Uniqueness of reverse analysis from conical indentation tests

Abstract

The curvature of the loading curve, the initial slope of the unloading curve, and the ratio of the residual depth to maximum indentation depth are three main quantitiesthat can be established from an indentation load-displacement curve. A relationship among these three quantities was analytically derived. This relationship is valid for elasto-plastic material with power law strain hardening and indented by conical indenters of any geometry. The validity of this relationship is numerically verified through large strain, large deformation finite element analyses. The existence of an intrinsic relationship among the three quantities implies that only two independent quantities can be obtained from the load-displacement curve of a single conical indenter. The reverse analysis of a single load-displacement curve will yield non-unique combinations of elasto-plastic material properties due to the availability of only two independent quantities to solve for the three unknown material properties.

Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm

“…As an example, we consider here the dual indenter geometry of a 60 and 80 pair. The main drawback of this method compared to method A is the computation time as for each inverse analysis iteration incr, two FE simulations are performed.…”

“…This method consists of using dimensionless functions to rebuild the s -e curve based on several points (e r ; s r ), from load-displacement curves of different conical indenters. Chollacoop et al, 11 Dao et al, 12 Tho et al, 60 and Zeng and Chiu 33 have demonstrated the robustness of the solution when the method is based on dual sharp indenters. This method has been used to assess stress strain properties of thin films 61,62 and the properties of the matrix of metal matrix composites.…”

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

“…In a typical identification procedure, it is expected that there exists a one-to-one correspondence between the input pattern (usually the indentation curve, also called a P-h curve) and the desired material parameters defining a postulated constitutive law. Unfortunately, the indentation problem is frequently ill-posed, and the existence of different "sibling" materials with distinct material properties but almost identical indentation behaviors has been reported more than once [6][7][8].…”

“…However, the uniqueness of the solution still remains a matter of discussion since different material parameter sets may give almost identical indentation curves [7,8]. Therefore, it is of high interest to improve the reliability of the inverse analysis by involving more information for identification.…”

Revelation of a functional dependence of the sum of two uniaxial strengths/hardness on elastic work/total work of indentation

“…Another line of thought is to correlate the whole set of load-displacement data, rather than hardness value alone, with a group of fundamental material elastoplastic properties, such as Young's modulus E, yield strength, Poisson's ratio , and stain-hardening exponent n. [3][4][5] However, Cheng and Cheng, 6 Capehard and Cheng, 7 and Tho et al 8 pointed out that uniquely determining a set of the material parameters from a single set of load-displacement curves was unlikely. Therefore, more recently, a new approach has been developed: using two conical indenters of different half included angles to produce independent load-displacement curves for deriving material properties like yield stress and hardening coefficient etc.…”