Size and strain gradient effects in dislocation based constitutive modelling
Creators: name: Molotnikov, Andrey
Publisher: name: Monash University
Year: 2017
Subjects: Uncategorized

description: The global trend to miniaturization of engineering structures across different industries, notably information, communication and biomedical industries, presents significant challenges to scientists and engineers. Due to the occurrence of specific effects and new features unknown in conventional metal forming, common forming operations cannot be simply replicated at micro scale. The new challenges cannot be addressed by experimentation alone. Neither are classical plasticity model adequate for accounting for the observed size effects that are critical for materials and process design. New constitutive models guided by microstructure considerations, and combining elements of dislocation theory and gradient plasticity in a physically sound and computationally economical way, are a promising answer to the demands of the nascent microforming industry. In this thesis, physically-based constitutive models described in terms of microstructural evolution have been developed. They account for the effect of the critical dimension of a work-piece on its mechanical response and provide information about the material behaviour required for design of microforming processes and equipment. The models presented utilise an approach in which the material is partitioned in two ’phases’: the dislocation cell walls and the cell interior. Several modifications of the model are proposed in order to account for two particular size effects associated with miniaturization. These can be expressed by two contradictory maxims: "smaller is weaker" and "smaller is stronger". Whereas the former applies when the dimensions of the specimen are decreased with respect to the pertinent microstructural length scale, such as the grain size, the latter holds when non-homogeneity of deformation at microscale becomes significant. The first effect is captured by a model that takes into account the geometrical dimensions of the specimen and also accounts for the microstructural features of the material, notably the average grain size. The second effect is represented by strain gradient models. In this thesis, two types of physically-based strain gradient models arising from two distinct physical mechanisms have been proposed. One originates from the occurrence of geometrically necessary dislocations and the other is associated with the reaction stresses due to plastic strain incompatibilities between neighbouring grains. The constitutive models developed have been implemented in the broadly used commercial finite element software ABAQUS via a specific user subroutine and additionally, a new type of user element has been proposed. A selection of case studies has demonstrated that the models are capable of describing the experimentally observed trends associated with miniaturization and possess a very good predictive capability. A significant advantage of this modelling approach is a relatively small number of adjustable parameters involved. Furthermore, these parameters have a clear physical meaning and can be identified in simple standardized tests. In summary, a physically sound, yet robust and user-friendly constitutive modelling frame has been developed, which can readily be used for simulations of microforming operations and the properties of the resulting parts and miniaturized structural members.