associated with the closure stress field behind the crack tapes. Two compositions of layers were used: (1) Si3N tip, which is similar to a crack bridging phenomenon (MIl, Stark, Germany), (2)Si3N4-30 wt% TiN (grade ening by the residual compressive stress is determined 2 wt% Al2O3 and 5 wt%Y2O3 additiver was used with acting in non-layered ceramics [11]. However, a tough- C, Stark, Germany). The silicon nitride by the overall crack length [12], while the toughening The mixtures of various compositions were milled in by the crack bridging depends only on the length incre- the ball mill for 5 h. The average grain size of the milled ment of the moving crack Crack bridging can provide powders was about I m. Crude rubber (4 wt%)was increased toughening by a factor of approximately 2 added to the mixture of powders as a plasticizer through [11]. Therefore, the residual compressive stresses can a 3% solution in petrol. The powders were then drie provide a significant increase in a ceramic's toughness leaving 2 wt% residual amount of petrol in the mixture &e Although fracture toughness of layered composite can After sieving powders with a 500 um sieve, granulated cause of the superposition of different effects like stress mill with 40 mm rolls was used for rolling. The velocity shielding and intrinsic properties of the structure, such of rolling was 1.5 m/min. The working pressure was as grain size, composition, interfaces, etc. In fractur about 10 mPa to obtain a relative of mechanics, both residual and applied stresses are usually 64%. The thickness of green tapes was 0.4-0.5 mm and included in the crack driving force. However it can be the width was 60-65 mm. Green tapes were stacked to- ful to consider residual stresses as part of the gether to form the desired layered structures and cera- ance. Thus, in laminates with residual compressive stress, mic samples were prepared by hot pressing the stacked the higher resistance to failure results from a reduction of tapes. The hot pressing was performed at 1820C and crack driving force rather than from an increase in the 30 MPa for 45 min without a protective atmosphere intrinsic material resistance to crack extension[12] Both monolithic and layered samples were produced A number of the symmetrical layered structures have The monolithic samples were fabricated from stacked already been considered in relevant publications [3,5, 10]. tapes of the same Si3 N4 or Si3N4-30 wt%TIN composi- However, real laminates show some asymmetry of their tions Layered samples were prepared using two different architecture due to random deviations during the fabri- designs. The first type of specimen was with the outer lay cation process. Sometimes the asymmetrical layered ers in residual compression (Si3 N4 layers); the second structure is designed to meet specific engineering type of specimen was with the outer layers in residual equirements. Another problem is that only a few tension(Si3 N4-30 wt% TiN layers). The laminate param authors have considered the effect of elastic moduli mis- eters, such as composition and thickness of layers match between layers on toughening and fracture and calculated bulk residual stresses are presented in behavior [13, 14]. It was shown that in order to obtain Table 1. The deviation in the measured thickness of the the higher resistance to failure, the tensile layer should layers was about 5%. Though both monolithic and lay be made as stiff as possible (i.e. a high elastic modulus), ered samples have been nominally prepared from materi- whereas the compressive layers should be as compliant als of the same grades using the same manufacturing as feasible (i.e. a low elastic modulus)[14]. However, techniques, in reality the samples were prepared from d the conditions of stable or unstable crack growth in ferent batches of similar compositions and therefore cer- ceramic laminates have not been considered in [13, 14]. tain variations between impurities, defects, and other The effect of the residual stress on the apparent frac- parameters were expected to exist ture toughness and crack growth in non-symmetric The specimens for mechanical tests pared by Si3N4-based layered composites is analyzed in this machining the hot pressed tiles. Standard mor bars of study. Special attention is paid to analytical modeling dimensions 50 x 4 x 3 mm were surface ground to the to estimate the fracture toughness as a function of crack specification stated in EN843-1 The bars were also cham length in laminates having different elastic moduli of lay- fered along the long edges with a chamfer angle at 45to a ers. The validity of the method is examined by a com- dimension of0. 12 +0.03 mm. The fracture toughness was parison of calculated and measured fracture toughness measured by the single edge V-notch beam(SEVNB) values. Crack propagation behavior for laminates with technique [15, 16]using Eq (1). The V-notches with a tip the residual compressive or tensile stress in top layers radii of an order of 10-15 um were made in the specimen is investigated as well. with a diamond saw, followed by a stainless steel blade notching, and finally a diamond abrasive to obtain a sharp tip for the notch. The elastic modulus was measured 2. Experimental by a standard for ending techniqu The coefficients of thermal expansion(CTE) of the The manufacturing steps of Si3N4-TiN based lami- monolithic materials were measured using 50 mm long nates included (a) ball milling of powders in certain pro- MOR bars with a Baehr Dil 802 dilatometer from room portions;(b) rolling of thin tapes;(c)hot pressing of temperature to 1 100C in a nitrogen/hydrogen atmosassociated with the closure stress field behind the crack tip, which is similar to a crack bridging phenomenon acting in non-layered ceramics [11]. However, a tough￾ening by the residual compressive stress is determined by the overall crack length [12], while the toughening by the crack bridging depends only on the length incre￾ment of the moving crack. Crack bridging can provide increased toughening by a factor of approximately 2 [11]. Therefore, the residual compressive stresses can provide a significant increase in a ceramic
s toughness. Although fracture toughness of layered composite can be measured experimentally, it is an apparent value be￾cause of the superposition of different effects like stress shielding and intrinsic properties of the structure, such as grain size, composition, interfaces, etc. In fracture mechanics, both residual and applied stresses are usually included in the crack driving force. However it can be use￾ful to consider residual stresses as part of the crack resist￾ance. Thus, in laminates with residual compressive stress, the higher resistance to failure results from a reduction of crack driving force rather than from an increase in the intrinsic material resistance to crack extension [12]. A number of the symmetrical layered structures have already been considered in relevant publications [3,5,10]. However, real laminates show some asymmetry of their architecture due to random deviations during the fabri￾cation process. Sometimes the asymmetrical layered structure is designed to meet specific engineering requirements. Another problem is that only a few authors have considered the effect of elastic moduli mis￾match between layers on toughening and fracture behavior [13,14]. It was shown that in order to obtain the higher resistance to failure, the tensile layer should be made as stiff as possible (i.e. a high elastic modulus), whereas the compressive layers should be as compliant as feasible (i.e. a low elastic modulus) [14]. However, the conditions of stable or unstable crack growth in ceramic laminates have not been considered in [13,14]. The effect of the residual stress on the apparent frac￾ture toughness and crack growth in non-symmetric Si3N4-based layered composites is analyzed in this study. Special attention is paid to analytical modeling to estimate the fracture toughness as a function of crack length in laminates having different elastic moduli of lay￾ers. The validity of the method is examined by a com￾parison of calculated and measured fracture toughness values. Crack propagation behavior for laminates with the residual compressive or tensile stress in top layers is investigated as well. 2. Experimental The manufacturing steps of Si3N4–TiN based lami￾nates included (a) ball milling of powders in certain pro￾portions; (b) rolling of thin tapes; (c) hot pressing of tapes. Two compositions of layers were used: (1) Si3N4 (M11, Stark, Germany), (2) Si3N4–30 wt% TiN (grade C, Stark, Germany). The silicon nitride was used with 2 wt% Al2O3 and 5 wt% Y2O3 additives. The mixtures of various compositions were milled in the ball mill for 5 h. The average grain size of the milled powders was about 1 m. Crude rubber (4 wt%) was added to the mixture of powders as a plasticizer through a 3% solution in petrol. The powders were then dried, leaving 2 wt% residual amount of petrol in the mixture. After sieving powders with a 500 lm sieve, granulated powders were dried to 0.5 wt% residual petrol. A roll mill with 40 mm rolls was used for rolling. The velocity of rolling was 1.5 m/min. The working pressure was about 10 MPa to obtain a relative tape density of 64%. The thickness of green tapes was 0.4–0.5 mm and the width was 60–65 mm. Green tapes were stacked to￾gether to form the desired layered structures and cera￾mic samples were prepared by hot pressing the stacked tapes. The hot pressing was performed at 1820 C and 30 MPa for 45 min without a protective atmosphere. Both monolithic and layered samples were produced. The monolithic samples were fabricated from stacked tapes of the same Si3N4 or Si3N4–30 wt% TiN composi￾tions. Layered samples were prepared using two different designs. The first type of specimen was with the outer lay￾ers in residual compression (Si3N4 layers); the second type of specimen was with the outer layers in residual tension (Si3N4–30 wt% TiN layers). The laminate param￾eters, such as composition and thickness of layers, and calculated bulk residual stresses are presented in Table 1. The deviation in the measured thickness of the layers was about 5%. Though both monolithic and lay￾ered samples have been nominally prepared from materi￾als of the same grades using the same manufacturing techniques, in reality the samples were prepared from dif￾ferent batches of similar compositions and therefore cer￾tain variations between impurities, defects, and other parameters were expected to exist. The specimens for mechanical tests were prepared by machining the hot pressed tiles. Standard MOR bars of dimensions 50 · 4 · 3 mm were surface ground to the specification stated in EN843-1. The bars were also cham￾fered along the long edges with a chamfer angle at 45to a dimension of 0.12 ± 0.03 mm. The fracture toughness was measured by the single edge V-notch beam (SEVNB) technique [15,16] using Eq. (1). The V-notches with a tip radii of an order of 10–15 lm were made in the specimen with a diamond saw, followed by a stainless steel blade notching, and finally a diamond abrasive to obtain a sharp tip for the notch. The elastic modulus was measured by a standard four-point bending technique. The coefficients of thermal expansion (CTE) of the monolithic materials were measured using 50 mm long MOR bars with a Baehr Dil 802 dilatometer from room temperature to 1100 C in a nitrogen/hydrogen atmos- 290 M. Lugovy et al. / Acta Materialia 53 (2005) 289–296