Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method

2003 ◽  
Vol 51 (7) ◽  
pp. 1267-1286 ◽  
Author(s):  
Soonsung Hong ◽  
Kyung-Suk Kim
Keyword(s):  
Projection Method ◽  
Cohesive Zone ◽  
Crack Tip ◽  
Cohesive Crack ◽  
Far Fields

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

A Crack Close to and Perpendicular to an Interface: Resolution of Anomalous Behavior With a Cohesive Zone

2019 ◽  
Vol 86 (3) ◽  
Author(s):  
George G. Adams
Keyword(s):  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Applied Pressure ◽  
Stress Singularity ◽  
Crack Tip ◽  
Anomalous Behavior ◽  
Work Of Adhesion ◽  
Bimaterial Interface ◽  
Zone Model ◽  
Finite Distance

In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

SGBEM for Cohesive Cracks in Homogeneous Media

2010 ◽  
Vol 454 ◽  
pp. 1-10 ◽  
Author(s):  
Luis Távara ◽  
Vladislav Mantič ◽  
Alberto Salvadori ◽  
Leonard J. Gray ◽  
Federico París
Keyword(s):  
Cohesive Zone ◽  
Numerical Results ◽  
Cohesive Crack ◽  
Bending Test ◽  
Mode I ◽  
Zone Model ◽  
Linear Elastic ◽  
Integral Equation Formulation ◽  
Crack Problems ◽  
Homogeneous Media

In this paper, the Symmetric Galerkin Boundary Element Method for Linear Elastic Fracture Mechanics is extended to non-linear cohesive cracks propagating through homogeneous linear elastic isotropic media. The cohesive model adopted is based on the concept of free energy density per unit undeformed area. The corresponding constitutive cohesive equations present a softening branch which induces a potential instability. Thus, a suitable solution algorithm capable of following the growth of the cohesive zone is needed, and in the present work the numerical simulation is controlled by an arc-length method combined with a Newton-Raphson algorithm for the iterative solution of nonlinear equations. The Boundary ElementMethod is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries of linear elastic domains. Moreover a Galerkin approximation scheme, applied to a suitable symmetric boundary integral equation formulation, ensures an easy and efficient treatment of cracks in homogeneous media and an excellent convergence behavior of the numerical solution. The cohesive zone model is applied to simulate a pure mode I crack propagation in concrete. Numerical results for three-point bending test are used to check the numerical results for mode I and are compared with some numerical results obtained by FEM analysis found in the literature.

scholarly journals Vector form Intrinsic Finite Element Based Approach to Simulate Crack Propagation

2017 ◽  
Vol 33 (6) ◽  
pp. 797-812 ◽  
Author(s):  
Y. F. Duan ◽  
S. M. Wang ◽  
R. Z. Wang ◽  
C. Y. Wang ◽  
E. C. Ting
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Integral Method ◽  
Crack Tip ◽  
Cohesive Crack ◽  
Vector Form ◽  
Mass Particle ◽  
Integral Methods ◽  
Stiffness Matrices ◽  
Cohesive Crack Propagation

AbstractThis paper presents a new approach to simulate the propagation of elastic and cohesive cracks under mode-I loading based on the vector form intrinsic finite element method. The proposed approach can handle crack propagation without requiring global stiffness matrices and extra weak stiffness elements. The structure is simulated by mass particles whose motions are governed by the Newton's second law. Elastic and cohesive crack propagation are simulated by proposed VFIFE-J-integral and VFIFE-FCM methods, respectively. The VFIFE-J-integral method is based on vector form intrinsic finite element (VFIFE) and J-integral methods to calculate the stress intensity factors at the crack tips, and the VFIFE-FCM method combines VFIFE and fictitious crack models (FCM). When the stress state at the crack tip meets the fracture criterion, the mass particle at the crack tip is separated into two particles. The crack then extends in the plate until the plate splits into two parts. The proposed VFIFE-J-integral method was validated by elastic crack simulation of a notched plate, and the VFIFE-FCM method by cohesive crack propagation of a three point bending beam. As assembly of the global stiffness matrix is avoided and each mass particle motion is calculated independently, the proposed method is easy and efficient. Numerical comparisons demonstrate that the present results predicted by the VFIFE method are in agreement with previous analytical, numerical and experimental works.

Effect of Grain Size on the Fracture Toughness of Bimodal Nanocrystalline Materials

2014 ◽  
Vol 936 ◽  
pp. 400-408 ◽  
Author(s):  
Ying Guang Liu ◽  
Xiao Dong Mi ◽  
Song Feng Tian
Keyword(s):  
Fracture Toughness ◽  
Stress Intensity Factor ◽  
Grain Size ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Critical Stress ◽  
Crack Tip ◽  
Critical Stress Intensity Factor ◽  
Coarse Grain

To research the effect of grain size on the fracture toughness of bimodal nanocrystalline (BNC) materials which are composed of nanocrystalline (NC) matrix and coarse grains, we have developed a theoretical model to study the critical stress intensity factor (which characterizes toughness) of BNC materials by considering a typical case where crack lies at the interface of two neighboring NC grains and the crack tip intersect at the grain boundary of the coarse grain, the cohesive zone size is assumed to be equal to the grain sizedof the NC matrix. Blunting and propagating processes of the crack is controlled by a combined effect of dislocation and cohesive zone. Edge dislocations emit from the cohesive crack tip and make a shielding effect on the crack. It was found that the critical stress intensity factor increases with the increasing of grain sizedof the NC matrix as well as the coarse grain sizeD. Moreover, the fracture toughness is relatively more sensitive to the coarse grain size rather than that of NC matrix.

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