Deformation field in deep flat punch indentation and the persistence of dead-metal zones

ABSTRACT

The indentation of metal by a flat punch is a model system for forming processes and intimately linked with hardness testing. Here, we perform first-in-class, high-fidelity finite element (FE) simulations in an arbitrary Lagrangian–Eulerian (ALE) framework to study the deformation field in deep punch indentation of annealed copper. The use of ALE allows indentation depth to punch width ratios as high as 1.6, while the use of Lagrangian tracer particles reveals pathlines of material transport. Field quantities such as the plastic strain, strain rate and velocity are obtained at high resolution. A low-strain, dead-metal zone (DMZ) that is stationary with respect to the indenter forms immediately below the punch. Crucially, it is found that DMZs are unavoidable in deep punch indentation, forming at the outset and irrespective of the coefficient of friction. However, the area of this zone shrinks as the indentation progresses at a rate that is inversely related to the friction. The simulations thus explain why Prandtl’s view of punch indentation, which incorporates DMZs, is physically more accurate than Hill’s view. The computations successfully reproduce the strain field inhomogeneity seen in recent in situ imaging experiments. While DMZ formation is impervious to the hardening model used, Zerilli–Armstrong hardening provides more accurate indentation force estimates than Johnson–Cook hardening. Lastly, the residual impression and factors affecting its shape are studied. The sides of impressed metal are never vertical, but at an inclination to it. Methods to modify such features, of potential interest in metal forming, are discussed briefly.

KEYWORDS:

• Indentation
• metals
• plastic deformation
• hardness
• finite element modelling

Acknowledgements

The author thanks Dr. Sieglinde Pfaendler for translation of sections of [2] and [3] from German.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Narayan K. Sundaram http://orcid.org/0000-0003-3285-0424

Notes

1 This is not, however, an issue if the simulation is restricted to very incipient indentation

2 Investigators have also used re-meshing [16] and Eulerian FE [28] to study deep indentation

3 The number of Lagrangian tracer particles is itself limited because each tracer adds a considerable post-processing burden.