The Surface Crack Problem for a Plate With Functionally Graded Properties

1997 ◽  
Vol 64 (3) ◽  
pp. 449-456 ◽  
Author(s):  
F. Erdogan ◽  
B. H. Wu
Keyword(s):  
Crack Opening ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Opening Displacement ◽  
Nonhomogeneous Layer ◽  
Edge Cracks ◽  
Graded Properties ◽  
Plane Elasticity Problem

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.

The Axisymmetric Crack Problem in a Nonhomogeneous Medium

1993 ◽  
Vol 60 (2) ◽  
pp. 406-413 ◽  
Author(s):  
M. Ozturk ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Shear Modulus ◽  
Mixed Mode ◽  
Crack Opening ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Nonhomogeneous Medium ◽  
Intensity Factors ◽  
Simple Simulation ◽  
Graded Properties

In this paper, the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by μ = μ0eαz. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formualated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter a for various loading conditions. Also given are some sample results showing the crack opening displacements.

scholarly journals Analytical Solution of a Crack Problem in a Radially Graded FGM

2009 ◽  
Vol 631-632 ◽  
pp. 115-120
Author(s):  
Suat Çetin ◽  
Suat Kadıoğlu
Keyword(s):  
Stress Intensity ◽  
Plane Strain ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Approximate Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Homogeneous Layer ◽  
Intensity Factors ◽  
Functionally Graded Layer

The objective of this study is to determine stress intensity factors (SIFs) for a crack in a functionally graded layer bonded to a homogeneous substrate. Functionally graded coating contains an edge crack perpendicular to the interface. It is assumed that plane strain conditions prevail and the crack is subjected to mode I loading. By introducing an elastic foundation underneath the homogeneous layer, the plane strain problem under consideration is used as an approximate model for an FGM coating with radial grading on a thin walled cylinder. The plane elasticity problem is reduced to the solution of a singular integral equation. Constant strain loading is considered. Stress intensity factors are obtained as a function of crack length, strip thicknesses, foundation modulus, and inhomogeneity parameter.

An Analysis of Cracking in a Layered Medium With a Functionally Graded Nonhomogeneous Interface

1996 ◽  
Vol 63 (2) ◽  
pp. 479-486 ◽  
Author(s):  
Hyung Jip Choi
Keyword(s):  
Layered Medium ◽  
Crack Problem ◽  
Crack Size ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Interfacial Region ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Transitional Layer ◽  
Homogeneous Surface

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The substrate is considered to be semi-infinite containing a crack perpendicular to the nominal interface. The stiffness matrix approach is employed as an efficient method of formulating the proposed crack problem. A Cauchy-type singular integral equation is then derived. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered medium. Specifically, the influences of the crack size and location and the layer thickness are addressed for various material combinations.

A NEW METHOD TO DETERMINE TENSILE-STRAIN SOFTENING CURVE OF QUASI-BRITTLE MATERIALS

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Ruimei An ◽  
Shujin Duan ◽  
Quanmin Guo
Keyword(s):  
Crack Opening Displacement ◽  
Tensile Strain ◽  
Strain Softening ◽  
Crack Opening ◽  
Crack Problem ◽  
Brittle Materials ◽  
Cohesive Crack ◽  
New Method ◽  
Opening Displacement ◽  
Softening Curve

Based on weight integration to obtain a closed solution of cohesive crack problem, a new method is proposed to determine the tensile-strain softening curve (TSC) for quasi-brittle materials. The key technique is to determine the weight function by superposition of the solution with different fictitious crack lengths to satisfy a given crack opening displacement within cohesive crack surfaces. As an example, a central crack problem under uniform tension with given crack opening displacement in the fracture process zone (FPZ) was analyzed, the corresponding TSC was determined, and then the solution for stress and displacement field was obtained.

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