Strain Energy Release Rate Analysis Research Articles

Delamination fracture in a functionally graded multilayered beam with material nonlinearity

The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress–strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity.

Strain-Energy Release Rate Analysis of Adhesive-Bonded Composite Joints with Prescribed Interlaminar Crack

Thesis [M.S] - Wichita State University, College of Engineering, Dept. of Aerospace Engineering

Curvature Effect on Fracture Toughness of Cracked Cylindrical Shells Bonded with Patches

Adhesively bonded patch repair has been widely used as an efficient and economical method to extend the service life of cracked structural components. Most of the currently available analysis methods and empirical databases for composite bonded patch repair to flat structures are computationally efficient and easy to use. However, the current knowledge on composite bonded repair for flat structures cannot be directly applied to curved repairs. A novel adhesive element developed by the authors in conjunction with a shell element is employed to investigate the fracture toughness at the crack tip of a cracked cylindrical shell bonded with a composite patch. To validate the present finite element model for curved composite patch repairs, the stress intensity factors in a flat composite patch repair are first computed by the strain energy release rate analysis method and compared with those available in the literature. For the curved patch repairs, a full three-dimensional finite element analysis is also conducted to validate the proposed numerical model. Some selected numerical examples are given to demonstrate the effect of curvature on the fracture toughness of a cracked cylindrical shell bonded with a composite patch subjected to different types of loading.

Three-Dimensional Effect in the Prediction of Flange Delamination in Composite Skin-Stringer Pull-off Specimens

Three-dimensional finite element modeling was used to analyze the delamination between the stiffener flange and the skin of a typical pull-off specimen representing a section of a stiffened skin panel. The finite element analysis results were used to calculate the total strain energy release rate and its Mode I, Mode II, and Mode III components along the delamination front through the width of the pull-off specimen. Three-dimensional modeling makes it possible to represent ply-by-ply lamina properties in the model. However, the ply-by-ply approach should not be used for highly angle ply laminates because of the strong transverse effect from adjacent plies. A smeared properties approach is more robust for the strain energy release rate analysis of delamination between ±45-degree angle ply laminates. The three-dimensional analysis indicates that delamination failure between the stiffener flange and the skin is dominated by Mode I and Mode II delamination modes. The three-dimensional analysis predicts delamination growth from the interior of the pull-off specimen width, and higher pull-off load is required to grow the delamination close to the free edges. The delamination initiation load along the interior of the pull-off specimen width does not change with the change of the width of the pull-off specimen. However, the wider specimen has stronger free edge effects than the narrower specimen. The lay-up of the skin and the flange can have significant effect on the delamination initiation load. Stiffening the skin and maintaining the compliant flange will increase the delamination initiation load.

On the intersonic crack propagation in an orthotropic medium

Motivaded by recent theoretical studies the elastodynamic response of an orthotropic material with a semi-infinite line crack, which propagates intersonically. is revisited through an approach which differs from those used in previous studies. The near tip stress and displacement fields are obtained for Mode I and Mode II of steady state crack propagation. The strain energy release rate analysis confirms that the Mode I is physically impossible due to the order of stress singularity, which is larger then one half. For Model II the order of stress is less than one half and it is shown that a steady state intersonic propagation is allowed only for a particular crack tip velocity which is a function of the material orthotropy.

Indentation-induced buckling of organic coatings part I: theory and analysis

The impact-induced buckling and delamination of a thin coating was analysed for the purpose of predicting the amount of coating removed when a single particle was launched, at a given velocity, against a coated substrate. A novel post-buckling analysis is presented in which the coating is modelled as a clamped disk prevented from buckling at an arbitrarily set inner radius, due to the presence of the indenting particle. A method for calculating the arrest strain energy release rate and mode mix of interfacial delamination cracks, based on the coupling of the presented buckling analysis with an existing strain energy release rate analysis [1] is then presented. A method to estimate the critical interfacial shear stress at crack initiation is also outlined. An accompanying paper [2] compares experimental results with the results of this analysis, and shows how the results can be used in the context of blast cleaning.

Modelling the effect of cracks on interlaminar shear strength

Short-beam shear tests of unidirectional carbon fibre/epoxy are analysed assuming shear deformations to be concentrated at the resin-rich interfacial layers between plies. A two-dimensional finite element model is used with linear elastic continuum elements to represent the plies, and non-linear springs to model the interfaces. This approach is shown to be satisfactory provided that there is a sufficiently large number of plies. The effect of cracks of varying length and at different positions is investigated. Linear elastic strain energy release rate analysis indicates that there is not sufficient energy for small cracks to propagate. In contrast, the non-linear interface modelling approach predicts that small cracks can have a significant effect on interlaminar shear strength. Excellent correlation is obtained with experimental data, and it shown that the presence of small defects is a plausible explanation for the scatter in results commonly observed in short-beam shear tests.

Failure of tapered composites under static and fatigue tension loading

One glass fiber-epoxy and two carbon fiber-epoxy rapidly tapered sections with dropped 0- and ±45-deg plies have been designed, manufactured, and tested. Under static loading, close to net section tensile strength was achieved. The glass fiber taper also achieved net section strength under tension fatigue loading, but the carbon fiber tapers showed a significant reduction in fatigue strength due to delamination from the ends of the terminating 0-deg plies. The most significant factor controlling strength is the number of plies dropped together. Unidirectional dropped plies are much more susceptible to delamination than ±45-deg plies. Satisfactory strength predictions can be made for both static and fatigue tension loading based on net section stresses and a simple equation for the strain energy release rate. This approach looks promising as the basis for a general method for designing tapered composites. APERED sections involving the progressive dropping of plies are prone to delamination, especially under fatigue loading. Such tapered sections are very commonly used to achieve changes in thickness. A typical example is a helicopter rotor blade, where increased thickness is necessary near the root. Normally a short tapered transition region is desirable. However, due to the lack of reliable methods for predicting delamination, a very gradual taper is usually used. A number of authors have investigated static strength of tapered laminates.18 However, there is no consensus on how to predict failure. Various approaches have been proposed based on maximum stresses,2 stresses averaged over a distance,6 stresses evaluated at a characteristic distance,8 and strain energy release rates.5 Several investigations on tension fatigue of tapered specimens have been published^11 The problem of predicting fatigue strength has not received very much attention, although in the latter study a method was proposed for predicting onset of unstable delamination based on strain energy release rate analysis.11 A program of research has been undertaken at Bristol University to investigate failure in tapered composites under static and fatigue loading. A series of tests on very simple symmetric specimens have enabled failure mechanisms to be studied.12 Much of the work has been on unidirectional material, avoiding some of the potential problems with edge effects. It has been found that the dominant failure mechanism for these specimens is delamination initiating above and below the ends of the terminating plies and propagating into the thick section along the interface between continuous and discontinuous plies. The results have indicated that the most important parameter affecting failure is the strain energy release rate associated with the terminating plies. Based on this work, a method has been proposed for predicting static strength of tapered specimens. A simple equation is used for calculating the strain energy release rate. This is then compared with a value of fracture energy deduced from a tension test on a constant thickness unidirectional specimen with the central plies cut across the complete width. Satisfactory correlation has been obtained for tapered unidirectional glass fiber-epoxy specimens under static tension and compression loading.13

Strain-Energy Release Rate Analysis of Plates with Postbuckled Delaminations

Delamination growth due to local buckling of a delamination was studied. Delamination growth was assumed to be related to the total strain-energy release rate, G. In order to calculate the distribution of G along the delamination front, a virtual crack closure technique was developed which is suitable for use with plate analysis. A check of the technique indicated that it is accurate. For square and rectangular delaminations, there is a large variation of G along the delamination front. Hence, self-similar growth is not ex pected. Whether a delamination grows in the load direction or perpendicular to the load direction was found to depend on the current delamination aspect ratio, the strain level, and the absolute size of the delamination.

Strain Energy Release Rate Analysis of the End-Notched Flexure Specimen Using the Finite-Element Method

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

Residual Thermal and Moisture Influences on the Strain Energy Release Rate Analysis of Edge Delamination

A laminated plate theory analysis is developed to calculate the strain energy release rate associated with edge delamination growth in a composite laminate. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. The strain energy release rate, G, increased when residual thermal effects were combined with applied mechanical strains, but then decreased when increasing moisture content was included. A quasi-three-dimensional finite element analysis indicated identical trends and demonstrated these same trends for the individual strain energy release rate components, G sub I and G sub II, associated with interlaminar tension and shear. An experimental study indicated that for T300/5208 graphite-epoxy composites, the inclusion of residual thermal and moisture stresses did not significantly alter the calculation of interlaminar fracture toughness from strain energy release rate analysis of edge delamination data taken at room temperature, ambient conditions.