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

Abstract

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

Thermo-mechanical XFEM crack propagation analysis of functionally graded materials

“…(31). The effect of two superimposed fields can be considered as [72] M l ¼ 2c 11 K aux I K I þc 12 K aux…”

“…Noda and Jin considered FGM cracks in semiinfinite media as perfectly insulated [28] while Borgi and Erdogan studied the same cracks using partial insulation [29,30] and FGM cracks were considered partially insulated by assuming a temperature drop across the crack surfaces by Ding and Li [31]. In non-insulated cracks, the heat conduction equation is solved by neglecting the crack existence and the results are applied as a force on the structure.…”

Thermoelastic analysis of nonhomogeneous structural materials with an interface crack under uniform heat flow

“…The subscript j( j = 1, 2, 3) indicates the homogeneous strip and two FGMs respectively. For the sake of mathematical convenience, the material properties are assumed to vary with a certain coordinate according to the same function in the fracture analysis of FGMs [10,13,17,18]. In this paper, the thermo-mechanical properties dependent on the y-coordinate are modeled as exponential function k 1 = k 2 exp(δ 1 y), μ 1 = μ 2 exp(β 1 y), α 1 = α 2 exp(γ 1 y), (1) …”

“…Different functionally graded materials with an interface crack subjected to thermal and mechanics loading has been studied by Ding and Li [13]. Petrova and Schmauder [14] considered the fracture criteria for a bi-material consisting of a homogeneous and a FGM with systems of internal defects.…”

Thermal Stress Analysis of an Embedded Crack in a Graded Orthotropic Coating-Substrate Structure

“…Ding and Li [22] studied the fracture problem of a functionally graded layered structure with an interface crack under thermal loading. The functionally graded plate with an array of periodically spaced surface cracks of alternating lengths subjected to thermal shocks is considered by Feng and Jin [23].…”