Effect of Lateral Constraint on the Mechanical Properties of a Closed-Cell Al Foam: Part II. Strain-Hardening Models
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TRODUCTION
IN a companion article, it was shown that the mechanical response of aluminum foams is different when compression tested with and without constraint.[1] In particular, specimens tested with lateral constraint were observed to exhibit a higher strain-hardening rate than samples tested without. The implications of such hardening on densification strains, energy absorbed, and the fatigue properties were also explored. Clearly, an indepth understanding of the causes and effects of hardening under constraint is of scientific and technological significance. Macrographs of samples deformed under constraint shown in Figure 5 (a) (Part I) reveal similarities as well as differences in the deformation micromechanisms with and without constraint.[1] Analytical constitutive models that rationalize the observed strain hardening are developed in this article, with a view to explore the possible sources of hardening. Two possible sources can be considered for the experimentally observed strain hardening in foam specimens tested under lateral constraint, as seen in Figure 4 (b) (Part I).[1] The application of the constraint prevents Poisson expansion and fundamentally changes the stress state from uniaxial to triaxial. This is expected to intrinsically affect deformation in the foam leading to strain hardening. The second possible source of hardS. KARTHIKEYAN, Assistant Professor, M. KOLLURI, Master of Engineering Student, and U. RAMAMURTY, Associate Professor, are with the Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India. Contact e-mail: ramu@materials. iisc.ernet.in Manuscript submitted November 20, 2006. Article published online July 20, 2007. 2014—VOLUME 38A, SEPTEMBER 2007
ening is extrinsic in the form of friction between the die steel sleeve and foam surface, which contributes to the stress required to deform the specimen. In the following sections, we will discuss these causes for hardening and develop a framework for modeling the observed behavior. II.
INTRINSIC STRAIN HARDENING DUE TO MULTIAXIALITY
A. Background Plastic deformation in metal foams occurs through the collective collapse of cells, with the bands typically perpendicular to loading direction.[2] This local deformation propagates from one band to another progressively, until all the cells are collapsed, leading to the plateau region in the stress-strain curve.[3–6] This is followed by a rapid stress rise with further strain corresponding to densification. However, as pointed out in Part I, different aluminum foams exhibit marginal to significant hardening and thus deviate from the perfect plateau behavior even in the absence of constraint.[7] Kenesei et al. attributed this hardening to structural variability, which causes the collapse of progressively stronger cell bands leading to the observed macroscopic hardening.[8] However, Figures 2 and 4(b) in Part I reveal very small strain hardening rates without constraint for the ALPORAS foams under consideration.[1] This observation is not completely unexpected. During def
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