MEASUREMENTS OF THERMAL RESIDUAL ELASTIC STRAINS IN FERRITE±AUSTENITE Fe±Cr±Ni ALLOYS BY NEUTRON AND X-RAY DIFFRACTIONS S. HARJO 1 , Y. TOMOTA 1 { and M. ONO 2 1 Department of Materials Science, Faculty of Engineering, Ibaraki University, 4-12-1, Nakanarusawa-cho, Hitachi, Ibaraki 316-8511, Japan and 2 Kyoto University Research Reactor Institute, Kumatori-cho, Sennan-gun, Osaka-fu 590-0494, Japan (Received 31 March 1998; accepted 3 August 1998) AbstractÐThe thermal residual elastic strains in ferrite (a) and austenite (g) phases in three kinds of a±g Fe±Cr±Ni alloys generated by quenching specimens from 1273 K into water (273 K), have been measured by means of a neutron diraction method. The phase-stresses are successfully determined by employing carefully prepared alloys with volume fractions of a in a range between 0% and 100%, whose chemical compositions are located on an equilibrium tie line of the Fe±Cr±Ni ternary phase diagram. The phase- stresses obtained are compressive for a phase and tensile for g phase, showing good agreement with those predicted by Eshelby and Mori±Tanaka theories. The stress measurements for these alloys were also car- ried out by X-ray diraction method. It is found that the conventional X-ray sin 2 c method under the assumption of plane stress condition is not applicable. The phase-stresses obtained by a triaxial X-ray stress measurement method are in good agreement with those obtained by neutron diraction method. # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION When a multi-phase alloy is heat-treated, internal stresses usually remain due to dierence in thermal expansion coecient between constituent phases. The distribution of such internal stresses in the cross section of a dual phase alloy specimen after quenched into water from an elevated temperature, are schematically drawn in Fig. 1. As can be seen, macroscopic residual stress (s M ij ) varies smoothly from the surface to internal region of the specimen. On heating or cooling, temperature changes more quickly at the surface than in the internal region of a specimen to result in yielding s M ij . If the elastic moduli are dierent between the two constituent phases, partitioning of s M ij would occur [1, 3]. In a dual phase alloy, microscopic residual stresses arise due to mis®t strains among grains of the constituent phases with dierent thermal expansion coecients. These stresses may vary from grain to grain and their averaged value over the each constituent phase is called thermal phase-stress (s ph ij ). It is very useful to measure s ph ij in multi-phase alloys, composites or functionally graded materials because s ph ij are closely related with the strength of the materials. X-ray diraction has widely been used for such stress measurement so far. However, information only near surfaces can be obtained because its penetration depth is limited within a shallow region near surface of the specimen. Thus, the stresses measured by X-ray diraction method become complicated consisting of s M ij and s ph ij that are partially relaxed due to the free surface [3]. On the other hand, application of neutron diraction to s ph ij measurement is attractive because of its high penetration power into a specimen. Residual stress measurements by neutron diraction method have been made not only for composites [1, 3±5] but also for commercially available materials [6±10]. Residual elastic strains related to s ph ij in metal matrix composites (MMCs) have successfully been measured by several workers [3±5, 11]. On the other hand, the stress measurements for dual phase alloys have not presented reasonable results yet [2, 12]. This is due to diculty of preparation of a stress- free reference material having identical chemical composition with that of a constituent phase in a dual phase alloy. In the case of MMCs, the reason- able results have been obtained because the refer- ence materials are easily prepared. In the present study, therefore, ®ve Fe±Cr±Ni alloys were prepared for s ph ij measurement, i.e. they are located along an equilibrium tie line of the tern- ary phase diagram [13], as shown in Fig. 2. This means that the volume fraction of ferrite (a) can be varied without changing its chemical compositions. The a and austenite (g) single phase alloys are then provided for the reference materials to evaluate thermal residual stresses in a and g phases in the a± g dual phase alloys. Acta mater. Vol. 47, No. 1, pp. 353±362, 1999 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/99 $19.00 + 0.00 PII: S1359-6454(98)00300-0 {To whom all correspondence should be addressed. 353