PSI - Issue 61

Toros Arda Akşen et al. / Procedia Structural Integrity 61 (2024) 268 – 276 2 Toros Arda Akşen, Bora Şener, Emre Esener, Ümit Kocabıçak, Mehmet Fırat / Structural Integrity Procedia 00 (2019) 000 – 000 1. Introduction The sheet forming operations yield complex loading modes, and the forming limit curve (FLC) is a crucial method for these operations. FLC accounts for the variation of the forming limits in different stress states. However, this tool necessitates toilsome and expensive mechanical tests and measuring systems. Therefore, companies tend to obtain the FLCs by employing numerical approaches such as the finite element (FE) method. However, obtaining FLC by FE method requires intensive knowledge involving plasticity and fracture. Therefore, an advanced material model, including an anisotropic yield locus presentation and a ductile fracture model, is highly recommended so as to acquire a precise FLC. In material forming, the material’s anisotropy is a s ignificant subject to be addressed. A yield criterion is expected to construct a convex yield locus, tackle anomalous issues, and demonstrate excellent performance in capturing the directionalities of several mechanical properties. The initial attempts partly failed to achieve all the requirements (Banabic (2010)). Recently, linear transformation-based criteria have become highly popular (Barlat et al. (2003), Barlat et al. (2005)). Although the capabilities of these models are enhanced, determining the pla stic flow’s direction is highly difficult (Banabic (2010)). Another anisotropic yield criterion family is the complete polynomial-based criteria. The criterion introduced by Gotoh (1977) was recently improved by Soare et al. (2008) at the point of the calibration procedure. These criteria can produce a convex yield surface and are simple in determining the plastic flow’s direction. It is significant to regard the material's anisotropy to estimate the fracture initiation's location. However, a ductile fracture model is indispensable for determining the failure initiation strain in sheet forming processes. Sheet metals may undergo different loading conditions, and these different loading histories alter the tearing strain. Determining the strain limits in different loading conditions is a cumbersome task. To this end, the material model should consider both the hydrostatic pressure and normalized maximum shear stress effects. The initial endeavors are focused on hydrostatic pressure (McClintock (1968), Cockcroft and Latham (1968), Oyane (1972)). Recently, the Lode angle parameter's influence has been included in the fracture models (Bai and Wierzbicki (2010), Lou et al. (2012), Mohr and Marcadet (2015)). The variation in equivalent plastic fracture strain for different loading paths is evaluated by the fracture loci estimated through the fracture models for ductile materials. The criteria discussed above were assessed in terms of fracture loci in the comparative works (Habibi et al., (2019), Kong et al. (2020)). However, the FLC predictions may be more enlightening for sheet forming operations. Besides, an extended forming limit diagram covering the uniaxial compression and equi-biaxial tension paths will elucidate the importance and the difference in incorporating the triaxiality and the Lode angle parameter influences. Moreover, the sheet’s anisotropic response was also disregarded in most comparative research (Habibi et al. (2019), Park et al. (2019)). In the current study, the capabilities of only triaxiality-based and both Lode parameter and triaxiality-based criteria were assessed regarding the constructed fracture locus and FLC. These criteria are VGM (void growth model) and MMC (modified Mohr-Coulomb) criteria. The fourth-degree complete polynomial yield criterion (HomPol4) was incorporated into the Marc software. The FLC results were compared with the experimental findings determined by Banabic (2016). 2. Material and Method This study concentrated on the fracture locus and fracture FLC prediction of AA6016-T4 alloy that is prevalently utilized in the automotive industry (Kim and Yang (2017)). Since aluminum alloys exhibit highly anisotropic features, a complete polynomial yield function was implemented so as to describe the material’s anisotropy precisely. Besides, two different ductile fracture models are employed in order to obtain the fracture-forming limit curves. These models are the VGM and the MMC criteria. This section meticulously explains the identification procedures of the polynomial anisotropic yield function and the ductile fracture mechanism. 269