Caloric and mechanical-work contributions to the forward/reverse asymmetry of martensitic transformation: A unified energy budget

The forward and reverse branches of a martensitic transformation are generally unequal. The natural expectation is that this asymmetry is dissipative in origin, set by the irreversibility of the hysteresis; we show that the asymmetry surviving in the cyclic steady state is not. Combining the thermodynamics of the stressed transformation with a dissipative, variational internal-variable model (a generalized standard material), we establish a single energy budget, q R − q F = − Δ C p ( T A − T M ) + ( W R − W F ) , with W = σ γ / ρ the specific mechanical work, joining the calorimetric latent-heat asymmetry and the mechanical-work asymmetry of the stress hysteresis — usually treated separately — as its two terms. In the steady state the dissipative contributions cancel: the dissipation, including any forward/reverse dissipation asymmetry, displaces only the hysteresis midpoint and drops out of the branch asymmetry, which reduces to a thermophysical state-function residue, − Δ C p ( T A − T M ) ; the ratio ( q R − q F ) / ( T A − T M ) = − Δ C p is exact for any dissipation law and invariant under scan protocol. Two limits make the budget operational: at equal forward/reverse load only the caloric residue survives, while in an isothermal superelastic loop the caloric gap vanishes and the calorimetric asymmetry directly meters the loop dissipation, q R − q F = − ( D F + D R ) . The budget yields falsifiable predictions: the steady-state asymmetry changes sign with composition through Δ C p , and a reversible, re-annealable cyclic transient — distinct from irreversible non-saturating fatigue — carries a sign fixed by sample preparation.