Strain hardening during constrained deformation of metal foams – Effect of shear displacement M. Mukherjee, a,b, * M. Kolluri, c F. Garcia-Moreno, a,b J. Banhart a,b and U. Ramamurty c a Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz, 14109 Berlin, Germany b Technische Universita ¨ t Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany c Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India Received 9 June 2009; accepted 19 June 2009 Available online 21 June 2009 The crush bands that form during plastic deformation of closed-cell metal foams are often inclined at 11–20° to the loading axis, allowing for shear displacement of one part of the foam with respect to the other. Such displacement is prevented by the presence of a lateral constraint. This was analysed in this study, which shows that resistance against shear by the constraint leads to the strain- hardening effect in the foam that has been reported in a recent experimental study. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Metal foam; Constrained deformation; Shear; Band; Strain hardening Closed-cell metal foams have received consider- able attention as they offer the advantage of high specific energy absorption. This is because of their ability to un- dergo large plastic strains (typically 60%, or even more) at a near-constant stress level under quasi-static compression. The large plateau in the plastic part of the stress–strain curve is due to the collective cell col- lapse in bands and propagation of cell crushing from one band to another. Normally, strain hardening in me- tal foams is insignificant. However, when the foam spec- imen is subjected to a lateral constraint, stresses required for plastic deformation increase with strain, implying an inducement of strain hardening by the constraint [1]. Such strain hardening has important implications espe- cially in the context of fatigue [2]. Karthikeyan et al. [3] identified multi-axial states of stress and frictional resistance between the deforming foam and the rigid constraint walls as the two main sources for the observed strain hardening. They analysed this by considering the cell collapse bands to be perpen- dicular to the loading direction. This, in turn, automati- cally precludes the possibility of any bulk shear displacement during deformation. However, experimen- tal evidence suggests that these bands may not necessarily be perpendicular to the loading axis. Often, the normal to the crush band planes is inclined with respect to the load- ing axis, both in the constrained [1,4] as well as uncon- strained [5] conditions. In the former case, the angle of inclination is small, as shown by metallography and X-ray tomography of foams subjected to constrained deformation [1,4]. This inclination converts the compres- sion loading into a shear along the inclined crush band. When there is no constraint, shear is allowed to take place. The presence of constraint can modify the stress state by preventing shear displacement. We investigate this possibility and examine the role of shear band incli- nation on strain hardening behaviour of metal foams in this paper. A closed-cell ALPORAS Ò aluminium alloy foam supplied by Shinko Wire (Japan) was used in this study. Processing details and relevant properties of this foam can be found in Ref. [6]. Four samples of 50  50 mm 2 cross-section and 100 mm height were electro-dis- charge-machined from a single large plate of ALPORAS foam. The thickness of the plate coincides with the load- ing direction. Two samples were tested with quasi-static compression loading, while the other two were tested with compression–compression fatigue loading. A die- steel sleeve of 50.8  50.8 mm 2 inner cross-section and 118 mm depth was used as lateral constraint during deformation. The inner area of the sleeve was chosen in such a way so that all samples could be fitted into the sleeve easily. Samples were fixed into the sleeve with 1359-6462/$ - see front matter Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2009.06.023 * Corresponding author. Address: Helmholtz-Zentrum Berlin, Hahn- Meitner-Platz, 14109 Berlin, Germany. Tel.: +49 30 8062 2820; fax: +49 30 8062 3059; e-mail: manas.mukherjee@gmail.com Available online at www.sciencedirect.com Scripta Materialia 61 (2009) 752–755 www.elsevier.com/locate/scriptamat