Thermoelastic stress analysis by means of a standard thermocamera

Thermoelastic analysis is a recently developed full-field, no-contact technique based on detecting temperature changes induced by a dynamic load proportional to its amplitude and synchronous with load history.1 In fact, it is known that a specimen changes its temperature when subjected to cyclic stresses; if the strain is elastic, the temperature change is produced by two main effects: elastoplasticity and thermoelasticity. The first phenomenon is due to microplasticity and energy dissipation inside a material, which causes mechanical energy to be converted into heat. Thermoelasticity can be explained by means of the first law of thermodynamics, whereby an increase in volume under adiabatic conditions is associated with a decrease in temperature, and vice versa.1 Thermoelasticity and elastoplasticity produce very different temperature patterns. The first induces a periodic temperature change, synchronous with loading history and proportional to the actual load amplitude, and the second produces a continuous temperature increment, which is related to both load amplitude and the number of cycles performed, and persists until thermal equilibrium is reached. The thermoelastic effect is usually neglected in standard thermography because it induces very small temperature changes compared to elastoplasticity, but it can be used for stress analysis because it is proportional to the amplitude of the first stress invariant (sum of principal stresses): this can be demonstrated for all isotropic material, with a linear stress/strain behaviour, on the basis of the first law of thermodynamics. In order to detect very small temperature changes (about 0.1 K in steel stressed at 100 MPa), thermoelastic stress measurements require suitable equipment; this is usually obtained by means of highly sensitive infrared detectors and a lock-in amplifier able to isolate that part of the temperature signal that is coherent with the load. Most modern differential thermocameras are equipped with focal plane array detectors and provide a full-field thermoelastic map in few seconds. In the literature, thermoelastic stress analysis (TSA) is usually undertaken using differential thermocameras,2,3 while standard thermocameras are mainly used for thermographic measurements in fatigue limit determination4 and only occasionally for TSA.5 In a previous study,6 the authors introduced a methodology to investigate the thermoelastic effect by means of an ordinary thermocamera; however, the experimental conditions were so strict that they seriously limited the applicability and usefulness of the methodology itself: the specimen had to be uniformly stressed and its constitutive material had to be isotropic. In the present study, these limitations have been overcome, thanks to the availability of a new thermocamera equipped with array detectors and the possibility of validating the results obtained against those provided by a differential thermocamera. The proposed methodology is based on a Fourier analysis of signals, performed through routines in Matlab™ code (The MathWorks, Natick, MA), whereby an accurate full-field thermoelastic map can be obtained from a sequence of standard thermographic images acquired by an ordinary thermocamera if the thermoelastic signal amplitude is estimated after flat-top windowing. As a result, this technique makes it possible to perform a meaningful TSA using a standard thermocamera, of particular benefit whenever, for reasons of cost or infrequent use, it is not possible to justify investing in a differential thermocamera.