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 3where 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