Elastic Versus Plastic Behavior

Quick
elastic – shape returns to original size after loading
elastic deformation – deformation of a material that is recovered when the applied load is removed
plastic – shape remains deformed after loading
plastic deformation – permanent deformation of a material when a load is applied, then removed

If the strains caused in a test specimen (typically this is with reference to a tensile testing machine) by the application of a given load disappear when the load is removed, the strain returns to zero, the shape resumes its original length, and the material behaves elastically. A material would behave plastically if the opposite occurs—the strains in the test specimen do not disappear when the load is removed.


Visualization
Elastic
Shape returns to original size after loading.		 Plastic
Shape remains deformed after loading.
 1. unloaded 
 2. loading 
 3. load removed 


Details

If a material has a well-defined yield point, the elastic limit, proportional limit, and yield point are essentially equal. So, the material behaves elastically and linearly as long as the stress remains less then the yield point stress. If the yield point is reached, yield takes place and when the load is removed the stress and strain decrease together in a linear fashion. This can be represented in the following figure along the line parallel to the elastic portion of the loading curve. The fact that the strain does not return to zero after removal of the load indicates that a permanent set or plastic deformation has occurred. For most materials, the plastic deformation depends not only upon the maximum value reached by the stress, but also upon the time elapsed before the load is removed. The stress-dependent part of the plastic deformation is referred to as slip, and the time-dependent part—which is also influenced by the temperature—as creep.

When a material does not possess a well-defined yield point, the elastic limit cannot be determined with precision. However, assuming the elastic limit equal to the yield strength as defined by the offset method results in only a small error. Referring to the following figure, it can be noted that the straight line used to determine point Y also represents the unloading curve after a maximum stress σY has been reached. While the material does not behave truly elastically, the resulting plastic strain is as small as the selected offset.


Loading, Unloading, and Loading Again, Both Tensile

A case will now be examined where the specimen is loaded, unloaded, then loaded again, using the same load and in the same direction. If, after being loaded and unloaded, the test specimen is loaded again, the new loading curve will closely follow the earlier unloading curve until it almost reaches point C; it will then bend to the right and connect with the curved portion of the original stress-strain diagram. We note that the straight-line portion of the new loading curve is longer than the corresponding portion of the initial one. Thus, the proportional limit and the elastic limit have increased as a result of the strain-hardening that occurred during the earlier loading of the specimen. However, since the point of rupture R remains unchanged, the ductility of the specimen, which should now be measured from point D, has decreased.


Loading, Unloading, and Loading Again, One Tensile and One Compressive

A case will now be examined where the specimen is again loaded, unloaded, and loaded again, with the same force both times except that the first load will be a tensile load and the second load will be a compressive load (in opposite direction to the first load). Assume a material of mild steel, for which the yield strength is the same in tension and in compression. The initial load is tensile and is applied until point C has been reached on the stress-strain diagram. After unloading, a compressive load is applied, causing the material to reach point H, where the stress is equal to -σY. Note that the portion DH of the stress-strain diagram is curved and does not show any clearly defined yield point. This is referred to as the Bauschinger effect. As the compressive load is maintained, the material yields along line HJ.

If the load is removed after point J has been reached, the stress returns to zero along line JK, and the slope of JK is equal to the modulus of elasticity. The resulting permanent set AK may be positive, negative, or zero, depending on the lengths of the segments BC and HJ. If a tensile load is applied again to the test specimen, the portion of the stress-strain diagram beginning at K (dashed line) will curve up and to the right until the yield stress has been reached.

If the initial loading is large enough to cause strain-hardening of the material (point C'), unloading takes place along line C'D'. As the reverse load is applied, the stress becomes compressive, reaching its maximum value at H' and maintaining it as the material yields along line H'J'. Note that while the maximum value of the compressive stress is less than the yield stress, the total change in stress between C' and H' is still equal to 2σY.

If point K or K' coincides with the origin A of the diagram, the permanent set is equal to zero, and the specimen may appear to have returned to its original condition. However, internal changes will have taken place and, while the same loading sequence may be repeated, the specimen will rupture without any warning after relatively few repetitions. This indicates that the excessive plastic deformations to which the specimen was subjected have caused a radical change in the characteristics of the material. Reverse loadings into the plastic range, therefore, are seldom allowed, and only under carefully controlled conditions. Such situations occur in the strengthening of damaged material and in the final alignment of a structure or machine.