Implicit algorithm for finite deformation hypoelastic–viscoplasticity in fcc metals

Abstract

SUMMARYAn implicit objective stress update algorithm is proposed for a hypoelastic-viscoplastic model. A thermal/dynamic yield function, which is derived based on the thermal activation analysis and dislocation interaction mechanisms, is used, along with the Consistency approach and the framework of additive viscoplasticity, in deriving the proposed model for fcc metals. The corotational formulation approach is utilized in developing the proposed model in the finite deformation field. For the case of the Newton-Raphson iteration method, a new expression for the consistent (algorithmic) tangent stiffness matrix of rate-dependent metals is derived by direct linearization of the stress update algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS. Numerical implementation for a simple tensile problem is used for validating the material parameters of the OFHC Copper under low and high strain rates and temperatures. The numerical results of the adiabatic true stress-true strain curves compare very well with the experimental data. The effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem. Results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh-independent results.

Coupled Thermomechanical Modeling of Small Volume FCC Metals

“…The material of the thin film is assumed to be copper and the material parameters of the VA-FCC model suggested by Voyiadjis and Abed [16,17] and Abed and Voyiadjis, [20] are used here. These parameters, along with the other required constants for the proposed nonlocal framework, are listed in Table 1.…”

“…Its order of magnitude can, however, be anywhere between 10* and lO'i"', which characterizes the highest rate value a material may reach as related to the reference (highest) dislocation velocity VQ. By making use of the Schmidt orientation tensor to relate the plastic shear strain rate at the microscale (following Orowan's equation (Orowan [46])) to the plastic strain rate tensor at the macroscale, the following definition of the reference strain rate in terms of the microstructure physical quantities is derived by Voyiadjis and Abed [17]:…”

“…For this propose a microstructural physical based constitutive relation proposed by Voyiadjis and Abed (see, e.g., Refs. [15][16][17][18][19][20]) is used here that incorporates a now rule characterizing the deformation behavior of face centered cubic (FCC) metals under different strain rates and temperatures. The effect of the material microstructural interface between two materials is also incorporated into the proposed formulation which allows the interface to follow its own yield behavior beside the being rate and temperature dependent.…”

Dynamic Localizations in HSLA-65 and DH-36 Structural Steel at Elevated Temperatures

“…Therefore, the return mapping algorithm, which is a speeial form of the baekward-Euler procedure, aims to circumvent the aforementioned drawbacks. In this regard, the elastic predictor-viscoplastic corree,-tor method is used for solving theprecedingconstitutive equations at which the very complex Jacobian matrix is reduced to a nonlinear relation in terms of a one scalar variable [18].…”

“…An implicit algorithm is employed in the elastoviscoplastic formulation in which a stress integration methodology that is called a "local rotated representation" is adopted [18]. The proposed framework is implemented in the well-known explicit commercial finite element software ABAQUS [19] by using the material subroutines T. The role of the material dependence in setting the character of the governing equations is illustrated in the context of a simple uniaxial tensile problem in order to check the effectiveness and the performance of the proposed framework and its FE implementation.…”