Understanding the Bauschinger effect

1.   Introduction

This brief write-up attempts to explain the definition of Bauschinger effect.

2.   Bauschinger effect

In most materials, plastic deformation in one direction will affect subsequent plastic response in another direction.

A material that is pulled in tension, for example, shows a reduction in compressive strength.This effect is calaled as the Bauschinger effect. The Figure 1 below illustrates this effect.

Figure 1: The Bauschinger effect

Above, a stress strain curve is drawn and the sequence 0-1-2 represents the loading direction. The material is first loaded in tension and yields at 1. At 2, the loading direction is reversed. Unloading occurs along the elastic line until the stresses become compressive. IF there was no directionality effect, the material would start flowing plastically at a stress equal to σ2. The idealized reverse curve is shown in the Figure 1. If the material did not exhibit a dependence on stress direction, the compressive curve would be symmetrically opposite to the tensile curve. The idealized curve is shown in dashed lines (the sequence 0-1R-2R). Thus, the compressive plastic flow after 0-1-2 tensile sequence should occur at magnitude equal to σ3 = σ2.

If the material exhibits the Bauschinger effect, this stress is decreased from σ₃ to σ_4.Hence, the material “softens” upon the inversion of the loading.

An actual example is shown in the Figure 2. The 0.2 % proof stress (the stress at which 0.2% plastic strain occurs) in compression is divided by the tensile stress that precedes it.These values are marked in the Figure 2 which shows three plain carbon steel and one alloy steel. It can be seen that the change in flow stress is quite significant and increases with the plastic strain in tension.

Thus, this factor cannot be ignored in design considerations when a component is to be subjected to compressive stresses in service after being plastically deformed in tension.

Figure 2: Ratio of the compressive flow stress (0.2% plastic strain)and tensile flow stress at different levels of plastic strain for different steels.