Barry D. Davidson

Evaluation of the accuracy of the four-point bend end-notched flexure test for mode II delamination toughness determination

Results are presented from an experimental study to investigate the accuracy of the four-point bend end-notched flexure (4ENF) test for the determination of mode II delamination toughness. In previous studies, 4ENF tests have yielded higher delamination toughnesses than the more commonly used three-point bend end-notched flexure (ENF) test. In a recent finite-element study, it was found that the higher toughnesses found by the 4ENF test cannot fully be attributed to frictional effects. This current study was performed in order to examine if the difference between ENF and 4ENF results is due to current methods used to determine crack length and compliance during a 4ENF test. It was found that if these two parameters are measured accurately then the 4ENF test yields toughnesses similar to those obtained from ENF testing.

An Analytical Investigation of Delamination Front Curvature in Double Cantilever Beam Specimens

An analytical investigation is conducted to determine the shape of a growing delamination and the distribution of the energy release rate along the delamination front in a laminated composite double cantilever beam specimen. Distributions of the energy release rate for specimens with straight delamination fronts and delamination front con tours for delaminations whose growth is governed by the fracture criterion that G = Gc at all points are predicted as a function of material properties and delamination length. The predicted delamination front contours are utilized to ascertain the effect of the chang ing shape of the delamination front on the value of the critical strain energy release rate as computed from double cantilever beam fracture toughness test data.

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.

Life Prediction Methodology for Composite Structures. Part II—Spectrum Fatigue

A previously developed model for predicting the life of composite structures under constant amplitude and two-stress level fatigue loadings is extended and applied to structures subjected to randomly-ordered loading spectra. The model is phenomenological and a limited amount of experimental data is required for its characterization. For uniaxially loaded laminates, this consists of static tension and compression strength distributions, S-N curves based on constant amplitude fatigue life distributions for two-to-three stress ratios, and a limited amount of two-stress level fatigue test results. The model is verified by comparing predicted fatigue life distributions to experimentally observed fatigue life data for a variety of laminates and load spectrums. Good correlation between theory and experiment is obtained for all loadings and laminates studied.

Effects of Mode Ratio, Ply Orientation and Precracking on the Delamination Toughness of a Laminated Composite

Results are presented from an investigation of the effects of mode ratio, interfacial ply orientation and precracking on the delamination toughness of a graphite/ epoxy composite. Delamination toughness tests were performed on specimens that exhibited growth at 00/00, 15°/15°, 15°/- 150, 30°/30° and 30°/-30° interfaces. Three mode ratios were considered. The double cantilever beam test was utilized for pure mode I, the end-notched flexure test was used for pure mode II, and the symmetrically delaminated single leg bending test was used for a mixed-mode condition, G,,IG, equal to approximately 0.4. All five interfaces were tested in both precracked and non-precracked conditions at each mode ratio. Also, for the 30°/30° and 30°/- 30° interfaces, two different stacking sequences were used to assess the effect of remote ply orientation on the perceived mode I and mode II toughness. For any mode ratio and interface angle, it was found that precracked toughness values were always lower than the corresponding nonprecracked result. No other consistent trends were observed in all of the data. For the mode I tests, the 30/30 interface exhibited the lowest toughness, for the mixed-mode tests, the 0/0 interface produced a minimum toughness, and for mode II no significant effect of interface angle on toughness was observed. These results are interpreted with the aid of recent three dimensional finite element analyses for energy release rate distributions along the delamination front for the different stacking sequences and test geometries. The accuracy of various data reduction techniques are also evaluated, and suggestions are made for future testing.

Effect of stacking sequence on energy release rate distributions in multidirectional dcb and enf specimens

Abstract Results are presented from a theoretical investigation of the effect of stacking sequence on energy release rate distributions in laminated composite double cantilever beam and end-notched flexure test specimens. Eight different stacking sequences are investigated; four of these will result in delamination growth at a 30°/30° interface and four will result in growth at a 30°/ — 30° interface. Each set of four sequences is chosen to exhibit varying amounts of coupling between the primary bending curvature and either the transverse bending curvature or the twist curvature. For a set number of plies, sequences that minimize one type of coupling will have increased coupling of the other type. The sequences chosen for study span a range of possible choices for practical use. Three-dimensional finite element analyses are used to obtain the total energy release rate and its distribution along an initially straight delamination front for the eight sequences under DCB and ENF loadings. As expected, for the DCB loading, peak energy release rates occur near the center of the specimens width, whereas for the ENF loading the peak occurs at one or both edges. It is shown that larger bending-twisting coupling results in larger asymmetries in the energy release rate, whereas larger longitudinal-transverse bending coupling results in larger peak values. Practical application to DCB and ENF testing is discussed.

Three-dimensional analysis of center-delaminated unidirectional and multidirectional single-leg bending specimens

Results are presented from a theoretical investigation of the effects of stacking sequence on the energy release rate in laminated composite single-leg bending test specimens. Deflections and energy release rates of unidirectional and multidirectional single-leg bending specimens are obtained by classical laminated plate theory based methods and by three-dimensional finite element analyses. It is shown that the distribution of energy release rate varies across the front of an initially straight delamination and that, regardless of stacking sequence, all three energy release rate components will occur. The percentage of the mode III energy release rate is generally small. Its relative magnitude, as well as the differences between the maximum and minimum values of all the energy release rate components, are shown to correlate with a non-dimensional ratio comprised of the flexural rigidities of the specimen. The classical plate theory based methods are shown to predict accurately both the total energy release rate and the average mode ratio, i.e. with respect to the full width of the specimen, for all stacking sequences evaluated.

Effect of Finite Width on Deflection and Energy Release Rate of an Orthotropic Double Cantilever Specimen

The problem of an orthotropic cantilevered plate subjected to a uniformly distributed end load is solved by the Rayleigh-Ritz energy method. The result is applied to laminated composite, double cantilevered specimens to estimate the effect of crack tip constraint on the transverse curvature, deflection and energy release rate. The solution is also utilized to determine finite width correction factors for fracture energy characterization tests in which neither plane stress nor plane strain conditions apply.

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.

Three Dimensional Analysis and Resulting Design Recommendations for Unidirectional and Multidirectional End-Notched Flexure Tests

Results are presented from a theoretical investigation of the effects of stacking sequence on the energy release rate in laminated composite end-notched flexure test specimens. Deflections and energy release rates of unidirectional and multidirectional ENF specimens are obtained by classical laminated plate theory, shear deformable plate theory, and three dimensional finite element analyses. It is shown that the distribution of energy release rate varies across the front of an initially straight delamination. The percentage of mode II and mode III energy release rates for the specimen, as well as the local peak values of the mode II, mode III and total energy release rates that occur at the specimens free edges are shown to correlate with a nondimensional ratio comprised of the specimens flexural rigidities. The results of the study are used as a basis for a proposed “ENF test design procedure” that may be used for the determination of appropriate specimen stacking sequences and test geometries for studying delamination growth at interfaces between plies at various orientations. The test design procedure minimizes the contributions to the energy release rate from residual thermal stresses, geometric nonlinearities, local mode II concentrations at the specimens free edges and local mode III effects.