An integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale

Transcription

1 An integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale Angelos Mintzas 1, Steve Hatton 1, Sarinova Simandjuntak 2, Andrew Little 2, Zhongyi Zhang 2 Magma Global Ltd 1 University of Portsmouth 2 ABSTRACT The increasing demand for ultra-deep water oil and gas extraction has led to the consideration of high performance materials, such as carbon fibre reinforced composites, in the manufacturing of risers. Whilst the unique properties of composites offer great capability in the design, the lack of field experience and of relevant design codes and standards raise concerns regarding appropriate design methodologies within the oil and gas community. In this study, an integrated design approach is proposed, whereby information from the micro-scale (i.e. at the fibre and matrix level) is used for the prediction of the structural response at the macro-scale (i.e. of the whole pipe). In order to do so, mathematical models describing the pipe behaviour at the micro, meso and macro-scales are developed and linked together. Experiments in all three length scales are performed in order to reveal the failure mechanisms associated with different loading conditions and to validate the proposed method. Predicted and experimental results from pipes subjected to internal pressure, tensile, compressive and bending loads as well as their combinations are presented and discussed. INTRODUCTION Composites are nowadays extensively used in automobile, marine, civil and aerospace industries with the latter being the main conductor of industrial level composite technology. Weight saving in aerospace has been a critical selection driver and the excellent strength to weight ratio of fibrous composites renders them ideal for lightweight applications. The significantly reduced weight of composite structures, when compared to conventional steel, aluminium and titanium ones, is not, however, the only advantage. Due to their microstructure, composites are inherently fatigue resistant and can be tailored to suit the particular application. For example, a structure with high corrosion resistance to seawater, CO 2 and H 2 S which has also the capability of operating at high strain levels (up to 1% operational strain) can be manufactured with the appropriate choice of matrix, fibre type and

2 orientation. It is therefore apparent that the utilization of high performance composites such as PEEK / carbon fibre, can potentially improve riser safety, reliability and field viability while at the same time reduce deployment and operational costs. Moreover, such materials will ultimately enable the industry to unlock the potential of ultra-deep water applications where conventional steel and non-bonded flexible risers have reached their operational limits. The oil and gas industry has identified the benefits of using composites as a potential offshore riser material for over 20 years. However, their utilization has been mostly limited to nonbonded flexible risers where the heavy, costly and fatigue sensitive steel armour wires are replaced by carbon fibre reinforced ones. Some of the reasons for the lack of composite applications in this industry include the lack of familiarity of composite technology, field experience, applicable test data and established design codes. A thorough understanding of the composite behaviour is therefore important in order to help address the aforementioned deficiencies. The development of a multi-scale design approach, whereby information at the micro-level (i.e. μm scale) is used for the prediction of the structural response at the macrolevel (i.e. m scale), is fundamental for the understanding of the complex failure mechanisms that develop within composite materials and thus for the prediction of their behaviour. MODELLING STRATEGY A graphical illustration of the pipe and its break-down into the three different length scales is shown in Figure 1. It should be noted here that unlike non-bonded flexible pipes, the composite pipes in this study are monolithic structures. The structure break-down into smaller components is therefore purely done for analysis purposes and does not correspond to any physical discontinuity. The pipe consists of a number of repeatable fibre groupings that are laid along predefined angles (θ) with the fibres being held together by a PEEK matrix fused in via a laser assisted thermoplastic process 1. Each of these groupings can be treated as the building block (meso-scale model) of the pipe. Consequently, each fibre grouping consists of thousands of individual fibres surrounded by PEEK matrix which can be now treated as the building block (micro-scale model) of the different fibre groupings. The response of the final pipe structure can be therefore predicted by merely using the behaviour of the constituent materials (i.e. carbon fibre and PEEK matrix) as an input. This provides a great flexibility to the design as pipes with any matrix / fibre combination and fibre orientation can be analysed. The predicting capability of this approach clearly depends on the proximity of the assumptions made at each length scale which can be, however, quantified by performing experiments on all three length scales. 1 This process is completely different to the usual thermoset processes as typically employed by aerospace industry and it is more controllable, repeatable and recordable.

3 MICRO SCALE MODELLING The random array of fibres within the PEEK matrix can be idealized as a periodic array of repetitive unit cells as shown in Figure 2. The response of a fibre grouping can be therefore defined by simulating a unit cell with periodic boundary conditions [1]. Due to the shape of the fibre, it becomes apparent that the response of the unit cell will be directionally dependant i.e. the overall material behaviour will be anisotropic. Five elastic constants are required for the characterization of a fibre grouping with fibres lying along the same direction [2]. These are the elastic modulus along the fibre directions (E 1 ) the elastic modulus transverse to the fibre direction (E 2 ) Poisson s ratio in 1-2 plane (v 12 ) the shear modulus in 1-2 plane (G 12 ) the shear modulus in 2-3 plane (G 23 ) E 1 and v 12 can be derived from the unit cell by applying a tensile load along the 1-direction and then obtaining the resulting displacements along the 1- and 2-directions, E 2 by applying a tensile load along 2-direction and obtaining the resulting displacement, G 12 by applying a shear load and obtaining the change in 1-2 angle and G 23 by applying a shear load and obtaining the change in 2-3 angle. The only input required for the simulations above is the volume fraction of either the matrix or the fibre and their constitutive behaviours. MESO AND MACRO SCALE MODELLING At the meso-scale level, the material is treated as a continuum having the anisotropic properties calculated from the micro-scale analysis. However, these properties correspond to the principal coordinate system of each fibre grouping (i.e coordinate system in Figure 1) and can be used as calculated only when the latter coincides with the global coordinate system (i.e. only if fibres are laid along θ = 90 o ). The material properties of the fibre groupings laid at angles θ 90 o, can be mathematically derived through a stiffness matrix transformation [3]. The pipe can be therefore treated as a layered structure with each layer corresponding to a group of fibres with the same direction. The layered version of element 186 in the ANSYS finite element software has the capability of modelling up to 1000 different such layers within the same element. This allows for the calculation of the stresses and strains at the meso-scale level while performing a single global analysis (i.e. on the whole pipe geometry) within reasonable computational time. Obtaining the stresses and strains at the meso-scale level is very important as most of the existing failure criteria for composites [4, 5, 6] are only applicable at this level. In this study, a maximum stress allowable along the fibre direction 2 was employed for the prediction of the pipe failure 2 Due to their microstructure, composites have less strength when subjected to compressive loads. The allowable tensile stress was obtained from testing unidirectional coupons with fibres along the loading direction. The allowable compressive stress was taken to be within 0.4 to 0.6 of the tensile one.

4 load with its value obtained from the unidirectional coupon tests described in the next section. EXPERIMENTAL PROGRAMME PEEK AND CARBON FIBRE TESTS The material properties of PEEK and carbon fibre have been provided by the manufacturers i.e. Victrex and Toray respectively and are given in Table 1. It should be noted here that carbon fibres exhibit transversely isotropic behaviour hence the 5 elastic constants. UNI-DIRECTIONAL COUPON TESTS For the experimental validation of the material properties obtained from the micro-scale model, two different coupon types have been tested. The first type is a cylindrical coupon with fibres laid along +45 o and -45 o angles as shown in Figure 3(a). Flat ±45 o coupon testing [7] is the most widely used method for obtaining the shear modulus G 12 and the shear strength S 12 of fibre reinforced composites. A cylindrical coupon is, however, preferred in this study because (a) it is loyal to the manufacturing procedure, (b) it can be easily tested in compression 3 and (c) there are no edge effects to contaminate the test results. The second type is a flat coupon with fibres laid along the X-direction as shown in Figure 3(b). By applying a tensile load and monitoring the longitudinal and transverse strains, the elastic properties E 1, v 12 and the tensile strength along the fibre direction X 11T can be obtained. Form the two tests above, three (i.e. E 1, v 12 and G 12 ) out of the five elastic constants needed for the meso-scale analysis have been obtained. Tests for the determination of E 2 are yet to be performed. However, E 2 corresponds to the modulus transverse to the fibre and is a matrix dominated property. Composite structures are designed to carry loads along the fibre direction and therefore small variations in the transverse properties do not significantly affect the load distribution within the structure. Tests for the determination of G 23 are difficult to perform and give high scatter. For this reason, DNV OS C501 code [8] suggests that G 23 is taken equal to G 12. COMPONENT TESTS Two 2 10 ksi rated pipe configurations have been tested, one designed to be flexible and one to have higher axial capacity. The flexible pipe consists of fibre groupings laid along two directions θ = a and θ = b where a, b 45 o. The same a, b angles are used in the axially 3 Shear behaviour of ± 45 composites is similar in tension and compression and thus shear properties can be defined via either tension or compression tests as indicated in DNV OS C501 [8]. The cylindrical shape of the designed coupon prevents it from buckling thus the latter can be easily loaded up to failure.

5 stiffer pipe with extra fibres laid along angle θ = c where c > 45 o. The characteristics of the two pipes are given in Table 2. For the qualification of the two pipe configurations, an extensive experimental testing programme has been completed which includes axial tension, axial compression, burst, collapse, bending and combined bending - burst tests. For the axial tension and compression a Tinius Olsen machine was used along with a video extensometer to monitor the strains. For the burst tests special end fittings were designed to simulate open-ended conditions and a video extensometer was used to monitor the strains at low pressure levels. For the bending and the combined bending - burst tests the purpose built rig shown in Figure 4 was used along with optical strain gages. Accurate strain data are not available for collapse therefore this test could not be used for the validation of the modelling method. A summary of the type and number of tests used for the model validation is given in Table 3. RESULTS AND DISCUSSION Tables with the predicted and experimental properties along with plots of the stress-strain response as obtained from analysis, coupon and pipe testing are given below. MICRO SCALE MODEL VALIDATION The number of coupon tests, the coefficient of variation and the mean experimental E 1, v 12 and X 11T values normalised by the predicted ones are given in Table 4. Predicted and experimental elastic properties are shown to be in very good agreement (within 4%). However, the predicted tensile strength is shown to be 26% higher than the experimental one. This is not surprising since this property is sensitive to the coupon manufacturing process and the test procedure. Having a benchmark value for the maximum achievable strength is very useful in assessing the quality of (a) the supplied materials, (b) the manufacturing process and (c) the experimental procedure. The mean experimental shear properties normalized by the predicted ones are given in Table 5. Predicted and experimental shear strengths and moduli are shown to be in extremely good agreement. This is because shear in 1-2 plane (see Figure 2) is a matrix dominated property. Therefore, provided the shear behaviour of PEEK is known, the shear response of the unidirectional carbon-peek composite can be accurately predicted. Parameters such as the coupon manufacturing process and the experimental procedure do not significantly affect shear strength. This is most probably due to the highly non-linear behaviour of PEEK which was also evident in the nearly elastic - perfectly plastic response of the ± 45 o coupons. MACRO SCALE MODEL VALIDATION Typical axial strain and hoop strain - stress curves as obtained from pipe compression tests and FE analyses are shown in Figure 5 and Figure 6 respectively. In both plots, the stresses are normalized against the predicted compressive failure stress of each pipe configuration. From Figure 5, it can be seen that FE overestimates the axial stiffness of both pipes by

6 approximately 15% to 20%. At normalized stresses greater than 0.5, this difference is partly due to the non-linear axial deformation of the pipe which is not taken into account in the current analysis. This does not, however, explain the differences in the linear region. FE gives much better predictions in the hoop direction, where, predicted and experimental stress - strain curves are shown to be in good agreement (see Figure 6). The failure stress of the (a / b) pipe is over-predicted by 21%, whereas, that of the (a / b / c) pipe is under-predicted by 5%. Typical axial strain and hoop strain - stress curves as obtained from pipe tension tests and FE analyses are shown in Figure 7 and Figure 8 respectively. The plotted stresses are normalized against the predicted tensile failure stress of each pipe configuration. These tests were run up to approximately 0.1 of the ultimate failure load to ensure loading within the linear region (could not be loaded to failure due to clamping restrictions). Similarly to the compressive tests, the axial stiffness is over-predicted in this case by approximately 10% to 15%, whereas, the hoop stiffness is once again accurately predicted. The variations of hoop strain with normalised internal pressure as obtained from the burst tests are plotted in Figure 9. Strains were monitored for pressures up to 7 % and 16% of the pressure capacity of the (a / b) and the (a / b / c) pipe respectively. In both cases, the predicted and experimental hoop strains are shown to be in very good agreement. After the low pressure tests, the video extensometer was removed and both pipes were taken to failure. The ratio of the experimental to the predicted burst pressure is 1.01 for the (a / b) pipe and 1.16 for the (a / b / c) pipe. It should be noted here that all the input properties used for the FE analyses of the pipe come directly from the micro-scale analysis without using any fit factors. This is because the latter were found to be in very good agreement with the ones obtained from unidirectional coupon testing. The only property taken from experimental data is the tensile strength along the fibre direction which was determined from tests on unidirectional coupons that have fibres along the loading direction. This is because the latter property was overestimated from the microscale analysis by 26% (see Table 4). The axial tension and compression tests revealed that the pipe axial stiffness is over-predicted by 10% to 20%. An axial stiffness knock down factor of 20% was therefore applied on the FE analyses for the prediction of the (a / b) pipe subjected to bending and combined internal pressure - bending loads. The axial strain versus the normalized bending moment for the pure bending test is shown in Figure 10. The structure was bent in the linear region and the FE results are shown to give good predictions. The experimental axial strains were measured in both tension and compression sides of the pipe to ensure that pure bending load was applied, whereas, the hoop strains were very close to zero and are thus not plotted. Figure 11 shows the axial and hoop strain versus the normalized bending moment for the (a / b) pipe subjected to bending and 690 bar internal pressure. It should be noted that the bending moment is normalised with the bending moment at failure as predicted for a pipe with zero internal pressure. Internal pressure relieves the axial stresses (due to the contraction in the axial direction) hence the higher bending capacity of the pipe (i.e. bending moment / bending

7 moment at failure = 1.5 in Figure 11). Experimental and FE predictions are shown to be in very good agreement. The tests show that the hoop strain - stress response is more accurately predicted than the corresponding axial one for both (a / b) and (a / b / c) pipe configurations (both pipes have more fibres along the hoop direction). Moreover, the strength predictions are more accurate when the pipes are loaded along the fibre direction (i.e. better strength predictions for (a / b / c) pipe when axially loaded and better predictions for the (a / b) pipe when tested in burst). The above indicate that the current modelling approach is more efficient in predicting the pipe response along the direction that is more heavily reinforced by fibres. This is not surprising given that the failure criterion employed is based on a maximum allowable tensile and compressive strength along the fibre direction. Coupon experiments for the determination of the transverse to the fibre properties are expected to help in the better understanding of the axial response of the pipe configurations studied. CONCLUSIONS A multi-scale modelling approach has been used in this study for the prediction of the response of composite pipes subjected to various loading conditions. This approach allows for the calculation of the stress / strain fields at different length scales within the structure and thus for the application of physically based failure criteria. The latter can be linked to the failure modes found in composites and can thus yield more accurate strength predictions. The maximum allowable tensile and compressive stress along the fibre direction was the failure criterion employed for the strength predictions in this study. Despite its simplicity, this criterion was shown to provide acceptable predictions especially for the cases where the pipe was loaded along the more highly reinforced directions. More sophisticated constitutive models (e.g. ones that can account for material non-linearity) and failure criteria must be employed in order to obtain more accurate predictions. The latter can be determined from micro-scale analyses combined with coupon testing. ACKNOWLEDGEMETS A portion of this work was carried out within the framework of the UK Knowledge Transfer Partnership scheme and the support of University of Portsmouth is gratefully acknowledged.

8 NOMENCLATURE COV Coefficient of Variation FE Finite Element MBR Minimum Bending Radius REFERENCES [1] Sun C. T. & Vaidya R.S., Prediction of Composite Properties from a Representative Volume Element. Comp. Sci. & Tech., 56 (1996) [2] Hull D. & Clyne T.W., An Introduction to Composite Materials. Cambridge University Press, (1996) 2 nd Edition. [3] S. G. Lekhnitski, Theory of Elasticity of an Anisotropic Elastic Body, San Francisco, Holden- Day, [4] Tsai, S. W. & Wu, E. M., A General Theory of Strength for Anisotropic Materials. Journal of Composite Materials., 5 (1971) [5] Puck, A. & Schurmann, H., Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models, Composites Science and Technology, 62 (2002) [6] Hashin, Z., Failure Criteria for Unidirectional Fiber Composites. J. Appl. Mech., 47 (1980) [7] ASTM D 3518 / D3518M - 94(2007) Standard Test Method for In-Plane Shear Response of Polymer Matrix Composite Materials by Tensile Test of a ±45 Laminate. [8] Det Norske Veritas Composite Components, Offshore Standard DNV-OS-C501, October TABLES AND FIGURES Table 1 - Material properties of PEEK and carbon fibres as provided by Victrex and Toray respectively Material E 11 (GPa) E 22 (GPa) G 12 (GPa) G 23 (GPa) v 12 X 11T (MPa) PEEK Carbon fibre * *G 23 is not provided by the manufacturer and is therefore assumed to be equal to G 12

9 Table 2 Characteristics of the 2 10 ksi rated pipe configurations tested Pipe Configuration Inner Diameter (mm) Outer Diameter (mm) Pipe characteristics Wall Thickness MBR (mm) 10 ksi composite pipe weight / 10 ksi steel pipe weight (a / b) pipe (a / b / c) pipe Table 3 Type and number of tests performed for model validation Pipe Configuration Number of tests for model validation Tension Compression Burst Bending Burst-bending (a / b) pipe (a / b / c) pipe Table 4 - Experimental and predicted properties along the fibre direction No. of coupons tested Property COV Mean Experimental / Predicted E 1 6.3% v % 0.98 X 11T 7.2% 0.74 Table 5 Experimental and predicted shear properties in 1-2 plane No. of coupons tested 5 Property COV Mean Experimental / Predicted G % 1.01 S % 1.02

10 Figure 1 Pipe break-down to smaller components for modelling purposes

11 Figure 2 Idealisation of a random array of fibres as a periodic array consisting of repetitive unit cells Figure 3 Unidirectional coupons for the determination of (a) the shear properties (i.e. G 12 and S 12 ) and (b) the properties along the fibre direction (i.e. E 11, v 12, X 11T )

12 Figure 4 Combined burst and bend rig assembly model Figure 5 Axial strain versus normalised stress as obtained from pipe compressive tests and FE predictions. Stresses are normalised against the predicted failure stress of each pipe configuration

13 Figure 6 Hoop strain versus normalised stress as obtained from pipe compressive tests and FE predictions. Stresses are normalised against the predicted failure stress of each pipe configuration Figure 7 Axial strain versus normalised stress as obtained from pipe tensile tests and FE predictions. Stresses are normalised against the predicted failure stress of each pipe configuration

14 Figure 8 Hoop strain versus normalised stress as obtained from pipe tensile tests and FE predictions. Stresses are normalised against the predicted failure stress of each pipe configuration Figure 9 Hoop strain versus normalised stress as obtained from internal pressure tests and FE predictions. Stresses are normalised against the predicted failure pressure of each pipe configuration

15 Figure 10 Axial strain versus normalised bending moment as obtained from the bending test on (a / b) pipe configuration and the FE predictions. Bending moment is normalised against the predicted bending moment at failure.

16 Figure 11 Axial and hoop strains versus normalised bending moment as obtained from the combined internal pressure - bending test on the (a / b) pipe configuration and the FE predictions. Bending moment is normalised against the predicted bending moment at failure of a pipe with zero internal pressure.