Converting the Instrumented Indentation Diagrams of a Ball Indenter into the Stress–Strain Curves for Metallic Structural Materials

Abstract

The available approaches to converting indentation diagrams into stress–strain curves are reviewed. It is noted that most studies on converting the instrumented indentation diagrams of a ball indenter into the stress–strain curves have been carried out within the uniform deformation limits using various computational and experimental approaches, including the finite element method and neural networks. In the authors’ opinion, however, it is reasonable to perform the conversion of one diagram to another using the established relationship between indentation and tension deformations. This makes it possible not only to perform the conversion with a higher accuracy but also to evaluate the mechanical properties under tension from the indentation characteristics. The formulas most frequently used to determine plastic deformation contain a relative indentation diameter as the main parameter. Meanwhile, at the same relative indentation diameter and a constant ratio between the average contact pressure (Meyer hardness) and the true tensile stress, the indentation and tensile strain values can be significantly different owing to different strain hardening abilities of materials. The authors have established a relationship between the true elastoplastic deformation in the tensile tests and the relative depth of an unrecovered indentation obtained with a ball indenter with allowance for the strain hardening parameter determined from the instrumented indentation diagram. On the basis of the established relationship, a technique for converting the instrumented indentation diagram into a stress–strain curve in the uniform deformation region with the determination of the yield strength, tensile strength, and ultimate uniform tension has been developed. The technique has been verified by testing steels and aluminum, magnesium, and titanium alloys with strongly different Young’s moduli, strength characteristics, plasticity, and strain hardening.