Elastic limit load and motion of dislocations

Elastic limit load is the maximum value of stress by virtue of which the material undergoes reversible deformation. If the elastic limit load is exceeded there are two scenarios: 

• the material fractures;
• The material starts to deform permanently, passing from an elastic regime to a plastic regime. 

Permanent deformation of materials (plastic) is related to the movement of dislocations. What materials can deform plastically? In what materials can dislocations move? In metallic materials, dislocations can move because the bond is not directional and the crystalline planes can slip and slide over each other; in ceramic materials, ionic and covalent solids, instead, dislocations exist but they are immobile, because either bond is strongly directional (covalent ceramics) or, as in case of ionic ceramics, there are problems of charge repulsion if planes slip, so in these materials dislocations cannot move (when they move the material fracture). 

This explains why in metals I will have a permanent plastic deformation once the elastic limit load is exceeded; vice versa in ceramics and glasses I will have fracture.  

There are two scenarios for a material undergoing the transition from elastic to plastic regime (see figure):

• in the elastic regime is visible a straight line, so strain and deformation are linked by direct proportionality (Hooke's law): in the left figure is visible a gradual transition to the plastic regime, then the curve changes slope (from linear to rounded); 
• in the figure on the right is visible a complex transition: around the elastic limit I have a stress oscillation. Beyond the elastic limit load I have microstructural arrangements of the material that make the stress fluctuate. Afterwards, the curve starts to rise again (plastic regime).

In both cases, the point of transition from elastic to plastic regime is called the yield point: in the figure on the left it coincides with the load at the elastic limit, in the curve on the right, on the other hand, an upper yield limit and a lower yield limit are defined. Typically the yield strength value is the average of the two. 

Materials stressed beyond the elastic limit either fracture without plastic deformation (glass and ceramics) or undergo irreversible deformation (plastic deformation).    

In the case of brittle material, the stress-strain curve following a tensile test is a straight line. At the elastic limit, the material fractures. 

In the other two cases (semi-ductile and ductile materials), there is plastic deformation which can vary considerably: it can be modest (semi-ductile material) or important (ductile material). The figure below right corresponds to the case in which the elastic limit load coincides with the yield strength, while the figure below left corresponds to the case in which there is an upper and a lower yield strength.