Part B: engineering ELSEVIER Composites: Part B 37(2006)530-541 Structure, nonlinear stress-strain state and strength of ceramic lltilayered O.N. Grigoriev a, *, A V. Karoteev ,E.N. Maiboroda I.L. Berezhinsky ,B K. Serdega DYu. ostrovo.vg. piskunoy Institute for Problems of Materials Science, NAS of Ukraine, 3 Krghizhanovskii Str, 03142 Kiev, Ukraine Institute of Physics of Semiconductors, NAS of Ukraine, Kiev, Ukraine Institute for Problems of Strength, NAS of Ukraine, Kiev, Ukraine d National University of Transport, Kiev, Ukraine Received 4 April 2005: received in revised form 7 September 2005: accepted 15 September 2005 Available online 27 April 2006 Abstract The effect of structure and residual stresses on the mechanical behavior of the SiC/TiB, multilayer composite ceramic materials was studied. The multilayered ceramics were obtained using the following scheme: a slip casting of thin films followed by a packet rolling and hot pressing. The use of B-SiC powders allowed to obtain Sic layers with porous structure reinforced by crystals. Such structures possess the relaxation ability of thermal strains that excludes formation of cracks during material production and provides enhanced strength of the SiC/TiB2 composite. Mechanical response of the laminated ceramic composites to static bending was studied experimentally. a procedure for solving the inverse problem using experimental data on the deformation of a laminated ceramic composite specimen in the form of a beam was developed. This approach allows the mechanical characteristics of the laminates to be predicted. The nonlinear stress-strain dependencies for the laminate as a quasi-homogeneous structure and for each of the two separate materials of the layers were obtained. The modeling of the stress-strain state of t aminate was performed. c 2006 Elsevier ltd. all rights reserved Keywords: A. Layered structures; A Laminates; B Residual/intemal stress; B Strength 1. Introduction zirconium borides to silicon carbide allows increasing strength for and fracture toughness by 50-100%.However, corrosion Laminated ceramic composites offer the best prospect for resistance of these ceramics decreases significantly which is rational use of the unique physical-mechanical properties of undesirable for the majority of high-temperature applications monolithic ceramics and ceramic-matrix composites providing Therefore, a design of the multilayer composites with a way to improve their durability, fracture toughness, corrosion external layers of corrosion resistive SiC and internal layers of and thermal resistance, wear, etc. [1-7 improved mechanical performance such as SiC/MeB2 may b Silicon carbide is one of the most promising ceramic promising. Moreover, in this type of material the external Sic materials for structural applications because of its unique layers are under thermal compression stresses due to their thermomechanical properties and high corrosion resistance. lower coefficient of thermal expansion compared with internal However, low fracture toughness and reliability of silicon SiC/MeB, layers. This will also increase apparent fracture carbide significantly limit its potential applications. The toughness as well as strength and reliability of laminates. The improvement of mechanical properties is possible under the studies over the last few years have shown that the increase in careful control of structure and is due to transition from strength and/or fracture toughness of multilayer ceramic monolithic ceramics to composites. In particular, it is well composites may provide increased tolerance against damages known [8-10) that the additions of 15-30% titanium and However, the production of such composites requires a solution to layer bonding problems. Also there is the possibility of generating new defects in the thermal stresses fields [11] E-mail address: oleggrig@ipms keiv. ua(O N. Grigoriev ) Therefore, optimization of both composite manufacturing 1359-8368/- see front matter o 2006 Elsevier Ltd. All rights reserved. conditions and its structure are very important to ensure elastic doi: 10.1016/j- composites. 2006.02.009 strain relaxation. The development and design of these
Structure, nonlinear stress–strain state and strength of ceramic multilayered composites O.N. Grigoriev a,*, A.V. Karoteev a , E.N. Maiboroda a , I.L. Berezhinsky a , B.K. Serdega b , D.Yu. Ostrovoi c , V.G. Piskunov d a Institute for Problems of Materials Science, NAS of Ukraine, 3 Krzhizhanovskii Str., 03142 Kiev, Ukraine b Institute of Physics of Semiconductors, NAS of Ukraine, Kiev, Ukraine c Institute for Problems of Strength, NAS of Ukraine, Kiev, Ukraine d National University of Transport, Kiev, Ukraine Received 4 April 2005; received in revised form 7 September 2005; accepted 15 September 2005 Available online 27 April 2006 Abstract The effect of structure and residual stresses on the mechanical behavior of the SiC/TiB2 multilayer composite ceramic materials was studied. The multilayered ceramics were obtained using the following scheme: a slip casting of thin films followed by a packet rolling and hot pressing. The use of b-SiC powders allowed to obtain SiC layers with porous structure reinforced by prismatic crystals. Such structures possess the relaxation ability of thermal strains that excludes formation of cracks during material production and provides enhanced strength of the SiC/TiB2 composite. Mechanical response of the laminated ceramic composites to static bending was studied experimentally. A procedure for solving the inverse problem using experimental data on the deformation of a laminated ceramic composite specimen in the form of a beam was developed. This approach allows the mechanical characteristics of the laminates to be predicted. The nonlinear stress–strain dependencies for the laminate as a quasi-homogeneous structure and for each of the two separate materials of the layers were obtained. The modeling of the stress–strain state of the laminate was performed. q 2006 Elsevier Ltd. All rights reserved. Keywords: A. Layered structures; A. Laminates; B. Residual/internal stress; B. Strength 1. Introduction Laminated ceramic composites offer the best prospect for rational use of the unique physical–mechanical properties of monolithic ceramics and ceramic-matrix composites providing a way to improve their durability, fracture toughness, corrosion and thermal resistance, wear, etc. [1–7]. Silicon carbide is one of the most promising ceramic materials for structural applications because of its unique thermomechanical properties and high corrosion resistance. However, low fracture toughness and reliability of silicon carbide significantly limit its potential applications. The improvement of mechanical properties is possible under the careful control of structure and is due to transition from monolithic ceramics to composites. In particular, it is well known [8–10] that the additions of 15–30% titanium and zirconium borides to silicon carbide allows increasing strength and fracture toughness by 50–100%. However, corrosion resistance of these ceramics decreases significantly which is undesirable for the majority of high-temperature applications. Therefore, a design of the multilayer composites with external layers of corrosion resistive SiC and internal layers of improved mechanical performance such as SiC/MeB2 may be promising. Moreover, in this type of material the external SiC layers are under thermal compression stresses due to their lower coefficient of thermal expansion compared with internal SiC/MeB2 layers. This will also increase apparent fracture toughness as well as strength and reliability of laminates. The studies over the last few years have shown that the increase in strength and/or fracture toughness of multilayer ceramic composites may provide increased tolerance against damages. However, the production of such composites requires a solution to layer bonding problems. Also there is the possibility of generating new defects in the thermal stresses fields [11]. Therefore, optimization of both composite manufacturing conditions and its structure are very important to ensure elastic strain relaxation. The development and design of these Composites: Part B 37 (2006) 530–541 www.elsevier.com/locate/compositesb 1359-8368/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2006.02.009 * Corresponding author. E-mail address: oleggrig@ipms.keiv.ua (O.N. Grigoriev)
O.N. Grigoriev et aL./Composites: Part B 37(2006)530-541 531 composites requires the determination of their mechanical Grinding and mixing of the batch components were carried characteristics such as of elastic moduli, strength, stiffness, out in a planetary ball mill. The powder particles after mixing stress-strain diagrams, distribution of phases of different have a sufficiently small grain size for hot pressing(2.5 and materials in the structure of a composite, and the magnitude 1. 1 m, respectively), ensuring optimum dispersion. The B4C and distribution of residual stresses in their volume. There are additives and in some cases. TiO, additives were introduced several analytical and experimental methods to solve these into SiC-and TiB2-based mixtures In the presence of TiO2, the problems [12-21] etc. The work presented here is based on the reactionary hot pressing with formation of secondary TiB analysis of experimentally obtained physical-mechanical during reaction T1O2+B. 2+Co took place. The characteristics of a composite [14-22]. This approach creates additives were introduced for reducing and matching of hot possibilities for theoretical investigation of a deformation pressing temperatures of various composition layers behavior of the developed composites We used a slip casting method for manufacturing lamina The effect of structure and residual stresses on strength of tapes. The ceramic tapes with a thickness 50 um were multilayer SiC(B. C)/MeB, composites was explored. A layer prepared from powders of various compositions. To remove structure (grain size, porosity etc. )was altered by using casting defects the tapes were folded in rolls and then rolled up different sintering additives, various raw materials (a- and to the thickness of 400 um. Fro B-SiC powders) as well as by changing the manufacturing required size were cut out and the packages containing 11-13 conditions. Residual thermal stresses are controlled by the pairs of alternating layers were obtained for the chosen composition of layers. Experimental studies on the mechanical compositions strength of the ceramic composite specimen were performed Hot pressing was carried out using a pilot induction hot using procedures and equipment described in [23-24] ress in graphite dies without chamber. The 2. Materials and procedures 1600-2150C, pressure 26-30 MP of isothermal densification 7-20 min, and heating rates were up to Two kinds of a-Sic powders were used: (1) technical 100%/min. Samples for testing of the mechanical properties abrasive powders, M5 grade, produced by the Zaporo abrasive plant, Ukraine, and(2)powders of UFO5 and UF10 sectioned dies grades from the Starck company, Germany. Both powders were ne specimens for mechanical tests in the form of a mixtures of polytypes: mainly 6H, 15R and 3C. TiB2 powders rectangular beam(Fig. 1a) were produced by sawing the (TC 6-09-03-7-75)from the Donetsk factory of chemical package into billets and polishing them with a diamond tool in reagents (Ukraine), and abrasive B4C powders from such a way that the layers throughout the thickness of the beam ere located as symmetrically as possible relative to the Zaporozhye abrasive plant(GOST 5744-74), were used as middle plane(Fig. 1b). Specimens of preset sizes were tested in sintering additives. Some properties of as-received powders are given in four-point bending(pure flexure, Fig. la)at room temperature Table 1 with a deformation rate(displacement of the cross-head of a The B-SiC powder, produced by Institute for Problems of testing machine)of 0.005 mm/min Vickers hardness was determined under the load of 5n. the Materials Science, had the content of 3C-polytype up to 100%o Sic powders were very different in their defectiveness and microstructure of composites was investigated by optical and sinterability. The powders UFO5 and M5 were characterized scanning electron microscopy(SEM), and the phase compe with low width of X-ray diffraction peaks and good resolution sIton--by X-ray diffraction(XRD) of Ka doublets and, therefore, had a high degree of structural perfection. XRD peaks of UF10, as well as of B-Sic powder 3. Results and discussion were very broad due to high density of defects(stacking faults, 3. 1. Characteristics of monolithic ceramics polytypes interlayer, and nonhomogeneous microstrains accordance with TEM data) which, apparently, facilitated an increase in their activity during sintering The bending strength of single-phase and heterogeneous ramics with composition similar to the ones in the layered composites is shown in Table 2. Single-phase silicon carbide Table 1 ceramics had high porosity (5-10%), average grain size 5-10 The characteristic of powder and up to 100 um for raw powders of a-SiC and B-SiC, Powder Size of particles, Content of oxy- Free carbon respectively. In the latter case the high grain size is due to grain dso(um) gen(wt%) (wt%) growth during B-a transformation of silicon carbide at hot pressing Hot pressing of pure silicon carbide without sintering 0.17 additives leads to the formation of porous coarse-grained B-Sic 0.1-0.2 ≤0.5×10 materials with the low strength(110-190 MPa). Introduction <0.1 of boron carbide allows to reduce porosity of ceramics to 1-3% with the relevant increasing of strength up to 300-370 MPa
composites requires the determination of their mechanical characteristics such as of elastic moduli, strength, stiffness, stress–strain diagrams, distribution of phases of different materials in the structure of a composite, and the magnitude and distribution of residual stresses in their volume. There are several analytical and experimental methods to solve these problems [12–21] etc. The work presented here is based on the analysis of experimentally obtained physical–mechanical characteristics of a composite [14–22]. This approach creates possibilities for theoretical investigation of a deformation behavior of the developed composites. The effect of structure and residual stresses on strength of multilayer SiC(B4C)/MeB2 composites was explored. A layer structure (grain size, porosity etc.) was altered by using different sintering additives, various raw materials (a- and b-SiC powders) as well as by changing the manufacturing conditions. Residual thermal stresses are controlled by the composition of layers. Experimental studies on the mechanical strength of the ceramic composite specimen were performed using procedures and equipment described in [23–24]. 2. Materials and procedures Two kinds of a-SiC powders were used: (1) technical abrasive powders, M5 grade, produced by the Zaporozhye abrasive plant, Ukraine, and (2) powders of UF05 and UF10 grades from the Starck company, Germany. Both powders were mixtures of polytypes: mainly 6H, 15R and 3C. TiB2 powders (TC 6-09-03-7-75) from the Donetsk factory of chemical reagents (Ukraine), and abrasive B4C powders from the Zaporozhye abrasive plant (GOST 5744-74), were used as sintering additives. Some properties of as-received powders are given in Table 1. The b-SiC powder, produced by Institute for Problems of Materials Science, had the content of 3C-polytype up to 100%. SiC powders were very different in their defectiveness and sinterability. The powders UF05 and M5 were characterized with low width of X-ray diffraction peaks and good resolution of Ka-doublets and, therefore, had a high degree of structural perfection. XRD peaks of UF10, as well as of b-SiC powder, were very broad due to high density of defects (stacking faults, polytypes interlayer, and nonhomogeneous microstrains, in accordance with TEM data) which, apparently, facilitated an increase in their activity during sintering. Grinding and mixing of the batch components were carried out in a planetary ball mill. The powder particles after mixing have a sufficiently small grain size for hot pressing (2.5 and 1.1 mm, respectively), ensuring optimum dispersion. The B4C additives and, in some cases, TiO2 additives were introduced into SiC- and TiB2-based mixtures. In the presence of TiO2, the reactionary hot pressing with formation of secondary TiB2 during reaction TiO2CB4C/TiB2CCO took place. The additives were introduced for reducing and matching of hot pressing temperatures of various composition layers. We used a slip casting method for manufacturing lamina tapes. The ceramic tapes with a thickness w50 mm were prepared from powders of various compositions. To remove casting defects the tapes were folded in rolls and then rolled up to the thickness of 400 mm. From the sheets, plates of the required size were cut out and the packages containing 11–13 pairs of alternating layers were obtained for the chosen compositions. Hot pressing was carried out using a pilot induction hot press in graphite dies without a vacuum chamber. The temperature of isothermal sintering was in the range of 1600–2150 8C, pressure 26–30 MPa, time of isothermal densification 7–20 min, and heating rates were up to 1008/min. Samples for testing of the mechanical properties having sizes 45!45!5 mm were produced in the multisectioned dies. The specimens for mechanical tests in the form of a rectangular beam (Fig. 1a) were produced by sawing the package into billets and polishing them with a diamond tool in such a way that the layers throughout the thickness of the beam were located as symmetrically as possible relative to the middle plane (Fig. 1b). Specimens of preset sizes were tested in four-point bending (pure flexure, Fig. 1a) at room temperature with a deformation rate (displacement of the cross-head of a testing machine) of 0.005 mm/min. Vickers hardness was determined under the load of 5 N. The microstructure of composites was investigated by optical and scanning electron microscopy (SEM), and the phase composition—by X-ray diffraction (XRD). 3. Results and discussion 3.1. Characteristics of monolithic ceramics The bending strength of single-phase and heterogeneous ceramics with composition similar to the ones in the layered composites is shown in Table 2. Single-phase silicon carbide ceramics had high porosity (5–10%), average grain size 5–10 and up to 100 mm for raw powders of a-SiC and b-SiC, respectively. In the latter case the high grain size is due to grain growth during b/a transformation of silicon carbide at hot pressing. Hot pressing of pure silicon carbide without sintering additives leads to the formation of porous coarse-grained materials with the low strength (110–190 MPa). Introduction of boron carbide allows to reduce porosity of ceramics to 1–3% with the relevant increasing of strength up to 300–370 MPa. Table 1 The characteristic of powders Powder Size of particles, d50, (mm) Content of oxygen (wt%) Free carbon (wt%) SiCM5 5 1.5 1–2 SiCUF05 1.47 0.55 – SiCUF10 0.7 1.2 0.17 b-SiC 0.1–0.2 %0.5!10K2 – TiB2 30 0.3 !0.1 B4C 20 1.5 2 O.N. Grigoriev et al. / Composites: Part B 37 (2006) 530–541 531
O.N. Grigoriev et al./Composites: Part B 37(2006)530-541 删斗 多缓汤0 多多 b多多 Fig. 1. Bending configuration(a)and structure of the cross-section of the specimen(b)(sizes in mm) Simultaneous introduction of 5% BC and 12% TiB, results in should follow from the Eshelby model. There are the edge an increase of strength up to 408 MPa(Table 2)and up to effects of redistribution of stresses, inhomogeneity of a stress 650 MPa at TiB 2 content of 20-25%0 The ceramics TiB2-B4C distribution across the thickness of layers. In particular, the has the strength of 415 MPa with a grain size of 5-10 um and extensive zone with tension stresses directed perpendicular to practically no porosity. The results of a detailed study of the the layers plane(ou>0) which are located near the edges. structure and mechanical behavior of Sic-TiB2-B4C ceramic Within this zone the delamination may occur. Moreover, system are presented in [9-10 various types of fracture and microcracking in composites may take place under the joint effect of both thermal and applied 3. 2. Laminated composites stresses Usually we know the parameters of materials for stress 3.2.1. Distribution of the internal stresses calculation with insufficient accuracy and calculated results At the first stage of work we studied the layered composites have only a qualitative nature. There is the need for with the maximum thermal expansion misfit between layers. experimental measurement of the stress fields in layered These systems have the highest probability of uncontrollable composites. Traditionally the tasks of the stress-strain fracture under the influence of thermal stresses measurements are performed by the diffraction methods, and In the temperature range 20-1500C the effective coeffi- first by XRD. These methods are well developed and universal cients of thermal expansion are 5.8 and 8.9/C for Sic in many cases. However, they usually require long measure- and TiB2, respectively, [25]. Within the framework of Eshelby ments and have other problems caused by the low intensity of model, there are the average stresses in a plane of layers [ 22I= X-ray peak lo331=1.4 GPa, tension of TiB2 and compression of Sic Also there is a problem of internal stress determination in According to accepted orientation of axes, the components microcrystals or between layers in layered composites, when 022 and 033 of principal stresses are in a plane of layers, the thickness of alternating layers is made from several microns whereas the au- component is perpendicular to the plane of up to 100s of microns. Therefore search and development of layers. As one can see, for TiB2-SiC laminates calculated alternative methods for determination of internal stresses is residual thermal stresses exceed a possible level of strength and should result in fracture. In practice, the level of thermal Table 2 stresses will be lower as a result of the viscoelastic relaxation Compositions and mechan due to the segregation of impurities on layer's boundaries, reinforced composites cal properties of monolithic ceramics and particles especially in composites based on the a-SiC powders, and also due to presence of the phase(B4C) with intermediate No. Composition of coefficient of thermal expansion (a=6.05X10/C in the ceramics(vol o) (SD, MPa) factor(%) temperature range of 20-1000C [251). l10(5 Finite element methods give more accurate estimation of 3 thermal stresses and the character of their distribution 26. The 4 M5+10%B4C calculations of the residual stresses in this work were done for 5 a- Siculo5+10%BC306(56 five-layer ABCBA symmetric configuration, where A-C are 6 a-SICUFO5+12% layers of ceramics: SiC, SiC +20% TiB2 and TiB2, respect- TiB, +5% B C TiB2+42% BC 415(53) ively(Fig. 2). The stress distribution is more complex, so it
Simultaneous introduction of 5% B4C and 12% TiB2 results in an increase of strength up to 408 MPa (Table 2) and up to 650 MPa at TiB2 content of 20–25%. The ceramics TiB2–B4C has the strength of 415 MPa with a grain size of 5–10 mm and practically no porosity. The results of a detailed study of the structure and mechanical behavior of SiC–TiB2–B4C ceramic system are presented in [9–10]. 3.2. Laminated composites 3.2.1. Distribution of the internal stresses At the first stage of work we studied the layered composites with the maximum thermal expansion misfit between layers. These systems have the highest probability of uncontrollable fracture under the influence of thermal stresses. In the temperature range 20–1500 8C the effective coeffi- cients of thermal expansion are 5.8 and 8.9!10K6 /8C for SiC and TiB2, respectively, [25]. Within the framework of Eshelby model, there are the average stresses in a plane of layers js22jZ js33jy1.4 GPa, tension of TiB2 and compression of SiC. According to accepted orientation of axes, the components s22 and s33 of principal stresses are in a plane of layers, whereas the s11-component is perpendicular to the plane of layers. As one can see, for TiB2–SiC laminates calculated residual thermal stresses exceed a possible level of strength and should result in fracture. In practice, the level of thermal stresses will be lower as a result of the viscoelastic relaxation due to the segregation of impurities on layer’s boundaries, especially in composites based on the a-SiC powders, and also due to presence of the phase (B4C) with intermediate coefficient of thermal expansion (aZ6.05!10K6 /8C in the temperature range of 20–1000 8C [25]). Finite element methods give more accurate estimation of thermal stresses and the character of their distribution [26]. The calculations of the residual stresses in this work were done for five-layer ABCBA symmetric configuration, where A–C are layers of ceramics: SiC, SiCC20% TiB2 and TiB2, respectively (Fig. 2). The stress distribution is more complex, so it should follow from the Eshelby model. There are the edge effects of redistribution of stresses, inhomogeneity of a stress distribution across the thickness of layers. In particular, the extensive zone with tension stresses directed perpendicular to the layers plane (s11O0) which are located near the edges. Within this zone the delamination may occur. Moreover, various types of fracture and microcracking in composites may take place under the joint effect of both thermal and applied stresses. Usually we know the parameters of materials for stress calculation with insufficient accuracy and calculated results have only a qualitative nature. There is the need for experimental measurement of the stress fields in layered composites. Traditionally the tasks of the stress–strain measurements are performed by the diffraction methods, and first by XRD. These methods are well developed and universal in many cases. However, they usually require long measurements and have other problems caused by the low intensity of X-ray peaks. Also there is a problem of internal stress determination in microcrystals or between layers in layered composites, when the thickness of alternating layers is made from several microns up to 100s of microns. Therefore search and development of alternative methods for determination of internal stresses is Fig. 1. Bending configuration (a) and structure of the cross-section of the specimen (b) (sizes in mm). Table 2 Compositions and mechanical properties of monolithic ceramics and particles reinforced composites No. Composition of ceramics (vol%) Bending strength (SD, MPa) Fluctuation factor (%) 1 b-SiC 190(40) 21 2 a-SiCM5 110(57) 52 3 a-SiCUF05 170(48) 28 4 a-SiCM5C10% B4C 372(71) 19 5 a-SiCUF05C10% B4C 306(56) 18 6 a-SiCUF05C12% TiB2C5% B4C 408(64) 17 7 TiB2C42% B4C 415(53) 13 532 O.N. Grigoriev et al. / Composites: Part B 37 (2006) 530–541
O.N. Grigoriev et aL./Composites: Part B 37(2006)530-541 604B91自 01p304560;:9:0z2 33 01203045060708090100Z2 aaea3n405060790地2 Fig. 2. Distribution of principal stresses o11, 022. 33(aHc)as well as o1(d)in laminated composites SiC/SiC-TiB2/TiB2 rgent. One of such alternative methods is optic-polarization Since, the magnitude of the signal is defined by phase traditionally used in crystallography to study transparent changes of a light wave reflected from a sample it provides materials and for simulation of the mechanic behavior a very high sensitivity for stress measurements. It was (polymers, glasses)[27] shown [30], that changes of anisotropic dielectric properties In the present work the polarization-modulation method is caused by stresses are comparable in magnitude with considered for study of internal stresses in composite materials. anisotropy of properties changes caused by the deformation It is suitable for research of transparent materials in of sample by its own weight due to gravity forces. The distribution of tensile residual stresses with a spatial resolution 10% atati, E transmittance mode and for opaque materials in reflection relative anisotropy of refractive index, arising from such mode. With this method it is possible to obtain local gravitational deformation in silicon crystal, does not exceed In this case the phase difference between two orthogonal polarized components of light with wavelength The optical scheme of experimental setup is shown in a of I cm is about 2X10 which corresponds approxi Fig. 3. The scheme performed as a Michelson interferometer mately one angular second however its peculiarity is the measurement of the phase In the case of polycrystalline ceramics the reflected beam polarized light wave cause by An=nx-y and arising at its result of interaction of reflections from 1 to 100 crystalgrana changes between two orthogonal components of linearly from accident beam of a diameter about 10 um is formed as a transmission (or reflection) through the sample. For this The state of polarization of the reflected light wave will be purpose the photoelastic modulator(PM)[28] is added into characterized by some average effective parameters of the scheme. This element represents a dynamic phase plate The alternating mechanical load of a suitable frequency of wo was applied to plate. During the period of one vibration the plate becomes the quarter wave or half wave plate depending on the magnitude of load. In the first case the linearly polarized light wave after passing through the plate is transformed in LG.126 circular polarized light, and in the second case it is transformed in linear orthogonally polarized light The principle of setup operation consists in the followin [29]. Radiation of the laser LG-126 (rad 0.63 or 1.15 um), polarized at the angle of 45 to the axis Y in the plane Xor equally divided on two light beams by the splitter. One of them is directed to a anisotropic reflector(), and another one is focused on a sample(S)by the lens(O1). The beams reflected from the reflector(R)and the sample are combined together and directed to the photodetector(PD)through the photoelastic Fig. 3. Optical scheme of polarization-modulated setup: LG-126-He-Ne modulator(PM) and polarizer(P). In the transmittance mode laser, S, sample: R, anisotropic reflector; PM, photoelastic modulator: the mirror is places behind the sample darizer pd
urgent. One of such alternative methods is optic-polarization traditionally used in crystallography to study transparent materials and for simulation of the mechanic behavior (polymers, glasses) [27]. In the present work the polarization-modulation method is considered for study of internal stresses in composite materials. It is suitable for research of transparent materials in transmittance mode and for opaque materials in reflection mode. With this method it is possible to obtain local distribution of tensile residual stresses with a spatial resolution of about 3 mm. The optical scheme of experimental setup is shown in a Fig. 3. The scheme performed as a Michelson interferometer however its peculiarity is the measurement of the phase changes between two orthogonal components of linearly polarized light wave cause by DnZnxKny and arising at its transmission (or reflection) through the sample. For this purpose the photoelastic modulator (PM) [28] is added into the scheme. This element represents a dynamic phase plate. The alternating mechanical load of a suitable frequency of u0 was applied to plate. During the period of one vibration the plate becomes the quarter wave or half wave plate depending on the magnitude of load. In the first case the linearly polarized light wave after passing through the plate is transformed in circular polarized light, and in the second case it is transformed in linear orthogonally polarized light. The principle of setup operation consists in the following [29]. Radiation of the laser LG-126 (lrad 0.63 or 1.15 mm), polarized at the angle of 458 to the axis Y in the plane XOY equally divided on two light beams by the splitter. One of them is directed to a anisotropic reflector (R), and another one is focused on a sample (S) by the lens (O1). The beams reflected from the reflector (R) and the sample are combined together and directed to the photodetector (PD) through the photoelastic modulator (PM) and polarizer (P). In the transmittance mode the mirror is places behind the sample. Since, the magnitude of the signal is defined by phase changes of a light wave reflected from a sample it provides a very high sensitivity for stress measurements. It was shown [30], that changes of anisotropic dielectric properties caused by stresses are comparable in magnitude with anisotropy of properties changes caused by the deformation of sample by its own weight due to gravity forces. The relative anisotropy of refractive index, arising from such gravitational deformation in silicon crystal, does not exceed 10K10. In this case the phase difference between two orthogonal polarized components of light with wavelength of 1 cm is about 2p!10K6 which corresponds approximately one angular second. In the case of polycrystalline ceramics the reflected beam from accident beam of a diameter about 10 mm is formed as a result of interaction of reflections from 1 to 100 crystal grains. The state of polarization of the reflected light wave will be characterized by some average effective parameters of Fig. 3. Optical scheme of polarization-modulated setup: LG-126—He–Ne laser; S, sample; R, anisotropic reflector; PM, photoelastic modulator; P, polarizer; PD, photodiode. Fig. 2. Distribution of principal stresses s11, s22, s33 (a)–(c) as well as s12 (d) in laminated composites SiC/SiC–TiB2/TiB2. O.N. Grigoriev et al. / Composites: Part B 37 (2006) 530–541 533
O.N. Grigoriev et al./Composites: Part B 37(2006)530-54 a) 1234 5 0.5mm (e)p 6 吕2 Fig. 4. Morphology of surface of double layer ceramic (a) and the curve of its scan by laser beam(b), the signal of photodiode versus the press applied to the sample double layer ceramic (c). ceramics, which depends on the structure and its physical state, zero represents the conditionally chosen origin of stresses including stresses or strains counting off. The vertical lines represent the conditionally Reflection of linearly polarized radiation from the sample drawn borders between the structurally different zones results the elliptically polarized light. The parameters of this including a porous one, near layers boundary, that was created ellipticity are defined by internal stresses or caused by external due to chemical interaction of layer components during loading. Both PM and P carry out dynamic analysis of sintering. The obtained curve of the stress distribution near polarization state of the light. The intensity of a circular boundary qualitatively fits more complex distribution than we component of elliptically polarized light is proportional to expected for simple case of two-layer configuration value of elastic stresses or deformations. Anisotropy of An Signal of the photodiode was calibrated against the pressure n-y is connected with stresses or deformations by ratio: applied to sample at the same conditions, at which the stresses An=T(ox-Oy) and An=p(Er-Ey), where T and p are- were registered. Using such calibration curve(Fig. 4c)the piezooptic and elastooptic coe fficients accordingly for each numerical magnitude of stresses was obtained for entire scan structural component of a material Results presented in Fig 4 show that the maximum stress drop For example, Fig. 4 shows the results of quantitati near boundary of layers is about 200 MP measurements carried out on a sample of Sic and Sic+ 20%TiB2 two-layered ceramics. The powders Sic and TiB2 3.2.2. Strength of laminates with the diameter of 5-10 um were taken to fabricate a sample Our studies have shown that in the composites containing The rectangular bar with the sizes 5x5X8 mm was cut out and the a-SiCMs Powders(the composites 1 and 2, Table 3)both polished for measurements types of layers(SiC and TiB 2) have a low porosity, which are Fig. 4b shows stresses registered at the scanning of a sample formed during sintering(Fig. 5a). Low relaxation ability of by the laser beam(=0.63 um and a diameter 50 um) along an such structures results in microcracking of composites with axis x according to Fig. 3. The horizontal line passing through types of fracture described in [11]
ceramics, which depends on the structure and its physical state, including stresses or strains. Reflection of linearly polarized radiation from the sample results the elliptically polarized light. The parameters of this ellipticity are defined by internal stresses or caused by external loading. Both PM and P carry out dynamic analysis of polarization state of the light. The intensity of a circular component of elliptically polarized light is proportional to value of elastic stresses or deformations. Anisotropy of DnZ nxKny is connected with stresses or deformations by ratio: DnZp(sxKsy) and DnZp(3xK3y), where p and p are— piezooptic and elastooptic coefficients accordingly for each structural component of a material. For example, Fig. 4 shows the results of quantitative measurements carried out on a sample of SiC and SiCC 20%TiB2 two-layered ceramics. The powders SiC and TiB2 with the diameter of 5–10 mm were taken to fabricate a sample. The rectangular bar with the sizes 5!5!8 mm was cut out and polished for measurements. Fig. 4b shows stresses registered at the scanning of a sample by the laser beam (lZ0.63 mm and a diameter 50 mm) along an axis x according to Fig. 3. The horizontal line passing through zero represents the conditionally chosen origin of stresses counting off. The vertical lines represent the conditionally drawn borders between the structurally different zones, including a porous one, near layer’s boundary, that was created due to chemical interaction of layer components during sintering. The obtained curve of the stress distribution near boundary qualitatively fits more complex distribution than we expected for simple case of two-layer configuration. Signal of the photodiode was calibrated against the pressure applied to sample at the same conditions, at which the stresses were registered. Using such calibration curve (Fig. 4c) the numerical magnitude of stresses was obtained for entire scan. Results presented in Fig. 4 show that the maximum stress drop near boundary of layers is about 200 MPa. 3.2.2. Strength of laminates Our studies have shown that in the composites containing the a-SiCM5 powders (the composites 1 and 2, Table 3) both types of layers (SiC and TiB2) have a low porosity, which are formed during sintering (Fig. 5a). Low relaxation ability of such structures results in microcracking of composites with types of fracture described in [11]. Fig. 4. Morphology of surface of double layer ceramic (a) and the curve of its scan by laser beam (b), the signal of photodiode versus the press applied to the sample of double layer ceramic (c). 534 O.N. Grigoriev et al. / Composites: Part B 37 (2006) 530–541