Sharif Digital Repository

Based on the Eshelby's equivalent inclusion method (EIM) and Hill's theorem on discontinuities of elastic fields across the interfaces, a theory for the determination of the stress intensity factors (SIFs) of arbitrarily oriented interacting cracks under non-uniform far-field applied stress (strain) is developed. As shown in this investigation the EIM proposed by Moschovidis and Mura can be extended for treatment of such problems, but their formulations are quite cumbersome and computationally inefficient. An alternative analytical approach is proposed that is computationally more efficient, and unlike the method of Moschovidis and Mura can easily handle complex problems of interacting... 

The fracture phenomenon is defined via the change of state of structure (entity) between the intact and the fractured end states as the function of the state variable. The twin state functions are defined for the transition of unit of the entity between its two end states. The state ratio is defined as the ratio of the two state functions. The property of the cracked structure is defined as the product of the structure property and the state ratio. The work is then used to derive the main parameters of the fracture mechanics. The work is verified via five examples. © 2016, Springer-Verlag Berlin Heidelberg  

The conventional energy release rate approach to the computation of the crack compliance in rotors is critically reviewed and its shortcoming is highlighted. The state functions and the generic compliance are introduced, defined, and verified. The proposed functions are defined based on the end states' conditions and are exact. The crack compliance of the shaft in torsion is explicitly defined as the function of the crack depth ratio and recommended as a good alternative to the classical procedure of the energy release rate method. The accuracy and efficiency of the work are verified by concise mathematical formulation and comparison of the results of the work with the others in four... 

Studying the reliability of cracked structures under different types of failure modes such as a mixture of Mode I and Mode II loadings has been of great importance in many applications. The purpose of this study is to evaluate the effects of different modes of loading, i.e. pure Mode I, pure Mode II and Mixed mode I/II loadings on the reliability of cracked structures via three typical case studies including 1st: through crack in a very wide plate, 2nd: cracked pressurized fuselage and 3rd: cracked fastener holes under actual geometries and loading conditions using the FORM, the fracture toughness and the equivalent SIF for Mixed mode I/II loading which is extracted by the Energy release... 

In this paper, the numerical studies on the semi-elliptical crack behavior in different locations of welded zones in the supporting structure of a spherical pressure vessel under an earthquake are presented. The cracks in the welded zones of supporting structures under earthquake effects may jeopardize the safety of spherical pressure vessels and result in catastrophic failure. A detailed finite element sub-modeling technique is carried out to compute the mixed-mode stress intensity factors along the crack front. Furthermore, crack behavior with different aspect ratios a/c: 0.25, 0.5, and 0.75 at the weld and the heat-affected zone of the supporting structure is evaluated. The... 

A smooth rigid circular anchor disk encapsulated by a penny-shaped crack is embedded in and unbounded transversely isotropic medium. The lamellar rigid disk exerts a nonuniform axisymmetric loading to the upper face of the crack. With the aid of an appropriate stress function and Hankel transform, the governing equations are converted to a set of triple integral equations which in turn are reduced to a Fredholm integral equation of the second kind. For some transversely isotropic materials the normalized stiffness of the system falls well outside of the envelope pertinent to isotropic media. It is shown that mode I stress intensity factor is independent of the material properties and solely... 

Due to inadequacy of the classical continuum theories at the nano-scale when dealing with defects, stress concentrators, and relevant deformation phenomena in solids, a refined approach that can capture the discrete atomic features of solids is essential. The inability to detect the size effect, giving unrealistically high values for some components of the stress field right on the edge of the stress concentrators, and infirmity to address the complex interaction between small inhomogeneities, cracks and as such when they are only a few nanometers apart, are among some of the drawbacks of the classical approach. An atomistic study which employs atomic finite element method in conjunction... 

The problem of crack modeling in 2D orthotropic media is considered. The extended finite element method has been adopted for modeling and analyzing a crack and its domain numerically. In this method, first the finite element model without any discontinuities is created and then the two-dimensional asymptotic crack-tip displacement fields with a discontinuous function are added to enrich the finite element approximation using the framework of partition of unity. The main advantage is the ability of the method in taking into consideration a crack without any explicit meshing of the crack surfaces, and the growth of crack can readily be applied without any remeshing. Mixed-mode stress intensity... 

Material properties and fracture characteristics are among the most prominent parameters that should be considered for a wide range of graphene applications. This article reviews recent advances in theoretical studies on the mechanical properties and fracture behaviors of graphene, focusing on the effect of various simulation models. Most studies investigated single-layer graphene sheets (SLGSs) under uniaxial tensile tests using different common interatomic potentials, particularly AIREBO. Although researchers have examined a similar problem, specifically for pristine graphene, the differences in the reported values are considerable. These discrepancies are most evident in fracture... 

Consider a lamellar inhomogeneity embedded in an unbounded isotropic elastic medium. When the elastic moduli of the lamellar inhomogeneity are zero it is a crack, if its elastic moduli are infinite it is an anticrack, and when its elastic moduli are finite it is called a quasicrack. Based on the Eshelby's equivalent inclusion method (EIM), the present paper develops a unified approach for determination of the exact closed-form expressions for modes I, II, and III stress intensity factors (SIFs) at the tips of lamellar inhomogeneities under a remote applied polynomial loading. © 2006 Elsevier Ltd. All rights reserved  

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... 

This paper presents a new procedure for determining the fracture toughness of rock-like specimens using the diametric compression test with the center-cracked horseshoe disk (CCHD) method. Using finite element analysis, a dimensionless stress intensity factor was obtained and a formula was rendered for determining mode I fracture toughness. To evaluate the accuracy of the measurement results produced by the CCHD method, fracture toughness experiments were conducted on the same rock-like material using the notched Brazilian disk (NBD) method. The CCHD tests were simulated using a two-dimensional particle flow code for validation of the experimental results, and a great agreement between the... 

Rocks and rock-like materials frequently fail under compression due to the initiation, propagation and coalescence of the pre-existing microcracks. The mechanism of microcrack coalescence process in rock-like materials is experimentally and numerically investigated. The experimental study involves some uniaxial compression tests on rock-like specimens specially prepared from portland pozzolana cement, mica sheets and water. The microcrack coalescence is studied by scanning electron microscopy on some of the prepared thin specimens. It is assumed that the mica sheets play the role of microcracks within the specimens. Some analytical and numerical studies are also carried out to simulate the...