Identification of material properties using indentation test and shape manifold learning approach

Abstract

The conventional approach for the identification of the work hardening properties of a material by an indentation test usually relies on the force-displacement curve. However, finite element modeling of the indenter-specimen system is a complex task, and the unicity of the solution to the inverse problem of identifying material parameters using the force-displacement curve is not always guaranteed. Also, the precise measurement of the displacement of the indenter tip requires the determination of the indenter frame compliance and indenter tip deformation. To alleviate these problems, we propose in this work an approach based solely on the 3D indentation imprint shape measured after indenter withdrawal, rather than relying on the minimization of the pointwise discrepancy between the experimental and simulated indentation curve. We first build a mathematical "shape space" of indentation shapes in which a lower-dimensional manifold of imprints admissible according to a postulated material constitutive law is approximated. Then, we solve the inverse problem by using a series of predictor-corrector algorithms minimizing the distance between the estimated solution and the experimental imprint in this shape space. We finally apply the proposed approach to indentation tests using a spherical tip indenter on two different materials: a C100 steel specimen and a specimen of the AU4G (AA2017) aluminium alloy.

Identification of material parameters using indentation test —study of the intrinsic dimensionality of P-h curves and residual imprints

“…Thus the embedded system is also called an α-space and the hyper-surface an α-manifold. Their constructions were detailed in [19] thus omitted here.…”

“…In our former work [19], we proposed an original approach for evaluating diverse material properties solely based on the residual imprint after withdrawing the indenter. This information, usually high-dimensional, was not employed in calculating the point-wise distance so as to characterize the discrepancy between simulated and experimental measured quantities.…”

“…First, by adopting the same FE model used in our last work [19], two databases, each containing 21 × 21 = 441 samples, were built up for indentation curves and imprint mappings by simulations with various hardening parameter combinations. The simulation parameters are equalspaced sampled from the design domain (n ∈ [0.2, 0.3], σ y ∈ [200, 240]) allowing a straightforward demonstration of connectivity in embedded α-space.…”

“…More recently, due to the significant development of manifold learning algorithms and its applications in the field of computational and applied mechanics, biomechanics, and especially in material science [14][15][16][17][18], our most recent work [19] recommended that the identification procedure be carried out within a α-space constructed by using only the residual imprint of an indentation test. The core idea is based on the fundamental hypothesis that, there exists a low-dimensional space in which the original higherdimensional data could be embedded and the identification is implemented over a manifold defined within the constructed shape space.…”

Multi-scale investigation of highly anisotropic zinc alloys using crystal plasticity and inverse analysis

“…Appropriate mechanical models and simulation tools capable of predicting the formability of rolled Zn sheets are needed to realize their full potential as engineering materials. Mechanical characterization typically involves the use of a variety of mechanical tests such as uniaxial and biaxial tensile tests (for ductile materials such as metals and alloys), different compression tests (for brittle and quasibrittle materials such as concrete) and relatively recent quasi-nondestructive tests such as instrumented indentation [2,3], with the ultimate aim of determining its macroscopic mechanical plastic behavior: (e.g. yield surface, strain hardening, Lankford coefficients).…”