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Polish Academy of Sciences

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K. Thermann


Recent publications
1.  Petryk H., Thermann K., Post-critical plastic deformation in incrementally nonlinear materials, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 0022-5096, DOI: 10.1016/S0022-5096(01)00131-4, Vol.50, No.5, pp.925-954, 2002

Abstract:
The formation of multiple macroscopic shear bands is investigated as a mechanism of advanced plastic flow of polycrystalline metals. The overall deformation pattern and material characteristics are determined beyond the critical instant of ellipticity loss, without the need of introducing an internal length scale. This novel approach to the modelling of post-critical plastic deformation is based on the concept of a representative nonuniform solution in a homogeneous material. The indeterminacy of a post-critical representative solution is removed by eliminating unstable solution paths with the help of the energy criterion of path instability. It is shown that the use of micromechanically based, incrementally nonlinear corner theories of time-independent plasticity leads then to gradual concentration of post-critical plastic deformation. The volume fraction occupied by shear bands is found to have initially a well-defined, finite value insensitive to the mesh size in finite element calculations. Further deformation depends qualitatively on details of the constitutive law. In certain cases, the volume fraction of active bands decreases rapidly to zero, leading to material instability of dynamic type. However, for physically hardening materials with the yield-vertex effect, the localization volume typically remains finite over a considerable deformation range. At later stages of the plane strain simulation, differently aligned secondary bands are formed in a series of bifurcations.

Keywords:
Plasticity, Shear bands, Material instability, Energy criterion, Bifurcation

Affiliations:
Petryk H. - IPPT PAN
Thermann K. - other affiliation
2.  Petryk H., Thermann K., Post-critical deformation pattern in plane strain plastic flow with yield-surface vertex effect, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, ISSN: 0020-7403, DOI: 10.1016/S0020-7403(00)00010-2, Vol.42, No.11, pp.2133-2146, 2000

Abstract:
This work is concerned with the formation of multiple macroscopic shear bands viewed as a mechanism of large plastic deformation of polycrystalline metals. The plastic deformation pattern in a time-independent material with a yield-surface vertex effect is investigated numerically in plane strain beyond the critical instant of ellipticity loss under quasi-static loading. The energy criterion of path instability applied to a family of post-critical solutions eliminates unstable paths and enables the overall deformation pattern to be determined, although the solutions remain locally indeterminate due to the absence of an internal length scale. In particular, the volume fraction of incipient shear bands is found to have a well-defined value irrespective of the mesh size in finite element calculations. As an apparently novel qualitative result, the formation of coarse, differently aligned secondary bands is observed at later stages of simulation.

Keywords:
Plasticity, Shear bands, Material instability, Energy criterion, Bifurcation

Affiliations:
Petryk H. - IPPT PAN
Thermann K. - other affiliation

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