A Theoretical Model for Elastic-Perfectly Plastic Flat Cylindrical Punch Indentation

Instrumented indentation is widely used to evaluate the hardness and other mechanical properties of materials. This requires a theoretical model for the indentation curve (load vs. penetration) based on the Young's modulus, Poisson's coefficient, yield stress, hardening exponent, friction, and shape of the indenter. Several papers have been devoted to modeling spherical, conical, or pyramidal indentation in cases of both elastic and plastic deformation; in contrast, there are relatively few theoretical studies on flat cylindrical punch in the elastic–plastic regime. Indeed the singularity in the stress field at the edge of the contact is difficult to solve even if the aim is only to obtain an approximate solution. In this paper, after reviewing the theoretical basis of flat cylindrical indentation for elastic and rigid-plastic materials three different steps have been used to describe the entire progress of penetration: pseudo-elastic, elastic–plastic and full plastic. This final condition begins when the entire contact area undergoes plastic deformation. Using this classification as the starting point, a new simplified equation represents the stiffness of the specimen under flat cylindrical indentation, taking into account the elastic–perfectly plastic behavior. Integrating this equation gives the curve of indentation for an elastic–perfectly plastic material. As the characteristic parameters of this equation are unknown, in this paper the results of an extended numerical investigation using finite-element models of many different materials facilitates their calculation and validates the model. Using this new model, the direct and the inverse problems of flat indentation can be solved with good accuracy as shown through several FEM analyses. Finally, considering that the new model does not take the hardening effect into account, experimental data from the literature facilitate the verification of the relevance of this approximation. This final check successfully assesses the accuracy and the usefulness of the new method.