Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach

Abstract

The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the “experimental” data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations (“noise”) superposed on the “experimental” data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress–strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress–strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress–strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement.

Extraction of mechanical properties of materials through deep learning from instrumented indentation

“…A NNbased surrogate model was used in order to reduce the number of finite-element method (FEM) conical indentation simulations to extract material properties (40). Besides NNs, other ML approaches have also been employed to solve the indentation problems, such as identification of plastic properties from conical indentation using Bayesian-type analysis (41). These methods, however, were generally cumbersome to use in practice as they required training using all data points within individual indentation loading (and/or unloading) curves or extensive iterations with finite-element simulations.…”

On the identification of power-law creep parameters from conical indentation

“…The equations of the Bayesian-type statistical approach used to infer the creep parameters n, σ0 and ϵ˙0 from an indentation depth versus time response, from a residual surface profile or from a combination of these are presented here. A more complete presentation, background on the methodology and references are given in [15].…”

“…Here, the Bayesian statistics-based approach of Zhang et al [15] is used to extract power-law creep parameters from the indentation depth versus time response and the residual surface profile. Finite-element solutions for three materials with very different power-law creep properties are considered to be the ‘experimental’ responses.…”

“…The questions addressed include: Can very different power-law creep parameters give nearly the same responses in load and hold indentation creep? There are sets of rate-independent plastic material parameters that have indistinguishable force versus depth responses in conical indentation but very different uniaxial responses [15–17]. Does using the residual surface profile in addition to or instead of the indentation depth versus time data improve the quality of the prediction?How sensitive is the predicted creep response to noise in the ‘experimental’ indentation data?How do the power-law creep properties obtained using the analytical steady-state creep results of Bower et al [1] and Ginder et al [2] compare with those predicted from the Bayesian-type statistical approach?…”

On the value of test data for reducing uncertainty in material models: Computational framework and application to spherical indentation

“…The measurement of the indenter displacement is affected by the compliance of the parts between the indenter and the displacement sensor. Therefore, when the knowledge of the machine compliance and the indenter is not readily available, the residual imprint, is introduced as the material response to identify the elastoplastic models [17][18][19]54]. The residual imprint response Y is represented as a function of the spatial coordinate X, e.g.…”