Investigating the potential of FGMs through numerical minimization of thermal stresses

Abstract

Functionally graded materials (FGMs) have the potential to reduce high stress concentrations near material interfaces.In the ITER divertor monoblock, this may be achieved by replacing the distinct W-Cu interface by an FGM, which gradually changes the coefficient of thermal expansion (CTE) from copper to tungsten. To assess the full potential of FGMs in improving the thermal and mechanical behavior, a first proof-of-principle study is performed in this paper to numerically optimize the tungsten volume fraction distribution of a W-Cu FGM based ITER monoblock for minimal thermal stresses using a simple thermal conduction model. We show that the optimizer can ensure that the temperature remains below the recrystallization temperature of tungsten and that it minimizes the chosen cost function, based on the fractional margin between the local temperature and melting temperature, in a computationally efficient way. Furthermore, the resulting design has a lower Von Mises stress measure at the original position of the W-Cu interface. However, a new material interface is introduced, which results in an additional undesired stress concentration. Future work should therefore aim at integrating a complete stress evaluation in the optimization method.

Optimized design of a tungsten–copper functionally graded material monoblock for minimal von Mises stress meeting the material operational temperature window

“…Different methods exist to reduce the amount of explicit constraints in the optimization problem. One option is constraint aggregation, already used by the authors in [24], where each state constraint was reformulated using a constraint aggregation function, resulting in one differential constraint. However, the resulting constraint only approximates the real constraints, and might lead to designs not satisfying the original constraints.…”

“…Furthermore, they neglected the contribution of the temperature dependence of material properties on the sensitivities to speed up the optimization process. During the same period, the authors of this paper also published a first proof-of-principle monoblock composition optimization using the adjoint approach (see also section 4) [24]. The key advantage of the adjoint approach is that it renders the cost of sensitivity calculation independent of the number of design variables, and does not require any model assumptions or simplifications to be accurate and efficient.…”

“…Adjoint techniques are already well-known in other engineering domains, such as aircraft design [25,26], but have also been applied recently to divertor shape [27,28], magnetic divertor [29,30] design, and parameter estimation [31]. The optimization in [24] was, however, based on an exclusively thermal model and cost function, and it was shown with a stress analysis that while the thermal model avoided embedding a full stress simulation into the optimization it was unable to correctly account for the locally high thermal stresses. In addition, the constraint aggregation approach used in that paper was only able to deal with the material temperature window constraints in an approximate way.…”

“…The paper is organized as follows: section 2 discusses an adequate cost function formulation for the monoblock, which represents the performance of the design. Because the work in [24] already indicated the importance of including stresses in the cost function, the von Mises (VM) stress and von Mises yield criterion (YC) will be taken as performance measures. Section 3 describes the model used to evaluate the necessary temperature and stress distributions.…”

Surface effect on vibration characteristics of bi-directional functionally graded nanobeam using Eringen’s nonlocal theory

“…The requirement of reliable mechanical and thermal performance of materials has discovered a new class of composite materials, namely, functionally graded materials (FGMs) [1,2]. These materials have a smooth continuous variation of material properties in one or more directions.…”