Delamination is a critical failure mode in composite structures, often driven by complex cyclic loading in multidirectional (MD) laminates. This study aims to characterize the influence of mode mixity, cyclic displacement ratios (Rd), and mode coupling on delamination growth in dissimilar material interfaces. To achieve this, two MD material systems, wet-layup and prepreg with initial delaminations along 0 degrees// +/- 45 degrees UD and woven plies and along 0 degrees/90 degrees// +/- 45 degrees woven plies, respectively, were evaluated using mixed-mode end-loaded split (MMELS) beam specimens. Fatigue tests were conducted at Rd ratios of 0.1, 0.5, and 0.75. The methodology employed the Virtual Crack Closure Technique (VCCT) within finite element analyses to determine energy release rates ci and phase angles throughout propagation. The core contribution of this work is the application of a modified Hartman-Schijve master curve to account for displacement ratio effects and normalize growth data. Results indicate that while the da/dN vs. cmax slopes for prepreg specimens varied with Rd, the wet-layup slopes remained unaffected. Crucially, despite these differences, both material systems yielded similar master curves, demonstrating the robustness of the proposed normalization approach. Mode-mixity analysis confirmed steady-state conditions dominated by the K1 component in both systems. This study provides a comprehensive framework for predicting fatigue delamination across diverse material interfaces, offering significant value for the design and safety assessment of complex composite architectures.

The purpose of this investigation is to assess the effect of fiber bridging on fatigue delamination propagation. Fiber bridging occurs when testing beam type laminates specimens consisting of unidirectional plies. Unidirectional double cantilever beam specimens composed of the carbon fiber reinforced polymer prepreg AS4/8552 were tested by means of fatigue cycling. A Paris relation was determined based on these tests. Fiber bridging in beam specimens composed of unidirectional plies causes the apparent fatigue delamination curves to exhibit slower growth predicting overly conservative results. In Part I of this study, the effect of fiber bridging was eliminated experimentally from the results. In Part II of this study, a cohesive zone model is developed and used to carry out finite element analyses to simulate the experiments, as well as to eliminate the influence of fiber bridging. Fatigue delamination propagation tests were carried out on UD DCB laminate specimens. Fiber bridging was observed. Measurements were made of the fiber bridging (FB) zone. In Part II, a cohesive zone model is used to quantify the effect of FB and eliminate it.

This is the second of two papers in which a novel numerical method to predict the debond failure of a secondary bonded pultrusion laminate is presented. In Part 1 of this study, experimental work was described which is used here in the development, calibration and validation of the numerical model. The structure investigated in this work may be represented by a bonded composite laminate with external ply-drops (PDs).In this part of the study, a fully coupled mixed mode cohesive zone model is developed which relies upon a traction-separation relation and the virtual crack closure technique to obtain the mode mixity. These are used to develop a hybrid fracture discrete element (HFDE). Fracture toughness tests, as well as tests on PD specimens are used to calibrate the model. Based on these tests, run-arrest fracture criteria are defined. The model is validated by comparing test results for two other PD specimen types to those obtained with the HFDE and finite element analyses.

In this investigation, three subjects are considered. First, the effect of the human factor is examined. In carrying out analyses of fatigue delamination propagation tests on laminate composites, the delamination length must be measured. The human effect on measurement of the delamination length a by different investigators is discussed. A limited influence of the human factor on the measurement of the delamination length a, as well as on delamination propagation rate da=dN, is observed in this study. Secondly, the paper proceeds to discuss the influence of the R-ratio on the fatigue delamination growth rate. It is found that a higher rate of crack/delamination propagation is associated with lower R-ratios which appears to contradict conventional wisdom. This behavior is confirmed in tests. Thirdly, a comparison between the fatigue propagation rates of two material systems is considered. It is concluded that the energy release rate used to assess these materials should not be normalized.

In this investigation nearly mode II initiation and resistance energy release rate values, required for delamination propagation, were determined based on quasi-static calibrated end loaded split (C-ELS) fracture tests. Two multi-directional (MD) carbon fiber reinforced polymer (CFRP) material systems were examined. The first was manufactured as a wet-layup, with an initial delamination between a unidirectional ply and a plain woven ply. The second was manufactured from a prepreg, with an initial delamination along an interface between two plain woven plies oriented differently. Two-dimensional finite element analyses (FEAs) of the tested specimens were performed. Based upon the FEA results, with use of the displacement extrapolation (DE) method, as well as the virtual crack closure technique (VCCT), stress intensity factors were calculated. The obtained values were used to determine the in-plane mixed-mode phase angle for each test, which indicated nearly mode II deformation. Fracture toughness resistance curves or R-curves were generated as a function of the delamination extension. The critical initiation and resistance energy release rate values were obtained from the stress intensity factors, as well as with the J-integral, which are local methods. In addition, the global experimental compliance method (ECM) was used. Small differences were observed between the results obtained by means of the two methods. From a comparison between the R-curves of the two material systems, it was seen that the initiation energy release rate values were higher for the prepreg by 25.5%. A greater difference was found in the increasing portion of the R-curves, as well as the steady state energy release rate values.

In carrying out fatigue delamination propagation tests to assess the propagation rate versus a function of the energy release rate, the question arises as to the necessary number of cycles required to properly characterize the behavior. Tests were performed elsewhere on two different carbon/epoxy, multidirectional woven composite laminates containing a delamination using constant amplitude cycling by means of displacement control for various cycle ratios. The aim was to carry out the tests for 3.0x106$$ 3.0\times 1{0}<^>6 $$ cycles. Most specimens complied with this requirement. In this study, the fatigue data are analyzed including the first 0.5x106$$ 0.5\times 1{0}<^>6 $$ cycles, the first 1.0x106$$ 1.0\times 1{0}<^>6 $$ cycles, the first 1.5x106$$ 1.5\times 1{0}<^>6 $$ cycles, and 3.0x106$$ 3.0\times 1{0}<^>6 $$ cycles. It was seen that although the delamination length versus the cycle number could be quite similar between different cycle ranges, the Paris relation constants could be significantly different. It is suggested to carry out tests for as many cycles as possible. Double cantilever beam (DCB) specimens fabricated from multidirectional woven material were considered.Two material systems were examined.Different cycle ranges were used: 0.5 x 106, 1.0 x 106, 1.5 x 106, and 3.0 x 106.It was found that more reliable results were obtained for longer cycle ranges.

The purpose of this investigation is to evaluate the contribution of fiber bridging to the energy release rate of a fracture resistance curve. Fiber bridging occurs when testing beam-type specimens consisting of unidirectional plies in a laminate. Unidirectional double cantilever beam specimens composed of the carbon fiber reinforced polymer prepreg AS4/8552 were tested using standard methods. In addition, a cohesive zone model was developed and used to carry out finite element analyses on the tested specimens. It was employed to calculate the contribution of fiber bridging to the R$$ R $$-curve which was determined from the tests. Fiber bridging in beam specimens increases the apparent fracture toughness of a composite laminate. A method has been proposed for evaluating its contribution to the energy release rate. In that way, an R$$ R $$-curve may be determined for which the effect of fiber bridging is eliminated.

In Part I of this paper, quasi-static fracture toughness tests were reported which were carried out on two carbon fiber reinforced polymer materials. One laminate was unidirectional and the second was composed of plies fabricated from a twill fabric. In Part II, which is presented here, micro-computerized tomography was performed providing a relationship between the observed experimental behavior and the micromechanical structure of the materials. This was carried out for the double cantilever beam (DCB), mixed mode bending (MMB) and end-notched flexure (ENF) specimens. Load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to obtain better insight into the failure mechanisms observed for DCB and ENF specimens.

This is the first of two papers which presents a novel numerical method to predict the debond failure of a secondary bonded pultrusion laminate. In this paper, experimental work will be described that will later be used in the development, calibration and validation of the numerical model, which will be discussed in the second paper. The structure investigated in this work may be represented by a bonded composite laminate with external ply-drops. The laminate is composed of unidirectional pultrusion carbon fiber reinforced polymer cured plies bonded together to produce a secondary bonded laminate. In order to investigate the different failure modes of the ply-drop structure, an element specimen denoted as a ply-drop specimen, was tested under two types of loadings: axial tension and bending. Testing procedures of this type of specimen are not well established. Thus, test protocols will be suggested. In addition, finite element analyses are carried out using established linear elastic fracture mechanics methods to investigate the conditions during debond failure and in order to assess the ability of the methods to predict the debond failure.

The Virtual Crack Closure Technique (VCCT) is a simple method that was found in the past to produce good results for determining stress intensity factors of cracks in homogeneous bodies and poor results for interface cracks. In recent papers, the VCCT was found to produce excellent results for two-dimensional interface cracks where many elements were used in the virtual crack extension (VCE). This approach is called here the Multi-VCCT. A criterion for the optimal number of elements used in the VCE was also found. Here, the M-VCCT is extended to three-dimensional interface crack problems. Results for three-dimensional problems containing a straight through finite length interface crack and a penny-shaped interface crack are presented. The interfaces include that between two homogeneous and isotropic dissimilar materials, as well as two transversely isotropic materials.

In Part I of this study, fracture toughness tests were carried out in modes I, II and mixed modes I/II on two laminate composites. Both composites contain carbon fibers in an epoxy matrix. One laminate is unidirectional and the second is composed of plies fabricated from a twill fabric. The tests were carried out using double cantilever beam, end-notched flexure and mixed mode bending specimens according to ASTM and ISO standards. This is an extensive and complete study of the in-plane, quasi-static fracture toughness (both initiation and resistance) of two material systems. In Part II of this study, micro-computerized tomography carried out on some of the specimens is reported. On the basis of these images, the experimental behavior was related to the micromechanical structure of the materials. In addition, load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to gain better insight into the failure behavior observed.

In this work, energy release rates evaluated by means of the virtual crack closure technique (VCCT) are analyzed for structures undergoing large deformations. For this, nonlinear finite element (FE) analyses are carried out on edge notched and pure shear specimens in Abaqus. Two hyperelastic constitutive material models: incompressible Mooney–Rivlin (I-MR) and incompressible Ogden (I-Ogden) were used. For the nonlinear elastic analyses, the relationship between the force and displacement at a node may not be linear. Hence, the nodal point forces need to be integrated over the corresponding displacements to evaluate the energy release rates. The need for transforming the nodal point forces and displacements into a local nodal coordinate system to determine the energy release rates and mode mixity is examined. The relation between the total energy release rates GT evaluated from the nodal point forces and displacements in the global and local nodal coordinate system is derived analytically and analyzed numerically. Finally, GT evaluated by VCCT for the pure shear and edge notched specimens are compared to the J-integral.

An interface crack between single crystal silicon (SC-Si) and silicone rubber was examined. Mixed mode fracture tests were performed on Arcan-type specimens at different mode mixities. It was observed during the tests that silicone rubber underwent large deformations before crack propagation. Nonlinear finite element analyses (FEAs) of the fracture tests were carried out in Abaqus. A cubic (anisotropic), linear elastic material model was used for SC-Si, while a Mooney–Rivlin (hyperelastic) model was used for the silicone rubber. The virtual crack closure technique (VCCT) which has been adopted for large deformations was employed to determine the energy release rates from the FEAs. A mixed mode failure criterion was obtained from the energy release rate data.

The purpose of this investigation is to evaluate the accuracy of global expressions of the energy release rates for laminate composite beam specimens. The specimens considered here are composed of multi-directional woven plies; they include double cantilever beam (DCB), mixed mode end loaded split (MMELS) and calibrated end loaded split (C-ELS) specimens. As a result of the layup, the upper and lower specimen arms possess different heights and stiffnesses. Global expressions that exist in the literature are used in the calculations. New expressions are developed to account for the differing stiffnesses. Results from tests carried out elsewhere are used in the calculations. The obtained results are compared to values found by means of finite element analyses. It was seen that for DCB specimens, the best results were obtained when the specimen arm heights and stiffnesses, together with a correction for the deflection and rotation at the delamination front, were accounted for. These are presented in Appendix A. For the MMELS specimens, the best comparison between the finite element results and the global expressions for the interface energy release rate was found when accounting for different specimen arm heights or both different specimen arm heights and stiffnesses but without the delamination length correction. The best results for the C-ELS specimens were obtained when both the specimen arm heights and stiffness were considered, together with the delamination length correction. Thus, it would appear that the global expressions may be used to estimate the energy release rate for beam type specimens.

Quasi-static fracture toughness tests were carried out on four types of beam specimens in order to determine the mixed mode I/II initiation fracture toughness of a secondary bonded laminate composed of uni-directional pultrusion composite plies. The tests included the double cantilever beam (DCB) test for pure mode I; the mixed mode end loaded split (MMELS) test for a mode I dominant mixed mode I/II ratio; the mixed mode bending (MMB) test for a mode II dominant mixed mode I/II ratio; and the calibrated end loaded split (C-ELS) test for pure mode II. Following the tests, the fracture surfaces were examined and related to the test behavior of each specimen. The results of the fracture toughness tests were used to establish a mixed mode I/II initiation fracture toughness criterion. Several criteria were examined.

The double cantilever beam (DCB) specimen has been used extensively to measure the mode I fracture toughness of laminate composites. There are standards which were developed for testing unidirectional (UD) material. In addition, this specimen has been used extensively for multi-directional laminates. Typically, fracture resistance curves are presented. To this end, calculation of the energy release rate is required. For UD specimens, there are expressions for this parameter given in the standards. They depend upon the applied load, the crack opening displacement, specimen dimensions and the axial Young's modulus or specimen compliance. For multi-directional composites, the specimen arms may not be symmetric. In this case, the arm heights differ, as well as their effective moduli. In this study, expressions are presented for all cases. That is, expressions for the energy release rate are presented in which the specimen arms are symmetric and in which their heights differ; these are found in the literature. In addition, new expressions for which the axial moduli also differ are developed. Calculations are made with these equations and compared to results obtained elsewhere using the finite element method and the conservative J-integral. It is seen that excellent agreement is achieved when both the different heights and moduli are accounted for, as well as a delamination length correction. The purpose of this investigation is to examine expressions for calculating the energy release rate in comparison to finite element analyses and to show that by taking into consideration the different specimen arm heights and stiffnesses, simple formulas may be used instead of the more complicated finite element analyses.

The coupled energy release rate may be used with the virtual crack closure technique (VCCT) method to determine the stress intensity factors of interface cracks. Different equations were presented over the years using this parameter. In recent papers, a new approach was presented by the authors. This approach includes two additional energy release rates, called here, the dual energy release rates. Here, the coupled and dual energy release rates are explored and well established. This leads to a new and more suitable equation for calculating the mode mixity or phase angle. In addition, a geometrical interpretation between the energy release rates for both homogeneous and interface crack problems is found. A problem of an interface crack between two linear elastic, isotropic, and homogeneous materials in an infinite body is presented. This problem emphasizes the advantage of the new equation, and the geometrical relation between the energy release rates is illustrated.

This paper is written on the occasion of J.R. Rice's 80th birthday. Basically, it presents two aspects of interface fracture mechanics, linear elastic and elasto-plastic, both of them reflecting the long experience of the two authors. Special attention has been focused on the seminal contribution of Jim Rice, still being a great inspiration to researchers in the field of fracture mechanics. Fundamentals that he developed enabled us to build versatile scientific and engineering tools that currently enable the solution of almost any problem related to cracks.

Several two- and three-dimensional mixed-mode interface failure criteria are proposed for predicting delamination failure in multidirectional, laminate composites. The proposed criteria, based on the stress intensity factors K-1, K-2, and K-III, as well as the critical interface energy release rate G(ic) and phase angles. and., are examined using results obtained from Brazilian disk mixed-mode fracture toughness tests. Two material systems are considered. The first contains a delamination along an interface between a unidirectional fabric and a plain woven fabric. The second is composed of a plain woven fabric with fibers oriented in different directions in succeeding plies. The former was manufactured by means of a wet-layup and the latter is a prepreg. Finally, a statistical analysis is carried out to obtain a failure curve or surface with a 10% probability of unexpected failure and a 95% confidence. These curves or surfaces may be used to predict failure of structures containing these laminates and to assist in composite design.