Unless you need rate-independence for something else, you don't need Chaboche just for the Bauschinger effect, so use a general kinematic hardening model instead, it's much easier to set up.
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I believe that you can combine the Chaboche model with other material models, to include the effects of strain hardening/softening, although I have not done it yet myself.
I have found that the Chaboche non-linear material model can predict greater ratchetting than an equivalent multi-linear kinematic hardening model under cyclic loading conditions.