Micromechanical modelling of strain path dependency in FCC metals

The analysis of the formability of metals is a traditional topic in mechanical engineering, which is still characterised by many open issues. In spite of many decades of research, this field continues to trigger new challenges, especially promoted by industrial progress. The growing need for more precision in forming processes and the exploitation of more complex manufacturing processes, necessitates a better understanding of the relevant micromechanical processes and the development of more sophisticated engineering tools. The physical origins of the complex deformation behaviour observed for metals, reside, among others, in the textural anisotropy of the material and the anisotropy of the dislocation structures accompanying the plastic deformation. The microscopic deformation mechanisms, associated with the presence and development of these microstructural entities, affect the macroscopical behaviour of a metal, altering its formability. This thesis addresses two major aspects of the formability analysis of metals, both based on the underlying evolving microstructure: (1) the prediction of forming limits and (2) the prediction of strain path change effects. The following sections shortly highlight the challenges in these fields, from which the research scope of the thesis has been derive

Strain path dependency in metal plasticity

A change in strain path has a significant effect on the mechanical response of metals. Strain path change effects physically originate from a complex microstructure evolution. This paper deals with the contribution of cell structure evolution to the strain path change effect. The material with cells is modelled to behave like composite consisting of a periodic 2D array of two types of elements: the hard cell walls and the soft cell interiors. For the scalar internal variables figuring in the model, the cell size, the wall thickness and the dislocation density inside the walls, evolution equations are proposed to describe the cell development and the cell dissolution. The validation of the model is performed by comparing the results with experimental data on the deformation behaviour of copper which was subjected to a sequence of two uniaxial tensile tests performed in different directions. The model is concluded to be capable to describe the material behaviour for monotonic deformation and complex deformation with a strain path change up to 45 . The model predicts the strain path change, its dependency on the amount of prestrain and on the amplitude of the strain change that are in good agreement with experimental data. The slip anisotropy should be taken into account to improve the model for an adequate prediction of the deformation behaviour after strong strain path changes

Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behaviour of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations

Strain path dependency in metal plasticity

A change in strain path has a significant effect on the mechanical response of metals. Strain path change effects physically originate from a complex microstructure evolution. This paper deals with the contribution of cell structure evolution to the strain path change effect. The material with cells is modelled to behave like composite consisting of a periodic 2D array of two types of elements: the hard cell walls and the soft cell interiors. For the scalar internal variables figuring in the model, the cell size, the wall thickness and the dislocation density inside the walls, evolution equations are proposed to describe the cell development and the cell dissolution. The validation of the model is performed by comparing the results with experimental data on the deformation behaviour of copper which was subjected to a sequence of two uniaxial tensile tests performed in different directions. The model is concluded to be capable to describe the material behaviour for monotonic deformation and complex deformation with a strain path change up to 45 . The model predicts the strain path change, its dependency on the amount of prestrain and on the amplitude of the strain change that are in good agreement with experimental data. The slip anisotropy should be taken into account to improve the model for an adequate prediction of the deformation behaviour after strong strain path changes

Numerical analysis of strain path dependency in FCC metals

Strain path dependency in FCC metals is often associated with the anisotropy induced by the dislocation cell structure in deformed metals. In this paper, the mechanical behaviour of metals under various nonuniform deformation paths is studied with the use of a recently developed dislocation cell structure model. It is shown that this model correctly captures the essential features of strain path change effects for moderate strain path changes, i.e. the anisotropy and the dependency on the amount of prestrain. Next, a numerical analysis is performed to assess the micromechanical origin of the modified reloading yield stress and the transient hardening after strain path changes. The separate influence of anisotropic effects due to the cell structure morphology and residual internal stresses are thereby addressed and illustrated. The transient hardening behaviour after a strain path change is related to the adjustment of the internal stresses to the new loading. Results obtained are consistent with related experimental findings reported in literature

The role of plastic slip anisotropy in the modelling of strain path change effects

Most industrial metal forming processes are characterised by a complex strain path history. A change in strain path may have a significant effect on the mechanical response of metals. This paper concentrates on the role of the plastic slip anisotropy in the strain path dependency of materials containing a dislocation cell structure. The cell structure model, developed in Viatkina et al. [Viatkina, E., Brekelmans, W., Geers, M., 2007. Modelling of the internal stress in dislocation cell structures. Eur. J. Mech. A: Solids 26(6), 982–998], is extended here by employing a crystal plasticity model for describing the local material behaviour. This, more physically based description of the plastic behaviour, allows accounting for plastic anisotropy resulting from the crystal lattice of a metal. The extended cell structure model accounts for four sources of anisotropy: (1) geometrical anisotropy due to the configuration of the cell structure, (2) anisotropy due to the internal stresses associated with the cell structure, (3) slip anisotropy and (4) textural anisotropy. The relative contributions of the four sources of anisotropy are discussed