The potential deformation energy in tension

Under the static specimen tension, the tensile force F increasing slowly from zero up to some significance, lengthens the specimen by the value, simultaneously accomplishing work W. This work is accumulated as a potential deformation energy U in the deforming specimen; ignoring insignificant energy losses (for example, heat), we conclude that

W = U

If the tension diagram is drawn in the (F, ) coordinates, then the diagram area, expresses the deformation work. Before the proportional limit the work is expressed by the OAK triangle area (see Fig. 2.3). So, the potential deformation energy of tension for the bar with the length with the constant cross section A and the same normal force N = F will be equal to

The total work spent on the specimen rupture is given by the OABDN figure area of the tension diagram, the NMD triangle area corresponds to the strain work vanishing at the specimen rupture.

The deformation work per a unit bar volume is the specific potential energy of deformation: