Fracture mechanics approach is to assess the process of crack propagation in a known stress field. The amount of material strength against the crack propagation is named Fracture toughness. In this research, different cracked samples are used to determine the Fracture toughness of different rocks. The methods proposed by ISRM (International Society for Rock mechanics) are two tests, i.e. three point bend test and short rod. The present research is based on the three point bent test. Also, in these tests two levels are utilized, 1-load control 2-displacement control, but in the present tests the level I is chosen for two types of rocks.

This paper studies the application of an inverse methodology for problem solving in Fracture mechanics using the finite element analysis. The method was applied to both detection of subsurface cracks and the study of propagating cracks. The procedure for detection of subsurface cracks uses a first order optimization analysis coupled with a penalty function to solve for the unknown geometric parameters associated with the internal flaw. The objective function is calculated from normalizing the finite element determined displacements by the prescribed ones at some arbitrary points of the damaged component. The technique was also used for determination of both 1-D and 2-D planar crack growth directions using the well known maximum strain energy release rate criterion. In all cases studied, a good agreement is achieved between the theoretical and/or the experimentally observed crack behavior and the developed technique.

In this paper, wheel-rail contact problem in the presence of rail surface crack is investigated. The reason for investigating this problem is significant effect of wheel-rail contact on stress intensity factors. In this research, by using finite element method and a commercial software, wheel-rail is modeled under partial slip rolling condition. Contact elements are used to model the interactions between the wheel-rail contact surfaces and the crack surfaces. Stress intensity factors are calculated through a numerical displacement extrapolation method. The effects of crack orientation, crack length, friction coefficient and contact on the stress intensity factors are studied. The results indicate that KII has greater values than KI. Therefore, shear mode may dominate the tip behavior in this wheel-rail contact problem. As the wheel passes over, the complicated crack edge deformation changes the direction of interfacial shear stress and this causes variation in KII. Fluctuation in KII is the main factor of fatigue crack propagation in the wheel-rail contact problem.

There are several methods to investigate the behavior of hot mix asphalt (HMA) at low temperatures. One of these methods is the use of principles of linear elastic Fracture mechanics (LEFM). In this paper, the LEFM principles is used to investigate the effects of different loading modes and temperatures on the Fracture resistance of HMA incorporating carbon fibers at subzero temperatures. Three-point Fracture tests were successfully performed on the semi-circular bend (SCB) specimen containing an asymmetric vertical edge crack under different modes of loading including pure mode I (pure tensile), pure mode II (pure shear) and mixed-mode I/II (tensile-shear). Critical stress intensity factors were then computed using the critical load obtained from the Fracture experiments and the geometry factors were determined from the finite element analyses. Results revealed that at all loading modes, modified HMA has higher resistance against crack growth than the unmodified HMA, particularly at low temperatures. Also, Fracture resistance of tested HMA was improved by 30-43 percent in the pure tensile mode, 13. 2-41 percent in the mixed mode (Me=0. 5), 10. 5-40 percent in the mixed mode (Me=0. 2) and 2-12. 5 percent in the pure shear mode.

This paper presents a model to simulate shear mode (mode II) of Fracture mechanics in concrete cold-joint. The simulation is performed using nonlinear static analysis of materials and geometry. The specimens used for modeling are S-shaped specimens used in the push-off test. The specimens modeled in three situations with 2, 4, and 6 steel connectors and validated with the results of corresponding the experimental specimens. The results of the analysis show that the proposed method has a good ability to simulate the behavior of the shear mode of Fracture mechanics in concrete cold-joint. The proposed simulation method can be useful to investigate the behavior of reinforced concrete frames with cold-joint and repair, retrofitting, and strengthening reinforced concrete structures.

In this paper, the causes of the crack initiation in cast iron bullion moulds in Meybod Steel Corporation are investigated and then some new geometrical models are presented to replace the current moulds. Finally, among the new presented models and according to the life assessment, the best model is selected and suggested as the replaced one. For this purpose, the three recommended moulds were modeled and analyzed by ANSYS software. First, a thermal analysis and then a thermo-mechanical coupled field analysis were performed on each three model. The results of the analysis are used to determine the critical zone. The critical zone is selected on the symmetric axis of the inner surface of the mould. By comparing the principle stress contours and temperature distribution contours of three models, one of the suggested models was selected as optimized geometrical model. Then, the crack modeling and the life assessment on the optimized model were implemented and the total life of the model was calculated. Comparison of the life of the optimized and the initial models shows an increase in the life of the suggested model. The results are verified with the experiments.

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric analysis method a suitable candidate for modelling discrete cracks. Moreover, the repetition of two different control points between two patches can create a discontinuity and also demonstrates a singularity in the stiffness matrix. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. Various numerical simulations for edge and center cracks demonstrate the suitability of the isogeometric analysis approach to Fracture mechanics.