Direct mapping of deformation in punch indentation and correlation with slip line fields
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J. Madariaga Center for Materials Processing and Tribology, School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47906-2023; and Department of Manufacturing, Mondragon University, Loramendi, 4-20500 Mondragon, Spain
S. Chandrasekara) Center for Materials Processing and Tribology, School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47906-2023 (Received 31 July 2008; accepted 30 September 2008)
Deformation field parameters in plane-strain indentation of a perfectly plastic solid with a punch have been mapped using particle image velocimetry, a correlation-based image analysis technique. Measurements of velocity and strain rate over a large area have shown that the deformation resembles that of the slip line field of Prandtl. A zone of dead metal is found to exist underneath the indenter adjoining which is a transition region of material flow similar to the centered-fan region in the slip line field. Shear bands demarcate the boundaries of these deformation regions. The observations suggest that a representative strain rate may be assigned to the indentation. By integrating the strain rate field along particle trajectories, the strains in the indentation region have been estimated. The strain values are seen to be large, 0.5 to 4, over a region extending to about twice the indenter half-width. A pocket of large strain, 4, is found to exist close to the edge of the indenter–specimen contact. Prandtl’s slip line field is modified based on the observations and used to estimate the strain field. The measurements of the deformation parameters are found to compare mostly favorably with the predictions of the slip line field and prior observations of indentation. The implications of these findings for analysis and interpretation of indentation hardness are briefly discussed.
I. INTRODUCTION
A long-standing problem in indentation hardness testing of solids is characterization of plastic strain and strain rate distribution around indentations.1–3 Interpretation of indentation tests for assessing material behavior has often relied on concepts such as representative strain, strain rate, and strain gradient, whose theoretical underpinnings are less than adequately established. Assessment of these concepts and description of the framework of indentation, e.g., friction condition, extent of plastic zone, and strain hardening, will be facilitated by detailed measurements of deformation field parameters such as velocity of material flow, strain rate, and strain,
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0094
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J. Mater. Res., Vol. 24, No. 3, Mar 2009
since these parameters contain far more information than is typically available in ensemble measurements of load– displacement and contact pressure. For example in punch indentation, the applied load is essentially insensitive to the nature of the friction condition along the punch– sample contact even though the deformation field varies widely with the friction condition.
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