ARTICLE Modeling nanoindentation using the Material Point Method Chad C. Hammerquist and John A. Nairn a) Wood Science and Engineering, Oregon State University, Corvallis, Oregon 97330, USA (Received 3 January 2018; accepted 16 March 2018) A numerical nanoindentation model was developed using the Material Point Method (MPM), which was chosen because it can handle both large deformations and dynamic contact under the indenter. Because of the importance of contact, prior MPM contact methods were enhanced to improve their accuracy for contact detection. Axisymmetric and full 3D simulations investigated the effects of hardening, strain-rate dependent yield properties, and local structure under the indenter. Convergence of load–displacement curves required small cells under the indenter. To reduce computation time, we used an effective nonregular grid, called a tartan grid and describe its implementation. Tartan grids reduced simulation times by an order of magnitude. A series of simulated load–displacement curves were analyzed as “virtual experiments” by standard Oliver–Pharr methods to extract effective modulus and hardness of the indented material. We found that standard analysis methods give results that are affected by hardening parameters and strain-rate dependence of plasticity. Because these parameters are not known during experiments, extracted properties will always have limited accuracy. We describe an approach for extracting more properties and more accurate properties by combining MPM simulations with inverse methods to fit simulation results to entire load–displacement curves. I. INTRODUCTION Humans have been using indentation to test material properties since the first person poked a stick into soft ground to see if it was firm enough to walk on. More modern techniques are described by Oliver and Pharr 1 who developed a method for analyzing microscale in- dentation experiments using the maximum indentation load, maximum indentation depth, and initial unloading stiffness. This method for analyzing nanoindentation, which is generally referred to as the “Oliver–Pharr method,” extracts material properties from nanoindenta- tion, load–displacement curves. Since then, much work has been done in analyzing, numerically modeling, and developing new experimental techniques. Most numerical modeling has used finite element analysis. 2–4 This paper describes a new simulation method for modeling nano- indentation using the particle-based Material Point Method (MPM). MPM has been used for modeling nanoindentation experiments 5 and for modeling coupled with molecular dynamics. 6 This paper describes new axisymmetric and 3D MPM simulations of nanoindentation that added three improvements to increase accuracy and efficiency of prior MPM simulations. 5 First, accurate modeling of nanoindentation requires that contact between the in- denter and the material is well modeled. We describe an improvement to the standard MPM contact algorithms 7–9 that more accurately detects contact based on displace- ments of the two material surfaces. Second, converged nanoindentation results require small cells under the indenter. We describe a mesh refinement scheme, called a “tartan” grid that allows for refined mesh under the indenter and larger cells elsewhere but maintains orthog- onality of standard MPM grids. The retained orthogonal- ity greatly simplifies implementation of tartan grids. Use of tartan grids significantly reduced computational time for axisymmetric simulations and made converged, 3D simulations feasible. Third, all MPM simulations used dynamic code with explicit time-stepping. Several tech- niques were used to suppress dynamic effects and noise. The new simulation methods led to output of load– displacement curves that faithfully represented quasi- static nanoindentation experiments. Each curve could be viewed as a “virtual experiment” on a material with precisely known material properties (e.g., rate-independent, nonlinear elastic properties with various nonlinear J 2 plasticity properties). We subjected a series of such “virtual experiments” to standard Oliver–Pharr analysis methods. The results show that such methods are reasonable but have limited accuracy for extraction of effective modulus or hardness. The problem is that extracted results depend on plasticity properties. Thus, when experiments are done on any unknown material, compromises have to be introduced into analysis methods. A potential method to avoid such compromises and to measure both more material properties and more-accurate material properties is to couple MPM a) Address all correspondence to this author. e-mail: john.nairn@oregonstate.edu DOI: 10.1557/jmr.2018.75 J. Mater. Res., Vol. 33, No. 10, May 28, 2018 Ó Materials Research Society 2018 1369 Downloaded from https://www.cambridge.org/core . IP address: 191.96.152.15, on 02 Dec 2019 at 20:45:22, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms . https://doi.org/10.1557/jmr.2018.75