Citation: Rickhey, F.; Hong, S. Stress Triaxiality in Anisotropic Metal Sheets—Definition and Experimental Acquisition for Numerical Damage Prediction. Materials 2022, 15, 3738. https://doi.org/10.3390/ ma15113738 Academic Editor: Francesco Freddi Received: 6 May 2022 Accepted: 20 May 2022 Published: 24 May 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). materials Article Stress Triaxiality in Anisotropic Metal Sheets—Definition and Experimental Acquisition for Numerical Damage Prediction Felix Rickhey and Seokmoo Hong * Department of Automotive and Mechanical Engineering, Kongju National University, Cheonan 31080, Korea; frrickhey@kongju.ac.kr * Correspondence: smhong@kongju.ac.kr Abstract: Governing void growth, stress triaxiality (η) is a crucial parameter in ductile damage prediction. η 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 η here. η is commonly derived via finite elemnt (FE) simulation. An alternative is presented here: based on analytical expressions, η is obtained directly from the strains in the critical zone. For anisotropic materials, η 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 η 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 η = 1/3. The ramifications associated with anisotropy become apparent for notched specimens, where η differences are highest; for shear specimens, the yield criterion and material-dependence is relatively moderate. This necessitates η 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 β and failure strain. Suggestions for deriving representative β and η are made. Keywords: stress triaxiality; anisotropy; sheet metal; ductile fracture; triaxiality failure diagram; digital image correlation 1. Introduction For the numerical prediction of damage in a sheet metal structure during forming or in crash events, a plethora of macroscopic ductile damage models has been developed. To reduce weight and consumption of resources, and thus increase efficiency, material of often-low ductility is exploited up to close to their strain limit, which renders these models increasingly important. Despite the large variety of damage models available today, what they share is the incorporation of the strong influence of triaxiality η on damage and fracture. This insight can be traced back to the early works by McClintock [1,2], Rice and Tracey [3], Hancock and Mackenzie [4], and Beremin [5], who already pointed out the importance of η in ductile damage. The inclusion of the anisotropic yield in damage models has gained attention recently. Ductile damage models can be divided into uncoupled and coupled models. Un- coupled, in this context, means that failure is judged based on the current state (e.g., equivalent strain, maximum principal stress, plastic dissipation, or some other measure) of a “virgin” material, i.e., without accounting for the damage-induced material softening with increasing deformation. Early prominent models are those by Rice and Tracey [3] and Johnson and Cook [6]; more recent models were presented, for example, by Bai and Materials 2022, 15, 3738. https://doi.org/10.3390/ma15113738 https://www.mdpi.com/journal/materials