T. Lube et al. / Journal of the European Ceramic Society 27(2007)1449-1453 1451 日 toughness >>1 KoAlo. -3.8 MPam"2 2-1./t 0 a=a/w Fig. 1. Influence of the thickness ratio A=taz/tA on the effective R-curve. The Fig. 2. Two clear tendencies provoking different fracture process. situation W=1.5 mm and N=7 layers has been chosen to present the result to a situation with homogeneous stiffness, the A-layers carries at the interface. It can be stated that the compressive stresses more load and the Az-layers less load, so that the calculated hield the material against flaws, while the tensile stresses have apparent toughness is overestimated in the alumina. a detrimental effect on the effective r-curve A second conclusion worth of note concerns the fracture pro- As it derives from Eq (5), the architecture(1)defines the cess. As shown in Fig. 2, two clearly different behaviours are residual stress field. It was the aim of this investigation to under- observed In both cases, while the crack is propagating through stand how the architecture influences the maximum shielding. layers under compression the shielding is increasing, reachin In Fig. 1, apparent R-curves are presented for different values a maximum at the interface, but the overall tendencies are dif- of a in the range 0.2-25. Low values of A corresponds to thin ferent. There are laminates for which the effective toughness alumina layers ta in comparison to tAz, and thus high compres- presents an overall increase with crack length, while there are sive stresses are present in these layers. That is the reason why laminates that show an overall decrease the shielding increases so steep in the alumina layers and a high Roughly speaking, those laminates in which the A stress intensity factor has to be applied to fail the specimen. For compressive stress is higher than the AZ-tensile stress, will high values of A, the thickness of alumina layers is much big- present a tendency of toughness increase as long as the crack ger than that of the AZ composite layers and as a result, high grows. Those laminates with a higher tensile stress present a ten- tensile stresses arise in the Az layers, while almost no compres- dency of toughness decrease, even reaching fictitious negative sive stress appears. That is the reason that the effective toughness values of effective toughness In the latter type of laminates, the drops in the AZ layers for these laminates. This kind of multilay- fracture process results in unstable failure after reaching a peak ers,could even present for all the crack lengths a lower apparent in the R-curve. On the other hand in laminates with a tendency of toughness, so its mechanical performance is not so interesting toughness increase, a controlled layer-by-layer fracture pattern as compared to laminates with A<I is observed. This behaviour has been experimentally observed An interesting conclusion drawn from Fig. I is the existence carrying out 4-point bending tests. 8 of an architecture that maximizes the shielding in the first inter The architecture A =hopt that maximizes the shielding in the face. Opposite to what could be expected, the highest surface first interface, also deserves some attention. In Fig 3 compressive stress(the highest A) does not correspond to the lope is presented covering the maximum shielding for each x highest shielding in the first layer. Since the maximum shield- Obviously all the maxima of these envelopes correspond to opt ing in the first layer is obtained at a distance equal to the outer Fig. 3 also presents the infuence of the different architecture layer thickness, the thickness ta plays an important role parameters(N and W)on shielding N modifies the residual stres This architecture that maximizes the apparent toughness at field thus influencing the shielding and w normalizes the crack the first interlayer is especially interesting when short cracks depth in the effective R-curve. The envelopes can be obtained are expected. Otherwise, for long cracks a laminate with A<1 by evaluating the effective R-curve at the first interface for each could be more adequate due to the overall increase of toughness architecture. The reader should keep in mind that for this work that is present in this type of multilayer. the stress field considered is given by Eq. (5)that introduces We caution the reader about the fact that a weight function some error in the outer layer since does not consider free sur that applies to a homogeneous material (E constant) has been face. FEM calculations demonstrate that the difference is not considered. This approximation results in an error of maximal significant in our case. 8 10% for the calculated stress intensity factor. The A/AZ lami- As one can appreciate from Fig 3 the architecture does not nate contains an AZ core that is less stiff than the A Compared influence the position of the maximum. This means that theT. Lube et al. / Journal of the European Ceramic Society 27 (2007) 1449–1453 1451 Fig. 1. Influence of the thickness ratio λ = tAZ/tA on the effective R-curve. The situation W = 1.5 mm and N= 7 layers has been chosen to present the results. at the interface. It can be stated that the compressive stresses shield the material against flaws, while the tensile stresses have a detrimental effect on the effective R-curve. As it derives from Eq. (5), the architecture (λ) defines the residual stress field. It was the aim of this investigation to under￾stand how the architecture influences the maximum shielding. In Fig. 1, apparent R-curves are presented for different values of λ in the range 0.2–25. Low values of λ corresponds to thin alumina layers tA in comparison to tAZ, and thus high compres￾sive stresses are present in these layers. That is the reason why the shielding increases so steep in the alumina layers and a high stress intensity factor has to be applied to fail the specimen. For high values of λ, the thickness of alumina layers is much big￾ger than that of the AZ composite layers and as a result, high tensile stresses arise in the AZ layers, while almost no compres￾sive stress appears. That is the reason that the effective toughness drops in the AZ layers for these laminates. This kind of multilay￾ers, could even present for all the crack lengths a lower apparent toughness, so its mechanical performance is not so interesting as compared to laminates with λ < 1. An interesting conclusion drawn from Fig. 1 is the existence of an architecture that maximizes the shielding in the first inter￾face. Opposite to what could be expected, the highest surface compressive stress (the highest λ) does not correspond to the highest shielding in the first layer. Since the maximum shield￾ing in the first layer is obtained at a distance equal to the outer layer thickness, the thickness tA plays an important role. This architecture that maximizes the apparent toughness at the first interlayer is especially interesting when short cracks are expected. Otherwise, for long cracks a laminate with λ  1 could be more adequate due to the overall increase of toughness that is present in this type of multilayer. We caution the reader about the fact that a weight function that applies to a homogeneous material (E constant) has been considered. This approximation results in an error of maximal 10% for the calculated stress intensity factor.5 The A/AZ lami￾nate contains an AZ core that is less stiff than the A. Compared Fig. 2. Two clear tendencies provoking different fracture process. to a situation with homogeneous stiffness, the A-layers carries more load and the AZ-layers less load, so that the calculated apparent toughness is overestimated in the alumina. A second conclusion worth of note concerns the fracture pro￾cess. As shown in Fig. 2, two clearly different behaviours are observed. In both cases, while the crack is propagating through layers under compression the shielding is increasing, reaching a maximum at the interface, but the overall tendencies are dif￾ferent. There are laminates for which the effective toughness presents an overall increase with crack length, while there are laminates that show an overall decrease. Roughly speaking, those laminates in which the A￾compressive stress is higher than the AZ-tensile stress, will present a tendency of toughness increase as long as the crack grows. Those laminates with a higher tensile stress present a ten￾dency of toughness decrease, even reaching fictitious negative values of effective toughness. In the latter type of laminates, the fracture process results in unstable failure after reaching a peak in the R-curve. On the other hand in laminates with a tendency of toughness increase, a controlled layer-by-layer fracture pattern is observed. This behaviour has been experimentally observed carrying out 4-point bending tests.18 The architecture λ = λopt that maximizes the shielding in the first interface, also deserves some attention. In Fig. 3, an enve￾lope is presented covering the maximum shielding for each λ. Obviously all the maxima of these envelopes correspond to λopt. Fig. 3 also presents the influence of the different architecture parameters (Nand W) on shielding.N modifies the residual stress field thus influencing the shielding and W normalizes the crack depth in the effective R-curve. The envelopes can be obtained by evaluating the effective R-curve at the first interface for each architecture. The reader should keep in mind that for this work the stress field considered is given by Eq. (5) that introduces some error in the outer layer since does not consider free sur￾face. FEM calculations demonstrate that the difference is not significant in our case.18 As one can appreciate from Fig. 3 the architecture does not influence the position of the maximum. This means that the