Estimation of Stress Triaxiality from optically measured Strain Fields

Nowadays, strain fields can be experimentally measured with high accuracy through digital image correlation (DIC). This kind of measurement is becoming standard when it comes to physical testing of materials. The information from such measurements is then often used in the calibration and validation of material cards to be later used in LS-DYNA. Especially regarding the prediction of failure, the experimentally measured strain fields can be quite helpful. Among several methods for the calibration of material cards, one method relies on the direct use of such strains in the definition of the failure curve as a function of the stress triaxiality ratio. However, in such method, the triaxiality is usually estimated from the simulation of the specimens adopted in the physical tests or, sometimes, it is estimated from analytical calculations based on the loading type and on the geometry of the specimen. It is however widespread known that the triaxiality typically varies during experiments. Therefore, it would be interesting to observe the evolution of the triaxiality throughout the physical test. As mentioned before, the typical way of doing this is through the use of numerical simulation to perform this task. In this paper, we concentrate efforts in developing a method to estimate the triaxiality distribution and evolution using information directly from the DIC measurement. To that end, a plane stress state is assumed and the strain ratio is calculated from the measured strains. The stress triaxiality ratio is, in turn, a relation between the hydrostatic and the equivalent stress. Therefore, in order to calculate the triaxiality from the strain field, a relationship between the strain ratio and the triaxiality has to be defined. This is only possible through the consideration of a constitutive (i.e., material) model. Typically, the J2-based plasticity model (commonly known as the von Mises model, e.g., *MAT_024 in LS-DYNA [1]) is used for this kind of task. However, our research on the topic has shown that this assumption may lead to wrong triaxialities even in cases when the triaxiality is known beforehand, for instance, in a uniaxial tensile test before necking. This error can be significantly reduced if the anisotropy of the material is also taken into account. To that end, we use a Hill-based transversely anisotropic material law in order to consider the effect of the anisotropy. After some mathematical derivations under the assumption of plane stress, negligible elastic strains and proportional loading, it is possible to find a closed-form relation between the strain ratio and the triaxiality including the effect of the R value. The results for an aluminum sheet show that the triaxiality is much better predicted using the new formula. Using a software dedicated to the evaluation and visualization of optically measured strain fields, it should be possible to plot triaxiality fields from experimental data that can be later used either for the calibration or validation of a material card. Furthermore, this novel technique can also be employed on the development of new specimen geometries in order to better assess the stress triaxiality ratios obtained with the new geometry without having to first calibrate a material card for that.