Cracking of a layered medium on an elastic foundation under thermal shock

The cladded pressure vessel under thermal shock conditions which is simulated by using two simpler models was studied. The first model (Model 1) assumes that, if the crack size is very small compared to the vessel thickness, the problem can be treated as a semi-infinite elastic medium bonded to a very thin layer of different material. However, if the crack size is of the same order as the vessel thickness, the curvature effects may not be negligible. In this case it is assumed that the relatively thin walled hollow cylinder with cladding can be treated as a composite beam on an elastic foundation (Model 2). In both models, the effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. The calculated results include the transient temperature, thermal stresses in the uncracked medium and stress intensity factors which are presented as a function of time, and the duration of cooling ramp. The stress intensity factors are also presented as a function of the size and the location of the crack. The problem is solved for two bonded materials of different thermal and mechanical properties. The mathematical formulation results in two singular integral equations which are solved numerically. The results are given for two material pairs, namely an austenitic steel layer welded on a ferritic steel substrate, and a ceramic coating on ferritic steel. In the case of the yielded clad, the stress intensity factors for a crack under the clad are determined by using a plastic strip model and are compared with elastic clad results

Thermal Shock In Periodic Edge-Cracked Plate Supported By Elastic Foundation

The study of the transient thermal stress problem for a periodic edge cracks in an elastic plate on an elastic foundations is investigated. This study may also be applied for circumferentially periodic cracked hollow cylinder under transient thermal stresses. Based on previous studies, the cylindrical shell may be modeled by a plate on an elastic foundation. The thermal stresses are generated due to sudden convective cooling on the boundary containing the edge cracks while the other boundary is insulated. The superposition technique is utilized to solve the problem. The perturbation problem is formulated by using the thermal stresses obtained from uncracked problem with opposite sign on the crack surfaces as the only external loading. This leads to hypersingular integral equation with the crack surface displacement as the only unknown function. The main output of this study is the transient stress intensity factors that are evaluated numerically. The parametric studies based on time (Fourier number), crack length, coefficient of heat transfer (Biot number), Periodic crack spacing and the stiffness of elastic foundation are investigated.  Keywords: Fracture mechanics, Thermal stresses, Periodic crack, Stress intensity  factor

Edge-cracked bimaterial systems under thermal heating

The 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