Stress Triaxiality in Anisotropic Metal Sheets-Definition and Experimental Acquisition for Numerical Damage Prediction

Governing void growth, stress triaxiality (eta) is a crucial parameter in ductile damage prediction. eta is defined as the ratio of mean stress to equivalent stress and represents loading conditions. Attempts at introducing material anisotropy in ductile damage models have started only recently, rendering necessary in-depth investigation into the role of eta here. eta is commonly derived via finite elemnt (FE) simulation. An alternative is presented here: based on analytical expressions, eta is obtained directly from the strains in the critical zone. For anisotropic materials, eta associated with a specimen varies with yield criterion and material (anisotropy). To investigate the meaning of triaxiality for anisotropic materials, metal sheets made of dual phase steel DP780, and zirconium alloy Zirlo are chosen. Analytical expressions for eta are derived for three popular yield criteria: von Mises, Hill48 and Barlat89. Tensile tests are performed with uniaxial tension, notch, and shear specimens, and the local principal strains, measured via digital image correlation (DIC), are converted to h. The uniaxial tension case reveals that only the anisotropic yield criteria can predict the expected eta = 1/3. The ramifications associated with anisotropy become apparent for notched specimens, where eta differences are highest; for shear specimens, the yield criterion and material-dependence is relatively moderate. This necessitates eta and, consequently, the triaxiality failure diagram (TFD) being accompanied by the underlying yield criterion and anisotropy parameters. As the TFD becomes difficult to interpret, it seems more advantageous to provide pairs of principal strain ratio beta and failure strain. Suggestions for deriving representative beta and eta are made.

Automated summary

This study investigates the crucial parameter of stress triaxiality (eta) in ductile damage prediction, particularly for anisotropic materials. It presents an alternative method to obtain eta directly from strains, and validates different yield criteria for predicting triaxiality. The findings have significant implications for damage prediction and design in materials.