Identification of Young's Modulus from Indentation Testing and Inverse Analysis

Abstract

In this study, a numerical method for the identification of the Young's modulus of linear elastic coated materials from continuous indentation test is first presented. The identification is based on an inverse analysis where the minimization of a cost functional is performed by a gradient descent algorithm. The main result is the computation of cost function gradient by using a direct differentiation technique, resulting in a timesaving method compared to the widely used finite difference method. The validity and illustration of this approach is shown through several numerical examples. The second part of this article is dedicated to the identification of elasto-plastic thin films Young's modulus. A new method is proposed, where the inverse analysis relies only on finite element computations for elastic materials.

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

“…where R is the radius of the spherical indenter (R=0.5 mm in our case), h is the penetration depth, h max is the maximal penetration depth, and F 1 and F 2 are the load for the two considered curves, respectively. This error is widely used in inverse analysis [21,24,25]. Because of the experimental conditions and the sample's dimensions, h max /R=0.23 was chosen.…”

Strong Graphene 3D Assemblies with High Elastic Recovery and Hardness

“…After eight measurements at various sites, the average hardness and Young's modulus were obtained to be 12.86 and 159.47 GPa, respectively (Table S1, Supporting Information). For film‐like materials, a generally accepted rule is to limit the indentation depth to 10%–20% of the film thickness to prevent errors related to the substrates . To confirm the above results, two‐layered SGA with a thickness of ≈400 nm (see Figure f) was tested eight times at the indentation depths of 30 and 60 nm, respectively (Figure b).…”

“…Figure shows the mechanical properties of SGA measured by a Hysitron nanoindenter equipped with a Berkovich tip . A typical load‐displacement curve of a one‐layer SGA was obtained at a constant loading/unloading rate of 50 µN s −1 (Figure a), and the corresponding optical monitoring window is presented in the inset of Figure a.…”

History effect on squeal with a mesoscopic approach to friction materials

“…A complementary approach to the direct identification formulae is to try to extract the information about the mechanical properties directly from the load-displacement 6 indentation curves, by making use of inverse analysis like [24]. Inverse analyses are generally based on the minimization of a cost function measuring the discrepancy between the experimental load-displacement curve and a simulated one.…”