18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS ADVANCED ACCELERATED TESTING METHODOLOGY FOR LONG-TERM LIFE PREDICTION OF CFRP M. Nakada * and Y. Miyano Materials System Research Laboratory, Kanazawa Institute of Technology, 3-1 Yatsukaho, Hakusan, Ishikawa 924-0838, Japan * Corresponding author (nakada@neptune.kanazawa-it.ac.jp) Keywords : Polymer composites, Accelerated testing, Fatigue life prediction Abstract The advanced accelerated testing methodology In this paper, we propose an advanced accelerated (ATM-2) for the long-term life prediction of CFRP testing methodology (ATM-2) which can be applied laminates exposed to an actual loading having to the life prediction of CFRP laminates exposed to general stress and temperature history is proposed in an actual load and environment history. First, three this paper. Three conditions as the basis of ATM-2 conditions as the basis of ATM-2 are introduced are introduced with the scientific bases. The long- with the scientific bases. One of these conditions is term fatigue strength of CFRP laminate under an the fact that the time and temperature dependence on actual loading is formulated based on the three the strength of CFRP is controlled by the conditions. The creep compliance and time- viscoelastic compliance of matrix resin [1]. Second, temperature shift factors of matrix resin, which the formulations of creep compliance and time- perform an important role for time and temperature temperature shift factors of matrix resin are carried dependence of long-term life of CFRP laminates, are out based on the time-temperature superposition also formulated based on the time-temperature principle. And the formulations of long-term life of superposition principle. The applicability of ATM-2 CFRP under an actual loading are carried out based is confirmed by predicting the long-term fatigue on the three conditions. Third, the applicability of strength of three kinds of CFRP laminates for ATM-2 for the long-term life prediction of three marine use. kinds of CFRP laminates is confirmed. 1 Introduction 2 ATM-2 Carbon fiber reinforced plastics (CFRP) are now The ATM-2 is established with three following being used for the primary structures of airplanes, conditions, (A) the failure probability is independent spacecrafts and others as well as ships, in which the of temperature and load histories, (B) the time and high reliability should be kept during the long-term temperature dependence of strength of CFRP is operation. Therefore, it would be expected that the controlled by the viscoelasticity of matrix resin. accelerated testing methodology for the long-term Therefore, the time-temperature superposition life prediction of CFRP structures exposed under the principle for the viscoelasticity of matrix resin holds actual environments of temperature, water, and for the strength of CFRP, (C) the strength others must be established. degradation of CFRP holds the linear cumulative damage law as the cumulative damage under cyclic A strategy of accelerated testing is shown as the loading. following steps, 1) data collections by accelerated testing, 2) durability design, 3) development of With the condition (A), the reference strength and highly reliable structures. First, the accelerated the failure probability can be obtained by measuring testing methodology should be established for the static strength of CFRP at an arbitrary strain rate polymer composites. Our developed methodology under room temperature [2]. With the condition (B), will be generic and can be applied to centrifuge, it is possible to calculate the strength variation of generator, flywheel, aircraft, wind turbine, marine CFRP by the viscoelastic compliance of matrix resin and automobile. determined by the creep compliance of matrix resin
and the history of load and temperature changed The viscoelastic compliance can be shown by the with time. With the condition (C), it is possible to following equation. calculate the strength degradation by load cycles ( ) undergoing to the linear cumulative damage law. σ τ d ' ( ) t ' ∫ − τ τ D t ' ' , T d ' ( ) ε The formulation for long-term fatigue strength of t ' , T c 0 τ ( ) d ' (2) 0 = = D * t ' , T 0 ( ) ( ) 0 σ σ CFRP exposed to an actual load and environment t ' , T t ' , T 0 0 history are conducted under the three conditions of ATM-2. The procedure for determining the where, D c shows the creep compliance of matrix materials parameters in the formulation of ATM-2 is resin and σ ( τ ’) shows the stress history. t ’ is the illustrated in Fig.1. reduced time at T 0 and can be shown by the following equation. τ d , (3) t ∫ = t ' ( ( ) ) τ a T T 0 0 where, a T o shows the time-temperature shift factor of matrix resin and T ( τ ) shows the temperature history. The fourth and fifth terms show the degradation by the cumulative damage under cyclic load. The N f and R in this term show the number of cycles to failure and the stress ratio at the final step, Fig.1 Procedure of ATM-2 * are the material parameters. respectively. n f and n f The k D shows the accumulation index of damage The long-term fatigue strength exposed to the actual defined as the following equation based on the loading where the temperature and load change with condition (C). time can be shown by the following equation based on the conditions of A, B and C. n n = ∑ , (4) i < k 1 D N = i 1 f i 1 ( ) ( ) [ ( ) ] σ = σ + − − log t ' , T , N , R , P log t ' , T log ln 1 P f 0 f f f0 0 0 α f where n i and N fi are the number of cycles and the ( ) ( ) D * t ' , T − 1 R ( ) ( ) number of cycles to failure at the loading of step i , − 0 − + * − n log n log 2 N n log 1 k ( ) r f f f D D t ' , T 2 respectively. c 0 0 (1) 3 Long-term Life Prediction of CFRP Laminates The first term of right part shows the scale parameter The long-term fatigue strength for three kinds of for the strength at the reference temperature T 0 , the CFRP laminates under Dry and Wet conditions are reduced reference time t 0 ’, the number of cycles to formulated by substituting the measured data in failure N f = 1/2 and the stress ratio R = 0. Eq.(1). Three kinds of CFRP laminates are plain woven T300 carbon fibers fabric/vinylester The second term shows Weibull distribution as the (T300/VE), plain woven T700 carbon fibers flat function of failure probability P f based on condition fabric/vinylester (T700/VE-F) and multi-axial (A). α is the shape parameter for the strength. knitted T700 carbon fibers fabric/vinylester (T700/VE-K) for marine use. These CFRP laminates were prepared under two conditions of The third term shows the variation by the Dry and Wet after molding. Dry specimens by viscoelastic compliance of matrix resin which holding the cured specimens at 150 o C for 2 hours in depend on temperature and load histories. n r is the air, Wet specimens by soaking Dry specimens in hot material parameter.
water of 95 o C for 120 hours were respectively prepared. 3.1 Creep compliance and time-temperature shift factors The creep compliances D c at various temperatures under Dry and Wet conditions shown in the left side of Fig.2 were shifted horizontally and vertically to construct the smooth master curve of D c shown in the right side of this figure. The master curve of D c can be represented by two tangential lines, whose slopes are m g and m r , respectively. With these parameters, the master curve of D c can be fit with the following equation, m m r g t ' t ' (5) = + + log D log D ( t ' , T ) log c c,0 0 0 t ' t ' 0 g where t ’ g is the reduced glassy time at T 0 . The parameters of D c ( t ’ 0 , T 0 ), t ’ g , m g and m r are determined by fitting the D c master curves shown in Fig.2. Fig.3 Horizontal and vertical shift factors The horizontal time-temperature shift factor a T o ( T ) and the vertical temperature shift factor b T o ( T ) are shown in Fig.3. Additionally, the storage moduli under Dry condition measured at various temperatures in the relative high temperature range were also shifted horizontally and vertically to construct the smooth master curve of storage modulus. These shift factors were formulated by Eqs.(6) and (7), ∆ ( ) H 1 1 ( ) = − − log a T 1 H T T T g 2 . 303 G T T 0 0 ∆ ∆ ( ( ) ) H 1 1 H 1 1 + − + − − − 1 1 1 H T T g 2 . 303 G T T 2 . 303 G T T g 0 g (6) ) ( ) ( ) ( = − − log b T b T T H T T (7) T 1 0 g [ ( 0 ) ( ) ] ( ( ) ) + − + − − − b T T b T T 1 H T T 1 g 0 2 g g where G is the gas constant, 8.314×10 -3 [kJ/(Kmol)], ∆ H 1 and ∆ H 2 are activation energies below and Fig.2 Master curves of creep compliance of matrix above the glass transition temperature T g . H is the resin
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