Abstract
In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.
Highlights
In recent decades, extensive research efforts have been made to develop a multilevel approach to constructing constitutive models for metals and alloys via the introduction of internal variables [1,2,3,4]
The issue regarding a comparison of the formulations for crystal plasticity models described above is considered
That is why the formulations in the rate form written in terms of the current configuration seem preferable to constructing advanced constitutive models able to take into account different deformation mechanisms and their complex interactions
Summary
Extensive research efforts have been made to develop a multilevel approach to constructing constitutive models for metals and alloys via the introduction of internal variables [1,2,3,4]. The crystal plasticity models obtained within the framework of this approach provide an opportunity to explicitly describe changes in the structure of the material (its anisotropic physical and mechanical macro-properties) and deformation mechanisms [5,6,7,8,9]. This validates the application of these models for studying and improvement of materials processing technologies, as well as for solving the problems associated with the development of new functional materials. These models provide the fulfillment of equilibrium conditions; the effective characteristics are determined using statistical averaging methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
