24 J. Rathore et al. The emergence of non-contact optical methods such as Digital Image Correlation (DIC) has made it possible to perform full-field deformation measurements [5]. Since the 1980’s DIC has been used extensively for evaluating mechanical properties of various materials at room temperatures and extreme conditions. The ability to analyze full-field measurements has the advantage of inspecting multi-stress modes present in a specimen or a part by probing specific regions of interest on the same field of view [6]. This capability has also allowed recently the design of unconventional specimen geometries that can imitate the complex loading modes found at the component level [6, 7]. This new approach of determining mechanical constitutive parameters has been coined as ‘Material Testing 2.0’ (MT2.0) by Pierron and Grediac [8]. Following this approach, several examples of novel specimens that capture more than one stress mode have been developed. For example, Khameneh et al. designed a specimen from which they examined the influence of tension regions and the geometry of shear region on the development of shear stress state in conjunction with FEA for fracture characterization of DP1180 steel [7]. Bensing et al. developed a specimen for evaluation of tensile and compression properties of thermoplastic polymers [6]. To further support the development of accelerated measurement of constitutive parameters, Jones et al. provided full-field DIC, and infrared thermography (IR) data tested at different rates and direction for seven unique geometries[9]. Multimodal stress state data becomes important in calibrating FEA models. For example, a general yield function developed by Lou et al. involves four stress modes analysis for computing hardening behavior that can exhibit differential and anisotropic hardening [10]. In this context, the research reported in this investigation presents an approach to design a specimen from which four independent stress states could be simultaneously activated at different regions and for the same load increment to allow measurements that provide the unknown coefficients of a J3-plasticity type constitutive model developed by Lou et al. This manuscript is organized as follows: section 2 presents details on the J3-plasticity model and the material information for the representative materials that the reported approach was applied. Section 3 provides details on the design of the complex shaped specimen. Section 4 shows validation efforts which included experiments in which DIC measurements and FEA results were used. The manuscript ends with concluding remarks on the overall usefulness of this approach and possible future steps. Background Plasticity model and Finite Element Analysis approach In this research, we are using the model developed by Lou et al. [10] and which intends to capture both anisotropy and multiple stress-state dependence in the plastic behavior. The Lou model is a J3 stress invariant type plasticity formulation, capable of describing the complex stress effects that could be present e.g., in metal forming. Equation 1 shows the definition of the yield surface for this model f (σy)=a(¯εp) b(¯εp)I1 +h J 3 2 −c(¯εp)J 2 3 1/2 −d(¯εp)J3i 1/3 −¯σUT (¯εp)=0, (1) where I1 is a stress invariant of the Cauchy stress tensor, andJ2 andJ3 are the stress invariants of the deviatoric stress tensor. The parameters “a”, “b”, “c” and “d” that appear in Eq. (1) are determined using experimental data and the four equations summarized in Eq. (2) a = √3¯σUT ¯σSS b = 1 3 ¯σSS ¯σPST − 1 d = 24 7 ¯σUT a¯σUC +b 3 − 1 a −b 3 c = 1 4 27−h27 1 a −b 3 +2di 2 (2) where ¯σUT, ¯σSS, ¯σPSTand ¯σUCare the von Mises equivalent stress at uniaxial tension, shear, plane strain tension and uniaxial compression states, respectively. Parameter “a” in the yield function provides scaling, “b” relates to pressure dependency, “c” defines curvature, and “d” is the strength differential. Based on different values of the hardening parameters and autodifferentiability the yield function can take the shape of yield surfaces such as von-Mises ( a =√3, b = 0, c = 0, d = 0 ), Drucker Prager ( a, b, c, d = 0 ), Cazacu Barlat ( a, b = 0, c = 0, d ) etc. Due to this ability of polymorphism, the Lou yield surface is considered as a robust candidate for mechanical behavior characterization. Figure 1 describes the triaxiality vs Lode mapping of the stress states required to calibrate the shape of the yield surface. The corresponding four types of specimen tests, i.e. dogbone (Uniaxial Tension - UT), notched tension (Plane Strain Tension), simple shear and cylinder
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