《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_high-toughness by laminated design

Enhanced fracture toughness by ceramic laminate design L A Gee*,R S. Dobedoe R Vann M. H. Lewis, G. Blugan and J Kuebler A review of the potential toughening and failure mechanisms for ceramic laminate materials presented. An integrated approach to the design of ceramic laminates incorporating biaxial residual stresses for specific applications is outlined. Restrictions placed on the laminate architecture to avoid spontaneous transverse cracking of the tensile layer are discussed. The phenomena of edge cracking and crack bifurcation are considered with reference to elastic moduli, Poissons ratio, mismatch in thermal expansion coefficients, temperature gradient and laminate architecture. The use of compressive layers to produce a material that exhibits a threshold strength and criteria for increasing the critical applied stress below which failure will not occur are reported. A single edge V-notched beam (SEVNB)test geometry was used to measure crack growth resistance(R curve) behaviour of multilayer Si3N4/Si3N4-TiN composites Fracture mechanics weight function analysis was applied to predict the R curve behaviour of multilayer composites having a stepwise change in composition. A conservative, non-optimised laminate design exhibiting apparent fracture toughness in excess of 17 MPa m is reported, in excellent agreement with the weight function analysis Keywords: Ceramic laminates, Crack bifurcation, Fracture toughness, Single edge V-notched beam test, Weight function analysis ntroduction the strength of such ceramics is technologically and furthermore weak interfaces are known to Ceramic materials are known to exhibit numerous mise certain properties. For example, high attractive properties including high strength, elastic ture corrosion resistance may be worsened due to modulus, hardness and chemical and thermal stability. defect density. The use of residual stres However, monolithic ceramic materials have intrinsic associated with thermal expansion mismatch within limitations owing to their I eliability and brittleness, ceramic laminate materials therefore offers an attractive which make them susceptible to catastrophic failure. An alternative mechanism to improve fracture behaviour. improvement in the fracture toughness of such ceramic Considerable attention has been concentrated on materials would inevitably expand the range of indus- residual stress induced cracking in laminates. This trial application problem is frequently encountered in electronic packa The design of ceramic composites with layered macro- ging, adhesive joining and other technologies. On structures is receiving considerable research attention cooling from an elevated temperature Toto a tempera because they exhibit decreased sensitivity to surface ture T. two materials with coefficients of thermal defects, and have been shown to demonstrate non- expansion(CTEs)aI and a2 forming a layered structure mechanical properties in multilayer systems is the ability to deflect propagating cracks. Two different mechanisms of crack deflection have previously been employed. EM=(a2-a1)dT (1) interfaces with adjacent layers or into layers exhibiting Now consider a balanced laminate (which experiences residual biaxial compressive stress.- Essentially, the first no bending forces)with alternating layers of thickness !1 and t, formed from materials I and 2 respectively. Away nechanism depends on matrix/interface strength ratio and from the free surface the residual stress perpendicular to has had varying degrees of success. However, controlling the layers is zero, whereas in the plane of the laminate it is uniform and biaxial. In material l( the layer with the ng Research Institute, Sheffield lower CTE), the residual, biaxial compressive stress on is dvanced Materials, Department of Physics, University of given by Coventry CV4 7AL, UK feral Laboratories for Materials Testing and Research, EMPA, 01- EM2 CH-8600 Bubendorf. Switzerland Corresponding author, email i gee @ shu. ac uk 2005 Institute of Materials, Minerals and Mining pted 2o February2。05 Dol1o.179/174367605X166 Advances in Applied Ceramics 2005 VOL 104 No 3 103

Enhanced fracture toughness by ceramic laminate design I. A. Gee*1 , R. S. Dobedoe2 , R. Vann2 , M. H. Lewis2 , G. Blugan3 and J. Kuebler3 A review of the potential toughening and failure mechanisms for ceramic laminate materials is presented. An integrated approach to the design of ceramic laminates incorporating biaxial residual stresses for specific applications is outlined. Restrictions placed on the laminate architecture to avoid spontaneous transverse cracking of the tensile layer are discussed. The phenomena of edge cracking and crack bifurcation are considered with reference to elastic moduli, Poisson’s ratio, mismatch in thermal expansion coefficients, temperature gradient and laminate architecture. The use of compressive layers to produce a material that exhibits a threshold strength and criteria for increasing the critical applied stress below which failure will not occur are reported. A single edge V-notched beam (SEVNB) test geometry was used to measure crack growth resistance (R curve) behaviour of multilayer Si3N4/Si3N4–TiN composites. Fracture mechanics weight function analysis was applied to predict the R curve behaviour of multilayer composites having a stepwise change in composition. A conservative, non-optimised laminate design exhibiting apparent fracture toughness in excess of 17 MPa m1/2 is reported, in excellent agreement with the weight function analysis. Keywords: Ceramic laminates, Crack bifurcation, Fracture toughness, Single edge V-notched beam test, Weight function analysis Introduction Ceramic materials are known to exhibit numerous attractive properties including high strength, elastic modulus, hardness and chemical and thermal stability. However, monolithic ceramic materials have intrinsic limitations owing to their poor reliability and brittleness, which make them susceptible to catastrophic failure. An improvement in the fracture toughness of such ceramic materials would inevitably expand the range of indus￾trial applications. The design of ceramic composites with layered macro￾structures is receiving considerable research attention because they exhibit decreased sensitivity to surface defects, and have been shown to demonstrate non￾catastrophic failure.1–6 A key feature that imparts good mechanical properties in multilayer systems is the ability to deflect propagating cracks. Two different mechanisms of crack deflection have previously been employed. Propagating cracks can be deflected either along weak interfaces with adjacent layers1–7 or into layers exhibiting residual biaxial compressive stress.8–11 Essentially, the first mechanism depends on matrix/interface strength ratio and has had varying degrees of success. However, controlling the strength of such ceramics is technologically difficult, and furthermore weak interfaces are known to compro￾mise certain properties. For example, high tempera￾ture corrosion resistance may be worsened due to the high defect density. The use of residual stress patterns associated with thermal expansion mismatch within ceramic laminate materials therefore offers an attractive alternative mechanism to improve fracture behaviour. Considerable attention has been concentrated on residual stress induced cracking in laminates. This problem is frequently encountered in electronic packa￾ging, adhesive joining and other technologies. On cooling from an elevated temperature T0 to a tempera￾ture T, two materials with coefficients of thermal expansion (CTEs) a1 and a2 forming a layered structure suffer a mismatch strain eM of: eM~ ðT0 T ð Þ a2{a1 dT (1) Now consider a balanced laminate (which experiences no bending forces) with alternating layers of thickness t1 and t2 formed from materials 1 and 2 respectively. Away from the free surface the residual stress perpendicular to the layers is zero, whereas in the plane of the laminate it is uniform and biaxial. In material 1 (the layer with the lower CTE), the residual, biaxial compressive stress s1 is given by: s1~{ eME1 0 1z t1E1 0 t2E2 0
(2) 1 Materials and Engineering Research Institute, Sheffield Hallam University, Sheffield S1 1WB, UK 2 Centre for Advanced Materials, Department of Physics, University of Warwick, Coventry CV4 7AL, UK 3 Swiss Federal Laboratories for Materials Testing and Research, EMPA, CH-8600 Du¨ bendorf, Switzerland *Corresponding author, email i.gee@shu.ac.uk
2005 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 18 August 2004; accepted 20 February 2005 DOI 10.1179/174367605X16671 Advances in Applied Ceramics 2005 VOL 104 NO 3 103

e et aL. Enhanced fracture toughness by ceramic laminate desig where Ei=E/(l-vi, and E and v are the Youngs modulus and Poissons ratio(i=l for the compressive lay nsile layer). In the lay greater coefficient of thermal expansion(material 2), the residual, biaxial, tensile stress is given by: (1/t2) For the experimental data shown below, subscripts 1 and 2 distinguish the thinner Si3 N4 compressive layers from the thicker TiN/Si, N4 composite tensile layers It has been demonstrated by numerous authors that periodically spaced compressive layers can prevent catastrophic propagation of cracks, giving a material that exhibits pseudo graceful failure. A stress intensity unction has been proposed. to describe how a crack propagating in the laminate is shielded from the applied tensile stress as a result of layers containing biaxial 1 Backscattered electron micrograph showing edge compressive stresses cracking in si3N,/Si3Na-48 wt-%TiB2 laminate: image K=(0+0(+2)m( width=160 um here a is the applied tensile stress, a is the half-crack thickness. In the centre of the compressive layer, length and tI and t2 are the thicknesses of the this stress has a sign opposite to that of the bulk compressive and tensile layers respectively. The magni- biaxial stress. Therefore, for a compressive, biaxial stress tude of the biaxial residual stress within the compressive state in the bulk material, there is a tensile stress layers an is given by equation(2)above. perpendicular to the layer at or near the free surface. The present paper will briefly review the design of These tensile stresses can naturally cause extension ceramic laminates incorporating controlled distributions of pre-existing cracks or flaws and have been termed of residual stress. The main laminate fracture failure edge or channel cracks. In addition, large cracks (of modes are considered and the proposed toughening the order of the thickness of the compressive layer. mechanisms discussed. The results presented are for hot typically 100-300 um) can act as critical defects pressed laminates based on silicon nitride, with particu- during the removal of ceramic billets from the hot late dispersions of titanium nitride or titanium diboride press die, potentially resulting in failure on control the thermal coefficient of expansion of manufacture lal layers. However, the phenomena reported are have calculated a critical compressive sle to all laminated ceramic systems incorporat- layer thickness te below which no edge cracks can lual stress distributions occur Edge cracking The nature and magnitude of the residual stresses in a where Kle is the intrinsic fracture toughness for a constants of the layers, including coefficient of thermal monolithic sample of material 1. An example of edge expansion(CTE), Youngs modulus, Poissons ratio cracking for a Si3N4 48 wt-%TiB, laminate is shown in bonding temperature, as indicated by equations(1H3). Fig. I In addition, the magnitude of the residual stress can be modified by adjusting the layer thickness. It may initially Bifurcation toughening appear to be a simple procedure to maximise the residual A crack propagating across a laminate results in the ress in a given laminate architecture, thereby toughen- formation of two free surfaces. In the vicinity of these ing the ceramic by closing propagating cracks due to free surfaces (by analogy with the stress state at a free compressive residual stress crack shielding (this would edge)the residual stress distribution is altered. In the effectively maximise a1 in equation (4). However, a compressive layer, the localised stress state near the free number of failure mechanisms exist that may reduce the surface created by the crack will be opposite in sign to magnitude of the residual stresses present by relaxation, the residual biaxial compressive bulk state. The resulting or which will critically damage the laminate component tensile stress parallel to the layer can result in fracture perpendicular to the layer and, in certain circumstances, It is well known that the residual stresses at the free bifurcation. This has been used to design laminates with surface of laminate materials differ from the bulk stress improved toughnes By analogy with the edge state. Both analytical models and finite element analysis cracking phenomenon, there should exist a critical layer how that although biaxial stresses exist far from thickness below which bifurcation does not occur. the surface, stress perpendicular to the layer plane exist However, empirical data from Rao and Lange-and near the free surface. This stress is highly localised, Ho et al. have demonstrated that, for bifurcation, a decreasing rapidly away from the surface to become factor of 2 is introduced into the critical thickness negligible at a distance of approximately the layer equation owing to geometrical differences between 104 Advances in Applied Ceramics 2005 VOL 104 No 3

where E9i5Ei/(12ni), and E and n are the Young’s modulus and Poisson’s ratio (i51 for the compressive layer, and 2 for the tensile layer). In the layer with the greater coefficient of thermal expansion (material 2), the residual, biaxial, tensile stress is given by: s2~{s1(t1=t2) (3) For the experimental data shown below, subscripts 1 and 2 distinguish the thinner Si3N4 compressive layers from the thicker TiN/Si3N4 composite tensile layers respectively. It has been demonstrated by numerous authors8–11 that periodically spaced compressive layers can prevent catastrophic propagation of cracks, giving a material that exhibits pseudo graceful failure. A stress intensity function has been proposed9,12 to describe how a crack propagating in the laminate is shielded from the applied tensile stress as a result of layers containing biaxial compressive stresses: K~sað Þ pa 1=2 zs1 1z t1 t2  2 p sin{1 t2 2a
{1   (4) where sa is the applied tensile stress, a is the half-crack length and t1 and t2 are the thicknesses of the compressive and tensile layers respectively. The magni￾tude of the biaxial residual stress within the compressive layers s1 is given by equation (2) above. The present paper will briefly review the design of ceramic laminates incorporating controlled distributions of residual stress. The main laminate fracture failure modes are considered and the proposed toughening mechanisms discussed. The results presented are for hot pressed laminates based on silicon nitride, with particu￾late dispersions of titanium nitride or titanium diboride used to control the thermal coefficient of expansion of individual layers. However, the phenomena reported are applicable to all laminated ceramic systems incorporat￾ing residual stress distributions. Edge cracking The nature and magnitude of the residual stresses in a laminate are a consequence of numerous physical constants of the layers, including coefficient of thermal expansion (CTE), Young’s modulus, Poisson’s ratio and bonding temperature, as indicated by equations (1)–(3). In addition, the magnitude of the residual stress can be modified by adjusting the layer thickness. It may initially appear to be a simple procedure to maximise the residual stress in a given laminate architecture, thereby toughen￾ing the ceramic by closing propagating cracks due to compressive residual stress crack shielding (this would effectively maximise s1 in equation (4)). However, a number of failure mechanisms exist that may reduce the magnitude of the residual stresses present by relaxation, or which will critically damage the laminate component itself. It is well known that the residual stresses at the free surface of laminate materials differ from the bulk stress state. Both analytical models and finite element analysis show that although biaxial stresses exist far from the surface, stress perpendicular to the layer plane exists near the free surface. This stress is highly localised, decreasing rapidly away from the surface to become negligible at a distance of approximately the layer thickness. In the centre of the compressive layer, this stress has a sign opposite to that of the bulk biaxial stress. Therefore, for a compressive, biaxial stress state in the bulk material, there is a tensile stress perpendicular to the layer at or near the free surface. These tensile stresses can naturally cause extension of pre-existing cracks or flaws and have been termed edge or channel cracks. In addition, large cracks (of the order of the thickness of the compressive layer, typically 100–300 mm) can act as critical defects during the removal of ceramic billets from the hot press die, potentially resulting in failure on manufacture. Ho et al.13 have calculated a critical compressive layer thickness tc below which no edge cracks can occur: tc~ K2 Ic 0: 34(1{n2)s2 1 (5) where KIc is the intrinsic fracture toughness for a monolithic sample of material 1. An example of edge cracking for a Si3N4–48 wt-%TiB2 laminate is shown in Fig. 1. Bifurcation toughening A crack propagating across a laminate results in the formation of two free surfaces. In the vicinity of these free surfaces (by analogy with the stress state at a free edge) the residual stress distribution is altered. In the compressive layer, the localised stress state near the free surface created by the crack will be opposite in sign to the residual biaxial compressive bulk state. The resulting tensile stress parallel to the layer can result in fracture perpendicular to the layer and, in certain circumstances, bifurcation. This has been used to design laminates with improved toughness.14–16 By analogy with the edge cracking phenomenon, there should exist a critical layer thickness below which bifurcation does not occur. However, empirical data from Rao and Lange12 and Ho et al.13 have demonstrated that, for bifurcation, a factor of 2 is introduced into the critical thickness equation owing to geometrical differences between 1 Backscattered electron micrograph showing edge cracking in Si3N4/Si3N4–48 wt-%TiB2 laminate: image width5160 mm Gee et al. Enhanced fracture toughness by ceramic laminate design 104 Advances in Applied Ceramics 2005 VOL 104 NO 3

Gee et al. Enhanced fracture toughness by ceramic laminate design Longitudinal cracks Channel cracks SiN /SiN-30 wt-%TiN abricated in EMPA. Switzerland SiaN,SiN 4 50 wt-%TN Longitudinal cracks Channel cracks SiN /Si N -70 wt-%TIN 100 wt-%TN Examples of severe transverse matrix cracking in Si3,Si3Na-TiN ceramic laminates bifurcation and edge cracking: hese tensile stresses are above a threshold limit as with the mechanism responsible for edge cracking, the stres (6) can drive pre-existing cracks across the layer and into adjacent compressive layers. This type of internal crack is important to note that ceramic laminate propagation has been termed tunnel or tensile cracking materials that are designed to exhibit bifurcation Ho and Suo have shown that for a given residual tensile toughening will inevitably demonstrate surface edge stress, there is a critical tensile layer thickness below cracking and associated problems. In addition, the which no tunnel or tensile cracking can occur, indepen- potential to use crack bifurcation as a toughening dent of the initial flaw size. Transverse cracking in the mechanism in laminate ceramics with layers consistin tensile layer can only occur if the layer thickness is above of intrinsically high fracture toughness material is a critical value given by extremely limited as a result of the coarse macrostruc ture indicated by equation(6). The critical compressive te- tof t layer thickness necessary to produce crack bifurcation increases as the square of the compressive layer material Figure 2 shows some examples of severe transverse ture toughness and is inversely roportional to the IIN biaxial compressive stress in the layer. Therefore, for a ceramic laminates. All of the laminates shown have material of fixed thickness, it is possible to increase nominally the same layer architecture. It can be clearly the compressive residual stress by reducing the low Cte observed that as the tin content is increased (i.e. as material layer thickness. However, for high fracture CTE mismatch is increased), more transverse or tunnel toughness composite materials, this will usually cracks are created owing to the increased tensile stress. reduce the layer thickness below the critical value for Materials designed to exhibit delamination, crack Threshold strength deflection or bifurcation (by controlling the residual Improved ceramic processing methods, which eliminate these mechanisms during sample cutting or machining. reduced flaw size and subsequent enhanced reliability of These restrictions and others also place considerable ceramic components. However, a statistical distribu- value on having well characterised materials as the tion in strength remains. Ideally, the distribution of trengths of a ceramic component should display a high Weibull modulus, or ideally threshold strength beha- viour(a strength below which there is zero probability of Tensile cracking failure). One possible route to obtaining threshold During laminate ceramic processing, large biaxial tensile strength behaviour is the controlled application of stresses can be generated in the high CTE material. If macroscopic stress distribution Advances in Applied Ceramics 2005 VOL 104 No 3

bifurcation and edge cracking: tco K2 Ic 0: 17 1{n2 ð Þs2 1 (6) It is important to note that all ceramic laminate materials that are designed to exhibit bifurcation toughening will inevitably demonstrate surface edge cracking and associated problems. In addition, the potential to use crack bifurcation as a toughening mechanism in laminate ceramics with layers consisting of intrinsically high fracture toughness material is extremely limited as a result of the coarse macrostruc￾ture indicated by equation (6). The critical compressive layer thickness necessary to produce crack bifurcation increases as the square of the compressive layer material fracture toughness and is inversely proportional to the biaxial compressive stress in the layer. Therefore, for a material of fixed thickness, it is possible to increase the compressive residual stress by reducing the low CTE material layer thickness. However, for high fracture toughness composite materials, this will usually reduce the layer thickness below the critical value for crack bifurcation unless considerable care is taken. Materials designed to exhibit delamination, crack deflection or bifurcation (by controlling the residual stress patterns) have also shown a propensity to fail by these mechanisms during sample cutting or machining. These restrictions and others also place considerable value on having well characterised materials as the laminate components. Tensile cracking During laminate ceramic processing, large biaxial tensile stresses can be generated in the high CTE material. If these tensile stresses are above a threshold limit, as with the mechanism responsible for edge cracking, the stress can drive pre-existing cracks across the layer and into adjacent compressive layers. This type of internal crack propagation has been termed tunnel or tensile cracking. Ho and Suo have shown that for a given residual tensile stress, there is a critical tensile layer thickness below which no tunnel or tensile cracking can occur, indepen￾dent of the initial flaw size.17 Transverse cracking in the tensile layer can only occur if the layer thickness is above a critical value given by: tc~ 4K2 Ic ps2 21 x (7) Figure 2 shows some examples of severe transverse matrix cracking in a number of Si3N4/Si3N4–TiN ceramic laminates. All of the laminates shown have nominally the same layer architecture. It can be clearly observed that as the TiN content is increased (i.e. as CTE mismatch is increased), more transverse or tunnel cracks are created owing to the increased tensile stress. Threshold strength Improved ceramic processing methods, which eliminate heterogeneities from the constituent powder, result in reduced flaw size and subsequent enhanced reliability of ceramic components.18 However, a statistical distribu￾tion in strength remains. Ideally, the distribution of strengths of a ceramic component should display a high Weibull modulus, or ideally threshold strength beha￾viour (a strength below which there is zero probability of failure). One possible route to obtaining threshold strength behaviour is the controlled application of macroscopic stress distributions. 2 Examples of severe transverse matrix cracking in Si3N4/Si3N4–TiN ceramic laminates Gee et al. Enhanced fracture toughness by ceramic laminate design Advances in Applied Ceramics 2005 VOL 104 NO 3 105

e et aL. Enhanced fracture toughness by ceramic laminate desig Rao et al. have demonstrated how a rearrangement -0.19277, A21=2. 55863, A 22=-12-6415, 423=197630, of equation (4)can lead to a threshold strength criterion A24=-10 9860 for ceramic laminates. This finding has significant During crack propagation in ceramic materials, an implications for the statistical strength distribution of interaction zone develops behind the crack front. within ceramic components. The threshold strength phenom- this interaction zone, the two crack surfaces are not enon exists as failure can only occur at an applied stress completely separated, leading to some crack-surface sufficient to drive the crack through the compressive interactions. These interactions are capable of trans- layers. Using this assumption, and by setting the crack itting stresses due to grain/grain friction, or via grain length a=(t2+ 2t1)/2 and K=Kie(the critical stress crack bridging. These types of interactions are respon- intensity factor for the compressive material), equation sible for R curve behaviour in monolithic ceramic 4)may be rearranged to produce an expression for materials. In the remaining discussion, the effect of threshold strength, i. e. the strength below which no both types of crack-surface interaction will be termed failure is possible ridging stresses abr. The stepwise residual stress pattern also acts in this interaction zone behind the propagating crack as well as at the crack tip. Compressive stresses (1+ behind the propagating crack act to close the crack whilst tensile stress regions act as further drivers for pening the crack. The stress intensity factor at the crack tip itself can therefore be deter principle of superposition, by summing the contribu Threshold strength is therefore dependent upon two tions of the applied stress Ka, the bridging stress Kbr and main factors for a given material system, the compres- the residual stress Kr sive stress and the ratio of tensile layer thickness to compressive layer thickness. To obtain high threshold Ka+Kr+kbr (11) streng th, the compressive stress should naturally Crack tip extension(measured by KR)is predicted to stress, the laminate architecture should be designed to Ko. For a crack with initial crack length ao, 4.ughness maximised. However, for a given maximum compressive occur when Ktip equ juals the intrinsic crack tip be compressive layers, thereby maximising the t lt ratio. laminate. as the crack (length a) advances through incorporate very small separations between successive The threshold strength phenomenon therefore trun- cates the statistical strength distribution, yielding an KR(a, o)=Ko(a)-Kr(a)-kbr(a, ao) (12) apparently high Weibull modulus material. Howeve If Ko, or and Obr are known(or can be calculated with this threshold strength calculation is only valid for sufficient precision), it becomes possible to predict(as a cracks that propagate straight through the compressive function of a)the R curve behaviour of a laminated layer without bifurcation or significant deflection. In structure. Lakshminaravanan et al.2223 and Moon such cases, where bifurcation is exhibited by the crack as et al.24, 25 have demonstrated how this can be used to it propagates through the compressive layer, a greater redict the fracture behaviour of layered ceramics threshold strength may be observed than predicted by the model. Quantitative prediction of threshold strength addition, weight function analysis makes it possible to in such cases is extremely complicated determine the separate effects of the residual stress Fracture mechanics weight function analysis distribution and the crack bridging closure stresses on Bueckner'9 first demonstrated that the stress intensity the measured R curve factor for an edge crack of depth a can be calculated by The present study considers the behaviour of multi weight function h(x a)(dependent upon geometry) and crack bifurcation. The use of weight function analysis any stress distribution a(x)acting normal to the fracture for modelling the apparent fracture toughness of plane(x is the distance along the crack measured from ceramic laminates is discussed with reference to optimis- ing the macrostuctural design. A laminate design oncept is presented that incorporates macrostructural K= h(x, a)o(x)d: 9 Constraints due to the matrix cracking phenomena, requirements for bifurcation, ASTM test bar geometry A suitable weight function for a single edge V-notched and the additional stress incurred during ceramic beam(SEVNB) sample and notch geometry has been achining. given by Fett and munz h(x,=/2)2 Experimental details (1-)2(1-#) Si3N4, Si3 Na-TiN and Si3N4-TiB, ceramics were pre- pared using commercially available a-Si3N4 powder (FCT Technology GmbH, Germany) with 5 wt-%Y2O3 (10)and 2 wt-%Al203 sintering aids and TiB2(H. C Starck, de F)or TIN (H. C. Starck). The required composi- using the following values for the coefficients Ayu tion was then ball milled in isopropanol for 5 h using (Ref.20):A0o=0.4980,Ao1=24463,A2=0·0700,A Si3Na milling media. Powders for roll compaction were 87, A04=-3-067, A10=0.54165, A1l=-5-0806, prepared by adding 4 wt-% crude rubber (plasticiser) A12=243447, A13=-32-7208, A14=181214, A20= with 3 wt-% petrol (solvent)to a mixture of the powders. 106 Advances in Applied Ceramics 2005 VOL 104 No 3

Rao et al.9 have demonstrated how a rearrangement of equation (4) can lead to a threshold strength criterion for ceramic laminates. This finding has significant implications for the statistical strength distribution of ceramic components. The threshold strength phenom￾enon exists as failure can only occur at an applied stress sufficient to drive the crack through the compressive layers. Using this assumption, and by setting the crack length a5(t2z2t1)/2 and K5KIc (the critical stress intensity factor for the compressive material), equation (4) may be rearranged to produce an expression for threshold strength, i.e. the strength below which no failure is possible: sthr~ KIc p t2 2 1z 2t1 t2 h i
1=2 zs1 1{ 1z t1 t2  2 p sin{1 1 1z2t1 t2 " # ! (8) Threshold strength is therefore dependent upon two main factors for a given material system, the compres￾sive stress and the ratio of tensile layer thickness to compressive layer thickness. To obtain high threshold strength, the compressive stress should naturally be maximised. However, for a given maximum compressive stress, the laminate architecture should be designed to incorporate very small separations between successive compressive layers, thereby maximising the t1/t2 ratio. The threshold strength phenomenon therefore trun￾cates the statistical strength distribution, yielding an apparently high Weibull modulus material. However, this threshold strength calculation is only valid for cracks that propagate straight through the compressive layer without bifurcation or significant deflection. In such cases, where bifurcation is exhibited by the crack as it propagates through the compressive layer, a greater threshold strength may be observed than predicted by the model. Quantitative prediction of threshold strength in such cases is extremely complicated. Fracture mechanics weight function analysis Bueckner19 first demonstrated that the stress intensity factor for an edge crack of depth a can be calculated by integrating over the entire crack length, the product of a weight function h(x,a) (dependent upon geometry) and any stress distribution s(x) acting normal to the fracture plane (x is the distance along the crack measured from the surface): K~ ða 0 h(x,a)s(x)dx (9) A suitable weight function for a single edge V-notched beam (SEVNB) sample and notch geometry has been given by Fett and Munz:20 h(x,a)~ 2 pa 1=2 1 1{ x a  1=2 1{ a W  3=2 1{ a w
3=2 zXAnm 1{ x a
nz1 a W
m  (10) using the following values for the coefficients Anm (Ref. 20): A0050.4980, A0152.4463, A0250.0700, A035 1.3187, A04523.067, A1050.54165, A11525.0806, A12524.3447, A135232.7208, A14518.1214, A205 20.19277, A2152.55863, A225212.6415, A23519.7630, A245210.9860. During crack propagation in ceramic materials, an interaction zone develops behind the crack front. Within this interaction zone, the two crack surfaces are not completely separated, leading to some crack–surface interactions.21 These interactions are capable of trans￾mitting stresses due to grain/grain friction, or via grain crack bridging. These types of interactions are respon￾sible for R curve behaviour in monolithic ceramic materials. In the remaining discussion, the effect of both types of crack–surface interaction will be termed bridging stresses sbr. The stepwise residual stress pattern also acts in this interaction zone behind the propagating crack as well as at the crack tip. Compressive stresses behind the propagating crack act to close the crack whilst tensile stress regions act as further drivers for opening the crack. The stress intensity factor at the crack tip itself can therefore be determined, using the principle of superposition, by summing the contribu￾tions of the applied stress Ka, the bridging stress Kbr and the residual stress Kr: Ktip~KazKrzKbr (11) Crack tip extension (measured by KR) is predicted to occur when Ktip equals the intrinsic crack tip toughness K0. For a crack with initial crack length a0, KR can be predicted as the crack (length a) advances through the laminate: KR(a,a0)~K0(a){Kr(a){Kbr(a,a0) (12) If K0, sr and sbr are known (or can be calculated with sufficient precision), it becomes possible to predict (as a function of a) the R curve behaviour of a laminated structure. Lakshminarayanan et al.22,23 and Moon et al.24,25 have demonstrated how this can be used to predict the fracture behaviour of layered ceramics containing macroscopic residual stress patterns. In addition, weight function analysis makes it possible to determine the separate effects of the residual stress distribution and the crack bridging closure stresses on the measured R curve. The present study considers the behaviour of multi￾layer TiN–Si3N4 laminar composites that did not exhibit crack bifurcation. The use of weight function analysis for modelling the apparent fracture toughness of ceramic laminates is discussed with reference to optimis￾ing the macrostuctural design. A laminate design concept is presented that incorporates macrostructural constraints due to the matrix cracking phenomena, requirements for bifurcation, ASTM test bar geometry and the additional stress incurred during ceramic machining. Experimental details Si3N4, Si3N4–TiN and Si3N4–TiB2 ceramics were pre￾pared using commercially available a-Si3N4 powder (FCT Technology GmbH, Germany) with 5 wt-%Y2O3 and 2 wt-%Al2O3 sintering aids and TiB2 (H. C. Starck, grade F) or TiN (H. C. Starck). The required composi￾tion was then ball milled in isopropanol for 5 h using Si3N4 milling media. Powders for roll compaction were prepared by adding 4 wt-% crude rubber (plasticiser) with 3 wt-% petrol (solvent) to a mixture of the powders. Gee et al. Enhanced fracture toughness by ceramic laminate design 106 Advances in Applied Ceramics 2005 VOL 104 NO 3

Gee et al. Enhanced fracture toughness by ceramic laminate design Silicon nitride Silicon nitride +30 wt-%TiN 3 Structure of Si3NSi3N/30 wt-%TiN laminates used for SEVNB testin These powders were dried to leave 2 wt-% residual petrol in the mixture. The mixture was then passed hrough a 500 um sieve to remove any coarse agglom- erates and further dried to leave 0.5 wt-% residual petrol. Ceramic green sheets of Si3 N4 or Si3 N4-TIN were prepared by roll tape compaction of this mixture using a roll mill with 40 mm diameter rolls. The velocity for olling was 1. 5 m min, with a working pressure of 100 MPa, yielding tapes of thickness 0-40.5 mm and width 60-65 mm. Monolithic and laminate ceramic samples were prepared by stacking the correct sequence of ceramic sheets into a graphite hot press die Si3 N4 and Si3 N4-TiN samples were hot pressed at 1780.C without protective atmosphere and at a pressure of 30 MPa for 0 min. Monoliths and laminates containing Si3 N4-TlB were hot pressed at 1580oC in a nitrogen atmosphere at 4 Backscattered electron micrograph of a laminate struc 30 MPa for 60 min. Finally the billets were surface ground ture and TiN homogeneity (image width=1 mm); b to the required thickness and machined into appropriate interfacial region showing strong bonding and low est bars with nominal dimensions of3×4×50mm. levels of porosity The sintered densities of the samples were measured by the water immersion method. The coefficient of thermal expansion(CTE)was determined for monolithic Results and discussion mples using a quartz dilatometer from room tempera ture to 1000 C. The strength and fracture toughness The physical and mechanical properties of monolithic were determined using an Instron universal testing ceramic Si3N4-TiN materials are reported in Table I achine with samples mounted in four point flexure The materials show a linear increase in density with with an inner span of 20 mm and outer span of 40 mm, added TIN consistent with the rule of mixtures. The and using a crosshead speed of 0-01 mm min Fracture toughness measurements were made on increase with addition of Tin owing to particulate SEVNB samples according to ASTM C1421 and toughening Fracture toughness reaches a maximum at Kuebler. 6 Youngs modulus and Poisson's ratio were approximately 40 wt-% and then decreases. CTE is determined by pulse echo ultrasound using longitudinal observed to increase rapidly with added TiN content, and shear waves separately. Microstructural character consistent with the findings of Larker et al.27 isation was conducted using a Jeol 6100 SEM using Figure 3 shows the non-optimised laminate macro- econdary electron and backscattered imaging modes. structure studied in the present paper. The architecture Weight function analysis was performed on laminate consists of outer compressive layers of Si3N4, approxi amples with dimensions 4x 3 x 50 mm using the mately 600 um thick, with alternating thicker tensile experimentally determined physical constants Si3 N4-30 wt-% Tin layers (approximately 600 um Table 1 Physical and mechanical properties of monolithic Si3N4-TiN ceramics Density, x 10 kg m-3 Kle, MPa m2 Strength, MPa E, GP CTE. K-1 I-%TiN 3-34 4-47 6849 02733 wt-%TIN 3483 4-61 8839 02738 wt-%TiN 7847 Advances in Applied Ceramics 2005 VOL 104 No 3 107

These powders were dried to leave 2 wt-% residual petrol in the mixture. The mixture was then passed through a 500 mm sieve to remove any coarse agglom￾erates and further dried to leave 0.5 wt-% residual petrol. Ceramic green sheets of Si3N4 or Si3N4–TiN were prepared by roll tape compaction of this mixture using a roll mill with 40 mm diameter rolls. The velocity for rolling was 1.5 m min21 , with a working pressure of 100 MPa, yielding tapes of thickness 0.4–0.5 mm and width 60–65 mm. Monolithic and laminate ceramic samples were prepared by stacking the correct sequence of ceramic sheets into a graphite hot press die. Si3N4 and Si3N4–TiN samples were hot pressed at 1780uC without a protective atmosphere and at a pressure of 30 MPa for 20 min. Monoliths and laminates containing Si3N4–TiB2 were hot pressed at 1580uC in a nitrogen atmosphere at 30 MPa for 60 min. Finally the billets were surface ground to the required thickness and machined into appropriate test bars with nominal dimensions of 364650 mm. The sintered densities of the samples were measured by the water immersion method. The coefficient of thermal expansion (CTE) was determined for monolithic samples using a quartz dilatometer from room tempera￾ture to 1000uC. The strength and fracture toughness were determined using an Instron universal testing machine with samples mounted in four point flexure with an inner span of 20 mm and outer span of 40 mm, and using a crosshead speed of 0.01 mm min21 . Fracture toughness measurements were made on SEVNB samples according to ASTM C1421 and Kuebler.26 Young’s modulus and Poisson’s ratio were determined by pulse echo ultrasound using longitudinal and shear waves separately. Microstructural character￾isation was conducted using a Jeol 6100 SEM using secondary electron and backscattered imaging modes. Weight function analysis was performed on laminate samples with dimensions 463650 mm using the experimentally determined physical constants. Results and discussion The physical and mechanical properties of monolithic ceramic Si3N4–TiN materials are reported in Table 1. The materials show a linear increase in density with added TiN consistent with the rule of mixtures. The critical stress intensity factor KIc is also observed to increase with addition of TiN owing to particulate toughening. Fracture toughness reaches a maximum at approximately 40 wt-% and then decreases. CTE is observed to increase rapidly with added TiN content, consistent with the findings of Larker et al. 27 Figure 3 shows the non-optimised laminate macro￾structure studied in the present paper. The architecture consists of outer compressive layers of Si3N4, approxi￾mately 600 mm thick, with alternating thicker tensile Si3N4–30 wt-% TiN layers (approximately 600 mm Table 1 Physical and mechanical properties of monolithic Si3N4–TiN ceramics Material Density, 6103 kg m23 KIc, MPa m1/2 Strength, MPa E, GPa n CTE, K21 Si3N4 3.216 4.26 790.2 303.1 0.24 3.0 Si3N4–10 wt-%TiN 3.348 4.47 684.9 311.3 0.27 3.3 Si3N4–20 wt-%TiN 3.483 4.61 883.9 317.3 0.27 3.8 Si3N4–30 wt-%TiN 3.641 4.71 784.7 329.5 0.26 4.1 3 Structure of Si3N4/Si3N4–30 wt-%TiN laminates used for SEVNB testing a b 4 Backscattered electron micrograph of a laminate struc￾ture and TiN homogeneity (image width51 mm); b interfacial region showing strong bonding and low levels of porosity Gee et al. Enhanced fracture toughness by ceramic laminate design Advances in Applied Ceramics 2005 VOL 104 NO 3 107

e et aL. Enhanced fracture toughness by ceramic laminate desig Modelling of SEVNB(K for ceramic laminates 12 SEVNB data AT=1150°c Toughness of monolithic silicon nitride .5 Crack depth(m 6 Measured and calculated R curve behaviour for SiaNy 5 Backscattered electron micrograph of 100 N vickers Si3Na-30 wt-%TiN laminates with essive surface trating effect of crack shielding due to compressive esidual stress(image width=240 um) exists owing to the small variation in test bar dimensions from sample to sample The number and extent of ceramic laminate failure thick)and thinner compressive layers of Si3 N4(approxI- mechanisms makes an integrated approach to their design mately 150 um thick) essential for optimisation of their physical properties. The Figure 4 shows a backscattered electron micrograph ability to maximise biaxial compressive stress in the low ken from a SiaN/Si3N--30 wt-%TiN laminate after CTE layer while maintaining the tensile stress below the hot pressing: the laminate macrostructure remaining intact. The microstructure exhibits a good homogeneous matrix cracking threshold(equation (7)) places severe dispersion of TiN of typical grain size 3 um with very stress in the tensile layer by increasing the tensile layer low porosity. Some elongated B-Si3N4 grains are thickness is not always beneficial as the critical thickness is observable in the range 1-5 um. The interface exhibits strong bonding with very little porosity. inversely proportional to the square of tensile stress. In order to optimise the fracture toughness of a given Figure 5 shows the effect of crack shielding due to laminate system it is necessary to have very good control 40 vol-%TiB2 laminate. The micrograph clearly demon- over the laminate thicknesses. For some laminate systems, this may exclude roll tape compaction as a strates the anisotropic residual stress pattern and the suitable consolidation technique owing to limitations on effect on cracks propagating parallel and perpendicular the thicknesses of the tapes produced. A more appro- Cracks propagating parallel to the layer are unaffected priate method is tape casting, which is capable of to the layer(caused by a vickers indentation at 100 N) producing tapes with thicknesses in the range by the biaxial compressive stress whilst those cracks 10-250 um In the opinion of the present authors, it is propagating perpendicular to the layer are greatly not beneficial to use crack bifurcation as the toughening suppressed by residual stress crack shielding. mechanism in Si,N based ceramics to the very Figure 6 shows the fracture toughness R curve beha- severe limitations these laminate structures confer on the viour of a Si3 N, Si3N4-30 wt-%Tin laminate with macrostructure. In addition. crack bifurcation necessi compressive surface layer. The apparent fracture tough- tates edge cracking, which itself is detrimental in most ness measured using a single edge V-notch beam config- engineering applications. However, if both edge crack uration is observed to rise with increasing crack dept ing and bifurcation are avoided in the design of the from values of 11.4 to 17. I MPa m. This compares laminate structure, significant increases in the apparent favourably with monolithic fracture toughness values of fracture toughness of the material are achievable, in 4.26 and 4-71 MPa m" The crack depth itself correlates addition to high threshold strengths. To date, the to the initial notched depth as no pop-in cracks were thickness of the compressive layers has been consider observed. All samples were observed to fail catastrophe- ably greater than the grain size; the extent to which cally, with no evidence of any discernible bifurcation or these phenomena may break down as the compressive deflection. The experimental data are compared with layer thickness approaches the ceramic grain size is theoretical fracture mechanics weight function analysis unknown values. The value for AT is related to the glass transition An integrated approach to the design of ceramic temperature of the ceramic grain boundary phase and laminates incorporating biaxial residual stress patterns represents the temperature from which stresses develop in has been advocated. An a priori knowledge of Youngs the material on cooling. Some variation between experi- modulus, Poisson,'s ratio, coefficient of thermal expan mentally determined and theoretically predicted KR values sion, fracture toughness and joining temperature of the is apparent. However, these are likely to occur because the component materials combined with knowledge of the weight function analysis can only be performed for an overall laminate thickness, enables the engineer to individual bar; deviation from the theoretical line therefore optimise the apparent fracture toughness using residual 8 Advances in Applied Ceramics 2005 VOL 104 No 3

thick) and thinner compressive layers of Si3N4 (approxi￾mately 150 mm thick). Figure 4 shows a backscattered electron micrograph taken from a Si3N4/Si3N4–30 wt-%TiN laminate after hot pressing; the laminate macrostructure remaining intact. The microstructure exhibits a good homogeneous dispersion of TiN of typical grain size 3 mm with very low porosity. Some elongated b-Si3N4 grains are observable in the range 1–5 mm. The interface exhibits strong bonding with very little porosity. Figure 5 shows the effect of crack shielding due to compressive residual stress in a Si3N4/Si3N4– 40 vol.-%TiB2 laminate. The micrograph clearly demon￾strates the anisotropic residual stress pattern and the effect on cracks propagating parallel and perpendicular to the layer (caused by a Vickers indentation at 100 N). Cracks propagating parallel to the layer are unaffected by the biaxial compressive stress whilst those cracks propagating perpendicular to the layer are greatly suppressed by residual stress crack shielding. Figure 6 shows the fracture toughness R curve beha￾viour of a Si3N4/Si3N4–30 wt-%TiN laminate with a compressive surface layer. The apparent fracture tough￾ness measured using a single edge V-notch beam config￾uration is observed to rise with increasing crack depth from values of 11.4 to 17.1 MPa m1/2. This compares favourably with monolithic fracture toughness values of 4.26 and 4.71 MPa m1/2. The crack depth itself correlates to the initial notched depth as no pop-in cracks were observed. All samples were observed to fail catastrophi￾cally, with no evidence of any discernible bifurcation or deflection. The experimental data are compared with theoretical fracture mechanics weight function analysis values. The value for DT is related to the glass transition temperature of the ceramic grain boundary phase and represents the temperature from which stresses develop in the material on cooling. Some variation between experi￾mentally determined and theoretically predicted KR values is apparent. However, these are likely to occur because the weight function analysis can only be performed for an individual bar; deviation from the theoretical line therefore exists owing to the small variation in test bar dimensions from sample to sample. The number and extent of ceramic laminate failure mechanisms makes an integrated approach to their design essential for optimisation of their physical properties. The ability to maximise biaxial compressive stress in the low CTE layer while maintaining the tensile stress below the matrix cracking threshold (equation (7)) places severe limitations on laminate architectural design. Reducing the stress in the tensile layer by increasing the tensile layer thickness is not always beneficial as the critical thickness is inversely proportional to the square of tensile stress. In order to optimise the fracture toughness of a given laminate system it is necessary to have very good control over the laminate thicknesses. For some laminate systems, this may exclude roll tape compaction as a suitable consolidation technique owing to limitations on the thicknesses of the tapes produced. A more appro￾priate method is tape casting, which is capable of producing tapes with thicknesses in the range 10–250 mm. In the opinion of the present authors, it is not beneficial to use crack bifurcation as the toughening mechanism in Si3N4 based ceramics owing to the very severe limitations these laminate structures confer on the macrostructure. In addition, crack bifurcation necessi￾tates edge cracking, which itself is detrimental in most engineering applications. However, if both edge crack￾ing and bifurcation are avoided in the design of the laminate structure, significant increases in the apparent fracture toughness of the material are achievable, in addition to high threshold strengths. To date, the thickness of the compressive layers has been consider￾ably greater than the grain size; the extent to which these phenomena may break down as the compressive layer thickness approaches the ceramic grain size is unknown. An integrated approach to the design of ceramic laminates incorporating biaxial residual stress patterns has been advocated. An a priori knowledge of Young’s modulus, Poisson’s ratio, coefficient of thermal expan￾sion, fracture toughness and joining temperature of the component materials combined with knowledge of the overall laminate thickness, enables the engineer to optimise the apparent fracture toughness using residual 5 Backscattered electron micrograph of 100 N Vickers indentation in Si3N4/Si3N4–40 vol.-%TiB2 laminate illus￾trating effect of crack shielding due to compressive residual stress (image width5240 mm) 6 Measured and calculated R curve behaviour for Si3N4/ Si3N4–30 wt-%TiN laminates with compressive surface layer Gee et al. Enhanced fracture toughness by ceramic laminate design 108 Advances in Applied Ceramics 2005 VOL 104 NO 3

Gee et al. Enhanced fracture toughness by ceramic laminate design stress crack shielding. This optimisation assumes that References he additional toughening mechanism of crack bifurca- on is avoided. Ceramic laminates can be designed 1. w.J. Clegg, K. Kendall, N. MeN. Alford, T. w. Button and J D exhibit a range of fracture behaviour, including cata Birchall: Nature. 1990. 347. 455-457 strophic, multistage bifurcation and delamination. In n,E. Carlstrom and w.J. Clegg: J.Er. Ceran.Soc,1998,18,1945-195 the present authors opinion, residual stress crack 3. J. B. Davis, A. Kristoffersson, E Carlstrom and w.J. Cleg shielding offers the best potential for maximising J.Am. Ceran.Soc,2000,83,2369-2374 apparent fracture toughness D. Kovar. M. D. Thoules and J W. Halloran: J. An Ceram. Soc. 5. D-H. Kuo and Kriven: Mater. Sci. Eng. A, 1998. 241 241-250 Conclusions 6. D -H. Kuo and w. M. Kriven: J. Anm. Cera. Soc. 1995. 78 a brief overview has been presented of some proposed 7. J.R. Mawdsley, D Kovar and J w. Halloran: J. Am. CeramSoc. toughening mechanisms and laminate failure mechanisms 2000 balanced, multilayer ceramics, containing periodic 8. B. Hatton and P.s. Nicholson: J. Am. Ceram Soc., 2001, 84, residual stress patterns. Multilayer ceramic composites may be designed to exhibit some unique mechanical 9. M. P. Rao, A.J. Sanchez-Herencia, G. E Beltz, R. M. MeMeeking and F. F. Lange: Science. 1999. 286. 102-105 properties. Theoretical critical thickness calculations 10. Z. Lences, P lik, M. Toriyama, M. E. Brito and S Kanzaki have been reported to avoid tensile matrix cracking J.Eur. Ceran.Soc,2000,20.347-355 and to incorporate or exclude both edge cracking and I1. P. Z. Cai, D. J. Green and G. L. Messing: J. Eur. Ceram. Soc. bifurcation by design. The previously reported model 998,5,2025-2034 describing the phenomena of threshold strength in 12. M. P. Rao and F. F. Lange: J. Am. Ceran. Soc., 2002, 85. laminar composites has been discussed. The powerful 13. S Ho, C. Hillman. F F. Lange and Z Suo: J Am Ceram Soc theoretical tool of fracture mechanics weight func 1995,78,2353-2359 tion analysis has been introduced. Silicon nitride based 14 M. Oechsner, C. Hillman and FF. Lange: J. Am. Ceram. Soc. ceramics with strong interfaces have successfully been 996,79,183438 Mater. 2003 manufactured by stacking and hot pressing green tapes N4-30 wt-%TIN. Apparent fracture ,s 35, 3otsi, M. Lugovy and V. Slyunyayev: M. Lugovy, N. Orlovskaya, V Slyunyayev, G Gogotsi, J. Kuebl oughness KIe was observed to increase from Sanchez-Herencia: Compos. Sci. TechnoL, 2002, 6 4-26 MPa m 2 for monolithic Si3N4 to 17 MPa m 819-830 17. S Ho and Z Suo: J. Appl. Mech., 1993, 60, 890-894 for a non-optimised laminate. The R curve behaviour 18. FF. Lange: J.A Ceram. Soc.,1989, 72,3 f a Si3N4/Si3N4-30 wt-%Tin laminate with surface 19. H. F. Bueckner: Z. Angew. Math. Mech. 1970. 50. 529-546 compressive stresses has been investigated using SEVNB 20. T. Fett and D. Munz: J. Mater. Sci. Lett., 1990.9.1403-1406 and demonstrated to agree well with theoretical predic- 21. D. B. Marshall and M. v. Swain: J. A. Ceram Soc., 1988, 71, tions based on fracture mechanics weight function analysis. 22. R. Lakshminarayanan, D. Shetty and R. Cutler: J. Am. Ceram. Soc.,1996.79,79-87 23. A. J. Blattner, R. Lakshminarayanan and D. Shetty: Eng. Fract. Acknowledgement 24. R. Moon, M. Hoffman, J. Hilden, K. Bowman, K. Trumble and Rodel: J. Am. Ceram. Soc. 2002. 85. 1505-1511 This work was supported by the European Commission 25. R Moon, M. Hoffman, J Hilden, K Bowman, K Trumble and under the Copernicus 2 programme. It is part of the J. Rodel: Eng. Fract. Mech, 2002. 69. 1647-166 26. J. Kuebler: Fract. Mech. Ceram. 2002. 13. 437-4 roject"Silicon nitride based laminar and functionally 27. R. Larker, L-Y. Wei, M. Olsson and B.Loberg:Proc.4th Int gradient ceramics for engineering application, proposal Symp. on Ceramic Materials and Components for Engines, (ed R NICA2-1999-10109 Carlsson): 1992. Amsterdam, Elsevier Applied Science. Advances in Applied Ceramics 2005 VOL 104 No3 109

stress crack shielding. This optimisation assumes that the additional toughening mechanism of crack bifurca￾tion is avoided. Ceramic laminates can be designed to exhibit a range of fracture behaviour, including cata￾strophic, multistage, bifurcation and delamination. In the present authors’ opinion, residual stress crack shielding offers the best potential for maximising apparent fracture toughness. Conclusions A brief overview has been presented of some proposed toughening mechanisms and laminate failure mechanisms in balanced, multilayer ceramics, containing periodic residual stress patterns. Multilayer ceramic composites may be designed to exhibit some unique mechanical properties. Theoretical critical thickness calculations have been reported to avoid tensile matrix cracking and to incorporate or exclude both edge cracking and bifurcation by design. The previously reported model describing the phenomena of threshold strength in laminar composites has been discussed. The powerful theoretical tool of fracture mechanics weight func￾tion analysis has been introduced. Silicon nitride based ceramics with strong interfaces have successfully been manufactured by stacking and hot pressing green tapes of Si3N4 and Si3N4–30 wt-%TiN. Apparent fracture toughness KIc was observed to increase from 4.26 MPa m1/2 for monolithic Si3N4 to 17 MPa m1/2 for a non-optimised laminate. The R curve behaviour of a Si3N4/Si3N4–30 wt-%TiN laminate with surface compressive stresses has been investigated using SEVNB and demonstrated to agree well with theoretical predic￾tions based on fracture mechanics weight function analysis. Acknowledgement This work was supported by the European Commission under the Copernicus 2 programme. It is part of the project ‘Silicon nitride based laminar and functionally gradient ceramics for engineering application’, proposal N1CA2-1999-10109. References 1. W. J. Clegg, K. Kendall, N. McN. Alford, T. W. Button and J. D. Birchall: Nature, 1990, 347, 455–457. 2. K. S. Blanks, A. Kristoffersson, E. Carlstro¨m and W. J. Clegg: J. Eur. Ceram. Soc., 1998, 18, 1945–1951. 3. J. B. Davis, A. Kristoffersson, E. Carlstro¨m and W. J. Clegg: J. Am. Ceram. Soc., 2000, 83, 2369–2374. 4. D. Kovar, M. D. Thoules and J. W. Halloran: J. Am. Ceram. Soc., 1998, 81, 1004–1012. 5. D.-H. Kuo and W. M. Kriven: Mater. Sci. Eng. A, 1998, 241, 241–250. 6. D.-H. Kuo and W. M. Kriven: J. Am. Ceram. Soc., 1995, 78, 3121–3124. 7. J. R. Mawdsley, D. Kovar and J. W. Halloran: J. Am. Ceram. Soc., 2000, 83, 802–808. 8. B. Hatton and P. S. Nicholson: J. Am. Ceram. Soc., 2001, 84, 571–576. 9. M. P. Rao, A. J. Sa´nchez-Herencia, G. E. Beltz, R. M. McMeeking and F. F. Lange: Science, 1999, 286, 102–105. 10. Z. Lencˇe´sˇ, P. Sˇajgalı´k, M. Toriyama, M. E. Brito and S. Kanzaki: J. Eur. Ceram. Soc., 2000, 20, 347–355. 11. P. Z. Cai, D. J. Green and G. L. Messing: J. Eur. Ceram. Soc., 1998, 5, 2025–2034. 12. M. P. Rao and F. F. Lange: J. Am. Ceram. Soc., 2002, 85, 1222–1228. 13. S. Ho, C. Hillman, F. F. Lange and Z. Suo: J. Am Ceram. Soc., 1995, 78, 2353–2359. 14. M. Oechsner, C. Hillman and F. F. Lange: J. Am. Ceram. Soc., 1996, 79, 1834–38. 15. G. Gogotsi, M. Lugovy and V. Slyunyayev: Strength Mater., 2003, 35, 248–259. 16. M. Lugovy, N. Orlovskaya, V. Slyunyayev, G. Gogotsi, J. Kuebler and A. J. Sa´nchez-Herencia: Compos. Sci. Technol., 2002, 62, 819–830. 17. S. Ho and Z. Suo: J. Appl. Mech., 1993, 60, 890–894. 18. F. F. Lange: J. Am. Ceram. Soc., 1989, 72, 3. 19. H. F. Bueckner: Z. Angew. Math. Mech., 1970, 50, 529–546. 20. T. Fett and D. Munz: J. Mater. Sci. Lett., 1990, 9, 1403–1406. 21. D. B. Marshall and M. V. Swain: J. Am. Ceram. Soc., 1988, 71, 399. 22. R. Lakshminarayanan, D. Shetty and R. Cutler: J. Am. Ceram. Soc., 1996, 79, 79–87. 23. A. J. Blattner, R. Lakshminarayanan and D. Shetty: Eng. Fract. Mech., 2001, 68, 1–7. 24. R. Moon, M. Hoffman, J. Hilden, K. Bowman, K. Trumble and J. Ro¨del: J. Am. Ceram. Soc., 2002, 85, 1505–1511. 25. R. Moon, M. Hoffman, J. Hilden, K. Bowman, K. Trumble and J. Ro¨del: Eng. Fract. Mech., 2002, 69, 1647–1665. 26. J. Kuebler: Fract. Mech. Ceram., 2002, 13, 437–445. 27. R. Larker, L.-Y. Wei, M. Olsson and B. Loberg: Proc. 4th Int. Symp. on Ceramic Materials and Components for Engines, (ed. R. Carlsson); 1992, Amsterdam, Elsevier Applied Science. Gee et al. Enhanced fracture toughness by ceramic laminate design Advances in Applied Ceramics 2005 VOL 104 NO 3 109

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