Short presentation of tensile testing

Solids are defined as bodies not being deformable, but a "solid" from the real world becomes deformed (and ends up breaking) under a sufficient stress. It is clear that this deformation depends together on the geometry of the object (length $L$ and section $S$), on the exerted force $F$ and on the intrinsic qualities of the material (technical constants, such as the Young's modulus $E$).

The standard ISO6892 [4] recommends to use test pieces having a specified shape, as depicted FIG. 1 (left). Whenever possible, the length $L_{0}$ of the central parallel part has to equal five times the equivalent diameter of the cross section $S_{0}$. Once introduced in the tensile test machine, the test piece is elongated at constant speed while the length $L$ and the force $F$ are recorded at equal time intervals.

FIG. : Experimental data, coded in $\left( \varepsilon , \sigma \right) \protect$.

When plotting the obtained data (cf. FIG. 1, right), it is convenient to normalize these data. Therefore, the standard $x$-coordinate is the deformation $\varepsilon =\Delta L_{0}/L_{0}$, defined as the quotient of effective lengthening by the initial length, and the standard ordinate is the stress $\sigma =F/S_{0}$, defined as the quotient (expressed in $M\! Pa$) of the exerted force by the initial section of the test piece. Such a graph generally indicates the existence of a zone where the phenomenon of elastic strain remains proportional, then one notes a zone of plastic deformation and finally a zone of flow.

From these data, several quanta of knowledge can be extracted. Among them, the slope $E$ of the proportional part of graph (i.e. the Young's modulus), is of top importance, since it appears in the Hooke's law, that can be stated as:

$$\sigma =E\times \varepsilon$$

i.e. doubling the length doubles lengthening, while doubling the section doubles withstanding (as long as you remain in the elastic domain).