Journal of the European Ceramic Society 18(1998)1945-1951 C 1998 Elsevier Science Limt Printed in Great Britain. All rights reserved PII:S0955-2219(98)00134-4 955-2219/98Asee front matter Crack Deflection in Ceramic Laminates Using Porous interlayers K. S Blanks, aA. Kristoffersson, E Carlstrom and W.J. Clegg* Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, CB2 3QZ, UK venska Keraminstitutet, Goteborg, Sweden Abstract would have the added advantage that any internal stresses due to differences in thermal expansion Ceramic laminates have been made from alternating coefficients between the lamina and interlayer lavers of silicon carbide and silicon carbide contain materials, which can cause delamination in these ing a fugitive polymer, which can be pyrolysed to systems, could be avoided produce porous interlayers. It is shown that such The possibility of using porous or intermittent interlayers can be used to deflect cracks and that the terlayers to deflect cracks was first investigated olume fraction of porosity, due to the added poly- by Atkins for use in fibrous polymer compo- mer, that is required to cause crack deflection is ites.9, 10 The approach has also been employed in approximately 04. A simple model has been devel- polymer laminates and metal matrix compo oped which describes the fracture behaviour of por- sites. 2 More recently the possibility of using such ous solids and also predicts the fraction of an interface in ceramic matrix composites has been porosity required to give crack deflection in the investigated, but it does not appear to be possible laminate and which is in good agreement with to produce an interface that will have both the experiment. C 1998 Elsevier Science Limited. All ability to deflect a crack and to have a sufficiently rights reserved low shear strength to enable fibre pull-out. 3, 14 In systems made by laminating either tapes or fibres separated by some crack deflecting interface, the 1 Introduction only source of toughening is crack deflection so that it is no le Previous work has demonstrated the benefits of trength That porous interlayers can deflect cracks laminating either strong ceramic layers or fibres n laminate type ceramic structures has already with crack deflecting interlayers to produce cer- been demonstrated , /The aim of this work, there amic components with enhanced resistance in fore, is to establish what levels of porosity are applications where there are high thermal loads.3,4 required to ensure crack deflection, at least for the Because the laminates are produced using ceramic situation where no residual stresses are present powders, the production method could potentially be used for many systems. However, to date the approach has only been demonstrated for a limited 2 Experimental range of systems due to the difficulty in finding uitable interfacial mater Slurries suitable for tape casting were made by To be useful. such an interfacial material must mixing the silicon carbide powder(Superior Gra chemically compatible with the laminae, so that it phite, HSC-059s)with distilled water and a dis can be both co-fired and later used at an elevated persing agent( Lignotech, Sweden, grade Wargonin emperature, and it must also reliably deflect Extra)at a concentration of 0.15% by weight of cracks. The requirement of chemical compatibility the silicon carbide and then ball milling for 24 h in suggests that both lamina and interlayer should a polyethylene jar using zirconia milling media ideally be made from the same material. This Before milling, the pH of the slurry was adjusted to 9 using ammonia solution. To produce handleable To whom correspondence should be addressed. Fax: +44. ceramic tapes, an acrylic styrene latex binder 01223-334567; e-mail: wjc1000@cus cam ac uk (Hoechst Perstorp grade Mowilith DM 765S)was 1945
1946 K. S. Blanks et al dded to the slurry and stirred for l h. the amount To investigate whether cracks could be deflected of latex polymer used was 0.3 by volume of the total at the porous interlayers, beams were cut from the solids, that is the silicon carbide and the latex. 5, 16 sintered plates approximately 0-5 mm thick, 2mm To make the pore-containing materials, poly- in breadth and 35mm long, using a diamond tetrafluoroethylene(PT F.E. ) particles with a dia- impregnated saw. These were then tested in three meter between 5 and 9 um(Goodfellow) were point flexure using a loading span of 30 mm added to the silicon carbide dispersion and gently mixed The same concentrations of dispersant and latex as above were used except that the P.T. F.E. 3 Results and discussion was included as one of the solids the volume fractions of P.T. F.E. quoted here are based on the It was found that interlayers which contained a volume of P.T. F.E. as a fraction of the volume of volume fraction of porosity of 0.34 or less, corre he P.T. F.E. and the silicon carbide together, Vst, sponding to a volume fraction of P T F E. particles and ranged between 0.35 and 0-65, using the den- of 0.45, did not reliably deflect cracks, as shown in sities of P.T. F.E. and silicon carbide as 2.20 and Fig. 2(a). It can be seen that the crack does change 3.21 Mgm. The resulting slurries were then direction somewhat, although this produces only sieved through a mesh with a fibre spacing of negligible increase in the resistance to crack 31 um to remove air bubbles growth. However, increasing the volume fraction The slurries were tape cast using a continuous of porosity due to the P T F.E. particles to 0-44 tape casting machine (Wallace Technical that is a volume fraction of P T F E. on the silicon Ceramics Inc, model tC 155)onto a polypropylene carbide of 0.55, caused the fracture behaviour to carrier tape moving at 20 mm s. This gave a total change such that extensive crack deflection occur drying time of 186s. The tapes were of a uniform red as shown in Fig. 2(b) thickness had smooth surfaces and were free of The most straightforward approach to consider visible pinholes. The gap between the doctor blade ing crack deflection at a porous interlayer and the carrier tape was 200 um and gave tapes simply treat the porous interlayer as a continuum with a thickness of approximately 100 um. The whose fracture and elastic properties are equal to sheets were then cut into squares 50x 50 mm the values obtained from bulk samples, allowing Squares of the P.T.F.E. -containing and P.T. F E- existing models for crack deflection to be used- free sheets were stacked alternately and pressed Most of these consider that crack deflection occurs together at room temperature at a pressure of when the driving force for the growth of the inter 40 MPa. Bonding at room temperature was possi facial crack equals the fracture energy of the interface ble because the, latex binder was above its glass at a lower load than that at which the driving force transition temperature of.. The resulting of the penetrating crack is equal to the fracture plates were then heated at 0.1C per min to 650 c energy of the matrix. 18,19 for 30 min under nitrogen to pyrolyse, the polymer However, it is clear that there are significant dif- and then heated under argon to 2050oC for 30 min. ferences between the way in which the crack is For material containing no added P T F.E. the observed to deflect and the situation that has been final density was 0.95 The volume fraction of pores in the green body that are caused by the added P.T. F E. particles, vg, is given by Slamovich and Lange 7as Vs 1-Vst+ Vst Pg is the volume fraction of the matrix material, in this case taken to be equal to that of the silicon carbide green body to which no P.T.F. E. has been added. If these pores are suf- ficiently large that they do not themselves sinter then they will shrink by the same amount as th surrounding matrix so that the volume fraction of pores in the body will remain constant during sin- tering. The fracture surface of a porous layer after Fig. 1. Showing the fracture surface of a porous silicon carbide sintering,containing a volume fraction of pores due porated by the addition into the tape casting slurry of a volume to the added P.T. F.E. of 0-44 is shown in Fig. fraction of P.T. F E particles on the silicon carbide of 0.5
Crack deflection in ceramic laminates using porous interlayers 1947 modelled. In particular, it is known from experi- energy, at least on the scale of the crack tip stress mental observations, supported by theoretical cal- field, is equal to that of the matrix. One might culations, that defects in an interface ahead of a therefore expect the crack to kink out of the inter- growing crack significantly affect the interfacial face immediately, as observed in the intertayer present case such defects exist in large numbe the containing the lower volume fraction of pores.In properties required for crack deflection. 20, 21 In this case ensuring that the crack travels in the For a homogeneous interface with a fracture interface means that the ligament of material nergy Ri, it has been shown that where a defect between the, crack tip and the pore ahead of it in lies in an interface ahead of a crack growing the interface must fracture, in other words through the lamina, the condition for continued crack deflection is Rig∠0.57 R、∠0 57 R where Rig is the fracture energy of the ligament of ceramic between the crack and the pore ahead of it, where Ro is the fracture energy of the lamina. Here as shown in Fig. 3. If this is correct it is clear that here, the defects sit in an interlayer, whose fracture solids, in monolithic form, is considered firy"o e. 2 the defect sits in an otherwise uniform interface the presence of the pores must somehow modi whose fracture energy is lower than that of the the fracture energy of the ligament. To examine matrix, In the experimental situation considered this idea further, the fracture behaviour of 3. 1 Fracture of porous solids Clearly, increasing the porosity reduces the amount of material to be broken and hence the amount of new surface to be created, so that, if only a single crack is growing, one might expect the fracture energy to vary according to the area fraction of ceramic material in the crack plane, as given by Rp= ro( where Rp and Ro, are the fracture energies of the porous and dense material respectively and a is the area fraction of porosity in the crack plane. If the crack grows in some random plane then the area fraction of pores is equal to the volume fraction of pores, P, giving Rp=ro(1-P) Interlayer(R) Pores 2. Showing the fracture path through a laminate made of n carbide lar separated by porous silicon carbide lay Lamina(R。) Li ers containing a volume fraction of added porosity of (a)0-34 and(b)0.44. Note that although there is some direction of the crack, there is no substantial crack Fig. 3. Showing a schematic of a deflected crack lying in a he former whilst there is extensive crack deflection in the latter
1948 K. S. Blanks et al. An expression for the toughness, T, can be green densities fall onto the same line, suggesting that obtained from this using the expression green density is unimportant, in contradictio with expressions that have been used elsewhere ER=72 fracture energy tends to be lower than would be and an appropriate expression for the Young predicted by considering the area of fracture of a modulus of the porous body, such as random crack plane through the sample, is that the crack seeks out pores, resulting in a fracture sur- Ep=E0(1-P2 face that contains a higher area fraction of pores For an ordered array of pores, there is a simply where Ep and Eo are the Young moduli of the quantified minimum in the solid area of material porous and dense materials respectively. This latter through which the crack may grow. It is known expression was chosen because it was found to that the Young modulus can be related to this describe well the Young moduli of the porous sili- minimum solid area and it would therefore be con carbide in this investigation. This gives the expected that the fracture energy would have the toughness of the porous body as same dependence on porosity. This minimum solid area and its variation with porosity has been cal Tp=T0(1-P)32 (4) culated for various different ordered arrays. Except at densities very close to the green density, it is where Tp and To are the fracture toughnesses of found that the minimum solid area can be related the porous and the ligament materials respectivel to the volume fraction of pores, P, by an expres- same form has also been derived for foams. 2 onlo where the toughness of the ligament is set equal to sion of the form25 that of the bulk material, To. An expression of the A exp-bP However, the fracture energy decreases more rapidly with increasing porosity than is predicted assuming a random crack plane, as shown in Fig 4, where A/Ao, is the fraction of the solid area com which shows data obtained from partially sintered pared with that when the body is fully dense and b alumina powders made from powder compacts is a constant which depends on the ordered array having different green densities. 4 The squares that is chosen. This expression breaks down close represent values for samples whose green density to the green density, where there is a very rapid was 0.50, whereas the circles represent samples change in the minimum solid area although there is which had a green density of 0-62. It is worth not- only a minimal change in the relative density and it ing that the data for these samples with different is for this reason that there is no apparent effect of The porous materials being studied here consi of essentially equiaxed pores in an otherwise dense ix. Following the approach the situation could be represented by ordering the 0.6 equiaxed (in this case spherical) pores and allowing the crack to grow through the plane containing the 0.4 ghest area fraction of pores, as shown in Fig. 5, which shows a planar crack growing through a 0.2 simple cubic array of pores In this case, the fraction of porosity in the crack 0:⊥⊥,,⊥111⊥⊥ plane, A, is equal to the area of a pore divided by the area of the base of the pore unit cell (the sha- Relative Density(1-P) ded square in Fig. 5). This is the minim Fig.4. Showing the relative fracture energy for samples of area of the material, 26,2/and is given by alumina made by partial sintering of green bodies with relative densities of 0-5(open circles)and 0.62(open squares). 24 Note that the rate at which the fracture energy decreases with por osity is greater than that given by eqn(3), which is represented by a dotted line. Also shown are the predicted fracture energy with porosity estimated by considering either where c the area of fracture(shown by a dashed line)or the increase in is the D is the spacing he stress intensity factor at the crack tip due to the presence The porosity, P, of the material is of nearby pores(shown by a continuous line)from eqn(5)and simply equal to the volume of a pore divided by the volume of the unit cell in Fig. 5
Crack deflection in ceramic laminates using porous interlayer 1949 The relative density of the material, (1-P), can shown in Fig. 7. It can be seen that putting a flaw therefore be written as just in front of the crack tip approximately dor the stress intensity factor at the crack tip s 4x33 (1-P) This would be seen as a reduction in the toughness 3D3 and he ence of the ligar material. The toughness of the ligament material is nd gives the fracture energy of the porous body as now given by the expression Rp=Rol1-T4 ∫3P12 The crack-flaw interaction can therefore be regar This is plotted onto Fig. 4, and it can be seen that, ded as providing an extra driving force for the despite the crudity of the approach, the agreement crack to propagate toward the flaw. This reduction with the experimental data is not unreasonable. in the toughness occurs even though the ligament is However, once the pore radius exceeds 0.5 D the made of the same material as the dense matrix pores begin to overlap. The relative density at this point is 048. At densities lower than this, eqn(5)is no longer valid because the volumes where the (a) pores overlap are not taken into account. How mary F ever, inspection of Fig. 5 shows that the area frac- tion of material in the crack plane will not reach zero until the porosity is extremely high, that is when c becomes equal to D/v2 An alternative approach is to consider the effect of the pores on the driving force of a crack growing through the porous solid. a similar problem has been addressed quantitatively by Gong and (b) Ligament intensity factor at the tip of a crack as a micro crack was moved closer to it, as shown in Fig. 6(a) Primary Crack They showed that the ratio of the stress intensity factor at the crack tip, if the flaw were not present Ko to that in the presence of the microcrack, KMa varies with the ratio of the distance of the faw Fig. 6.(a)a short flaw lying ahead of a crack as from the crack to the half-size of the flaw, d c, as considered by Gong and Horii. 28 When the flaw is close to the crack tip, that is d/ c is close to unity, the presence of the faw significantly increases the stress intensity factor at the tip of the primary crack.(b) The modification to the situation con- sidered above, where the tip of the primary crack lies at a pore and another pore lies ahead 5 Fig. 7. Showing how the normalised stress-intensity factor at Fig. 5. Showing a planar crack growing through a MA/Ko) depends on the relative distance d from Gong and Hori gts plotted are rack tip(d/ c). The po porous material containing a cubic lattice of spherical po
1950 K. S. Blanks et al This approach can be adapted if we consider the crack to grow from pore to pore observed in porous silicon nitride, so that there is a pore at the end of the crack and another a distance d ahead of it, as shown in Fig. 6(b). The sharp 06E057 crack tip and the microcrack are, therefore replaced by pores. Whilst this situation may appear °0.4 to be very different to that considered by gong and Did Not Horii. Alford et al. have shown that the strengths Deflect Deflect of alumina and titania materials containing essen L⊥_1 tially pore-shaped faws were accurately predicted 02 by assuming that the pores were sharp penny Relative Density (1-P) shaped cracks Fig. 8. Showing how the value of (KMA/Ko varies with the In eqn (4), which relates the toughness of the relative density, p of the body, that is(1-P). Crack deflection ligaments to the fracture toughness of the porous is predicted to occur where(Ko/ Kma) is less than 0.57, uivalent to a porosity of 0.37, or a relative density of 0.63 body, it was assumed that the appropriate value Aiso shown is the relative density below which no crack for the ligament toughness was that of the dense matrix material. That is where there is no interac which extensive deflection was obtained(corresponding to tion between the crack and the pores. However, as P=0.44). It can be seen that there is good agreement between the observations and the predictions the pores become closer to the tip of the main crack the apparent toughness of the ligament is reduced as explained above, giving the toughness good agreement not only with the previous of the body as approach but also with the experimental values 7=7(ku=P 3.2 Crack deflection at porous interlayers For a crack to continue growing in the interface, as shown in Fig 3, then there must some interaction where Ko/ KMA depends on the ratio of pore spa- between the growing (interfacial) crack and the cing to pore radius(d/c),as defined in Fig. 6(b). pores ahead of it, which lowers the toughness, and This gives the fracture energy of a porous body as hence the fracture energy of the ligament between the crack and the nearest interfacial pore R≈R(Ko)(1-P The toughness of the ligament, Tlig, is given in eqn(6)and assuming that the modulus of the liga ment material is not dependent on the direction in The crack-pore interaction therefore reduces the which the crack grows, the ratio of the fracture fracture energy of the material, as might be expec- energies is given by ted. As the body with the pores arranged in a sim- ple cubic array gave good agreement with the RI fracture energy, it is therefore assumed that this R KMA gives a good approximation to the interpore spa cings seen by the crack as it fluctuates through the so, from eqn(1), crack deflection will occur if array of pores For the cubic array of spherical pores shown in K Fig. 5 the volume fraction of pores, P, is related to <0·57 MA the spacing and size of the pores by the expression The corresponding value of d/c(expressed in d/4x)\1/3 of the volume of porosity, P)which will just deflection, can be obtained from Fig. 8. It is pre- given value of P to be estimated, which can in turn range observed experimentally hieorovided the dicted that crack deflection will occu This allows, the appropriate value of d/c for a porosity is greater than 0-37 is within the be used to determine the relevant values of Ko/KMA using Fig. 7. Substituting P and the appropriate value of Ko/ KMa allows the fracture 4 Conclusions energy of the porous body, Rp, to be determined.A comparison of this approach with the other values A simple model has been presented which predicts shown in Fig. 4, where it can be seen to give the fracture behaviour of porous solids. It is shown
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