PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 468–475 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

Digital Image Correlation (DIC) is a full-field non-contact 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 is used to capture consecutive images with digital cameras during the deformation period to evaluate the variations in surface characteristics and understand the behavior 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). Tensile measurements often involve an extensometer or electromechanical strain gage. However, DIC has become one of the most valuable tools for plastic strain measurement of metal alloys since it readily provides plastic strains beyond diffuse necking which cannot be obtained with the use of extensometers. Recent application of DIC to advanced high strength steels such as press hardened boron steel and dual-phase steels may be found in [(Kang et al. 2007; Savic & Hector 2007; Tarigopula et al. 2008; Mohr & Oswald 2008; Ghadbeigi et al. 2010)]. Since DIC can measure the 3D deformation variation on structural constructions, it is capable to link experimental results with numerical simulations in an elegant way. In 2012, a study was conducted on ductile structures in which basic principle on plastic material identification was measured by DIC and compared to Finite Element (FE) simulations (Lecompte et al. 2012). They determined the hardening behaviour and the yield locus based on uniaxial and biaxial tensile test. Moreover, a high speed digital image correlation system was used to characterize the full field plastic deformation of AA6061-T6 Aluminium alloy at high strain-rates under compressive and torsion loads (Owolabi et al. 2013). In the case of thermomechanical loading conditions, DIC was used to identify the mechanical response of nickel super alloy Hastelloy X under thermal and mechanical cycling under uniaxial and biaxial stress states (Swaminathan et al. 2014). In the perspective of elastoplastic mechanics, DIC plays a substantial role to identify the plastic deformation (Savic et al. 2010); Crystal plasticity parameter identification and the grain morphology map (Dave et al. 2009; Bertin et al. 2016); study of the fractured structured to measure stress intensity factor (Tavares et al. 2015)(Roux et al. 2009). Meshless methods are advanced discretization techniques which allow to discretize the problem physical domain using only an unstructured nodal distribution (Belytschko et al. 1996)(Gu 2005; Nguyen et al. 2008). In meshless methods, th e field functions (shape functions) are approximated within an ‘influence - domain’ rather than an element. In meshless methods, the ‘influence - domain’ concept corresponds to the “ element ” concept in the Finite Element Method (FEM)(Zienkiewicz & Taylor 1994) (Belinha 2014) . In the FEM formulation, ‘elements’ cannot overlap each other. In opposition, in meshless methods the ‘influence domains’ may and must overlap ea ch other. It is possible to define and classify a numerical method by three fundamental modules: the field approximation (or interpolation) function, the used formulation and the numeric integration scheme (Belinha 2014). The meshless Natural Neighbour Radial Point Interpolation Method (NNRPIM) uses mathematic concepts, such as the Voronoï Diagrams (Voronoï 1908a) and the Delaunay tessellation (Delaunay 1934), to construct the influence cells, which is the basic structure of the nodal connectivity in the NNRPIM (Belinha 2014), and the background integration mesh (Belinha 2014). Both these numerical structures are totally dependent on the nodal discretization. Unlike the FEM, where geometrical restrictions on elements are imposed for the convergence of the method, in the NNRPIM there are no such restrictions, permitting a random nodal distribution for the discretized problem. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed with the Radial Point Interpolators (RPI) (Wang & Liu 2002a) (Wang & Liu 2002b) (Liu 2009). The RPI functions possess the delta Kronecker property, facilitating the enforcement of boundary conditions, which can be directly imposed as in the FEM. The RPI function construction is simple and its derivatives are easily obtained (Belinha 2014). Additionally, it is possible to find some elasto-plastic research works on meshless methods using the natural neighbor concept, such as the meshless natural neighbor method (Zhu et al. 2006) and the hybrid natural element method (Ma et al. 2014). In this work, the DIC, FEM and NNRPIM are used to analyze a bi-failure specimen made of an Aluminum alloy AA6061-T6 considering a small strain formulation and assuming an isotropic elasto-plastic material behavior with an isotropic hardening. To develop and verify the NNRPIM in the elasto-plastic analysis, a non-linear algorithm is used so- called “ Newton-Raphson ” relied on the initial stiffness method and the stress state is thus returned to the yield surface following a backward-Euler scheme (Crisfield 1991).