**MODULUS OF RESILLINCE: **

**Fig :1 **

Suppose ‘ s_{x}‘ in strain energy equation is put equal to s_{y} i.e. the stress at proportional limit or yield point. The resulting strain energy gives an index of the materials ability to store or absorb energy without permanent deformation

So

The quantity resulting from the above equation is called the Modulus of resilience

The modulus of resilience is equal to the area under the straight line portion ‘OY' of the stress – strain diagram as shown in Fig .4 and represents the energy per unit volume that the material can absorb without yielding. Hence this is used to differentiate materials for applications where energy must be absorbed by members.

**MODULUS OF TOUGHNESS: **

**Fig :2 **

Suppose ‘Î' [strain] in strain energy expression is replaced by Î_{R} strain at rupture, the resulting strain energy density is called modulus of toughness

From the stress – strain diagram, the area under the complete curve gives the measure of modules of toughness. It is the materials.

Ability to absorb energy upto fracture. It is clear that the toughness of a material is related to its ductility as well as to its ultimate strength and that the capacity of a structure to withstand an impact Load depends upon the toughness of the material used.