C R Chen et al. Acta Materialia 55(2007)409-421 919922 h=1.42 mm aX Cross-section F/2 symmetry plane Longitudinal section z=0 Fig. 1. Geometry of the four-point-bending test arrangement of the laminate specimen consisting of layers of A- and AZ-material Results of the fracture toughness tests on the multilayer composite Tip location Fr(N IC(M 117 n AZ 8.4 ble explanations for this difference. The first is that some lie in planes parallel to the y-z plane. The arrangement cutting-induced phase transformation occurs when produc- and thickness of the laminae can be taken from the long ing the notch. In the machine used, the force used while tudinal section at z=0(Fig. lb). In this longitudinal sec cutting the notch cannot be controlled. The second possible tion, an integration path I is marked surrounding a reason for the discrepancy is that the notch radius of about rectangle Q2far with the area hLy. The length Ly will be var 5 um is certainly small enough for the alumina, with its ied to obtain different paths T. The six interfaces, num- grain size of approximately 5 um, but it is quite large for bered from 1 to 6, intersect the integration path I at the AZ-microstructure, which has a grain size of approxi- y=0 and y= Ly. The normal unit vectors to the interfaces mately 0.7 um. This could cause an overestimation of the as well as to the integration path I are designated n. The fracture toughness. Therefore, to be on the safe side, we crack with variable length a is located in the plane y=0; decided to use the lower value of the indentation measure- the crack front is assumed to be parallel to the line x=0 ment in the paper. Fig. Ic presents a cross-section at y=0. The average Ko values and the corresponding Jo values are also listed in Table 1. It is seen that the fracture tough- 4.2. The residual stress state ness values of the composite are significantly larger than the corresponding intrinsic values of the A and Az-materials The specimens are fabricated at high temperatures. Due It should be noted here that the Jo values characterize the to the difference in the Cte, a cooling from the sintering fracture initiation toughness of the materials; in the ceramic temperature to the room temperature 20C introduces a ommunity the term"fracture energy is often used residual stress state(see e.g. [I]. At high temperatures, relaxation processes prevent the development of residual 4. Numerical modeling stresses. The main reason is that the az-material exhibits extensive plasticity between 1200C and the sintering tem- 4. 1. Description of the model perature [17]. Therefore, an upper reference temperature is the effective temperature The global setting is depicted in Fig. la. The laminate is calculated. This reference temperature was determined in beam is supported at a distance S, of 20 mm and loaded [18]as Tref=1160C, leading to an effective temperature by a pair of loads at a distance S2 of 10 mm. The laminae difference AT=-l140Cble explanations for this difference. The first is that some cutting-induced phase transformation occurs when produc￾ing the notch. In the machine used, the force used while cutting the notch cannot be controlled. The second possible reason for the discrepancy is that the notch radius of about 15 lm is certainly small enough for the alumina, with its grain size of approximately 5 lm, but it is quite large for the AZ-microstructure, which has a grain size of approxi￾mately 0.7 lm. This could cause an overestimation of the fracture toughness. Therefore, to be on the safe side, we decided to use the lower value of the indentation measure￾ment in the paper. The average K0 values and the corresponding J0 values are also listed in Table 1. It is seen that the fracture tough￾ness values of the composite are significantly larger than the corresponding intrinsic values of the A- and AZ-materials. It should be noted here that the J0 values characterize the fracture initiation toughness of the materials; in the ceramic community the term ‘‘fracture energy’’ is often used. 4. Numerical modeling 4.1. Description of the model The global setting is depicted in Fig. 1a. The laminate beam is supported at a distance S1 of 20 mm and loaded by a pair of loads at a distance S2 of 10 mm. The laminae lie in planes parallel to the y z plane. The arrangement and thickness of the laminae can be taken from the longi￾tudinal section at z =0 (Fig. 1b). In this longitudinal sec￾tion, an integration path C is marked surrounding a rectangle Xfar with the area hLy. The length Ly will be var￾ied to obtain different paths C. The six interfaces, num￾bered from 1 to 6, intersect the integration path C at y = 0 and y = Ly. The normal unit vectors to the interfaces as well as to the integration path C are designated n. The crack with variable length a is located in the plane y = 0; the crack front is assumed to be parallel to the line x = 0. Fig. 1c presents a cross-section at y = 0. 4.2. The residual stress state The specimens are fabricated at high temperatures. Due to the difference in the CTE, a cooling from the sintering temperature to the room temperature 20 C introduces a residual stress state (see e.g. [1]). At high temperatures, relaxation processes prevent the development of residual stresses. The main reason is that the AZ-material exhibits extensive plasticity between 1200 C and the sintering tem￾perature [17]. Therefore, an upper reference temperature is introduced from which the effective temperature difference is calculated. This reference temperature was determined in [18] as Tref = 1160 C, leading to an effective temperature difference DT = 1140 C. Fig. 1. Geometry of the four-point-bending test arrangement of the laminate specimen consisting of layers of A- and AZ-material. Table 2 Results of the fracture toughness tests on the multilayer composite Specimen B (mm) h (mm) a (mm) Tip location Ffr (N) KIC (MPa pm) J appr IC ðJ=m2 Þ 1 2.72 1.42 0.10 In A 117 6.1 98 2 2.64 1.42 0.21 In AZ 110 8.4 188 3 2.64 1.42 0.18 In A 103 7.3 142 C.R. Chen et al. / Acta Materialia 55 (2007) 409–421 411