Influence of uniaxial stress on the lamellar spacing of eutectics

摘要

Directional solidification of lamellar eutectic structures submitted touniaxial stress is investigated. In the spirit of an approximation first usedby Jackson and Hunt, we calculate the stress tensor for a two-dimensionalcrystal with triangular surface, using a Fourier expansion of the Airyfunction. crystal with triangular surface in contact with its melt, given thata uniaxial external stress is applied. The effect of the resulting change inchemical potential is introduced into the standard model for directionalsolidification of a lamellar eutectic. This calculation is motivated by anobservation, made recently [I. Cantat, K. Kassner, C. Misbah, and H.M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient producessimilar effects as a strong gravitational field in the case of dilute-alloysolidification. Therefore, the coupling between the Grinfeld and theMullins-Sekerka instabilities becomes strong, as the critical wavelength of theformer instability gets reduced to a value close to that of the latter.Analogously, in the case of eutectics, the characteristic length scale of theGrinfeld instability should be reduced to a size not extremely far from typicallamellar spacings. In a Jackson-Hunt like approach we average the undercooling,including the stress term, over a pair of lamellae. Following Jackson and Hunt,we assume the selected wavelength to be determined by the minimum undercoolingcriterion and compute its shift due to the external stress. we realize theshifting of the wavelength by the application of external stress. In addition,we find that in general the volume fraction of the two solid phases is changedby uniaxial stress. Implications for experiments on eutectics are discussed.