A Quantitative Treatment of the Lattice Softening of Shape Memory Alloys

Abstract

The shape memory effect is most commonly observed in β phase alloys which transform martensitically and exhibit the so-called C’ anomaly (1,2). This anomalous elastic behaviour is characterized by the following properties of the elastic shear constant C’ = (C₁₁–C₁₂)/2:

• (i) its temperature coefficient becomes positive on approaching the equilibrium temperature T_o from above;

• (ii) its magnitude decreases with changes in composition which raise T_o;

• (iii) its magnitude is of the order of 0.1 ≲ C’ ≲ 0.7 × 10¹¹dynes cm⁻²(l0¹⁰ Nm⁻²), i.e. unusually low, at M_s;

• (iv) consequently, the elastic anisotropy factor A = C₄₄/C’ is anomalously high, since C₄₄ shows normal behaviour.

In other words the lattice becomes increasingly softer against {llo}<llo> shears as the teperature or composition approaches the instability with respect to a martensitic teansformation. Fig. 1 shoes data of this behavious for a β₂-NiAl alliy series which will be treated as an example in this paper.