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 martensitic transformation and the strains resulting from the transformation. This model which separates the nucleation strain from the subsequent net transformation strain, is shown to be superior to any of the constitutive models currently available. 2002 Elsevier Science Ltd. all rights reserved I 1. What is transformation toughening?. 467 1. 2. Where do martensitic transformations fit in? 13. Martensitic transformations in ceramics 2. Martensitic transformations 2. 1. The phenomenological theory 2.2. Correspondences, variants and twins 474 2.3. The shape strain, stress-induced transformation and 3. The tetragonal to monoclinic transformation in zirconia 485 3. 1. Early work on the transformation in zirconia 3.2. Ceria-zirconia(Ce-TZP) 3.3. Yttria-zirconia (Y-TZP 494 3. 4. Magnesia-zirconia(Mg-PSZ) 3.5. The transformation in dispersed particles and 3.6. The tetragonal-orthorhombic and orthorhombic->monoclinic transformations 3.7. Summar 14 4. Transformation toughening 516 41. Introduction 4.2. The early history of transformation toughening 4.3. The development of theories of transformation toughening in zirconia.523 4.4. Constitutive modelling 4.5. Comparison between established theories and experiment .. 4.6. The role of the shape strain in stress-induced transformation a crystallographic model for transformation toughening 4.7. Summary 5. Discussion and conclusions 547 5.1. Martensitic transformations and transformation toughening....... 547 5.2. The characteristics of an ideal transformation toughened ceramic 5.3. Evaluation of alternative transformation toughened ceramics 5.4. Conclusions Acknowledgements References 553
' $ / ' $ !""! ; 0 * , 152 A B152 ! A . B158 % 12" ! 12 ! $ 12 !! = $ ' 121 !% $ ( ( 128 % ) 1?7 % ; ' ) 1?7 %! = () 3=(C4 1?? %% D () 3D(C4181 %1 () 3(0C4188 %7 $ $ 7"8 %5 7 %2 07 1 1 7 5 1 , 7 5 1! 7 ? 1% $ ) 7!% 11 = 7!5 17 = $ ' +$ 7%" 15 $ ( $ 7%1 12 0715 7 E 712 7 712 7! 71? 7% ; 718 71 = 77 * ' 77% 77% 151 ,- - . #-"- &! " / , $! ! 0 1 2)344
P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 Nomenclature am, bm, cm crystallographic axes of monoclinic zirconia ao, bo, co crystallographic axes of orthorhombic zirconia crystallographic axes of tetragonal zirconia components of matrix used for transformation of axes the Bain strain -the strain required to convert one crystal structure to another tra Ion strain resistance to crack extension in martensite resistance to crack extension in austenite additional energy absorbed by stress-induced martensitic transformation per unit increase in crack length the magnitude of the lattice invariant shear 'L half height of the transformation zone(wake)surrounding a crack empirical parameter representing deviatoric component of overall transformation strain-see Eq (4.8) fracture toughness of material before transformation fracture toughness of material after transformation L the lattice invariant shear (LIS) in a martensitic transformation- normally slip or twinning net shear parameter-see Eq(4.10) rotation needed to make the undistorted plane in a martensitic transformation into an unrotated plane-i e. into the undistorted and unrotated habit plane the radius of an oblate spheroid of thickness 2t, where K<R he shape strain in a martensitic transformation. This consists of an invariant plane strain - a shear'y' together with a uniaxial expansion or contractions. Note that 5 must be equal to the volume change Av associated with the transformation the magnitude of the shape strainS stress assistance. SA= AUWORK -see Eq (4.11) elastic strain energy(per unit volume)of a martensite plate, usually in the form of an oblate spheroid of thickness ' and radius‘R deviatoric stre the semi-thickness of an oblate spheroid additional, small strain used by Hayakawa and Oka to "de-twin"the tetragonal domains in Y-TZP the dimensions 't' and'r' for a martensite nucleus of critical size volume fraction of particles or second phase
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P.M. Kelly, L.R. Francis Rose/ Progress in Materials Science 47(2002)463-557 slope of transformation toughening Eq (4.6) chemical free energy change(per unit volume)associated with a phase transformation △Kr transformation toughening contribution A UINTERNAL additional internal energy associated with the transformed volume- normally the energy of the substructure, such as additional interfaces between self-accommodating variants Proportional to the total area of these interfaces AUsurFace the surface energy of the interface of a martensite plate or embryo embedded in the parent phase Proportional to the AUstrain the strain energy of a martensite plate or embryo embedded in a rigid matrix. Proportional to the volume of the nucleus/embryo change in volume (per unit volume) associated with a transformation change in Iree energy nucleation energy barrier, i.e. the energy that must be overcome to form a martensite nucleus or embryo empirical hardening parameter angle between the a and c axes in a monoclinic crystal the shear component of the shape strain's'in a martensitic transformation the dilatational component of the shape strain's'in a martensitic ransformation. Normally, 5 is equal to the volume change(An) associated with the transformation shear modulus issons ratio the surface energy(per unit area) of an interface he non shape-dependent component of the strain energy per unit volume(SE). For an oblate spheroid of radius 'R'and semi- thickness, SE=(/R)y applied stress components of the applied stress- see Eq (4.11) Ez or Ez total strain resolved in the direction z, or the component of strain in the direction critical stress to'trigger'the stress-induced martensitic transformation parameter representing"intensity or strength of transformation-see Eq (4.5) deviatoric component of strain- see Eq(4.7) dilatational component of transformation strain total shape strain associated with transformation- see Eq (4.9)
7 $ ;/ 3154 8 3$ 4 ' $ . ,I;I* ' ' ( $ 0L *=; $ $ $ $ 9 0*,I $ + $ 9 ( 3$ 4 ' 9 9 $ $ ' ! + $ $ HG $ $ HG I / 3(4 ' G 3$ 4 $( $ $ $ 3$4 $ H"G ( HG $J39"4 $$ 5 $ $$ ;/ 31 4 ) )) : $ : H G ( $ $ H G ;/ 3174 5 $ ;/ 3124 ;; $ ; $ ' ;/ 3184 155 ,- - . #-"- &! " / , $! ! 0 1 2)344
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
<-<- 9 = , $ $ $ / M 6%N $ $ $ $ ( ( $ . 0 ( / ( $ $ ( O ' $ 9 , ' ( , $ ' ( $ ( $ $ ' + * / ' $ ' $$ $ $ . $ $ ' ' $ ' , 3 $ 4 ' ( $ ( $ M1N . ( ' O $ $ $ ' , ' ' P $ $ 0 $ ' L $$ ( $ $ ) ! , ( $ ) $ M 34N O - ' ' H'G M 3 4N , ' I $ $ H G O Q = ( + ;/ 31 % 4 ,- - . #-"- &! " / , $! ! 0 1 2)344 152