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

Simulated resultsSimulated results

[θlower, θupper] = [0.4π,0.6π]

* Mandell et al. (1982)

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

90°方向

Initial damage

N = 1000(cycles)

N = 20000(cycles)DEG 0

D

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

lf = 0.02 mm lf = 0.2 mm lf = 0.3 mm lf = 1.0 mm

Simulated resultsSimulated results

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

Effect of fiber length on fatigue lifeEffect of fiber length on fatigue life

Fatigue damage in UD composites (0.1mm)Fatigue damage in UD composites (0.1mm)

Initial cycle

After 11 cycle

After 31 cycle

Fatigue damage in UD composites (2.1mm)Fatigue damage in UD composites (2.1mm)

Initial cycle After 3204cycle 3205 cycle, Applied strain=0.564%