The decrease of yield stress (0.1% proof stress) due to the Bauschinger effect was measured by the torsion test at room temperature, using thin pipes of Cu, α-Brass, iron-steel, Ti, Zr and Mg.
In the case of pre-straining γ and unloading, the yield stress is τ
F for the forward direction and τ
R for the reverse direction. Then, the decrease of yield stress is τ
B=τ
F−|τ
R| (called the Bauschinger stress).
The authors found a new relation between pre-strain γ and Bauschinger stress τ
B.
The results are as follows:
(1) The following relation was found experimentally:
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where
k and
m are constants characteristic of materials, which are controlled by grain-size and metallurgical structure. In the case of the absence of the Bauschinger effect,
k=0.
(2) Extending the above equation, the yield condition under a multi-axis stress, including the Bauschinger effect, was newly obtained as follows:
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f: plastisity potential,
J2: second-order stress invariant, ε
ij and σ
ij: components of strain and stress tensor,
K0: shear yield stress. Here, ε
ijm is the same in sign as ε
ij and its absolute value is the
m-th power of ε
ij. The above equation is reasonable because it includes the strain history and the first-order term of stress, and because additional term
k·ε
ijm·σ
ij has the dimension of energy.
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