mode-II Energy Release Rates Research Articles

An extended peridynamic model equipped with a new bond-breakage criterion for mixed-mode fracture in rock-like materials

This paper develops a numerical model based on two-parameter extended bond-based peridynamics with a new bond-breakage criterion to simulate mixed-mode fracture in rock-like materials. This model requires only four basic parameters: Young’s modulus, Poisson’s ratio, and Mode-I and Mode-II energy release rates. Tensile and shear cracks can be distinguished explicitly from mixed-mode fracture phenomena by decomposing the bond potential into dilatational and deviatoric terms. The m- and δ-convergence studies are first performed on the gypsum specimen with a single flaw subjected to uniaxial compression. The initialization and propagation of wing cracks (tensile cracks), quasi-coplanar and oblique secondary cracks (shear cracks) are successfully captured. As an example application, the crack initiation, propagation and coalescence processes of gypsum specimens with various double-flaw configurations are investigated. Under uniaxial compression, three typical types of crack coalescence patterns characterized by shear cracking or mixed tensile-shear cracking are obtained. In all cases, the numerical results predicted by the developed approach agree well with the experimental observations, both qualitatively and quantitatively.

Interlaminar fracture analysis in the GI – GII – GIII space using prestressed transparent composite beams

This work presents the mixed mode I/II/III prestressed split-cantilever beam specimen for the fracture testing of composite materials. The newly designed system is the superposition of the mode-I double-cantilever beam, mode-II end-loaded split, and mode-III modified split-cantilever beam specimens. The three fracture modes are combined by prestressing the mode-I and mode-II energy release rates at the same time, while the mode-III loading is provided by a testing machine. It is shown that the system is able to provide any combinations of the mode-I, mode-II, and mode-III energy release rates. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass/polyester composite specimens. The experimental data is reduced by the virtual crack-closure technique. It is shown that the energy release rates are non-uniformly distributed along the crack front which involves that the model results must be evaluated pointwise, and initiation was expected at the point where the highest total energy release rate appeared. Finally, based on the present and previous results, a three-dimensional fracture surface was determined in the GI – GII – GIII space.

Effects of residual thermal stresses on the debond characterization of sandwich beams

The crack tip element method is applied to the formulation of energy release rates associated with face sheet debonding of sandwich beams with residual thermal stresses using the bi-layer Timoshenko beam model. Special attention is paid to the energy release rates of DCB and MMB tests for debond characterization. Mode-I and mode-II energy release rates are formulated including residual thermal stresses. The derived analytical results are verified by comparison with finite element analysis. The effect of residual thermal stresses on the evaluated apparent fracture toughness, resulting from the neglect of residual thermal stresses in the standard evaluation methods, is discussed.

Prestressed composite specimen for mixed-mode I/II cracking in laminated materials

This article presents the mixed-mode I/II prestressed end-loaded split specimen for the fracture testing of composite materials. The system is based on the fact that one of the two fracture modes is provided by the prestressed state of the specimen, and the other one is increased up to fracture initiation using a testing machine. The novel beam-like specimen is able to provide any combination of the mode-I and mode-II energy release rates. A simple closed-form solution is developed using beam theory as a data reduction scheme and for the calculation of the energy release rates in the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass—polyester composite specimens. If only crack propagation onset is involved, then the prestressed mixed-mode beam specimen can be used to obtain the fracture criterion of transparent composite materials in the G I—GII plane.

Energy release rates of bi-material interface crack including residual thermal stresses: Application of crack tip element method

Crack tip element method is applied to the formulation of the energy release rate associated with interfacial crack growth of laminates with residual thermal stresses using the Timochenko beam model. Special attention is paid to the energy release rates of double cantilever beam and mixed-mode bending tests of bi-material specimens, and mode-I and mode-II energy release rates are formulated including residual thermal stresses. The derived results are verified by the comparison to finite element analysis, and the effect of residual thermal stresses on the mode mixity of the double cantilever beam and mixed-mode bending tests is discussed.

熱残留応力を考慮した層間き裂進展に関するエネルギー解放率：Ｃｒａｃｋ Ｔｉｐ Ｅｌｅｍｅｎｔ法による定式化

Crack tip element (CTE) method is applied to the formulation of energy release rate associated with interfacial crack growth of laminates with arbitrary layups and residual thermal stresses using the Timochenko beam model. Special attention is paid to the energy release rates of mixed mode bending (MMB) test, and mode-I and mode-II energy release rates are formulated including residual thermal stresses. The results derived are verified by the comparison to finite element analysis, and the effect of residual thermal stresses on the mode mixity of the MMB test is discussed.

The effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries

Cohesive-zone models have been used to study the effects of strength and toughness on the delamination of beam-like geometries. The conditions under which linear-elastic interfacial mechanics provide a good frame-work for predicting failure of such systems have been studied. It has been determined that the phase angle derived from LEFM calculations provides an excellent description of the partitioning between the mode-I and mode-II energy-release rates over a wide range of fracture-length scales. In particular, the nominal phase angle can be a useful parameter, even when the fracture-length scale is so large that the interface stresses do not exhibit the expected inverse-square-root dependence. The analysis has also shown that nominal phase angles with a magnitude greater than 90° can have physical significance, provided the interface layer is thick enough to accommodate compression without crack-surface contact. Finally, the role of modulus mismatch has been studied. A length scale introduced by the cohesive strength allows a crack-tip phase angle to be established, when LEFM predicts oscillating stress fields at the crack tip. This crack-tip phase angle is shifted from the nominal phase angle based on a characteristic geometrical length by an amount that depends on the cohesive parameters of the interface and the modulus mismatch. It has been shown that, as a result of this shift, both modulus mismatch parameters can influence the strength of an interface.

Energy-Based Automatic Mixed-Mode Crack-Propagation Modeling

Based on an energy principle and a virtual crack extension technique, a practical finite-element modeling approach for the automatic mixed-mode two-dimensional (2D) linear elastic fracture mechanics (LEFM crack-propagation analysis has been developed. By decomposing the displacement field obtained from a conventional finite-element analysis into symmetric and antisymmetric displacement fields with respect to the crack, the Mode-I and Mode-II energy release rates can be determined using a generalization of the stiffness derivative method, and the corresponding stress intensity factors can then be calculated. The load at which a crack propagates and the propagation direction can be determined using one of the well-established mixed-mode crack-propagation criteria. Unlike the previously developed approaches to crack propagation, this approach does not require the use of symmetric crack-tip mesh, crack-tip singular elements, which greatly simplifies the subsequent remeshing process to allow for crack propagation. The automatic crack-propagation process is achieved by using a simple and efficient local 2D remeshing algorithm that can be easily programmed. Convergence studies, mesh sensitivity studies, and the practical use of the new approach are presented through various example problems.