The engineering stress-strain curve is one of the most convenient characterizations of the constitutive behavior of materials that can be obtained directly from uniaxial experiments. We propose that the engineering stress-strain curve may also be directly converted from the load-depth curve of a deep spherical indentation test via new phenomenological formulations of the effective indentation strain and stress. From extensive forward analyses, explicit relationships are established between the indentation constraint factors and material elastoplastic parameters, and verified numerically by a large set of engineering materials as well as experimentally by parallel laboratory tests and data available in the literature. An iterative reverse analysis procedure is proposed such that the uniaxial engineering stress-strain curve of an unknown material (assuming that its elastic modulus is obtained in advance via a separate shallow spherical indentation test or other established methods) can be deduced phenomenologically and approximately from the load-displacement curve of a deep spherical indentation test.
This work is supported by National Science Foundation (NSF Grant No. CMMI-0643726), by World Class University (WCU) program through the National Research Foundation of Korea (Grant No. R32-2008-000-20042-0), and by National Natural Science Foundation of China (NSFC Grant No. 50928601). The authors are grateful for the experimental data and valuable discussion with Prof. Akio Yonezu (Osaka University, Japan).