## Friday, August 2, 2013

### STRESS STRAIN RELATIONSHIP FOR DUCTILE MATERIAL

stress-strain diagram for ductile material
·         When a ductile material like mild steel bar of uniform cross section is subjected to a gradually increasing tensile load up to fracture using universal testing machine.
·         The relationship between stress and strain is generally of the form as shown

The following are the salients points on the curve:
1>LIMIT OF PROPORTIONALITY: IN This range the strain is proportional to the stress and the graph is a straight line. Point is called limit of proportionality.it is the value of stress up to which stress and strain has a constant ration and hooke’s law is obeyed.
2>ELASTIC LIMIT:At point A the curve deviates from the straight line.if the load is increased beyond A up to the point B, the material behaves in elastic manner that is on the removal of  the load the whole deformation will vanish.the value of stress corresponding to point B up to which the material behaves in an elastic manner is called the elastic limit. Te specimen if stressed beyond this limit not return back to its original position when the load is removed and there will be a permanent deformation of the body called permanent set. Up to point B the material will be in elastic range and beyond it will be in the plastic range. Two points which are proportional limit and elastic limit are very close to each other and in some cases they may coincide also.
3>UPPER YIELD POINT: point c is called upper yield point at this point there is an increase in strain even though there is no increase in stress(load). A formation of creep makes the specimen plastic and the material begins to  flow.the value of stress corresponding to point C  is called yield stress or yield strength. The yield stress defined as that unit stress which will cause an increase in length without an increase in load. At this stage strain is .125 and stress in 250 n/mm2.
4>LOWER YIELD POINT:  A load may rise and fall while yielding occurs. This is indicating by wavy appearance of the stress-strain graph between C And D. point D corresponding to the lower yield point. After yielding has ceased at D further stress and strain can be obtained by increasing the load.
5>ULTIMATE LOAD POINT: after increasing the load beyond the yield point the stress strain curve rises till the point E  is reached which is called ultimate(maximum) load point.the stress corresponding to this point is also max and is called ultimate stress or ultimate tensile strength or tensity. This stress is about 370 to 400 n/mm2.at this stage cross section area at particular start reducing very fast. This is called neck formation.
6> BREAKING LOAD POINT: up to point E  the cross sectional area of te specimen goes on uniformly decreasing forming a neck or waist and the load required to cause further extension is also reduced.as the elongation continues cross sectional area becomes smaller and smaller ultimately the specimen is broken at F into  two pieces giving cup cone type of ductile fracture.point F is called breaking load point and the stress corresponding to this point is called breaking stress or rupture or breaking strength of the material. At

this stage strain is 20 to 25%.