Stress-Strain diagrams

Brittle material - The stress -Strain diagram for a brittle material like cast iron is .There is

is  very little elongation and reduction in area of the specimen for such materials .The yield point is not marked at all .The straight line portion of the diagram is also very small .

Figure 2.3. Stress strain diagram for a brittle material.  
Stress -Strain diagram for brittle material

Ductile material - The Stress-Strain diagram for a ductile material like mild steel.The

curve starts from the origin O showing thereby that there is no initial Stress or Strain in the test specimen . Up to point 'A' Hooke's low is obeyed and Stress is proportional to Strain .Therefor oa is a straight line and point a is called the limit of  proportionality and the Stress at point a is called the proportional limit Stress The portion of the diagram between ab is not

Stress-Strain diagrams for ductile material

a straight line but upto point the material remains elastic on removal  of the load , no permanent set is formed and the path is retracted .The point is called the elastic limit point and the Stress corresponding to that is called the elastic limit Stress in actual practice the point a and b are so close to each other that it becomes difficult to differentiate between them. Beyond the point B the material goes to the plastic stage until the upper yield point 'c' is reached . At this point the cross sectional area of the material starts decreasing and the Stress decreases to lower value to a point d, called the lower yield point.  Corresponding to point c, the Stress is known as upper yield point Stress and corresponding to the d, the Stress is know as the lower point Stress, At point d the specimen elongates by a considerable amount without any increase in Stress and up to point e , the portion d,e is called the yield of the material at constant Stress .From point e
on wards the Strain hardening phenomena becomes predominant and the Strength of the material increase thereby requiring more Stress for deformation until point f is reached . Point f is called the ultimate point and the Stress corresponding to this point is called the ultimate Stress It is the maximum Stress to which the material can be subjected in a simple tensile test . At point f the necking of the material begins and the cross sectional area decreasing at a rapid rate . Due to this local necking the Stress in the material goes on decreasing inspite of the fact that actual Stress intensity necking goes on increasing Ultimately the specimen breaks at point g, known as the breaking point and the corresponding Stress is called the nominal breaking Stress based upon the original area of cross section . Where as the true Stress at fracture is the ratio of the breaking load to the reduced area of the cross section at the neck  The initial portion of the diagram are show in exagerated scale.

Sometimes it is not possible to locate the yield point quite accurately in order to determine the yield strength of the material . For such material for yield point Stress is defined at some particular value of the permanent set. It has been observed that if load is removed in the plastic range then the unloading path line is parallel to the straight portion of the Stress - Strain diagram as shown . The commonly used value of permanent set for determining the value of yield strength for mild steel 0.2 per cent of the maximum Strain


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