General Crack-Tip Fields for Stationary and Steadily Growing Interface Cracks in Anisotropic Bimaterials

1993 ◽  
Vol 60 (1) ◽  
pp. 183-189 ◽  
Author(s):  
X. Deng
Keyword(s):  
Crack Tip ◽  
Antiplane Shear ◽  
Polar Coordinates ◽  
Bimaterial Interface ◽  
Series Expansions ◽  
Displacement Fields ◽  
Interface Cracks ◽  
Stress And Displacement Fields ◽  
Special Cases ◽  
Anisotropic Bimaterials

This study builds upon some recent results in the literature regarding the asymptotic behavior of bimaterial interface cracks, and gives the general form, both oscillatory and nonoscillatory, of the crack-tip stress and displacement fields for stationary and steadily growing interface cracks in anisotropic bimaterials, which are equivalent to complete Williams-type series expansions. Special cases, such as cracks in homogeneous anisotropic materials and interface cracks with decoupled antiplane shear and in-plane deformations, are discussed briefly. Explicit series expansions of the stress and displacement fields in crack-tip polar coordinates are derived for both stationary and steadily propagating interface cracks in isotropic bimaterials.

scholarly journals NUMERICAL PHOTOMECHANICS: NUMERICAL PROCESSING OF PHOTOELASTICITY EXPERIMENTS AND ITS APPLICATION TO THE PROBLEMS OF FRACTURE MECHANICS PROBLEMS

2017 ◽  
Vol 19 (9.2) ◽  
pp. 63-73
Author(s):  
T.E. Gerasimova ◽  
P.N. Lomakov ◽  
L.V. Stepanova
Keyword(s):  
Experimental Study ◽  
Experimental Investigation ◽  
Asymptotic Expansion ◽  
Fracture Mechanics ◽  
Asymptotic Expansions ◽  
Strain State ◽  
Crack Tip ◽  
Displacement Fields ◽  
Photoelasticity Method ◽  
Stress And Displacement Fields

On the basis of photoelasticity method the experimental study of near crack tip stressed strain state in specimens under mixed loading conditions is performed. Carried out experimental investigation allows to obtain coefficients of full asymptotic expansions of stress and displacement fields in the vicinity of the crack tip and alos to find coefficients of highest approach in Williams full asymptotic expansion.

scholarly journals On stationary and moving interface cracks with frictionless contact in anisotropic bimaterials

1993 ◽  
Vol 443 (1919) ◽  
pp. 563-572
Keyword(s):  
Crack Problem ◽  
Stress Singularity ◽  
Crack Tip ◽  
Substantial Part ◽  
Open Crack ◽  
Interface Cracks ◽  
Complete Representation ◽  
Crack Tip Fields ◽  
Out Of Plane ◽  
Anisotropic Bimaterials

The asymptotic structure of near-tip fields around stationary and steadily growing interface cracks, with frictionless crack surface contact, and in anisotropic bimaterials, is analysed with the method of analytic continuation, and a complete representation of the asymptotic fields is obtained in terms of arbitrary entire functions. It is shown that when the symmetry, if any, and orientation of the anisotropic bimaterial is such that the in-plane and out-of-plane deformations can be separated from each other, the in-plane crack-tip fields will have a non-oscillatory, inverse-squared-root type stress singularity, with angular variations clearly resembling those for a classical mode II problem when the bimaterial is orthotropic. However, when the two types of deformations are not separable, it is found that an oscillatory singularity different than that of the counterpart open-crack problem may exist at the crack tip for the now coupled in-plane and out-of-plane deformation. In general, a substantial part of the non-singular higher-order terms of the crack-tip fields will have forms that are identical to those for the counterpart open-crack problem, which give rise to fully continuous displacement components and zero tractions along the crack surfaces as well as the material interface.

Antiplane Shear Interface Cracks in Anisotropic Bimaterials

1991 ◽  
Vol 58 (2) ◽  
pp. 399-403 ◽  
Author(s):  
Kuang-Chong Wu ◽  
Yu-Tsung Chiu
Keyword(s):  
Stress Intensity ◽  
Lower Bound ◽  
Cross Sections ◽  
Antiplane Shear ◽  
Numerical Results ◽  
Composite Body ◽  
Interface Cracks ◽  
Integral Equation Formulation ◽  
Anisotropic Bimaterials ◽  
Shear Interface

An analysis of antiplane shear interface cracks in a finite anisotropic composite body is presented. The analysis is done by a new complex-variable integral equation formulation based on the solutions of a dislocation and body force in an infinite composite body. Numerical results of the stress intensity factors are presented for the composite bodies with finite rectangular cross-sections under uniform shear. The composite bodies are formed by bonding an orthotropic material to an isotropic material. The numerical results show that there exists a lower bound for the stress intensity factor for a fixed crack-length-to-height ratio and that the lower bound is attained in the case of isotropic bimaterial.

Elastic Fields Around the Cohesive Zone of a Mode III Crack Perpendicular to a Bimaterial Interface

2007 ◽  
Vol 74 (5) ◽  
pp. 1049-1052 ◽  
Author(s):  
W. Zhang ◽  
X. Deng
Keyword(s):  
Cohesive Zone ◽  
Bimaterial Interface ◽  
Mode Iii ◽  
Displacement Fields ◽  
Mode Iii Crack ◽  
Elliptic Coordinates ◽  
Elastic Fields ◽  
Stress And Displacement Fields

Asymptotic stress and displacement fields near the cohesive zone ahead of a semi-infinite Mode III crack normal to a bimaterial interface are derived using elliptic coordinates.

Dynamic Crack-Tip Stress and Displacement Fields Under Thermomechanical Loading in Functionally Graded Materials

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Kwang Ho Lee ◽  
Vijaya Bhaskar Chalivendra ◽  
Arun Shukla
Keyword(s):  
Functionally Graded Materials ◽  
Maximum Shear Stress ◽  
Crack Tip ◽  
Functionally Graded ◽  
Dynamic Crack ◽  
Loading Conditions ◽  
Thermomechanical Loading ◽  
Displacement Fields ◽  
Graded Materials ◽  
Stress And Displacement Fields

Thermomechanical stress and displacement fields for a propagating crack in functionally graded materials (FGMs) are developed using displacement potentials and asymptotic analysis. The shear modulus, mass density, and coefficient of thermal expansion of the FGMs are assumed to vary exponentially along the gradation direction. Temperature and heat flux distribution fields are also derived for an exponential variation of thermal conductivity. The mode mixity due to mixed-mode loading conditions around the crack tip is accommodated in the analysis through the superposition of opening and shear modes. Using the asymptotic stress fields, the contours of isochromatics (contours of constant maximum shear stress) are developed and the results are discussed for various crack-tip thermomechanical loading conditions.

scholarly journals APPLICATION OF QUARTER-POINT SINGULAR ELEMENT IN FINITE ELEMENT METHOD TO SIMULATION OF CRACK TIP BEHAVIOR

2010 ◽  
Vol 13 (2) ◽  
pp. 5-13
Author(s):  
Thien Tich Truong ◽  
Bang Kim Tran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Crack Tip ◽  
Singular Element ◽  
Displacement Fields ◽  
Mathematical Background ◽  
Stress And Displacement Fields ◽  
Calculation Results ◽  
Element Method

Fracture mechanics is a new branch in engineering. The development of modern mathematical background with different numerical methods has supported fracture mechanics to solve many complex fracture problems in practice effectively. This article introduces the application of quarter - point singular element in finite element method to simulate crack tip behavior in two dimensional problems. The ANSYS and FRANC2D programs are used to compute stress intensity factor, simulate the stress and displacement fields near crack tip and simulate crack propagation. The calculation results are compared with analytical results and the results in other articles.

Stress and Displacement Fields at a Transient Crack Tip Propagating in Functionally Graded Materials

2007 ◽  
Vol 345-346 ◽  
pp. 481-484
Author(s):  
Kwang Ho Lee ◽  
Gap Su Ban
Keyword(s):  
Functionally Graded Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Stress Fields ◽  
Displacement Fields ◽  
Graded Materials ◽  
Transient Motion ◽  
Stress And Displacement Fields ◽  
Displacement Potentials ◽  
Nonhomogeneous Materials

Stress and displacement fields for a transient crack tip propagating along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density under a constant Poisson's ratio are developed. The equations of transient motion in nonhomogeneous materials are developed using displacement potentials and the solution to the displacement fields and the stress fields for a transient crack propagating at nonuniform speed though an asymptotic analysis.

Sign in / Sign up

Export Citation Format

Share Document