Thermoelastic Stress Analysis in the Presence of Biaxial Stresses in Titanium: Effect of the Mean Stress on Errors in Stress Evaluation

Abstract

Abstract Background Thermoelastic Stress Analysis (TSA) is a contactless technique capable of estimating superficial stresses on components subjected to dynamic loads. Surface stresses can be obtained by means of calibration methods that require the assessment of the thermoelastic constants. However, these methods can lead to errors in stress evaluation in those materials where the effect of the mean stress on the thermoelastic signal cannot be neglected (e.g., titanium). Objective The aim is the development of an analytic formulation of error made in first stress invariant amplitude evaluation for a biaxial stress state, when neglecting mean stress effect. Methods By considering the general theory of thermoelastic stress analysis accounting for the mean stress effect, the formulation of the thermoelastic effect in the presence of a biaxial stress state was obtained. The results were compared to those obtained by a numerical simulation and the proposed formulation has been validated for titanium by means of experimental tests. Results Firstly, the new formulation of thermoelastic temperature variations accounting for mean stress effect in presence of a biaxial stress state was provided. Secondly, an error analysis provided an analytical formulation for the error made in case mean stress effect is neglected for different case studies. Conclusions The error in stress evaluation can be considered as the error originating from the use of an incorrect calibration formula (traditional one)”. The new analytical formulation accounting for the general theory of thermoelastic stress analysis allows to account for the mean stress on titanium in the presence of a uniaxial and biaxial stress states and to evaluate the error made in neglecting such a second order effect when using TSA.