Boundary conditions, temperatures, and stress intensity factors under arbitrary thermal transients via the inverse route

A common threat to components is thermal shock from operational steady-state or transient thermal-states; an analysis of this type of problem ultimately requires the determination of stress intensity factors (SIF). For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable. Although more practical from a measurement standpoint, the inverse problem where the boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. Despite these difficulties, the inverse problem can be readily solved using a least-squares determination of polynomial coefficients based on a generalized direct solution to the Heat Equation. Once the unknown surface temperature history is determined, the resulting polynomial can also used with the generalized direct solution to determine the temperature and stress distributions as a function of time. For a semi-infinite slab with both edge- and surface-cracks, excellent agreement was seen with known solutions when this method was employed. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature. The method can also be implemented as part of a finite-element solution for more complex geometries when closed-form solutions do not exist.