Crystal plasticity modeling of non-Schmid yield behavior: from Ni₃Al single crystals to Ni-based superalloys

Abstract

A crystal plasticity finite element (CPFE) framework is proposed for modeling the non-Schmid yield behavior of L12 type Ni3Al crystals and Ni-based superalloys. This framework relies on the estimation of the non-Schmid model parameters directly from the orientation- and temperature-dependent experimental yield stress data. The inelastic deformation model for Ni3Al crystals is extended to the precipitate (γ′) phase of Ni-based superalloys in a homogenized dislocation density based crystal plasticity framework. The framework is used to simulate the orientation- and temperature-dependent yield of Ni3Al crystals and single crystal Ni-based superalloy, CMSX-4, in the temperature range 260–1304 K. Model predictions of the yield stress are in general agreement with experiments. Model predictions are also made regarding the tension–compression asymmetry and the dominant slip mechanism at yield over the standard stereographic triangle at various temperatures for both these materials. These predictions provide valuable insights regarding the underlying (orientation- and temperature-dependent) slip mechanisms at yield. In this regard, the non-Schmid model may also serve as a standalone analytical model for predicting the yield stress, the tension–compression asymmetry and the underlying slip mechanism at yield as a function of orientation and temperature.

Dislocation density‐based constitutive model for cyclic deformation and softening of Ni‐based superalloys

“…Constitutive models for the evolution of the mobile and immobile dislocation densities have been adopted from previous studies, 29,33,[44][45][46] where they have been implemented in crystal plasticity and J 2 plasticity models to study the deformation of metallic alloys, including Ni-based superalloys. Their evolution rates are of the form:…”

“…These values are in the same range as earlier studies. 45,53,61,62 Specifically, the value of the dislocation immobilization parameter, k I , has generally been assumed to be about 80%-90% of the dislocation multiplication parameter, k M : 44 Physically, these govern the rate of generation of mobile dislocation density and their conversion to immobile dislocation densities. The dynamic recovery parameter, k D , generally governs the hardening rate at higher values of plastic strain, that is, the higher the value of this parameter, the higher the saturation in the stress-strain response.…”

$ρ$-CP: Open Source Dislocation Density Based Crystal Plasticity Framework for Simulating Thermo-Mechanical Deformation

“…The driving force for dislocation glide on a slip system is of the form: τ α − χ α , where τ α is the aforementioned resolved shear stress, while χ α is the slip system-level backstress representative of directional hardening. For material systems where non-Schmid deformation is observed, additional contributions to the driving force may also be considered [71,72]. The signum function (represented by sgn) accounts for the direction of forward and backward slip due to positive and negative values of τ α − χ α , respectively.…”

“…The slip system-level backstress, χ α , may also considered as an additional ISV for applications where simulating cyclic loading and Bauschinger effect is of interest. The equations are adopted from previous studies [68,71,67,66,72,74], where the application of these substructure evolution models has been demonstrated to study thermomechanical deformation in various materials systems.…”

“…We present a physically-based crystal plasticity constitutive modeling framework that accounts for substructure evolution due to underlying mechanisms of dislocation strengthening, interaction and evolution during plastic deformation. The constitutive model (or its variant) has been previously used for studying orientation-dependent deformation and residual strain development in Zr alloys [66], process-induced residual strain development during additive manufacturing [67], irradiation hardening and plastic flow localization in ferritic-martensitic steels [68,69,70], and orientation-and temperature-dependent yield stress prediction due to non-Schmid stresses in bcc-Fe [71] and single crystal Ni-based superalloys [72]. While these former studies were material-specific and implemented in the form of Fortran subroutines, we present a more general C++ based implementation of the constitutive model in this work, in order to facilitate the user to run crystal plasticity finite element simulations for the desired application, with minimum code development or implementation.…”