scholarly journals Stress intensity factors for cusp-type crack problem under mechanical and thermal loading

2021 ◽  
Vol 37 ◽  
pp. 327-332
Author(s):  
F M Chen ◽  
C K Chao ◽  
C C Chiu ◽  
N A Noda
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Thermal Loading ◽  
Crack Problem ◽  
Auxiliary Function ◽  
Thermal Loads ◽  
Intensity Factors ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
Combined Loads

Abstract The general solutions of the stress intensity factors (SIFs) for a cusp-type crack problem under remote uniform mechanical and thermal loads are presented in this work. According to the complex variable theory and the method of conformal mapping, a symmetric airfoil crack is mapped onto a unit circle, and both the temperature and stress potentials are used to solve the relevant boundary-value problems. By introducing the auxiliary function and applying the analytical continuation theorem, the SIFs at the cusp-type crack tip can be analytically determined. The obtained SIF results are dependent on the geometric configurations of the cusp-type crack components and the magnitudes of the mechanical and thermal loads. For some combinations of combined loads, the SIF is maximized, and the system has a high risk of damage.

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.

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.

scholarly journals Stress Intensity Factors for a Non-Circular Hole with Inclusion Layer Embedded in a Cracked Matrix

Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Chenchun Chiu ◽  
Shaochen Tseng ◽  
Chingkong Chao ◽  
Jheyuan Guo
Keyword(s):  
Stress Intensity ◽  
Circular Hole ◽  
Composite Structures ◽  
Failure Behavior ◽  
Uniform Load ◽  
Intensity Factors ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
The Matrix ◽  
Stress Functions

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.

Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Ratnesh Khandelwal ◽  
J. M. Chandra Kishen
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Thermal Loading ◽  
Thermal Stresses ◽  
Body Force ◽  
Bimaterial Interface ◽  
Intensity Factors ◽  
Linear Elastic ◽  
Domain Integral ◽  
Bimaterial Interface Crack

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J2 integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the Jk domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the Jk integral. The proposed method is validated by solving standard problems with known solutions.

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.

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