《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-SiC-1

Materials Processing Technology ELSEVIER Journal of Materials Processing Technology 155-156(2004)1986-1994 www.elsevier.com/locate/jmatprotec The low velocity impact loading of Al2O3/SiC whisker reinforced ceramic composit Khaled A. Al-Dheylan King Fahad University of petroleum and Minerals, Saudi arabia Abstract Ceramic composite materials possess both low toughness and low impact resistance. However, the incorporation of ceramic whiskers ito the microstructure of ceramic matrix has been shown to produce a ceramic composite with improved toughness and greater strength. This paper studies both experimentally and theoretically the dynamic behavior of SiCw/AlO, ceramic composites under low velocity pact loading. The main objective of this paper is to determine the effects of dynamic flexural stresses on impact resistance, failure modes nd toughening mechanisms of whisker-reinforced composites. To accomplish this objective, several samples of this composite material using different SiC whisker volume fractions were designed and fabricated, and then tested at low-velocity impact loading. A theoretical low impact velocity was formulated, and its predictions are compared to impact test results. In addition, correlations between impact test results and these composites material properties are also included in this study C 2004 Elsevier B. v. All rights reserved Keywords: Ceramic composites; Low-velocity, Impact; Al2O3/SiC 1. Introduction tal effect is usually attributed to processing defects [1] Re- ported that improper control of whisker/matrix interfaces in In recent years, advanced ceramic composite materials whisker reinforced ceramics, results in failure to produce en- have been a real material option in many structural applica- hanced toughening of these composites [2]. Suggested that tions. However, applications for these composites are lim- the increase in fracture toughness of the SiCw/Al2O3 com- ted because these composites are brittle, difficult to process, posite was mainly due to crack deflection by SiC whiskers and exhibit both low toughness and low impact resistance. with some whisker pullout limited to one or two whisker In many applications where ceramic composites must be diameters. They added that the greatest increase in tough used as structural components, severe loading rates, such as ness occurs when the crack plane is perpendicular to the object impact or tool dropping, can cause crack initiation, whisker axis. Whisker pullout takes place when the stress rapid crack propagation, and fracture. In order to prevent transferred to the whisker during fracture of the matrix is ential o phic failure in these structural components, it is less than the fracture strength of the whisker, generating a essential for us to obtain new information characterizing the shear strength greater than the interfacial shear strength of dynamic behavior of these composites, so that their energy the whisker-matrix interface absorption capabilities can be established Other researchers noted that toughness in SiCw/AlO Many researchers in the past focused on the incorpora- opposites may be increased by crack bridging [3].When tion of ceramic whiskers and fibers into the microstructure a crack propagates in the matrix without damaging intact of the ceramic matrix to produce a composite with improve whiskers these whiskers bridge the crack behind the crack mechanical properties. A newly developed ceramic compos- tup. As the whisker-matrix interface debonds, the crack tup ite, which has received wide attention, is designed by in- pproaches the interface and whisker bridging occurs orporating SiC whiskers into the microstructure of Al2O3 Under low-velocity impact, both the geometry of the matrix. In cases where whisker additions result in decrease entire structure and the material properties play a sig- in fracture stress of SiCw/Al2O3 composites, the detrimen- nificant role in the response of the structure. As impact velocity increases, the response becomes more localized (this is especially true for impact by light projectiles) and E-mail address: dheylan @kfupm.edu. sa(KA. Al-Dheylan) is more affected by the composition of the material near front matter c 2004 Elsevier B V. All rights reserved doi:10.1016 matprotec2004.04.398

Journal of Materials Processing Technology 155–156 (2004) 1986–1994 The low velocity impact loading of Al2O3/SiC whisker reinforced ceramic composite Khaled A. Al-Dheylan King Fahad University of Petroleum and Minerals, Saudi Arabia Abstract Ceramic composite materials possess both low toughness and low impact resistance. However, the incorporation of ceramic whiskers into the microstructure of ceramic matrix has been shown to produce a ceramic composite with improved toughness and greater strength. This paper studies both experimentally and theoretically the dynamic behavior of SiCw/Al2O3 ceramic composites under low velocity impact loading. The main objective of this paper is to determine the effects of dynamic flexural stresses on impact resistance, failure modes, and toughening mechanisms of whisker-reinforced composites. To accomplish this objective, several samples of this composite material using different SiC whisker volume fractions were designed and fabricated, and then tested at low-velocity impact loading. A theoretical solution to the transverse impact problem of whisker-reinforced ceramic composite plates by striking these plates with solid projectiles, at low impact velocity was formulated, and its predictions are compared to impact test results. In addition, correlations between impact test results and these composites’ material properties are also included in this study. © 2004 Elsevier B.V. All rights reserved. Keywords: Ceramic composites; Low-velocity; Impact; Al2O3/SiC 1. Introduction In recent years, advanced ceramic composite materials have been a real material option in many structural applica￾tions. However, applications for these composites are lim￾ited because these composites are brittle, difficult to process, and exhibit both low toughness and low impact resistance. In many applications where ceramic composites must be used as structural components, severe loading rates, such as object impact or tool dropping, can cause crack initiation, rapid crack propagation, and fracture. In order to prevent such catastrophic failure in these structural components, it is essential for us to obtain new information characterizing the dynamic behavior of these composites, so that their energy absorption capabilities can be established. Many researchers in the past focused on the incorpora￾tion of ceramic whiskers and fibers into the microstructure of the ceramic matrix to produce a composite with improved mechanical properties. A newly developed ceramic compos￾ite, which has received wide attention, is designed by in￾corporating SiC whiskers into the microstructure of Al2O3 matrix. In cases where whisker additions result in decrease in fracture stress of SiCw/Al2O3 composites, the detrimen￾E-mail address: dheylan@kfupm.edu.sa (K.A. Al-Dheylan). tal effect is usually attributed to processing defects [1]. Re￾ported that improper control of whisker/matrix interfaces in whisker reinforced ceramics, results in failure to produce en￾hanced toughening of these composites [2]. Suggested that the increase in fracture toughness of the SiCw/Al2O3 com￾posite was mainly due to crack deflection by SiC whiskers, with some whisker pullout limited to one or two whisker diameters. They added that the greatest increase in tough￾ness occurs when the crack plane is perpendicular to the whisker axis. Whisker pullout takes place when the stress transferred to the whisker during fracture of the matrix is less than the fracture strength of the whisker, generating a shear strength greater than the interfacial shear strength of the whisker–matrix interface. Other researchers noted that toughness in SiCw/Al2O3 composites may be increased by crack bridging [3]. When a crack propagates in the matrix without damaging intact whiskers, these whiskers bridge the crack behind the crack tup. As the whisker–matrix interface debonds, the crack tup approaches the interface and whisker bridging occurs. Under low-velocity impact, both the geometry of the entire structure and the material properties play a sig￾nificant role in the response of the structure. As impact velocity increases, the response becomes more localized (this is especially true for impact by light projectiles) and is more affected by the composition of the material near 0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.matprotec.2004.04.398

K.A. Al-Dheylan/ournal of Materials Processing Technology 155-156 (2004)1986-1994 the impact center than the geometry of the whole structure samples of silicon carbide whisker(SiCw)alumina matrix (Al2O3) ceramic composites were designed and fabricated Because ceramic materials are inherently brittle, with using different SiC whisker volume fractions; these ceramic relatively low resistance to crack extension originating at composites were then subjected to low velocity impact, and pre-existing defects, energy release in ceramics is more the damage sustained was quantified and assessed likely achieved through the formation of fracture surfaces rather than through plastic or viscoelastic processes, as ompared to the more ductile materials of similar strength 2. Experimental set-up and procedures levels 5]. Once a crack starts to propagate under the influ- ence of a transient load, crack branching often takes place The following materials were used to produce SiCw/Al2O3 Cracks branch in order to dissipate the excess energy caused ceramic composite samples by a rapid energy release rate exceeding the rate of surface energy absorbed by a single crack SiC whisker: beta phase(cubic) with average diameters When thin monolithic ceramic structures are subjected to of0.3-1.0um. transverse,low-velocity impacts by rigid spherical projec- 0.05% Mgo Alumina powder(Al2O3): high purity 99.95% alumina; ain ave tiles, local effects caused by local loading may eventually ge size of 0.5 um; average surface area of 6.3m/ be small. Therefore, the response of the ceramic material. WG-300: SiCw/AlO powder: 33 vol. SiC(ACMC to the global dynamic bending of the structure becomes the limiting factor in determining its impact strength. However, Whiskers): 67 vol. Al2O3(Reynolds matrix not all of the impact energy given up by the projectile is SiCw/Al2O3 ceramic composite samples were manufactured converted into bending energy of the specimen [6]. Ana- using tape casting and hot pressing, for the tape-cast spec- lyzed the flexural strength and energy absorbed by alumina imens, and powder cast and hot pressing, for the wG-300 (A12O3)during Charpy-impact fracture and demonstrated specimens. Details of the specific processing parameters that the apparent measured energy needs be corrected for used to fabricate the composite samples are listed in [10] machine compliance to obtain the true energy absorbed by The final dimension of the hot pressed SiCw/Al2O3 im- the specimen in loading to failure pact specimens measured 1.80 in. x 1.80 in. x 0.185 in. Al Another important aspect in determining the impact laminates were polished with l um Diamet diamond air- strength of ceramic materials is the method by which sprays and a synthetic silk polishing cloth, using a Planpol mpact strength is measured [7]. Compared the impact automatic polisher. In addition, property bars measuring strengths of eight ceramic materials obtained using an in- 0.185 in. x 0.250 in. x 1.80 in. were cut from laminates cremental impact test method with test results obtained These bars were used for material characterization and ma- using the ASTM D256 single-blow test method, and found terial property testing that the incremental impact test results were five to eight times lower than those results obtained by the ASTM D256 method [8]. Attributed this difference in magnitude of im- 3. Materials characterization pact strengths to the so called"toss factor", defined as the algebraic difference between the energy measured in the Elastic moduli for AlzO3 /SiCw ceramic composites were ASTM tests and the energy required to just fracture the ce- measured using the AstM standard resonance test method ramic specimen as determined by means of the incremental where measurements were made on rectangular bars cut impact test method from propertys laminates with their longitudinal axes Several researchers in the field of low-velocity impact of perpendicular to the hot pressing direction. The bending monolithic ceramic materials have also attempted to corre- strength of Al2 O3/SiCw composites, produced in this study, late their impact test results with the mechanical properties were determined according to the ASTM C1161-90 standard of these materials [9]. Reviewed several experimental data flexural strength test method. Rectangular composite sam- reported by others to determine the impact energy of a num- ples of 0. 185 in. x 0. 250 in, cross-section and 1. 80 in. span ber of brittle materials, and discussed their significance in were placed inside a four-point support fixture, such that terms of material properties and test conditions. He con- polished surfaces of the inner span were loaded in tension cluded that for some brittle materials, including monolithic Fracture toughness values(Kic)for the Al2O3/SiCw ce- aluminas, when corrections are made for toss energy and en- ramic composites were measured in the present study using ergy lost in the machine, the resulting impact strength will the modified indentation toughness technique developed by be related to the elastic stored energy at the initiation of Cook and Lawn [11]. Three indentations of proper size were fracture introduced and aligned 4 mm apart on the tensile surfaces The main objective of this paper is to determine the effects of the inner span of four-point bend rectangular specimens, of dynamic flexural stresses on the impact resistance, failure using Vickers diamond indenters. The specimens were in modes, and toughening mechanisms of whisker reinforced dented such that the crack arms emanating from the indenta- ceramic composites. To accomplish this objective, several tion corners were perpendicular and parallel to the specimen

K.A. Al-Dheylan / Journal of Materials Processing Technology 155–156 (2004) 1986–1994 1987 the impact center than the geometry of the whole structure [4]. Because ceramic materials are inherently brittle, with relatively low resistance to crack extension originating at pre-existing defects, energy release in ceramics is more likely achieved through the formation of fracture surfaces rather than through plastic or viscoelastic processes, as compared to the more ductile materials of similar strength levels [5]. Once a crack starts to propagate under the influ￾ence of a transient load, crack branching often takes place. Cracks branch in order to dissipate the excess energy caused by a rapid energy release rate exceeding the rate of surface energy absorbed by a single crack. When thin monolithic ceramic structures are subjected to transverse, low-velocity impacts by rigid spherical projec￾tiles, local effects caused by local loading may eventually be small. Therefore, the response of the ceramic material to the global dynamic bending of the structure becomes the limiting factor in determining its impact strength. However, not all of the impact energy given up by the projectile is converted into bending energy of the specimen [6]. Ana￾lyzed the flexural strength and energy absorbed by alumina (Al2O3) during Charpy-impact fracture and demonstrated that the apparent measured energy needs be corrected for machine compliance to obtain the true energy absorbed by the specimen in loading to failure. Another important aspect in determining the impact strength of ceramic materials is the method by which the impact strength is measured [7]. Compared the impact strengths of eight ceramic materials obtained using an in￾cremental impact test method with test results obtained using the ASTM D256 single-blow test method, and found that the incremental impact test results were five to eight times lower than those results obtained by the ASTM D256 method [8]. Attributed this difference in magnitude of im￾pact strengths to the so called “toss factor”, defined as the algebraic difference between the energy measured in the ASTM tests and the energy required to just fracture the ce￾ramic specimen as determined by means of the incremental impact test method. Several researchers in the field of low-velocity impact of monolithic ceramic materials have also attempted to corre￾late their impact test results with the mechanical properties of these materials [9]. Reviewed several experimental data reported by others to determine the impact energy of a num￾ber of brittle materials, and discussed their significance in terms of material properties and test conditions. He con￾cluded that for some brittle materials, including monolithic aluminas, when corrections are made for toss energy and en￾ergy lost in the machine, the resulting impact strength will be related to the elastic stored energy at the initiation of fracture. The main objective of this paper is to determine the effects of dynamic flexural stresses on the impact resistance, failure modes, and toughening mechanisms of whisker reinforced ceramic composites. To accomplish this objective, several samples of silicon carbide whisker (SiCw)/alumina matrix (Al2O3) ceramic composites were designed and fabricated using different SiC whisker volume fractions; these ceramic composites were then subjected to low velocity impact, and the damage sustained was quantified and assessed. 2. Experimental set-up and procedures The following materials were used to produce SiCw/Al2O3 ceramic composite samples: • SiC whisker: beta phase (cubic) with average diameters of 0.3–1.0
m. • Alumina powder (Al2O3): high purity 99.95% alumina; 0.05% MgO; grain average size of 0.5
m; average surface area of 6.3 m2/g. • WG-300: SiCw/Al2O3 powder: 33 vol.% SiC (ACMC Whiskers); 67 vol.% Al2O3 (Reynolds matrix). SiCw/Al2O3 ceramic composite samples were manufactured using tape casting and hot pressing, for the tape-cast spec￾imens, and powder cast and hot pressing, for the WG-300 specimens. Details of the specific processing parameters used to fabricate the composite samples are listed in [10]. The final dimension of the hot pressed SiCw/Al2O3 im￾pact specimens measured 1.80 in. × 1.80 in. × 0.185 in. All laminates were polished with 1
m Diamet diamond air￾sprays and a synthetic silk polishing cloth, using a Planpol automatic polisher. In addition, property bars measuring 0.185 in. × 0.250 in. × 1.80 in. were cut from laminates. These bars were used for material characterization and ma￾terial property testing. 3. Materials characterization Elastic moduli for Al2O3/SiCw ceramic composites were measured using the ASTM standard resonance test method, where measurements were made on rectangular bars cut from property’s laminates with their longitudinal axes perpendicular to the hot pressing direction. The bending strength of Al2O3/SiCw composites, produced in this study, were determined according to the ASTM C1161-90 standard flexural strength test method. Rectangular composite sam￾ples of 0.185 in. × 0.250 in. cross-section and 1.80 in. span were placed inside a four-point support fixture, such that polished surfaces of the inner span were loaded in tension. Fracture toughness values (KIC) for the Al2O3/SiCw ce￾ramic composites were measured in the present study using the modified indentation toughness technique developed by Cook and Lawn [11]. Three indentations of proper size were introduced and aligned 4 mm apart on the tensile surfaces of the inner span of four-point bend rectangular specimens, using Vickers diamond indenters. The specimens were in￾dented such that the crack arms emanating from the indenta￾tion corners were perpendicular and parallel to the specimen

K.A. Al-Dheylan/Journal of Materials Processing Technology 155-156 (2004)1986-1994 load was applied until the sample fractured, sient signal coming from impacted specimens. A 2211 se- where surface inspections revealed that fractures initiated ries Tektronix storage oscilloscope, with memory capability from one of the three indentations. The crack lengths ema- was used to capture the amplified transient signals, so that nating from the two remaining indentations, perpendicular these signals may be recalled for analysis. Finally, an exter- to the tensile direction, were then measured and averaged to nal method of triggering the oscilloscope's time base sweep give the critical crack length(cm). The fracture toughness was designed for the present tests; this triggering method is (Kic) was calculated using a relationship between the max explained in [10] imum stress at failure(om)and critical crack length(cm) outlined in [10] 5. Analysis The equation of motion for a thin rectangular plate sub 4. Low-velocity impact testing of Al2 O3/SiCw jected to transverse impact loading is given by(Fig. 1) ceramic plates d-w DVw= P(x, y, t)-Sh (1) 4.1. Description of the impact test apparat where P(x, y, t) is the forcing function due to impact, Sh The impact-testing machine used in this study is the the mass density per unit area, and D the flexural rigidity Dynatup Model 8250 drop tower impact machine, with its of the plate. The natural frequency equation of the simply complete GRG 730-I computerized data system. Both the orted plate is given by instrumented tup and detector collect data, which is acquired by the machines computerized data Umn=J (2) system. The data systems then analyze, manipulate, and isplay this data in the form of force, energy, deflection, The solution to the equation of motion for the deflection of the plate w(x, y, t)may be derived by separating the response A square support fixture assembly, of flat edges, was con- into a function of position Wmn(r, y)and of time, Tmn(n) structed to hold and impact test Al2O3/SiCw ceramic plates and then expand the solution, [10]. The impactor, which was used to strike the ceramic of the eigenfunctions such thar (x, y, o) in an infinite series plate, is a cylindrical indenter(tup) with a 0.5 in. diamete spherical head, machined from D2 tool steel and hardened to Rockwell C of 58-60. The square fixture is screwed to w(x, y, t) a steel base plate assembly, which is mounted and fastened into the Dynatup impact machine where Wmn(x, y) are the normal modes. For a simply sup- In addition, CEA-06-125 WT series strain gages were ce- ported plate, the normal modes take the form mented to the center of the tensile surface of the ceramic specimen to measure directly transient strain signals com- Wmn(x, y)=Amn sin ing from the strained specimen during impact, in the 0 and 90 directions of the plate. A P-3500 strain gage bridge Tmm(0=/Fmn(r) sinum(t -r)dr (band width of dC to 4000 Hz) served to amplify the tran- the striker is freely falling impacting thickness h=0.142 in =0.25in ngth, a=1.80 The Plate is simply supported on all edges Fig. 1. Low-veloci act of a thin, simply supported plate by a spherical striker of mass m and radius R

1988 K.A. Al-Dheylan / Journal of Materials Processing Technology 155–156 (2004) 1986–1994 length. The load was applied until the sample fractured, where surface inspections revealed that fractures initiated from one of the three indentations. The crack lengths ema￾nating from the two remaining indentations, perpendicular to the tensile direction, were then measured and averaged to give the critical crack length (cm). The fracture toughness (KIC) was calculated using a relationship between the max￾imum stress at failure (σm) and critical crack length (cm) outlined in [10]. 4. Low-velocity impact testing of Al2O3/SiCw ceramic plates 4.1. Description of the impact test apparatus The impact-testing machine used in this study is the Dynatup Model 8250 drop tower impact machine, with its complete GRG 730-I computerized data system. Both the instrumented tup and velocity detector collect the impact data, which is acquired by the machine’s computerized data system. The data systems then analyze, manipulate, and display this data in the form of force, energy, deflection, and time. A square support fixture assembly, of flat edges, was con￾structed to hold and impact test Al2O3/SiCw ceramic plates [10]. The impactor, which was used to strike the ceramic plate, is a cylindrical indenter (tup) with a 0.5 in. diameter spherical head, machined from D2 tool steel and hardened to Rockwell C of 58–60. The square fixture is screwed to a steel base plate assembly, which is mounted and fastened into the Dynatup impact machine. In addition, CEA-06-125 WT series strain gages were ce￾mented to the center of the tensile surface of the ceramic specimen to measure directly transient strain signals com￾ing from the strained specimen during impact, in the 0◦ and 90◦ directions of the plate. A P-3500 strain gage bridge (band width of DC to 4000 Hz) served to amplify the tran￾Fig. 1. Low-velocity impact of a thin, simply supported plate by a spherical striker of mass m and radius R. sient signal coming from impacted specimens. A 2211 se￾ries Tektronix storage oscilloscope, with memory capability, was used to capture the amplified transient signals, so that these signals may be recalled for analysis. Finally, an exter￾nal method of triggering the oscilloscope’s time base sweep was designed for the present tests; this triggering method is explained in [10]. 5. Analysis The equation of motion for a thin rectangular plate sub￾jected to transverse impact loading is given by (Fig. 1): D∇4w = P(x, y, t) − Sh ∂2w ∂t2 (1) where P(x, y, t) is the forcing function due to impact, Sh the mass density per unit area, and D the flexural rigidity of the plate. The natural frequency equation of the simply supported plate is given by: wmn = π2
m2 a2 + n2 b2 D Sh (2) The solution to the equation of motion for the deflection of the plate w(x, y, t) may be derived by separating the response into a function of position wmn(x, y) and of time, Tmn(t), and then expand the solution, w(x, y, t) in an infinite series of the eigenfunctions such that w(x, y, t) = ∞ m=1 ∞ n=1 wmn(x, y)T(t) where wmn(x, y) are the normal modes. For a simply sup￾ported plate, the normal modes take the form wmn(x, y) = Amn sin mπx a  sin nπy b  (3) Tmn(t) = 1 wmn  t 0 Fmn(τ)sinwmn(t − τ) dτ (4)

K.A. Al-Dheylan/ournal of Materials Processing Technology 155-156 (2004)1986-1994 where Eb=()3(1-3)S2a4 02= 8x2E2 P(x, y, t)wmn dx dy h The normal mode amplitude, Amn is given by [10 2 nau The point-load forcing function is modeled as being uni- nTU\ I formly distributed over a small area, u x v(Fig. 1); hence Fmn() may be written as Y=∑∑sm2("2)sm(2)sm nJl abp(t) √Sabm2mn3 nIU X SIn Therefore, the equation of the plate deflection [101 6. Results and discussions w(r, y, t) Ts sin Two sets of Al2 O3/SiCw composites were processed dif- ferently and used for this study: tape- cast and wG-300 X sin(mtu nJU nnx Al2O3/SiCw composites b, mown Fig. 2 shows the typical SEM micrograph of a fractured F(T) sin wmn(t-t)dt surface produced by a four-point bending test for the 10% SiCw tape-cast composite. The alumina matrix has a mi m=1, 3, 5..., n=1, 3, 9...(7) crostructure which consists of fine grains about 1-3 um in size and small round scattered pores (much smaller than 5. 1. Calculating maximum dynamic stress the grains) that appear to be inside the grains. The Sic whiskers appear to be 0.3-0.6 um wide and upto 36 um The force-time relations, F( may be approximated by a long. Table I summarizes the material property results for half-sine curve [12] in terms of the maximum contact load, both the tape-cast and wG-300 ceramic composites Fo, as F(= Fo sin (t/t2), where t2 is the contact duration. It is noted here that elastic modulus test results for the For a square plate, a= b, centrally impacted, s=n=a/2, 30% SiCw tape-cast composite, which contains the smaller maximum stresses occurs at the outer thickness, z= h/2 at diameter Arco-type whiskers, are relatively low because the x=a/2, y=b/2. Hence, for a square contact area(u= bulk density for this composite only reached 97%of its u), the maximum dynamic bending stress(o,)max is [10] theoretical density(TD) The test values reported in Table I for bending strer represent the mean of three tests for the 5, 10, 20 )m=a34-)3 30% SiCw composites, the mean of two tests for the 0% x SI- 2 where TSInWmnt-Wmnt2 sin(/12) 2 5.2. Estimating dynamic strain energy of the plate in bending For a square plate centrally impacted, the strain energy of the plate in bending Eb may be written as a function of Fig. 2. SEM micrograph of fracture surface showing the microstructure maximum bending stress as [10] of a 10 vol. Al2O3/SiCw ceramic composite

K.A. Al-Dheylan / Journal of Materials Processing Technology 155–156 (2004) 1986–1994 1989 where Fmn(t) =   P(x, y, t)wmn dx dy. The normal mode amplitude, Amn is given by [10] Amn = 2 √abSh (5) The point-load forcing function is modeled as being uni￾formly distributed over a small area, uxv (Fig. 1); hence, Fmn(t) may be written as: Fmn(t) = 8abP(t) uv  Shabπ2mn sin nπξ a sin nπu 2a  × sin nπv 2b  (6) Therefore, the equation of the plate deflection [10] w(x, y, t) = 16 π2uvSh ∞ m=1 ∞ n=1 sin mπξ a sin uπξ b × sin mπu 2a  sin nπv 2b  1 mnwmn sin mπx a  × sin nπy b   t o F(τ)sin wmn(t − τ) dτ m = 1, 3, 5..., n = 1, 3, 9... (7) 5.1. Calculating maximum dynamic stress The force–time relations, F(t) may be approximated by a half-sine curve [12] in terms of the maximum contact load, F0, as F(t) = F0 sin(πt/t2), where t2 is the contact duration. For a square plate, a = b, centrally impacted, ζ = n = a/2, maximum stresses occurs at the outer thickness, z = h/2 at x = a/2, y = b/2. Hence, for a square contact area (u = v), the maximum dynamic bending stress (σx)max is [10]: (σx)max = 8EF0 a2u2Sh(1 − ν2) m2 + νn2 mnwmn × sin2 mπ 2  sin2 nπ 2  sin mπu 2a  × sin nπu 2a  Kmn (8) where Kmn = t2  π sinwmnt − wmnt2 sin(πt/t2) (π2 − t 2 2w2 mn)  5.2. Estimating dynamic strain energy of the plate in bending For a square plate centrally impacted, the strain energy of the plate in bending Eb may be written as a function of maximum bending stress as [10]: Eb = (σx)2 max(1 − ν2)Shu2a4 8π2E2 ∞ m=1 ∞ n=1 X Y2 Kmn t2 2  (9) where X = ∞ m=1 ∞ n=1 sin2 mπ 2  sin2 nπ 2  sin mπu 2a  × sin nπu 2a  1 mn wmn, Y = ∞ m=1 ∞ n=1 sin2 mπ 2  sin2 nπ 2  sin mπu 2a  × sin nπu 2a  m2 + νn2 mnwmn 6. Results and discussions Two sets of Al2O3/SiCw composites were processed dif￾ferently and used for this study: tape-cast and WG-300, Al2O3/SiCw composites. Fig. 2 shows the typical SEM micrograph of a fractured surface produced by a four-point bending test for the 10% SiCw tape-cast composite. The alumina matrix has a mi￾crostructure which consists of fine grains about 1–3
m in size and small round scattered pores (much smaller than the grains) that appear to be inside the grains. The SiC whiskers appear to be 0.3–0.6
m wide and upto 36
m long. Table 1 summarizes the material property results for both the tape-cast and WG-300 ceramic composites. It is noted here that elastic modulus test results for the 30% SiCw tape-cast composite, which contains the smaller diameter Arco-type whiskers, are relatively low because the bulk density for this composite only reached 97% of its theoretical density (TD). The test values reported in Table 1 for bending strength represent the mean of three tests for the 5, 10, 20, and 30% SiCw composites, the mean of two tests for the 0% Fig. 2. SEM micrograph of fracture surface showing the microstructure of a 10 vol.% Al2O3/SiCw ceramic composite

K.A. 4l-Dheylan /Journal of Materials Processing Technology 155-156 (2004)1986-1994 Table I Material properties for Al2O3/SiCw ceramic composites SiCw(vol%) cm(um) E(Gpa) KC(MPa/in) ob(MPa) △ theory 0 389 4.03 830.2 000 00gg48 60 4049 775.7 theory 657. 20 549.7 WG-300 0204060801012 pact force, pounds SiCw alumina, and the mean of five tests for the WG-300 Fig. 3. Impact amplitude vs. dynamic stress for 10 vol%SiCw/Al203 composites Table 1 also lists the fracture toughness Kic. values cal- culated from the equations developed by Cook and Lawn [11], and critical crack length, cm, The fracture toughness strain recorded for the 10% SiCw composites are 920 lb and values which are listed in Table I represent the mean of three 1180 microstrain, respectively and five tests per composite for the tape-cast and wG-300 Fig. 3 shows a typical curve of stresses at maximum im- composites, respectively. All specimens were indented with pact loads plotted against the maximum load for various ickers diamond indenters at indentation loads of 7 kg for Al2O3/SiCw ceramic composites. In this plot o refers to the tape-cast and 5 kg for the WG-300 specimens stress, and numbers I and 2 denote principal directions of the plate, parallel and perpendicular to one of its length, 6.1. Low-velocity impact test results spectively. The stress at maximum load was calculated based on measured strain and the measured elastic modulus values The average energy required to break e v weakest for these ceramic composites. The average numbe Al2O3/SiCw ceramic specimens was determ mental impacts sustained by these specimens before fracture 0.30 ft lb. this value corresponds to a crosshead weight of is II for the tape-cast and 4 for the dry-cast WG-300 speci- 2.86 Ib, and a drop height of 1.25 in. All subsequent incre- mens. The average fracture load, fracture strain,and fracture mental impact tests were performed using an initial drop stress for the eight tape-cast specimens is 715 1b, 910 uin. /in height of 1. 125 in, and this height was increased in incre (0.091%), and 73 ksi, respectively. The average fracture load ments until fracture. Once the average energy required to for 17 WG-300 specimens is 491 Ib, while the average fra break the ceramic samples was determined, the incremen- ture strain and stress are 944 pin. / in. (0.094%)and 48. 3 ksi tal impact test method provided a fairly accurate method respectively. Fig 3 also includes the theoretical calculations energy absorbed by the ceramic specimen, in addition to ply supported, thin plates subjected to central impacts. In obtaining dynamic stress/strain curves for each ceramic each of these calculations we have substituted for the load amplitude(Fo) and time to maximum load(to) from each The apparent measured energy (Ea) recorded by the load-time record, which were measured directly by the D rented tup is a combination of energy absorbed by the spec- natup Impact Machine. Furthermore, in carrying out these imen(Eb)and the machine(Em). The energy absorbed by the theoretical predictions, the area of the loaded square patch, specimen in bending(Eb)is estimated from measured frac- U, is assumed to have an equivalent circular area with a di ture stresses for those specimens bonded with strain gages, ameter equal to the impactor radius(U2=R2, where R is the tup radius). This approximation means the loaded patch and this energy is compared to the true measured energy is only 6% of the total 1. 8 in. x 1.8 in plate area. The con- (AEo), where AEo is obtained from Ea. Finally, the energy absorbed by the machine(Em) is estimated using equations vergence of the series in Eq(8)was accomplished after 35 derived in [10]; this energy is added to the energy absorbed terms in each summation(m 35 35). The by the specimen(Eb), and the sum(Eb+Em)is compared to son between the approximate theoretical predictions and test AEo. The total apparent energy(Ea)absorbed during impact results indicates that the theoretical calculations, which are consists of initiation energy(energy at maximum load)and about 70-85% of the experimental values generally, agree propagation energy (energy after maximum load). For all with the experimental results specimens tested in this study, propagation energy amounted to only a small fraction of the total absorbed energy (ap- 6.2. Estimating the impact fracture energy in bending for proximately 10-15%), which is typical of brittle fractures. A2O3/SiC ceramic composites Maximum(or fracture)load and strain at maximum load are other impact parameters, which can be extracted from load The impact energy in bending absorbed by the specimen and strain history records. Typical fracture load and fracture at fracture(Eb) was calculated based on measured fracture

1990 K.A. Al-Dheylan / Journal of Materials Processing Technology 155–156 (2004) 1986–1994 Table 1 Material properties for Al2O3/SiCw ceramic composites SiCw (vol.%) cm (
m) E (Gpa) KIC (MPa √ in) σb (MPa) 0 90 389 4.03 830.2 5 80 400 4.19 638.5 10 97 400 5.43 775.7 20 97 406 6.23 657.1 30 104 291 6.31 549.7 WG-300 89 293 5.86 426.8 SiCw alumina, and the mean of five tests for the WG-300 composites. Table 1 also lists the fracture toughness KIC. Values cal￾culated from the equations developed by Cook and Lawn [11], and critical crack length, cm, The fracture toughness values which are listed in Table 1 represent the mean of three and five tests per composite for the tape-cast and WG-300 composites, respectively. All specimens were indented with Vickers diamond indenters at indentation loads of 7 kg for the tape-cast and 5 kg for the WG-300 specimens. 6.1. Low-velocity impact test results The average energy required to break the weakest Al2O3/SiCw ceramic specimens was determined to be 0.30 ft lb.; this value corresponds to a crosshead weight of 2.86 lb, and a drop height of 1.25 in. All subsequent incre￾mental impact tests were performed using an initial drop height of 1.125 in., and this height was increased in incre￾ments until fracture. Once the average energy required to break the ceramic samples was determined, the incremen￾tal impact test method provided a fairly accurate method for measuring the approximate impact stress reached and energy absorbed by the ceramic specimen, in addition to obtaining dynamic stress/strain curves for each ceramic composite. The apparent measured energy (Ea) recorded by the instru￾mented tup is a combination of energy absorbed by the spec￾imen (Eb) and the machine (Em). The energy absorbed by the specimen in bending (Eb) is estimated from measured frac￾ture stresses for those specimens bonded with strain gages, and this energy is compared to the true measured energy (#E0), where #E0 is obtained from Ea. Finally, the energy absorbed by the machine (Em) is estimated using equations derived in [10]; this energy is added to the energy absorbed by the specimen (Eb), and the sum (Eb+Em) is compared to #E0. The total apparent energy (Ea) absorbed during impact consists of initiation energy (energy at maximum load) and propagation energy (energy after maximum load). For all specimens tested in this study, propagation energy amounted to only a small fraction of the total absorbed energy (ap￾proximately 10–15%), which is typical of brittle fractures. Maximum (or fracture) load and strain at maximum load are other impact parameters, which can be extracted from load and strain history records. Typical fracture load and fracture Fig. 3. Impact amplitude vs. dynamic stress for 10 vol.% SiCw/Al2O3 composite. strain recorded for the 10% SiCw composites are 920 lb and 1180 microstrain, respectively. Fig. 3 shows a typical curve of stresses at maximum im￾pact loads plotted against the maximum load for various Al2O3/SiCw ceramic composites. In this plot σ refers to stress, and numbers 1 and 2 denote principal directions of the plate, parallel and perpendicular to one of its length, re￾spectively. The stress at maximum load was calculated based on measured strain and the measured elastic modulus values for these ceramic composites. The average number of incre￾mental impacts sustained by these specimens before fracture is 11 for the tape-cast and 4 for the dry-cast WG-300 speci￾mens. The average fracture load, fracture strain, and fracture stress for the eight tape-cast specimens is 715 lb, 910
in./in. (0.091%), and 73 ksi, respectively. The average fracture load for 17 WG-300 specimens is 491 lb, while the average frac￾ture strain and stress are 944
in./in. (0.094%) and 48.3 ksi, respectively. Fig. 3 also includes the theoretical calculations using Eq. (8) derived for predicting stress amplitudes of sim￾ply supported, thin plates subjected to central impacts. In each of these calculations we have substituted for the load amplitude (F0) and time to maximum load (t0) from each load–time record, which were measured directly by the Dy￾natup Impact Machine. Furthermore, in carrying out these theoretical predictions, the area of the loaded square patch, U2, is assumed to have an equivalent circular area with a di￾ameter equal to the impactor radius (U2 = πR2, where R is the tup radius). This approximation means the loaded patch is only 6% of the total 1.8 in. × 1.8 in. plate area. The con￾vergence of the series in Eq. (8) was accomplished after 35 terms in each summation (m = 35, n = 35). The compari￾son between the approximate theoretical predictions and test results indicates that the theoretical calculations, which are about 70–85% of the experimental values generally, agree with the experimental results. 6.2. Estimating the impact fracture energy in bending for Al2O3/SiC ceramic composites The impact energy in bending absorbed by the specimen at fracture (Eb) was calculated based on measured fracture