Fig. 1. Bauschinger effect stress strain curve[2]

Question:
I have heard of the Bauschinger effect but don’t understand it. Can you help?

Answer:
In situations involving plastic deformation many factors are at work including:
  • Grain size and grain-boundary deformation (including low-angle grain boundaries)
  • Yield-point transition (from elastic to plastic deformation)
  • Solid-solution (hardening) mechanisms
  • Strengthening from second-phase particles
  • Strain hardening due to cold working and/or point defects
  • Strain aging
  • The Bauschinger effect
When plastic deformation in one direction is followed by plastic deformation in the opposite (or nearly opposite) direction such as during cold forming, the internal stress distribution within the material changes with a resulting change in material properties. This directional strain hardening results in an increase in yield strength in the direction of the applied force and a drop in yield strength in the opposite direction. This drop in yield strength is known as the Bauschinger effect.

Perhaps it is easier to understand using a graphical representation (Fig. 1), where the tensile stress and strain are treated as positive and the compressive stress and strain as negative. Thus, if an annealed specimen is loaded in tension from 0 to B, that is, beyond its elastic limit (point A) and then unloaded, its resultant condition is represented by point C. The elastic limit of the material (in tension) is represented by the change Set. If the same specimen is then loaded in compression, it follows the path CDE where D is the elastic-limit point on the compression curve so that the elastic limit in compression now is the change S'ec. The Bauschinger effect results in S'ec < Set.

If instead, the annealed specimen were loaded directly in compression, the elastic limit of the annealed material in compression would be Sec and would be equal in magnitude to Set. In other words, Set = Sec, so S'ec < Set and S'ec < Sec.

A similar reasoning would apply if the annealed specimen were initially loaded in compression past the elastic limit, unloaded and then next loaded in tension. Here the resulting elastic limit in tension would be smaller than the elastic limit of the annealed material in compression.

Whenever either a tensile or compressive load is applied beyond the elastic limit, the corresponding tensile limit or compressive limit is reduced; and the more the load exceeds the elastic limit, the greater the reduction, up to a limit.

The Bauschinger effect was originally stated in terms of the elastic limit, however, yield strength is used interchangeably (the reason for this is that the elastic limit and the yield point are located close to each other on the stress-strain curve). The Bauschinger effect applies to very small strains only.

The Bauschinger effect is a manifestation of a phenomenon called “dislocation pile-ups.” The predicted stress–strain response is sensitive to the grain aspect ratio, and the grain boundaries give rise to a back stress that inhibits subsequent nucleation at the dislocation sites. The back stress from the dislocation pile-ups provides the driving force for dislocation activity during the early stages of unloading. First, dislocation pile-ups collectively stretch out, with dislocations gliding back on their slip planes and subsequently new dislocations (with an opposite sign from those generated during loading) are nucleated. On reloading, there is a significant knee in the stress–strain curve due to the dislocations present.