All the studies on the thermoelastic behaviour of materials, including the revised higher order theory on the thermoelastic effect, are based on several assumptions that limit the application of such theory to the cases of isotropic materials in the presence of uniaxial residual stresses and undergoing uniaxial applied loads. These assumptions lead to some discrepancies in the description of the real thermoelastic behaviour of materials in the presence of residual stresses. In this work, by rewriting the thermoelastic equation in a different way, it was possible to study the behaviour of homogeneous and non-isotropic materials undergoing any loading conditions and residual stresses. Firstly, the error made by the calibration procedures of thermoelastic stress analysis (TSA) data in the presence of residual stresses has been investigated. Then, a statistical analysis was carried out to determine the minimum value of residual stress which would lead to significant and measurable variations in the thermoelastic signal. The simulations involved two non-ferrous metals: AA6082 and Ti6Al4V, which exhibit a specific thermoelastic behaviour.

Background The Stress Intensity Factor (SIF) is used to describe the stress state and the mechanical behaviour of a material in the presence of cracks. SIF can be experimentally assessed using contactless techniques such as Thermoelastic Stress Analysis (TSA). The classic TSA theory concerns the relationship between temperature and stress variations and was successfully applied to fracture mechanics for SIF evaluation and crack tip location. This theory is no longer valid for some materials, such as titanium and aluminium, where the temperature variations also depend on the mean stress. Objective The objective of this work was to present a new thermoelastic equation that includes the mean stress dependence to investigate the thermoelastic effect in the proximity of crack tips on titanium. Methods Westergaard’s equations and Williams’s series expansion were employed in order to express the thermoelastic signal, including the second-order effect. Tests have been carried out to investigate the differences in SIF evaluation between the proposed approach and the classical one. Results A first qualitative evaluation of the importance of considering second-order effects in the thermoelastic signal in proximity of the crack tip in two loading conditions at two different loading ratios, R = 0.1 and R = 0.5, consisted of comparing the experimental signal and synthetic TSA maps. Moreover, the SIF, evaluated with the proposed and classical approaches, was compared with values from the ASTM standard formulas. Conclusions The new formulation demonstrates its improved capability for describing the stress distribution in the proximity of the crack tip. The effect of the correction cannot be neglected in either Williams’s or Westergaard’s model.

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