C R Chen et al. Acta Materialia 55(2007)409-421 laminate planes can be promoted (anti-shielding) or diamond paste. The procedure yields a notch with a tip retarded(shielding) by the different elastic properties(elas- radius of about 15 um(measured at the lateral surfaces tic mismatch) of the laminae [1]. The spatially varying before fracture). This should assure a reliable fracture residual stress state can have a similar effect [13]. toughness measurement [15](see below ). Four-point-bend- The goals of this paper are, therefore, to present an ing tests were conducted in a commercial Zwick Z010 alternative procedure -the method of configurational (or machine under room conditions (34% relative humidity material) forces- to predict the fracture toughness of a and a temperature of 20C) ceramic multilayer composite which takes these spatial The fracture toughness Kic was determined from the inhomogeneities into account. These numerical predictions expression [14] will then be compared with experimental fracture tough less data. Furthermore, we will outline a generally applica- K F S,-s, 3 (1) ble concept of how to exploit the method of configurational Bh h 2(1-7) forces which would also be applicable for the design of lay- with ered composite materials with improved fracture resistance 2. Materials and processing Tapes of alumina(A)and an alumina-zirconia compos- Y=1.9887-13267 3.49-0687+1.35y2)(1-y) e(az were produced by tape casting at ISTEC Faenza, Italy. The AZ composite consists of 60 vol. Al_O3 and 40 vol %3Y-TZP, which is ZrO, with 3 mol %Y,O3. The In the above relations, F is the fracture load and S, sheets were alternatively stacked, forming a multilayer that (=20 mm) and S2(=10 mm) are the support span lengths was sintered at 1550C. As result, a seven-layer laminate The initial crack length, a, was measured after the tests, ta- was obtained with the structure A/AZ/A/AZ/A/AZ/A, in ken as an average of three measurements on the fracture which the thickness of the individual A- and AZ-layers surface are 190 and 220 um, respectively. More details about pro- Three specimens of the multilayer composite with vari- cessing can be found elsewhere, especially data about the ous initial crack lengths were tested(see Fig. Ib). In the composition of the slurry necessary to produce the tapes [6]. first specimen the crack tip was located in the middle of A complete characterization of the material layers was the first layer, in the second specimen it was shortly behind performed. The results are presented in Table 1. The elastic and in the third shortly beyond the interface with the sec- onstants, Youngs modulus E and Poisson's ratio v, were ond layer (interface 1). The initial geometries and the measured at room temperature by an impulse excitation results of the experiments are listed in Table 2. As well as chnique. The coefficient of thermal expansion( CTE)a the Kic values, the loads at fracture Ffr are also given. was measured between room temperature and the reference Additionally, approximate JIc values are listed which are temperature 1160C by means of a dilatometer (see calculated from the relation J=(1-22)K/E, using vol- below). The average CtE values are listed in Table 1. Also ume-averaged values of Poissons ratio, v=0. 25, and presented are the total thickness of the four A-layers (A, Youngs modulus, E=375 GPa nd the three Az-layers tAz in the multilayer are given The intrinsic fracture toughness Ko of the A and aZ which are needed in Appendix I material was determined by testing multilayered homoge- neous specimens consisting of only A-an 3. Fracture mechanics experiments respectively. Indentation toughness values following [16] were determined, and these are presented in Table 1. In The fracture toughness of the composite was measured addition, VAMAS-ESIS experiments were also performed on single edge V-notched beams, following the VAMAs- For the A-layers the VAMAS-ESIS procedure gave exactly ESIS procedure [14]. Bar-shaped specimens with length the same value as the indentation procedure: K0=3.8+0.3 L=28 mm, width h= 1.42 mm and thickness B 2.5 mm MPa vm. For the AZ-layers, however, the VAMAS-ESIS were cut from the original plates using a diamond saw(see values show a big scatter and higher mean value: KAZ Fig. la). The notches were machined in a home-made auto- 5.4+ 1.0 MPa vm compared with K0=4.3+0.1 matic device which uses a razor blade sprinkled with MPa vm from the indentation tests. There are two possi- Table l propertIes f(mm) E(GPa) x(10-6K-) Ko(MPa vm) AlO3(A 392±5 0.24±0.04 8.64±0.03 3.8±0.2 35±2 AlO -ZrO(AZ 0.66 305±4 0.26±0.03 9.24±0.02 4.3±0.1 7士3laminate planes can be promoted (anti-shielding) or retarded (shielding) by the different elastic properties (elas￾tic mismatch) of the laminae [1]. The spatially varying residual stress state can have a similar effect [13]. The goals of this paper are, therefore, to present an alternative procedure – the method of configurational (or material) forces – to predict the fracture toughness of a ceramic multilayer composite which takes these spatial inhomogeneities into account. These numerical predictions will then be compared with experimental fracture tough￾ness data. Furthermore, we will outline a generally applica￾ble concept of how to exploit the method of configurational forces which would also be applicable for the design of lay￾ered composite materials with improved fracture resistance. 2. Materials and processing Tapes of alumina (A) and an alumina–zirconia compos￾ite (AZ) were produced by tape casting at ISTEC Faenza, Italy. The AZ composite consists of 60 vol.% Al2O3 and 40 vol.% 3Y-TZP, which is ZrO2 with 3 mol.% Y2O3. The sheets were alternatively stacked, forming a multilayer that was sintered at 1550 C. As result, a seven-layer laminate was obtained with the structure A/AZ/A/AZ/A/AZ/A, in which the thickness of the individual A- and AZ-layers are 190 and 220 lm, respectively. More details about pro￾cessing can be found elsewhere, especially data about the composition of the slurry necessary to produce the tapes [6]. A complete characterization of the material layers was performed. The results are presented in Table 1. The elastic constants, Young’s modulus E and Poisson’s ratio m, were measured at room temperature by an impulse excitation technique. The coefficient of thermal expansion (CTE) a was measured between room temperature and the reference temperature 1160 C by means of a dilatometer (see below). The average CTE values are listed in Table 1. Also presented are the total thickness of the four A-layers tA, and the three AZ-layers tAZ in the multilayer are given which are needed in Appendix 1. 3. Fracture mechanics experiments The fracture toughness of the composite was measured on single edge V-notched beams, following the VAMAS– ESIS procedure [14]. Bar-shaped specimens with length L = 28 mm, width h = 1.42 mm and thickness B 2.5 mm were cut from the original plates using a diamond saw (see Fig. 1a). The notches were machined in a home-made auto￾matic device which uses a razor blade sprinkled with diamond paste. The procedure yields a notch with a tip radius of about 15 lm (measured at the lateral surfaces before fracture). This should assure a reliable fracture toughness measurement [15] (see below). Four-point-bend￾ing tests were conducted in a commercial Zwick Z010 machine under room conditions (34% relative humidity and a temperature of 20 C). The fracture toughness KIC was determined from the expression [14] KIC ¼ F B ffiffiffi h p S1 S2 h 3 ffiffi c p 2ð1 cÞ 1:5 Y ð1Þ with c ¼ a h and Y ¼ 1:9887 1:326c ð3:49 0:68c þ 1:35c2Þcð1 cÞ ð1 þ cÞ 2 ð2Þ In the above relations, F is the fracture load and S1 (=20 mm) and S2 (=10 mm) are the support span lengths. The initial crack length, a, was measured after the tests, ta￾ken as an average of three measurements on the fracture surface. Three specimens of the multilayer composite with vari￾ous initial crack lengths were tested (see Fig. 1b). In the first specimen the crack tip was located in the middle of the first layer, in the second specimen it was shortly behind and in the third shortly beyond the interface with the sec￾ond layer (interface 1). The initial geometries and the results of the experiments are listed in Table 2. As well as the KIC values, the loads at fracture Ffr are also given. Additionally, approximate JIC values are listed which are calculated from the relation J ¼ ð1 m2ÞK2 =E, using vol￾ume-averaged values of Poisson’s ratio, m ¼ 0:25, and Young’s modulus, E ¼ 375 GPa. The intrinsic fracture toughness K0 of the A and AZ material was determined by testing multilayered homoge￾neous specimens consisting of only A- and AZ-layers, respectively. Indentation toughness values following [16] were determined, and these are presented in Table 1. In addition, VAMAS–ESIS experiments were also performed. For the A-layers the VAMAS–ESIS procedure gave exactly the same value as the indentation procedure: KA 0 ¼ 3:8  0:3 MPa pm. For the AZ-layers, however, the VAMAS–ESIS values show a big scatter and higher mean value: KAZ 0 ¼ 5:4  1:0 MPa pm compared with KAZ 0 ¼ 4:3  0:1 MPa pm from the indentation tests. There are two possi￾Table 1 Material properties Material t (mm) E (GPa) m (–) a (106 K1 ) K0 (MPa pm) J0 (J/m2 ) Al2O3 (A) 0.76 392 ± 5 0.24 ± 0.04 8.64 ± 0.03 3.8 ± 0.2 35 ± 2 Al2O3–ZrO2 (AZ) 0.66 305 ± 4 0.26 ± 0.03 9.24 ± 0.02 4.3 ± 0.1 57 ± 3 410 C.R. Chen et al. / Acta Materialia 55 (2007) 409–421