Distribution Of Strain Energy Release Rate Research Articles

Mode III fracture of composite laminates with elastic couplings in edge ring crack torsion test

AbstractIn this work, the distribution of the strain energy release rate (SERR) at the crack front of carbon fiber‐reinforced polymer laminates with elastic coupling is analyzed using the edge ring crack torsion (ERCT) test configuration. The SERR at the delamination front is calculated by virtual crack closure technique (VCCT). Elastic coupling laminates, including bending‐extension (BE) and bending‐torsion (BT) ones with different stacking sequences are studied. The effect of two different loading boundary conditions on the SERR distribution of laminates is also investigated. The results demonstrate that the distribution of SERR is significantly affected by the elastic coupling and stacking sequence. In addition, elastic coupling introduces mode I and mode II components in the ERCT configuration. However, their contribution is negligible. In comparison to unidirectional laminates, better uniformity of SERR distribution can be obtained in the BE and BT laminates. Pure mode III fracture without non‐uniformity is achievable by designing the elastic coupling of laminates. The obtained results can provide guidance for the standardization of the ERCT configuration used for the measurement of mode III fracture toughness.

Mode III numerical analysis of composite laminates with elastic couplings in split cantilever beam configuration

This paper presents numerical analysis of the mode III strain energy release rate (SERR, GIII) distributions along delamination front in carbon fiber reinforced plastic (CFRP) and hybrid fiber reinforced plastic (HFRP) laminates exhibiting elastic couplings. The beam models were analyzed by using the split cantilever beam (SCB) tests configuration. Influence of elastic coupling phenomenon on mode III SERR distributions was investigated numerically in Abaqus/CAE software environment by using the virtual crack closure technique (VCCT). In addition, two different boundary conditions (BCs) were considered. Results revealed, that critical strain energy release rates distributions obtained for bending-twisting (BT) and bending-extension (BE) elastically coupled laminates were found to be strongly irregular and skewed which is not desirable in the point of view of experimental determination of mode III fracture toughness. On the other hand, application of different materials compositions in the form of HFRP laminates slightly decreased negative effect of elastic couplings on mode III SERR widthwise distributions but this field have to be more developed and explored.

Mesh size sensitivity analysis for interlaminar fracture of the fiber-reinforced laminated composites

The virtual crack closure technique is a well-known finite element–based numerical method used to simulate fractures and it suits well to both of two-dimensional and three-dimensional interlaminar fracture analysis. In particular, strain energy release rate during a three-dimensional interlaminar fracture of laminated composite materials can successfully be computed using the virtual crack closure technique. However, the element size of a numerical model is an important concern for the success of the computation. The virtual crack closure technique analysis with a finer mesh converges the numerical results to experimental ones although such a model may need excessive modeling and computing times. Since, the finer element size through a crack path causes oscillation of the stresses at the free ends of the model, the plies in the delaminated zone may overlap. To eliminate this problem, the element size for the virtual crack closure technique should be adjusted to ascertain converged yet not oscillating results with an admissible processing time. In this study, mesh size sensitivity of the virtual crack closure technique is widely investigated for mode I and mode II interlaminar fracture analyses of laminated composite material models by considering experimental force and displacement responses of the specimens. Optimum sizes of the finite elements are determined in terms of the force, the displacement, and the strain energy release rate distribution along the width of the model.

A modelling technique for calculating stress intensity factors for structures reinforced by bonded straps. Part II: Validation

In this second part of the two-part paper validation of the 2D FE modelling technique described in the first part is presented for a range of test configurations. Each mechanism that influences crack growth behaviour of strap reinforced structures is modelled for different substrate geometries, strap materials and dimensions in order to test the accuracy and robustness of the methodology. First, calculated through-thickness strain energy release rate distribution is compared with the result of a 3D FE model to validate this 2D model. Second, calculated disbond areas, thermal residual stresses and their redistribution with crack propagation are validated against experimental measurements. Third, influence of geometric nonlinearity and the need to use the alternate analysis method described in part I are demonstrated by examples, and errors generated by not following this analysis rule are given. Finally, using the 2D model calculated stress intensity factors, fatigue crack growth rates and lives are predicted for different specimens, strap materials and applied stress levels and are compared with the experimental tests. Good or acceptable agreement has been achieved for each case.

Redesign of the ECT Test for Mode III Delamination Testing. Part I: Finite Element Analysis

A series of finite element analyses (Part I) and tests (Part II) on various modifications of the edge crack torsion (ECT) test have been conducted in an effort to render the test more suitable for characterizing mode III delamination in laminated composites. To this end, two ECT specimen configurations were considered. The first configuration involves loading the specimen at a single location, and the second configuration involves a symmetric double load point application. Investigations were conducted on the effect of specimen overhang, along the length and width direction, on the inferred strain energy release rate distributions across the delamination front. Stress distributions in the vicinity of the delamination front were used to infer the corresponding modes I, II, and III strain energy release rate distributions. Results indicate the single and double loading configurations exhibiting similar stress distributions along the delamination front. Specimens with short crack lengths and small amounts of overhang yielded the most uniform distribution of mode III loading along the delamination front.

Instability of delaminated composite cylindrical shells under combined axial compression and bending

Abstract Composite cylindrical shells and panels are widely used in aerospace structures. These are often subjected to defects and damage from both in-service and manufacturing events. Delamination is the most important of these defects. This paper deals with the instability analysis of delaminated composite cylindrical shells subject to pure bending and also combined bending and axial compression, using the finite element method. The combined double-layer and single-layer of shell elements are employed, which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the strain energy release rate along the delamination front. The results show that under pure bending, laminated cylindrical shells are more sensitive to the presence of delamination, than they are under pure axial compression. It was also observed that the effects of delamination are more apparent when the composite cylindrical shells are subjected to combined axial compression and bending. In this case, with a slight increase of the applied bending moment, the strain energy release rate distribution on the compressive side of the cylinder changes drastically.

Characterization of Curing Stress Effects on Fracture Behavior of FRP Laminated Composites with Embedded Delaminations

A detailed study on the effect of curing stresses on interlaminar delamination crack growth behavior in fiber-reinforced polymeric (FRP) composites is presented. At a given applied load or displacement, the strain energy release rate distribution along the delamination front with and without considering the effects of curing stresses are compared. In this analysis, results are presented for elliptical delaminations embedded between plies of different orientations in the laminate. A full three-dimensional coupled-field finite element analysis has been conducted to study the delamination crack growth behavior due to curing stress effects. A superposition procedure along with the modified crack closure integral technique based on the concepts of linear elastic fracture mechanics is employed to evaluate the individual modes of strain energy release rates during delamination propagation. It has been observed that the residual thermal stresses developed during the curing stages in manufacturing of FRP laminated composites significantly affect the onset and growth of delamination. The asymmetric behavior of interlaminar fracture energy along the delamination front is found to depend upon the stacking sequence, neighboring ply orientation, thermoelastic anisotropy, and material heterogeneity at the interface of laminated composites.

Closed form solution for strain energy release rate distribution in debonded one-edge free postbuckled composite flanged joints

A closed form model predicting debond growth in composite flanged joints is presented. This model calculates the non-uniform distribution of strain energy release rate ( G) across the crack front. Such a model is useful for assessing the effects of partial debonds in adhesively-bonded joints that are subjected to compressive loads. The model’s accuracy is gauged by comparison of the G profile prediction with finite element analysis (FEA) based virtual crack closure technique (VCCT) calculations. For the woven glass/epoxy joints analyzed, it was found that the closed form model predicted the peak values of G to within 20% of the FEA calculated values when the applied far-field strain ε o was greater than 1.3 times the strain at which the flange first buckles, i.e., the critical buckling strain ε cr. At moderate loads ( ε o < 1.3 ε cr), peak values of G were greatly under-predicted due to the nonlinear FEA predictions of ε cr being lower than the analytical values. Since the amount of strain applied beyond buckling ( ε o − ε cr) drives postbuckling deformation, the FEA predictions for G tend to exceed the closed form values. Physical insight into which material and geometric parameters strongly affect this problem is gained due to the analytical model being presented in closed form. Such expressions are useful in conducting trade-off studies for damage tolerant designs and for making decisions related to maintenance and repair.

Global buckling behaviour and local damage propagation in composite plates with embedded delaminations

Finite element models were developed to study global, local and mixed mode buckling behaviour of composite plates with embedded delaminations under compression. The global modelling results were compared with corresponding experimental results. It is shown that the numerical results for embedded delaminations agree very well with the experimental results, whereas the difference between the results was high for delaminations located at the edge of the plates. It is also shown that at lower loading levels the interaction of global and local buckling is negligible. At higher loading levels the strain energy release rate distribution and the delamination growth potential at the delamination front strongly depend on the shape of the debonded region and the local buckling mode. It was observed that the local buckling mode was highly influenced by the laminate stacking sequence. In the course of global buckling, a parametric study was carried out to investigate the influence of the delamination size, shape and alignment of a series of composite plates.

A shell/3D modeling technique for the analysis of delaminated composite laminates

A shell/3D modeling technique was developed for which a local solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local 3D model and the global structural model which has been meshed with shell finite elements. Double Cantilever Beam, End Notched Flexure, and Single Leg Bending specimens were analyzed first using full 3D finite element models to obtain reference solutions. Mixed mode strain energy release rate distributions were computed using the virtual crack closure technique. The analyses were repeated using the shell/3D technique to study the feasibility for pure mode I, mode II and mixed mode I/II cases. Specimens with a unidirectional layup and with a multidirectional layup were simulated. For a local 3D model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Fracture mechanics analyses for skin-stiffener debonding

Fracture mechanics analyses on two debond configurations are presented. The debond configurations analyzed were flange-skin strip and skin-stiffener configurations. Three-dimensional (3D) finite element analyses were performed using 20 noded isoparametric elements to model the debond configurations. Two methods that use the virtual crack closure technique (VCCT) were used to evaluate the strain energy release rate distributions across the debond front. In the first method the strain energy release rates ( G-values) are calculated at the center of each element that are on the crack plane and along the crack front. In the second method the strain energy release rates are calculated at all the corner nodes of the elements that are on the crack plane and along the crack front. Both methods gave nearly identical G-distributions for the debond configurations studied. The 3D G-distributions obtained by these methods were compared to plane strain and shell analyses results from the literature for the flange-skin strip configuration. Good agreement was obtained; the plane strain results are ca 7% higher while the shell analysis results are ca 3% higher than the present 3D results. Analyses of the skin-stiffener configuration showed the G-distributions converged rapidly as the number of layers used to model the stiffener is increased. These convergence studies showed that there is a boundary layer effect near the ends of the debond and there is an elevation in the G-values in the region of the blade (web) of the stiffener. The analysis also showed that mode-II is the dominant mode for this debond configuration.

Strain energy release rate distributions for double cantilever beam specimens

A 24-ply composite double cantilever-beam specimen under mode I (opening) loading has been analyzed by a 3D FEM code that calculated along a straight delamination starter for several different specimen materials. An isotropic specimen was found to have a strain-energy release rate distribution which varied along its delamination front due to the boundary-layer effect and another effect associated with the anticlastic curvature of the bent specimen arms. A 0-deg graphite-reinforced epoxy specimen had a nearly-uniform strain-energy release rate distribution which dropped only near the edge, due to the boundary-layer effect, and a +/- 45-deg graphite/epoxy specimen exhibited a pronounced strain-energy release rate variation across the specimen width.

Modeling of delamination in composite laminates using a layer-wise plate theory

The layer-wise laminate theory of Reddy is extended to account for multiple delaminations between layers, and the associated computational model is developed. Delaminations between layers of composite plates are modeled by jump discontinuity conditions at the interfaces. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational model presented is validated through several numerical examples.

Predicted and Observed Effects of Stacking Sequence and Delamination Size on Instability Related Delamination Growth

A three-dimensional, geometrically nonlinear finite element analysis was used to calculate strain-energy release rate distributions for several laminates which exhibited instability-related delamination growth. Two stacking sequences, (0/90/90/0)6 and (90/0/0/90)6 were considered. The specimens were fabricated with a double layer of 0.013 mm Kapton film located between the fourth and fifth plies, thereby simulating a delamination. Initial delamination sizes were 30, 40, or 60 mm in diameter. The static strain corresponding to delamination growth was determined experimentally. Comparison of the analytical and experimental results indicated that delamination growth was governed by the magnitude of GI.