Interface fracture mechanics evaluation by correlation of experiment and simulation

We present a new methodology for the identification of a zone cohesive model that describes material failure. The material under consideration fails by crazing. The study is conducted at the micron scale in order to capture and analyze the fracture mechanism. The crack tip displacement fields are measured optically by Digital Image Correlation. The local stress intensity factors (mode I and II) and the location of the equivalent elastic crack tip are calculated during the loading. The variation of the location of the equivalent crack tip is used to track the initiation and growth of the process zone, up to the onset of crack propagation. These experimental measurements are used to define the appropriate parameters in a cohesive zone model. The methodology addresses the onset of crazing, the traction–separation profile and the maximum opening corresponding to the local nucleation of a crack. The cohesive parameters that are derived from the experimental data are consistent with results available in the literature. In addition, the model enables the characterization of the normal and tangential mode of the cohesive model.

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

Automatic crack tip localization in enormous DIC images to in-situ characterize high-temperature fatigue crack growth behavior

The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics. Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function q 1 , as appropriately normalised kernel function, which inherently satisfies all the specific requirements on q 1 : The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic plastic fracture mechanics, including the combination with elastic plastic constitutive models is straightforward. • New algorithm to calculate J-Integral developed in Smoothed Particle Hydrodynamics (SPH). • New approach for calculating gradient of J-Integral weighting function q 1 analytically. • Confirmed accuracy of J-integral results from SPH compared to FEM results.

Delamination propagation in fibrous laminates is often accompanied by development of a damage zone, within which intact fibers bridge the crack faces that constitutes a major toughening mechanism. A direct experimental assessment of the crack closure tractions due to bridging fibers is a challenging task. In addition, when the length of the bridging zone becomes comparable with the laminate linear dimensions, referred to as large scale bridging, the extent of bridging can be influenced by the laminate size and layup. Hence, traction-separation relations used in computational methods to predict fracture do not always rely on solid experimental evidence of large scale bridging and for numerical convenience simple linear traction-€“separation expressions are often considered. In this work, a semi-experimental methodology is employed to identify the contribution of large scale bridging to delamination resistance of unidirectional and cross-ply carbon fiber/epoxy laminates. Double cantilever beam specimens of different thickness are prepared and subjected to monotonic and fatigue mode I loadings. In selected specimens, optical fibers with multiplexed fiber Bragg grating (FBG) sensors are embedded. The strain distribution in the vicinity of the crack plane is monitored by FBG sensors. The strain data are used in an inverse identification procedure to quantify the bridging tractions and the energy release rate (ERR) due to the bridging. Subsequently, the identified tractions are implemented in a cohesive zone model to simulate delamination propagation. Employing the aforementioned approach, specimen thickness dependence of large scale bridging in delamination of unidirectional laminates is investigated. The results indicate that onset of delamination is independent of the specimen geometry. However, the extent of the bridging zone and the plateau level of delamination resistance both significantly increase with increasing the specimen thickness. The maximum traction at the crack tip is independent of the specimen size while the length of the steady state bridging zone scales linearly with the thickness of laminate. Moreover, the nonlinear rate of tractions decay is inversely proportional to the specimen thickness. It is shown that the tractions decay parameter is controlled by the curvature of the specimen arm. Evaluation of bridging effects on fatigue delamination of unidirectional laminates indicates that the stable phase of fatigue crack growth is more extended in the thicker specimens and the critical ERR increases by increasing the specimen thickness. Similar to the trend observed in monotonic delamination, fatigue delamination in the thicker specimens is accompanied by a longer bridging zone in which the bridging tractions decay with a lower rate. The maximum bridging traction at the crack tip is independent of the specimen thickness. It is demonstrated that the traction-separation relation and the ERR due to the large scale bridging depend on the ply orientations at the crack interface whereas ERR values at the onset of delamination are almost the same. As compared to delamination of a unidirectional specimen, crack propagation in cross-ply laminate is accompanied by a smaller bridging zone, but fiber bridging in the cross-ply specimens is more efficient. The adopted methodology in this work provides a robust assessment of large scale bridging and is a step towards a better understanding of delamination in fiber reinforced composites.

The use of interlayers in modeling interface crack propagation

Modelling of anisotropic damage at a crack tip in composite laminates

Characteristic of crack tip fields for dynamic fracture in anisotropic materials

Energy release rates in rubber during dynamic crack propagation

ABSTRACTThe mode I displacement field in the near crack tip region is assumed to be depicted by its partition into an elastic field and a plastic field. Then, each part of the displacement field is also assumed to be the product of a reference field, a function of space coordinates only, and of an intensity factor, function of the loading conditions. This assumption, classical in fracture mechanics, enables one to work at the global scale since fracture criteria can be formulated as a function of the stress intensity factors only. In the present case, the intensity factor of the plastic part of the displacement field measures crack tip plastic flow rate at the global scale. On the basis of these hypotheses, the energy balance equation and the second law of thermodynamics are written at the global scale, i.e. the scale of the K‐dominance area. This enables one to establish a yield criterion and a plastic flow rule for the crack tip region. Then, assuming a relation between plastic flow in the crack tip region and fatigue crack growth allows an incremental model for fatigue crack growth to be built. A few examples are given to show the versatility of the model and its ability to reproduce memory effects associated with crack tip plasticity.

The evolution of crack tip displacement and strain fields during uniaxial, room temperature, low‐cycle fatigue experiments of Nickel superalloy compact tension specimens was measured by a digital image correlation approach and was further used to validate a cyclic plasticity model and corresponding deformation calculations made by a finite elements methodology. The experimental results provided data trends for the opening displacements and near crack tip strains as function of cycles. A finite element model was developed to capture test conditions for a measured crack size. The model captures crack tip plasticity by using a constitutive model calibrated against stress‐strain measurements performed on a round bar. Similar quantities were extracted from the model predictions to compare with the digital image correlation measurements for model validation purposes. This type of direct comparison demonstrated that the computational model was capable to adequately capture the crack opening displacements at various stages of the specimen's fatigue life, providing in this way a tool for quantitative cyclic plasticity model validation. In addition, this integrated experimental‐computational approach provides a framework to accelerate our understanding related to interactions of fatigue test data and models, as well as ways to inform one another.

A three dimensional adaptive multiscale method for crack growth in Silicon

DeterminingK and related stress-field parameters from displacement fields

An energy method based on beam theory is proposed to determine the strain energy release rate of an existing crack in composite laminates. The developed analytical method was implemented in isotropic materials, and the obtained strain energy release rate of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated, and basic trends leading to crack propagation to one side of the crack were established. A correction factor was introduced to improve the accuracy of the strain energy release rate for small cracks. The singularity at the crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. The calculated strain energy release rate of a crack in a composite beam has been verified by comparing with a finite element model.

Composite patch repairs of aluminum structures used in marine and aerospace industries are designed using closed form solutions assuming thin, plane stress, linear-elastic structures or numerical methods for repairs of thick aluminum. Both methods are based on linear elastic fracture mechanics and compare crack tip predictions to a critical strain energy release rate or stress intensity. Analytical and numerical predictions are reasonable for linear-elastic behavior, but these methods do not account for elastic-plastic behavior at the crack tip that initiates above the linear-elastic limit and continues until the ultimate load. This research used digital image correlation and finite element analysis to study the full field displacement and J-integral ahead of the crack tip for un-patched and patched center crack tension specimens loaded monotonically to failure. Free surface crack tip strain and J-integral behavior remained an intrinsic property of the aluminum directly related to the crack opening displacement (COD) and were independent of one sided composite patch reinforcement. However, the crack tip bending deformations induced by the patch reinforcement increased the COD by 20% over the un-patched behavior after patch failure, most likely due to observed changes in the formation of the plastic zone ahead of the crack. Comparison of test results and analytical predications indicated a significant difference between linear elastic and elastic plastic predictions beyond the linear-elastic limit highlighting the need to utilize elastic plastic fracture mechanics and the J-integral to optimize composite patched center crack tension specimens for ultimate load.