To reveal constitutive behaviour of materials, different types of experiments are performed in the metal forming lab at the University of Waterloo. These tests characterize the anisotropic and asymmetric plastic response of materials under different stress states. To obtain full-field strain measurements, stereoscopic digital imagine correlation techniques are utilized.

Significant vehicle weight reduction can be achieved by adopting advanced materials such as non-ferrous metals like aluminum and magnesium alloys. However, due to pronounced plastic anisotropy, classical yield criteria such as von Mises, Hosford, or Hill48 models are unable to accurately describe the yielding behaviour of these materials. To overcome this issue, advanced yield functions with higher flexibility are required.

Yield surface of an aluminum alloy sheet with advanced yield functions such as the Yld2004-18p yield function:

Yield surface of an aluminum alloy sheet with advanced yield functions such as the Yld2004-18p yield function

In addition, forming operation of non-ferrous materials is usually performed at elevated temperatures. Therefore, constitutive response of materials should be analyzed at higher temperatures and the modelling approach would require a fully coupled thermo-mechanical framework.

Yield surfaces and constitutive response of a rare-earth magnesium alloy sheet at different temperatures:

Alternatively, the use of models that employ a non-associative flow rule has been on the rise in recent years since decoupling yield function and plastic potential greatly simplifies the calibration procedure and can improve accuracy over associative models. This is of great advantage specifically for magnesium alloys with complex anisotropic behaviour.

Modelling complex evolving anisotropy and tension-compression asymmetry of Mg alloy using the non-AFR:

As opposed to the associative flow rule than can predict formation of four ears in cup drawing of a 7000 series aluminum sheet, the non-associative flow rule can capture formation of eight ears and is in agreement with experimental observation.

Modelling earing profiles in 7000 series aluminum sheet using AFR versus non-AFR: