Speaker
Description
The quantitative prediction of macroscopic mechanical properties of materials requires the consideration of the material microstructure. The focus of this talk is on metallic material systems with lamellar microstructures, such as NiAl-Cr(Mo) [1] or binary Fe-Al [2]. These consist of individual domains in which the materials constituents are arranged in fine layers (thickness in the micrometre range) with a distinct layer normal direction. The layer interfaces act as obstacles for dislocations, leading to dislocation pileup and subsequently to an increase in the macroscopic yield stress. This effect strongly depends on the width of the layers of the individual phases.
We propose a physically motivated material model for the mechanical behaviour of a single domain. To this end, we describe the microstructure of the domain as a rank-1 laminate, which allows for efficient two-scale homogenisation. Exact localisation relations are used to explicitly resolve the local stress and strain fields. Within the framework of gradient crystal plasticity [3,4], the yield conditions take the form of a system of coupled Fredholm integro-differential equations for the plastic slip, which is solved semi-analytically.
The model allows for a physically motivated description of the Hall-Petch effect, taking into account the material contrast and relative orientation of the constituents, as well as the lamella widths.
[1] D. Wicht, M. Schneider and T. Böhlke, On Quasi-Newton methods in fast Fourier transform-based micromechanics, International Journal for Numerical Methods in Engineering 121 (2019) 1665-1694
[2] A. Schmitt, K.S. Kumar, A. Kauffmann, M. Heilmaier, Microstructural evolution during creep of lamellar eutectoid and off-eutectoid FeAl/FeAl2 alloys, Intermetallics, Volume 107, (2019), Pages 116-125
[3] H. Erdle, T. Böhlke, Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks, Proc. R. Soc. A 479 (2023) 20220737.
[4] Morton E. Gurtin, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, Journal of the Mechanics and Physics of Solids, Volume 50, Issue 1, (2002), Pages 5-32
