《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_Al2O3-Ni-thermal stress.pdf_大学文库

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

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 4-point-bend sample Tensile sample Fig. 7. Sections used to extract the opening displacement samples(Fig. 7). The displacement of each point along these sections is correlated from the dic data with tIme There are many problems associated with measuring a full COd profile. There have been a number of attempts to measure COD for ceramic/metal composite laminates using different techniques. All of which requires the specific pre-determined, well-defined crack position to measure the COD [14, 15]. Moreover, roughness of the crack edges can create enormous errors in the measurements(especially in the near-tip region)[14]. The methodology adopted in extracting the COd is not based on guessing but rather a well-defined fitting procedure of the displacement profile of the opposite face of the crack. This technique does not require a pre- determined, well-defined crack position. The displacement of the opposite face of the crack MUSt be parallel (due to symmetry) and if fitting results in a different line slope(non-parallel lines)this is considered to be one contribution to the error bars were the other contribution comes from the residual of fitting. The judgment is simply made by taking the difference in the vertical axis value as the COd independent on where the absolute crack position Is. From one image, the displacement for one section in the y-direction is plotted, versus, the y-position(see ig. 8). Then the opening displacement is the vertical separation between the two lines. From a series of such figure, the evolution of opening displacement with time is determined. It is important to emphasize here that in the constrained sandwich test, only a single ligament is under test and the crack face will almost undergo rigi body motion as the load is exclusively carried by the metal ligament and the opening displacement is indepen- dent of the position of the section(as long as it is away from the tip) and the four different sections used to extract the opening displacement are expected to give the same results Close to the crack tip for low stiffness materials(not herein as E= 303 GPa for alumina) the constraining material near the ligament might deform iving a different measured opening displacement. It is important to note this is not an actual crack but rather a constrained metal layer(ligament). Only a small portion of the metal deforms inducing a high tri-axial stress state characterizing this behavior [10, 11, 28, 29 The stress developed in two Ni layer thicknesses (load from the load cell divided by the initial cross-section trea of the ligament) and the calculated opening displacement from the image analysis are now calculated

samples (Fig. 7). The displacement of each point along these sections is correlated from the DIC data with time. There are many problems associated with measuring a full COD profile. There have been a number of attempts to measure COD for ceramic/metal composite laminates using different techniques. All of which requires the specific pre-determined, well-defined crack position to measure the COD [14,15]. Moreover, roughness of the crack edges can create enormous errors in the measurements (especially in the near-tip region) [14]. The methodology adopted in extracting the COD is not based on guessing but rather a well-defined fitting procedure of the displacement profile of the opposite face of the crack. This technique does not require a predetermined, well-defined crack position. The displacement of the opposite face of the crack MUST be parallel (due to symmetry) and if fitting results in a different line slope (non-parallel lines) this is considered to be one contribution to the error bars were the other contribution comes from the residual of fitting. The judgment is simply made by taking the difference in the vertical axis value as the COD independent on where the absolute crack position is. From one image, the displacement for one section in the y-direction is plotted, versus, the y-position (see Fig. 8). Then the opening displacement is the vertical separation between the two lines. From a series of such figure, the evolution of opening displacement with time is determined. It is important to emphasize here that in the constrained sandwich test, only a single ligament is under test and the crack face will almost undergo rigid body motion as the load is exclusively carried by the metal ligament and the opening displacement is independent of the position of the section (as long as it is away from the tip) and the four different sections used to extract the opening displacement are expected to give the same results. Close to the crack tip for low stiffness materials (not herein as E = 303 GPa for alumina) the constraining material near the ligament might deform giving a different measured opening displacement. It is important to note this is not an actual crack but rather a constrained metal layer (ligament). Only a small portion of the metal deforms inducing a high tri-axial stress state characterizing this behavior [10,11,28,29]. The stress developed in two Ni layer thicknesses (load from the load cell divided by the initial cross-section area of the ligament) and the calculated opening displacement from the image analysis are now calculated. Fig. 7. Sections used to extract the opening displacement. 576 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 3 Summary of the measured yield stress for different samples Metal thickness. mm As received. MPa HT(unconstrained), MPa 440 COD Least squares fitted lines 002 y-position along the section, mm Fig. 10. Extracting COD crack. As the crack plane is a symmetry axis, the absolute displacement profile from the opposite sides of the crack face should match. In other word, fitting the displacement extracted from the DIC should result in par allel lines were vertical difference correspond to the opening displacement. The opening displacement(the average vertical separation between the lines) was fitted to the Cod profiles(Fig. 10). A standard deviation on the order of 3 x 10-mm was estimated resulting in a10% error for a Cod=0.003 mm suggesting a rea- sonable accuracy The COd associated with crack initiation was calculated for each crack size and Fig. ll shows its profile via experiment and fitted data. The measured values on approaching the crack tip are within the resolution of the experimental setup. The latter can be increased by enhancing the image resolution i.e using a smaller field-of- view in the crack zone, however, for the present study, a full CoD profile is the objective 3. 2. Finite-element modeling of the Cod profiles in NilAl2O3 laminates A finite-element model was used to generate CoD profiles for different crack sizes in the multi-layer Ni/Al2O3 laminates. Commercial software+ was used, wherein a three-dimensional quarter sample(due to symmetry) was modeled. An eight-node quadrilateral element was used and the loading rollers were modeled ia shell elements. Al2O3 is assumed elastic, nickel elastic-perfectly plastic, and the loading rollers were mod eled as rigid 2 Ni ligaments bridging the crack are introduced as non-linear springs attached across each bridged layer he latter was taken as the response of a single ligament determined experimentally 3 Matlab r133. Mathworks Inc 4 LSDYNA 970. LSTC

crack. As the crack plane is a symmetry axis, the absolute displacement profile from the opposite sides of the crack face should match. In other word, fitting the displacement extracted from the DIC should result in parallel lines were vertical difference correspond to the opening displacement. The opening displacement (the average vertical separation between the lines)3 was fitted to the COD profiles (Fig. 10). A standard deviation on the order of 3 · 103 mm was estimated resulting in 10% error for a COD = 0.003 mm suggesting a reasonable accuracy. The COD associated with crack initiation was calculated for each crack size and Fig. 11 shows its profile via experiment and fitted data. The measured values on approaching the crack tip are within the resolution of the experimental setup. The latter can be increased by enhancing the image resolution i.e.; using a smaller field-ofview in the crack zone, however, for the present study, a full COD profile is the objective. 3.2. Finite-element modeling of the COD profiles in Ni/Al2O3 laminates A finite-element model was used to generate COD profiles for different crack sizes in the multi-layer Ni/Al2O3 laminates. Commercial software4 was used, wherein a three-dimensional quarter sample (due to symmetry) was modeled. An eight-node quadrilateral element was used and the loading rollers were modeled via shell elements. Al2O3 is assumed elastic, nickel elastic-perfectly plastic, and the loading rollers were modeled as rigid. Ni ligaments bridging the crack are introduced as non-linear springs attached across each bridged layer. The latter was taken as the response of a single ligament determined experimentally. Table 3 Summary of the measured yield stress for different samples Metal thickness, mm Constrained, MPa As received, MPa HT (unconstrained), MPa 0.125 440 185 62 0.25 178 215 62 Fig. 10. Extracting COD. 3 Matlab R133, Mathworks Inc. 4 LSDYNA 970, LSTC. 578 W. Mekky, P.S. Nicholson / Engineering Fracture Mechanics 73 (2006) 571–582

《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Al2O3-Ni-thermal stress

《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_Al2O3-Ni-thermal stress