Mechanics of plastic flow past a narrow-angle wedge indenter

ABSTRACT

The indentation of a metal specimen by a narrow-angle wedge produces extreme plastic deformation, with an effect akin to cutting into the metal. Simulation of such processes is challenging, and complicated by the need to model material separation along the indentation symmetry axis. Here we use an Arbitrary Lagrangian Eulerian (ALE) framework to enforce the symmetry boundary conditions (bcs) in their original, `strong’ form, as well as conventional Lagrangian FE to impose the bcs in a complementary, `weak’ form. Taken together these two cases, representing perfectly strong and perfectly weak interfaces, produce accurate bounds on the mechanical response for indentation by wedges with semi-apical angles as small as 15 degrees, and encompass intermediate cases that would require complicated models of ductile failure. The method accurately predicts the transition from the cutting pattern to the non-cutting (radially compressive) pattern as the apical angle is increased. In combination with Lagrangian particle tracking, the simulations reveal the deformation pattern as well as strain, strain-rate, and velocity fields in narrow angle indentation at high resolution. Interestingly, the strong form predicts a thin (tens of microns), near-wall layer of intense plastic strain, which has been observed recently in indentation experiments. With the exception of this feature, the strong and weak bc solutions are quite similar. The present approach reveals insights about plastic flow past narrow obstacles in a range of related problems including cone penetration and machining, and suggests using narrow-angle indentation as a way to probe material failure.

KEYWORDS:

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

Acknowledgments

This work was partly supported by DST-SERB grant #EMR/2017/002621. The author thanks Dr. S. Keralavarma (IIT Madras), Prof. S. Chandrasekar (Purdue), and Dr. K.Viswanathan (IISc) for helpful discussions, and two anonymous referees for helpful suggestions.

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 issue arose during a discussion with Profs. R. McMeeking and S. Chandrasekar some years ago.

2 To avoid confusion, the terms sharp / blunt are used exclusively for the indenter tip radius, while narrow/wide is used to refer to the apical angle.

3 That such a tensile region exists is beyond doubt, but its size and location may depend on R_tip.

Additional information

Funding

This work was supported in part by a grant from the Science and Engineering Research Board, Department of Science and Technology, Government of India: [grant number EMR/2017/002621].