PREDICTION OF OPEN HOLE COMPRESSIVE FAILURE FOR QUASI-ISOTROPIC CFRP LAMINATES

Transcription

1 PREDICTION OF OPEN HOLE COMPRESSIVE FAILURE FOR QUASI-ISOTROPIC CFRP LAMINATES Y. Miyano*, T. Hioki and M. Nakada Materials System Research Laboratory, Kanazawa Institute of Technology, Hakusan, Japan * miyano@neptune.kanazawa-it.ac.jp Keywords: Polymer composites, Micromechanics of failure, Life prediction Abstract The procedure of MMF/ATM method combined with accelerated testing methodology (ATM) and the stress-based micromechanics of failure (MMF) is proposed for the fatigue life prediction of the structures made of CFRP laminates. The validity of MMF/ATM method is confirmed through the following two steps. As the first step, the master curves of MMF/ATM critical parameters of CFRP are determined by measuring the static and fatigue strengths at elevated temperatures in the longitudinal and transverse, tension and compression directions of unidirectional CFRP. As the second step, the open hole compression (OHC) fatigue strengths of quasi-isotropic CFRP laminates as an example of CFRP structures are measured at elevated temperatures, and these experimental data are compared with the predicted results by using the master curves of MMF/ATM critical parameters of CFRP based on MMF/ATM method. 1. Introduction The accelerated testing methodology (ATM) [1] was proposed for the prediction of long-term fatigue strength of CFRP laminates based on the time-temperature superposition principle (TTSP). Based on ATM, the long-term fatigue strength for CFRP laminates can be predicted by measuring the short-term fatigue strengths at elevated temperatures. The applicability of ATM was confirmed for CFRP laminates combined with PAN based carbon fibers and thermosetting resins [2-4]. Furthermore, ATM was developed into the advanced ATM in which the formulation for the master curves of time-temperature dependent fatigue strength was performed based on Christensen s theory [5] which describes statistically the crack kinetics in viscoelastic body [6]. The failure criteria of separated fiber and matrix in polymer composites have been developed and the failure of composite structures has been predicted based on the analyses on micromechanics, laminates and structure levels. Recently, the stress-based micromechanics of failure (MMF) have been proposed by Sung-Kyu Ha and others [7] for polymer composite with viscoelastic matrix. In this paper, the procedure of MMF/ATM method combined with ATM and MMF is proposed for the fatigue life prediction of the structures made of CFRP laminates. The validity of MMF/ATM method is confirmed through the following two steps. As the first step, 1

2 the master curves of MMF/ATM critical parameters of CFRP are determined by measuring the static and fatigue strengths at elevated temperatures in the longitudinal and transverse, tension and compression directions of unidirectional CFRP. As the second step, the open hole compression (OHC) fatigue strengths of quasi-isotropic CFRP laminates as an example of CFRP structures are measured at elevated temperatures, and these experimental data are compared with the predicted results based on MMF/ATM method by using the master curves of MMF/ATM critical parameters of CFRP. 2. Procedure of MMF/ATM method The procedure of proposed MMF/ATM method is shown schematically in Figures 1 and 2. Figure 1 shows the first step for the prediction procedure by MMF/ATM method that is the process of determination of MMF/ATM critical parameters. First, the viscoelastic modulus in the transverse direction of unidirectional CFRP is measured at various temperatures. The master curve and the time-temperature shift factor are determined by using these test data based on the TTSP. Second, the static and fatigue strengths in the typical four directions of unidirectional CFRP are measured at various temperatures at a single loading rate and single loading frequency, respectively. The strengths in four directions are the longitudinal tension X, the longitudinal compression X, the transverse tension Y and the transverse compression Y, respectively. Third, the master curves of these strengths are determined by using the measured data and the time-temperature shift factor for viscoelastic modulus. Fourth, the master curves of four MMF/ATM critical parameters, the fiber tensile strength T f, the fiber compressive strength C f, the matrix tensile strength T m, and the matrix compressive strength C m are determined through the method described in [8]. Figure 1. First step for prediction procedure by MMF/ATM method: Determination of MMF/ATM critical parameters Figure 2 shows the second step for the prediction procedure by MMF/ATM method that is the life determination of CFRP structures. With the master curves of the MMF/ATM critical parameters, the long-term strength prediction of CFRP becomes possible. Three-step stress analyses are necessary to process the test result, including stress analysis for homogenous CFRP structures and CFRP laminates in macro level and stress analysis for the constituents in micro level by stress amplification. From the master curves of MMF/ATM critical parameters 2

3 and failure criteria for fiber and matrix, the strength of CFRP structure under arbitrary time to failure and temperature can be determined. The details of ATM and MMF are introduced at the previous papers [7,8], so that the explanation of ATM and MMF is neglected in this paper. Figure 2. Second step for prediction procedure by MMF/ATM method: Life determination of CFRP structures 3. Determination of MMF/ATM critical parameters 3.1 Long-term static strength of unidirectional CFRP The test specimens were fabricated from unidirectional CFRP of T300/2500 which consists of T300 carbon fibers and epoxy resin All the laminates were cured at 135 o C for 2 hours by the autoclave technique and postured at 160 o C for 2 hours. The aging treatment for postcured specimen was conducted at 110 o C for 50 hours. The Wet specimens by soaking the aged specimen (Dry specimen) in hot water of 95 o C were prepared. The water weight content of wet specimen was 1.9%. The volume fraction of fibers for Dry and Wet specimens is approximately The dynamic viscoelastic tests were performed for various frequencies and temperatures for the transverse direction of unidirectional CFRP to get the viscoelastic compliance of matrix resin. The static tests for the following four directions of unidirectional CFRP were carried out at various temperatures. Longitudinal tension tests under static loading were carried out according with SACMA 4R-94. Longitudinal bending tests under static loading were carried out according with ISO to get the longitudinal compressive static strength. Transverse bending tests under static loading were carried out according with ISO to get the transverse tensile static strength. Transverse compression tests under static loading were carried out according with SACMA 1R-94. The master curve of creep compliance and the time-temperature shift factor for matrix resin were determined by the creep compliances measured at various temperatures based on TTSP. The master curves of static strengths for four directions of unidirectional CFRP were 3

4 determined by the static strengths for the corresponding direction of unidirectional CFRP measured at various temperatures and the time-temperature shift factor for matrix resin. The details of measuring process and measured data are neglected in this paper. 3.2 MMF/ATM critical parameters of unidirectional CFRP The master curves of MMF/ATM critical parameters T f, C f, T m and C m determined from the master curves of static strengths and the mechanical properties of unidirectional CFRP under the procedure shown in Figure 1 are shown in Figure 3. (a) T f and C f (b) T m and C m Figure 3. Master curves of MMF/ATM critical parameters 4. Life determination of CFRP structures based MMF/ATM method As an example of life determination of CFRP structures based on MMF/ATM method, the long-term open hole compressive (OHC) strength for quasi-isotropic laminates (QIL) was predicted by using the master curves of MMF/ATM critical parameters. The stacking sequence of CFRP laminates is [45/0/-45/90] 2s and the open hole specimen has the configurations with the thickness of 4mm, the width of 38.1mm and the diameter of 6.35mm for the prediction. Figures 4 and 5 show the failure index distribution maps for each layer and failure mode for the static loading at room temperature for Dry and Wet conditions, where k Tf and k Cf are the failure index of carbon fibers under tension and compression and k Tm and k Cm are the failure index of matrix resin under tension and compression. When one of these four failure indexes at one of four layers of 45 o, 0 o, -45 o and 90 o reaches to unity, the initial failure of laminates occurs. The numbers in the maps show the maximum of failure index in each layer and failure mode. These maps show that the failure index of 0 o layer and k Cf reaches firstly to unity at the corner of open hole for Dry condition and that the failure index of 45 o layer and k Cm reaches firstly to unity at the corner of open hole for Wet condition. Figure 6 shows the failure 4

5 indexes for four failure modes and four layers at the corner of open hole for Dry and Wet conditions. It is cleared that the OHC static failure of QIL was triggered by fiber compressive failure in 0 o layer for Dry condition as shown in Figure 6(a) and that the OHC static failure of QIL was triggered by matrix compressive failure in 45 o layer for Wet condition as shown in Figure 6(b). Figure 4. Failure index distribution map of static load under Dry condition (T=25 o C, t =1 min, s =353 MPa) Figure 5. Failure index distribution map of static load under Wet condition (T=25 o C, t =1 min, s =300 MPa) 5

6 (a) Dry condition (T=25 o C, t =1 min, s =353 MPa) (b) Wet condition (T=25 o C, t =1 min, s =300 MPa) Figure 6. Failure indexes at the corner of open hole under static loading The predicted master curves of static OHC strengths for QIL for Dry and Wet conditions were calculated based on the MMF/ATM method using the master curves of MMF/ATM critical parameters, where the initiation of failure is defined as both of the compressive failure of fibers of 0 o layers and the compressive failure of matrix at the corner of open hole. These predicted results are shown in Figure 7. Figure 7. Prediction of OHC static strength 5. Experimental confirmation for OHC static strengths of quasi-isotropic CFRP laminates for Dry and Wet conditions The static compression tests were performed for quasi-isotropic CFRP laminates with a central hole for dry and Wet conditions as shown in Figure 8. Figure 9 shows the fractographs at the corner of open hole under static loading at T=25 o C for Dry condition, in which the compressive static load was stopped at 92% level of failure load. The microbuckling of fibers in 0 o layer (2nd, 6th) of surface layer are observed near the edge of hole. Figure 10 shows the fractographs at the corner of open hole under static loading at T=25 o C for Wet condition, in which the compressive static load was stopped at 82% level of failure load. The transverse cracks in 45 o layers (1st and 5th) are observed near the edge of hole. It was cleared from these 6

7 results that the predicted initial failure position, layer and failure mode agree well with the experimental ones for static loading for Dry and Wet conditions. The measured static strengths are shown in Figure 7. All of these experimental results are triggered from the compression of fibers in 0 o layers at the corner of hole. These results agree well with the predicted ones for all region of time to failure t. Figure 8. Static compression test for QIL CFRP laminates with a central hole Surface 45 layer (1st) 0 layer (2nd) -45 layer (3rd) 90 layer (4th) 45 layer (5th) 0 layer (6th) -45 layer (7th) Center 90 layer (8th) Figure 9. Initial failure at the corner of hole of QIL CFRP laminates under static loading (Dry condition, =0.92 s, T=25 o C, V=0.1 mm/min) Surface 45 layer (1st) 0 layer (2nd) -45 layer (3rd) 90 layer (4th) 45 layer (5th) 0 layer (6th) -45 layer (7th) Center 90 layer (8th) Figure 10. Initial failure at the corner of hole of QIL CFRP laminates under static loading (Wet condition, =0.82 s, T=25 o C, V=0.1 mm/min) 7

8 6. Conclusion MMF/ATM method for the life prediction of the structures made of CFRP laminates was proposed in this paper. The validity of MMF/ATM method was confirmed through the following two steps by using CFRP laminates of T300/2500 for Dry and Wet conditions. As the first step, the master curves of MMF/ATM critical parameters of CFRP laminates were determined by measuring the static strengths at elevated temperatures in the longitudinal and transverse, tension and compression directions of unidirectional CFRP for Dry and Wet conditions. As the second step, the open hole compression (OHC) static strength of quasiisotropic CFRP laminates with failure modes for Dry and Wet conditions were predicted based on MMF/ATM method by using the master curves of MMF/ATM critical parameters of CFRP. And these OHC strengths were measured at elevated temperatures for comparing with the predicted results. The predicted initial failure position, layer and failure mode as well as the predicted strengths agree well with the experimental ones for Dry and Wet conditions. AKNOWLEDGEMENTS The authors thank the Office of Naval Research for supporting this work through an ONR award with Dr. Yapa Rajapakse and Dr. Kenji Uchino. The authors thank Professor Richard Christensen, Stanford University as the consultant of this project. REFERENCES [1] Miyano Y., Nakada M., McMurray M. K. and Muki R., Prediction of Flexural Fatigue Strength of CFRP Composites under Arbitrary Frequency, Stress Ratio and Temperature, Journal of Composite Materials 31 (1997): [2] Miyano Y., Nakada M. and Muki R., Applicability of Fatigue Life Prediction Method to Polymer Composites, Mechanics of Time-Dependent Materials 3 (1999): [3] Miyano Y., Nakada M., Kudoh H. and Muki R., Prediction of Tensile Fatigue Life under Temperature Environment for Unidirectional CFRP, Advanced Composite Materials 8 (1999): [4] Miyano Y., Nakada M. and Sekine N., Accelerated Testing for Long-term Durability of FRP Laminates for Marine Use, Journal of Composite Materials 39 (2005): [5] Christensen R. M. and Miyano Y., Stress Intensity Controlled Kinetic Crack Growth and Stress History Dependent Life Prediction with Statistical Variability, International Journal of Fracture 137 (2006): [6] Christensen R. M., An Evaluation of Linear Cumulative Damage (Miner s Law) Using Kinetic Crack Growth Theory, Mechanics of Time-Dependent Materials 6 (2002): [7] Ha, S. K., Jin, K. K. and Huang, Y., Micro-Mechanics of Failure (MMF) for Continuous Fiber Reinforced Composites, Journal of Composite Materials 42 (2008): [8] Cai, H., Miyano, Y., Nakada, M., and Ha, S. K., Long-term Fatigue Strength Prediction of CFRP Structure Based on Micromechanics of Failure, Journal of Composite Materials 42 (2008):