Since the advent of nanoindentation (a tool used by materials scientists to mechanically probe small volumes of material), researchers have continued to extend the range of applications and properties that can be measured using this technology. Traditionally speaking, nanoindentation testing has allowed researchers to measure the modulus of elasticity of a material, i.e., the resistance to non-permanent deformation, as well as the hardness, i.e., the resistance to local permanent deformation. However, in so far as the property of hardness is concerned, L. Tuckerman said it best when he stated that hardness is “a hazily conceived conglomeration or aggregate of properties of a material, more or less related to each other.”

In other words, hardness is not an innate material property and does not provide us with fundamental insights into a material's behavior under tensile and compressive stresses and strains. That being said, nanoindentation researchers have continued to improve upon the range of properties that can be measured. As such, spherical indentation stress-strain curve evaluation has become a reality and continues to improve in terms of serving as a reliable alternative to traditional tensile testing. As of late, The Cote Research Lab in Materials Science and Engineering at WPI has been contributing to the advancement of stress-strain curve extraction from spherical nanoindentation. As a result, we have been building off of the work by Pathak, Kalidindi, Weaver and others, and are currently working with our computer/data science colleagues to build a Python-based program that includes the refinements to the spherical nanoindentation stress-strain method established by Letiner et al.

At the same time, the Data-Driven Materials Science research group is currently exploring the use of statistical and machine learning tools for enhancing the capabilities of nanomechanical mapping experimentation. Nanomechanical mapping experimentation, which is also referred to in the literature as nanoindentation grid analysis, enables researchers to rapidly collect mechanical property data within a predefined array of indent locations, thus leading to datasets containing 10,000 idents per sample for one measurement. Such data and the insights gleaned from analyzing the data through a data science lens, rather than a materials science framework, can enable researchers and nanoindenter operators with the ability to identify the area fraction and therefore volume fraction of M-number of phases present within the material and the phase specific mechanical properties as well. This effort has relied upon probability density function analysis and deconvolution; K-Means Clustering analysis and deconvolution; and cumulative density function analysis and deconvolution, among others.

Tacit assumptions have been made about the suitability of two primary data-driven deconvolution algorithms concerning large (10,000+) data sets captured using nanoindentation grid array measurements, including (1) probability density function determination and (2) k-means clustering and deconvolution. Recent works have found k-means clustering and probability density function fitting and deconvolution to be applicable; however, little forethought was afforded to algorithmic compatibility for nanoindentation mapping data. The present work highlights how said approaches can be applied, their limitations, the need for data pre-processing before clustering and statistical analysis, and alternatively appropriate clustering algorithms. Equally spaced apart indents (and therefore measured properties) at each recorded nanoindentation location are collectively processed via high-resolution mechanical property mapping algorithms. Clustering and mapping algorithms also explored include k-medoids, agglomerative clustering, spectral clustering, BIRCH clustering, DBSCAN clustering, OPTICS clustering, and HDBSCAN clustering. Methods for ranking the performance of said clustering approaches against one another are also considered herein.

We have completed a fully-functional python program capable of processing and applying over 8 different clustering methods on inputted nanoindentation datasets. The current trajectory is to build a functioning user interface for material science researchers to upload data and subsequently perform and contrast multiple clustering algorithms on said data.