Availableonlineatwww.sciencedirect.com SCIENCE DIRECT. Engineering Fracture Mechanics ELSEVIER Engineering Fracture Mechanics 73(2006)571-582 www.elsevier.com/locatelengfracmech The fracture toughness of Ni/Al2O3 laminates by digital image correlation I: Experimental crack opening displacement and R-curves Waleed Mekky, Patrick S. Nicholson * I Ceramic Engineering Research Group, Department of Materials Science and Engineering, McMaster Unicersity. Hamilton. Ont. Canada las 4L7 Received 22 February 2005: received in revised form 17 June 2005: accepted 18 September 2005 Available online 23 November 2005 Abstract D he crack opening displacement of laminates made of alumina/nickel was measured using digital image correlation C). The crack opening displacements were validated with a finite-element model that uses the characteristic bridg- ing-stress bridging-displacement relationship obtained experimentally by testing a constrained nickel sandwich in tension. The method is a simple accurate way of measuring the crack opening displacement( CoD) in ceramic/metal laminates o 2005 Elsevier Ltd. All rights reserved. Keywords: Digital image correlation; Crack opening displacement; Fracture: Ceramic/metal laminates 1. Introduction Ceramic/metal laminates are potential candidates for applications requiring enhanced fracture-, and dam- age-, tolerance properties. Incorporation of layers of ductile phase greatly enhances composite fracture tough- ness by bridging a crack in the brittle phase [1-3] which results in R-curve behavior. The geometrical dependence of the latter leads to complexities in characterizing the fracture resistance and associated tough ening mechanisms [4, 5]. Therefore, the geometry-independent, material characteristics which give rise to the R-curve must be determined [6]. With ductile-phase bridging, the information required is the constitutive rela tion between the bridging stress, Obr, and the crack opening displacement(CoD), 8, i.e. the description of bridging-stress evolution as a function of the COD, abr(O)[7-9 ea For a single metal ligament constrained by ceramic, this relation is not straight-forward nor available cept for few cases in the literature [10, 11, 2 Corresponding author. Tel. +l 905 525 9140/27249: fax: +l 905 528 9295. -mail address: nichols(@mcmaster. ca(PS Nicholson) Fellow of the American Ceramic Society 0013-7944S.see front matter 2005 Elsevier Ltd. All rights reserved doi: 10. 1016/j-engfracmech 2005.09.005
The fracture toughness of Ni/Al2O3 laminates by digital image correlation I: Experimental crack opening displacement and R-curves Waleed Mekky, Patrick S. Nicholson *,1 Ceramic Engineering Research Group, Department of Materials Science and Engineering, McMaster University, Hamilton, Ont., Canada L8S 4L7 Received 22 February 2005; received in revised form 17 June 2005; accepted 18 September 2005 Available online 23 November 2005 Abstract The crack opening displacement of laminates made of alumina/nickel was measured using digital image correlation (DIC). The crack opening displacements were validated with a finite-element model that uses the characteristic bridging-stress bridging-displacement relationship obtained experimentally by testing a constrained nickel sandwich in tension. The method is a simple, accurate way of measuring the crack opening displacement (COD) in ceramic/metal laminates. 2005 Elsevier Ltd. All rights reserved. Keywords: Digital image correlation; Crack opening displacement; Fracture; Ceramic/metal laminates 1. Introduction Ceramic/metal laminates are potential candidates for applications requiring enhanced fracture-, and damage-, tolerance properties. Incorporation of layers of ductile phase greatly enhances composite fracture toughness by bridging a crack in the brittle phase [1–3] which results in R-curve behavior. The geometrical dependence of the latter leads to complexities in characterizing the fracture resistance and associated toughening mechanisms [4,5]. Therefore, the geometry-independent, material characteristics which give rise to the R-curve must be determined [6]. With ductile-phase bridging, the information required is the constitutive relation between the bridging stress, rbr, and the crack opening displacement (COD), d, i.e. the description of bridging-stress evolution as a function of the COD, rbr(d) [7–9]. For a single metal ligament constrained by ceramic, this relation is not straight-forward nor available except for few cases in the literature [10,11,2]. 0013-7944/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2005.09.005 * Corresponding author. Tel.: +1 905 525 9140/27249; fax: +1 905 528 9295. E-mail address: nicholsn@mcmaster.ca (P.S. Nicholson). 1 Fellow of the American Ceramic Society. Engineering Fracture Mechanics 73 (2006) 571–582 www.elsevier.com/locate/engfracmech
w. Mekky, P S. Nicholson Engineering Fracture Mechanics 73(2006)571-582 CCD Camera Fig. 1. Digital image correlation setup. Modeling the R-curve behavior of metal/ceramic laminates is a challenge where two approaches can be used (1) The R-curve and d(x, a)can be calculated from the bridging-stress relation, obr(O), measured in a single ligament test [1, 121. (2)The bridging-stress relation, Obr(0), (and consequently the r-curve) can be calculated from the measured COD,(x,a)[13,14 Measuring the COd is complicated and, as absolute values get smaller, special instrumentation is needed For a ceramic or ceramic-matrix composite, scanning electron microscopy, fluorescence spectroscopy and AFM have been utilized [14, 15]. As high resolution is involved, these techniques require specific sample pre- paration and special care to determine correct values of displacement. The maximum opening displacement for ceramic/metal laminates is z an order-of-magnitude larger than ceramics which renders measurement less complicated One promising methodology for COd determination is the digital image correlation technique [16-22 Two images acquired at different states of stress are compared, one before deformation, the other after(named referenceand 'deformed,, images a pattern of any shape with good contrast is applied to the specimen surface and deforms therewith. The test sample is viewed with a high-resolution CCD camera(Fig. 1), and as the crack propagates, the deforma- tion(and displacement) during loading are evaluated via digital image correlation. Initial image processing defines the set of correlation areas across the viewed area thus continuous measurements can be made to determine the extent of cracking, i.e.; the test is not required to stop, or even hold. This paper describes he DiC results and the R-curve generated. A companion paper covering the modeling of R-curve behavior based on bridging-stress estimations from COD follows 2. Experimental Ceramic/metal laminates of alumina and nickel were fabricated by diffusion bonding. 25.4 x 25.4 mm- (AD96 mid-film substrates) of alumina were obtained from CoorsTek ( Colorado, USA). Nickel sheets (cold-rolled, annealed) were obtained from Good Fellow Metal Ltd(Cambridge, UK). The range of thick nesses used are listed in Table I and the mechanical properties of the supplied alumina in Table 2 Two tests were conducted. The first, uniaxial tension of a bonded Ni layer in a sandwich of two alumina plates 2.54 mm thickness each. This Ni is plastically constrained and the characteristic bridging-stress, bridg- ing-displacement relation, d8), is obtained. Two thicknesses of Ni were used in this test, 0.125 and 0.250 mm. The second test was, four-point bend of multi-layer laminate. The latter was fabricated to study laminate R-curve behavior. Eight layers of Al2O3 alternated seven layers of Ni, alumina being top and bottom Metal layers were cut into squares 25.4 mm from 150 x 150 cm sheets side and ultrasonically cleaned in eth anol for 30 min then acetone for I h. The Ni and Al2O3 layers for the two different set of samples were placed ide a graphite die and hot pressed at 15 MPa and 1200C in helium
Modeling the R-curve behavior of metal/ceramic laminates is a challenge where two approaches can be used: (1) The R-curve and d(x,a) can be calculated from the bridging-stress relation, rbr(d), measured in a singleligament test [11,12]. (2) The bridging-stress relation, rbr(d), (and consequently the R-curve) can be calculated from the measured COD, d(x,a) [13,14]. Measuring the COD is complicated and, as absolute values get smaller, special instrumentation is needed. For a ceramic or ceramic–matrix composite, scanning electron microscopy, fluorescence spectroscopy and AFM have been utilized [14,15]. As high resolution is involved, these techniques require specific sample preparation and special care to determine correct values of displacement. The maximum opening displacement for ceramic/metal laminates is ’ an order-of-magnitude larger than ceramics which renders measurement less complicated. One promising methodology for COD determination is the digital image correlation technique [16–22]. Two images acquired at different states of stress are compared, one before deformation, the other after (named reference and deformed, images). A pattern of any shape with good contrast is applied to the specimen surface and deforms therewith. The test sample is viewed with a high-resolution CCD camera (Fig. 1), and as the crack propagates, the deformation (and displacement) during loading are evaluated via digital image correlation. Initial image processing defines the set of correlation areas across the viewed area. Thus continuous measurements can be made to determine the extent of cracking, i.e.; the test is not required to stop, or even hold. This paper describes the DIC results and the R-curve generated. A companion paper covering the modeling of R-curve behavior based on bridging-stress estimations from COD follows. 2. Experimental Ceramic/metal laminates of alumina and nickel were fabricated by diffusion bonding. 25.4 · 25.4 mm2 (AD96 mid-film substrates) of alumina were obtained from CoorsTek (Colorado, USA). Nickel sheets (cold-rolled, annealed) were obtained from GoodFellow Metal Ltd. (Cambridge, UK). The range of thicknesses used are listed in Table 1 and the mechanical properties of the supplied alumina in Table 2. Two tests were conducted. The first, uniaxial tension of a bonded Ni layer in a sandwich of two alumina plates 2.54 mm thickness each. This Ni is plastically constrained and the characteristic bridging-stress, bridging-displacement relation, r(d), is obtained. Two thicknesses of Ni were used in this test, 0.125 and 0.250 mm. The second test was, four-point bend of multi-layer laminate. The latter was fabricated to study laminate R-curve behavior. Eight layers of Al2O3 alternated seven layers of Ni, alumina being top and bottom. Metal layers were cut into squares 25.4 mm from 150 · 150 cm sheets side and ultrasonically cleaned in ethanol for 30 min then acetone for 1 h. The Ni and Al2O3 layers for the two different set of samples were placed inside a graphite die and hot pressed at 15 MPa and 1200 C in helium. Fig. 1. Digital image correlation setup. 572 W. Mekky, P.S. Nicholson / Engineering Fracture Mechanics 73 (2006) 571–582
w. Mekky, P S. Nicholson Engineering Fracture Mechanics 73(2006)571-582 Table I Different samples prepared for the analysis Al,O3 thickness tc, mm Ni thickness Thickness ratio, t/tm 0.1 0.635 2.54 0.254 Table 2 Mechanical properties of AD96 AL,O Density(p), g/cm3' Average grain size, um Flexural strength(MOR), MPa tic modulus GPa 303 sons ratio(v) Hardness GPa Tensile strength, MPa 221 Fracture toughness(Ki). MPa m"/2 Edges of the final bonded samples were removed(<I mm from all sides )and specimens were sliced out each with 4 mm thickness (five specimen from each diffusion bonded sample prepared) The sandwich Al2O3/Ni/AlO3 tensile test samples were double notched through the Al2O3 with a diamond blade(102 x 0.3 x 12.7 mm). Notched samples were tested in an Instron Servo Hydraulic machine and a sharp crack was then extended from the root of each notch by carefully loading the sample The multi-layered laminates were notched through one metal layer, the notch root residing in the third (alu- mina)layer. Bending prior to testing generated a sharp crack to the second metal layer so the initial (notch size) to(sample width) was ao/w=0.36. A four point bend fixture was employed with 10 mm inner-,and 20 mm outer, spans(Fig. 2). Loading rollers were used to minimize contact frication while contact damage is not expected because of the high compressive strength of alumina(see Table 2) Tensile samples were aligned with one side facing the CCD camera(Vosskuhler 1300F) This ensured mea surement of opening displacement in the Ni ligament All samples were sprayed with white and black ink to produce, 'dots, to act as features easily correlated uring the deformation. The field of view employed in the analysis was 5x 5 mm* with a recording resolution of 1000 x 1000 pixels- and image displacement accuracy of 0.01 pixels leading to a best achievable accuracy of Fig. 2. Four point-bend sample (all dimensions are +0.05 mm)
Edges of the final bonded samples were removed (<1 mm from all sides) and specimens were sliced out each with 4 mm thickness (five specimen from each diffusion bonded sample prepared). The sandwich Al2O3/Ni/Al2O3 tensile test samples were double notched through the Al2O3 with a diamond blade (102 · 0.3 · 12.7 mm). Notched samples were tested in an Instron Servo Hydraulic machine and a sharp crack was then extended from the root of each notch by carefully loading the sample. The multi-layered laminates were notched through one metal layer, the notch root residing in the third (alumina) layer. Bending prior to testing generated a sharp crack to the second metal layer so the initial (notch size) to (sample width) was a0/w = 0.36. A four point bend fixture was employed with 10 mm inner-, and 20 mm outer-, spans (Fig. 2). Loading rollers were used to minimize contact frication while contact damage is not expected because of the high compressive strength of alumina (see Table 2). Tensile samples were aligned with one side facing the CCD camera (Vossku¨hler 1300F). This ensured measurement of opening displacement in the Ni ligament. All samples were sprayed with white and black ink to produce, dots, to act as features easily correlated during the deformation. The field of view employed in the analysis was 5 · 5 mm2 with a recording resolution of 1000 · 1000 pixels2 and image displacement accuracy of 0.01 pixels leading to a best achievable accuracy of Table 1 Different samples prepared for the analysis Al2O3 thickness tc, mm Ni thickness tm, mm Thickness ratio, tc/tm 0.635 0.125 5.08 0.381 0.125 3.04 0.254 0.125 2.03 0.635 0.25 2.54 0.381 0.25 1.52 0.254 0.25 1.01 Table 2 Mechanical properties of AD-96 Al2O3 Property, units Value Density (q), g/cm3 3.72 Average grain size, lm 6 Flexural strength (MOR), MPa 358 Elastic modulus, GPa 303 Poissons ratio (m) 0.21 Compressive strength, GPa 2068 Hardness, GPa 11.5 Tensile strength, MPa 221 Fracture toughness (KIc), MPa m1/2 4–5 Fig. 2. Four point-bend sample (all dimensions are ±0.05 mm). W. Mekky, P.S. Nicholson / Engineering Fracture Mechanics 73 (2006) 571–582 573
574 w. Mekky, P S. Nicholson Engineering Fracture Mechanics 73(2006)571-582 75 Φ=10mm 75 mm Fig 3. Dimensions of the unconstrained metal tensile test sample 5x 10m. Two subset sizes were used in the analysis namely 9x9 and 15 x 15 pixels with a subset spacing anging from 5 to 9 pixels The unconstrained yield stress of Ni was determined in tension for as-received and for samples subjected to the same heating cycle as used in the hot pressing of the laminates. Dog-bone tensile samples were machined from the as-received Ni sheets(0. 125 mm and 0.25 mm thickness)and Fig 3 shows the dimensions thereof. a The cross-head displacement employed was 0.01 mm/min and the average image rate was 1/0.2 s. This rate es the best combination of slow-loading and fast-image capture As the crack is observed from the surface and reaches the next metal layer, it is always true that inside the ample the crack tip touches the metal layer and, due to the high constraint thereat small scale yielding con- ditions apply and the crack front is assumed a line. This enables the crack length(a), to be calculated from mage analysis as tunneling effect is insignificant [23, 24]and the corresponding critical load (P), from the load cell output, i.e. KR BV亓(a/) where B is sample thickness, Wis sample width and fa/w) is a dimensionless function can be found elsewhere for four-point bend sample [25]. R-curves were calculated from KR results using Eq (1) 3. Results and discussion Careful processing of samples is essential to avoid any art effects that may develop as a result from unde sired defects. One major problem is the edge cracking that arises from residual thermal stresses developing during cooling from the bonding temperature. These stresses are maximum at the sample edges leading to the development of cracks or partial debonding along the interface. Taking that into account, the alumina used is a fully sintered plate and the processing pressure during bonding is 15 MPa(well below the fracture stress of alumina in compression(or tension))cracking in alumina layers is impracticable. Moreover, this load was applied at the maximum temperature(1200oC) to insure better bonding. Also to avoid extensive thermal residual stresses, samples were slow cooled. Then its edges were shaved before cutting or machining. These precautions were taken even though no edge cracking was observed The SEM photograph of a samples after bending(Fig. 4)clearly shows a single, macroscopic, crack. Such was observed for samples with metal/ceramic ratio 2.5 i. e(Im/te <2.5)[23, 24]. The latter is an important requisite for a valid R-curve No debonding occurs suggesting the interface is strongly bonded(Fig. 5)[26,27]. Back-scatter images of Ni/Al2O3 in Fig. 6 shows that reaction products exist at the interface with an average thickness <0.5 um 3. 1. The digital image correlation technique (DIC) Commercial software, was used to analyze the DIC images. 0.05 mm-separation sections (lines )were con- structed along the crack profile in the four-point bend and two along each notch of the double-edge, tensile, ARAMIS. Trilion Inc
5 · 108 m. Two subset sizes were used in the analysis namely 9 · 9 and 15 · 15 pixels2 with a subset spacing ranging from 5 to 9 pixels. The unconstrained yield stress of Ni was determined in tension for as-received and for samples subjected to the same heating cycle as used in the hot pressing of the laminates. Dog-bone tensile samples were machined from the as-received Ni sheets (0.125 mm and 0.25 mm thickness) and Fig. 3 shows the dimensions thereof. The cross-head displacement employed was 0.01 mm/min and the average image rate was 1/0.2 s. This rate gives the best combination of slow-loading and fast-image capture. As the crack is observed from the surface and reaches the next metal layer, it is always true that inside the sample the crack tip touches the metal layer and, due to the high constraint thereat small scale yielding conditions apply and the crack front is assumed a line. This enables the crack length (a), to be calculated from image analysis as tunneling effect is insignificant [23,24] and the corresponding critical load (P), from the load cell output, i.e.; KR ¼ P B ffiffiffiffiffi Wp f ða=W Þ ð1Þ where B is sample thickness, W is sample width and f(a/W) is a dimensionless function can be found elsewhere for four-point bend sample [25]. R-curves were calculated from KR results using Eq. (1). 3. Results and discussion Careful processing of samples is essential to avoid any art effects that may develop as a result from undesired defects. One major problem is the edge cracking that arises from residual thermal stresses developing during cooling from the bonding temperature. These stresses are maximum at the sample edges leading to the development of cracks or partial debonding along the interface. Taking that into account, the alumina used is a fully sintered plate and the processing pressure during bonding is 15 MPa (well below the fracture stress of alumina in compression (or tension)) cracking in alumina layers is impracticable. Moreover, this load was applied at the maximum temperature (1200 C) to insure better bonding. Also to avoid extensive thermal residual stresses, samples were slow cooled. Then its edges were shaved before cutting or machining. These precautions were taken even though no edge cracking was observed. The SEM photograph of a samples after bending (Fig. 4) clearly shows a single, macroscopic, crack. Such was observed for samples with metal/ceramic ratio < 2.5 i.e. (tm/tc < 2.5) [23,24]. The latter is an important requisite for a valid R-curve. No debonding occurs suggesting the interface is strongly bonded (Fig. 5) [26,27]. Back-scatter images of Ni/Al2O3 in Fig. 6 shows that reaction products exist at the interface with an average thickness < 0.5 lm. 3.1. The digital image correlation technique (DIC) Commercial software,2 was used to analyze the DIC images. 0.05 mm-separation sections (lines) were constructed along the crack profile in the four-point bend and two along each notch of the double-edge, tensile, Fig. 3. Dimensions of the unconstrained metal tensile test sample. 2 ARAMIS, Trilion Inc. 574 W. Mekky, P.S. Nicholson / Engineering Fracture Mechanics 73 (2006) 571–582
w. Mekky, P S. Nicholson Engineering Fracture Mechanics 73(2006)571-582 Nickel macroscopic crack propagating within the laminate Nickel Alumina g. 5. Crack impinging on the interface with no debonding ALO N Fig. 6. Back-scattering image of the interface formed between Ni and Al2O3
Fig. 4. Single macroscopic crack propagating within the laminate. Fig. 5. Crack impinging on the interface with no debonding. Fig. 6. Back-scattering image of the interface formed between Ni and Al2O3. W. Mekky, P.S. Nicholson / Engineering Fracture Mechanics 73 (2006) 571–582 575