# Volume change during tensile test

During tensile test, why does the specimen's(let's say mild steel) volume changes during elastic deformation and does not change during plastic deformation?

## 1 Answer

In short, elastic deformation of crystalline structures (like steel) happen on an atomic scale, where the bonds of the atoms in the lattice are stretched. This allows for a change in how close the individual atoms are packed together.
If you remove the load, the energy stored within these bonds can be reversed (comparable to a spring), therefore it's only elastic.

On the other hand, plastic deformation happens along gliding planes, for example between individual crystals (inter-crystalline) or within the crystal itself (intra-crystalline). During plastic deformation crystals "slide" along that plane, they perform a translation which is permanent, therefore plastic. The crystalline structure itself remains more or less unaffected during that translation, therefore no volumetric change occurs.

• Is this effect (volume change) applicable to all materials, or are we only talking about metals (per OP's example)? Is the effect related to the magnitude of Poisson's ratio in any way? I'm not being critical, just trying to learn something new. – AsymLabs Jul 19 '18 at 18:21
• The effect is completely dependent on the Poisson's ratio; a Poisson's ratio of 0.5 implies no volumetric change for tensile stretching or compressive contraction of a bar/rod, for example, in the elastic regime. Try calculating the volumetric strain $\epsilon_x+\epsilon_y+\epsilon_z$ for various loading configurations using generalized Hooke's Law to gain insight. – Chemomechanics Jul 20 '18 at 2:28
• @AsymLabs: A lack of plastic volumetric contraction is found in other materials than metals as well, provided that the material does have a distinct plastic region. As far as I know there is no material that shows plastic volumetric contraction. – Andrew Jul 20 '18 at 10:00
• @Andrew Yes I was thinking of this behaviour in the context of other commonly used construction materials such as bituminous concrete and Portland cement concrete, for example. This behaviour (volumetric change in the elastic zone) is not usually a subject of concern in practice, but could prove to be quite important in certain circumstances. – AsymLabs Jul 21 '18 at 9:21
• @Chemomechanics Thank you for this. Reason I'm asking is that I've investigated certain types of layered structures with computer simulations of elastic behaviour/stress development under various loading and temperature conditions (the Poisson's Ratio of the material varies with temperature seasonally and with depth). The equations of course are well established but out of interest I will revisit them to consider just how they address volumetric change. It may be that the underlying assumption is that the element is volumetrically constrained. – AsymLabs Jul 21 '18 at 9:43