Thermal Stress Analysis for Functionally Graded Plates with Modulus Gradation, Part II

Abstract

Background

The gradation of thermal expansion coefficient was analyzed in the earlier study. The analytical formulation derived here, which is quite different, should be validated to understand the thermal stress distribution in a laminated composite and functionally graded material. Besides this solution, a validated numerical model can also be used to optimize the material gradation of plates in terms of sustainability.

Objective

To validate the analytical formulation derived here, an experimental model is presented to understand the thermal stress concentration for functionally graded and laminated composite plates. A numerical model is also validated to extend to understand the effects of the number of layers, the thickness of a layer, the gradation function, the ratio of elastic moduli, and the coating.

Methods

The experimental problems in the production of the experimental models with layers of different elastic moduli are discussed here. In the experimental analysis, a three-dimensional photoelastic stress analysis of two- and four-layer composite plate was used to mechanically model the thermal expansion. The analytical solution for the thermal stress in a free plate was derived by the strain suppression method based on the principle of superposition. The numerical models were analyzed using finite element software. The step variation in the experiment was used as a reference point for a continuous or multi-layer (> 2) step variation of material coefficients in the models.

Results

The variation of stress concentration is shown for various cases of laminated and continuous gradations of elastic modulus. The four-layer experimental model provides the difference in thermal stress distribution as a result of a layered coating. The validated analytical and numerical models provide reasonable results. An empirical formula to optimize the material gradation in terms of elastic modulus is derived.

Conclusions

The experimental model can be used to analyze thermal stress in functionally graded materials. The gradations of the material in the plate or the coating of the plates can be optimized by the validated analytical and numerical models. The empirical formula can be used to determine the elastic modulus of the coating to minimize the stress concentration.