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

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

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

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

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

Off-Axis Test-Plane Stress Power Law

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

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

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

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

NONLINEAR RATE DEPENDENT CONSITUTIVE MODEL-Continued

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

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

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

VERIFICATION OF CONSTITUTIVE MODEL

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

Compressive Failure Kink Band

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

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

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

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

DYNAMIC MICROBUCKLING MODEL

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

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

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

EXPERIMENTAL RESULTS AND MODEL PREDICTION- MICROBUCKLING

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.