hown in Fig. 4 in white and gray colors, respectively. within the third si3N4-30 wt% TiN layer with a residual vales as he rack reaches its maximum or minimum tensile stress. There is no continuous growth of the crack As approaches the interface with a new in this case. The crack starts to propagate, then becomes layer of an opposite stress sign. For the first Si3N4 top arrested, after this it continues to grow again. The crack layer with compressive stress, the calculated apparent arrest results in a"pop-in"event at the load-displace- fracture toughness increases from 3. 9 to 17 MPa m ment diagram(Fig. 5). A stress of such"pop-in"event as a function of the crack length parameter. The exper- is the onset stress of crack propagation. This stress, as imentally measured Kapp values, presented as solid cir- well as an initial notch length was used to calculate cles in Fig. 4(a), show an excellent fit with the the measured apparent fracture toughness. Experimen- calculated values. The crack length parameters for the tally measured values of Kapp fit well with the calculated experimentally measured Kapp were calculated from numbers. The experimental data can be considered to be the initial notch lengths. All experimentally measured two different sets. The first set includes the Kapp meas- oints are located on close to a straight line between ured with notch tips within the first Si3N4-30 wt% the coordinate origin and the maximum Kapp point at TIN and the second Si3 N4 layers. The failure of all sam the interface between the first and second layers. The ples from the first set occurred at 116 2 MPa. The second failure of all samples occurred at 351+ 13 MPa. The set includes two Kapp values measured with notch tips calculated Kapp decreases in the second Si3N4-30 wt% within the third Si3N4-30 wt% TiN layer. The failure TiN layer with a residual tensile stress from 17 to of these two samples occurred at 71+ I MPa. The insert 5 MPa m", followed by the next increase from 5 to Fig 4(b)shows an optical micrograph of two parts of 14 MPa m"in the third Si,N4 layer with a residual the Si3 N4/Si3 N4-30 wt% TiN laminate sample with the compressive stress. The insert in Fig. 4(a) shows an V-notch placed in the Si3N4-30 wt% TiN top layer with optical micrograph of two parts of the Si3,Si3N4- a residual tensile stress after the SEVNB test. As one can 30 wt% TiN laminate sample with a V-notch in see from the optical image, the crack path deviates the top layer with residual compressive stress after strongly from a straight line with 90 crack deflection the SEVNB test. As one can see, there is a rela- occurring in the center of each Si3 N4 layer with a resid tively straight crack path with no sharp crack devia- ual compressive stress. While traveling only a short dis tion, deflection, or bifurcation during the crack tance of about a Si3 N4-30 wt% TiN layer thickness along a centerline the crack kinks out into the Si3N4- Fig. 4(b) shows the calculated apparent fracture 30 wt% TiN layer with a residual tensile stress toughness as a function of the crack length parameter d in the Si3N,/Si3 N4-30 wt% TiN laminate with a resid ual tensile stress in the outer layers. The toughness de- 6. Discussion creases from 3.9 to 0.8 MPa m 2 within the first Si3N4-30 wt% TiN layer as the crack reaches the first The calculations indicate an unambiguous trend for interface. Toughness increases from 0. 8 to 6. 4 MPa the apparent fracture toughness behavior. The Kapp in m"in the second Si3 N4 layer with a residual compres- creases in the layers with a residual compressive stress sive stress, and it decreases again from 6. 4 to l MPa m and decreases in the layers with a residual tensile stress 80 op-in load --1------- Deflection(μm) Fig. 5. Load-displacement diagram of SEVNB sample with pop-inshown in Fig. 4 in white and gray colors, respectively. As one can see, Kapp reaches its maximum or minimum values as the crack approaches the interface with a new layer of an opposite stress sign. For the first Si3N4 top layer with compressive stress, the calculated apparent fracture toughness increases from 3.9 to 17 MPa m1/2 as a function of the crack length parameter. The exper￾imentally measured Kapp values, presented as solid cir￾cles in Fig. 4(a), show an excellent fit with the calculated values. The crack length parameters for the experimentally measured Kapp were calculated from the initial notch lengths. All experimentally measured points are located on close to a straight line between the coordinate origin and the maximum Kapp point at the interface between the first and second layers. The failure of all samples occurred at 351 ± 13 MPa. The calculated Kapp decreases in the second Si3N4–30 wt% TiN layer with a residual tensile stress from 17 to 5 MPa m1/2, followed by the next increase from 5 to 14 MPa m1/2 in the third Si3N4 layer with a residual compressive stress. The insert in Fig. 4(a) shows an optical micrograph of two parts of the Si3N4/Si3N4– 30 wt% TiN laminate sample with a V-notch in the top layer with residual compressive stress after the SEVNB test. As one can see, there is a rela￾tively straight crack path with no sharp crack devia￾tion, deflection, or bifurcation during the crack propagation. Fig. 4(b) shows the calculated apparent fracture toughness as a function of the crack length parameter a˜ in the Si3N4/Si3N4–30 wt% TiN laminate with a resid￾ual tensile stress in the outer layers. The toughness de￾creases from 3.9 to 0.8 MPa m1/2 within the first Si3N4–30 wt% TiN layer as the crack reaches the first interface. Toughness increases from 0.8 to 6.4 MPa m1/2 in the second Si3N4 layer with a residual compres￾sive stress, and it decreases again from 6.4 to 1 MPa m1/2 within the third Si3N4–30 wt% TiN layer with a residual tensile stress. There is no continuous growth of the crack in this case. The crack starts to propagate, then becomes arrested, after this it continues to grow again. The crack arrest results in a ‘‘pop-in’’ event at the load–displace￾ment diagram (Fig. 5). A stress of such ‘‘pop-in’’ event is the onset stress of crack propagation. This stress, as well as an initial notch length was used to calculate the measured apparent fracture toughness. Experimen￾tally measured values of Kapp fit well with the calculated numbers. The experimental data can be considered to be two different sets. The first set includes the Kapp meas￾ured with notch tips within the first Si3N4–30 wt% TiN and the second Si3N4 layers. The failure of all sam￾ples from the first set occurred at 116 2 MPa. The second set includes two Kapp values measured with notch tips within the third Si3N4–30 wt% TiN layer. The failure of these two samples occurred at 71 ± 1 MPa. The insert in Fig. 4(b) shows an optical micrograph of two parts of the Si3N4/Si3N4–30 wt% TiN laminate sample with the V-notch placed in the Si3N4–30 wt% TiN top layer with a residual tensile stress after the SEVNB test. As one can see from the optical image, the crack path deviates strongly from a straight line with 90 crack deflection occurring in the center of each Si3N4 layer with a resid￾ual compressive stress. While traveling only a short dis￾tance of about a Si3N4–30 wt% TiN layer thickness along a centerline, the crack kinks out into the Si3N4– 30 wt% TiN layer with a residual tensile stress. 6. Discussion The calculations indicate an unambiguous trend for the apparent fracture toughness behavior. The Kapp in￾creases in the layers with a residual compressive stress and decreases in the layers with a residual tensile stress Fig. 5. Load–displacement diagram of SEVNB sample with pop-in. 294 M. Lugovy et al. / Acta Materialia 53 (2005) 289–296