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Elastic and plastic behavior of materials

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stress-strain curve for materials represents the behavior of materials under loading. The materials act elasticity if loaded within the elastic region. in figure no:1 the material loaded in tension from point O to point A. this load occurred within the elastic region. if we remove the load. all the strain will be recovered and specimen or material will go back to original shape and size. it is not necessary for the stress-strain curve to be linear at elastic region. so materials will recover the strain totally if it is loaded and unloaded within elastic region.







Figure-1

if the material loaded beyond the elastic region. in this case, part of the strain will be recovered after unloading. in figure no:2 we loaded the material to point B beyond the elastic region. if we unload the material. the material will follow line B-C. line B-C is parallel to the initial portion of the loading curve or to the tangent of the stress-strain curve at the origin for the materials where stress-strain curve is not linear for the elastic region.  strain will be recovered partially. strain recovered from point D to C. residual strain from point C to point O is irrecoverable. this called permanent set. therefore material will deform permanently. 
 in figure no:2 point E represents the boundary between the elastic region and the plastic region. beyond this point, the material will be considered plastic and part of strain will not recover. in general point E value slightly higher the proportional limit. for some material such as mild steel point E or yielding point considered to be the proportional limit because the difference is minimal. rubber exhibits totally different behavior. rubber deform elastically in a great amount beyond the proportional limit
Figure-2


if the loading and unloading of material repeated within the elastic region. the material will exhibit the same behavior and strain will be recovered. and material will back to original shape and size. if we loaded the material beyond the elastic region. the internal structure of the material will be altered. in figure no:3 material load to point B beyond the elastic region. a portion of strain recovered and part C-O was not recovered. now if we load the material again.a new stress-strain curve will be developed. The loading will begin from point C and continue to point B. line C-B is parallel to the tangent of the origin of stress-stress. beyond point B stress-strain curve will follow the original curve. for materials reloaded after exhibiting plastic deformation. a new stress-strain curve will be developed. the new stress-strain curve will have an elastic region. C-B is the elastic region for our case. the new proportional limit is B. new proportional limit will be higher than the old limit.

Figure-3




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