PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 981–988 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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deformations with significant through-thickness necking in which 3D stress states develop and dictate the fracture event of the metal sheet. The use of numerical methods such as the Finite Element Method, FEM, to handle large plastic deformations, has created the possibility to analyze, with a success, a forming process during its development stage, including damage and fracture (Teixeira et al. 2009). The reliability of the numerical simulation to predict material behavior requires an accurate mechanical characterization. Nevertheless, the increasing application of a new generation of materials demands an analysis and development of new techniques to determine their mechanical behavior for different types of loads (Isik et al. 2015). Recent developments in automotive engineering have shown that the optimal design of components requires reliable simulation tools to predict their fracture. Other examples include the damage of components through different types of loading states. From technical and economical perspectives, it is of foremost importance to detect potentially critical members at the early stage of component development (C.H.L.J. et al. 2009)(Marzbanrad et al. 2013). So, the use of efficient and accurate numerical techniques would allow to reduce the experimental trial-and-error cycles between design and final product stages. In order to investigate the fracture of sheet metal materials for different levels of stress triaxiality, a new experimental approach is considered, based on the specimen geometry developed by (Alves & Driemeier 2010; Driemeier et al. 2015) for plate materials, designated by bi-failure specimen. Since a sheet metal is used in this work possessing a small thickness, some changes were implemented on the specimen, such that cracks are most likely to initiate in different sections. Due to the difficulty to obtain the strain fields with the standard mechanical gages, e.g. strain gage, Digital Image Correlation, DIC, is used to measure the full-deformation field. Using this new experimental/optical technique, the fracture in sheet metals can be analyzed experimentally for a range of stress triaxialities. Computationally, efficient constitutive models of damage and plasticity are required for accurate modelling of material behaviour, since it is the damage variable or porosity that progressively affects the strength and stiffness of the material until failure. These models are said to be coupled. Classical examples are damage model from Lemaitre Classical examples are damage model from (Lemaitre 1985a; Lemaitre 1985b) and Gurson-Tvergaard-Needleman (GTN) poroplasticity model originally proposed by (Gurson 1977) and modified by (Tvergaard 1982a; Tvergaard & Needleman 1984). Models for the evolution of the damage variable have been proposed in the literature, considering the influence of parameters such as stress triaxiality and, more recently, Lode parameter (Xue & Wierzbicki 2008; Basaran 2011; Brünig et al. 2014). It is already stated that the damage variable becomes anisotropic after a certain level of deformation. Second order damage tensors are proposed by (Chaboche 1990; Voyiadjis & Kattan 1992). Particularly, over the past decades, several other authors have included to the original Gurson or GTN model, effects such as nucleation of voids (Chu & Needleman 1980) consideration of non-spherical voids (Gologanu et al. 1994), void size (Monchiet & Bonnet 2013) amongst others. 1.1. Digital Image Correlation Digital Image Correlation (DIC) is an advanced optical technique to experimentally measure the deformation fields. A mathematical solution is employed to examine DIC data taken while a specimen is in mechanical tests. This technique acts to capture consecutive images with digital cameras during the deformation period to evaluate the variations in surface characteristics and understand the behaviour of the specimen while is subjected to incremental loads. To apply this method, the specimen must be prepared by attaching a random dot pattern, also known as speckle pattern, to its surface (Cintrón & Saouma 2008). Basically, this approach starts up with an image prior to the load applied on, which will be the reference image and then a series of images are captured over the deformation process known as deformation images. Besides, all these images illustrate a different random dot pattern relative to the initial non-deformed reference image. With a computer software program, the change amongst patterns can be determined by correlating all reference image ’s pixels with any of deformed image, and an evolving displacement map is obtained thereof. Müller et al. (Müller & Saackel 1979) conducted their research on digital image processing in 1979 to evaluate its use for completely automatic analysis of photoelastic fringe patterns. After that, its early extension was presented by McNeill et al. in 1987 to determine the stress intensity factors (SIF) using DIC approach (McNeill et al. 1987). They focused on the experimental and analytical approaches to obtain results for various specimen geometries. Moreover,