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A novel test rig for measuring bending fatigue using resonant behaviour
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Procedia Structural Integrity 13 00 (2018) 1470–1475 Structural Integrity Procedia (2016) 000–000
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
A novel test rig for measuring bending fatigue using resonant A novel test rig for measuring bending fatigue using resonant XV Portuguese Conference on Fracture,behaviour PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal behaviour a C P Okekea,b *, A N Thiteaa, Jof F Durodola and M T Greenrodbb blade of an Thermo-mechanical a high a,b modeling apressure turbine C P Okeke *, A N Thite , J F Durodola and M T Greenrod Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Oxford – OX33 1HX, UK airplane gas turbine engine Department of Mechanical Engineering and London Mathematical Oxford Brookes Oxford – OX33 1HX, UK Wipac Ltd, Road, Sciences, Buckingham, MK18 1BH, University, UK a a
b b
Wipac Ltd, London Road, Buckingham, MK18 1BH, UK
P. Brandãoa, V. Infanteb, A.M. Deusc*
Abstract AbstractaDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, A novel test rig for bending fatigue test that based on specimen resonant behaviour has been developed. Determining bending fatigue Portugal A novel testofrig for bending fatigue testthe thatstandard based ontest specimen resonant behaviour developed. Determining bending fatigue properties polymer materials with systems is Técnico, challenging, andhasinbeen some casesAv.results unattainable. is b IDMEC, Department of Mechanical Engineering, Instituto Superior Universidade de Lisboa, Roviscoare Pais, 1, 1049-001This Lisboa, properties oftrue polymer materials the astandard testofsystems is challenging, and in some cases results are unattainable. This is particularly of polymers thatwith exhibit high level non-linearity and large deflection. This novel test setup is similar to that of Portugal c point bending particularly true of arrangement polymers thatresulting exhibit ainhigh level of non-linearity and large deflection. This novel test setup is 1, similar to that of four a simple support. The loading isUniversidade achieved bydeinertial effect of small masses mounted on CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, fourtest point bendingAarrangement resulting in atosimple support. loading is achieved by inertial effect of small massesThe mounted on the specimen. vibration shaker is used base excite the The specimen at the first resonance frequency until it breaks. proposed Portugal the test specimen. A vibration shaker is used to base theofspecimen at the first resonance until it breaks. The proposed test setup reduces the time taken to obtain Stress v/s excite number cycles (S/N) curves, typically frequency 1/10th of the universal testing machine test setup reducesThe theeffect time of taken to obtain Stress number cycles (S/N) curves, typically 1/10th of the universal testing machine based approach. nonlinearities can bev/s reduced byofapplication of larger loads at higher frequencies using large acceleration based approach. The effect of nonlinearities can be reduced byproposed application of largerare loads at higher frequencies using large acceleration and smaller deflection combination. The results based on the approach in good agreement with tensile fatigue results. It Abstract and smaller deflectionused combination. Thethe results based on theproperties proposedof approach are in good with tensilethe fatigue results. It has been successfully to determine bending fatigue Polycarbonate (PC) agreement of which determining tensile fatigue has been successfully usedtotomodern determine the bending ofsubjected Polycarbonate (PC) of which determining theand tensile fatigue properties were difficult obtain. The significance of thisproperties novel are test rig is that toit accelerates thedemanding fatigue testing allows the During their operation, aircraft enginefatigue components increasingly operating conditions, properties were to properties obtain. The significance of that this cannot novel test rig is that it existing accelerates the fatigue testing and allows the determination of difficult the fatigue someblades. materials be cause obtained with systems. especially the high pressure turbine of (HPT) Such conditions these parts to undergo different types of time-dependent determination of the fatigue properties of some materials that cannot be obtained with existing systems. degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict © the 2018creep The Authors. Published by Elsevier B.V.data records (FDR) for a specific aircraft, provided by a commercial aviation behaviour of HPT blades. Flight © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. company,under wereresponsibility used to obtain and mechanical data for three different flight cycles. In order to create the 3D model Peer-review of thethermal ECF22 organizers. Peer-review responsibility ECF22 needed forunder the FEM analysis,ofa the HPT bladeorganizers. scrap was scanned, and its chemical composition and material properties were Keywords: Resonant, Polymer, Fatigue, Bending, Novel,and Rig,different Deflectionsimulations were run, first with a simplified 3D obtained. The data that was gathered was Tensile, fed intoNonlinearity, the FEM model Keywords: Resonant, Bending, Rig,with Deflection rectangular blockPolymer, shape, inFatigue, order to better Tensile, establishNonlinearity, the model,Novel, and then the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a can be useful in the goal of predicting turbine blade life, given a set of FDR data. 1. model Introduction
1. Introduction
©Determining 2016 The Authors. Published Elsevier B.V. bending fatiguebyproperties of polymer materials with the standard test systems is challenging, and in Peer-review under responsibility of the Scientificpolymer Committee of PCF 2016. Determining bending fatigue properties with thethat standard test systems challenging, andand in some cases results are unattainable. This is of particularlymaterials true of polymers exhibit a high levelisof non-linearity
some cases results are unattainable. is particularly of polymers exhibit a high level offatigue non-linearity and large deflection. These characteristicsThis have a significanttrue influence on the that determination of bending properties. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. large deflection. These characteristics have a significant influence on the determination of bending fatigue properties.
* Corresponding author. Tel.: +44-(0)1865-423011 * Corresponding Tel.: +44-(0)1865-423011 E-mail address:author. [email protected], [email protected] E-mail address: [email protected], [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. Peer-review underauthor. responsibility the ECF22 organizers. * Corresponding Tel.: +351of218419991. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.303
2
C P Okeke et al. / Procedia Structural Integrity 13 (2018) 1470–1475 C P Okeke et al/ Structural Integrity Procedia 00 (2018) 000–000
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There are different ways in which bending fatigue load can be generated; these include centrifugal forces, dead weights electro-magnetic forces, pneumatic forces, hydraulic forces etc. These methods were discussed in Weibull (1962). Most of these methods of bending fatigue load application are particularly designed for metallic materials; they may not be suitable for characterising the bending fatigue of polymers due to their large driving load. Polymers have low bending load and therefore require a system of low load application. Currently, the hydraulic and pneumatic mechanisms are the most commonly used load applications in the fatigue of polymers. However, they come with challenges, the minimum rating force for servo-hydraulic system is typically 5kN and some polymers have lower bending load than this. For this reason, the hydraulic system is mostly used for measuring the tensile fatigue of polymers. The servo-pneumatic system has the potential to achieve minimum load down to 1kN, however, due to the compressible nature of air, the operating frequency is low and the performance can be unstable. With low test frequency, the time taken to obtain fatigue property (S-N curve) is longer. To reduce the time taken to characterise the fatigue life of polymers, high frequency system is required. This is where the use of specimen resonant frequency as a test frequency offers significant advantage. The resonant fatigue test system allows the application of larger loads at higher frequencies. There has been some recent work on the development of resonant bending fatigue test rig; however, they are largely focused on the large scale structures. Schneider (2018) developed a resonant bending fatigue testing system to measure the fatigue life of a large-scale structure. The imbalance rotors were used to generate vibrational driving force. The system was able to determine the fatigue life of a structure four times faster than the standard hydraulic system. Maillet et al. (2013) developed a new test methodology based on structural resonance for mode 1 fatigue delamination growth in a unidirectional composite. The set-up which is a mass-spring-specimen dynamic system designed to resonate, was ten times faster than the standard system without heat generation. Bertini (2007) were able to characterise the resonant fatigue property of full scale oil drill string connections in a very short time by using a resonant test rig. The resonance fatigue test system offers a great advantage over standard fatigue test systems by exploiting specimen resonance to accelerate testing. The objective of this paper was to develop a test rig for measuring bending fatigue using resonant behavior. This novel test setup is similar to that of four point bending arrangement resulting in a simple support. The loading is achieved by inertial effect of small masses mounted on the test specimen. A vibration shaker is required to base excite the specimen at the first resonance frequency until it breaks. The proposed system was validated using fatigue property tests on Polymethyl-methacrylate (PMMA) based on the standard test system. After proving the validity of this novel rig, it will then be used to determine the bending fatigue properties of Polycarbonate (PC) of which determining the tensile fatigue properties with the standards test system was not successful. The significance of this novel test rig is that it accelerates the fatigue testing and allows the determination of the fatigue properties of materials that cannot be obtained using existing systems. 2. Resonant fatigue test rig design The design of the proposed fatigue test system uses similar support conditions to that of four point bending arrangement ASTM (D7774-12) resulting in a simple support. The loading is based on inertial effect by having two double sided small masses mounted on the test specimen. The schematic diagram of the test set-up is shown in Fig 1. The supports and the loading masses are designed to have cylindrical surfaces; this is to avoid undesirable failure of the test specimen as a result of surface wear induced stress concentration. The clamping of the test specimen to the supports and the attachment of the loading masses to the specimen are achieved with minimal tightening torque. The value of torque to be used is dependent on the material to be tested. In accordance to the four point loading principle, the maximum axial stress on the test specimen is constant between the two loading masses. However, when a notch is introduced at the midpoint of the specimen (centre of the two loading masses), the maximum stress on the specimen will be located at the root of the notch. The total input force required to drive the system is the sum of the forces on the double loading masses which is given as: 𝐹𝐹 � 𝐹𝐹� � 𝐹𝐹� 𝐹𝐹� � 𝑚𝑚� 𝑦𝑦� ,
𝐹𝐹� � 𝑚𝑚� 𝑦𝑦�
���
���
where 𝑚𝑚 and 𝑦𝑦� are the additional mass elements on the specimen and the drive acceleration, respectively. The use of a notch ensures that the fatigue failure occurs at the desired place. However, the stress concentration factor due to the notch has to be accounted for. The maximum stress at the root of the notch is given as:
C P Okeke et al. / Procedia Structural Integrity 13 (2018) 1470–1475 C P Okeke et al/ Structural Integrity Procedia 00 (2018) 000–000
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𝜎𝜎��� � 𝐾𝐾� 𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎
where 𝐾𝐾� is stress concentration factor and for U-type notch used in this study Pilkey (2004), it is given as: 𝐾𝐾� � �.��� � �.����
ℎ 𝑟𝑟
h and r are the depth and radius of the notch, respectively. The nominal stress is defined as: 𝜎𝜎 �
6𝑀𝑀 𝑑𝑑�
�3� ��� ���
And the bending moment 𝑀𝑀 is given as: 𝑀𝑀 �
3
𝑃𝑃 𝐿𝐿� 𝐹𝐹𝐹𝐹� . � 2 3 6
where 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹� are applied force and support span, respectively. m1
𝑦𝑦� �
�6� 𝑦𝑦� �
m2
Load span (L2) Support span (L1)
Figure 1: Four-point based resonant, fatigue test specimen and loading
Figure 2: Shaker table adaptor and the test specimen along with fixture.
3. Experimental The materials used in this study were PMMA and PC respectively. The PMMA specimens of rectangular shape were cut out from an optical plate that was injection moulded at Wipac, while PC specimens were cut out from standard A1 injection moulded dumb bell specimens supplied by manufacturer, Albis. The dimensions of the specimens of both materials apart from PMMA of 2.8mm thickness were 170mm x 10mm x 4mm. A U-type notch of 2mm radius and 6mm depth was introduced at the centre of the specimen as shown in Fig 3. The fatigue testing was based on three load levels - 80%, 60% and 40% material yield strength. At every load level, five specimens were tested and the number of cycles to failure was logged for every specimen. The input acceleration
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for all three load levels was obtained by taking the ratio of the calculated specimen response acceleration to the experimentally obtained transmissibility of the first resonance. The loading was achieved by inertial effect of two small masses mounted on the test specimen. A V721 electrodynamic vibration shaker was used to base excite the specimen at the first resonance frequency until it breaks. The testing was conducted at the room temperature. The complete test set-up is shown in Fig 4. 170mm
10m
6mm
2mm
PC: 4mm PMMA: 2.8mm Figure 3: Test specimen
Figure 4: Experimental test set-up
4. Results and validation 4.1. Fatigue life of PMMA – tensile vs resonance bending Fig 5(a) shows acceleration–fatigue life curve (a-N curve) of PMMA material obtained using the new resonance bending fatigue test rig with resonance of 45Hz. This acceleration-fatigue life curve was converted to stress-fatigue life (S-N curve) and validated with S-N curve of the same material obtained with standard tensile method; both curves are shown in Fig 5(b). The tensile fatigue test was performed under the room temperature in accordance to standard ASTM (D7791-12) using computer controlled SI-Plan servo hydraulic machine. A sinusoidal load waveform with fixed frequency of 5Hz was used. The fatigue life obtained using the novel resonance bending fatigue rig was in excellent agreement with that of standard tensile method. The difference in stress amplitude was that the stress amplitude of resonance bending fatigue was based on bending strength while for tensile fatigue it was based on tensile strength. The bending strength is always higher than the tensile strength and for this material, the bending strength was 1.27 higher than the tensile strength. The curve shows scatter in the fatigue life which increases as the stress amplitude decreased. This is a known phenomenon in characterising the fatigue life of materials. This phenomenon was attributed to the specimen surface condition Schijve (2001). At a high stress the effect of specimen surface imperfection to the crack nucleation is less significant as the loading is more dominant. However, as the stress amplitude decreases, the surface condition starts to play a role in the fatigue life as the crack nucleation can be enhanced by the surface imperfection. The surface conditions can vary between specimens which results in variations of fatigue life between specimens at low amplitude. One of the important contributing factors in this scatter that must not be ignored is inter-sample variations. Polymers are prone to manufacturing variability; this means that material properties will vary across specimens of the same material batch.
C P Okeke et al. / Procedia Structural Integrity 13 (2018) 1470–1475 C P Okeke et al/ Structural Integrity Procedia 00 (2018) 000–000
70
(a)
25
(b)
5 Resonance Bending Tensile
60
Stress (MPa)
Drive Acceleration (m/s²)
1474
20 15
50 40 30
10
20
5
1000
10000
Log Nf
100000
1000
10000
Log Nf
100000
Figure 5: Fatigue life curve of PMMA (a) a-N curve, (b) S-N curve
4.2. Fatigue life of PC – tensile vs resonance bending The tensile fatigue of polycarbonate (PC) material was carried out in accordance with standard ASTM (D7791-12). Again a test frequency of 5Hz and three levels of stress amplitude, 80%, 60% and 40% of material yield strength were used to determine the S-N curve. The test specimens were standard A1 injection moulded dumb bell BS EN ISO (5272) supplied by manufacturer, Albis. The length, width and thickness of the narrow portion of the specimen are 80mm, 10mm and 4mm respectively. As can be seen in fig 6(a), at the load level corresponding to 80% and 60% material yield strength, realistic fatigue property could not be obtained. The specimens failed outside the gauge length and the life cycles were significantly higher than expected - similar life was obtained at the three load level which could not be true. The minimum and maximum number of cycles to failure at 80% loading is 18453 and 35143 respectively. At 60% loading, the minimum and maximum number of cycles to failure is 20428 and 34711, and at 40% loading it is 26059 and 39547 respectively. This does not represent the true fatigue failure of crack initiation and propagation and therefore thermal effect was examined. The specimen surface temperature was determined during fatigue test using a thermoscouple and an infrared camera – Keysight U5856A. At 80% loading, the temperature of the sample rose to 37.2°C leading to specimen temperature difference of 15.7°C. The specimen temperature rise at 60% loading was 5.3°C, and at 40% loading, it was 0.5°C which can be considered as insignificant. At 80% and 60% loading, the specimen failed outside the gauge length, the region of the fracture showed melted texture. It was considered that the higher number of cycles to failure seen at these load levels was due to thermal softening. The specimen became more ductile as a result of heat buildup and the tendency to stretch maximised in a way that it became more ductile. Test frequency of 5Hz may seemed low to generate thermal failure, however, it should be noted that load amplitude play an important role in thermal failure, so it is the combination of frequency and loading. As a viscoelastic material, PC is sensitive to test frequency and load amplitude. In some polymers, where viscoelastic effects are large, a notable temperature rise can take place at a very low frequency as observed by Sauer et al. (1980). Crawford (1998) noted that even at a lower frequency, the thermal softening failure can take place at a high stress level.
Stress (MPa)
60
70
(a)
60
Stress (MPa)
70
50 40 30 20 10 15000
(b)
50 40 30 20
30000
Log Nf
50000
10 2000
10000
Log Nf
Figure 6: Fatigue life of PC – (a) Tensile fatigue, (b) Resonance bending fatigue
50000
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The difficulty in obtaining the tensile fatigue property of PC inspired the development of this resonance fatigue test rig. The resonance bending fatigue test was performed as described above. The specimen was prepared as in fig 3. A cycling frequency of 50Hz which was the resonance frequency of the specimen and three levels of stress amplitude, 80%, 60% and 40% of material yield strength were used to determine the S-N curve. The specimen temperature was measured at every load level. The measured specimen temperature varied in opposite directions to that of tensile fatigue, instead of rising, the temperature was falling, but with a smaller difference. This is an evidence of self-induced cooling. At 80% loading, the specimen temperature dropped from ambient of 22.57°C to 16.93°C giving a 5.64°C temperature difference. At 60% and 40% load levels, specimen temperature difference of 2.19°C and 0.21°C were measured. It appears that the new resonance test set-up does not only accelerate the fatigue test but also eliminates the concern of specimen internal heating by means of self-induced cooling due to the specimen vibration, which results in true fatigue curve. It can be seen from Fig 6(b) that the true fatigue life curve was obtained at every load level. 5. Conclusions A novel test rig for bending fatigue test that is based on specimen resonant behaviour has been developed. This novel test setup support conditions are similar to that of four point bending arrangement. The loading is achieved by inertial effect of small masses mounted on the test specimen. A vibration shaker is required to base excite the specimen at the first resonance frequency until it breaks. The time taken by the new setup to obtain S/N curves was ~1/10th of the universal testing machine based approach. The fatigue properties obtained were comparable to the results based on tensile fatigue properties. Furthermore, the setup was successfully used to determine the bending fatigue properties of Polycarbonate (PC) of which determining the tensile fatigue properties with the standards test system was not successful. The specimen temperature decreases with increased load amplitude by means of self-induced cooling due to the specimen vibration, which eliminates concerns of thermal failure. The significance of this novel test rig is that it accelerates the fatigue testing and allows the determination of the fatigue properties of materials that cannot be obtained with existing methods. Acknowledgements This research has been funded by Wipac Ltd. The authors would like to acknowledge Albis for providing the Polycarbonate specimens. We also wish to thank Jan Goodrich for his immense support in the design of the resonant test rig. References American Society for Testing and Materials: ASTM D7791-12. Standard Test Method for Uniaxial Fatigue Properties of Plastics. American Society for Testing and Materials: ASTM D7774-12. Standard Test method for Flexural Fatigue Properties of Plastics. British Standards Institution: BS EN ISO 527-2: 2012. Plastics — Determination of tensile properties, Part 2: Test conditions for moulding and extrusion plastics. W. Weibull., 1962. Fatigue Testing and Analysis of Results, 1st Edition, Elservier. Sebastian Schneider., Ralf Herrmann., Steffen Marx., 2018. Development of a resonant fatigue testing facilirty for large-scale beams in bending. Elsevier, International Journal of Fatigue 113 (2018) 171-183. I. Miillet., L. Michel., G. Rico., M. Fressinet., Y. Gourinat., 2013. A new test methology based on structural resonance for mode 1 fatigue delamination growth in an unidirectional composite. Composite structures vol. 97.pp. 353-362. ISSN 0263-8223. L. Bertini., M. Beghini., C. Santus., A. Baryshnikov., 2007. Resonant test rigs for fatigue full scale testing of oil drill string connections. Elsevier, International Journal of Fatigue 30 (2008) 978-988. R J Crawford., 1998. Plastics Engineering., Third Edition. Butterworth Heinemann. Richard W. Hertzberg., John A. Manson., 1980. Fatigue of Engineering Plastics. Academic Press. Jaap Schijve., 2001. Fatigue of Engineering and Materials. Kluwer Academic Publishers. J.A. Sauer., G.C. Richardson., 1980. Fatigue of Polymers. International Journal of Fracture, Vol. 16, No. 6.
ScienceDirect ScienceDirect
Structural Integrity Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
Procedia Structural Integrity 13 00 (2018) 1470–1475 Structural Integrity Procedia (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
A novel test rig for measuring bending fatigue using resonant A novel test rig for measuring bending fatigue using resonant XV Portuguese Conference on Fracture,behaviour PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal behaviour a C P Okekea,b *, A N Thiteaa, Jof F Durodola and M T Greenrodbb blade of an Thermo-mechanical a high a,b modeling apressure turbine C P Okeke *, A N Thite , J F Durodola and M T Greenrod Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Oxford – OX33 1HX, UK airplane gas turbine engine Department of Mechanical Engineering and London Mathematical Oxford Brookes Oxford – OX33 1HX, UK Wipac Ltd, Road, Sciences, Buckingham, MK18 1BH, University, UK a a
b b
Wipac Ltd, London Road, Buckingham, MK18 1BH, UK
P. Brandãoa, V. Infanteb, A.M. Deusc*
Abstract AbstractaDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, A novel test rig for bending fatigue test that based on specimen resonant behaviour has been developed. Determining bending fatigue Portugal A novel testofrig for bending fatigue testthe thatstandard based ontest specimen resonant behaviour developed. Determining bending fatigue properties polymer materials with systems is Técnico, challenging, andhasinbeen some casesAv.results unattainable. is b IDMEC, Department of Mechanical Engineering, Instituto Superior Universidade de Lisboa, Roviscoare Pais, 1, 1049-001This Lisboa, properties oftrue polymer materials the astandard testofsystems is challenging, and in some cases results are unattainable. This is particularly of polymers thatwith exhibit high level non-linearity and large deflection. This novel test setup is similar to that of Portugal c point bending particularly true of arrangement polymers thatresulting exhibit ainhigh level of non-linearity and large deflection. This novel test setup is 1, similar to that of four a simple support. The loading isUniversidade achieved bydeinertial effect of small masses mounted on CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, fourtest point bendingAarrangement resulting in atosimple support. loading is achieved by inertial effect of small massesThe mounted on the specimen. vibration shaker is used base excite the The specimen at the first resonance frequency until it breaks. proposed Portugal the test specimen. A vibration shaker is used to base theofspecimen at the first resonance until it breaks. The proposed test setup reduces the time taken to obtain Stress v/s excite number cycles (S/N) curves, typically frequency 1/10th of the universal testing machine test setup reducesThe theeffect time of taken to obtain Stress number cycles (S/N) curves, typically 1/10th of the universal testing machine based approach. nonlinearities can bev/s reduced byofapplication of larger loads at higher frequencies using large acceleration based approach. The effect of nonlinearities can be reduced byproposed application of largerare loads at higher frequencies using large acceleration and smaller deflection combination. The results based on the approach in good agreement with tensile fatigue results. It Abstract and smaller deflectionused combination. Thethe results based on theproperties proposedof approach are in good with tensilethe fatigue results. It has been successfully to determine bending fatigue Polycarbonate (PC) agreement of which determining tensile fatigue has been successfully usedtotomodern determine the bending ofsubjected Polycarbonate (PC) of which determining theand tensile fatigue properties were difficult obtain. The significance of thisproperties novel are test rig is that toit accelerates thedemanding fatigue testing allows the During their operation, aircraft enginefatigue components increasingly operating conditions, properties were to properties obtain. The significance of that this cannot novel test rig is that it existing accelerates the fatigue testing and allows the determination of difficult the fatigue someblades. materials be cause obtained with systems. especially the high pressure turbine of (HPT) Such conditions these parts to undergo different types of time-dependent determination of the fatigue properties of some materials that cannot be obtained with existing systems. degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict © the 2018creep The Authors. Published by Elsevier B.V.data records (FDR) for a specific aircraft, provided by a commercial aviation behaviour of HPT blades. Flight © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. company,under wereresponsibility used to obtain and mechanical data for three different flight cycles. In order to create the 3D model Peer-review of thethermal ECF22 organizers. Peer-review responsibility ECF22 needed forunder the FEM analysis,ofa the HPT bladeorganizers. scrap was scanned, and its chemical composition and material properties were Keywords: Resonant, Polymer, Fatigue, Bending, Novel,and Rig,different Deflectionsimulations were run, first with a simplified 3D obtained. The data that was gathered was Tensile, fed intoNonlinearity, the FEM model Keywords: Resonant, Bending, Rig,with Deflection rectangular blockPolymer, shape, inFatigue, order to better Tensile, establishNonlinearity, the model,Novel, and then the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a can be useful in the goal of predicting turbine blade life, given a set of FDR data. 1. model Introduction
1. Introduction
©Determining 2016 The Authors. Published Elsevier B.V. bending fatiguebyproperties of polymer materials with the standard test systems is challenging, and in Peer-review under responsibility of the Scientificpolymer Committee of PCF 2016. Determining bending fatigue properties with thethat standard test systems challenging, andand in some cases results are unattainable. This is of particularlymaterials true of polymers exhibit a high levelisof non-linearity
some cases results are unattainable. is particularly of polymers exhibit a high level offatigue non-linearity and large deflection. These characteristicsThis have a significanttrue influence on the that determination of bending properties. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. large deflection. These characteristics have a significant influence on the determination of bending fatigue properties.
* Corresponding author. Tel.: +44-(0)1865-423011 * Corresponding Tel.: +44-(0)1865-423011 E-mail address:author. [email protected], [email protected] E-mail address: [email protected], [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. Peer-review underauthor. responsibility the ECF22 organizers. * Corresponding Tel.: +351of218419991. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.303
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C P Okeke et al. / Procedia Structural Integrity 13 (2018) 1470–1475 C P Okeke et al/ Structural Integrity Procedia 00 (2018) 000–000
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There are different ways in which bending fatigue load can be generated; these include centrifugal forces, dead weights electro-magnetic forces, pneumatic forces, hydraulic forces etc. These methods were discussed in Weibull (1962). Most of these methods of bending fatigue load application are particularly designed for metallic materials; they may not be suitable for characterising the bending fatigue of polymers due to their large driving load. Polymers have low bending load and therefore require a system of low load application. Currently, the hydraulic and pneumatic mechanisms are the most commonly used load applications in the fatigue of polymers. However, they come with challenges, the minimum rating force for servo-hydraulic system is typically 5kN and some polymers have lower bending load than this. For this reason, the hydraulic system is mostly used for measuring the tensile fatigue of polymers. The servo-pneumatic system has the potential to achieve minimum load down to 1kN, however, due to the compressible nature of air, the operating frequency is low and the performance can be unstable. With low test frequency, the time taken to obtain fatigue property (S-N curve) is longer. To reduce the time taken to characterise the fatigue life of polymers, high frequency system is required. This is where the use of specimen resonant frequency as a test frequency offers significant advantage. The resonant fatigue test system allows the application of larger loads at higher frequencies. There has been some recent work on the development of resonant bending fatigue test rig; however, they are largely focused on the large scale structures. Schneider (2018) developed a resonant bending fatigue testing system to measure the fatigue life of a large-scale structure. The imbalance rotors were used to generate vibrational driving force. The system was able to determine the fatigue life of a structure four times faster than the standard hydraulic system. Maillet et al. (2013) developed a new test methodology based on structural resonance for mode 1 fatigue delamination growth in a unidirectional composite. The set-up which is a mass-spring-specimen dynamic system designed to resonate, was ten times faster than the standard system without heat generation. Bertini (2007) were able to characterise the resonant fatigue property of full scale oil drill string connections in a very short time by using a resonant test rig. The resonance fatigue test system offers a great advantage over standard fatigue test systems by exploiting specimen resonance to accelerate testing. The objective of this paper was to develop a test rig for measuring bending fatigue using resonant behavior. This novel test setup is similar to that of four point bending arrangement resulting in a simple support. The loading is achieved by inertial effect of small masses mounted on the test specimen. A vibration shaker is required to base excite the specimen at the first resonance frequency until it breaks. The proposed system was validated using fatigue property tests on Polymethyl-methacrylate (PMMA) based on the standard test system. After proving the validity of this novel rig, it will then be used to determine the bending fatigue properties of Polycarbonate (PC) of which determining the tensile fatigue properties with the standards test system was not successful. The significance of this novel test rig is that it accelerates the fatigue testing and allows the determination of the fatigue properties of materials that cannot be obtained using existing systems. 2. Resonant fatigue test rig design The design of the proposed fatigue test system uses similar support conditions to that of four point bending arrangement ASTM (D7774-12) resulting in a simple support. The loading is based on inertial effect by having two double sided small masses mounted on the test specimen. The schematic diagram of the test set-up is shown in Fig 1. The supports and the loading masses are designed to have cylindrical surfaces; this is to avoid undesirable failure of the test specimen as a result of surface wear induced stress concentration. The clamping of the test specimen to the supports and the attachment of the loading masses to the specimen are achieved with minimal tightening torque. The value of torque to be used is dependent on the material to be tested. In accordance to the four point loading principle, the maximum axial stress on the test specimen is constant between the two loading masses. However, when a notch is introduced at the midpoint of the specimen (centre of the two loading masses), the maximum stress on the specimen will be located at the root of the notch. The total input force required to drive the system is the sum of the forces on the double loading masses which is given as: 𝐹𝐹 � 𝐹𝐹� � 𝐹𝐹� 𝐹𝐹� � 𝑚𝑚� 𝑦𝑦� ,
𝐹𝐹� � 𝑚𝑚� 𝑦𝑦�
���
���
where 𝑚𝑚 and 𝑦𝑦� are the additional mass elements on the specimen and the drive acceleration, respectively. The use of a notch ensures that the fatigue failure occurs at the desired place. However, the stress concentration factor due to the notch has to be accounted for. The maximum stress at the root of the notch is given as:
C P Okeke et al. / Procedia Structural Integrity 13 (2018) 1470–1475 C P Okeke et al/ Structural Integrity Procedia 00 (2018) 000–000
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𝜎𝜎��� � 𝐾𝐾� 𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎𝜎
where 𝐾𝐾� is stress concentration factor and for U-type notch used in this study Pilkey (2004), it is given as: 𝐾𝐾� � �.��� � �.����
ℎ 𝑟𝑟
h and r are the depth and radius of the notch, respectively. The nominal stress is defined as: 𝜎𝜎 �
6𝑀𝑀 𝑑𝑑�
�3� ��� ���
And the bending moment 𝑀𝑀 is given as: 𝑀𝑀 �
3
𝑃𝑃 𝐿𝐿� 𝐹𝐹𝐹𝐹� . � 2 3 6
where 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹� are applied force and support span, respectively. m1
𝑦𝑦� �
�6� 𝑦𝑦� �
m2
Load span (L2) Support span (L1)
Figure 1: Four-point based resonant, fatigue test specimen and loading
Figure 2: Shaker table adaptor and the test specimen along with fixture.
3. Experimental The materials used in this study were PMMA and PC respectively. The PMMA specimens of rectangular shape were cut out from an optical plate that was injection moulded at Wipac, while PC specimens were cut out from standard A1 injection moulded dumb bell specimens supplied by manufacturer, Albis. The dimensions of the specimens of both materials apart from PMMA of 2.8mm thickness were 170mm x 10mm x 4mm. A U-type notch of 2mm radius and 6mm depth was introduced at the centre of the specimen as shown in Fig 3. The fatigue testing was based on three load levels - 80%, 60% and 40% material yield strength. At every load level, five specimens were tested and the number of cycles to failure was logged for every specimen. The input acceleration
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for all three load levels was obtained by taking the ratio of the calculated specimen response acceleration to the experimentally obtained transmissibility of the first resonance. The loading was achieved by inertial effect of two small masses mounted on the test specimen. A V721 electrodynamic vibration shaker was used to base excite the specimen at the first resonance frequency until it breaks. The testing was conducted at the room temperature. The complete test set-up is shown in Fig 4. 170mm
10m
6mm
2mm
PC: 4mm PMMA: 2.8mm Figure 3: Test specimen
Figure 4: Experimental test set-up
4. Results and validation 4.1. Fatigue life of PMMA – tensile vs resonance bending Fig 5(a) shows acceleration–fatigue life curve (a-N curve) of PMMA material obtained using the new resonance bending fatigue test rig with resonance of 45Hz. This acceleration-fatigue life curve was converted to stress-fatigue life (S-N curve) and validated with S-N curve of the same material obtained with standard tensile method; both curves are shown in Fig 5(b). The tensile fatigue test was performed under the room temperature in accordance to standard ASTM (D7791-12) using computer controlled SI-Plan servo hydraulic machine. A sinusoidal load waveform with fixed frequency of 5Hz was used. The fatigue life obtained using the novel resonance bending fatigue rig was in excellent agreement with that of standard tensile method. The difference in stress amplitude was that the stress amplitude of resonance bending fatigue was based on bending strength while for tensile fatigue it was based on tensile strength. The bending strength is always higher than the tensile strength and for this material, the bending strength was 1.27 higher than the tensile strength. The curve shows scatter in the fatigue life which increases as the stress amplitude decreased. This is a known phenomenon in characterising the fatigue life of materials. This phenomenon was attributed to the specimen surface condition Schijve (2001). At a high stress the effect of specimen surface imperfection to the crack nucleation is less significant as the loading is more dominant. However, as the stress amplitude decreases, the surface condition starts to play a role in the fatigue life as the crack nucleation can be enhanced by the surface imperfection. The surface conditions can vary between specimens which results in variations of fatigue life between specimens at low amplitude. One of the important contributing factors in this scatter that must not be ignored is inter-sample variations. Polymers are prone to manufacturing variability; this means that material properties will vary across specimens of the same material batch.
C P Okeke et al. / Procedia Structural Integrity 13 (2018) 1470–1475 C P Okeke et al/ Structural Integrity Procedia 00 (2018) 000–000
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(a)
25
(b)
5 Resonance Bending Tensile
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Stress (MPa)
Drive Acceleration (m/s²)
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20 15
50 40 30
10
20
5
1000
10000
Log Nf
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1000
10000
Log Nf
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Figure 5: Fatigue life curve of PMMA (a) a-N curve, (b) S-N curve
4.2. Fatigue life of PC – tensile vs resonance bending The tensile fatigue of polycarbonate (PC) material was carried out in accordance with standard ASTM (D7791-12). Again a test frequency of 5Hz and three levels of stress amplitude, 80%, 60% and 40% of material yield strength were used to determine the S-N curve. The test specimens were standard A1 injection moulded dumb bell BS EN ISO (5272) supplied by manufacturer, Albis. The length, width and thickness of the narrow portion of the specimen are 80mm, 10mm and 4mm respectively. As can be seen in fig 6(a), at the load level corresponding to 80% and 60% material yield strength, realistic fatigue property could not be obtained. The specimens failed outside the gauge length and the life cycles were significantly higher than expected - similar life was obtained at the three load level which could not be true. The minimum and maximum number of cycles to failure at 80% loading is 18453 and 35143 respectively. At 60% loading, the minimum and maximum number of cycles to failure is 20428 and 34711, and at 40% loading it is 26059 and 39547 respectively. This does not represent the true fatigue failure of crack initiation and propagation and therefore thermal effect was examined. The specimen surface temperature was determined during fatigue test using a thermoscouple and an infrared camera – Keysight U5856A. At 80% loading, the temperature of the sample rose to 37.2°C leading to specimen temperature difference of 15.7°C. The specimen temperature rise at 60% loading was 5.3°C, and at 40% loading, it was 0.5°C which can be considered as insignificant. At 80% and 60% loading, the specimen failed outside the gauge length, the region of the fracture showed melted texture. It was considered that the higher number of cycles to failure seen at these load levels was due to thermal softening. The specimen became more ductile as a result of heat buildup and the tendency to stretch maximised in a way that it became more ductile. Test frequency of 5Hz may seemed low to generate thermal failure, however, it should be noted that load amplitude play an important role in thermal failure, so it is the combination of frequency and loading. As a viscoelastic material, PC is sensitive to test frequency and load amplitude. In some polymers, where viscoelastic effects are large, a notable temperature rise can take place at a very low frequency as observed by Sauer et al. (1980). Crawford (1998) noted that even at a lower frequency, the thermal softening failure can take place at a high stress level.
Stress (MPa)
60
70
(a)
60
Stress (MPa)
70
50 40 30 20 10 15000
(b)
50 40 30 20
30000
Log Nf
50000
10 2000
10000
Log Nf
Figure 6: Fatigue life of PC – (a) Tensile fatigue, (b) Resonance bending fatigue
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The difficulty in obtaining the tensile fatigue property of PC inspired the development of this resonance fatigue test rig. The resonance bending fatigue test was performed as described above. The specimen was prepared as in fig 3. A cycling frequency of 50Hz which was the resonance frequency of the specimen and three levels of stress amplitude, 80%, 60% and 40% of material yield strength were used to determine the S-N curve. The specimen temperature was measured at every load level. The measured specimen temperature varied in opposite directions to that of tensile fatigue, instead of rising, the temperature was falling, but with a smaller difference. This is an evidence of self-induced cooling. At 80% loading, the specimen temperature dropped from ambient of 22.57°C to 16.93°C giving a 5.64°C temperature difference. At 60% and 40% load levels, specimen temperature difference of 2.19°C and 0.21°C were measured. It appears that the new resonance test set-up does not only accelerate the fatigue test but also eliminates the concern of specimen internal heating by means of self-induced cooling due to the specimen vibration, which results in true fatigue curve. It can be seen from Fig 6(b) that the true fatigue life curve was obtained at every load level. 5. Conclusions A novel test rig for bending fatigue test that is based on specimen resonant behaviour has been developed. This novel test setup support conditions are similar to that of four point bending arrangement. The loading is achieved by inertial effect of small masses mounted on the test specimen. A vibration shaker is required to base excite the specimen at the first resonance frequency until it breaks. The time taken by the new setup to obtain S/N curves was ~1/10th of the universal testing machine based approach. The fatigue properties obtained were comparable to the results based on tensile fatigue properties. Furthermore, the setup was successfully used to determine the bending fatigue properties of Polycarbonate (PC) of which determining the tensile fatigue properties with the standards test system was not successful. The specimen temperature decreases with increased load amplitude by means of self-induced cooling due to the specimen vibration, which eliminates concerns of thermal failure. The significance of this novel test rig is that it accelerates the fatigue testing and allows the determination of the fatigue properties of materials that cannot be obtained with existing methods. Acknowledgements This research has been funded by Wipac Ltd. The authors would like to acknowledge Albis for providing the Polycarbonate specimens. We also wish to thank Jan Goodrich for his immense support in the design of the resonant test rig. References American Society for Testing and Materials: ASTM D7791-12. Standard Test Method for Uniaxial Fatigue Properties of Plastics. American Society for Testing and Materials: ASTM D7774-12. Standard Test method for Flexural Fatigue Properties of Plastics. British Standards Institution: BS EN ISO 527-2: 2012. Plastics — Determination of tensile properties, Part 2: Test conditions for moulding and extrusion plastics. W. Weibull., 1962. Fatigue Testing and Analysis of Results, 1st Edition, Elservier. Sebastian Schneider., Ralf Herrmann., Steffen Marx., 2018. Development of a resonant fatigue testing facilirty for large-scale beams in bending. Elsevier, International Journal of Fatigue 113 (2018) 171-183. I. Miillet., L. Michel., G. Rico., M. Fressinet., Y. Gourinat., 2013. A new test methology based on structural resonance for mode 1 fatigue delamination growth in an unidirectional composite. Composite structures vol. 97.pp. 353-362. ISSN 0263-8223. L. Bertini., M. Beghini., C. Santus., A. Baryshnikov., 2007. Resonant test rigs for fatigue full scale testing of oil drill string connections. Elsevier, International Journal of Fatigue 30 (2008) 978-988. R J Crawford., 1998. Plastics Engineering., Third Edition. Butterworth Heinemann. Richard W. Hertzberg., John A. Manson., 1980. Fatigue of Engineering Plastics. Academic Press. Jaap Schijve., 2001. Fatigue of Engineering and Materials. Kluwer Academic Publishers. J.A. Sauer., G.C. Richardson., 1980. Fatigue of Polymers. International Journal of Fracture, Vol. 16, No. 6.