This TLP has covered the basics of how mechanical testing of metals is carried out, aimed at study of the onset and development of plastic deformation and how it affects the "strength" (failure stress) and ductility. It is based on continuum mechanics - ie there is no detailed consideration of the mechanisms of plasticity or of effects such as anisotropy and inhomogeneity that could arise from microstructural features. The plasticity, and also the consequential necking and fracture that are likely to occur under tensile loading, are characterised by constitutive laws. Two commonly-used expressions are described here. Their usage in FEM modelling is outlined, aimed at obtaining detailed information about the stress and strain fields that are generated during different types of test.
Perhaps unsurprisingly, there are relatively few sources that provide background information regarding something as basic as uniaxial mechanical testing, although there are, of course, plenty of books and websites that cover the fundamentals of stress analysis etc. Among relatively recent books in this area, with an accent on FEM, are the following:
“Practical Stress Analysis with Finite Elements”, Bryan J. MacDonald, Glasnevin publishing (2007), ISBN:978-0-9555781-0-6.
“Structural and Stress Analysis: Theories, Tutorials and Examples”, Jianqiao Ye, Taylor & Francis (2008), ISBN:0-203-02900-3.
Regarding Indentation Plastometry, which is a very recent development, there are as yet no published books and indeed the software necessary to implement the technology is not yet widely available in user-friendly, commercially mature form. However, there are websites that describe the methodology, where such access is likely to become available in due course. Notable among these is https://www.plastometrex.com/..