MPa√m and ΔK_II/ΔK_I > 1.6. In 7075-T6, the condition of shear mode crack initiation is expressed by ΔK_II > 8 MPa√m and ΔK_II/ΔK_I > 1.6, and continuous crack growth in shear mode is observed only in the case of ΔK_I/ΔK_II, 0. The threshold condition of fatigue crack growth in tensile mode is described by the maximum tensile stress criterion, which is given by Δσ_θmax √2πr 1.6MPa√m, in both aluminum alloys. The direction of shear mode crack growth approaches the plane in which K_I decreases and K_II increases towards the maximum with crack growth. da/dN-ΔK_II relations of the curved cracks growing in shear mode under mixed mode loading agree well with the da/dN-ΔK_II relation of a straight crack under pure mode II loading.     

Crack paths under mixed mode loading

Long fatigue cracks that initially experience mixed mode displacements usually change direction in response to cyclic elastic stresses. Eventually the cracks tend to orient themselves into a pure mode I condition, but the path that they take can be complex and chaotic. In this paper, we report on recent developments in techniques for tracking the crack path as it grows and evaluating the strength of the mixed mode crack tip stress field.     

Elasto-plastic behavior of thermoplastic composite laminates under cyclic loading

An experimental and numerical study of the elasto-plastic behavior of thermoplastic matrix composite laminates under static and cyclic loads is presented. Off-axis and angle ply specimens cut from laminates of poly(ether ether ketone) (PEEK) reinforced with continuous carbon fibers have been tested under cyclic sinusoidal tensile loads and the hysteresis loops have been monitored. A micro mechanical model, which includes a parabolic criteria based on the plastic behavior of the matrix, has been adopted to study the composite non-linear behavior and a correlation between plastic deformation and a strong rise of damping and temperature at high stresses is outlined. Good agreement is shown between theory and experimental results. The mathematical mdoel presented here can be used to predict the visco-elastic-plastic response of the material at high stresses and its influence in the fatigue damage.