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Underlying Material Response for Lüders-Like Instabilities

► The underlying material response of partially unstable materials is measured. ► This is done for Lüders deformed steel and a shape memory alloy. ► They both exhibit an up-down-up response. ► The extracted responses used in numerical models reproduce the structural responses.

 The initial yielding of some low carbon steels exhibits a material instability known as Lüders banding. This is a dislocation driven phenomenon that macroscopically manifests as inhomogeneous deformation. For example, in a displacement controlled uniaxial test Lüders banding leads to coexistence of two deformation regimes while the stress remains relatively unchanged. Shape memory alloys whose behavior is governed by solid–solid phase transformations, in some temperature regimes exhibit similar localizations albeit reversible. Such localizations have undesirable consequences in structural applications such as stretch marks and structural instabilities. Modeling of this behavior in order to assess its consequences in structures is hampered because the true material response over the stress plateau is unknown. This work used an experimental technique, outlined in Shioya and Shiroiri (1976) that extracts the underlying material response of such materials from a tensile test. Laminates consisting of face-strips of a hardening material and an unstable core, if properly designed, can suppress the inhomogeneous deformation of the core resulting in a monotonically increasing response. This method revealed that both steel and NiTi strips have up-down-up responses. The extracted responses incorporated in finite element models are shown to reproduce both the laminate experiments and the behavior of strips made of unstable materials alone.

 Hallai, J.F. and Kyriakides, S. (2013) "Underlying material response for Lüders-like instabilities", International Journal of Plasticity 47, 1-12.

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