Edge-cracked bimaterial systems under thermal heating

Abstract

a b s t r a c tThe problem of thermoelastic edge-cracking in two-layered bimaterial systems subjected to convective heating is considered. The medium is assumed to be insulated on one surface and exposed to sudden convective heating on another surface containing the edge crack. It is known that, when a bimaterial system's surface is heated, compressive stresses arise near the heating surface, forcing the crack surfaces together over a certain cusp-shaped contact length. It is also known that, for a cooled bimaterial systems surface, tensile stresses take place close to the cooling surface and tend to open the crack. So, the edge cracked heating surface problem is treated as an embedded crack with a smooth closure condition of the crack surfaces, with the crack contact length being an additional unknown variable. Superposition and uncoupled quasi-static thermoelasticity principles are adopted to formulate the problem. By using a Fourier integral transform technique, the mixed boundary value problem is reduced to a Cauchy type singular integral equation with an unknown function as the derivative of the crack surface displacement. The numerical results of the stress intensity factors for an edge crack and a crack terminating at the interface, are calculated and presented as a function of time, crack length, heat transfer coefficient, and thickness ratio for two different bimaterial systems, namely a stainless steel layer welded on ferritic steel and a ceramic layer coating on ferritic steel.

Analysis of Thermal Stress Intensity Factors for Edge Cracked Bimaterial System

“…As a plane strain problem in z-direction, the transient thermal stresses produced in the un-cracked medium may be obtained by the following formula [6] )] , ( ) (…”

“…where the constants E ,ν ,α designate the Young's modulus, Poisson's ratio and coefficient of thermal expansion, respectively. The time-dependent parameters ) ( 0 t  denotes the uniform strain at 0  x and ) (t  represents the radius of curvature at 0  x [6]. The stress intensity factor is therefore extracted from the finite element solution with the following formula [7]…”

“…in the case of plane strain problem. By endowing the coating and substrate with some material constants, a series of runs were performed to duplicate various results obtained by Rizk and Hrairi [6].…”