ICF10 Honolulu (USA) 2001 Vol. C
ORAL REFERENCE: ICF100438OR FRACTURE TOUGHNESS AND FRACTURE PROCESSES IN DUCTILE METALLIC FOAMS C. Motz and R. Pippan Erich Schmid Institute of Material Science, Austrian Academy of Sciences, A-8700 Leoben, Austria ABSTRACT For structural applications of aluminium foams, besides tensile and compressive behaviour, fatigue and energy absorbing the fracture mechanic behaviour is important. Fracture mechanic tests were performed on compact tension (CT) specimens of sizes from W=50 mm to W=300 mm made of ALPORAS® foams with different densities. In addition to standard tests, in-situ fracture experiments in a scanning electron microscope were performed. Besides the load and the load line displacement also crack extension via a potential drop technique, crack tip opening displacement and local deformations were measured. The deformation is strongly localized on different length scales. In front of the notch root a fracture process zone with concentrated deformation develops. The crack propagates through the foam building many secondary cracks and crack bridges. The determination of fracture toughness values in terms of stress intensity factor K, J-integral and crack tip opening displacement is discussed. The comparison of the K vs. ∆a (crack extension), J vs. ∆a and COD vs. ∆a with the actual fracture processes at the crack tip and load displacement response reveals that COD5 gives the most reliable values to characterize the fracture toughness. The critical values for COD5 range from 0.35 mm to 1.0 mm depending on the relative density of the foam. KEYWORDS metallic foams, cellular solids, fracture toughness, fracture processes, local deformation. INTRODUCTION In the last few years metallic foams, e.g. made of aluminium or magnesium alloys, have become commercially available due to improvements in the manufacturing processes. This new class of materials exhibits partly unusual mechanical properties compared to common metals. For successful design of load bearing structural elements, besides the well-investigated compression and energy absorbing behaviour [14], also the fracture behaviour and fracture toughness values are needed. Until now only a limited number of publications [5-7] addressing this topic are available. The aim of this investigation is to provide a closer look at fracture processes and the determination of fracture toughness values for these foams. Thus, standard fracture mechanic tests and additionally in-situ fracture tests in the scanning electron microscope were performed do determine fracture processes and fracture toughness values. For the tests, an ALPORAS® aluminium foam, which is commercially available, with different densities was used. Standard fracture mechanic parameters, like stress intensity factor K, J-integral and crack opening displacement COD, were
determined. All investigations were accompanied with local surface strain measurements, which show the development of the fracture process zone during crack initiation and crack propagation. EXPERIMENTAL SETUP Specimen preparation All investigations were carried out on ALPORAS® aluminium foams with two densities, 0.25 g/cm3 and 0.40 g/cm3. Chemical composition, production route and material properties of these foams are described in [8]. Standard compact tension (CT) specimens with a size range of W=50 mm to W=300 mm and a thickness of B=30 mm were used. The specimens were machined with a diamond wire saw to avoid damage of the foam. All specimens had an open surface, whereby the average cell size of the foam was about 3.5 mm. For the pre-crack a diamond wire saw cut with a notch tip radius of about 150 µm was used, which gave undistinguishable experimental results compared to specimens pre-cracked in fatigue (see also [9]). Standard fracture mechanic tests Standard fracture mechanic tests were carried out on a displacement controlled universal mechanic testing machine at room temperature and at a cross-head speed of 0.2 mm/min for specimen sizes W≤100 mm and 0.5 mm/min for W>100 mm. The load and the load line displacement were measured with a standard load cell and a clip gauge, respectively. Additionally, the crack or notch opening displacement (COD) was determined with a videoextensiometer 5 mm behind the initial crack tip. The crack extension was monitored by a potential drop technique and was verified by optical observations. Images from the foam surface were taken at different load line displacements with a CCD-camera at a resolution of 1528x1146 pixels and were used for local surface deformation measurements and for documentation of the crack extension, subsequently. The procedure for local deformation measurements is described in detail in [10]. In-situ experiments In order to investigate crack initiation, crack propagation and local deformations during crack growth, in-situ fracture tests in the scanning electron microscope (SEM) were performed. Due to the restricted space inside the SEM the specimen size is limited to W=50 mm and B=25 mm. A small in-situ loading device, with a displacement rate of 0.15 mm/min, was used to fracture the CT-specimens. In order to assign the different stages of the fracture process to the load versus load line displacement curve, the load and the displacement were measured too. Images from the foam surface, containing 1 to 6 cells, with a resolution up to 4000x3200 pixels were taken at different load line displacements. Subsequently, these images were analysed to measure crack extension, local deformations and to identify the fracture processes. RESULTS AND DISCUSSION Standard fracture mechanic tests Due to the somewhat unusual mechanical behaviour of ductile metallic foams, e.g. a marked stress plateau in compression, a deformation dependence of the Young’s modulus or strain localisation during deformation, also in the fracture mechanics tests some atypical effects can be expected. Fig. 1 shows a typical load F and crack extension ∆a versus load line displacement vLLD curve and a corresponding surface deformation map for a foam with a density of 0.40 g/cm3. It is evident from the load curve that these foams reveal only a very small linear elastic stage, followed by an extended plastic regime. The plastic deformation is strongly localised in a fracture process zone (FPZ), which can bee seen in the surface strain maps and can result in micro cracking of some high strained cell walls. In the region of the peak load a main crack starts from the notch root and propagates in a relatively large FPZ through the specimen, whereby the load decreases. This is usually accompanied with a characteristic kink in the crack extension curve, followed by a regime of larger crack growth rate. Both, the load and the crack extension curve, show in the region of stable crack growth a certain waviness, which is related to the inhomogeneous structure of the foam and results in a variation in the local crack growth resistance.
Figure 1 Load and crack extension versus load line displacement curve (left image) and corresponding surface strain map at a crack extension of 5 mm (right image, ε=x100%) for an ALPORAS® aluminium foam CT-specimen with a density of 0.40 g/cm3, W=100 mm and B=30 mm. Because of the wide plastic regime in the load versus load line displacement curve no valid fracture toughness values in terms of the critical stress intensity factor KIC according to ASTM E399 could be obtained with the specimen sizes used in this investigation. The calculated KQ values are relatively low and vary between 0.35 to 1.0 MPa.m1/2 depending on the density of the foam. Fig. 2 shows K versus crack extension ∆a curves for two foams with different densities. Both foams reveal an increase of the fracture toughness with crack propagation up to a crack extension of about 5 mm (it looks like a R-curve behaviour). This toughness enhancement with increasing ∆a is caused by plasticity, but also toughening mechanisms like crack bridging [6] and the formation of a FPZ containing localised yielding and micro cracking may contribute. In the region of larger crack extensions a decrease of K can be observed, which is dramatically in the case of the lower density foam. The “softening mechanisms” that are causing this drop in K (and also in the plastic limit load ratio F/FY) are not clear until now. Figure 2 Stress intensity factor K versus crack extension ∆a curve for two foams with a density of 0.25 g/cm3 (left image) and 0.40 g/cm3 (right image). CT-specimens with W=290 mm and B=30 mm were used. Fig. 3 shows the load - plastic limit load ratio versus load line displacement plots for the same two foams as depicted in Fig. 2. Also in the load - plastic limit load ratio F/FY (load divided by the corresponding plastic limit load) curves a significant drop in the region of larger crack extensions (or larger load line displacements) can be observed. Especially the lower density foam (0.25 g/cm3) reveals a dramatically drop in the plastic limit load ratio. It seems that both foams do not reach the stage of full plastification (F/FY=1). But due to the very small linear elastic regime of these foams it is difficult to measure the yield stress σy. So
the absolute values of the F/FY ratios depend on the chosen yield stress and may differ slightly, if σ0.1, σ0.2 or σ0.5 are used for the yield strength. Figure 3 Plastic limit load ratio F/FY versus load line displacement curves for the two foams, which are depicted in Fig. 2. Left image shows the foam with the density of 0.25 g/cm3 and the right image the foam with 0.40 g/cm3. Since valid fracture toughness values based on KIC could not be obtained in these tests, single specimen Jintegral determinations according to ASTM standard E813 and E1152 were performed. Fig. 4 shows Jintegral versus crack extension plots for different specimen sizes and different foam densities. Although in all J-integral tests the specimen size criterion was fulfilled, a certain size dependence of the initial J-value J0.2 and the J-curve can be observed. Furthermore, the initial part of the J-integral curves shows an atypical shape and a large scatter, which makes the determination of initial J-values, like Ji or J0.2, according to the standards difficult or impossible. A typical plateau in the J-integral curves that is associated with a steady state J-value JSS, as reported in [6], cannot be observed in all samples. For the foams with lower densities a decrease in the J-integral curve at large crack extensions is evident. This is in agreement with the previous observations in the K vs. ∆a and F/FY vs. vLLD curves. In general, the application of ASTM standards (E813, E1152), which are designed for solid metals, to metallic foams is problematic. Due to their special mechanical behaviour, metallic foams exhibit a different response in the fracture mechanic tests as assumed in common standards. Figure 4 J-integral versus crack extension plots for different specimen sizes and at a constant density of 0.25 g/cm3 (left image) and for different densities at constant specimen size (right image). The described methods calculate from the global mechanical response the fracture toughness values (stress intensity factor K, J-integral). A more direct method is provided by the crack opening displacement (COD) concept. In this investigation the COD5 value is used, which is measured 5 mm behind the initial crack tip or
notch root [11]. Fig. 5 shows COD5 and CTOD (crack “tip” opening displacement, which is determined 5 mm behind the actual crack tip; in our case this corresponds to 1.5 times the mean cell diameter) versus crack extension curves for two foams with different densities. It was found that the COD5 curves show a characteristic kink at low crack extensions (about ½ of the mean cell diameter), which can be associated with an “initial” fracture toughness value. The CTOD curves that deliver an actual fracture toughness value did not show a decrease at larger crack extensions, which is in contrast to the K vs. ∆a and J vs. ∆a curves. It seems that the possible softening mechanisms do not influence the resistance against crack propagation in terms of CTOD or crack tip opening angle, but have an impact on the general mechanical behaviour of the CT-specimens. Further detailed investigations are needed to identify the softening mechanisms and to find an approbate method for the determination of fracture toughness values in terms of J. Figure 5 COD5 and CTOD versus crack extension curves for two foams with different densities, 0.25 g/cm3 (left image) and 0.40 g/cm3 (right image). Figure 6 SEM micrograph from the region in front of the notch root of an in-situ cracked CT-specimen after a crack extension of about 6 mm (left image) and local in-cell-wall strain map from the first cell in front of the notch root at crack initiation, showing the plastic zone (right image, 4000 pixels are equivalent 3.3 mm). Strains are given in loading direction, ε=x100%, and the black lines mark the boundaries of the cells. In-situ fracture tests With a small loading device in-situ fracture tests in the scanning electron microscope (SEM) were performed to investigate the fracture processes. Loading of the specimen results in a very early, inhomogeneous plastic deformation of the foam. The strains are localised on different length scales. On the lower level, the cell walls, only some small regions in the walls are deformed, whereby the rest remains nearly undeformed. An
example is depicted in Fig. 6. On the higher length scale, the cell structure, only few weaker cells show larger deformations (see Fig. 1). With increasing load a fracture process zone develops in front of the notch root, which contains localised plastic yielding and micro cracking. At about 80% of the peak load a main crack starts from the notch root to propagate through the foam structure. This is accompanied by building of crack bridges up to 1 - 3 cell sizes behind the crack tip and by micro cracking of cell walls in the FPZ (see Fig. 6). The crack follows the path of lowest fracture resistance, which is in general the path with the thinnest cell walls. CONCLUSION Standard fracture mechanic tests based on the stress intensity factor, the J-integral and the COD concept were performed on ALPORAS® aluminium foams with different densities. Additionally, in-situ fracture tests in the SEM and local surface deformation measurements were carried out. The surface strain measurements reveal a very localised deformation of the foam on different length scales. During the crack growth a large fracture process zone develops, which contains localised plastic yielding and micro cracking of several cell walls. Due to the very small linear elastic part in the load versus load line displacement curve no valid KIC values according to ASTM E399 could be obtained. Although all performed J-integral tests were valid, the standard determination of fracture toughness values in terms of an initial J-value is not useful. The ASTM standards are optimised for solid metals and their application to ductile metallic foams is usually not possible and they should be adapted to the special properties of the foams. It was found that measurements of crack opening displacement in terms of COD5 gives a better approach to useful fracture toughness values. ACKNOWLEDGEMENT The financial support by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung and of the Österreichischen Nationalbankfonds (Project P13231PHY/FWF535) is gratefully acknowledged. REFERENCES 1. H. Bart-Smith, A.-F. Bastawros, D. R. Mumm, A. G. Evans, D. J. Sypeck, H. N. G. Wadley, (1998) Acta Mater. 46, 10, 3583-3592 2. H. Fusheng, Z. Zhengang, G. Junchang, (1998) Metall. and Mat. Trans. 29A, 2497-2502 3. R. Gradinger, F. G. Rammerstorfer, (1999) Acta Mater. 47, 1, 143-148 4. E. Andrews, W. Sanders, L.J. Gibson, (1999) Mat. Science and Eng. A270, 113-124 5. Y. Sugimura, J. Meyer, M.Y. He, H. Bart-Smith, J. Grenstedt, A.G. Evans, (1997) Acta Mater. 45, 12, 5245-5259 6. O.B. Olurin, N.A. Fleck, M.F. Ashby, (2000) Mat. Science and Eng. A291, 136-146 7. C. Motz, R. Pippan, Proc. ECF13, M. Fuentes, M. Elices, A. Martin-Meizoso & J.M. MartinezEsnaola, Eds., Elsevier Sciences (2000), 160c1.pdf (CDROM), 1-8 8. T. Miyoshi, M. Itoh, S. Akiyama, A. Kitahara, (2000) Adv. Eng. Materials 2, No. 4, 179-183 9. K.Y.G. McCullough, N.A. Fleck, M.F. Ashby, (1999) Acta Mater. 47, 2331-2343 10. A. Tatschl (2000), Neue experimentelle Methoden zur Charakterisierung von Verformungsvorgängen, Ph.D. thesis, University of Leoben, Austria 11. K.H. Schwalbe, A. Cornec, Fatigue of Eng. Mat. (1991), 14, 405-412
ICF100866OR/Yoru Wada Fracture toughness characterization of hydrogen embrittled Cr-Mo steel Yoru WADA and Yasuhiko TANAKA1) 1)Muroran Research laboratory, The Japan steel Works,ltd 4-Chatsu machi Muroran city, Hokkaido, 051-8505 JAPAN ABSTRACT Since pressure vessels for petroleum use are operated at high temperature high pressure hydrogen gas, it is a special concern whether a crack at a stressed region grow by internal hydrogen embrittement (I.H.E.) mechanism during shutdown low to temperature ambience. In this study, fracture mechanics tests were conducted to clarify how hydrogen assisted crack of 2.25Cr-1Mo steels grows under I.H.E. condition. Hydrogen was pre-charged inside of the steel by high pressure, high temperature hydrogen autoclave and tests were conducted at room temperature air ambience. As a result, for the majority of steels tested, the stress intensity factor at hydrogen crack growths by I.H.E. mechanism were very low at initiation (=KIH∼30MPa·m1/2)) and grows faster if an active, rising load was applied. The old 60's made generation steel, which has higher temper embrittlment susceptibility, exhibited a higher crack velocity and resulted in fast fracture (KIC-H) during rising loading. On the contrary, if a load was applied for a static, fixed crack mouth displacement manner (i.e. falling load condition), the crack velocity significantly decreased and finally stopped to give a higher threshold stress intensity factor (=Kth) except for higher strength steel. Higher strength steel (; Enhanced 2.25Cr-1Mo grade material) tended to continue to propagate despite under fixed displacement condition and falls on to a very low Kth. KEYWORDS I.H.E., Hydrogen charging, 2.25Cr-1Mo steel,KIH, KIC-H, Kth INTRODUCTION In the pressure vessel with overlay or attachment of stainless steel inside of the wall, a high stress may be arised at discontinuous and complex structure area due to thermal expansion mismatch between stainless steel
(SS) and base Cr-Mo steel. Furthermore, when pressure vessel cooled down to ambient temperature, hydrogen atoms absorbed inside of the Cr-Mo steel rather accumulates between interface of SS and Cr-Mo steel than degassing outside of the wall which may cause disbonding or initiation of hydrogen embrittled cracking. Figure 1 shows the calculation example of shutdown procedure. It is shown from the analysis that the crack at welded structure driving force arises at stainless structure welded area. Therefore, special attention should be paid whether the crack at the interface of stainless steel and Cr-Mo base initiates and penetrates through wall, which may cause final collapse of the entire vessel. In this study, fracture mechanics tests were conducted to investigate how hydrogen assisted cracking of 2.25Cr-1Mo steels grows by I.H.E. mechanisms examining loading method, materials toughness level and steel strength. NOMENCLATURE RL :Rising load CD :Constant Displacement KIH :Stress intensity for onset of subcritical crack growth Kth :the threshold intensity factor for hydrogen charging environment. KIC-H:material toughness measured in the hydrogen charging environment. MATERIALS Table 1 shows chemical composition of steels tested. Impurities Si, P and Sn were intentionally added to simulate the old temper embrittled steel controlling J-factor=(Si+Mn)x(P+Sn)x104 wt% level. After hot rolling, those heats were subjected to the quenched and tempered heat treatment + PWHT at 690°C for 8hrs. followed by step cooling. Table 2 shows mechanical properties. Low J steel is the new generation made steel with high fracture toughness at room temperature. Mid J and High J steels were temper embrittled by step cooling. The compact tension specimen were machined and Ni/Au were plated to prevent hydrogen degassing from inside of the steel. Hydrogen were charged in autoclave at 420°C, 12MPa for 48hrs followed by water quenching to room temperature and preserved in liquid nitrogen container until fracture mechanics test in air environment. CRACK GROWTH BEHAVIOR Effect of loading condition Slow rising load (:RL) and constant displacement(:CD)loading method (Figure 2) were applied on hydrogen crack growth testing. Load was controlled by Crack Mouth Opening Displacement(CMOD) with a speed of 0.00003mm/sec. efficacious for hydrogen embrittlement 1). Crack was monitored by D.C. potential drop method. Figure 3 shows typical result of RL+CD test. Crack initiation was occurred after 3hrs of a rising load test. Continuous propagation was observed during rising load applied. After CMOD kept constant, the crack growth rate decreased and finally stopped after 12hrs.. Figure 4 shows the repetitional RL and CD test. Subsequent imposing of rising load obviously enhances crack growth, whereas crack growth was deactivated by keeping CMOD constant. Finally, a remarkable increase in crack growth observed in the later RL stage and resulted in fast fracture.
K and da/dt relation Typical relationship between K and crack growth rate (da/dt) for 610MPa tensile strength steel is shown in Figure 5. Under RL condition, crack start to grow rapidly at low initiation point KIH, and continue to propagate at relatively constant speed of 10-4mm/sec order of magnitude for KI level ranging from 30 to 80MPa·m1/2 . After CMOD kept constant, KI and da/dt relationship can be drawn as steeper falling line, which finally reaches threshold slightly decreasing from holded KI. Since repetitional RL+CD result indicate that crack stops at any holded KI level (<KIC-H), threshold Kth may exist in between KIH and KIC-H affected by the holded CMOD value. Effect of temper embrittlement KIH were measured by RL condition for a temper embrittled old and newer high toughness heats and were plotted as a function of its material’s FATT in Figure 6. Regardless of FATT of its heat, majority of steels exhibits low initiation sensitivity of cracking; KIH=30MPa·m1/2. K-curves for Low J and Mid J steels are compared in Figure7. Initiation occur at low KI point in two heats, but cracking resistibility is higher for low J steel, whereas Mid J steel cracking propagates in low KI and led to KIC-H. Fracture appearances are compared in Figure 8. Intergranular cracking was dominant in Mid J steel whereas LowJ steel heat exhibits almost quasi-cleavage with some intergranular fracture surfaces. Although difference in fracture surfaces recognized, the role of hydrogen on the initiation kinetics should still to have to be studied. Effect steel strength level Crack growth measurement of RL+CD tests were conducted for enhanced and annealed heat and results are shown together in Figure 9. Three heats show entirely different cracking characteristics respectively where the enhanced heat exhibited a very aggressive propagation under long term CD condition, on the other hand, the only little cracking was observed in the annealed heat. These tendency indicates that the higher strength steel is susceptible to delayed type cracking under static CD condition falls on to lower Kth and lower strength steel as well as was already suggested by the previous studies.2) SUMMARY Crack growth characteristics for a variety of 2.25Cr-1Mo steels were clarified and summarized. Schematic illustration of K and da/dt relationship is shown in Figure 10. 1. Imposing of active rising load obviously enhances crack initiation and growth rate, whereas crack growth was deactivated by keeping CMOD constant. 2. Crack start to grow rapidly at low initiation point KIH, and continue to propagate at relatively constant speed and as KI level increases, fast fracture occurs at KIC-H. 3. Initiation of cracking KIH did not make much difference in temper embrittled and new high toughness steel. But cracking resistibility is higher for low J steel, whereas Mid J steel propagates cracking in low KI and reached KIC-H. 4. The higher strength steel is susceptible to delayed type cracking under static CD condition falling on to lower Kth and lower strength steel as well as was already suggested by the previous studies.
REFERENCES 1) J.Watanabe, T.Ishiguro, T, Iwadate and K.Ohnishi(1987), Hydrogen Embrittlement of 21/4Cr-1Mo and 3Cr- 1Mo- 0.25V-B Pressure Vessel Steels”,presented at API/MPC Task Group Meeting on Materials for Pressure Vessels May 1987 2) W.E.Erwin and J.G.Kerr(1982);WRC Bulletin 275,2
Table1 Chemical compositions(wt%) and mechanical properties of steels tested Steel C Si Mn P S Cr Mo Sn Sb J-factor FATT ℃ TS MPa Low J 0.14 0.08 0.55 0.005 0.0007 2.42 1.08 0.010 0.0011 95 -76 613 Mid J 0.15 0.25 0.55 0.015 0.0013 2.39 1.03 0.024 0.0009 312 6 623 Annealed 0.15 0.24 0.53 0.013 0.0013 2.45 1.02 0.022 0.0006 270 7 552 Enhanced 0.16 0.28 0.40 0.009 0.0150 2.16 1.01 0.004 0.001 88 4 668 J-factor=(Si+Mn)X(P+Sn)x104 0 10 20 30 40 0 100 200 300 400 500 KI Temp. Pressure KI, (10xMPam1/2), Temp.(℃) Elapsed time (hr.) 4 6 8 10 12 14 16 18 Pressure (MPa) MODEL SS Attachment Crack 145mm 6 mm SS Base Figure 1 Example of shutdown temeperature, pressure and calculated result of crack loading at a bottom shell section with a stainless attachment t (hr) CMOD t (hr) CMOD RL RL CD CD CD RL RL 0.00003mm/sec. Figure 2 Loading pattern for hydrogen embrittlment fracture mechanics test
0.78 0.79 0.80 0.81 0.82 2.25Cr-1Mo(610MPa) 3ppm, tested in air R.T. 3.5T-CT,J-factor=96 Potential Drop (V) Elapsed time (hr.) 4 8 12 16 200 300 400 500 600 KIH C.D. Crack Load R.L. R.L. R.L. C.D. Load (kN) 0 5 10 15 20 25 30 0 1 2 3 4 Δa H (mm) Crack Extention Load (kN) Elapsed Time (hr) Load 0 10 20 30 2.25Cr-1Mo(610MPa) 5ppm, tested in air R.T. 1T-CT,J-factor=154 RL CD Figure3 Typical crack growth behavior of RL+CD test Figure 4 Crack growth behavior of repetitional RL and CD loading 20 40 60 80 100 10-9 10-8 10-7 10-6 1x10-5 1x10-4 10-3 10-2 2.25Cr-1Mo(610MPa) 5ppm, tested in air R.T. 1T-CT,J-factor=96 KIH Kth CD RL KI(MPa m1/2) da/dt (mm/sec.) Figure 5 K and da/dt relationship of a RL+CD test 0 2 4 6 8 10 12 40 80 120 160 200 KIC-H KIH Low J Mid J Δa (mm) K total (MPa√m) -80 -40 0 40 80 120 0 100 200 300 400 500 3-5ppm 1.5ppm Half solid: Unstable Fracture KIH(J) KIC(J) KIH(J) (MPa√m) FATT ( ℃) Figure 7 K-curves of Mid J and Low J heats Figure6 KIH and KIC for a variety of temper embrittled steels
Fatigue Crack (b) Fatigue Crack (a) Figure 8 Fractography of Low J (a) and Mid J (b) heats 0 5 1015202530 0 1 2 3 4 5 2.25Cr-1Mo 5ppm, tested in air R.T. 1T-CT Enhanced (TS=680MPa) Annealed (TS=453MPa) Low J (TS=610MPa) RL CD Δa (mm) Elapsed Time (hr.) Figure 9 Crack growth measurement of RL+CD tests for various strength steel KIH Kth KIC-H Log da/dt Effect of temper embrittlement Effect of strength Log K Rising Load Constant Disp. Figure 10 Schematical illustration of I.H.E. crack growth curve of 2.25Cr-1Mo steel
POSTER REFERENCE: 0711 FRACTURE TOUGHNESS ENVELOPE OF A LIMESTONE ROCK AT HIGH CONFINING PRESSURE AND TEMPERATURE N. A. Al-Shayea1 and K. Khan2 1 Civil Engineering Department, KFUPM, Dhahran 31261, Saudi Arabia 2 Research Institute, KFUPM, Dhahran 31261, Saudi Arabia ABSTRACT Fracture locus or envelope under a mixed-mode I-II loading can be obtained by plotting the normalized mode-II versus mode-I fracture toughness values. The envelope obtained can be used as a criterion for fracture failure for that material. However, testing conditions have a strong impact on that envelope. The objective of this paper is to present some results of an experimental program that was made to obtain fracture toughness envelope for a limestone rock from Saudi Arabia. Brazilian disks with an inclined central notch were tested under diametral compression, to get variety of mixed mode I-II fracture cases. Tests were conducted using disks with different sizes, and different notch type. Tests were made at different confining pressure from 0 to 28 MPa, and different temperature from 27 to 116oC. Fracture toughness envelopes for the tested rock were obtained for both positive and negative regions (opening and closing of the crack) and at various environmental conditions. A quadratic equation, which fit the experimental results more satisfactory, were proposed as a failure criteria. One of the major contributions of this paper is the effect of high confining pressure and temperature on the fracture toughness envelopes of rocks. KEY WORDS Rock fracture, mixed Mode I-II, fracture envelope, high temperature and pressure. INTRODUCTION Studying the fracture toughness of rocks at elevated temperatures and confining pressures is valuable for a number of practical situations such as hydraulic fracturing used to enhance oil and gas recovery from a reservoir, and the disposal or safe storage of radioactive waste in underground cavities. Based on the loading type, there are three basic crack propagation modes in a fracture process, namely: Mode I (extension, opening), Mode II (shear, sliding), and Mode III (shear, tearing). Any combination of these modes can occur as a mixed-mode. Most, if not all, studies in the past have focused on fracture toughness determination under confining pressures only for Mode-I failure conditions. Nevertheless, due to randomly oriented cracks in rocks and/or in-situ stress conditions, cracks tend to propagate under the influence of a combined action of the basic
failure modes called mixed mode [1,2]. In the case of rocks, the combination of Mode-I and ModeII (mixed Mode I-II) failure is more common. Therefore, consideration of mixed Mode I-II loading in addition to pure Mode-I becomes important in fracture toughness investigation. Due to this mixed mode failure pattern, in addition to mode-I, fracture toughness under mode-II becomes important to be considered. When Brazilian disks with an inclined central notch are tested under diametral compression (Figure 1), a variety of mixed mode I-II fracture cases are obtained. For a particular material, a fracture locus or envelope can be obtained by plotting normalized modeII versus mode-I fracture toughness. The envelope obtained could be used as a failure criterion in fracture toughness study for a particular material and testing condition in a way similar to the use of Mohr-Coulomb failure envelope for strength. Usually, the fracture toughness of rock is determined at ambient conditions. However, under varying temperatures and confining pressures, the measured fracture toughness has been shown to vary. The fracture toughness behavior of a deep-seated rock formation requires the testing to be conducted in a manner that simulates the in-situ conditions such as temperature and confining pressure. THEORETICAL BACKGROUND Facture Toughness When a notched rock specimen is subjected to an externally applied load, stress concentrates in the vicinity of the crack tip. When this concentrated stress reaches a critical value, failure occurs due to propagation of the preexisting crack. The fracture toughness is then calculated in terms of the stress intensity factor (SIF). In this paper, a circular Brazilian disk with a central notch under diametrical compression (Figure 1) was used to investigate fracture toughness. The following mathematical expressions, proposed by Atkinson et al. [3], were used for the fracture toughness calculation: K P a RB N I I = π (1) K P a RB N II II = π (2) where, KI is Mode-I stress intensity factor; KII is Mode-II stress intensity factor; R is radius of the Brazilian disk; B is thickness of the disk; P is compressive load at failure; a is half crack length; and NI and NII are non-dimensional coefficients which depend on a/R and the orientation angle ( β) of the notch with the direction of loading. For linear elastic fracture mechanics (LEFM), the small crack approximation proposed by Atkinson et al. [3] can be used to determine the values of NI and NII for half crack to radius ratio (a/R ≤ 0.3), as follows: ( )2 2 2 2 ) (1 4 cos 4 sin 1 4 sin a R N I β β β ∗ − + = − (3) ( )( ) [ ]2 2 5 2 8cos a R N II − = + β (4) Fracture toughness for pure Mode-I ( β = 0) is taken as KIC; and that for pure Mode-II ( β ≈ 29 o) is taken as KIIC.
β P P R 2a Figure 1: A schematic for Brazilian disk under diametrical compression Failure Theories There are numerous failure criteria for crack initiation and propagation under mixed mode I-II loading condition. The most popular ones are: (1) the maximum tangential stress (σ) criterion, (2) the maximum energy release rate (G) criterion, and (3) the minimum strain energy density (S) criterion. The available experimental data shows that no distinct theoretical failure criterion is applicable to all cases. Also, these criteria imply that KIC is larger than KIIC, while experimental data show the opposite. Moreover, due to the fact that the existing failure criteria were developed based on the tensile loading rather than the compressive, they hold good only in the positive region (crack opening) and cannot predict the fracture behavior in the negative zone (crack opening) Many researchers have recommended using empirical relations for practical applications. Huang and Wang [4] and Sun [5] have used one of three empirical equations of straight line, ellipse, and homogenous quadratic to fit the experimental fracture toughness data in the (KI/ KIC)-(KII/ KIIC) plane. Also, an exponential relationship was used [6,7]. EXPERIMENTAL PROGRAM Sample Preparation Rock blocks were collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Cores were obtained from these blocks using 98 mm and 84 mm coring tube pits. Cores were sliced into circular disks using a high-speed circular saw. The thickness (B) of the sliced disks was in the range of 20-24 mm. A notch was machined in the center of the disks. Straight notch was made using a 0.25 mm diamond-impregnated wire saw, while chevron notch was made using a slow-speed circular saw. The notch making process is explained in more details elsewhere [8]. Rock properties The investigated limestone rock was beige in color. Its physical properties included a dry density of 2.586 gm/cm3, a specific gravity of 2.737, and porosity of 5.4%. The mechanical characteristics included a uniaxial unconfined compressive strength of 105 MPa, a tensile strength of 2.31 MPa, a modulus of elasticity of 54 GPa, and a Poisson’s ratio of 0.276.
Testing A strain-controlled loading frame having a capacity of 100 KN was used for the load application with a strain rate of 0.08 mm/min. Disk specimens were diametrically loaded with different values of the crack inclination angle ( β) ranging from 0° to 75° with a 15° increment. The applied load and load-point displacement were acquired using a computerized data logger. Tests were made at ambient conditions, at high confining pressure σ3) of 28 MPa, and at high temperature of 116°. The details of the experimental program can be found elsewhere [9]. RESULTS AND DISCUSSIONS The values for mode I and mode II fracture toughness (KI) and (KII) were determined using equations 1 to 4. Table 1 summarizes the values of KIC and KIIC at different conditions for straight notch. For all conditions, KIC is smaller than KIIC, in contrary to the values provided by the famous failure theories. Figure 2-a shows the variation of KI and KII with β for D = 98 mm, at different conditions. It can be seen that the high confining pressure has a tremendous impact on the fracture toughness, while the effect of high temperature has a minor effect. The normalized fracture toughness values of (KI/KIC) and (KII/KIIC) were determine for various cases. The plot of (KII/KIIC) vs. (KI/KIC) is named the fracture toughness envelope, which is the fracture locus for the general mixed-mode I-II loading. Crack initiates when a point ((KI/KIC), (KII/KIIC)) falls on the envelope. Figure 2-b gives a comparison between fracture toughness envelopes at different conditions (ambient, σ3 = 28 MPa, and T = 116 °C). Figure 3-a shows fracture toughness envelopes for D = 98 and 84 mm, at both positive region (crack opening) and negative region (crack closing). Also, Figure 3-b shows similar results for straight and Chevron notches. A second-degree polynomial was used to fit the experimental data at various conditions, and at both positive and negative region, Figures 2 to 3. The general form of the fitting is: ( ) ( ) ( )2 I IC I IC II IIC K K A B K K C K K + = + (5) where, A, B, and C are the coefficient for the second order polynomial used for the regression. The values of A, B, and C for various experimental conditions are tabulated in Table 2. It can be seen from Figure 6 that the results for all three conditions fall into a relatively close bound in the positive zone; however, distinct regions of data exist in the negative side. Note that the results for the specimens tested at high temperature fall close to the data for ambient conditions in the negative zone revealing that the fracture toughness is not very much affected by the temperature used in this study. However, fracture toughness envelope at high confining pressure, in the negative region, is extremely lower than that at ambient condition. TABLE 1 COMPARISON BETWEEN KIC, KIIC, AND THEIR RATIO AT VARIOUS CONDITIONS Condition Diameter (mm) KIC (Mpa m1/2 ) KIIC (Mpa m1/2 ) KIIC/KIC 98 0.42 0.92 2.19 Ambient 84 0.35 0.75 2.14 84 1.19 1.49 1.25 σ3 = 28 MPa 98 1.57 2.18 1.39 T = 116°C 98 0.52 1.00 1.92
0 102030405060708 β -4 -3 -2 -1 0 1 2 3 KI , KII (MPa m1/2) (deg.) ΚΙ ( ΚΙΙ ( ΚΙ (σ 3= 28 ΚΙΙ (σ 3= 28 ΚΙ ( ΚΙΙ ( D = 98 mm a/R = 0.3 0 -4 -3 -2 -1 0 1 KI / KIC 0 1 2 KII / KIIC Straight Notch a/R = 0.3 D = 98 mm Condition Ambient σ3= 28 T=116oC (a) (b) Figure 2: Compar ison of (a) fracture toughness, (b) fracture envelopes -3 -2 -1 0 1 KI / KIC 0 1 2 KII / KIIC a/R = 0.3 D = 98 mm Notch Type Straight Chevron -3 -2 -1 0 1 KI / KIC 0 1 2 KII / KIIC Straight Notch a/R = 0.3 D 84 mm 98 mm (a) (b) Figure 3: Fracture envelopes for Brazilian disks with (a) different D, (b) different notches TABLE 2 REGRESSION PARAMETERS FOR VARIOUS CONDITIONS Positive Region Negative Region Condition Notch Type D (mm) A B C A B C Chevron 98 0.9589 1.2436 −2.1709 0.9811 −0.1746 −0.0799 Straight 84 0.8664 −0.9402 0.0928 1.0797 0.1162 −0.0203 Ambient Straight 98 1.0891 −0.3701 −0.7584 1.0779 −0.3120 −0.1616 σ3 = 28 MPa Straight 98 1.0290 0.0461 −1.1663 1.0399 −0.0670 −0.1779 T = 116°C Straight 98 1.1046 0.6635 −1.7977 1.0759 −0.0882 −0.0661
CONCLUSIONS For the investigated limestone rock, the effect of confining pressure on KIC and KIIC is much more significant than the effect of temperature. KIC increased by 274% under σ3 = 28 MPa, but the corresponding value at T = 116°C was 24%. KIIC increased by 137% under σ3 = 28 MPa, but the corresponding value at T = 116°C was only 9%. Also, the effect of confining pressure on KIC is much more significant than its effect on KIIC. The above observations lead to the conclusion that the Mode-II component may be the most critical mode controlling failure at high values of temperature and confining pressure. ACKNOWLEDGEMENTS The authors acknowledge the support of King Fahd University of Petroleum and Minerals for providing computing and laboratory facilities. REFERENCES 1. Whittaker, B. N., Singh, R. N. and Sun, G. (1992), “Rock Fracture Mechanics; Principles, Design and Applications”, Developments in Geotechnical Engineering, Elsevier Publishers, Netherlands. 2. Lim, I. L., Johnston, I. W. and Choi, S. K., Assessment of mixed mode fracture toughness Testing methods for rock., Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 31, No. 3,. pp. 265-272 (1994). 3. Atkinson, C., Smelser, R. E. and Sanchez, J. (1982), “Combined Mode Fracture via the Cracked Brazilian Disk”, Intl. Journal of Fracture, Vol. 18, pp. 279-291. 4. Huang, J. and Wang, S. (1985), “An Experimental Investigation Concerning the Comprehensive Fracture Toughness of Some Brittle Rocks”, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., Vol. 22, No. 2, pp. 99-104. 5. Sun, G.X. (1990), Application of Fracture Mechanics to Mine Design, PhD Thesis, Dept. of Mining Engineering, University of Nottingham, England. 6. Awaji, H. and Sato, S. (1978), “Combined Mode Fracture Toughness Measurement by the Disk Test”, Journal of Engineering Materials and Technology, Vol. 100, pp. 175-182. 7. Lim, I. L., Johnston, I. W., Choi, S. K. and Boland, J. N. (1994), “Fracture Testing of a Soft Rock with Semicircular Specimens Under Three Point Bending-Part 1”, Int. J.Rock Mech. Min. Sci & Geomech. Abstr., Vol. 31, No. 3, pp. 185-197. 8. Khan, K., and Al-Shayea, N. A., “Effects of Specimen Geometry and Testing Method on MixedMode I-II Fracture Toughness of a Limestone Rock from Saudi Arabia”, Rock Mechanics and Rock Engineering, July-Sept. 2000, 33 (3), 179-206. 9. Al-Shayea, N. A., Khan, K. and Abduljauwad, S.N., “Efffects of Confining Pressure and Temperature on Mixed-Mode (I-II) Fracture toughness of a Limestone Rock Formation”, International Journal of Rock Mechanics and Rock Sciences, June 2000, 37 (4), 629-643.
ICF100907OR FRACTURE TOUGHNESS OF NIOBIUM/SAPPHIRE INTERFACES: EFFECT OF INTERFACE DOPING AND ION ASSISTED DEPOSITION G. S. Was1 and H. Ji2 1Departments of Nuclear Engineering and Radiological Sciences, and Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109, USA 2Optoelectronics Division, Agere Systems, Reading, PA 19612, USA ABSTRACT In this work, the effect of chemical composition and crystal orientation relationship on the interface fracture toughness of niobium/sapphire system was studied. We used several techniques to assess the interface fracture toughness, including microscratch, microwedge scratch, and delamination of patterned lines. Results showed a general trend of the effect of silver at the interface where the interface fracture toughness decreased with the amount of silver. Ion bombardment during film deposition (IBAD) significantly increased the interface fracture toughness through a combination of interface mixing and a controlled orientation relationship. KEYWORDS Niobium, interface fracture toughness, delamination, ion bombardment, films, microwedge, microscratch INTRODUCTION The overall objective of this project was to control the fracture toughness of the interface between niobium films and sapphire substrates by controlling the interface properties. Scratch tests have shown [1] that the interface fracture toughness correlates with silver interlayer thickness for niobium films deposited by electron beam evaporation. It has also been shown [2] that ion bombardment during film deposition can be used to strengthen the interface by matching the crystal orientation across the interface and by interface mixing. Therefore, the approach used in this project involved both weakening the interface by doping it with silver [3,4] and strengthening it by controlling the orientation relationship and the degree of interface mixing. Quantitative techniques for measuring interface fracture toughness in thin films are not well developed. In this paper, we have deduced values of interface fracture toughness using observations of failures that occurred during microscratching, microwedge scratching and from an analysis of bucking and curling of patterned niobium lines on sapphire. We were also able to assess the effectiveness of simultaneous ion bombardment during film deposition on the interface fracture toughness. RESULTS AND DISCUSSION
Microscratch Experiments Four sets of samples were made where a set constituted a series of depositions with varying interface silver level. All the films have a thickness of about 100 nm, as measured by the Dektak3 profilometer. The amount of silver at the niobium/sapphire interface varies from less than 0.8 monolayers to 6.4 monolayers as measured by RBS. Details of the experiment are given in ref. [5]. All samples with measurable silver level (>0.8 monolayer) at the interface failed during the scratch test with the niobium films delaminating from the sapphire substrates in a “brittle manner”. The failure was characterized by multiple spallations as the film detached from the substrate (Fig. 1a). Buckling was also observed along the scratch track in areas prior to the first spall. The tangential load shows abrupt changes corresponding to the spalls and the breakthroughs of pile-up material in front of the indenter. Interfacial toughness can be obtained from the geometry of the first spallation and the tangential load at which it happened. On the other hand, there was no indication of interfacial failure during the scratch test for the sample with <0.8 monolayer of silver at the interface, as well as the sample without silver . The film underwent ploughing with no evidence of delamination (Fig. 1b). No value of interface fracture toughness was estimated for these two samples because of the absence of interfacial failure. (a) (b) Figure 1: SEM micrographs of scratch tracks for (a) sample with interface delamination ( PVD, 4.2 monolayers of silver), and (b) sample without interface delamination ( PVD, < 0.8 monolayers of silver). The results from microscratch test showed a strong correlation between the interface fracture toughness and the amount of silver at the interface, as plotted in Fig. 2a. This result is in good agreement with the general trend of the interface fracture toughness as a function of the work of adhesion. As been pointed out by Elssner et al. [2], the interface fracture toughness Gc, increases exponentially with the work of adhesion Wad: , where the exponent n is a function of the orientation of the metal constituent. They found that the value of n for the (100) interface plane of niobium is 1.9, and that for the (110) interface plane of niobium is 3. Gc ∝WAd n The leveling off in interface fracture toughness at a silver level of 4.2 monolayers implies that the silver coverage reached 100% at a level of 4.2 monolayers. For the interface without silver, the work of adhesion (Wad) is that of pure niobium/sapphire: 800 mJ/m2 [6]. For interfaces that have 100% coverage of silver, it was found that the interface fracture occurred at the silver/sapphire interface [7], which has a work of adhesion of 150 mJ/m2 [8]. Assuming a linear interpolation of the work of adhesion for intermediate value of silver coverage, Fig. 2a can be replotted as a function of the work of adhesion (Fig. 2b). A least square fit of this curve using a power law function gave a value of 3.0 for the exponent n in Eq. 3. This result is in very good agreement with the value of 3.0 obtained by Elssner et al. [2].
0 2 4 6 8 10 12 0 100 200 300 400 500 600 Work of adhesion (mJ/m 2 ) 0 2 4 6 8 10 12 0 2 4 6 8 10 Interface fracture toughness (J/m2) Silver level (monolayer) Interface fracture toughness (J/m2) Gc ∝ Wad 3.0 (a) (b) Figure 2: Interface fracture toughness of niobium/sapphire interface as a function of (a) silver level at the interface, and (b) work of adhesion of the interface, and a least squares power law fit yielding n = 3.0. Microwedge scratch test Samples with and without silver at the interface experienced interface delamination under the microwedge scratch test. As shown in Fig. 3a, a portion of the film with a constant width was spalled. The tangential load at which the interface delamination occurred was recorded, and the strain energy release rate is calculated by Gerberich et al. [9] A decrease in interface fracture toughness due to the presence of silver at the interface is observed. The average interface fracture toughness for the sample without silver at the interface is 12.44 J/m2, while the average interface fracture toughness for the sample with silver at interface is 4.54 J/m2. The estimated values of the interface fracture toughness are consistent in magnitude with that of other metal/ceramic system where for W/SiO2 interface Gc was found to be 16 J/m2 and 4 J/m2 for 1.5 µm and 0.5 µm thick films, respectively [10]. This result is also consistent with the silver effect found by the microscratch test where the presence of silver weakened the interface of niobium/sapphire. (a) (b) 20 µm Figure 3: Micrographs of microwedge scratch tracks of (a) the PVD sample with 6.4 monolayer of silver at niobium/sapphire interface , and (b) a PVD sample with no silver at the interface. Analysis of buckles and curls in patterned lines Interface fracture toughness was also estimated from the delamination of patterned niobium lines on sapphire substrates. Both curls and buckles were found on some PVD samples. Buckling usually occurs when the film detaches from the substrate in the middle of the line, and curling occurs when the detachment is at one end of the line.
Interface fracture toughness from buckled lines Buckling was observed for niobium films on sapphire substrate in the patterned line forms, with interfacial silver levels range from 2.5 monolayer to 7.6 monolayer. Figure 4a shows a representative micrograph of the buckles. The buckles indicate that the residual stress in the niobium film must be compressive. The buckle height and length for buckled lines were measured from the photo. The stress in the niobium film can be determined using the analysis of buckle height given by Hutchinson and Suo [11]. The values of the film stress and the interface fracture toughness for lines that delaminated in the form of buckles ranges from 1.17 GPa to 5.57 GPa in compression, and the interface fracture toughness ranges between 0.62 J/m2 and 13.6J/m2. Given a 3% error in the measurement of the buckle height, the error in the film stress and interface fracture toughness is less than 5%. tilt angle 40Þ tilt angle 40Þ (a) (b) Figure 4: SEM pictures of (a) buckled niobium lines on sapphire substrate (PVD, 3.0 monolayers of silver), and (b) curled photoresist/niobium bilayer lines on a sapphire substrate with lines detached from the substrate at the niobium/sapphire interface (PVD, 2.1 monolayers of silver). The arrows point to buckles. While the magnitude of the stress is not unreasonable for niobium films given hardness measurement of 6 GPa [12], the reason that these films are in compression is unknown. A possible explanation for the formation of the buckles that does not require compressive residual stress in niobium is that the buckles formed at an earlier stage under external force induced by processing or an interface defect (e.g. gas bubble at the interface), causing the niobium to yield. However, optical inspection of the sample showed no observable defects before the photoresist was stripped off. Interface fracture toughness from curled lines Figure 4b is a SEM micrograph of the PVD sample with 2.1 monolayers of silver at the niobium/sapphire interface . The photo was taken after the dry etch step when lines were first observed to detach from the substrate. The final step of the photolithography process (stripping the photoresist) was omitted from this sample. Therefore the sample is a bilayer with a 1.35 µm thick photoresist layer on top of a 0.1 µm thick niobium film, deposited on a sapphire substrate which was pre-deposited with silver. As shown in Fig. 4b, the lines were detached from the substrate at one end. The detached portion of the bilayer (photoresist and niobium) curled up, indicating that there was a stress gradient in the bilayer system in which the stress in the photoresist is tensile relative to the niobium film. The observation of buckles next to the curled ends indicates that the stress in the niobium film must be compressive. Given the radius of the curvature, R, of the curls, and the niobium film stress of -1.32 GPa determined from the buckling analysis on a sample with similar deposition condition , the stress in the photoresist is estimated to be 38 MPa in tension. The fracture toughness of the interface, determined using the analysis in ref. [11], is 0.95 J/m2. As shown in Fig. 4b, both buckling and curling occurred on the same sample. This can be explained by the stress states in
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