Identification of the hardening law of materials with spherical indentation using the average representative strain for several penetration depths

The identification of plastic properties with spherical indentation has been the subject of many studies in the last decades. In the present work, a new method for the determination of the hardening law of materials using the load–displacement curve of a spherical indentation test is proposed. This method is based on the use of an average representative strain. The advantage of the proposed average representative strain is that it is strictly obtained from the material in response to the indentation test. By using various values of penetration depth, the proposed method gives the range of strain for which the hardening law is precisely identified and allows determining a confidence domain that takes into account experimental imprecision and material heterogeneity. The influence of penetration depth and the error formula on the identified Hollomon hardening law are discussed in the present study. The present study clarifies many problems that were observed in previous studies such as the uniqueness of solution and the sensitivity of the indentation test to the plastic parameters of the Hollomon hardening law.