Crack Kinking Criterion Research Articles

Crack Path Selection in Thermally Loaded Borosilicate/Steel Bibeam Specimen

We have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the K II = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture test results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.

Plane-Strain Crack Problem in Transversely Isotropic Solids for Hydraulic Fracturing Applications

This paper aims at understanding and predicting how pressurized cracks propagate in anisotropic brittle solids, a situation frequently encountered in hydraulic fracturing. Special attention is paid to transverse isotropy, often used to model shale. Although the theory of linear elastic fracture mechanics of anisotropic solids is well established at present, this paper shows that the application of Muskhelishvili’s formalism to Lekhnitskii’s anisotropic complex potentials provides a powerful tool to extend the validity of the classical tools of isotropic fluid-driven crack models to the anisotropic case, provided that the appropriate elastic constants are used. These elastic constants are identified and derived in closed form for transversely isotropic solids. The constants are shown to be directly related to quantities easily measured in a laboratory at macroscopic scale through indentation tests and acoustic measurements. Moreover, several crack-kinking criteria are compared. Contrary to the isotropic case, the crack-kinking criteria are not consistent among themselves, even in the case of a pure pressure loading. The orientation at which it is easier to propagate an already existing crack is sought. A critical crack length, below which this crack orientation is the one of minimal stiffness felt by the crack, is identified.

3D adaptive finite element modeling of non-planar curved crack growth using the weighted superconvergent patch recovery method

In this paper, an adaptive finite element analysis is presented for 3D modeling of non-planar curved crack growth. The fracture mechanical evaluation is performed based on a general technique for non-planar curved cracks. The Schollmann’s crack kinking criterion is used for the process of crack propagation in 3D problems. The Zienkiewicz–Zhu error estimator is employed in conjunction with a weighted SPR technique at each patch to improve the accuracy of error estimation. Applying the proposed technique to 3D non-planar curved crack growth problems shows significant improvements particularly at the boundaries and near crack tip regions. Several numerical examples are presented to illustrate the robustness of the proposed technique.

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material, and to extract the fracture parameters of stress intensity factor KI and KII, and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where KII is not necessarily equal to zero.

Dynamic crack kinking from a PMMA/Homalite interface

The behavior of a pre-existing, dynamically loaded, interfacial crack kinking away from the interface separating two materials was experimentally investigated under dynamic loading conditions. Dynamic fracture experiments were performed on pre-cracked bimaterial panels of PMMA bonded with Homalite-100 impact loaded using a high-speed gas gun. By varying the location of impact, a large range of mixed mode loading at the crack tip was produced. Information about the stress state surrounding the crack tip was obtained through use of the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography. The high-speed interferogram corresponding, to the time of crack initiation was analyzed in each case to find the preinitiation mode mixity at the crack tip. Measurement of both the local initiation mode mixity and the crack kink angle allows for possible extension of existing quasi-static interface crack kinking criteria, such as maximum opening stress or maximum energy release rate, to the case of dynamic loading. It was found that for bimaterial systems with small material property mismatch, such as the PMMA/Homalite system, the maximum opening stress criterion accurately predicts the relation between crack tip mode mixity and resulting kink angle for small initial crack kinking speeds.

Axial Multiple Crack Propagation and Crack Kinking Criteria in Pressurized Fuselage

In order to clarify the effect of tear strap in airplane fuselage on crack arrest, experimental research and numerical simulation were carried out in this study. Interaction of multiple axial pre-cracks in a pressurized fuselage was investigated using a small-scale model of an idealized fuselage. The strain between multiple cracks under the situation of rapid crack propagation was measured. The experimental results of a rupturing model fuselage represented the variations of stress intensity factors KI and KII in the mixed mode and the remote stress components σox with crack extension. Deformation at the tips of asymmetrical cracks along the stringer was analyzed by a hybrid method using a finite element analysis program, MDC DYTRAN. The recorded crack velocities were in good agreement with the results of finite element analysis. The crack kinking location, kinking angle and the off-axis crack trajectory were also predicted by numerical analysis and the validity of the calculated results was discussed in comparison with the experimental data.

Revisited criterion to prevent kinking of a crack out of a bi-material interface under the presence of in-plane residual stresses––a global approach

Path stability of a crack propagating along an interface between elastically dissimilar layers under the presence of in-plane thermal residual stresses was considered using a numerical analysis. It was predicted that in-plane residual stresses control the energetic conditions to prevent crack kinking out of the interface only through the change in the stress state near the crack tip due to its own contribution to the singular stress field like globally applied loadings. On the other hand, it was predicted that the crack kinking criterion itself, uniquely determined for a given phase angle and a modulus mismatch parameter, is not affected by the residual stress. The numerical results herein suggests that contribution form the residual stress regarding the fracture behaviour of an interface crack is global events and thus supports the assertion elsewhere that fracture process within a K-dominant field can no longer be treated as local problem alone once globally applied residual stress term is involved.

Dynamic Crack Curving under Mixed-Mode Loading. Tear-Strap Effect with MSD.

A hybrid experimental-numerical investigation was used to determine the effectiveness of a tear strap in the presence of MSD. The 2024-T 3 aluminum alloy biaxial fracture specimens, 0.81 mm thick, were loaded to failure with loads simulating the hoop stress and the differential axial load generated by an unsymmetrical flap opening. MSD was simulated by s side groove along the crack path. The results showed that a previously developed mixed mode crack kinking criterion effectively predicted crack kinking, or lack thereof, of a running crack approaching the tear strap. The crack propagated through the tear strap in the presence of continuous MSD and kinked when MSD terminated at the tear strap.

Axial crack propagation and arrest in a pressurized cylinder: An experimental-numerical analysis

The feasibility of using a previously developed crack-kinking criterion to predict crack arrest at a tear strap in a pressurized fuselage was studied with instrumented axial rupture tests of 21 models of an idealized fuselage. A rapidly propagating axial crack, which was initiated from a precrack, kinked immediately upon extension and propagated diagonally until it turned circumferentially and propagated along the tear straps. An elastodynamic finite element analysis of the rupturing model fuselage yielded the mixed-mode stress intensity factors,KI andKII, and the remote stress component, σOX. This numerical procedure was also used to predict the crack trajectories in full-scale fuselage rupture tests. All numerical results agreed well with their measured counterparts regardless of size.

Axial Crack Propagation and Crack Kinking Criteria in Pressurized Fuselage.

The crack arrest capability of a tear strap in a pressurized precracked fuselage was studied through instrumental axial rupture tests of small-scale models of an idealized fuselage. Upon pressurization, rapid crack propagation was initiated at an axis through crack along the stringer and immediately kinked due to the mixed mode I and II states caused by the one-sided opening of the crack flap. The diagonally running crack turned at the tear straps. Dynamic finite element analysis of the rupturing cylinder showed that the crack kinked and also ran straight in the pressure of a mixed mode state according to a modified two-parameter crack kinking criterion.

Axial Crack Propagation and Crack Kinking Criteria in Pressurized Fuselage.

The crack arrest capability of a tear strap in a pressurized precracked fuselage was studied through instrumental axial rupture tests of small-scale models of an idealized fuselage. Upon pressurization, rapid crack propagation was initiated at an axis through crack along the stringer and immediately kinked due to the mixed mode I and II states caused by the one-sided opening of the crack flap. The diagonally running crack turned at the tear straps. Dynamic finite element analysis of the rupturing cylinder showed that the crack kinked and also ran straight in the presence of a mixed mode state according to a modified two-parameter crack kinking criterion.

Crack arrest at a tear strap under mixed mode loading

A hybrid experimental-numerical investigation was undertaken to establish a crack kinking criterion and hence crack arrest at a tear strap under mixed mode crack tip deformation. Experimentally determined crack velocities and crack paths from 2024-T3 and 7075-T6 aluminum alloys, cruciform fracture specimens, 0.81 mm thick with a 25.4 mm wide and 0.81 mm thick tear strap, were input to a dynamic finite element code to compute the necessary fracture parameters. These results were then used to verify three-parameter crack extension and curving criteria under mixed mode loading.

Dynamic Crack Curving under Mixed-Mode Loading.

A hybrid experimental-numerical investigation was undertaken to establish a crack kinking criterion and hence crack arrest at a tear strap under mixed-mode crack-tip deformation. Experimentally determined crack velocities and crack paths for 2024-T3 and 7075-T6 aluminum alloy, cruciform fracture specimens, 0.81 mm thick. with a 25.4-mm-wide and 0.81-mm-thick tear strap, were input to a dynamic finite-element program to compute the necessary fracture parameters. These results were then used to verify three-parameter crack extension and curving criteria under mixed-mode loading.