P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 (a) Nucleation Str (The strain involved in triggering the transformation) oa (b) Net Transformation Strain CThe strain left behind in the transformed wake Includes the effects of self-accommodation) (a) Cardioid shaped transformed region at the tip of a stationary crack. Between p=+60, the This is compensated by an increase in toughness due to transfor n in the region between I =60 and 300.(b)Transformedwake'of half-height h, after the crack has moved forward by a distance 8a. The stress-induced martensitic transformation is"triggered by the nucleation strain at the interface of the growing transformed region, and this strain determines the size and shape of the region. The strain left behind in the transformed" is the net transformation strain, which takes into account self-accommodation and the formation of other martensite variants first place is what governs the height 2h of the transformed zone. But it is not essential for this nucleation strain to be the same as that eventually left in the trans- formed wake. If the first stress-induced martensite unit(plate/nucleus)is embedded in a relatively rigid matrix, then it will inevitably generate internal stresses, which will modify the local stress field. Subsequent transformation in the vicinity of the initial martensite plate will respond to this altered local stress field, provided the transformation crystallography allows this. As a result, the final assemblage of martensite plates may well include a component of self-accommodation and have an overall net transformation strain that differs significantly from the strains associated with the initial nucleation of a single martensite plate. This is an important point, which will be discussed in more detail late
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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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P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 normal train Fig. 2. Invariant plain strain s, composed of a shear component y parallel to the habit plane(shaded)and a expansion/contraction E(=An normal to the habit plane. Note that the strain is zero in the direction perpendicular to s and to the habit plane normal. the lattice invariant shear L, a rotation R will be required to ensure that the undis- torted plane is also unrotated So, the shape strain S can be divided(mathematically) into three component strains 1. A lattice invariant shear (LIS)L, which is inhomogeneous on a macroscopic scale, and is the additional strain required to make the overall strain an invariant ane strain 2. The Bain strain B, which is simply the strain required to convert the crystal structure of the parent lattice to that of the product. Note that, in general, B is not an invariant plane strain, although in some cases it may be close to one 3. A rigid body rotation R, which ensures that the habit plane is unrotated The total shape strain (s)is given by the equation S=RBL (2.1) where the order of the strains has no physical significance. Despite the fact that the theory is phenomenological, rather than mechanistic, the steps involved in Eq.(2.1) can be illustrated schematically as shown in Fig 3
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