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Application of A Phenomenological Viscoplasticity Model to The Stress Relaxation Behavior of Unidirectional and Angle-ply Laminates at High Temperature. Y. Masuko and M. Kawai Institute of Engineering Mechanics and Systems, University of Tsukuba, Tsukuba 305-8573 , Japan. Outline.

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Application of A Phenomenological Viscoplasticity Model to The Stress Relaxation Behavior of Unidirectional and Angle-ply Laminates at High Temperature

Y. Masuko and M. Kawai

Institute of Engineering Mechanics and Systems,

University of Tsukuba, Tsukuba 305-8573 , Japan

outline
Outline

Background

Objectives

Experimental results

Predicted results

Summary

matrix dominated behavior of pmcs

PMC Laminates:

Shear loading

Off-axis loading

Polymer Matrix:

Matrix-Dominated Behavior of PMCs

・Creep

・Stress relaxation

Time dependent responses

objectives
Objectives

STRESS RELAXATION BEHAVIOR OF CFRP

Experimental Observation:

 Unidirectional Laminates

 Angle-Ply Laminates

Unidirectional laminate

Applicability of Viscoplasticity Model:

Angle-ply laminate

 Ply Model

 Laminate Model

material system

Unit: mm

20

50

100

50

1

1.70

Material System

T800H/Epoxy#3631(Cure temperature: 180˚C, Tg = 215˚C)

Specimens

Fiber Orientation:

Angle-ply specimens:

Off-axis specimens:

[]12 = 0˚, 10˚, 30˚, 45˚, 60˚, 90˚

[±]3s = [±30]3s,[±45]3s, [±60]3s

experimental procedure

e

b

c

R

a

5 h

Time

・Constant total strains for stress relaxation tests

xf

R  e1 e2 e3

xf

1< 2 = xf < 3)

e

e1

e2

e3

Experimental Procedure

Stress Relaxation Test (100˚C)

a-b : Loading

(1.0 mm/min; Stroke control )

Stroke control

b-c :Relaxation Period

(5 hours; Stroke control)

stress strain curves for cfrp

Unidirectional laminate

Angle-ply laminate

Displacement

1.0 mm/min

y

y

x

x

Time

Stress-Strain Curves for CFRP
off axis stress relaxation of ud cfrp

s

eR = Const

y

y

x

x

eR

e

Off-Axis Stress Relaxation of UD-CFRP





stress relaxation of angle ply cfrp

s

eR = Const

y

y

x

x

eR

e

Stress Relaxation of Angle-ply CFRP





modeling of time dependent behavior 1 3
Modeling of Time-Dependent Behavior (1/3)

ASSUMING Time-Dependent Elasticity:

modeling of time dependent behavior 1 31

Schapery model

Heredity integral form

Modeling of Time-Dependent Behavior (1/3)

ASSUMING Time-Dependent Elasticity:

Nonlinear viscoelasticity (VE) modeling

Favored in polymer research

modeling of time dependent behavior 2 3
Modeling of Time-Dependent Behavior (2/3)

ASSUMING Time-Dependent

Plasticity:

loading unloading behavior of ud cfrp
Loading-Unloading Behavior of UD-CFRP

s

y

y

x

x

e

12

12

modeling of time dependent behavior 2 31

Gates-Sun model

Nonlinear differential form

Modeling of Time-Dependent Behavior (2/3)

ASSUMING Time-Dependent Plasticity:

Nonlinear viscoplasticity (VP) modeling

Technically, more profitable

modeling of time dependent behavior 3 3
Modeling of Time-Dependent Behavior (3/3)

ASSUMING Time-Dependent

ElastoPlasticity:

Nonlinear VE + VP modeling

Ha-Springer model

Tuttle et al. model

A difficulty in distinguishing between VE and VP components

viscoplasticity modeling of time dependent behavior
Viscoplasticity Modeling of Time-Dependent Behavior

Unidirectional Lamina

Modified Gates-Sun model

Angle-ply Laminate

Modified Gates-Sun model

+

Classical Lamination Theory

(CLT)

sun chen model 1989

a66= 1.3

Effective

Stress

Effective

Plastic-strain

Effective stress -

effective plastic strain curves

Off-axis stress-plastic strain curves

Sun-Chen Model (1989)
modified gates sun model
Modified Gates-Sun Model

Effective Stress:

Effective Overstress:

Hardening Variable:

r

H

H

Effective stress -

effective internal strain curves

Effective Plastic Strain Rate:

Effective stress -

effective plastic strain curves

modified gates sun model1
Modified Gates-Sun Model

Off-Axis Loading

x

q

y

where

Off-axis Specimen

off axis creep curves for ud cfrp

y

y

x

x

Off-Axis Creep Curves for UD-CFRP

12

12

s

C = Const

C

e

identification of material constants 1
Identification of Material Constants—1

Q1=24 MPa

Q2=80 MPa

b1=750

b2=45

r0=17 MPa

r

r

r

Effective stress -

effective internal strain curves

Off-axis creep curve for q = 10˚

identification of material constants 2
Identification of Material Constants—2

Effective

plastic strain rate

Effective

overstress

K=79 MPa・minm

m=0.205

r

Effective stress -

effective plastic strain rate curves

r0

Effective stress -

effective internal strain curves

predicted off axis stress stain curves modified gates sun model
Predicted Off-Axis Stress-Stain Curves(Modified Gates-Sun Model)

1.0 mm/min

y

Displacement

q

x

Time

Material Constants

a66=1.3

Q1=24 MPa

Q2=80 MPa

b1=750

b2=45

r0=17 MPa

K=79 MPa・minm

m=0.205

Unidirectional laminate

predicted off axis stress relaxation curves
Predicted Off-Axis Stress Relaxation Curves

s

eR = Const

y

y

x

x

eR

e

12

12

elastic unloading due to local strain recovery

Stroke

Control

x

y

Strain Gauge

(2 mm)

Displacement

(100 mm)

Elastic Unloading due to Local Strain Recovery
predicted off axis stress relaxation curves with strain recovery
Predicted Off-Axis Stress Relaxation Curveswith Strain Recovery

s

eR = eR (tR)

y

y

x

x

eR

e

12

12

predicted stress strain curves for angle ply laminates
Predicted Stress-Strain Curves for Angle-Ply Laminates

Displacement

1.0 mm/min

y

y

x

x

Time

3S

3S

fiber rotation due to deformation of angle ply laminate
Fiber Rotation due to Deformation of Angle-Ply Laminate

(Sun, Herakovich, Wisnom)

x

y

b’

b

a’

a

q

q

predicted stress strain curves for angle ply laminates with fiber rotation
Predicted Stress-Strain Curves for Angle-Ply Laminateswith Fiber Rotation

Displacement

1.0 mm/min

y

y

x

x

Time

3S

3S

predicted stress relaxation of angle ply laminates
Predicted Stress Relaxation of Angle-Ply Laminates

s

eR = Const

y

y

x

x

eR

e

3S

3S

predicted stress relaxation of angle ply laminates with strain recovery
Predicted Stress Relaxation of Angle-Ply Laminates with Strain Recovery

s

eR = eR (tR)

y

y

x

x

eR

e

3S

3S

conclusions
Conclusions

Stress relaxation effects at high temperature in unidirectional and angle-ply CFRP laminates were examined.

Simulation was also performed using a ply viscoplasticity model and CLT.

The stress relaxation effects are clearly observed in all specimens of unidirectional and angle-ply laminates.

The stress relaxation rate rapidly decreases to vanish in a short period, regardless of the ply orientations and the sustained strain levels.

Predictions using the ply viscoplasticity model and CLT together with a consideration of the local strain recovery agree well with the experimental results.

Good predictions of the stress relaxation behavior confirm that the stress relaxation behavior is consistent with the creep behavior.