Maximum Tangential Principal Stress Research Articles

Modelling interacting cracks through a level set using the element-free Galerkin method

A multiple crack weight technique with a level set method is proposed to model multiple cracks using a coarse meshfree nodal discretization. A new level-set structure is presented to handle multiple cracks and their propagation using the maximum tangential principal stress criterion. The level sets are updated with respect to the new crack tip positions. The problem of modelling interacting cracks in isotropic and bi-materials is studied using a new variant of the element-free Galerkin method. The stress intensity factors (SIFs) and energy release rates for interacting cracks in isotropic and homogenous materials, including a crack at a bi-material interface are determined using the standard interaction integral. Case studies involving crack-crack interactions, doubly and triply kinked cracks are analysed to demonstrate the simplicity and the effectiveness of the proposed approach.

The effect of remote and internal crack stresses on mixed-mode brittle fracture propagation of open cracks under compressive loading

The standard mixed-mode fracture propagation models, based on near-tip stress approximations, have limited application for fractures under far-field compressive loading. Most studies in engineering mechanics have focused on extending or modifying the standard models to solve mixed-mode fracture propagation under tensile loading. However, for geomechanics and geologic applications, the ambient stress is compressive, and internal fluid pressure or frictional stress can play an important role in the near-tip stress field altering the predicted propagation path. In this study, we modify the maximum tangential principal stress (MTPS) criterion to improve fracture propagation path predictions relative to published experimental results under both tensile and compressive external loadings. In addition, new experimental results on open cracks under compressive loading were consistent with our proposed model. Accurate propagation path predictions are independent on whether small scale yielding conditions are met in the experiments. Overall, the modified MTPS-criterion proved capable for predicting propagation paths for open cracks under compressive far-field loading.

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method

A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported.

Experimental and finite element study on stable crack growth in three point bending

Experimental and finite element results are presented on mode I and mixed mode (involving I and II only) stable crack growth under static loading through an aircraft grade aluminium alloy (D16AT) in three point bending. The results include load-displacement diagrams, J-integrals, plastic zones, tunneling (or crack front curving), etc. During experiment a substantial amount of tunneling is observed, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as ao/w increases. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum load is observed to be as high as 1.6 times the initiation load in the whole range examined. From the finite element study it is seen that, in a mixed mode, the J-integral at the onset of extension is the lowest compared with the values at the later stages. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line. The direction of initial crack extension in a mixed mode can be predicted through an elastic finite element analysis and using the criterion of maximum tangential principal stress. The study also indicates that the load-displacement diagram associated with a mixed mode stable crack growth can be predicted reasonably accurately using the criterion of crack opening angle.

Criteria for brittle fracture in biaxial tension

The criteria of maximum tangential stress, maximum tangential principal stress, maximum tangential strain and strain energy density are applied to the problems of slit and elliptical cracks under remote uniform biaxial tension. The predicted direction of crack extension and the critical load are compared with experimental results reported by other investigators. The unstable crack paths are determined. The four criteria differ in the case of unequal tension; the strain energy density criterion is the least satisfactory. The criteria of maximum tangential strain and strain energy density can be modified to give a good prediction of critical load.

Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field

Prediction of the angle of initial crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential principal stress (MTPS), maximum tangential strain (MTSN), and strain energy density (SED) are compared for slit and elliptical cracks under pure shear loading and elliptical cracks under uniaxial compressive loading. Results presented here complement those in Part I of this investigation. Some of the theoretical predictions have been compared with data available in the literature.

Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field Part I: Slit and elliptical cracks under uniaxial tensile loading

Predictions for the angle of crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential strain (MTSN) and strain energy density (SED) for angled slit and elliptical cracks under uniaxial tensile loading are compared. The tangential stress associated with the MTS criterion need not be a principal stress and a new approach to this criterion is suggested. A criterion based on maximum tangential principal stress (MTPS) is proposed. Predictions by these two criteria are compared. Some difficulties associated with the application of the SED criterion are indicated. A new basis, which permits a unification of all the criteria in respect of prediction of critical load, is suggested. Some of the results have been compared with data available in the literature.

Theoretical and experimental studies on the extension of cracks subjected to concentrated loading near their faces to compare the criteria for mixed mode brittle fracture

The criteria of maximum tangential stress (MTS), maximum tangential principal stress (MTPS), maximum tangential strain (MTSN) and strain energy density (SED) are applied to problems of infinite sheets with straight cracks loaded at or very near their faces by in-plane point loads. Prediction of the direction of initial crack extension, critical load and unstable crack path are made. Unlike the results reported earlier by various investigators predictions by the four criteria differ substantially. The accuracy in respect of prediction of crack path is checked experimentally for a particular loading. The results indicate that a modification of the definition of the criteria of MTSN and SED is beneficial.