STRESS STRAIN CURVE FOR DUCTILE AND BRITTLE

MATERIALS

Mechanics Of Structures-1

HOOKE’S LAW & ELASTIC MODULI

Hooke’s law states that: “ When a body is loaded within elastic limit, the stress is proportional to strain developed” or “Within the elastic limit the ratio of stress applied to strain developed is a constant”

The constant is known as Modulus of elasticity or Elastic modulus or Young’s modulus

Mathematically within elastic limitStress/Strain=σ/e=E

σ= P/A; e =ΔL/LE=PL/A Δ L

HOOKE’S LAW & ELASTIC MODULI

Young's modulus (E) is generally assumed to be the same in tension or compression and for most of engineering applications has a high numerical value. Typically, E=210 x 10^9 N/m² (=210 GPa) for steel

Modulus of rigidity, G= τ/φ= Shear stress/ shear strain

Factor of safety= Ultimate stress/Permissible stress In most engineering applications strains do not

often exceed 0.003 so that the assumption that deformations are small in relation to orginal dimensions is generally valid

 stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other

strain is the measure of the deformation of the material.

The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress).

Ductile Materials:>Ductile materials will withstand large strains before the specimen ruptures.>Ductile materials often have relatively small Young’s moduli and ultimate stresses.>Ductile materials exhibit large strains and yielding before they fail.>Steel and aluminum usually fall in the class of Ductile Materials

Brittle Materials:>Brittle materials fracture at much lower strains.>Brittle materials often have relatively large Young’s moduli and ultimate stresses.>Brittle materials fail suddenly and without much warning.>Glass and cast iron fall in the class of  Brittle Materials.

Steel generally exhibits a very linear stress-strain relationship up to a well defined yield point

Typical regions that can be observed in a stress-strain curve are: Elastic region,  Yielding,  Strain Hardening,  Necking and Failure

Stress-Strain Curve for Textile Fibre

Elastic Behavior

If the specimen returns to its original length when the load acting on it is removed, it is said to response elastically

Yielding A slight increase in

stress above the elastic limit will result in permanent deformation. This behavior is called yielding 

The stress that causes yielding is called yield stress σy.

The deformation that occurs is called plastic deformation

Strain Hardening When yielding has

ended, a further load can be applied to the specimen, resulting in a cure that rises continuously but becomes flatter until it reaches a maximum stress referred to as ultimate stress, σu.

The rise in the curve is called Strain Hardening

Necking & Fracture After the ultimate

stress, the cross-sectional area begins to decrease in a localized region of the specimen, instead of over its entire length. The load (and stress) keeps dropping until the specimen reaches the fracture point.