# Stress & Strain Curve of ductile material in tension | GATE Lectures | ME

Stress is basically the internal resistive for induced inside the material per unit area. This internal resistive force will be induced inside the material only when the material is in equilibrium. Normal stress is the stress induced inside the material when the load is acting perpendicular to area of cross section and shear stress is the stress induced inside the material when the load is acting parallel to the area of cross section.

Strain is the ratio of change in dimensions to the original dimensions of the material. Linear strain is corresponding to linear changes and volumetric strain is corresponding to volumetric changes. Also if the strain is caused by normal stress it is called normal strain and the strain caused by shear stress is called shear strain.

In finding **stresses and strains**, if we take initial dimensions we call them as conventional/engineering values and if we take instantaneous values they are called as true values.

In stress strain curve of ductile materials, up to proportionality limit stress and strain are proportional to each other and also elastic in nature. After that proportionality disappears and only elasticity remains. That limit is called elastic limit. After elastic limit from a point plasticity starts and that point is called yield limit. From this point there is no need for increase of stress. This region is called as plastic or yielding region. After that a region starts where increase of stress is required to increase the strain. This region is called as strain hardening region. In this region the curve goes to a peak and the stress corresponding to this is called as Ultimate stress. After this Ultimate stress the material undergoes necking and eventually fractures. As we are plotting the curve between conventional values of stress and strain we take initial values of area of cross section which was larger hence the curve goes down and fracture occurs at a lower value of stress.

**Hook’s law** is given by Robert Hook when he observed that load and elongation are proportional to each other in a spring load system. The same phenomenon was observed in elastic solids up to proportionality limit. Hence Hook’s law is valid up to proportionality limit only.

If the machine element is unable to perform its objective we say that machine element got failed. Ductile materials fail by yielding. Hence yield stress is the strength of the material in ductile materials. In stress strain curve of mild steel it is very easy to identify the yield point but not in materials like Aluminium and Copper. In those elements a line is drawn with slope of Young’s modulus to intersect the curve. That point of intersection is called as Proof stress. So designing of the elements made up of these materials is done according to proof stress.

In mild steel, iron and carbon are present. Carbon occupies the interstitial volume between the iron atoms. As the interstitial volume is less than the size of the carbon atom there is normal contact force between the atoms leading to upper yielding point. But after yielding the interstitial volume increases and normal contact force decreases leading to lower yielding point.