An Elastic Moduli Independent Approximation to the Radius of Curvature of the Bimetallic strip

Abstract

A parametric approach has been used to derive an approximate formula for the prediction of the radius of curvature of a thin bimetallic strip that at initial ambient temperature, is both flat and straight, but at above ambient temperature, forms into an arc of a circle. The formula enables the evaluation of the radius of curvature of the strip as a function of heating or cooling. A formula for calculating the radius of curvature of a bimetallic strip already exists, and was produced by Timoshenko in his paper on Bimetallic Thermostats. The formula by Timoshenko has been vigorously tested, tried and proven and accepted in countless papers and journals since its original publication. The parametric approach solution introduced in this work gives an approximate solution to the Timoshenko formula for equal thicknesses of two mating metals within the bimetallic. The Khatkhate Singh Mirchandani (KSM) formula presented here is taken from the first order approximation derived by Angel and Haritos by incorporating the ratio of Young's modulus of the bimetallic materials. Furthermore, researchers in this area have proven that the Young's modulus does not have a significant effect on the radius of curvature. Taking this fact into consideration, the authors have suitably incorporated a correction modifier purely based on the coefficient of thermal expansion (CTE) of the materials. The simulation results and the overall close agreement with the Timoshenko formula has been put forward here. Also, the solution derived by the authors Khatkhate et.al shows better prediction as compared to the solutions derived by other researchers.

The Influence of Flame Exposure and Solid Particle Erosion on Tensile Strength of CFRP Substrate with Manufactured Protective Coating

“…The deformation will depend on both the coating material used and the thickness ratio of the substrate to the coating and can be determined analytically using Equation (1) [ 36 ]. where:…”

“…Another disadvantage of the presented solution is that as a result of the difference in thermal expansion of the substrate material and the forming coating, the sample will be slightly bent when cooled and removed from the autoclave (Figure 9). The deformation will depend on both the coating material used and the thickness ratio of the substrate to the coating and can be determined analytically using Equation ( 1) [36].…”

“…If we compare the result from Table 4 for the quartz sand coating with the calculation from Equation (1), the difference is 18.7%. The deformation will depend on both the coating material used and the thickness ratio of the substrate to the coating and can be determined analytically using Equation (1) [36].…”