Unit cell simulation of fatigue damage in short fiber reinforced plastic composites

Transcription

1 Unit cell simulation of fatigue damage in short fiber reinforced plastic composites T. Okabe, M. Nishikawa and H. Imamura (Tohoku University) Masahiro Hashimoto (Toray Industries)

2 Introduction Discontinuous-fiber reinforced plastics Lightweight Superior formability High cycle molding (Thermoplastic matrix system) Promising materials for automotive application Radiator core support (Injection molding) Door inner (Press molding)

3 Discontinuous vs Continuous Lack of mechanical strength of discontinuous-fiber reinforced plastics is limiting its application. Short (discontinuous) fiber Long (Continuous) fiber (a) (b) (a)interfacial debonding, (b)matrix damage Fiber breakage Conventional short fiber composite couldn t use up the strength of reinforcement fiber.

4 Periodic cell simulation Unit cell of short fiber reinforced composites (Carbon/epoxy) Fiber length distribution 300 fibers 81,537 nodes 7,378 quadrilateral elements for fibers 15,784 triangle elements for matrix We simulated the random-oriented short fiber composites. The average fiber length is about 100mm and close to the real fiber length in polymer composites made by the injection molding.

5 Outline of numerical simulation Periodic cell simulation(2) First, this approach divided the strain and displacement into macroscopic one and microscopic one. Then, the microscopic displacement field is calculated by controlling the macroscopic strain. Therefore, the displacement field in a unit cell is calculated when the macroscopic average strain is given.

6 Modeling of micro damages in short fiber composites Fiber break Weibull model Matrix cracking Damage mechanics Interface Embedded process zone Damage mechanics model is used to express the complicated damage in a matrix. Constitutive law is given with internal damage D by Evolution law of damage variable D is given by Void expansion term referring to Gurson, Shizawa et al. D = 0 D = 1 Shear failure term Intact Completely damaged A, B 0, B 1 are phenomelogical parameters.

7 Simulated results [θ lower, θ upper ] = [0.4π,0.6π] * Mandell et al. (1982)

8 Fatigue damage progress of the matrix Kachanov damage mechanics Kachanov LM. Introduction to Continuum Damage Mechanics Evolution law of fatigue damage N = 1000 (cycles) is used in this study

9 Flow chart Start Static incremental analysis (Tension loading and unloading) Calculate maximum hydrostatic pressure during the incremental analysis (for all integration points) Calculate fatigue damage increment and stress degradation for N cycles No Final failure Stop Yes

10 Previous experiments by Ha, Yokobori and Takeda (1999) Tensile stress: 0 32 MPa

11 Previous experiments by Ha, Yokobori and Takeda (1999) DEG 0 DEG 45 DEG Damage size (mm) 90 0 Number of cycles

12 Initial damage Simulated results D DEG 0 N = 20000(cycles) 90 N = 1000(cycles)

13 Simulated results DEG 45 N = 4000(cycles) DEG 90 DEG 45 DEG 0 Agree with the experiments

14 Effect of fiber length on damage mode Fracture modes of short fiber reinforced composite differ from that of long fiber reinforced composite. Continuous (long) fiber Fiber Discontinuous (short) fiber Debonding between fiber and matrix Crack Fiber break Loading direction Fiber * from Sato et al. (1991) In this presentation, we discuss how the short fiber reinforced composites are broken.

15 Thermoplastic press sheet with carbon fiber Materials Thermoplastic resin Carbon fiber mat Sheet + Features Long fiber length Good fiber dispersion In-plane random fiber orientation Thermoplastic matrix Strength Formability (a) Overview (b)cross sectional area Fig. Photos of the sheet

16 Strength and formability Strength Tensile strength (MPa) GMT (Vf20%) GMT: Glass mat thermoplastics SMC:Sheet molding compound SMC (Vf40%) Composite Made of sheet (Vf20%) Formability 0 GF/PP CF/ CF/ Vinyl Ester Polypropylene Strength of in-plane reinforced materials Exhibits good flowability, complex shape is easily fabricated Much superior to conventional short fiber composite

17 Unit cell model for the unidirectional short fiber composites Fiber modeling Cumulative failure probability Matrix modeling Evolutionary equation of damage variable D Void expansion term referring to Gurson, Shizawa et al. Shear failure term A, B 0, B 1 are phenomelogical parameters.

18 Simulated results l f = 0.02 mm l f = 0.2 mm l f = 0.3 mm l f = 1.0 mm

19 Stress strain curves Fiber-breaking mode Fiber-avoiding mode Initial stiffness of the composite increases as l f increases. When l f 0.1mm, the initiation of matrix cracking causes the critical failure. When 0.1mm < l f < 0.5mm, the crack is trapped. But, the failure is caused by the fiber-avoiding. When l f 0.5mm, the failure is determined by the fiber-breaking of the neighboring.

20 Theoretical model for the fiber length effect on the composite s s strength (GLS model) Duva & Curtin (1995) The length of discontinuous fibers is represented by the density of initial broken segments in the fiber. L 2L T Averaged stress carried by the fibers is equal to the composite stress (Duva et al.) σ Φ ( ) 1 = V f σ f 1 e Φ Φ = 2d b L T N = 2 L L T = 2L T d L 0 ρ σ f σ 0 In calculating the stress-transfer length L T, we used the solution of elastic-plastic hardening shear-lag model (Okabe and Takeda, 2000).

21 Composite strength versus averaged fiber stress Fiber failure Fiber avoiding Kelly & Tyson Curtin 228 µm 403 µm Kelly & Tyson length is shorter to get fiber failure mode (high strength). Duva & Curtin has a good agreement with experiments

22 Effect of fiber length on fatigue life

23 Fatigue damage in UD composites (0.1mm) Initial cycle After 11 cycle After 31 cycle

24 Fatigue damage in UD composites (2.1mm) Initial cycle After 3204cycle 3205 cycle, Applied strain=0.564%