Thermal stresses due to thermal expansion anisotropy in materials with preferred orientation

Abstract

Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Thermal stresses result from thermal expansion incompatibility in materials during the temperature change., Sources of thermal stresses include thermo- mechanical mismatch between two materials [1, 2], non-uniform temperature distribution in a material [3] and thermal expansion anisotropy in a single- phase material [4, 5]. The first two types of thermal stress have been studied extensively. The third type of thermal stress can be classified into stresses at the microscopic and the macroscopic levels. Examples of stresses at the microscopic level exist in single- phase polycrystalline materials, where localized thermal stresses arise from thermal expansion mis- match among randomly orientated grains [4]. Stres- ses at the macroscopic level can exist in materials with preferred crystallographic orientation [5]. A brief discussion of these macroscopic stresses is the topic of the present letter. Thermal expansion anisotropy is introduced in materials (especially non-cubic materials) with pre- ferred crystallographic orientation. This texture can occur during deposition of a coating on a substrate, a process that has been used extensively for fabrica- ting electronic and optical components. A particular crystal plane of the coating is often found to be parallel to the deposition surface. Hence, a large degree of anisotropy in properties, such as thermal expansion, can exist between the directions parallel and perpendicular to the deposition surface [6, 7]. For example, boron nitride crucibles can be synthes- ized by chemical vapour deposition on a mandrel, which results in the basal planes of the boron nitride structure being oriented parallel to the deposition surface. As a result, the textured boron nitride crucible has a thermal expansion coefficient in the radial direction (i.e. the direction perpendicular to the deposition surface) about 14 times of that in the tangential direction (i.e. the direction parallel to the deposition surface) [8]. Highly oriented supercon- ducting YBa2Cu30 x coatings on fibres with the basal planes of the coating material parallel to the fibre surface have been produced recently, and the thermal expansion coefficient of the coatings in the radial direction is found to be about four times of that in the tangential direction [9, 10]. This preferred orientation in the YBa2Cu30 x coating provides a very important contribution to increasing the current density in the direction of the fibre axis. Experimental evidence of macroscopic thermal (~ us Government. Contract No. DE-ACO5-84OR21400. stresses due to preferred orientation-related thermal expansion anisotropy has been found. For example, delamination of boron nitride crucibles is a frequent problem during cooling from the fabrication tem- perature [5], a failure mode that is consistent with the existence of the residual tensile stress in the radial direction. Extensive cracking due to the residual stress is also observed in the textured superconducting YBa2Cu3Ox coating during cooling which, in turn, results in low current density and low strength of the superconducting coating [9, 10]. The macroscopic thermal stresses due to thermal expan- sion anisotropy have been analysed for a two-dimen- sional case [5]. The results showed that radial tension, and combined tangential tension and com- pression, are induced in boron nitride crucibles during cooling. The purpose of the present letter is to visualize these thermal stresses schematically. Stresses due to thermal expansion anisotropy arise because of different thermal expansion coefficients in the radial and tangential directions in a cylindrical geometry during a temperature change. To facilitate visualizing the origin of these stresses, stresses are considered for a two-dimensional solid circle as shown in Fig. 1, where the radial thermal expansion coefficient, o#, is higher than the tangential thermal expansion coefficient, ol0, and b is the radius of the circle. Before cooling, an element that is originally at position