A Micropillar Compression Methodology for Ductile Damage Quantification
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immense efforts have been made to understand the microstructural damage mechanisms (e.g., microcracks and microvoids) observed in the new highstrength metals (e.g., dual-phase steels, advanced aluminum alloys, etc.) to understand and predict the complex material behavior and failure of these advanced materials. Next to these qualitative analysis efforts, there has also been significant interest in the quantitative analysis of the damage activity, not only to allow the comparative analysis (of the damage-sensitivity) required to optimize these new microstructures but also to predict their complex mechanical behavior through continuum damage models. However, the accurate quantification of ductile damage is a significant challenge and (contrary to popular belief) not trivially possible using the existing morphology based experimental techniques (e.g., electron micrography, X-ray microtomography, and highly sensitive mass and volume measurements).[1–3] These methodologies probe a geometric damage parameter based on either void area fraction, void volume fraction, or porosity density, which do allow for a qualitative analysis C.C. TASAN, Postdoctoral Researcher, is with the Materials Innovation Institute (M2i), P.O. Box 5008, 2600 GA Delft, The Netherlands, and is also with the Department of Microstructure Physics and Alloy Design, Max-Planck-Institut fu¨r Eisenforschung GmbH, MaxPlanck-Str. 1, 40237 Du¨sseldorf, Germany. J.P.M. HOEFNAGELS, Assistant Professor, and M.G.D. GEERS, Full Professor, are with the Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands. Contact e-mail: [email protected] Manuscript submitted July 17, 2011. Article published online December 14, 2011 796—VOLUME 43A, MARCH 2012
of damage mechanisms to optimize damage-sensitive microstructures. However, the geometric damage parameter does not probe directly how the deformation mechanics is affected by the amount of damage, damage morphology, or interaction effects.[4,5] Therefore, a mechanical property-based experimental technique is needed that directly probes the mechanical influence of deformation-induced damage (rather than its geometry), with sufficiently high spatial resolution to capture high strain and damage gradients. The indentation-based methodology,[6] where deformation-induced hardness degradation is probed to quantify a mechanical damage parameter D, has received considerable attention as the most promising mechanical approach to fulfill these requirements.[1,7–9] This methodology was extended by Guelorget et al.[9] to probe the damage parameter from the degradation of the indentation modulus (obtained via the Oliver-Pharr methodology[10]) through DE ¼ 1
ED E
½1
where ED is the indentation modulus of the damaged material and E is the indentation modulus in the undeformed state. This extension is significant as degradation of the modulus connects directly to the damage definition employed in continuum damage models.* *The fact that the indentation modulus may differ from
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