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.     

Effect of clamping force on the delamination onset and growth in bolted composite laminates

Clamping force is a key element that alters the mechanism and sequence of failure in bolted joints of composite laminates. The mode of failure in bolted joints can be controlled by geometrical parameters and the preferred fail safe mode of failure is ‘bearing’ which generally consists of matrix cracks, delamination and fibre microbuckling. Three-dimensional (3-D) pinned (without clamping force) and bolted (1 kN clamping force) joint models were developed in [0/90]_s carbon fibre reinforced plastic (CFRP) laminates to show the clamping force effect on the onset and growth of delamination. It is shown that delamination was resulted from the shear stress components (Mode II & III) at the interface and the contribution of the out-of-plane component (Mode I - opening), so the clamping force, was negligible without modelling the in-plane failure modes and their coupling with delamination, which will be considered in future work.     

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.     

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.     

Characterization of damage onset in glass-ceramic matrix composite angle-ply laminates

The tensile mechanical properties of a series of model [0/θ/0] glass-ceramic matrix composite angle-ply laminates have been measured at room temperature in an attempt to characterize the onset of damage in this class of material as a function of fibre orientation. The material selected for this study was a silicon carbide fibre-reinforced calcium aluminosilicate composite. The experimentally determined values of composite elastic modulus, strength and first ply failure stress have been compared with those predicted from classical laminate theory. Work carried out to date has shown that at high angles of θ, the damage onset of [0/θ/0] laminates is accurately predicted by the Tsai-Hill first ply failure stress whilst at low angles of θ the onset of damage is in reasonable agreement with that predicted by the Aveston-Cooper-Kelly model for multiple fracture (with the Tsai-Hill failure criterion predicting the ultimate strength of the composite). However, these models give no account of the mechanisms by which failure occurs and assume well-defined and single-valued failure strengths. In reality, glass-ceramic matrices have a distribution of strengths as a result of the inherent flaws within them and an attempt to quantify this has been made by mechanical and structural evaluation of the monolithic matrix material.     

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 delamination growth rates and thresholds of composite laminates under mixed mode loading

The effect of delamination resistance on fatigue crack growth behavior of composite laminates is studied. The strain energy release rate normalized to fatigue delamination resistance (G_cf) is proposed as a controlling parameter to evaluate the fatigue crack growth rates and thresholds. Compared to previously developed G_cf determination method, the compliance approach presented in this paper shows obvious advantages, such as no interruption to the fatigue crack growth and independence on the specimen dimensions. Based on this approach, the fatigue delamination growth rates and thresholds of carbon/bismaleimide composite laminates under mixed I/II mode loadings are determined experimentally.     

Experimental study on delamination migration in composite laminates

The transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, was investigated experimentally. The test method used promotes delamination growth initially along a 0/θ ply interface, which eventually migrates to a neighbouring θ/0 ply interface. Specimens with θ = 60° and 75° were tested. Migration occurs in two main stages: (1) the initial 0/θ interface delamination turns, transforming into intraply cracks that grow through the θ plies; this process occurs at multiple locations across the width of a specimen, (2) one or more of these cracks growing through the θ plies reaches and turns into the θ/0 ply interface, where it continues to grow as a delamination. A correlation was established between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses.Overall, the experiments provide insight into the key mechanisms that govern delamination growth and migration.     

Cohesive modeling of delamination in Z-pin reinforced composite laminates

The mode I interlaminar fracture in Z-pin reinforced composite laminates is modeled using a cohesive volumetric finite element (CVFE) scheme. The test configuration used in this study is a Z-pin reinforced double cantilever beam specimen. A bilinear rate-independent but damage-dependent cohesive traction–separation law is adopted to model the fracture of the unreinforced composite and discrete nonlinear spring elements to represent the effect of the Z-pins. The delamination toughness and failure strength of the Z-pin reinforced composites are determined by a detailed comparison study of the numerical modeling results with experimental data. To further reduce the computational effort, we introduce an equivalent distributed cohesive model as a substitute for the discrete nonlinear spring representation of the Z-pins. The cohesive model is implemented on various test problems with varying failure parameters and for varying spatial Z-pin reinforcement configurations showing good agreement with the experimental results.     

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 °.     

Stress intensity factors as the fracture parameters for delamination crack growth in composite laminates

A “mutual integral” approach is used to calculate the mixed-mode stress intensity factors for a free-edge delamination crack in a laminate under tensile loading conditions. This “mutual integral” approach, for generalized plane strain conditions, is based on the application of the path-independent J integral to a linear combination of three solutions: one, the problem of the laminate to be solved using the quasi 3-D finite element method, the second, an “auxiliary” solution with a known asymptotic singular solution, and the third, the particular solution due to the out-of-plane loading. A comparison with the exact solutions is made to determine the accuracy and efficiency of this numerical method. With this “mutual integral” approach, it was found that the calculated mixed-mode stress intensity factors of the free-edge delamination crack remain relatively constant as the crack propagates into the laminate. It was also found that the fracture criterion based on the mixed-mode stress intensity factors is more consistent with the experimental observations than the criterion based on the total energy release rate, and hence demonstrates the importance of the ability to calculate each individual component of the stress intensity factors. Furthermore, it was found that the fracture toughness measurements from double cantilever beam specimens can be used directly to predict the onset of delamination crack growth between two dissimilar laminae. Using these fracture toughness measurements from the double cantilever beam specimens, some examples are given to show that the fracture criterion based on the mixed-mode stress intensity factors can accurately predict the failure load for various laminates under tensile loading conditions.     

Prediction of the onset of mode III delamination in carbon-epoxy laminates

The aim of this paper is to determine a method for accurately predicting the onset of mode III delamination in multi-layered structures. A software called DEILAM and a model of plates called M4-5N are used to evaluate the stresses in the laminate. This model has already been validated [Mechanics of Materials 34 (2002) 217]; it yields finite values and a delamination onset criterion involving the maximum value of the interfacial stresses can be thus considered. One single parameter appears in the criterion and is identified by means of tensile tests. The criterion obtained is able to reproduce thickness effects. Two application examples with two materials are considered and in both examples the theoretical predictions are very accurate.     

吸湿后复合材料层合板快速加热分层扩展数值模拟

为研究复合材料层合板吸湿后的分层现象,首先建立了吸湿后复合材料层合板快速加热导致分层损伤的有限元模型,并对ABAQUS有限元软件进行二次开发,通过UAMP子程序模拟吸湿后复合材料快速加热时水分汽化引起的局部高压载荷作用下层合板分层扩展与载荷施加过程;然后,采用该模型预测了饱和吸湿T650-35/HFPE-II-52碳纤维聚酰亚胺复合材料层合板快速加热至310 ℃时产生的分层现象,并将数值模拟与文献实验结果对比;最后,运用该模型分析了树脂吸湿量和富脂区树脂聚集体积对层合板分层损伤面积的影响。结果表明:建立的有限元模型有效;快速加热后,层合板的分层损伤面积随树脂吸湿量的增加而增加;当富脂区树脂聚集体积较小时,其对层合板快速加热后分层损伤面积影响较小,但当富脂区树脂聚集体积增加到一定值后,层合板分层损伤面积随富脂区树脂聚集体积的增加而显著增加。所得结论表明,使用ABAQUS的UAMP子程序建立的有限元模型可以有效分析吸湿后复合材料层合板快速加热导致的分层现象。      

Experimental investigation of delamination buckling of stitched composite laminates

In the current investigation, effects of through-the-thickness stitching with two different types of aramid threads, Kevlar^® and Twaron^® threads, on the buckling loads of delaminated glass/epoxy composite laminates are studied. Buckling loads are predicted based on the Southwell, Vertical displacement and Membrane strain plot methods by using the experimental data. From the Southwell, Vertical displacement and Membrane strain plot methods it is observed that stitching either by Kevlar^® or Twaron^® threads is effective in improving the buckling strength of glass/epoxy composite laminates when the delamination length is greater than 0.5L, L being the length of the laminate. For long delaminations, Kevlar^® stitched glass/epoxy composite laminate is best in retaining its buckling strength when re-loading is done. Southwell plot method tends to overestimate the buckling loads as the data obtained from this method are influenced by the breakages in the glass/epoxy composite laminate buckling test specimens.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

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.     

Prediction of impact induced penetration and delamination in thick composite laminates

A static punch curve was used as the ‘structural constitutive model’ to capture the highly nonlinear behavior of the laminate in the penetration process of thick laminates. A penetration model based on a ring element was first used to simulate the static punch curve. The model was then used to predict the dynamic penetration process of large panels using the information obtained from the static punch curve of a smaller specimen. The model was shown to predict the penetration process for short and long projectiles. The area of the target that becomes delaminated during impact was shown to increase when the impact velocity was increased until the ballistic limit, beyond which the delamination area decreases with an increase in impact velocity. This phenomenon and the area that is delaminated for different size targets at different impact velocities were accurately predicted by the ring element model in conjunction with a critical shear strain criterion.     

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.