Crack Tip Element Analysis Research Articles

Predicting buckling-driven delamination propagation in composite laminates: An analytical modelling approach

Robust and efficient predictions of buckling-driven delamination propagation, enabled by a novel analytical modelling approach, are presented. The model considers full mechanical coupling (extension-shear, extension-bend, extension-twist/shear-bend and bend-twist), contact and mode-mixity and thus significantly enhances the capabilities of current analytical approaches. A problem description in cylindrical coordinates enables the evaluation of the energy release rate along the delamination boundary. The model uses an energy formalism to determine the post-buckling deformation and a crack-tip element analysis employing force and moment resultants acting on the delamination boundary to determine the energy release rate. Composite panels with circular thin-film delaminations and various multi-directional stacking sequences are investigated for in-plane compressive loading. Predictions of applied strains causing delamination growth, i.e. threshold strain, show good agreement with published experimental data and 3D finite element analysis. A parametric study varying the ratio of delamination size to depth is performed. Based on the findings obtained, governing deformation characteristics of buckling-driven delamination growth are identified and insight into damage tolerant design of composite laminates is obtained, which is of particular interest for compression after impact (CAI) strength of composite structures.

Quasi-Three-Dimensional Crack Tip Element Analysis for Evaluation of Total Energy Release Rate in Composite Laminates

An analytical quasi-three-dimensional crack tip element model is developed to provide a quick assessment of the delamination behavior for composite laminates. A closed-form solution for the average total strain energy release rate is obtained by taking into consideration of all the displacement components defined in the classical laminated plate theory. By means of numerical experiments, it is shown that the presented method can predict the average total strain energy release rates with satisfactory accuracy for a relatively large variety of composite layups under opening and in-plane-shearing loading conditions. It indicates that the influence of out-of-plane transverse displacements on the total energy release rate can be significant for certain type of layups even under in-plane loading conditions. Furthermore, an orthotropic parameter is introduced to represent the influence of out-of-plane transverse effects.

Applicability of the crack tip element analysis for damage prediction of composite T-joints

The expanding application of polymeric composite materials in the Aerospace industry has led to the extension of its application to other industries such as the marine industry. A typical joint between the hull and bulkhead used in a monocoque structure is known as a T-joint. It consists of composite overlaminates over a shaped fillet to allow the transmission of direct and membrane shear stresses. The CTE (crack tip element) method offers the capability to provide accurate results with minimum computational resources. It is also an excellent damage prediction tool for composite laminates where oscillatory singularity exists at the crack tip. This paper describes the application of the CTE method for damage prediction of the T-joint. Issues involved in the current modeling approach and recommended solutions are discussed.

A unified approach to quantify the role of friction in beam-type specimens for the measurement of mode II delamination resistance of fibre-reinforced polymers

This paper presents an approach that captures the effect of frictional force in beam-type specimens that are used for delamination tests in shear mode (mode II), including end-notched flexure (ENF), end-loaded-split (ELS), 4-point bend ENF (4ENF) and over-notched-flexure (ONF) tests. The approach is based on crack tip element analysis, and produces a single parameter that quantifies the role of the frictional force on the energy release rate for delamination. The parameter is a combination of the coefficient of friction of the contact surfaces and dimensions of specimens used in the tests. Accuracy of the parameter for quantifying the frictional force effect is evaluated by comparing the prediction with that based on finite element modeling. The comparison shows excellent agreement. Therefore, the study concludes that the parameter provides an accurate measure of the frictional force effect on the energy release rate for delamination in the beam-type specimens.

Accuracy assessment of a three-dimensional, crack tip element based approach for predicting delamination growth in stiffened-skin geometries

Experimental observations of delamination growth in two stiffened-skin geometries are compared to predictions made using a three-dimensional crack tip element based approach. Each geometry consists of a six-ply graphite/epoxy skin co-cured to a six-ply, hat-shaped stiffener containing a preimplanted teflon delamination between the skin and stiffener at the stiffener termination point. One stiffened-skin geometry was loaded in three-point bending and the other had in-plane tension loads applied to the skin. To predict delamination growth, a three-dimensional crack tip element analysis was first performed on each geometry in order to determine the total energy release rate, G, as well as its mode I, II and III components, G I, G II and G III, respectively. These results were used to define a mode mix at each point along the delamination front, G s/G, where G s=G II + G III. To obtain the delamination toughness, G c, it was assumed that G c exhibits the same dependence on G s/G as on GII/G, where the results for G c versus G II/G were taken from an earlier experimental study. Next, a comparison of the energy release rate to the toughness at each position along the delamination front was performed, and these results were scaled appropriately in order to predict the sequence of loads and corresponding locations at which the delamination will advance. The predictions were then compared to experimental results that included c-scan images of the test specimens taken at each increment of observed growth, and very good quantitative and qualitative correlations were obtained for both geometries. These results indicate the practicality of, and considerable computational savings that may be achieved by, employing crack tip element analyses for delamination growth predictions in realistic structural geometries.

Evaluation of energy release rate-based approaches for predicting delamination growth in laminated composites

A variety of energy release rate-based approaches are evaluated for their accuracy in predicting delamination growth in unidirectional and multidirectional laminated composites. To this end, a large number of unidirectional and multidirectional laminates were tested in different bending and tension configurations. In all cases, the critical energy release rate was determined from the tests in the most accurate way possible, such as by compliance calibration or the area method of data reduction. The mode mix from the tests, however, was determined by a variety of different approaches. These data were then examined to determine whether any of the approaches yielded the result that toughness was a single-valued function of mode mix. That is, for an approach to have accurate predictive capabilities, different test geometries that are predicted to be at the same mode mix must display the same toughness. It was found that variously proposed singular field-based mode mix definitions, such as the β=0 approach or basing energy release rate components on a finite amount of crack extension, had relatively poor predictive capabilities. Conversely, an approach that used a previously developed crack tip element analysis and which decomposed the total energy release rate into non-classical components was found to have excellent predictive capabilities. It is postulated that this approach is more appropriate for many present-day laminated composites.

An unsymmetric double cantilever beam test for interfacial fracture toughness determination

An unsymmetric double cantilever beam test is described and its suitability for the determination of interfacial fracture toughness is evaluated. The test specimen consists of a beam type geometry comprised of two materials, one ‘top’ and one ‘bottom’, with a crack at one end along the bimaterial interface. The specimen is loaded in a splitting fashion similar to that of a conventional double cantilever beam test. Due to the dissimilar in-plane and out-of-plane deformations of the two legs, the load vs deflection response of the specimen is found to be nonlinear. A nonlinear plate theory is used to predict the deformations of the specimen, and these results are used in a crack tip element analysis to determine energy release rate and mode mixity. The analytical predictions are verified by comparisons to results from two-dimensional, geometrically nonlinear finite element continuum analyses for a variety of typical materials and test geometries. It is shown that, by varying the relative thicknesses of the two materials, the unsymmetric double cantilever beam test can be used on most bimaterial pairs to determine interfacial fracture toughness over a reasonably wide range of mode mixities.

An efficient procedure for determining mixed-mode energy release rates in practical problems of delamination

A computationally efficient procedure is presented for the prediction of mixed-mode strain energy release rates in practical problems of delamination. In this procedure, an analytical crack tip element analysis is used for the determination of all singular field quantities. By comparison with two- and three-dimensional finite element results, the procedure is shown to be accurate for mixed-mode problems where mode I, mode II and/or mode III crack tip singularities are present. The procedure is applicable for those cases where a near-tip inverse-square-root singularity exists, as well as those where an oscillatory singularity exists. For these latter cases, an alternative approach to using oscillatory field quantities to characterize crack advance is suggested.

A single leg bending test for interfacial fracture toughness determination

A single leg bending test is described and its suitability for interfacial fracture toughness testing is evaluated. The test specimen consists of a beam-type geometry comprised of two materials, one ‘top’ and one ‘bottom’, with a split at one end along the bimaterial interface. A portion of the bottom material in the cracked section of the beam is removed and the geometry is loaded in three-point bending. Thus, the reaction force of the support at the cracked end is transmitted only into the material comprising the top portion of the beam. The test is analyzed by a crack tip element analysis and the resulting expressions for energy release rate and mode mixity are verified by comparison with finite element results. It is shown that, by varying the thicknesses of the two materials, the single leg bending test can be used to determine the fracture toughness of most bimaterial interfaces over a reasonably wide range of mode mixities.

An Analytical Crack-Tip Element for Layered Elastic Structures

A previously developed linear elastic crack-tip element analysis is reviewed briefly, and then extended and refined for practical applications. The element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for delamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a “mode mix parameter,” Ω, as obtained from a separate continuum analysis is necessary to complete the mode mix decomposition. This parameter depends upon the elastic and geometrical properties of the materials above and below the crack plane, but not on the loading. A relatively simple finite element technique for determining the mode-mix parameter is presented and convergence in terms of mesh refinement is studied. Specific values of Ω are also presented for a large number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, an approach is described which allows a unique, physically meaningful value of fracture mode ratio to be defined. This approach is shown to provide predictions of crack growth between dissimilar homogeneous materials that are equivalent to those obtained from the oscillatory field solution. Application of the approach to delamination in fiber-reinforced laminated composites is also discussed.

Effect of stretching—shearing coupling on instability-related delamination growth

Results are presented from a combined theoretical and experimental investigation into the effect of stretching—shearing coupling on the buckling and growth of near-surface delaminated regions. Honeycomb sandwich laminates with graphite/epoxy face sheets containing preimplanted, through-width delaminations were tested in compression. Two layups were tested. Each layup contained delaminated regions with identical in-plane and flexural moduli; however, one layup exhibited stretching—shearing coupling, whereas the other did not. Delamination buckling was predicted using a cylindrical buckling analysis, and energy release rates and fracture mode ratios were obtained by a crack tip element analysis. Delamination growth was predicted using a linear, mixed-mode delamination growth law. Significantly different delamination buckling and growth strains were predicted for the two layups. Predicted delamination buckling and growth strains correlated well with experimental results.

Analysis of instability-related delamination growth using a crack tip element

One-dimensional delamination buckling and growth is analyzed using closed form cylindrical buckling and crack tip element analyses. A cylindrical buckling analysis is used to determine the strains, curvatures, deflections, forces, and moments in a buckled region bounded by the laminate free surface and a near-surface delamination. These results are used as input into a linear crack tip element analysis to obtain the total energy release rate and individual mode I and mode II components. Geometric nonlinearities are accounted for through the loading on the crack tip element. Total energy release rate and fracture mode ratio as found by this new technique are shown to agree with nonlinear finite element results.