1. APPLICATION OF COHESIVE ELEMENT TO BIMATERIAL INTERFACE
N. Chandra H. Li C. Shet
Department of Mechanical Engineering
FAMU/FSU College of Engineering
Florida State University
Tallahassee, FL 32210

2. STUDIED IN THIS WORK THE TWO COHESIVE MODELS
Xu and Needleman’s model[1]
Lin’s model[2]
Interface parameters
Work of normal separation,
Work of tangential separation,
Normal displacement jump,
Tangential displacement jump,
Interface characteristic-length, and
Xu and Needleman’s model
Interface potential and traction
where

3. Figure 1. (a) Normal Traction, , across the interface as a function of with .
(b) Variation of shear traction, , with for
(a)
(b)

4. Critical tangential separation, Critical normal separation,
Lin’s bilinear model
Interface parameters
Critical tangential separation,
Critical normal separation,
Interface characteristic-length parameters,
Interface normal and tangential strength, and
Traction-separation law
For ) ) )

5. Figure 2. Normal traction as a function of the normal separation
for (b) Shear traction vs. shear separation for

6. SIMULATION PROCESS FOR PUSH-OUT TEST
To simulate the single fiber push-out test, the elastic constitutive behavior is assumed for the fiber, and the matrix is assumed to be a rate independent elastic-plastic material. The temperature dependency of the elastic and in elastic properties of the constituent phases is included in a piece-wise linear manner. The analysis is done in the following three steps:
In this step, the cooling process after the composite consolidation at high temperature is modeled.
When a thin slice is cut out of the bulk composite plate, the residual stresses tend to relax. This is simulated by removing the existing tying constraints and boundary conditions from the top and bottom and allowing the stresses in the specimen to relax and reach equilibrium, symmetrical about a plane passing through the center of the specimen thickness.
Axial displacement is applied to the punch till the fiber slides out of the matrix after the entire length of the fiber gets debonded.

7. THE ABAQUS MODEL FOR PUSH-OUT TEST SIMULATION
Matrix
Interface
Fiber
0.63mm
Information of the model
No. of element: 4800
element type: Axisymmetric 4-node coupled temperature-displacement element
No. of cohesive element: 240
Contact pair was used at interface
using large deformation

8. THERMAL RESIDUAL SHEAR STRESS DISTRIBUTION
ALONG INTERFACE AFTER COOLING

9. CALCULATIONAL RESULTS FROM THE TWO MODELS
Comparison of Load-displacement plots from exponential and bilinear models
Displacement( m)
Displacement( m)

10. Simulation restults from Lin’s model1
0.1
0.4
Effect of on force-displacement curve
0.7
1.0 1 3 3 2 4 4 2 5 1
Displacement( m)
Displacement( m)

11. The evolution of cohesive traction and energy
Case 1: ,

12. Case 2: ,

13. Case 3: ,

14. Case 4: ,

15. Effect of work of shear separation on force-displacement curve

16. THE SIMULATED PROCESS OF PUSH-OUT TEST
After cooling
Beginning of loading
Debonding occur
Complete debonding

17. Effect of shear strength on force-displacement curve