1. Testing and Modeling Rate Dependent
Properties of Polymeric Composites Using Off-axis Specimens
C.T. Sun
School of Aeronautics and Astronautics
Purdue University
West Lafayette, Indiana
USA
CompTest2003
28-30 January 2003
Chalons en Champagne

2. Off-Axis Composite Under Uniaxial Load
a state of combined stress

3. Objectives Nonlinear constitutive model for UD composites
Rate dependent behavior
Compressive strength –static and dynamic

4. Nonlinear Behavior in Fiber Composites
Off-Axis Testing
Anisotropic
Nonlinear
Off-Axis Stress-Strain Curves
Unidirectional S2Glass/8553

5. Plastic Potential and Flow Rule
One-Parameter Plastic Potential
Transversely isotropic
No plastic strain in the fiber direction
Satisfies transverse isotropy

6. Off-Axis Test-Plane Stress
Power Law

7. Master Curve in Effective Stress and Effective Plastic Strain
a66 is determined by collapsing the
off-axis curves into a master curve

8. NONLINEAR RATE DEPENDENT
CONSTITUTIVE MODEL
Effective stress
Effective plastic strain rate
Viscoplasticity model

9. NONLINEAR RATE DEPENDENT CONSITUTIVE MODEL-Continued
e=10-4 /S .
Off-axis test results
a66 = 6

10. NONLINEAR RATE DEPENDENT CONSITUTIVE MODEL-Continued
A=4.0E-17
A=1.0E-16
A=2.8E-16
n=5.2

11. NONLINEAR RATE DEPENDENT CONSITUTIVE MODEL-Continued

12. COMPRESSION TEST Quasi-Static Dynamic
Compression tests were performed on 5° and 10° off-axis S2/8552
glass/epoxy composites at strain rates from 10-4/s to 1000/s.
Specimen
Hard steel q x Y
10 mm
6 mm
Applied displacement
Strain gage
Quasi-Static
Dynamic

13. SPLIT HOPKINSON BAR TEST
15 degree
AS4/3501-6
unlapped
and
unlubricated

14. SPLIT HOPKINSON BAR TEST- Continued
Lapped and lubricated
AS4/3501-6
15 degree
S2/8552

15. VERIFICATION OF CONSTITUTIVE MODEL

16. COMPRESSIVE FAILURE MODELS
Rosen (1965):
Idealize the composite as a series of perfectly aligned beam
embedded in elastic matrix.
Two modes of failure: extension and shear.
Shear mode 12
Shear mode
Extension mode

17. Compressive Failure Kink Band

18. COMPRESSIVE FAILURE MODELS
Argon(1972)
a kinking failure mechanism due to fiber misalignment and
composite shear yielding. sx sx

19. COMPRESSIVE FAILURE MODELS
Budiansky (1983)
Budiansky and Fleck (1993)

20. COMPRESSIVE FAILURE MODELS
Sun and Jun (1994)
Fiber microbuckling in nonlinear matrix including fiber misalignment effect sf sm tm s

21. Need a nonlinear rate dependent constitutive model
Microbuckling Model P P
Viscoplastic
Elastic
Need a nonlinear rate dependent constitutive model

22. DYNAMIC MICROBUCKLING MODEL

23. G12 TANGENT SHEAR MODULUS û ë ú ù ê é = G For off-axis composites ep -

24. SIMPLIFIED MODEL For small value of q, sinq 0 ~ ~
Further simplification

25. EFFECT OF SHEAR STRESS EXAS HIS/DX6002 Carbon/epoxy composites*, v
=65% f
400
800
1200
1600
2000
-100
-50 50
100
Applied shear stress t
(Mpa)
Compressive strength s c
Test (Jelf and Fleck)
Model prediction
Fiber misalignment = 2 o

26. EXPERIMENTAL RESULTS AND MODEL PREDICTION- MICROBUCKLING

28. Conclusions The use of off-axis composite specimens to
establish rate dependent nonlinear constitutive
models is convenient.
The microbuckling model together with the rate dependent nonlinear constitutive model can predict the static and dynamic compressive failure of UD composites.