journal J. Ha. Cera. Soc,8121337-4302000 Evaluation of Damage Evolution in Ceramic-Matrix Composites Using Thermoelastic Stress Analysis Thomas j. Mackin" and Mark C. Roberts Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 Thermoelastic stress analysis(TSA)has been used to monitor wherein the He and Hutchinson debonding criterion has been used to measure full-field hydrostatic stress maps across the ever tough composites that use strong interfaces have been entire visible surface of a sample, to quantify the stress fabricated. 7. The key difference results from the toughening redistribution that is caused by damage and to image the mechanism: a class Ill material does not need to have a weak existing damage state in composites. Stress maps and damage nterface to develop considerable stress redistribution, local non- images are constructed by measuring the thermoelastic and linearity, and notch insensitivity. Furthermore, the pivotal work of dissipational thermal signatures during cyclie loading. To Aveston et al. clearly showed that the addition of strongly bonded xplore the general utility of the method, test samples of fibers to a brittle matrix resulted in a composite with greatly everal ceramic-matrix and cement-matrix composites have enhanced strength and toughness. The mechanism of stress redis- been fabricated and tested according to a prescribed damage tribution, in this instance, was multiple matrix cracking(class l) schedule. the model materials have been chosen to illustrate In any case, the underlying fundamental phenomenon is the the effect of each of three damage mechanisms: a single crack development of a nonlinear material response that redistributes that is bridged by fibers, multiple matrix cracking, and shear stress away from regions of concentrated stress bands. It is shown that the TSA method can be used to quantify Changes in the fiber, matrix, and interface properties will affect the effect of damage and identify the operative damage mech- the active damage mechanism, as well as the extent of stress nism. Each mechanism is identified by a characteristic the redistribution. Fiber and matrix properties are easily measured mal signature and each is shown to be effective at redist using standard testing methods, 0, whereas interface properties ting stress and diffusing stress concentrations. The proposed can be determined using hysteresis, 2-4 pullout and frictional xperimental method presents a new way to measure the heating, or fiber push-out tests. 16-2 However, the mesoscopic and macroscopic effect of the changes in these properties has not been easy to quantify. We present a noncontacting technique to evaluate the stress-concentration factors. stress redistribution damage evolution, classification of damage, and damage tolerance in CMCs. The technique uses the thermoelastic effect to measur SIGN guidelines and protocols must be developed for ceramic- the hydrostatic stress state across the entire surface of a stressed atrix composites(CMCs)to gain acceptance in engineering body. This noncontacting method can be used to measure changes applications. In particular, it is especially important to quantify the in the hydrostatic stress distribution and hydrostatic stress- allowable design loads. Brittle constituent composites are known concentration factors as a composite is damaged. In addition to be reliant on inelastic mechanisms(such as interface failure quantifying the stress redistribution, we show that the damage matrix cracking, fiber failure, and fiber pullout) to enhance mechanism can be imaged and identified, thereby assigning a ductility and redistribute stress away from locations of concen- mechanism and damage classification to the measured changes in trated stress However the extent of the stress redistribution is not stress distribution. The results that we present clearly indicate that substantial stress redistribution does occur in brittle constituent well-known. Recent research has classified the macroscopic mech- anisms of stress redistribution into three general categories: class I, composites, and that each damage mechanism can effectively class Il, and class Ill (see Fig. 1)2- Class I damage is the hange the notch sensitivity of a material development of a single matrix crack that is bridged by fibers. class ll damage involves the development of multiple cracks in the matrix before fiber failure, and class Ill damage involves the Il. Thermoelastic Stress Analysis development of a shear-damage zone parallel to the loading Thermoelastic stress analysis (TSA) uses the thermoelastic direction. The operative damage mechanism, as well as the extent effect to relate adiabatic changes in the stress state of a material to of stress redistribution in a particular composite, will be dependent changes in the specimen temperature. 4/ The effect is summa- on the composite constituent properties, as well as the properties of rized by the thermoelastic equation Brittle constituent composites commonly use an interphase to △T=-KT0△σ (1a) nsure interfacial debonding, this debonding provides a weak link that enables fiber bridging and pullout. The " weak interface where AT is the change in temperature that is caused by a change paradigm has been a key aspect of brittle composite design, in hydrostatic stress(Ao= yAokk), To the ambient specimen temperature, and K the thermoelastic constant. K is given by B N. Cox-contributing editor (1b) where a is the coefficient of thermal expansion, p the density, and C the specific heat at constant volum In the TSA method, a low-amplitude sinusoidal stress is applied to the specimen, which creates a thermal response that is in-phase 337
Evaluation of Damage Evolution in Ceramic-Matrix Composites Using Thermoelastic Stress Analysis Thomas J. Mackin* and Mark C. Roberts Mechanical and Industrial Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801 Thermoelastic stress analysis (TSA) has been used to monitor damage evolution in several composite systems. The method is used to measure full-field hydrostatic stress maps across the entire visible surface of a sample, to quantify the stress redistribution that is caused by damage and to image the existing damage state in composites. Stress maps and damage images are constructed by measuring the thermoelastic and dissipational thermal signatures during cyclic loading. To explore the general utility of the method, test samples of several ceramic-matrix and cement-matrix composites have been fabricated and tested according to a prescribed damage schedule. The model materials have been chosen to illustrate the effect of each of three damage mechanisms: a single crack that is bridged by fibers, multiple matrix cracking, and shear bands. It is shown that the TSA method can be used to quantify the effect of damage and identify the operative damage mechanism. Each mechanism is identified by a characteristic thermal signature, and each is shown to be effective at redistributing stress and diffusing stress concentrations. The proposed experimental method presents a new way to measure the current damage state of a composite material. I. Introduction DESIGN guidelines and protocols must be developed for ceramicmatrix composites (CMCs) to gain acceptance in engineering applications. In particular, it is especially important to quantify the effect of stress concentrations, such as notches and holes, on the allowable design loads. Brittle constituent composites are known to be reliant on inelastic mechanisms (such as interface failure, matrix cracking, fiber failure, and fiber pullout) to enhance ductility and redistribute stress away from locations of concentrated stress.1 However, the extent of the stress redistribution is not well-known. Recent research has classified the macroscopic mechanisms of stress redistribution into three general categories: class I, class II, and class III (see Fig. 1).2–4 Class I damage is the development of a single matrix crack that is bridged by fibers, class II damage involves the development of multiple cracks in the matrix before fiber failure, and class III damage involves the development of a shear-damage zone parallel to the loading direction. The operative damage mechanism, as well as the extent of stress redistribution in a particular composite, will be dependent on the composite constituent properties, as well as the properties of the interface. Brittle constituent composites commonly use an interphase to ensure interfacial debonding; this debonding provides a weak link that enables fiber bridging and pullout. The “weak interface” paradigm5 has been a key aspect of brittle composite design, wherein the He and Hutchinson6 debonding criterion has been viewed as a necessary condition for toughening. Recently, however, tough composites that use strong interfaces have been fabricated.7,8 The key difference results from the toughening mechanism: a class III material does not need to have a weak interface to develop considerable stress redistribution, local nonlinearity, and notch insensitivity. Furthermore, the pivotal work of Aveston et al. 9 clearly showed that the addition of strongly bonded fibers to a brittle matrix resulted in a composite with greatly enhanced strength and toughness. The mechanism of stress redistribution, in this instance, was multiple matrix cracking (class II). In any case, the underlying fundamental phenomenon is the development of a nonlinear material response that redistributes stress away from regions of concentrated stress. Changes in the fiber, matrix, and interface properties will affect the active damage mechanism, as well as the extent of stress redistribution. Fiber and matrix properties are easily measured using standard testing methods,10,11 whereas interface properties can be determined using hysteresis,12–14 pullout and frictional heating,15 or fiber push-out tests.8,16–25 However, the mesoscopic and macroscopic effect of the changes in these properties has not been easy to quantify. We present a noncontacting technique to evaluate the stress-concentration factors, stress redistribution, damage evolution, classification of damage, and damage tolerance in CMCs. The technique uses the thermoelastic effect to measure the hydrostatic stress state across the entire surface of a stressed body. This noncontacting method can be used to measure changes in the hydrostatic stress distribution and hydrostatic stressconcentration factors as a composite is damaged. In addition to quantifying the stress redistribution, we show that the damage mechanism can be imaged and identified, thereby assigning a mechanism and damage classification to the measured changes in stress distribution. The results that we present clearly indicate that substantial stress redistribution does occur in brittle constituent composites, and that each damage mechanism can effectively change the notch sensitivity of a material. II. Thermoelastic Stress Analysis Thermoelastic stress analysis (TSA) uses the thermoelastic effect to relate adiabatic changes in the stress state of a material to changes in the specimen temperature.26,27 The effect is summarized by the thermoelastic equation:26–33 DT 5 2kT0Ds (1a) where DT is the change in temperature that is caused by a change in hydrostatic stress (Ds 5 1⁄3Dskk), T0 the ambient specimen temperature, and k the thermoelastic constant. k is given by k 5 a rCv (1b) where a is the coefficient of thermal expansion, r the density, and Cv the specific heat at constant volume. In the TSA method, a low-amplitude sinusoidal stress is applied to the specimen, which creates a thermal response that is in-phase B. N. Cox—contributing editor Manuscript No. 190235. Received April 27, 1998; approved July 30, 1999. Supported by the National Science Foundation (NSF). *Member, American Ceramic Society. J. Am. Ceram. Soc., 83 [2] 337–43 (2000) 337
338 Journal of the American Ceramic Sociery-Mackin and Roberts Class I ClassⅢ Matrix Cracking + Fiber Failure Matrix Cracking: No Fiber Failure Shear Band Formation Fig. 1. Schematic depiction of the three classes of damage that have been identified in CMCs the applied stress. The peak-to-valley temperature change that is in-phase with the peak-to-valley applied dilatational stress is given by26-28, 34-36 △T=-KT0△ Ukk sin or (2) where o is the cyclic load frequency, Ao,k the stress range, and I A key aspect of this effect is that spatial variations in the applied stress(Aokk(,y))will appear as a spatial distribution in tempera ture(Al(x y)). The applied cyclic stress must be of sufficient frequency to approximate adiabatic conditions in order to mini- mize heat transfer from regions of high stress to regions of low stress. For the Ao(r y) range that have been applied during the testing of the present materials, AT( y)=0.1-0.03.C. An infrared (IR)imaging system, 26, 27, 37-41 A sinusoidal load fre- quency ceramic materials and is the frequency that has been used in this study. Typically, thermoelastic images are collected at loads <10% of the proportional limit, to ensure that damage does not ccumulate during the time that is required to measure the spatia temperature distribution and, in addition, alleviate frictional heat ing that is caused by dissipation. We have observed that the subject materials can be imaged at loads up to 90% of the proportional limit without the occurrence of dissipational heating. In any case, the mscf is calculated by dividing the maximum signal adjacent to the of a steel sample with a center hole, dissipational heating is measured by examining the IR signal that lags the applied load by 90. Then, the applied load is adjusted to ole by the average far-field signal. eliminate this signal and provide a signal that is purely thermoelas- tic. In the present tests, a TSA system(Delta-Therm 1000, Stress Photonics, Madison, WI) with a 128 X 128 array of iR detectors measured over a spot size of 120 um that is centered at a distance was used to measure the surface temperatures of cyclically loaded of 180 um from the notch root. This signal is divided by the test samples. This TSA system allows full-field measurements of far-field hydrostatic signal to calculate an MSCF value. As the the surface-temperature distribution of standard-sized test samples damage progresses, stress redistribution will result in a reduction 30 s at a spatial resolution of 120 um and a temperature in the stress-concentration factor. The method that is presented resolution of -0.003 K enables a quantitative measure of the effect of damage on the local In the present set of experiments, stress redistribution is quantified by measuring a modified stress-concentration factor stress-concentration factor. Figure 2 illustrates the method, using a (MSCF) at the root of machined notches over a range of applied specimen that has been fabricated with a hole in its center The experimentally measured MSCF is given by the ratio of the notch root by the average far-field signal and then multiplying the far-field signal. Using the temperature map that is shown in Fig. 2, quotient by the ratio of the far-field to net-section widths the experimentally measured MSCF value has been determined to MSCF=△(1w be 2. 66. This value is almost identical to that obtained following Peterson's handbook, where the elastically calculated stress ation factor(SCF)is 2.6 where a is the notch depth and 2w is the specim The MSCf, as defined is a measure of the hy stress- concentration factor. In practice, the user interrog and computes an average signal over a spot siz measurements are not reliable within 120 um of the sample thus, the measured MSCF is the ratio of the hydrostatic tPeferson's Stress Concentration Factors, 2nd Ed. wiley. New York. 1997
with the applied stress. The peak-to-valley temperature change (DT) that is in-phase with the peak-to-valley applied dilatational stress is given by26–28,34–36 DT 5 2kT0Dskk sin vt (2) where v is the cyclic load frequency, Dskk the stress range, and t the time. A key aspect of this effect is that spatial variations in the applied stress (Dskk(x,y)) will appear as a spatial distribution in temperature (DT(x,y)). The applied cyclic stress must be of sufficient frequency to approximate adiabatic conditions in order to minimize heat transfer from regions of high stress to regions of low stress. For the Ds(x,y) range that have been applied during the testing of the present materials, DT(x,y) 5 0.1°–0.03°C. An infrared (IR) imaging system is the only practical means of measuring these temperatures.4,26,27,37–41 A sinusoidal load frequency of 10 Hz results in adiabatic cyclic-temperature changes in ceramic materials and is the frequency that has been used in this study. Typically, thermoelastic images are collected at loads ,10% of the proportional limit, to ensure that damage does not accumulate during the time that is required to measure the spatial temperature distribution and, in addition, alleviate frictional heating that is caused by dissipation. We have observed that the subject materials can be imaged at loads up to 90% of the proportional limit without the occurrence of dissipational heating. In any case, dissipational heating is measured by examining the IR signal that lags the applied load by 90°. Then, the applied load is adjusted to eliminate this signal and provide a signal that is purely thermoelastic. In the present tests, a TSA system (Delta-Therm 1000, Stress Photonics, Madison, WI) with a 128 3 128 array of IR detectors was used to measure the surface temperatures of cyclically loaded test samples. This TSA system allows full-field measurements of the surface-temperature distribution of standard-sized test samples in 30 s at a spatial resolution of 120 mm and a temperature resolution of ;0.003 K. In the present set of experiments, stress redistribution is quantified by measuring a modified stress-concentration factor (MSCF) at the root of machined notches over a range of applied loads. The MSCF is defined by dividing the TSA signal at the notch root by the average far-field signal and then multiplying the quotient by the ratio of the far-field to net-section widths: MSCF 5 DTlocal DTfar-field S 1 2 a wD (3) where a is the notch depth and 2w is the specimen width. The MSCF, as defined, is a measure of the hydrostatic stressconcentration factor. In practice, the user interrogates the IR image and computes an average signal over a spot size of 120 mm. The measurements are not reliable within 120 mm of the sample edges; thus, the measured MSCF is the ratio of the hydrostatic stress measured over a spot size of 120 mm that is centered at a distance of 180 mm from the notch root. This signal is divided by the far-field hydrostatic signal to calculate an MSCF value. As the damage progresses, stress redistribution will result in a reduction in the stress-concentration factor. The method that is presented enables a quantitative measure of the effect of damage on the local stress-concentration factor. Figure 2 illustrates the method, using a steel specimen that has been fabricated with a hole in its center. The experimentally measured MSCF is given by the ratio of the maximum local signal at the notch root divided by the average far-field signal. Using the temperature map that is shown in Fig. 2, the experimentally measured MSCF value has been determined to be 2.66. This value is almost identical to that obtained following Peterson’s handbook,† where the elastically calculated stress concentration factor (SCF) is 2.67. † Peterson’s Stress Concentration Factors, 2nd Ed. Wiley, New York, 1997. Fig. 2. Representative TSA image of a steel sample with a center hole; the MSCF is calculated by dividing the maximum signal adjacent to the hole by the average far-field signal. Fig. 1. Schematic depiction of the three classes of damage that have been identified in CMCs. 338 Journal of the American Ceramic Society—Mackin and Roberts Vol. 83, No. 2
February 2000 Evaluation of Damage Evolution in CMCs Using TS IlL. Materials IV. Experimental Procedur To demonstrate the general utility of the TSa method, (I Constitutive Response lution and stress Unidirectional tensile specimens 25.4 mm wide and 15-20 cm long were cut from each material. Aluminum tabs were bonded to ecause they were expected to exhibit different damage the ends of each specimen, to diffuse the gripping stresses during nisms testing Specimens were tested using a servohydraulic load frame (1) An eight-harness satin weave 0/90 composite par f with hydraulic grips (Instron, Danvers, MA). A clip-on-type AL2O fiber-reinforced AL,O-matrix(AL,O,/AL,O,)composite that extensometer was used to measure elongational strain in the was fabricated by R. Goettler at McDermott Labs. This sample had specimens, whereas the load values were recorded using a 22000- a carbon coating on the alumina fibers to promote debonding Ib load cell (2) Composites of portland cement that was reinforced with Because of the damage tolerance of the materials that were nidirectional, alkali-resistant glass fiber (Cem-fil, Vetrotex involved, testing to ultimate failure was difficult. In several Wichita Falls, TX). These composites were fabricated in-house specimens, shear cracks extended from the notches to the grips using a filament-winding process. Fiber tows were passed and specimen cracking often affected the extensometer reading through a portland cement slurry and wound on an octagonal Failure commonly occurred at the grips, which provided lower bound estimates of the tensile strength. These values were used to (3) Sample composites of a polyureasilazane matrix(which is determine the subsequent damage loads for notched sample test- a polymer precursor to SiAlON or SiC)(CERASET, Lanxide ing. Figure 3 shows a compilation of the stress-strain response of erformance Materials, Newark, DE) that was reinforced with each material. Note the relative linearity of the tensile stress-strain nidirectional S-2 and E-glass fiber. These composites were curves for these materials. which would suggest little damage fabricated using the same process as that for the cement compos- tolerance. However, the following sections will show that all these ites described previously for the material in choice(2) materials exhibit active nonlinear mechanisms that enable stress (4) Unidirectional Cem-fil glass-fiber-reinforced portland ce- redistribution and considerable damage tolerance ment composite samples that were modified using a clay plasti- cizer in the portland cement. These composites were fabricated in the same manner as those for the material in choice(2) (2) Damage Evolution ()Specimens that were machined from a commercially Double-edge-notched samples were fabricated from each mate- available industrial cut-off blade(Avery Abrasives, Inc., Trum- ial, as described in Table I. Edge notches were cut using a bull, CT) that consisted of an alumina-fiber-reinforced phenolic diamond blade that was 0.5 mm thick. The double-edge -notch matrix that was reinforced with two layers of a woven glass fabric geometry was used to guarantee damage initiation at a known amples were machined from a cut-off blade 30 in. in diameter and location. Two coats of commercial flat-black spray paint were 0. 25 in thick. Plain-weave glass-fiber mattes were bonded onto pplied to the specimen to ensure constant emissivity across the either side of the matrix, which resulted in a sandwich structure of entire specimen. An adequate drying time (-2 d)was required for matrix between glass mattes. consistent results Glass fiber/CERASET 300 Glass Fiber/Portland Glass fiber/modified portland 250 H Glass fiber/Phenoli Alumina/Alumina 200 150 100 0.6 0.7 Strain(%) Fig. 3. Representative tensile stress-strain curves for each composite
III. Materials To demonstrate the general utility of the TSA method, damage evolution and stress redistribution were evaluated using five different composite systems. The following materials were chosen because they were expected to exhibit different damage mechanisms: (1) An eight-harness satin weave 0/90 composite panel of Al2O3-fiber-reinforced Al2O3-matrix (Al2O3/Al2O3) composite that was fabricated by R. Goettler at McDermott Labs.42 This sample had a carbon coating on the alumina fibers to promote debonding. (2) Composites of portland cement that was reinforced with unidirectional, alkali-resistant glass fiber (Cem-fil, Vetrotex, Wichita Falls, TX). These composites were fabricated in-house, using a filament-winding process.43 Fiber tows were passed through a portland cement slurry and wound on an octagonal mandrel. (3) Sample composites of a polyureasilazane matrix (which is a polymer precursor to SiAlON or SiC) (CERASET, Lanxide Performance Materials, Newark, DE) that was reinforced with unidirectional S-2 and E-glass fiber. These composites were fabricated using the same process as that for the cement composites described previously for the material in choice (2). (4) Unidirectional Cem-fil glass-fiber-reinforced portland cement composite samples that were modified using a clay plasticizer in the portland cement. These composites were fabricated in the same manner as those for the material in choice (2). (5) Specimens that were machined from a commercially available industrial cut-off blade (Avery Abrasives, Inc., Trumbull, CT) that consisted of an alumina-fiber-reinforced phenolic matrix that was reinforced with two layers of a woven glass fabric. Samples were machined from a cut-off blade 30 in. in diameter and 0.25 in. thick. Plain-weave glass-fiber mattes were bonded onto either side of the matrix, which resulted in a sandwich structure of matrix between glass mattes. IV. Experimental Procedure (1) Constitutive Response Unidirectional tensile specimens 25.4 mm wide and 15–20 cm long were cut from each material. Aluminum tabs were bonded to the ends of each specimen, to diffuse the gripping stresses during testing. Specimens were tested using a servohydraulic load frame with hydraulic grips (Instron, Danvers, MA). A clip-on-type extensometer was used to measure elongational strain in the specimens, whereas the load values were recorded using a 22 000- lb load cell. Because of the damage tolerance of the materials that were involved, testing to ultimate failure was difficult. In several specimens, shear cracks extended from the notches to the grips, and specimen cracking often affected the extensometer readings. Failure commonly occurred at the grips, which provided lowerbound estimates of the tensile strength. These values were used to determine the subsequent damage loads for notched sample testing. Figure 3 shows a compilation of the stress–strain response of each material. Note the relative linearity of the tensile stress–strain curves for these materials, which would suggest little damage tolerance. However, the following sections will show that all these materials exhibit active, nonlinear mechanisms that enable stress redistribution and considerable damage tolerance. (2) Damage Evolution Double-edge-notched samples were fabricated from each material, as described in Table I. Edge notches were cut using a diamond blade that was 0.5 mm thick. The double-edge-notch geometry was used to guarantee damage initiation at a known location. Two coats of commercial flat-black spray paint were applied to the specimen to ensure constant emissivity across the entire specimen. An adequate drying time (;2 d) was required for consistent results. Fig. 3. Representative tensile stress–strain curves for each composite. February 2000 Evaluation of Damage Evolution in CMCs Using TSA 339
ournal of the American Ceramic Sociery--Mackin and Roberts Table I. Double-Edge-Notched Sample Dimensions AL2O3/Al,O3 152 25.76 3.18 Glass fiber and cement Glass fiber/modified portland cement Glass fiber/CERASET 3676 Glass fiber/phenolic resin 12.7 The glass fiber/phenolic resin composite sample had only a single-edge notch. The stress-strain response of each material was used to deter mine a damage schedule of steadily increasing stresses. Notched amples were loaded to a prescribed fraction of the ultimate rength and then unloaded. Then, a 10 Hz cyclic load was applied at an amplitude that was a fraction of the damage load, and TSA images were acquired. The load range was chosen to provide good signal response without generating damage during image acquisi- tion. Following image acquisition, the damage load then was increased incrementally, and the cycle was repeated until specimen failure. This procedure provided an interrupted picture of the evolution of damage as recorded by the TSA images During cyc slip)can generate frictional heating. Furthermore, the frictional Fig. 4. TSA images of the Al2O3/AL2O, sample after loading to(a)10 heating occurs at twice the loading frequency. That is, at both the and(b)90 MPa. A cyclic stress range of 1-5 MPa was used during image maximum and minimum loads, there is no relative displacement acquisition between the fiber and the matrix and the maximum frictional worl occurs at the midpoint of the cyclic loading. Heat that is generated by frictional work interacts with the thermoelastic signal and gener- ates a thermal signal that is out-of-phase with the applied cyclic stress By examining the out-of-phase response, any locations of frictional dissipation can be identified. Regions of relative fiber sliding appear Is"hot spots in the out-of-phase images and are used in a new damage-imaging methodology Our experience has shown that dam- age in the form of shear bands, as well as multiple matrix cracks, is identified easily by examining the out-of-phase response. However, during thermoelastic image acquisition, the magnitude of the applied cyclic loads is adjusted to eliminate the out-of-phase signal, which ensures that no dissipational heating occurs during collection of the in-phase thermoelastic images. The cyclic loads applied during acquisition of the in-phase thermoelastic signal are a small on of the dama a) However, to facilitate damage imaging following thermoelastic image acquisition, the amplitude of the applied cyclic loads is increased to Fig. 5. Damage images of the A,O/AL,O3 composite, showing the evolution of shear bands with ing g applied stress. The images were natch the last previous monotonic damage load level. These higher acquired using cyclic stresses of (a)5-10 MPa and(b)5-90 MPa. cyclic-load amplitudes generate dissipation and improve the out-of phase signal response. Acquisition of the out-of-phase images re- quires <I min, which exposes the sample to <600 cycles at elevated load levels. Collection of the in-phase images al ways precedes To assess changes in the stress distribution. line scans were collection of the out-of-phase damage images drawn across the notch plane on the in-phase images. These line scans have been normalized by the average signal from a line scan in the far field and multiplied by the net-section/far-field area ratio ults and discussion Fig. 6). The value of the normalized line scans at the notch root provides a measure of the effective stress-concentration factor(Eq Figures 4(a)and(b) show representative in-phase TSA images (3)). The MSCF value decreased as the damage level increased of the Al,O3/Al2O3 composite material after loading from an initial average value of MscF 2 75 at a damage load of loads of 10 and 90 MPa, respectively. Each of the in-ph 10 MPa to a value of MSCF= 1.58 after loading to 90 MPa. These was collected at an applied cyclic stress range of 1-5 MPa line scans indicate that the growth of shear bands blunted the notch Out-of-phase damage images(Fig. 5) were collected root and decreased the stress-concentration factor that was asso- ranges of 5-10 MPa and 5-90 MPa. These images reveal a distinct ciated with the notches thermal signature(Fig. 5(b)that is consistent with the presence of Samples of the unidirectional-Cem-f1l/portland cement compos- shear bands that emanate from the notch root, perpendicular to the ite were notched and tested as described previously; these sampl notch plane. In a previous study, TSA images of a composite exhibited substantial stress redistribution. Evaluation of either the composed of a carbon matrix that has been reinforced with carbon in-phase( Fig. 7)or out-of-phase(Fig 8)images suggest that the fiber(C/C composite)were pared with X-ray radiographs to operative damage mechanism is the formation of shear bands that verify the presence of the shear-band damage mechanism. The grow the entire length of the specimen and are distributed across TSA signature of the damage that was observed in the C/C the specimen. This phenomenon is especially evident in Fig. 8, composite is almost identical in character to that observed in the where frictional dissipation appears as vertical bands in the imag present Al,O/AL,O3 composite which is consistent with the formation of shear bands. Line scans
The stress–strain response of each material was used to determine a damage schedule of steadily increasing stresses. Notched samples were loaded to a prescribed fraction of the ultimate strength and then unloaded. Then, a 10 Hz cyclic load was applied at an amplitude that was a fraction of the damage load, and TSA images were acquired. The load range was chosen to provide good signal response without generating damage during image acquisition. Following image acquisition, the damage load then was increased incrementally, and the cycle was repeated until specimen failure. This procedure provided an interrupted picture of the evolution of damage as recorded by the TSA images. (3) Damage Imaging During cyclic loading, dissipation mechanisms (such as fiber slip) can generate frictional heating.15 Furthermore, the frictional heating occurs at twice the loading frequency. That is, at both the maximum and minimum loads, there is no relative displacement between the fiber and the matrix and the maximum frictional work occurs at the midpoint of the cyclic loading. Heat that is generated by frictional work interacts with the thermoelastic signal and generates a thermal signal that is out-of-phase with the applied cyclic stress. By examining the out-of-phase response, any locations of frictional dissipation can be identified. Regions of relative fiber sliding appear as “hot” spots in the out-of-phase images and are used in a new damage-imaging methodology. Our experience has shown that damage in the form of shear bands, as well as multiple matrix cracks, is identified easily by examining the out-of-phase response. However, during thermoelastic image acquisition, the magnitude of the applied cyclic loads is adjusted to eliminate the out-of-phase signal, which ensures that no dissipational heating occurs during collection of the in-phase thermoelastic images. The cyclic loads applied during acquisition of the in-phase thermoelastic signal are a small fraction of the damage load. However, to facilitate damage imaging following thermoelastic image acquisition, the amplitude of the applied cyclic loads is increased to match the last previous monotonic damage load level. These higher cyclic-load amplitudes generate dissipation and improve the out-ofphase signal response. Acquisition of the out-of-phase images requires ,1 min, which exposes the sample to ,600 cycles at elevated load levels. Collection of the in-phase images always precedes collection of the out-of-phase damage images. V. Results and Discussion Figures 4(a) and (b) show representative in-phase TSA images of the Al2O3/Al2O3 composite material after loading to damage loads of 10 and 90 MPa, respectively. Each of the in-phase images was collected at an applied cyclic stress range of 1–5 MPa. Out-of-phase damage images (Fig. 5) were collected at stress ranges of 5–10 MPa and 5–90 MPa. These images reveal a distinct thermal signature (Fig. 5(b)) that is consistent with the presence of shear bands that emanate from the notch root, perpendicular to the notch plane. In a previous study, TSA images of a composite composed of a carbon matrix that has been reinforced with carbon fiber (C/C composite) were compared with X-ray radiographs to verify the presence of the shear-band damage mechanism.2,4 The TSA signature of the damage that was observed in the C/C composite is almost identical in character to that observed in the present Al2O3/Al2O3 composite. To assess changes in the stress distribution, line scans were drawn across the notch plane on the in-phase images. These line scans have been normalized by the average signal from a line scan in the far field and multiplied by the net-section/far-field area ratio (Fig. 6). The value of the normalized line scans at the notch root provides a measure of the effective stress-concentration factor (Eq. (3)). The MSCF value decreased as the damage level increased, from an initial average value of MSCF 5 2.75 at a damage load of 10 MPa to a value of MSCF 5 1.58 after loading to 90 MPa. These line scans indicate that the growth of shear bands blunted the notch root and decreased the stress-concentration factor that was associated with the notches. Samples of the unidirectional-Cem-fil/portland cement composite were notched and tested as described previously; these samples exhibited substantial stress redistribution. Evaluation of either the in-phase (Fig. 7) or out-of-phase (Fig. 8) images suggest that the operative damage mechanism is the formation of shear bands that grow the entire length of the specimen and are distributed across the specimen. This phenomenon is especially evident in Fig. 8, where frictional dissipation appears as vertical bands in the image, which is consistent with the formation of shear bands. Line scans Table I. Double-Edge-Notched Sample Dimensions Composite Length (mm) Width (mm) Thickness (mm) Notch depth (mm) Al2O3/Al2O3 152 25.76 3.30 3.18 Glass fiber/portland cement 178 25.96 6.00 4.75 Glass fiber/modified portland cement 160 25.18 7.00 3.26 Glass fiber/CERASET 18.5 24.87 6.39 4.75 Glass fiber/phenolic resin† 203.2 76.15 6.87 12.7 † The glass fiber/phenolic resin composite sample had only a single-edge notch. Fig. 4. TSA images of the Al2O3/Al2O3 sample after loading to (a) 10 and (b) 90 MPa. A cyclic stress range of 1–5 MPa was used during image acquisition. Fig. 5. Damage images of the Al2O3/Al2O3 composite, showing the evolution of shear bands with increasing applied stress. The images were acquired using cyclic stresses of (a) 5–10 MPa and (b) 5–90 MPa. 340 Journal of the American Ceramic Society—Mackin and Roberts Vol. 83, No. 2
February 2000 Evaluation of Damage Evolution in CMCs Using TSA 10 MPa Damage Load 30 MPa Damage Load -60 MPa Damage Loa 90 MPa Damage Load 0.5 -9.357012546752337502.33754675701 935 Distance Between Notches(mm) Fig. 6. Normalized line scans between the notches in the Al,O,Al,O, composite, showing a reduction in stress concentration with increasing applied stress (b) Fig. 7. TSA images of the glass fiber/portland cement composite after loading to(a)10,( b)20, and(c)40 MPa. A cyclic applied stress of 1-10 MPa was across the notch plane revealed a decrease in stress concentration Damage evolution in the glass-fiber/phenolic-matrix composite from mSCf 2.0 at a damage load of 10 MPa to mScf =1.25 ropagated as a single crack that was bridged by fibers. Figure 13 at a damage load of 40 MPa shows in-phase thermal maps that reveal a distinct band of fibers A second type of fiberglass-reinforced portland cement com- bridging a single matrix crack. Double-edge notches resulted in ite was prepared using a clay-matrix additive. This specimen unstable crack propagation, therefore, a single-edge notch was cut also exhibited substantial stress redistribution, as demonstrated by erpendicular to the fiber orientation to attain stable crack growth. hase tsa The matrix crack propagated across the entire sample width clay additive had a dramatic effect on the operative damage leaving an intact bridging zone across the net section. This sample mechanism, changing it from the class Ill mechanism(shear clearly exhibits the class I damage mechanism(single crack that is bands)to the class II mechanism(multiple matrix cracking). The bridged by fibers) Unidirectional samples of the glass-fiber/CERASET-matrix composites exhibited substantial stress redistribution and complete Thermoelastic stress analysis(TSA)was used to document the net-section stress failure(Fig. 11). The operative damage mecha nset and growth of damage in several brittle constituent compos- nism was identified as shear bands by examining the out-of-phase ites In-phase images were used to quantify the stress distribution images(Fig. 12). Inspection of the in-phase images in Fig. ll show the materials, whereas out-of-phase imaging was used to capture that the sample redistributes stress across the net section between an image of the damage state. The out-of-phase imaging consti- the notches and effectively behaves as a sample with a reduced logy for observing and measuring damage in cross-sectional area lastic imaging of these materials permitted
across the notch plane revealed a decrease in stress concentration from MSCF ' 2.0 at a damage load of 10 MPa to MSCF 5 1.25 at a damage load of 40 MPa. A second type of fiberglass-reinforced portland cement composite was prepared using a clay-matrix additive. This specimen also exhibited substantial stress redistribution, as demonstrated by the in-phase TSA images (Fig. 9). However, the addition of the clay additive had a dramatic effect on the operative damage mechanism, changing it from the class III mechanism (shear bands) to the class II mechanism (multiple matrix cracking). The resulting damage images (Fig. 10) clearly show the evolution of multiple matrix cracks. Unidirectional samples of the glass-fiber/CERASET-matrix composites exhibited substantial stress redistribution and complete net-section stress failure (Fig. 11). The operative damage mechanism was identified as shear bands by examining the out-of-phase images (Fig. 12). Inspection of the in-phase images in Fig. 11 show that the sample redistributes stress across the net section between the notches and effectively behaves as a sample with a reduced cross-sectional area. Damage evolution in the glass-fiber/phenolic-matrix composite propagated as a single crack that was bridged by fibers. Figure 13 shows in-phase thermal maps that reveal a distinct band of fibers bridging a single matrix crack. Double-edge notches resulted in unstable crack propagation; therefore, a single-edge notch was cut perpendicular to the fiber orientation to attain stable crack growth. The matrix crack propagated across the entire sample width, leaving an intact bridging zone across the net section. This sample clearly exhibits the class I damage mechanism (single crack that is bridged by fibers). VI. Conclusions Thermoelastic stress analysis (TSA) was used to document the onset and growth of damage in several brittle constituent composites. In-phase images were used to quantify the stress distribution in the materials, whereas out-of-phase imaging was used to capture an image of the damage state. The out-of-phase imaging constitutes a new methodology for observing and measuring damage in composites. Thermoelastic imaging of these materials permitted Fig. 6. Normalized line scans between the notches in the Al2O3/Al2O3 composite, showing a reduction in stress concentration with increasing applied stress. Fig. 7. TSA images of the glass fiber/portland cement composite after loading to (a) 10, (b) 20, and (c) 40 MPa. A cyclic applied stress of 1–10 MPa was used during image acquisition. February 2000 Evaluation of Damage Evolution in CMCs Using TSA 341
ournal of the American Ceramic Society-Mackin and Roberts (b) (c Images were acquired using an applied cyclic stress of(a)1-10 MPa, (b)1-20 MPa, and(c)1-40 MP uted shear bands with increasing applied stress Fig. 8. Damage images of the glass fiber/portland cement composite, showing the formation of distr (b) (a) (b) Fig. 9. TSA images of the glass fiber/modified portland cement Fig. 11. TSA images of the glass fiber/CERASET composite after composite after loading to (a)5.7 and (b)14.2 MPa. An applied cyclic oading to(a) 20 and(b)80 MPa. A cyclic stress amplitude of 1-5 MPa stress of 1-5 MPa was used during image acquisition. (a (b) Fi the glass fiber/CERASET composite, stress amplitudes of (a)10-20 MPa and(b)10-80 MB red using cyclic revealing the formation of shear bands. Images were acqu Damage images of the glass fiber/modified portland cement showing the evolution of multiple matrix cracks. Images were MPa. usIng cyclic stress amplitudes of (a)1-5.7 MPa and(b)1-14.2 during the formation of damage zones at the notch roots. The measured reductions in the stress concentration factor were associated both a qualitative picture of how affects the stress ith local changes in the constitutive response that mechanistically distribution in composites and a tive measure of the resulted from combinations of fiber, matrix, and interface fracture damage by defining and tracking a I tress concentratio Stress redistribution occurred as a consequence of damage-induced factor(MSCF) at locations of concentrated stress. The MSCF softening, which led to lower notch-root stresses in each of the tested value that was computed from normalized TSA images decreased
both a qualitative picture of how damage affects the stress distribution in composites and a quantitative measure of the damage by defining and tracking a modified stress concentration factor (MSCF) at locations of concentrated stress. The MSCF value that was computed from normalized TSA images decreased during the formation of damage zones at the notch roots. The measured reductions in the stress concentration factor were associated with local changes in the constitutive response that mechanistically resulted from combinations of fiber, matrix, and interface fracture. Stress redistribution occurred as a consequence of damage-induced softening, which led to lower notch-root stresses in each of the tested composites. Fig. 9. TSA images of the glass fiber/modified portland cement composite after loading to (a) 5.7 and (b) 14.2 MPa. An applied cyclic stress of 1–5 MPa was used during image acquisition. Fig. 10. Damage images of the glass fiber/modified portland cement composite, showing the evolution of multiple matrix cracks. Images were acquired using cyclic stress amplitudes of (a) 1–5.7 MPa and (b) 1–14.2 MPa. Fig. 11. TSA images of the glass fiber/CERASET composite after loading to (a) 20 and (b) 80 MPa. A cyclic stress amplitude of 1–5 MPa was used during image acquisition. Fig. 12. Damage images of the glass fiber/CERASET composite, revealing the formation of shear bands. Images were acquired using cyclic stress amplitudes of (a) 10–20 MPa and (b) 10–80 MPa. Fig. 8. Damage images of the glass fiber/portland cement composite, showing the formation of distributed shear bands with increasing applied stress. Images were acquired using an applied cyclic stress of (a) 1–10 MPa, (b) 1–20 MPa, and (c) 1–40 MPa. 342 Journal of the American Ceramic Society—Mackin and Roberts Vol. 83, No. 2
February 2000 Evaluation of Damage Evolution in CMCs Using TS 343 "E. Vagaggini, J.-M. Domergue, and A. G. Evans, Relationships between ites: I, Theory,J. Am. Ceram. Soc., 78 [101 (1995 IJ.-M. Domergue, E. Vagaggini, and A. G. Evans, " Relationships between Hysteresis Measurements and the Constituent Properties of Ceramic Matrix Compos- imental Studies on Unidirectional Materials, J. An. Ceram. Soc., 78 14J.-M. Domergue, F. E. Heredia, and A. G. Evans, "Hysteresis Loops and the osites, " J. Am. Ceram. Soc. holmes and C. Cho, "Experimental Observations of Fi eating in C.-H. Such, "Evaluation of Interfacial Shear Strength, Residu and Coefficient of Friction for Fiber-Reinforced Ceramic Compo P. D Jero and R. J Kerans, "" The Contribution of Interfacial Roughness to S (b) Friction of Ceramic Fibers in a Glass Matrix, Scr. Metall. Mate D Jero, R.J. Kerans, and T. A Parthasarathy,"Effect of Interfacial Rou ages after loading to(a)ll and(b)13 MPa. Frictional Stress Measured Using Pushout Tests, "J.Am. Ceram Soc. 74[ ation of a single crack that is bridged by w.C. Carter, E. P. Butler, and E. R. Fuller, ""Micro-mechanical Aspects of Asperity-Controlled Friction in Fiber-Toughened Ceramic Composites, Scr Met ter.,25,579-84(1991) In addition to quantifying the stress redistribution, the operative P D. Warren, T. J. Mackin, and A G. Evans, "Design, Analysis and Application damage mechanism in each material was 上k9192s dissipational signal that was 90 out-of- with the applied al Analysis of the Fiber cyclic load. The out-of-phase signal of and Push-Out Tests, J.Anm. Ceram. dissipational heating and high thermal contrast in the damage slicon Cadet Bo Dsnlichate glass D, K sitest a ceracris s ofn p fintona n zones. This method has become a new tool to measure the current Pushout Tests, "J. dm Ceram Soc, 74(1j115-22(1991). damage state in a material. Combined use of the in-phase and 2J. W. Hutchinson and H M. Jensen, "Models of Fiber Debonding and Pullout in out-of-phase images provides a measure of the damage and its Brittle Composites wuth Friction, Mech. Mater. 9.139-63(1990) effect on the stress distribution of a material and the mechanisms Sliding Behavior of Sapphire Fibers in TiAl and Glass Matrices, "J. Am. Ceram Soc., evo 7512]358-62(1 In addition to basic studies of damage, the present method ai, and B Cotterell, "Fracture of Fiber-Reinforced Materi- has become an appealing new nondestructive evaluation tool. ,39,550-72(1988 proposed method of damage monitoring is a noncontacting tool to Analysis of Isotropic Materials", Ph.D. measure the hydrostatic stress distribution in a material, as well as Thesis. Department of Engineering Mechanics, The University of wisconsin- a tool to visualize the operative damage mechanism. It can be used 27N. Harwood and W. M. Cummings, Thermoelastic Stress Analsis. Adam Hilger aid materials development by relating damage mechanisms to the underlying material properties, it also can be used in service A. K. Wong, J. G. Sparrow, and s. A Dunn, "On The Revised Theory of the applications to measure the current health of a composite compo Thermoelastic Effect, J Phys. Chem. Solids, 49[]395-400(1988) Constant or ent. In-service damage measurements will require a source of Thermoelastic Parameter?,J Phys. Chem. Solids, 48[8]749-53(1987) oscillating stress: the stresses do need not be sinusoidal. Recent research conducted by Stress Photonics has shown that high Mer nsky and R. J. O'Connell, "Bulk Thermoelastic Attenuation of Com- quality TSa images can be collected using a random input stress B. Budiansky, "Thermal and Thermoelastic Properties of Isotropic Composites J Compos Mater., 4, 286-95(1970) to drive the subject material. Thus, the vibrations that are "M. w. Zymansky, Heat and Thermodynamics, Sth Ed. McGraw-Hill, New York, normally present in service(e. g, vibrations due to engine opera- tion) may be sufficient to enable in situ measurements of the E, A. Jackson, Equilibrium Statistical Mechanics, Prentice-Hall International current stress state in composite components. Sciences. Prentice-Hal E. Bakis, H. R. Yih, w. w. Stinchcomb, and K. L. Reifsnider, ""Damage References A. Simonds, C. E. Bakis, and w. w, Stinchcomb, "Effects of Matrix G. Evans, F. w. Zok, and T J. Mackin, The Sta Ighness on Fatigue Response of Graphite Fiber Composite Laminates," ASTM wre Mechanical Behavior e Spec. Tech, Publ., 1012, 5-18(1989 pp 3-84. Edited by S. V. Nair and K Jakus. Butterworth-Heinemann, Newton, MA, in Unidirectional Ceramic-Matrix Composites,"J.Am. Ceram Soc., 75(10 T. J. Mackin, T. E. Purcell, M. Y. He, and A. G. Evans, "Notch Sensitivity and (1992) Stress Redistribution in Three Ceramic-Matrix Composit w.w.Stinchcomb and C. E. 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In addition to quantifying the stress redistribution, the operative damage mechanism in each material was identified by imaging a dissipational signal that was 90° out-of-phase with the applied cyclic load. The out-of-phase signal provides a measure of dissipational heating and high thermal contrast in the damage zones. This method has become a new tool to measure the current damage state in a material. Combined use of the in-phase and out-of-phase images provides a measure of the damage and its effect on the stress distribution of a material and the mechanisms of damage evolution. In addition to basic studies of damage, the present methodology has become an appealing new nondestructive evaluation tool. The proposed method of damage monitoring is a noncontacting tool to measure the hydrostatic stress distribution in a material, as well as a tool to visualize the operative damage mechanism. It can be used to aid materials development by relating damage mechanisms to the underlying material properties; it also can be used in service applications to measure the current health of a composite component. In-service damage measurements will require a source of oscillating stress: the stresses do need not be sinusoidal. Recent research conducted by Stress Photonics has shown that highquality TSA images can be collected using a random input stress to drive the subject material.44 Thus, the vibrations that are normally present in service (e.g., vibrations due to engine operation) may be sufficient to enable in situ measurements of the current stress state in composite components. References 1 A. G. Evans, F. W. Zok, and T. J. Mackin, The Structural Performance of Ceramic Matrix Composites, High Temperature Mechanical Behavior of Ceramic Composites; pp. 3–84. Edited by S. V. Nair and K. Jakus. Butterworth–Heinemann, Newton, MA, 1995. 2 T. J. Mackin, T. E. Purcell, M. Y. He, and A. 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