ICF10 Honolulu (USA) 2001 Vol. D
ORAL REFERENCE: ICF100939OR POST-IMPACT FATIGUE BEHAVIOR OF HIGH TEMPERATURE POLYMER MATRIX COMPOSITES Kazumi HIRANO National Institute of Advanced Industrial Science and Technology (AIST), METI. Namiki 1-2, Tsukuba-shi, Ibaraki-ken 305-8564, JAPAN ABSTRACT Recently, the feasibility studies have been done as a part of evaluating and predicting long-term durability performance of candidate composite and structures in Japan Supersonic Research Program for 2nd Generation Supersonic Civil Transport in order to achieve through long-term and short-term tests under conditions simulating SST flight, development of associated predictive and accelerated test methods, and assessment of durability performances for design. This paper discussed in details the long-term durability, especially post-impact fatigue performance of the interesting and candidate high temperature polymer matrix composites and summarized the effects of low-velocity impact damage on fatigue behavior in a comparison with the open-hole fatigue behavior. KEYWORDS: Post-impact Fatigue, High Temperature Polymer Matrix Composites, Fully Reversed Tension-compression Fatigue, Low-velocity Impact Damage, Residual Compressive Strength INTRODUCTION Recently, the feasibility studies have been done as a part of evaluating and predicting long-term durability performance of candidate polymer matrix composite materials and structures in Japan Supersonic Research Program for 2nd Generation Supersonic Civil Transport [1] in order to achieve through long-term and short-term tests under conditions simulating SST flight, development of associated predictive and accelerated test methods, and assessment of durability performances for design. It is very important for a wide practical use of polymer matrix composites how to ensure the impact damage tolerance for long-term structural integrity. Generally, static compressive strength of laminated composites can be significantly reduced by delamination. Delamination can develop at a free edge, particularly at a hole, where inter-laminar stresses are very high. Delamination can also develop from low-velocity impact. Impact damages have strong influences on not only static strength characteristics but also fatigue behavior. Relatively little information is available on the post-impact fatigue behavior of advanced high temperature thermosetting and thermoplastic polymer matrix composites as compared with conventional epoxy matrix composites. The objective of this paper is to investigate the post-impact fatigue behavior between the interesting high temperature polymer matrix composites. The low-velocity impact damage was introduced into a narrow coupon type laminated specimen and then performed the fully reversed tension-compression fatigue tests. The effects of low-velocity impact damages on fatigue lives were summarized for both the screening of new
composite materials and the determination of a baseline fatigue design allowable for ensuring the long-term structural integrity of primary structural components. MATERIALS AND EXPERIMENTAL PROCEDURE Materials The materials chosen in this study are carbon fiber reinforced, toughened bismaleimide (BMI), G40-800 /5260, thermoplastic polyimide, IM600/PIXA-M and thermosetting polyimide, MR50K/PETI-5. They are laid up into a 32-ply quasi-isotropic laminate with a [+45˚/0˚/-45˚/90˚]4s stacking sequence. Room temperature mechanical and chemical properties [2] are summarized in Table 1. TABLE 1 Summary of mechanical and chemical properties G40-800/5260 IM600/PIXA-M MR50K/PETI-5 OHT MPa 569 461 426 Tensile modulus GPa NA 58.2 55.1 OHC MPa 385 309 317 Compressive modulus GPa 57.2 60 53.8 CAI (1500 in.·lb/in.) 358 383 298 Tg ˚C 274 235 250 Test Specimens Post-impact fatigue specimens A narrow coupon type specimen with same configuration and dimensions to open-hole (6.35 mm-dia.) fatigue specimen was used for the post-impact fatigue test. After machining from the as-fabricated panels, the impact damage was introduced at the center of specimen. Figure 1 shows the configuration and dimensions of the post-impact fatigue specimen. All specimens were nondestructively inspected before testing to document machining defects. There was no biasing of damage development due to initial defects. t 1 38.1 40 70 40 5 5 (160) Impact damage Figure 1: Post-impact fatigue test specimen dimensions Test Equipment and Procedure Impact test Impact load was directly applied on a coupon type specimen by using an instrumented drop-weight impact tester. The test fixture used for the impact portion of this study contained a 30 mm-diameter opening. A free-falling mass impacted at the center of the specimen. The impactor set-up and test fixture are shown in Fig. 2. The total weight of the impactor with a 12.7 mm diameter steel spherical tup was approximately 1.9 kg. The impact acceleration and impact force were measured using a piezoelectric accelerometer and two strain gages mounted on the impactor. The impact acceleration and impact force were recorded with a digital data acquisition system. The coupon-type specimens were mounted in the holder (see Fig. 2), and the bolts were torqued to 49 J. The instrumented impactor was centered above the coupon-type specimen at the required height to impact the desired impact energy per unit thickness. After the impactor struck the specimen, a piece of thick GFRP was quickly moved between the fixture and specimen to prevent the impactor from repeatedly hitting the
specimen. Three series of impact energy per unit thickness of 1668, 3336 and 6672 J/m (equal to 1500 in.·lb/in.), which are very low as compared with an industry standard for evaluating thick, quasi-isotropic laminates, were chosen. Open-hole and post-impact fatigue tests The open-hole fatigue and post-impact fatigue tests were performed with load controlled-mode, sinusoidal wave-form, at a constant cyclic frequency of 5 Hz using the personal computer-controlled MTS materials testing system with a environmental chamber kept temperature at 23±1˚C and relative humidity at 50±2%. All specimens were loaded in fully reversed tension-compression fatigue with R= -1. Cyclic stress versus strain curves were continuously measured by using extensometer (gauge length 25.4 mm) mounted on the specimen side edge, and monitored stiffness changes as a means of evaluating damage accumulation during fatigue loading. Laser optical microscope, SEM and soft X-ray radiograph examinations were also conducted at various fatigue cycles in order to examine fatigue damages initiated and propagated from both impact damaged area and a root of initial circular hole. 8.43kN 0.5ms (a) Impactor set-up and test fixture (b) G40-800/5260 (3336 J/m) Figure 2: An instrumented drop-weight impact tester and impact force versus time record RESULTS AND DISCUSSION Impact Damage An example of typical impact force versus time record is shown for G40-800/5260 in Fig. 2(b). The peak impact force in a case of impact energy per unit thickness of 3336 J/m was approximately 14.75 kN. The force-time signals for all the impact tests were almost consistent for every material. The impactor rebounded on the first collision and was out of the way before the test specimen rebounded. The high-frequency oscillations throughout the load-time histories are mostly ringing of the impactor and vibrations of the specimens. Before and after impact, each specimen was nondestructively evaluated to examine the extent of impact damage by laser optical microscope, soft X-ray and C-scanned ultrasonic examinations. The plastically deformed area at the impact surface was measured with the use of the laser optical microscope. The impact energy versus maximum depth of plastically deformed area relationships are shown in Fig. 3. At lower energy level, there is almost linear relationship regardless of materials. The G40-800/5260 composite had an even smaller plastically deformed area. The standard deviation was calculated for each of the impact area data sets. It showed a small variation especially within no fiber breakage damages for every material. This low standard deviation indicates that the impacts were consistent and repeatable. Typical internal damage patterns observed by soft X-ray examinations are shown in Figs. 4(a), (b) and (c) for impact energy per unit thickness of 6672 J/m. The IM600/PIXA-M had a larger impact damaged area.
They had many transverse cracks in every 0˚, ±45˚ and 90˚ laminate layers and delaminations especially at -45˚/90˚ interlayer. There are much differences in extents of un-symmetric internal impact damages fundamentally depending on both toughness of matrix resin and inter-lamellar properties. Figure 4 also shows that these impact damaged area doesn’t spread to whole specimen width within the limits of this experiment. 0 0.4 0.8 1.2 0 2 4 6 Impact energy J/mm Maximum depth mm ○ G40-800/5260 □ MR50K/PETI-5 △ IM600/PIXA-M 8 Figure 3: Relationships between impact energy and maximum depth of plastically deformed area 10mm 10mm 10mm (a) G40-800/5260 (b) IM600/PIXA-M (c) MR50K/PETI-5 Figure 4: Soft X-ray examinations of impact damages (Impact energy per unit thickness: 6672 J/m) Post-impact Tension-compression Fatigue To assess the effects of impact damage on fully reversed tension-compression fatigue behavior, the S-N curves were compared with the smooth and open-hole specimens. Minimum gross compressive stresses are plotted against cycles to failure (log scale) in Figs. 5 to 7. Linear least squares regression fits to the data are also drown. These figures show that there is a remarkable influence of low-velocity impact damage and fatigue lives rapidly decreases with increasing of impact energy. There is much influence for IM600/PIXA-M with a larger impact damaged area and a lower residual compressive static strength after impact. On the other hand, the normalized S-N curves in terms of static strength are consistent with those of open-hole specimens regardless of materials. It is concluded here that the decreases of fatigue lives fundamentally resulted from the reduction of static strength after impact damage. It is successfully predicted the fatigue lives of impact damaged specimen from normalized S-N curve and residual compressive static strength. It is very interesting that there is also a distinguishable knee point in the S-N curves of impact
damaged specimen resulted from the transition in fatigue failure mode from compressive failure in the low cycles region to tensile failure in the high cycles region. There is no transition in fatigue failure mode in the whole cycles region for the MR50K/PETI-5. 0 100 200 300 400 10-1 101 103 105 107 −σ σ Cycles to Failure Nf R= -1 G40-800/5260 ○ Open Hole △ Impact Damage (3336 J/m) 0 0.2 0.4 0.6 0.8 1 10-1 101 103 105 107 Cycles to Failure Nf min / Static Strength σ R= -1 G40-800/5260 ○ Open Hole △ Impact Damage (3336 J/m) (a) S-N curves (b) Normalized S-N curves Figure 5: Comparisons of post-impact fatigue lives with open-hole specimens for G40-800/5260 0 100 200 300 400 10-1 101 103 105 107 min max MPa -σ σ Cycles to Failure Nf R= -1 IM600/PIXA-M ○ Open Hole △ Impact Damage (3336 J/m) 0 0.2 0.4 0.6 0.8 1 10-1 101 103 105 107 Cycles to Failure Nf min / Static Strength σ R= -1 IM600/PIXA-M ○ Open Hole △ Impact Damage (3336 J/m) (a) S-N curves (b) Normalized S-N curves Figure 6: Comparisons of post-impact fatigue lives with open-hole specimens for IM600/PIXA-M 0 100 200 300 400 10-1 101 103 105 107 min max MPa −σ σ Cycles to Failure Nf R= -1 MR50K/PETI-5 ○ Open Hole △ Impact Damage (3336 J/m) □ Impact Damage (6672 J/m) 0 0.2 0.4 0.6 0.8 1 10-1 101 103 105 107 min / Static Strength σ Cycles to Failure Nf R= -1 MR50K/PETI-5 ○ Open Hole △ Impact Damage (3336 J/m) □ Impact Damage (6672 J/m) (a) S-N curves (b) Normalized S-N curves Figure 7: Comparisons of post-impact fatigue lives with open-hole specimens for MR50K/PETI-5 We have urgently done the following researches in order to achieve through long-term and short-term tests under conditions simulating SST flight, development of associated predictive and accelerated test methods,
and assessment of durability performances for design. - Failure mode transition in open-hole fully reversed, tension-compression fatigue behavior [3] - High temperature open-hole compressive fatigue behavior [4] - Moisture absorption effects on open-hole fatigue behavior [5] -Thermo-mechanical response under the simulated SST flight cycles [6] and long-term durability analysis and database [7] CONCLUSIONS (1) There is a quite difference in the extent of low-velocity impact damages among the high temperature polymer matrix composites. For low-impact damage, compared on equal impact energy level, the residual compressive static strengths of the G40-800/5260 were slightly greater than those of the IM600/PIXA-M and MR50K/PETI-5. (2) There is a remarkable influence of low-velocity impact damage on fatigue lives. The IM600/PIXA-M with a larger impact damaged area and a lower residual compressive static strength after impact has lower fatigue lives than those of the G40-800/5260 and MR50K/PETI-5.The G40-800/5260 composite was more resistant to initial impact damage, but the MR50K/PETI-5 composite was more tolerant to fatigue damage after impact. (3) The normalized S-N curves in terms of static strength are consistent with those of open-hole specimens regardless of materials. The decreases of fatigue lives fundamentally resulted from the reduction of static strength after impact damage. It is successfully predicted the fatigue lives of low-velocity impact damaged specimen from normalized S-N curve and residual compressive static strength. ACKNOWLEDGEMENTS This resea Ministry Committe REFERENCES . Hirano, K., Strategies for R&D on Construction and Preparation of Design Database for Advanced in 2. NEDO Report, Studies on Establishment of Long-term Durability Testing and Methodologies for High 3 erature Polymer Matrix Com4 ption Effect on Open-hole Fatigue Behavior for 5 istics for 6 . and Yamaguchi, Y., Thermo-mechanical Response under 7 Database for Advanced rch has been conducted as a part of Japan Supersonic Research Program under the supports of of Economy, Trade and Industry. The author also highly appreciated members of Technical e of Research Institute of Metals and Composites for Future Industry (RIMCOF). 1 Composite Materials, J. of the Japan Society for Composite Materials, Vol.26, No.1 (2000), PP.3-8 ( Japanese) Temperature Polymer Matrix Composites, March 31, 2000 (in Japanese) . Hirano, K., Long-term Durability Performance for Advanced High Temp posites, To be published in ICCM-13, June 25-29, 2001 . Hirano, K., Miyake, S. and Yoshida, H., Moisture Absor High Temperature Polymer Matrix Composites, To be presented at ICCE/8, August 5-11, 2001 . Hirano, K., Miyake, S. and Yoshida, H., Comparisons of Open-hole Fatigue Strength Character High Temperature Polymer Matrix Composites for the Next Generation Aircraft, To be published in Proc. of APCFS&ATEM’01, October 20-22, 2001 . Hirano, K., Suzuki, T., Miyake, S., Noda, M the Simulated SST Flight Profile and Residual Open-hole Tension/Compression Strength Characteristics for Advanced High Temperature Polymer Matrix Composites, To be presented at 5th International Conference on Durability Analysis of Composite Systems, November 6-9, 2001 . Hirano, K., Current Status and Future Prospects on Establishment of Design Composites and Structures in Japan, To be presented at 7th Japan International SAMPE Symposium & Exhibition, November 13-16, 2001
ORAL REFERENCE: ICF100691OR PREDICTING THE FATIGUE-LIFE OF STRUCTURAL ADHESIVE JOINTS A.J. Kinloch, A.J. Curley1, H. Hadavinia, and A.C. Taylor Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, Exhibition Road, London SW7 2BX, UK. 1Present address: Kingston University, School of Computer Science and Electronic Systems, Kingston upon Thames, London, KT1 2EE, UK. ABSTRACT A fracture-mechanics approach has been used to predict the cyclic-fatigue performance of the adhesively-bonded single-lap joint and a typical bonded component, represented by an adhesivelybonded ‘top-hat’ box-beam joint. The joints were tested under cyclic-fatigue loading in either a ‘wet’ or ‘dry’ environment, respectively. Several steps were needed to predict the cyclic-fatigue lifetime of these joints. Firstly, fracture-mechanics tests were used to obtain the relationship between the rate of fatigue crack growth per cycle, da/dN, and the maximum strain-energy release-rate, Gmax, applied during the fatigue cycle for the adhesive/substrate system under investigation, in both a ‘dry’ and a ‘wet’ test environment. Secondly, analytical and finite-element theoretical models were developed to describe the variation of the strain-energy release-rate, G, with crack length, a, as a function of the applied fatigue loads, for the single-lap joint and the ‘tophat’ box-beam joint. Thirdly, the experimental results from the short-term fracture-mechanics tests, obtained under similar test conditions and in the same environment as were used for the single-lap or bonded box-beam joints, were combined with the modelling results from the theoretical studies. This enabled the cyclic-fatigue performance of the single-lap or bonded box-beam joints to be predicted over relatively long time-periods. The agreement between the theoretical predictions and the experimentally-measured cyclic-fatigue behaviour for the joints was found to be very good. KEYWORDS Adhesives, Fatigue, Finite-element analysis, Fracture mechanics, Lifetime predictions.
INTRODUCTION The use of adhesive bonding in industry has greatly increased in recent years. However, its use in truly structural applications is still often limited. This is mainly due to a lack of confidence in the performance of adhesive joints, since the mechanical performance of the joints may deteriorate upon being subjected to cyclic-fatigue loading, especially if the joints are also exposed to a moist environment [1-4]. Thus, the ability to quantitatively describe this reduction in performance and to predict the lifetime of bonded joints would be a powerful tool, enabling manufacturers to make wider and more efficient use of adhesive bonding. In the present paper, mild-steel substrates have been employed which have been bonded using a rubber-toughened hot-curing epoxy adhesive. Firstly, fracture-mechanics tests are undertaken to identify the relationship between the rate of fatigue crack growth per cycle, da/dN, as a function of the maximum strain-energy release-rate, Gmax, applied during a fatigue cycle. These cyclic-fatigue tests are conducted in both a 'dry' environment of 23±1°C and 55 % relative humidity, and a 'wet' environment of immersion in distilled water at 28±1°C. Secondly, the cyclic fatigue of bonded (uncracked) single-lap joints in the ‘wet’ environment is studied. Analytical and finite-element models are developed to describe the variation of the maximum strain-energy release-rate, Gmax, with the length, a, of the growing fatigue crack in the adhesively-bonded single-lap joints. These models are then combined with the results from the above experimental fracture-mechanics data, which have also been conducted under cyclic-fatigue loading in the appropriate environment. These combined expressions are integrated between the initial (i.e. intrinsic or Griffith) flaw size, ao, and the crack length at final failure. Hence, the predicted number of cycles to failure for the lap joints may be deduced as a function of the cyclically-applied load. These predictions are compared with the experimental results, and the accuracy of the two approaches (i.e. via the analytical and the finite-element modelling studies) assessed. The sensitivity of the predictions to the boundary conditions employed, for example to the initial flaw size, is also discussed. The fracture-mechanics approach to lifetime prediction described above assumes that the cyclic-fatigue life of the lap joints is dominated by the propagation of cracks, rather than the initiation of such cracks. Thus, it is of some importance to establish whether this assumption is indeed correct, and therefore a backface-strain technique [3,5,6] is used to investigate crack growth in the lap joints during the fatigue tests. Thirdly, a finite-element model is used to predict the rate of crack growth in a typical adhesivelybonded component subjected to cyclic-fatigue loading, but in this case in a ‘dry’ environment. The component selected is a bonded ‘top-hat’ box-beam, loaded from one end of the bonded ‘top-hat’ section in a cantilever-bending mode. The predictions of the expected cyclic-fatigue life are again compared with the experimental results. RESULTS AND DISCUSSION Fracture-mechanics data The fracture-mechanics data were obtained using tapered double-cantilever beam (TDCB) adhesive-joint specimens and the experimental results obtained relate the rate of cyclic-fatigue crack growth, da/dN, to the maximum strain-energy release-rate, Gmax, applied during a fatigue cycle, see Figure 1 for example. Obviously, the fracture-mechanics tests need to be conducted under similar test conditions as the joints, or components, whose service-life is to be predicted. It is also important to ensure that the TDCB fatigue test specimens do indeed exhibit a similar locus of
failure as observed in the joints, or components, whose lifetime is to be predicted. The locus of failure of the different joints was therefore studied to ensure that this was indeed the case. It was found that the threshold strain-energy release-rate, Gth, below which no cyclic-fatigue crack growth occurred, as measured in the ‘dry’ environment, was significantly lower than the value of the adhesive fracture energy, Gc, determined under monotonic loading. Further, the value of Gth, was often further reduced if the cyclic-fatigue tests were conducted in water, as opposed to the ‘dry’ environment. Since the time-scales of such ‘wet’ cyclic-fatigue tests are relatively short, they act as a very effective accelerated test technique and may readily be used to ‘rank’ the durability of adhesive joints. For example, ‘wet’ fatigue tests may be employed to compare, and develop, different and novel types of surface treatments for polymeric and metallic substrates - this is of particular importance since the surface treatment employed may have a major effect on the durability of the bonded joint. Now, it is well established that the linear, central, region (labelled ‘Region II’ in Figure 1) of the plot of the relationship between logarithmic da/dN and Gmax may be modelled by using an expression based upon the Paris Law [7]: n DG dN da max = (1) where D and n are obtained by fitting the above equation to the experimental data. However, as may be seen in Figure 1, the complete relationship between logarithmic da/dN and Gmax is of a sigmoidal form. A lower-bound occurs at the fatigue threshold, Gth, where the crack growth rate is negligible (‘Region I’ in Figure 1) and an upper-bound occurs which is equivalent to the adhesive fracture energy, Gc, measured at a constant displacement-rate (‘Region III’ in Figure 1). Thus, the relationship between logarithmic da/dN and Gmax may be better expressed by a modified form of the Paris Law, namely [8,9]: − − = 2 1 max max max 1 1 n c n th n G G G G DG dN da (2) where Gth and Gc are the values of the cyclic-fatigue threshold and constant displacement-rate adhesive fracture energies respectively. The empirical constants n1 and n2 may again be obtained by fitting the above expression to the experimental data. For example, the data obtained from the 'wet' cyclic-fatigue tests on steel TDCB specimens bonded with the epoxy adhesive give D and n values of 1.37 x 10-13m2/N.cycle and 3.64 respectively. The relationship based upon Eqn. 1 is shown in Figure 1, together with the experimental data. The modified relationship, Eqn. 2, is also shown in Figure 1, and the values of n1 and n2 were found by fitting Eqn. 2 to the experimental data. Modelling The first step in modelling the cyclic-fatigue lifetime of the bonded joints and components is to obtain an expression to describe the experimentally-measured fracture-mechanics data, i.e. the relationships between the rate of crack growth per cycle, da/dN, and the maximum strain-energy
release-rate, Gmax, in a fatigue cycle as given in Eqns. 1 or 2, see above. Secondly, the variation of Gmax with crack length in the joint is theoretically modelled, using either an analytical or a finiteelement approach. In the present work, both analytical and finite-element approaches were used for the single-lap joints, though only the finite-element approach was used for the bonded component. Finally, these data are combined and the resulting expression is integrated and, hence, the long-term cyclic-fatigue life of the joint may be predicted. Predictions: Lap joints The cyclic-fatigue lifetimes in the ‘wet’ environment for the single-lap joints predicted using the finite-element model are compared with the experimental results in Figure 2. The overall agreement between this numerical method, as well as via the analytical method, and the experimental results is relatively good, bearing in mind that the fatigue life has been predicted from first principles with no empirical ‘fitting factors’ being employed. For example, the finite-element modelling studies give a threshold value of the maximum load, Tmax, per unit width in a fatigue cycle which could be applied to the lap joint of approximately 75 kN/m. This is equivalent to about 25% of the initial failure load, or fracture stress, of the lap joints. This predicted value of 75 kN/m may be compared with the measured value of 90 kN/m, which equivalent to 30% of the initial fracture strength of the lap joints. However, as may be seen from Figure 2, whilst the agreement from the finite-element models around the threshold portion of the Tmax versus Nf plots is good, the agreement is clearly poorer as one moves to higher values of Tmax; i.e. to lower values of Nf . Nevertheless, it may be argued that predicting a lower limit, threshold, load (below which cyclic-fatigue crack growth will not be observed) is the appropriate design philosophy in the case of adhesively-bonded joints. The present models are clearly capable of achieving very good predictions in this respect. It should also be noted that, as discussed above, an upper- and a lower-bound value of the initial flaw size, ao, may be calculated. However, as may be seen from Figure 2, the sensitivity of the predictions of the fatigue life upon the value of the initial flaw size via any of the above models and expressions is negligible. Predictions: Bonded component The adhesively-bonded ‘top-hat’ box-beam joint was tested under cyclic-fatigue loading in the ‘dry’ environment, and the predicted rate of crack growth per cycle, da/dN, for a given crack length, a, was calculated using Equation 1. For these predictions, the values of the strain-energy release-rate, Gmax, as a function of the length, a, of the propagating cyclic-fatigue crack were calculated from the finite-element model of the bonded component. The values of D and n, that are also needed, were obtained from the experimental fracture-mechanics data (see above), from tests conducted of course in the ‘dry’ environment. The experimental results and the predictions are shown in Figure 3 and, as may be seen, the agreement between the predicted values and the experimental data is very good. CONCLUSIONS The main aim of the work described in the present paper has been to predict the service-life of bonded joints and components when they are exposed to cyclic-fatigue loading. The basic idea derives from the fact that the cyclic-fatigue fracture-mechanics data may be gathered in a relatively short time-period, but may be applied to other designs of bonded joints and components, whose service-life may then be predicted over a far longer time-span. Thus, cyclic-fatigue fracture mechanics test have been conducted, and the results then combined with analytical and finiteelement models, to predict the fatigue performance of bonded single-lap joints and a bonded ‘tophat’ box-beam joint. The theoretical predictions were compared with the experimental results and the agreement was found to be very good.
ACKNOWLEDGEMENTS The authors would like to acknowledge the EPSRC for their support. Dr. A.C. Taylor is a Royal Academy of Engineering Post-Doctoral Research Fellow, and would like to thank the Royal Academy of Engineering for their support. REFERENCES 1. Kinloch, A.J. (1987) Adhesion and Adhesives: Science and Technology. Chapman and Hall, London. 2. Mostovoy, S. and Ripling, E.J. (1966) Journal of Applied Polymer Science, 10, 1351. 3. Curley, A.J., Hadavinia, H., Kinloch, A.J. and Taylor, A.C. (2000) Int. J. Fract., 103, 41. 4. Kinloch, A.J., Little, M.S.G. and Watts, J.F. (2000) Acta Mater., 48, 4543. 5. Imanaka, M., Haraga, K. and Nishikawa, T. (1995) Journal of Adhesion, 49, 197. 6. Zhang, Z., Shang, J.K. and Lawrence, F.V., Jr. (1995) Journal of Adhesion, 49, 23. 7. Paris, P.C. and Erdogan, F. (1963) Journal of Basic Engineering, 85(4), 528. 8. Martin, R.H. and Murri, G.B. (1990) ASTM STP, 1057, 251. 9. Kinloch, A.J. and Osiyemi, S.O. (1993) Journal of Adhesion, 43, 79. -8 -6 -4 -2 0 2 log(da/dN), mm/cycle 1 1.5 2 2.5 3 log Gmax, J/m2 Gmax, J/m2 10 32 100 315 1000 Gth= 20J/m 2 Gc=450J/m 2 Paris Law Modified Paris Law Region II Region III Region I Figure 1: Logarithmic crack growth rate per cycle, da/dN, versus logarithmic, and linear, Gmax, for the cyclic-fatigue fracture-mechanics tests performed in the ‘wet’ environment of 28oC and water immersion. The relationships for Eqns. 1 and 2 are shown by the solid lines.
0 50 100 150 200 250 300 Maximum load per unit width, Tmax, kN/m 1 2 3 4 5 6 7 Number of cycles, Nf, to failure 10 10 10 10 10 10 10 10 ao=135µm ao=85µm 8 Figure 2: The number, Nf, of cycles to failure in a ‘wet’ environment for the single lap joints as a function of the maximum load, Tmax, per unit width applied in a fatigue cycle. The points represent the experimental data whilst the lines are the predicted lifetimes using the finite-element model. Theoretical results are given for ao values of 85 or 135µm by the solid and dashed lines, respectively. -7 -6 -5 -4 -3 -2 -1 log(da/dN), mm/cycle 75 100 125 150 175 200 Crack length, mm Side B Side A FE prediction Experimental results Prediction Figure 3: Logarithmic rate of crack growth per cycle, da/dN, versus the length, a, of the propagating cyclic-fatigue crack for the bonded ‘top-hat’ component tested in a ‘dry’ environment. The open points represent the experimental data, whilst the solid line is the predicted crack growth rate from using the finite-element model.
ORAL/POSTER REFERENCE: ICF10093PR Prediction for Dry Sliding Wear in P/M Alloy: A back-propagation ANN approach Mohammed E. Haque 1 and K. V. Sudhakar 2 1 Department of Construction Science, Texas A&M University, College Station, TX 77843-3137, USA 2 Department of Industrial and Engineering Technology, Central Michigan University, Mount Pleasant, MI 48859, USA ABSTRACT An artificial neural network (ANN) based model was developed, trained and evaluated for studying the dry sliding wear behavior of Fe-2%Ni based powder metallurgy (P/M) alloy as a function of heat treatment. The P/M alloy in the as-sintered (designated AS, hardness 7 HRC) as well as in the hardened and tempered at 813 K (designated HT1), and at 593 K (designated HT2) conditions having hardness 30 HRC and 40 HRC respectively were investigated for their wear behavior. Several different ANN back-propagation models with different layers/slabs connections, weights with various weight updating methods, and activation functions including logistic, symmetric logistic, linear, Gaussian, and Gaussian complement were trained. The presented ANN back-propagation model with logistic activation function exhibited the excellent statistical performance both in the training and evaluation phases. The wear rate was found to decrease initially and remain almost constant with increasing sliding distance in all the samples. This was consistent with the experimental observations. Based on the ANN trained model, wear rate predictions were made for higher hardness (60 HRC) for steel with varying percent of carbon contents (0.3%, 0.4% and 0.6%). Since, the ANN trained model exhibited excellent comparison with the experimental results, it will provide a useful predictor for dry sliding wear rates in powder metallurgy alloys. KEYWORDS Wear rate; artificial neural network (ANN); powder metallurgy (P/M) alloy; dry sliding wear; sliding distance INTRODUCTION Artificial Neural Networks (ANNs) are revolutionary computing paradigms that try to mimic the biological brain. These ANNs are modeling techniques that are especially useful to address problems where solutions are not clearly formulated [1] or where the relationships between inputs and outputs are not sufficiently known. ANNs have the ability to learn by example. Patterns in a series of input and output values of example cases are recognized. This acquired “knowledge” can then be used by the ANN to predict unknown output values for a given set of input values. Alternatively, ANNs can also be used for classification. In this case, the Artificial Neural Networks’ output is a discrete category to which the item described by the input values belongs. ANNs are composed of simple interconnected elements called processing elements (PEs) or
artificial neurons that act as microprocessors. Each PE has an input and an output side. The connections are on the input side correspond to the dendrites of the biological original and provide the input from other PEs while the connections on the output side correspond to the axon and transmit the output. Synapses are mimicked by providing connection weights between the various PEs and transfer functions or thresholds within the PEs. Figure 1 illustrates a simple processing element of an ANN with three arbitrary numbers of inputs and outputs [2]. y Output signal to other PEs (corresponds to the axon in biological neurons) y y y = f(T) Transfer function T = Σ (wi xi) Activation function w2 w3 w1 Synaptic weights Inputs coming from other PEs (corresponds to the dendrites of a biological neuron) X2 X3 X1 Figure 1 Processing element of an ANN model with three arbitrary numbers of inputs and outputs The activation of the PE results from the sum of the weighted inputs and can be negative, zero, or positive. This is due to the synaptic weights, which represent excitatory synapses when positive (wi>0) or inhibitory ones when negative (wi<0). The PEs output is computed by applying the transfer function to the activation, which as a result of the synaptic weights, can be negative, zero, or positive. The type of transfer function to be used depends on the type of ANN to be designed. Currently, back-propagation is the most popular, effective and easy to learn model for complex networks [2,3]. To develop a back-propagation neural network, a developer inputs known information, assigns weight to the connections within the network architecture, and runs in the networks repeatedly until the output is satisfactorily accurate. The weighted matrix of interconnections allows the neural networks to learn and remember [4]. In essence, back propagation training adapts a gradient-descent approach of adjusting the ANN weights. During training, an ANN is presented with the data thousands of times (called cycles). After each cycle, the error between the ANN outputs and the actual outputs are propagated backward to adjust the weights in a manner that is mathematically guaranteed to converge [5]. The powder metallurgy processing has the advantage of forming near net shaped components. The advantages of producing complex shapes with close dimensional control at high density (porosity <2%) are 2
the distinct advantages of this process. There is no published research data in the area of artificial neural network for predicting the wear behavior for P/M alloys. Hence artificial intelligence approach has been used in the present study so that the recent investigation [6] on wear behavior of P/M alloys can be interpreted over a wide range of processing/design parameters. ANN BACKPROPAGATION MODEL The neural network used for the proposed model was developed with NeuroShell 2 software by Ward Systems Group, Inc., using a back-propagation architecture with multi- layers jump connections, where every layer (slab) is linked to every previous layer. The network was trained for wear rate. The inputs were sliding distance (500 through 6000 m), hardness (7 HRC, and 40 HRC), and carbon contents (0.3% and 0.4%), and outputs were the wear rate. The number of hidden neurons, for which the logistic activation function, f(x)=1/{1+ exp(-x)} was used, was determined according to the following formula [7]: Number of hidden neurons = 0.5(Inputs + Outputs) + √(Number of training patterns) Training data for the neural network training was obtained from the recent research work [6]. In the research dry sliding wear rate tests were carried out on a standard pin-on-disc machine. The data consisted of variation of wear rates with sliding distance as a function of heat treatments. Three different heat treatments were used which were: (1) AS, as-sintered, (2) HT1, hardened and tempered at 813 K, and (3) HT2, hardened and tempered at 593 K. Materials with two different carbon contents of 0.3% and 0.4% were tested. The training sets (total 100 experimental data points) included data corresponding to heat treatments 'AS' and 'HT2', and data corresponding to 'HT1' treatment (total 50 experimental data points) were used to evaluate the trained model. Training ANN model Network training is an act of continuously adjusting their connection weights until they reach unique values that allow the network to produce outputs that are close enough to the desired outputs. This can be compared with the human brain, which basically learns from experience. The strength of connection between the neurons is stored as a weight-value for the specific connection. The system learns new knowledge by adjusting these connection weights. The learning ability of a neural network is determined by its architecture and by the algorithmic method chosen for training. The training method usually consists of one of three schemes: (1) Unsupervised learning where no sample outputs are provided to the network against which it can measure its predictive performance for a given set of inputs. The hidden neurons must find a way to organize themselves without help from the outside. (2) Reinforcement learning where the connections among the neurons in the hidden layer are randomly arranged, then reshuffled as the network is told how close it is to solving the problem. Reinforcement learning is also called supervised learning, because it requires a teacher. The teacher may be a training set of data or an observer who grades the performance of the network results. Both unsupervised and reinforcement suffers from relative slowness and inefficiency relying on a random shuffling to find the proper connection weights. (3) Back propagation method is proven highly successful in training of multi-layered neural nets. The network is not just given reinforcement for how it is doing on a task. Information about errors is also filtered back through the system and is used to adjust the connection weights between the layers, thus improving performance. The accuracy of the developed model, therefore, depends on these weights. Once optimum weights are reached, the weights and biased values encode the network’s state of knowledge. Thereafter, using the network on new cases is merely a matter of simple mathematical manipulation of these values. 3
In the present research, several different ANN back-propagation trial models with different layers/slabs connections, weights and activation functions (including linear, Tanh, Tanh15, Sine, Symmetric Logistic, Gaussian, Gaussian Complement, etc.) were trained. In addition, pattern selections including “Rotation” and “Random” were used with weight updates using Vanilla, Momentum and TurboProp. The presented ANN back-propagation model with logistic activation function, "Rotation" for pattern selection, and "TurboProp" for weight updates was the best one among all other trials, which converges very rapidly to reach the excellent statistical performance (as illustrated in System Performance). Figure 2 demonstrates the graphical comparisons between the actual experimental data and the network predicted output during training and evaluation phases. They clearly demonstrate very good agreement between the actual and predicted performance. 0 5 10 15 20 25 30 35 0 1000 2000 3000 4000 5000 6000 Sliding distance (m) Wear rate X 10-13 (m3/m) Experimental (AS, 0.3% C) ANN (AS, 0.3% C) - Network Training Experimental (HT2, 0.3% C) ANN (HT2, 0.3% C) - Network Training Experimental (AS, 0.4% C) ANN (AS, 0.4% C) - Network Training Experimental (HT2, 0.4% C) ANN (HT2, 0.4% C) - Network Training Experimental (HT1, 0.3% C) ANN (HT1, 0.3% C) - Network Evaluation Experimental (HT1, 0.4% C) ANN (HT1, 0.4% C) - Network Evaluation Figure 2 Wear rate vs. sliding distance - ANN training and evaluation performance System Performance The neural network used for the presented model demonstrated an excellent statistical performance as indicated by the R2 and r values. During network training, R2 was obtained as 0.9993 and 0.9237 during network evaluation, which were very close to 1.0 indicating a very good fit between the actual and the network prediction. R2 is a statistical indicator usually applied to multiple regression analysis, and can be calculated using the following formulae [7]: R2 = 1 - (SSE/SSyy) Where SSE = Σ (y - y)2, SSyy = Σ (y - y) 2, y is the actual value, y is the predicted value of y, and y is the mean of the y values. 4
The correlation coefficient, r is a statistical measure of the strength of the relationship between the actual vs. predicted outputs. The r coefficient can range from -1 to +1. It will show a stronger positive linear relationship when r is closer to +1, and a stronger negative linear relationship when r is closer to -1. During network training, r values were obtained as 0.9997, and 0.9699 during network evaluation, which were very close to +1.0 indicating a very good fit between the actual and the network prediction. The following formulae [7] were used to calculate r: r = SSxy / √ (SSxx SSyy) Where SSxy = Σ xy - (1/n){( Σ x)( Σ y)} SSxx = Σ x 2 - (1/n)( Σ x)2 SSyy = Σ y 2 - (1/n)( Σ y)2 where n equals the number of patterns, x refers to the set of actual outputs, and y refers to the predicted outputs. PREDICTION OF WEAR RATE Based on the ANN trained model, wear rates were predicted as a function of sliding distance for P/M steel having hardness 60 HRC and carbon contents at 0.3%, 0.4%, and 0.6% as shown in Figure 3. It may be observed that the wear rate is sensitive and decreasing with the increase in carbon content up to about 4000 m sliding distance. Beyond a sliding distance of 4000 m, the wear rate remains constant and the same 1.5 2 2.5 3 3.5 4 0 1000 2000 3000 4000 5000 6000 Sliding distance (m) Wear rate X 10-13 (m3/m) ANN Prediction (60 HRC, 0.3% C) ANN Prediction (60 HRC, 0.4% C) ANN Prediction (60 HRC, 0.6% C) Figure 3 ANN network predicted wear rate vs. sliding distance 5
irrespective of the carbon contents. Figure 3 clearly predicts that the P/M alloy with 0.6% carbon content and 60 HRC hardness has the minimum wear rate (i.e. having maximum wear resistance) as compared to the other cases having lower carbon contents (0.4% & 0.3%). This is a valid observation since the addition of carbon usually contributes to improved hardness (by forming interstitial solid solution of carbon in iron lattice) in steel and thereby resulting in improved wear resistance property. CONCLUSIONS ANN Back-propagation model developed for studying the dry sliding wear behavior of powder metallurgy (P/M) alloys exhibited results consistent with the experimental findings. The prediction of wear behavior for P/M steel at higher hardness and/or higher carbon content is accurate and reliable with the expected trend. Hence, the present ANN based model can be used successfully over a wide range/combination of wear properties in P/M steel. REFERENCES 1. Chester, M. (1993) Neural Networks - A Tutorial, Prentice Hall: Englewood Cliffs, NJ, USA 2. Haque, M.E., Sudhakar, K.V. (2001) ANN based Prediction Model for Fatigue Crack Growth in DP Steel. Fatigue & Fracture of Engineering Materials and Structures. (IN PRESS) 3. Haque, M.E., Sudhakar, K.V. (2001) Prediction of Corrosion-Fatigue behavior of DP Steel through Artificial Neural Network. International Journal of Fatigue, Vol. 23, Issue 1, pp. 1-4 4. Obermeier, K., and Barron, J. (1989) Time to Get Fried Up, BYTE,14 (8) pp. 227-233 5. Rumelhart, D., Hinton, G., and Williams, R. (1986) "Parallel distributed processing," MIT Press, Cambridge, MA., USA 6. K. V. Sudhakar, P. Sampathkumaran, and E. S. Dwarakadasa (2000) Dry sliding wear in High Density Fe-2%Ni based P/M alloys, WEAR (242), pp. 207-212 7. NeuroShell 2 User's Manual (1996) Ward Systems Group, Inc., Frederick, MD, USA 6
ICF100412OR PREDICTION OF DUCTILE CRACK GROWTH IN POLYETHYLENE USING MEASURED TRACTION – SEPARATION CURVES K. C. Pandya1, A. Ivankovic2 and J. G. Williams2 1BP (Grangemouth), Applied Technology 7, Bo’ness Road, Grangemouth, Stirlingshire FK3 9XH, UK 2Department of Mechanical Engineering, Imperial College of Science, Technology and Medicine, Exhibition Road, London SW7 2BX, UK ABSTRACT An accurate prediction of ductile fracture employing a cohesive zone modelling approach depends critically on the choice of the cohesive law used to characterise the material in the crack tip damage zone. A successful new method for direct experimental measurement of this law in tough pipe grade polyethylene has been described recently. Results indicate significant and quantifiable effects of rate and geometrical constraint on the measured cohesive zone parameters: energy of separation and cohesive strength. Here we present a cohesive zone model within the finite volume method to predict crack initiation and propagation history in a tough PE80 type pipe grade polyethylene. A family of experimentally measured rate dependent traction curves is used as a means of establishing the local fracture process. Model predictions indicate that the cohesive zone parameters are not constant but change with both time and position along the crack path depending on the prevailing rate and degree of constraint. By accounting for rate and constraint effects in this manner it should be possible to maintain perceptible physical validity in the representation of the behaviour of the crack tip process region, something not always apparent in many existing cohesive zone models. KEYWORDS Crazing, Polyethylene, Cohesive zone model, Ductile crack growth INTRODUCTION Conventional fracture mechanics methods are unable to achieve meaningful predictions of ductile crack growth in present-day high strength steels or tough engineering polymers. This is because for these materials, the choice of a single characterising fracture parameter such as a unique stress intensity factor or energy release rate is often a wholly inadequate representation of the material behaviour. The introduction of a material specific process zone ahead of the crack tip appears to
provide a means of overcoming this limitation. Cohesive zone models utilise some form of traction – separation law to describe the material degradation and load carrying capacity due to local deformation within the zone. Using this approach it becomes possible to segregate the local work of fracture from general plasticity within the continuum and thus to predict the global fracture response from a description of the local microstructural behaviour. Medium density polyethylene may exhibit different modes of fracture, such as rapid crack propagation or slow crack growth, depending upon the prevailing loading rates and temperature. Both rapid crack propagation and slow crack growth are believed to be associated with the formation of a craze ahead of the crack tip. During slow crack growth large scale deformation does not occur, but rather the damage is highly localised. It is this fact that allows the postulation of a thin layer of material, in the most simple case along a prescribed single crack path with an associated cohesive law, to be used for the prediction of crack growth under low rates of loading. General applications of the cohesive zone model include modelling of ductile fracture under quasistatic loading [1] and the analysis of dynamic fracture problems [2,3]. It is increasingly becoming clear, however, that for such models to retain physical reality the cohesive zone parameters must be updated with time, allowing for local mechanisms such as rate dependent hardening and softening or variations in constraint along the crack path to be taken into account in the quantification of the local work of fracture [4,5,6,7]. Pandya and Williams have reported a scheme to measure the cohesive zone law as a function of rate and constraint [8,9] in a range of polyethylenes. These measurements were used for the numerical prediction of crack growth in a rate independent analysis using the finite volume method, which showed reasonable comparison with the measured macroscopic load behaviour [10]. Here we include rate dependence in this numerical scheme by incorporating a family of measured traction – separation curves into the model. MEASUREMENT OF COHESIVE LAW The techniques used in the measurement of cohesive zone parameters in tough polyethylene have been described in detail elsewhere [8,9]. In summary, rectangular bars were cut from pressed sheet of dimensions of 16 x 16 x 100 mm and circumferential notches were introduced by rotating the specimen in a lathe so as to produce a highly constrained circular ligament within a square section bar. The specimens were then tested in tension on a screw driven Instron. As the damage is confined within this ligament it is possible to measure the localised traction – separation behaviour of a given material over a range of applied rates. Both notch depth, which affects the degree of constraint, and the applied displacement rate have an effect on the measured law as indicated in Figure 1. Decreasing Rate Separation Traction Decreasing Constraint Figure 1: Schematic illustration of the effect of changes in constraint and rate on the measured cohesive law
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