Issue 41

L. Patriarca et alii, Frattura ed Integrità Strutturale, 41 (2017) 277-284; DOI: 10.3221/IGF-ESIS.41.37 278 hand, studies on stationary and propagating cracks in polycrystalline material is still an open field where many contributions [6-7] focused primarily on the effects of strain field transmission across grain boundaries. The adoption of Voronoi structures was used to study the effect of a stationary crack in a C(T) polycrystalline specimen [8], the results pointed to analyze the heterogeneity of stress and strain fields acting at the crack tip. Most of the works related to CPFE modeling consider random generated structures and use experiments for macro-scale comparisons. A link between Crystal Plasticity (CP) simulations and experiments at meso-scale and micro-scale is still an open field of research. Surface localizations can be nowadays performed at sub-grain scales by Digital Image correlation (DIC) and subsequently compared with the CPFE results to have a feedback on the predictive capabilities of the models. In the current work, simulations and experiments were conducted on a Nickel based super-alloy, Haynes 230 [9]. The study of nickel-based super-alloys is increasing through the years as these materials show high mechanical properties and excellent resistance to corrosion at high temperatures. The present analysis was performed on a single notched polycrystalline specimen which was pre-cracked in compression. The investigation concerns the study of the residual strain field generated at the tip of a quasi-static crack. Grain orientation and geometry were detected by Electron Backscatter Diffraction (EBSD) technique. Concurrently, the experimental evaluation of the strain field was performed adopting high resolution sub-grain DIC strain measurements. Numerically, the CPFE simulations were conducted considering the real geometry of the specimen and adopting a CP algorithm implemented in Warp3D [10]: this code allows to represent the material behavior at the grain scale thanks to the adoption of physical and kinematics models, which for FCC materials, like Ni-based super-alloy, associate the plastic deformations mainly to dislocation motion according to the active slip systems. In the following sections are presented the adopted CP model, the CP parameters identification for the investigated alloy and finally the experimental procedure and the simulations involving the quasi-static crack. C RYSTAL P LASTICITY M ODEL he mechanical behavior of grains can be modeled with an elastic-plastic model where the crystals’ kinematics is considered as a combination of dislocation motion, rotation of the crystalline matrix and elastic deformation [7,11]. The deformation gradient multiplicative decomposition can be written as [12]:  e p F F F (1) where F is the deformation gradient, e F and p F are, respectively, its elastic and plastic components. By the analysis of these gradients it is possible to obtain the formulation for the objective stress function which needs to be integrated by the finite element solver [13]. To solve the problem, the definition of an hardening rule is required in the formulation of the slip rate along the slip plane   s :                   1 0 n s s s (2) where   0 is a reference strain rate,    s is the resolved shear stress, n is the exponent of the slip rate,   is the shear strength which requires the definition of the hardening model. The hardening law, originally proposed in [14] by Follansbee and Kocks, implemented in Warp3D has the following expression:                          0 0 ˆ , , , p a y p p T T T (3) The shear strength   is temperature and rate dependent;  ˆ a is the athermal and rate-independent component influencing the yield strength;   y is the thermal and rate dependent component of the yield strength;  accounts for the work