AHo MIlollurglco Vol 29. pp 447 10 4% Pcrgamon Press Ltd 1981 Prmwd m Great Br~lam Oool-6160’81 ‘0?01-0447SO2.00/0 MARTENSITIC TRANSFORMATIONS IN ZIRCONIA- PARTICLE SIZE EFFECTS AND TOUGHENING A. G. EVANS, N. BURLINGAME, M. DRORY and W. M. KRIVEN Materials Science and Mineral Engineering. University of California, Berkeley. CA 94720. U.S.A. (Receiced 25 March 1980: in rerisedjorm 20 May 1980) Abstrac&-The incidence of martensic transformations in systems containing Zr02 particles (or precipi- tates) depends upon the size of the particles. The origin of this size effect is demonstrated lo reside in the twinned or variant structure of the transformed phase. by virtue of a surface area related strain energy term. Predicted critical particle sizes correlate quite well with observations on two Zr02 systems. The particle size effect can also be incorporated into toughening analyses, in order lo predict both optimum toughening conditions and toughening trends. The predictions again correlate favorably with toughness data for ZrO, containing materials. R&urn&-Le dkclenchement de transformations martensitiques dans des sys3mes contenant des pal-ti- cules (ou des pr&ipitCs) de Zr02 dtpend de la taille des particules. Nous dimontrons que I’origine de cet effet de taille reside dans la structure ma&e ou en variantes de la phase transform&e, par I’intermtdiaire d’un terme d’energie tlastique lie g une surface. Les tailles critiques thtoriques de particules sont en assez bon accord avec les expkriences dans deux systimes B Zr02. L’effet de taille des particules peut itre igalement pris en compte dans les analyse du durcissement. de.maniire g en prCvoir les conditions optimales ainsi que le sens de variation. Ici encore. les prCvisions sont en bon accord avec les donnCes dans les matCriaux contenant des particules de ZrO*. Zusammcnfasmng-Das Auftreten martensitischer Umwandlungen in Systemen. die Zr02-Teilchen (oder Ausscheidungen) enthalten. hiingt von der GriiBe der Teilchen ab. Es wird gezeigt, daD die Ursache dieses GrSBenefTektes in der Zwillings- oder Variantenstruktur der umgewandelten Phase liegt, und zwar iiber einen mit der GriiRe der Oberflglche zusammenhiingenden Verzerrungsenergieterm. Die ausgerech- neten kritischen TeilchengraBen stimmen gut mit Beobachtungen an zwei ZrO,-Systemen iiberein. Die TeilchengrSRe kann ebenfalls bein Analysen der ZBhigkeit beriicksichtigt werden. urn sowohl Bedingun- gen ftir die optimale Ziihigkeit als such den Verlauf der Ziihigkeit zu beschreiben. Diese Voraussagen stimmen wiederum gut mit Zahigkeitsdaten tir Meterialien mit ZrO,-Teilchen iiberein. 1. INTRODUCTION Martensitic transformations (involving a tetragonal to monoclinic crystal structure change) have been observed in zirconia precipitates [i-3] or particles [4,5]. The incidence of this transformation depends upon the size of the particle [l-3] : a phenomena that has not been adequately exp1ained.t The initial intent of the present paper is to identify the origin of the size effect and to provide a basis for the quantitative pre- diction of the critical transformation condition. These results contain implications for the increase in frac- ture toughness that can be achieved in the presence of a size distribution of predominantly tetragonal ZrOl particles [S, 73. The interpretation of toughening effects in systems containing zirconia particles thus constitutes a second theme of the paper. Martensitic transformations in zirconia can occur in accord with either of the two lattice invariant t A size e&t has been anticipated for situations in which the transformation yields microcracks [6] (notably. single phase polycrystalline Zr02). However, the trans- formation of isolated ZrO, particles is not usually ac- companied by microcracking [ 1.31. An alternative expla- nation must be sought for these systems. deformation processes. twinning or slip [8,9]. A rela- tively large shear is expected to accompany trans- formation for most permissable lattice invariant pro- cesses (eiz. a shear strain along the habit plane of c 14%). This large shear strain results in the forma- tion of a series of variants (Fig. 1); especially when the transformation occurs within particles embedded in a matrix (such that the macroscopic shape deformation is subject lo constraint). Transformed particles thus contain a series of sheared plates in which alternate plates have experienced shear deformations of oppo- site sign (Fig. I). A significant macroscopic shear is not expected, therefore, whenever there are either a large number of variants or, in general, for an even number of variants. The strain energy change that accompanies the martensitic tranformation should be strongI influenced by the variant or twin structure of the mar- tensite. Evidently, for a particle of specified size, the higher the variant (twin) density, the lower is the strain energy, and the larger the interface energy. The energy changes attributed to the twinned structure of the martensite are considered to be the source of the transformation size effect.