Transient internal crack problem for a nonhomogeneous orthotropic strip (Mode I)

The elastodynamic response of an infinite non-homogeneous orthotropic material with an interfacial finite crack under distributed normal and shear impact loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some materials are obtained. Interfacial cracks between two different materials and between two pieces of the same material but different fiber orientation are considered. Bimaterial formulation of a crack problem is shown to converge to the mono-material formulation, derived independently, in the limiting case when both materials are the same.

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“…Stress intensity factor in the Laplace transform domain can be expressed as (Itou, 2001;Chen et al, 2002)…”

Section: Stress Intensity Factormentioning

confidence: 99%

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

Lira-Vergara

Rubio-González

2005

Int J Fract

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“…Here, κ = 3−4ν for plane strain and κ = (3−ν)/(1+ν) for generalized plane stress. Equations (10) subjects to the following boundary conditions…”

Section: Problem Formulationmentioning

confidence: 99%

Thermal stress intensity factors for an interface crack in a functionally graded layered structures

Ding

Xing

2010

Arch Appl Mech

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The fracture behavior of a functionally graded layered structure (FGLS) with an interface crack under thermal loading is investigated. Considering new boundary conditions, it is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The problem is formulated in terms of a system of singular integral equations. Numerical results are presented to show the influence of the material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors (TSIFs).Keywords Functionally graded layered structure (FGLS) · Thermal resistance · Thermal stress intensity factors (TSIFs) IntroductionOne of the purposes for developing functionally graded materials (FGMs) is to replace the conventional homogeneous materials to reduce the magnitude of residual and thermal stresses and thus to increase the bonding strength where the materials are subjected to extremely high thermal loading. In designing components involving FGMs, an important aspect of the problem is the question of mechanical failure, specifically the fracture failure [1]. Fatigue and fracture characterization of materials and related analysis require the solution of certain standard crack problems. So far, many crack problems in FGMs have been solved to obtain the crack tip thermal stress intensity factors (TSIFs) by assuming the elastic properties varying due to functional forms [2][3][4][5][6][7].Assuming the perfect thermal insulation of the crack surfaces, Noda and Jin [8] studied the crack problem for an infinite functionally graded material (FGM) subjected to a steady-state heat flux over the crack surfaces by assuming continuously varying thermal properties. Choi et al. [9] studied the crack problems in FGM-like nonhomogeneous materials under thermal loading. The properties of practical FGMs, nevertheless, may vary in an arbitrary manner. Chen et al. [10] investigated the mode I surface crack problem for an orthotropic-graded strip under transient loading.Considering the partial insulation along the crack surfaces, Borgi and Erdogan [11,12] considered the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem of an embedded partially insulated crack in a graded coating bonded to a homogeneous substrate under thermal and mechanical loading is considered by Borgi et al [13]. In their studies, the continuity conditions of the temperature field and heat flux along the crack axis, outside the crack and along the interface are considered.In this paper, consider new boundary conditions, assuming that the interface crack is partially insulated and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction

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“…the integral transform and singular integral equation technique. For the isotropic and orthotropic FGMs under the pure mechanical load, several researchers have studied the fracture problems with various geometries and crack modes (e.g., Delale and Erdogan, 1983;Ozturk and Erdogan, 1993;Konda and Erdogan, 1994;Chen and Erdogan, 1996;Erdogan and Wu, 1997;Ozturk and Erdogan, 1997;Ozturk and Erdogan, 1999;Chen et al, 2002), and, in this respect, Erdogan (1995) has written an excellent review article. At the same time, the thermal fracture behavior of FGMs is also the studying focus, and many authors carried out the corresponding investigation for various geometries and thermal load conditions (e.g., Noda and Jin, 1993;Jin and Noda, 1994;Wu and Erdogan, 1996;Dag et al, 1999), and Noda (1999) has written another excellent review article on the subject of thermal fracture mechanics.…”

Section: Introductionmentioning

confidence: 99%

Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure

Chen

2005

Int J Fract

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The thermal fracture problem of an interface crack between a graded orthotropic coating and the homogeneous substrate is investigated by two different approaches. For the case that most of the material properties in the graded orthotropic coating are assumed to vary as an exponential function, the integral transform and singular integral equation technique is used to obtain some analytical results. In order to analyze the case with more complex material distribution, an interaction integral is presented to evaluate the thermal stress intensity factors of cracked functionally graded materials (FGMs), and then the element-free Galerkin method (EFGM) is developed to obtain the final numerical results. The good agreement is obtained between the numerical results and the analytical ones. In addition, the influence of material gradient parameters and material distribution on the thermal fracture behavior is also presented.

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Transient internal crack problem for a nonhomogeneous orthotropic strip (Mode I)

Cited by 66 publications

References 11 publications

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

Thermal stress intensity factors for an interface crack in a functionally graded layered structures

Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure

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