《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_martensitic transformation ic ceramics.pdf_大学文库

PERGAMON Progress in Materials Science 47(2002)463-557 cience The martensitic transformation in ceramics its role in transformation toughening Patrick M. Kelly a, * L.R. Francis Rose Department of Mining, Minerals and Materials Engineering, The University of Queensland, Brisbane, Queensland 4072, Australia b Aeronautical and Maritime Research Laboratory, Defence Science and Technology Organisation Fisherman's Bend. victoria 3207. Australia Received I March 2000; accepted 3 July 2000 Abstract e This paper reviews the current knowledge and understanding of martensitic transforma- ons in ceramics-the tetragonal to monoclinic transformation in zirconia in particular. This martensitic transformation is the key to transformation toughening in zirconia ceramics. A ery considerable body of experimental data on the characteristics of this transformation is now available. In addition, theoretical predictions can be made using the phenomenological theory of martensitic transformations. As the paper will illustrate, the phenomenological theory is capable of explaining all the reported microstructural and crystallographic features f the transformation in zirconia and in some other ceramic systems. Hence the theory, sup ported by experiment, can be used with considerable confidence to provide the quantitative data that is essential for developing a credible, comprehensive understanding of the transfor- mation toughening process A critical feature in transformation toughening is the shape strain that accompanies the transformation. This shape strain, or nucleation strain, determines whether or not the stress- induced martensitic transformation can occur at the tip of a potentially dangerous crack. If transformation does take place, then it is the net transformation strain left behind in the transformed region that provides toughening by hindering crack growth. The fracture mechanics based models for transformation toughening, therefore, depend on having a full inderstanding of the characteristics of the martensitic transformation and, in particular, on being able to specify both these strains. A review of the development of the models for transfor mation toughening shows that their refinement and improvement over the last couple of decades has been largely a result of the inclusion of more of the characteristics of the stress-induced martensitic transformation. The paper advances an improved model for the stress-induced Corresponding author. Tel: +61-7-3365-3738: fax: +61-7-3365-3888. - mail address: p. kelly minmet uq. edu. au(P. M. Kelly) 0079-6425/02/S- see front matter C 2002 Elsevier Science Ltd. All rights reserved

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P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 effective or Von mises stress critical mean stress- criterion for stress-induced transformation longitudinal strain in uniaxial test-see Eq (4.13b) 1. Introduction I.I. What is transformation toughening? In simple terms, transformation toughening is the increase in fracture toughness of a material that is the direct result of a phase transformation occurring at the tip of an advancing crack. There are a number of essential requirements for successful transformation toughening [1-3]. First, there must be a metastable phase present in the material and the transformation of this phase to a more stable state must be capable of being stress-induced in the crack-tip stress field. Second, the transforma- tion must be virtually instantaneous and not require time-dependent processes such as long-range diffusion. Third, it must be associated with a change of shape and/ volume. It is this latter feature the deviatoric character of the transformation that allows it to be stress-induced. It also provides the source of the toughening because the work done by the interaction of the crack-tip stresses and the transfor mation strains dissipates a portion of the energy that would normally be available for crack extension. An alternative, but essentially equivalent, way of regarding the toughening process is as a form of crack shielding, where the transformation strains generate local stresses that oppose further crack opening. Finally, to ensure that there is a net increase in toughness of the material, the transformed product must not be significantly more brittle than the parent phase from which it forms. This was a problem in early work on TRIP(transformation induced plasticity) steels, because the initial material was relatively tough and the stress-induced transformation pro- duced a more brittle phase around the advancing crack [4]. The benefit of transfor mation toughening was effectively compensated by the intrinsic brittleness of the product phase and in some steels there was little net toughening. In transformation toughened ceramics, which emerged nearly a decade later, the starting material was just as brittle as the transformed product phase. So, in this case, a positive, net transformation toughening was observed The essence of transformation toughening can be illustrated in Fig. 1. Under an applied load stress-induced transformation occurs at the crack tip and produces a transformation zone of height 2h. In most of the mechanistic models of transfor- mation toughening this initial process zone at the tip of a stationary crack [Fig. 1(a) has no net effect on the toughness of the material. However, as the crack grows, a wake'of transformed material is left behind [Fig. I(b). It is the strains remaining in this wake of transformed material that lead to an increase in toughness note that the primarily deviatoric strain responsible for 'triggering ' the transformation in the

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P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 Although the detailed mechanisms of transformation toughening are more com lex than this simple description and may vary from material to material, the reli- ance on the strains associated with the transformation is universal. without these transformation strains there would be no possibility of a stress-induced transformation-no transformation, no transformation toughening. In addition the transformation strains or more correctly the energy they absorb or the degree of crack-tip shielding they produce-gives rise to the observed toughening. So the whole topic of transformation toughening is dominated by a phase transformation that is associated with a change of shape and /or volume 1. 2. Where do martensitic transformations fit in? A martensitic transformation is a change in crystal structure(a phase change)in the solid state that is athermal. diffusionless and involves the simultaneous. co- operative movement of atoms over distances less than an atomic diameter, so as to result in a macroscopic change of shape of the transformed region [5-11]. The first requirement for a transformation that could lead to transformation toughening is this diffusionless character. If nothing more than small"shuffles"or co-operative atom movements are required, without the need to"reconstruct the crystal struc ture, then the transformation can proceed at a speed approaching that of the velo- city of sound in the crystal [10]. Martensitic transformations satisfy this requirement. However, this alone is not enough. The other requirement is associated with the change of shape -the displacive character of the transformation. It is usually postulated that martensitic transformations are a subset of the overall class of diffusionless, displacive transformations [9, 12, 13]. What is seen as distinguishing a martensitic transformation from other diffusionless, displacive transformations is that the shape change- the displacive component- is relatively large and domi- nated by shear, as opposed to the normally small volume changes. Only in a true martensitic transformation is the resulting shape change sufficiently large that the associated strain energy exerts a dominant influence on the transformation. This is very succinctly expressed in the definition put forward by Cohen et al. [9]: "A mar tensitic transformation is a lattice-distortive, virtually diffusionless structural change having a dominant deviatoric component and associated shape change such that strain energy dominates the kinetics and morphology during the transformation. " In terms of the requirements for transformation toughening outlined above, the martensitic transformation is absolutely ideal. The diffusionless nature ensures a high-speed transformation and the dominant deviatoric strain means that the transformation is readily stress-induced Diffusion-controlled, reconstructive trans- formations, even if they exhibit a shape change, would be far too slow to lead to transformation in time to effect a growing crack. At the same time, rapid diffusion- less transformations that only minor displacive strains are of little use because they will show a ability to be stress-induced. So the two unique features of a martensitic mation- high speed and a change of shape of he transformed volume are both essential if transformation toughening is to

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P. M. Kelly, L.R. Francis Rose/Progress in Materials Science 47(2002 )463-557 1.3. Martensitic transformations in ceramics Although originally associated with the transformation in quenched steels that leads to extraordinary increases in strength and hardness, martensitic transforma- tions also occur in a number of minerals and ceramics and these have been studied for decades [12, 14-16]. However, the worldwide interest in martensitic transforma- tions in non-metallic materials exploded with the discovery of transformation toughening in zirconia ceramics [1]in 1975. The toughness of a traditionally brittle ceramic could be increased by a factor of 4 or more. This held out the prospect of developing engineering ceramics that could be safely used in structural applications, their other superior properties - wear resistance, low density, high melting point-would give them an advantage over their metallic rivals. Experimental and heoretical work on transformation toughening in ceramics blossomed. The litera- ture in the 1980s and early 1990s was inundated with publications on zirconia and nternational conferences specifically devoted to zirconia were held at least once a year. G This review is primarily concerned with the important connection between trans- ormation toughening and the martensitic transformation responsible for the toughening. As a result, attention will be concentrated almost exclusively on the transformation in zirconia - the main ceramic system that has, to date, exhibited any significant transformation toughening. Readers interested in the broader field of martensitic transformations in non-metallic materials -ceramics and minerals should consult one of the excellent review articles in the literature [12, 15] The dominant role of the shape strain in transformation toughening means that any credible model for the transformation toughening process must rely on having a sound knowledge of the shape strain associated with the martensitic transformation Where can this data be obtained for zirconia? In principle the shape strain can be determined experimentally. To date however, there have been relatively few quanti tative experimental measurements reported [17, 18] and these have only provided values for the overall magnitude of the shape strain, with no real indication of its crystallographic direction or the relative amounts of shear and dilatation. In view of the microscopic scale on which the transformation occurs, this dearth of experi mental data is not at all surprising An alternative source for the values of the shape strain is the theoretical predic tions of the crystallographic or phenomenological theory of martensitic transfor- mations(PTMT)[19-24]. Of course it is essential to be confident that the phenomenological theory does give reliable predictions for the shape strain. Section 3 provides a detailed comparison between the theoretical predictions and the experimental results for zirconia collected over the last 30 years. The absolutely excellent agreement between theory and experiment indicates that the transforma tion in zirconia obeys the predictions of the phenomenological theory better than many other martensitic transformations in metals and ceramics. Hence, any pre dicted values for the shape strain are likely to be extremely reliable. Before com mencing this comparison, the next section (Section 2) will cover the general formulation of the crystallographic or phenomenological theory, explore some

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P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 important aspects of the theoretical predictions and look at some particular features of martensitic transformations that are relevant to transformation toughening - the correspondence, variants, twins, self-accommodation and the role of stress in indu- cing transformatio 2. Martensitic transformations 2.1. The phenomenological theory The phenomenological theory describes the crystallography of a martensitic transformation in purely mathematical terms, and is not meant to represent the physical mechanism by which one lattice becomes another. The various versions of the theory [20-23, 25, 26), which are all essentially equivalent, are capable of predict ing a number of crystallographic features of the transformation that can be tested experimentally. The basis of the theory is that the overall macroscopic strain associated with the transformed region(the shape strain S) must be an invariant plane strain (i.e. a strain which leaves one particular plane in the two phases the habit plane - undistorted and unrotated during the transformation). The use of an invariant plane strain is intimately linked with the formation of a transformed region that is plate-like in shape with the habit plane of the plate being the invariant plane. In fact, it was the observation that the product of a martensitic transformation invariably consisted of thin, discus-like, lenticular plates that led to using the invariant plane strain concept as the basis for the phenomenological In general, an invariant plane strain(IPS)consists of an expansion(or contrac tion)(E)normal to the invariant plane together with a shear(r)in a direction lying n the invariant plane. This is illustrated in Fig. 2. Note that the strain in the direc tion perpendicular to both the normal to the invariant plane and the shear direction is zero, and that, if there is any volume change(An associated with the transfor mation, then this must be contained in the expansion(or contraction) normal to the invariant plane -i.e. =AV. In more mathematical terms, to ensure that S is an invariant plane strain, one of its principal strains must be zero and the other two must be of opposite sign. In general, the strain required to convert the crystal structure of the parent phase to hat of the product(the Bain strain B)will not satisfy these conditions-ie. B is not itself an invariant plane strain. Hence, in order to ensure that the final, overall strain Sis an IPS, another strain is required. This strain must not alter the crystal structure of the new product phase resulting from the Bain strain B, but it must change the shape of the transformed volume in such a way that it satisfies the conditions for an IPS. This additional strain L is known as the lattice invariant shear (LIs). It is inhomogeneous on a macroscopic scale, but has no effect on the crystal structure on a microscopic or atomic scale-1e it is lattice invariant. Typical examples of a LIs are slip or twinning, both of which leave the structure of the crystalline material subjected to such shears unaltered. Finally, after combining the Bain strain B and

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《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_martensitic transformation ic ceramics

《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_martensitic transformation ic ceramics