Theoretical study on cracking behavior in two-phase alloys Cr–Cr2X (X=Hf, Nb, Ta, Zr)

To examine the importance of thermal expansion mismatch on cracking in two-phase Cr–Cr2X (X=Hf, Nb, Ta, Zr) alloys, we have calculated the coefficients of thermal expansion (CTE) of Cr and Laves-phase Cr2X alloys by local-density-functional approach. A Debye model is used to approximate the phonon contribution through the elastic acoustic response. The sound velocities are determined by the calculated elastic constants and associated anharmonicity. The calculation shows that the CTE of Cr at high temperatures is notably larger than those of Cr2X. If the difference in CTE between Cr and Cr2X is a primary source of crack initiation, our results fail to explain the experimental observation that, among these four Cr–Cr2X alloy systems, the ingot cracking is present mainly in Cr–Cr2Nb. We suggest that for the cracking to occur,the presence of thermal mismatch stresses are retained by a hard and supersaturated Cr matrix (e.g. due to the relatively high solubility of Nb in Cr in the case of Cr–Cr2Nb). On the other hand, the softer Cr matrix can accommodate thermal misfit dislocations plastically even though the CTE difference between Cr and Cr2X is large.