# Unveiling the Strain Rate Sensitivity of G18 NiCrMo3-6 CAST Steel in Tension/Compression Asymmetry
## 1 Introduction
The most common and appropriate way to handle this asymmetry is to use multiple yield surface definitions [4; 5; 6; 7; 8]. The similar and relatively straight-forward application of this kind of modeling strategy is also used by the commercial finite-element software, ABAQUS/Standard. It uses a \(J_{2}\) plasticity formulation in compression modes; whereas, in tensile stress states, a Rankine-cube-like yield function is defined [9]. In this regard, the studies of [PERSON] and [PERSON] [10] and [PERSON] et al. [11] have a distinguishing characteristic, which is that they performed a benchmark analysis among existing possible multi-surface yield surface definitions. In particular, there also studies which were devoted to micro-mechanically motivated material models; either they were embedded with unit cells and homogenization or microstructural interactions that were coupled with macro-mechanics [12]. Some of them clearly included detailed microstructural analysis and quantitative metallography as in the studies of [PERSON] et al. [13], [PERSON] et al. [14], and [PERSON] et al. [15]. From this perspective, [PERSON] has also proposed new hydrostatic yield locus definitions [16] which have certain advantages, especially for industrial applications. The main advantage is that the yield locus definition does not depend on the hardening of the matrix (defect-free portion of the material); thus, the yield definition contains two specific void volume functions which act on macro effective and (von Mises) hydrostatic stress separately. This type of yield expression provides significant ease in mathematical manipulations and especially in partial differentials. Indeed, the need for material parameter extraction is also limited. In industry-driven research, a constitutive model that reduces the need for extensive experimental effort in material parameter extraction and simplifies the time integration scheme--without compromising the complexity of the physical problem--is invaluable. This is particularly important in FEA analyses where computational efficiency is crucial. Therefore, this model (Cocks'89) and some of its derivations are studied in some of the following research [17; 18]. Recently, the Cocks'89 model was implemented to assess the mechanical performance of cast aluminum samples by our research group [19]. Moreover, determination of SRS was also performed for various types of materials. However, the SRS-related research generally focused on parameter extraction through experimental methods [20; 21; 22; 23] or theoretical formulations [24; 25]. The current contribution differs from those researches in such a way that SRS was experimentally obtained as a function of strain and strain rate and this parameter was buried into the constitutive material model (UMAT file) as a state variable. For that purpose, uni-axial tension and compression tests were conducted for 0.001, 0.1, and 10 (s\({}^{-1}\)) strain rates using a Gleeble thermo-psychical simulator machine. The necessary data pro cessing procedures were performed aiming to detect the SRS parameter in an asymmetric and rate-dependent fashion. And lastly, these valuable data were coupled with a modified Cocks'89-based formalism to account for rate dependency and tension/compression asymmetry. Although G18 NiCrMo3-6 is widely used in engineering designs especially for structural purposes, there is very limited information in the literature, in particular regarding its material parameters. The existing literature data on G18 NiCrMo3-6 are mostly related to the empirical and/or theoretical relationship between the process parameters and final mechanical properties [26; 27]. This study intends to fill this technical gap which would probably assist any further constitutive modeling efforts henceforth regarding the G18 NiCrMo3-6 material. The SRS parameter in tension/compression states is quantified, and an advanced visco-elasto-plastic material model, along with its parameters, is provided for the studied material.