Mathematical Modeling on the Residual Stresses in Coatings Due to Heat Treatments

Abstract

Coatings are implemented on engineering metals and alloys to augment the surface properties such as hardness as well as resistance to wear and corrosion. Heat treatments of coated metals/alloys are performed to aid in the progress of the bonding of the coatings to the substrate. During the air cooling process, the difference in the compositions of the coating and the substrate materials causes them to cool at different rates, which leads to straining in them. The paper presents the research on the mathematical investigation to evaluate the residual stresses in coatings caused due to heat treatments and subsequent air cooling. The mathematical modelling is executed to formulate the equations to represent the residual stresses retained in the coatings due to the heat treatments and subsequent air cooling. Air cooling undergoes two stages namely the initial quenching phase and the final cooling phase. During the quenching phase, the strain was expressed by considering the elastic, plastic and thermal strain components. Poisson’s ratio, deviatoric stress differential of the modulus of plasticity, coefficient of thermal expansion and change in temperature are used to express the elastic, plastic and thermal strain components. During the final cooling phase, the strain was expressed by considering only the elastic and thermal stain components, as the plastic staining the coating material generally does not occur during the final cooling phase and occurs only during the initial quenching phase. From the strain components, the residual stresses for the coatings in the x, y and z axis were formulated. Thus, the total residual stress is the sum total of stresses caused during the initial quenching phase and the final cooling phase.