Sharif Digital Repository

In this paper, a polygonal finite element method is presented for crack growth simulation with minimum remeshing. A local polygonal mesh strategy is performed employing polygonal finite element method to model the crack propagation. In order to model the singular crack tip fields, the convex and concave polygonal elements are modified based on the singular quarter point isoparametric concept that improves the accuracy of the stress intensity factors. Numerical simulations are performed to demonstrate the efficiency of various polygonal shape functions, including the Wachspress, metric, Laplace and mean value shape functions, in modeling the crack tip fields. Eventually, analogy of the... 

The phase field approach (PFA) for the interaction of fracture and martensitic phase transformation (PT) is developed, which includes the change in surface energy during PT and the effect of unexplored scale parameters proportional to the ratio of the widths of the crack surface and the phase interface, both at the nanometer scale. The variation of these two parameters causes unexpected qualitative and quantitative effects: shift of PT away from the crack tip, "wetting" of the crack surface by martensite, change in the structure and geometry of the transformed region, crack trajectory, and process of interfacial damage evolution, as well as transformation toughening. The results suggest... 

In this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in a 2D finite element mesh. The Zienkiewicz-Zhu error estimator is employed in conjunction with a modified SPR technique based on the recovery of gradients using analytical crack-tip fields in order to obtain more accurate estimation of errors. The optimization of crack-tip singular finite element size is achieved through the adaptive mesh strategy. Finally, several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of computational algorithm in calculation of fracture parameters and prediction of crack path pattern. © 2008 Elsevier... 

New enrichment functions are proposed for crack modelling in orthotropic media using the extended finite element method (XFEM). In this method, Heaviside and near-tip functions are utilized in the framework of the partition of unity method for modelling discontinuities in the classical finite element method. In this procedure, by using meshless based ideas, elements containing a crack are not required to conform to crack edges. Therefore, mesh generation is directly performed ignoring the existence of any crack while the method remains capable of extending the crack without any remeshing requirement. Furthermore, the type of elements around the crack-tip remains the same as other parts of... 

In this article, the extended finite element method is employed to solve problems, including weak and strong discontinuities. To this end, a level set framework is used to represent the discontinuities location, and the Heaviside and Branch function are included in the standard finite element method. The case of two arbitrary curved cracks is solved numerically and stress intensity factor (SIF) values at the crack tips are calculated based on the evaluation of the crack tip opening displacement. Afterwards, J-integral methodology is adopted to evaluate the SIFs for isotropic and anisotropic bi-material interface crack problems. Numerical results are verified with those presented in the... 

The critical strain energy release rate for crack initiation, J ci , was measured under mode I loading for SAC305 solder joints between two copper substrates. Fracture tests were performed using double cantilever beam specimens at a strain rate of 0.03 s −1 . Different bond-line widths (i.e., joint size in the out-of-plane dimension) and thicknesses, were examined. The fracture force per unit width and J ci (the average value of four J-integral contours encircling the crack tip) were relatively insensitive to the width of the joint ranging from 8 mm to 21 mm. Variations in bond-line thickness (i.e., 150 μm, 250 μm and 450 μm) also had an insignificant influence on the fracture energy of... 

The critical strain energy release rate for crack initiation, J ci , was measured under mode I loading for SAC305 solder joints between two copper substrates. Fracture tests were performed using double cantilever beam specimens at a strain rate of 0.03 s −1 . Different bond-line widths (i.e., joint size in the out-of-plane dimension) and thicknesses, were examined. The fracture force per unit width and J ci (the average value of four J-integral contours encircling the crack tip) were relatively insensitive to the width of the joint ranging from 8 mm to 21 mm. Variations in bond-line thickness (i.e., 150 μm, 250 μm and 450 μm) also had an insignificant influence on the fracture energy of... 

The fracture behavior of a hybrid-rubber-modified epoxy system was investigated. The modified epoxy included amine-terminated butadiene acrylonitrile (ATBN) rubber and recycled tire particles as fine and coarse modifiers, respectively. The results of the fracture toughness (K IC) measurement of the blends revealed synergistic toughening in the hybrid system when 7.5-phr small particles (ATBN) and 2.5-phr large particles (recycled tire) were incorporated. Transmission optical micrographs showed different toughening mechanisms for the blends; fine ATBN particles increased the toughness by increasing the size of the damage zone and respective plastic deformation in the vicinity of the crack... 

Classical continuum mechanics fails to give accurate solution near the crack tip, moreover, it implies that a solid is able to sustain an infinite stress at the Griffith-Inglis crack tips. Among other critical issues is the inability of the classical approach to sense the size effect. For these reasons, for more in-depth understandings and accurate behavioral predictions, it is essential to develop some atomistic methods which properly accounts, not only for the structure but also the long and short range atomic interactions effectively. In this work the interaction of inhomogeneity and crack under polynomial loading is simulated by using the many body Rafii-Tabar and Sutton potential... 

An efficient enrichment strategy is presented for modeling stress singularities in multi-material problems and crack-tips terminating at a bi-material interface within the X-FEM framework. The eigen-function expansion method is employed to evaluate eigen-values and asymptotic fields around singular points. The generalized stress intensity factors are defined on the basis of direct and interaction integral techniques. Numerical examples are solved for different types of eigen-values, and the convergence study is performed to investigate the accuracy of the proposed enrichment strategy. The results indicate that the proposed method has superior accuracy, higher convergence rate and lower... 

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is... 

A thermodynamically-consistent phase field approach for crack propagation which includes the following novel features is presented. (1) Scale dependency was included by relating the length scale to the number of cohesive interatomic planes at the crack tip. Because of this, the developed theory is applicable from the atomistic to the macroscopic scales. (2) The surface stresses (tension) are introduced by employing some geometrical nonlinearities even in small strain theory. They produce multiple contributions to the Ginzburg-Landau equation for crack propagation. (3) Crack propagation in the region with compressive closing stresses is eliminated by employing a stress-state-dependent kinetic... 

Purpose: The purpose of this paper is to provide a theoretical analysis of the fracture behavior of multiple axisymmetric interface cracks between a homogeneous isotropic layer and its functionally graded material (FGM) coating under torsional loading. Design/methodology/approach: In this paper, the authors employ the distributed dislocation technique to the stress analysis, an FGM coating-substrate system under torsional loading with multiple axisymmetric cracks consist of annular and penny-shaped cracks. First, with the aid of the Hankel transform, the stress fields in the homogeneous layer and its FGM coating are obtained. The problem is then reduced to a set of singular integral equations... 

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is... 

The competition and interaction of two edge cracks within the triangular lattice of an fcc material are addressed. We have also examined the effect of presence of a nanovoid in the vicinity of one of the crack-tips, on the competition of the cracks. An atomic scale finite element method (AFEM) [B. Liu, Y. Huang, H. Jiang, S. Qu, K.C. Hwang, The atomic-scale finite element method, Comput. Methods Appl. Mech. Eng. 193 (2004) 1849-1864], based on the Morse interatomic potential, is employed to explore the events in the (1 1 1) plane. Particular attention is given to the phenomenon of brittle-to-ductile transition (BDT) that occurs during crack propagation. © 2007 Elsevier B.V. All rights... 

Mixed-mode fracture mechanics analysis of an embedded arbitrarily oriented crack in a two-dimensional functionally graded material using plane elasticity theory is considered. The material properties are assumed to vary exponentially in two planar directions. Then, employing Fourier integral transforms with singular integral equation technique, the problem is solved. The stress intensity factors (SIFs) at the crack tips are calculated under in-plane mechanical loads. Finally, the effects of crack orientation, material non-homogeneity, and other parameters are discussed on the value of SIF in mode I and mode II fracture  

Charpy impact energy of the produced Al6061-SiCp laminated nanocomposites by mechanical alloying was modeled by adaptive neuro-fuzzy interfacial systems (ANFIS) in both crack divider and crack arrester configurations. The model was constructed by training, validating and testing of 171 gathered input-target data. The thickness of layers, the number of layers, the adhesive type, the crack tip configuration and the content of SiC nanoparticles were five independent input parameters utilized for modeling. The output parameter was Charpy impact energy of the nanocomposites. The performance of the proposed models was evaluated by absolute fraction of variance, the absolute percentage error and...