STRESS-STRAIN DIAGRAM AND STRESS-STRAIN UNDER AXIAL LOADING


EXPERIMENTAL SET UP

The test specimen is kept in the testing machine which is used to apply a centric load "p". As the load increases the distance "L" is measured with the help of dial gauge and the elongation " L-Lo" is recorded for each value of load(P).A second dial gauge is often used to determine the change in the diameter of the specimen. From each pair of reading of elongation and load we can determine the stress by dividing the load (P) by original cross section area (Ao) of specimen. Also strain can be obtained by dividing the new or increased length (L-Lo)with original length(L).

The stress-strain graph is obtained by plotting strain on abscissa axis and stress on ordinate.

Stress-strain diagram of various material vary widely and different tensile test conducted on the same material may yield different result, depending on temperature of specimen and speed of loading.



FOR DUCTILE MATERIALS:-

Stress strain diagram for ductile material is as fallows:-

STRESS- STRAIN DIAGRAM


Elastic range 

Under elastic range stress is directly proportional to the strain. It means that as the stress increases, equivalent strain is induced in it. The body has tendency to come to its original shape when stress is removed in the elastic range.


Yield stress:-

This is point beyond which material exhibit plastic property and before which it is somewhat elastic.
Material starts flowing plastic ally beyond yield point. From lower yield point with small increase in stress results in large plastic deformation which ultimately leads to failure of material. Point E represents ultimate stress beyond which material finally fractures.
The various materials that falls under this category are aluminum, steel, gold, malleable cast iron etc.

FOR BRITTLE MATERIALS:-

STRESS STRAIN FOR BRITTLE MATERIALS


In case of brittle materials the graph obtained is quite different from that of ductile material. The figure below depicts the stress-strain diagram of brittle material.

There is no upper yield or lower yielding point in brittle materials. After elastic limit is material is further stressed then it undergoes brittle fracture at point B. Such phenomenon is exhibited by materials like glass, wood etc.

       STRESS AND STRAIN -AXIAL LOADING

Stress is created in various members and connections by the load applied to the structure of machine. Another important aspect of analysis and design of structure relates to deformation caused by the loads applied to structure. Clearly, it is important to avoid deformation so large that it may prevent the structure from fulfilling the purpose for which it was intended. But the analysis of deformation may also help us in determination of stress. Indeed, it is not always possible to determine forces in the members of a structure by applying only the principle of statics. This is because statics is based on assumption of undeformable rigid structure. By considering engineering structures as deform able and analyzing the deformation in various member, it will be possible for us to compute forces that are statically indeterminate i.e. indeterminate within framework of statics.

To determine the actual distribution of stresses within a member, it is thus necessary to analyze the deformations that take place in that member. First, the normal strain "e" is the member defined as the deformation per unit length. Plotting the stress "sigma" verses the strain "e" as the load applied to the member is increased yields a stress strain diagram for the material used. From such a diagram we can determine some important properties of the material, such as 

1) Modulus of elasticity
2) Elastic limit
3) Upper yield point
4) Lower yield point
5) Ultimate stress
6) Breaking/rupture point

For the stress strain diagram, we can also determine whether the strain in the specimen will disappear after the load has been removed-in which case the material is said to behave in elastic manner or will have permanent deformation. The phenomenon of fatigue causes structure or machine component to fail after a very large number of repeated loading, even though the stress remains in the elastic range.

Normal strain under axial loading:-

A body "BC" of cross section area "A" suspending as shown in figure from point "B". When load "P" is applied at point "C" the body tends to elongate by delta amount. It is interesting to observe that if the same body is applied to load "2P" then for the same length and same deformation delta they should have cross sectional area 2A.

Normal strain under axial loading can be defined as deformation per unit length of rod.

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