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)
IntroductionIntroduction
Discontinuous-fiber reinforced plastics
・Lightweight
・Superior formability
・High cycle molding
Promising materials for
automotive application
Radiator core support Door inner(Injection molding) (Press molding)http://www.calsonickansei.co.jp/ http://www.jgmt.net/
(Thermoplastic matrix system)
Fiber breakage (a)Interfacial debonding, (b)Matrix damage
(a)(b)
Conventional short fiber composite couldn’t use up the strength of reinforcement fiber.
Long (Continuous) fiberShort (discontinuous) fiber
Lack of mechanical strength of discontinuous-fiber reinforced plastics is limiting its application.
Discontinuous vs ContinuousDiscontinuous vs Continuous
Periodic cell simulationPeriodic cell simulation
Unit cell of short fiber reinforced composites (Carbon/epoxy)
81,537 nodes7,378 quadrilateral elements for fibers
15,784 triangle elements for matrix
Fiber length distribution
300 fibers
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.
Periodic cell simulation(2)Periodic cell simulation(2)Outline of numerical simulation
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.
Modeling of micro damages in short fiber composites Modeling of micro damages in short fiber composites
Fiber break Weibull modelMatrix cracking Damage mechanicsInterface Embedded process zone
Damage mechanics model is used to express the complicated damage in a matrix.
Evolution law of damage variable D is given by
Void expansion term referring to Gurson, Shizawa et al.
Shear failure term
A, B0, B1 are phenomelogical parameters.
Constitutive law is given with internal damage D by
D = 0 IntactD = 1 Completely damaged
Fatigue damage progress of the matrixFatigue damage progress of the matrix
※ Kachanov LM. Introduction to Continuum Damage Mechanics
Kachanov damage mechanics
Evolution law of fatigue damage
∆N = 1000 (cycles) is used in this study
Flow chartFlow chart
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
Final failure
StopYes
No
Start
Previous experiments by Ha, Yokobori and Takeda (1999)Previous experiments by Ha, Yokobori and Takeda (1999)
Tensile stress: 0 32 MPa
Previous experiments by Ha, Yokobori and Takeda (1999)Previous experiments by Ha, Yokobori and Takeda (1999)
DEG 0° DEG 45 DEG 90
0°
45°
90°
Number of cycles
Dam
age
size
(mm
)
Simulated resultsSimulated results
DEG 45N = 4000(cycles)
DEG 90> DEG 45> DEG 0→Agree with the experiments
Effect of fiber length on damage modeEffect of fiber length on damage mode
Loading directionFiber break
FiberContinuous (long) fiber
In this presentation, we discuss how the short fiber reinforced composites are broken.
Fracture modes of short fiber reinforced composite differ from that of long fiber reinforced composite.
Discontinuous (short) fiber
* from Sato et al. (1991)Fiber
Debonding between fiber and matrix
Crack
Thermoplastic press sheet with carbon fiberThermoplastic press sheet with carbon fiber
Fig. Photos of the sheet
Carbon fiber mat
Thermoplasticresin
(b)Cross sectional area
Sheet
(a) Overview
Strength
Formability
・Long fiber length
・Good fiber dispersion
・In-plane random fiber orientation
・Thermoplastic matrix
Features
+
Materials
Strength and formabilityStrength and formability
Formability
Much superior to conventional short fiber composite
Strength
Exhibits good flowability,complex shape is easily fabricated
GMT(Vf20%)
SMC(Vf40%)
CompositeMade of sheet
(Vf20%)
GF/PP CF/ CF/
GMT: Glass mat thermoplastics
Polypropylene
SMC:Sheet molding compound
Vinyl Ester
Strength of in-plane reinforced materials
0
100
200
300
400
Ten
sile
stre
ngth
(MPa
)
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, B0, B1 are phenomelogical parameters.
Unit cell model for the unidirectional short fiber compositesUnit cell model for the unidirectional short fiber composites
Fiber-avoiding mode
Fiber-breaking mode
Initial stiffness of the composite increases as lf increases.
When lf ≤ 0.1mm, the initiation of matrix cracking causes the critical failure.
When 0.1mm < lf < 0.5mm, the crack is trapped. But, the failure is caused by the fiber-avoiding.
When lf ≥ 0.5mm, the failure is determined by the fiber-breaking of the neighboring.
Stress Stress –– strain curvesstrain curves
(GLS model) Duva & Curtin (1995)
( )Φ−∞ −
Φ= eV ff 11σσ
+===Φ
ρ
σσ
000
1222 fTTTb L
dLLLNLd
Averaged stress carried by the fibers is equal to the composite stress (Duva et al.)
The length of discontinuous fibers is represented by the density of initial broken segments in the fiber.
2LT
L
In calculating the stress-transfer length LT, we used the solution of elastic-plastic hardening shear-lag model (Okabe and Takeda, 2000).
Theoretical model for the fiber length effect Theoretical model for the fiber length effect on the compositeon the composite’’s strengths strength
Composite strength versus averaged fiber stressComposite strength versus averaged fiber stress
Kelly & Tyson
Curtin
228 µm
403 µm
Kelly & Tyson length is shorter to get fiber failure mode (high strength).
Fiber failure
Fiber avoiding
Duva & Curtin has a good agreement with experiments
Fatigue damage in UD composites (0.1mm)Fatigue damage in UD composites (0.1mm)
Initial cycle
After 11 cycle
After 31 cycle