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.

scholarly journals The Crack Problem in Bonded Nonhomogeneous Materials

1991 ◽  
Vol 58 (2) ◽  
pp. 410-418 ◽  
Author(s):  
F. Erdogan ◽  
A. C. Kaya ◽  
P. F. Joseph
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Stress Singularity ◽  
Crack Tip ◽  
Plane Elasticity ◽  
Primary Objective ◽  
Intensity Factors ◽  
Shear Moduli ◽  
Square Root Singularity

In this paper the plane elasticity problem for two bonded half-planes containing a crack perpendicular to the interface is considered. The primary objective of the paper is to study the effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors. The two materials are, thus, assumed to have the shear moduli μ0 and μ0exp(βx), x = 0 being the diffusion plane. Of particular interest is the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r−α, 0<α<1, in this problem the stresses have a standard square root singularity regardless of the location of the crack tip. The nonhomogeneity constant β has, however, considerable influence on the stress intensity factors.

The Mixed Mode Crack Problem in a FGM Layer

2003 ◽  
Author(s):  
X. Long ◽  
F. Delale
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Crack Problem ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Multiphase Composites ◽  
Fgm Layer ◽  
First Time

Functionally graded materials (FGMs) are multiphase composites whose composition, microstructure and properties vary gradually. They can be tailored to meet the requirements encountered in practice through the design of their constituents. In this paper, analytical expressions for stress intensity factors off mixed-mode cracks in a FGM strip have been derived for the first time. A parametric study, by varying both the geometric and material parameters, is conducted to determine their effects on the stress intensity factors.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Analysis of Multiple Rigid-Line Inclusions for Application to Bio-Materials

2007 ◽  
Author(s):  
Pawan S. Pingle ◽  
Larissa Gorbatikh ◽  
James A. Sherwood
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Building Blocks ◽  
Duality Principle ◽  
Inclusion Problem ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Aspect Ratios ◽  
Rigid Line

Hard biological materials such as nacre and enamel employ strong interactions between building blocks (mineral crystals) to achieve superior mechanical properties. The interactions are especially profound if building blocks have high aspect ratios and their bulk properties differ from properties of the matrix by several orders of magnitude. In the present work, a method is proposed to study interactions between multiple rigid-line inclusions with the goal to predict stress intensity factors. Rigid-line inclusions provide a good approximation of building blocks in hard biomaterials as they possess the above properties. The approach is based on the analytical method of analysis of multiple interacting cracks (Kachanov, 1987) and the duality existing between solutions for cracks and rigid-line inclusions (Ni and Nasser, 1996). Kachanov’s method is an approximate method that focuses on physical effects produced by crack interactions on stress intensity factors and material effective elastic properties. It is based on the superposition technique and the assumption that only average tractions on individual cracks contribute to the interaction effect. The duality principle states that displacement vector field for cracks and stress vector-potential field for anticracks are each other’s dual, in the sense that solution to the crack problem with prescribed tractions provides solution to the corresponding dual inclusion problem with prescribed displacement gradients. The latter allows us to modify the method for multiple cracks (that is based on approximation of tractions) into the method for multiple rigid-line inclusions (that is based on approximation of displacement gradients). This paper presents an analytical derivation of the proposed method and is applied to the special case of two collinear inclusions.

scholarly journals A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3581 ◽  
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

A Method to Extract Interface Stress Intensity Factors Using Interlayers

2005 ◽  
Author(s):  
Sridhar Santhanam
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Interface Stress ◽  
Mode I ◽  
Universal Relation ◽  
Intensity Factors ◽  
Infinite Blocks

A method is presented here to extract stress intensity factors for interface cracks in plane bimaterial fracture problems. The method relies on considering a companion problem wherein a very thin elastic interlayer is artificially inserted between the two material regions of the original bimaterial problem. The crack in the companion problem is located in the middle of the interlayer with its tip located within the homogeneous interlayer material. When the thickness of the interlayer is small compared with the other length scales of the problem, a universal relation can be established between the actual interface stress intensity factors at the crack tip for the original problem and the mode I and II stress intensity factors associated with the companion problem. The universal relation is determined by formulating and solving a boundary value problem. This universal relation now allows the determination of the stress intensity factors for a generic plane interface crack problem as follows. For a given interface crack problem, the companion problem is formulated and solved using the finite element method. Mode I and II stress intensity factors are obtained using the modified virtual crack closure method. The universal relation is next used to obtain the corresponding interface stress intensity factors for the original interface crack problem. An example problem involving a finite interface crack between two semi-infinite blocks is considered for which analytical solutions exist. It is shown that the method described above provides very acceptable results.

Sign in / Sign up

Export Citation Format

Share Document