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

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

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

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 ) ) )

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

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.

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

THERMAL RESIDUAL SHEAR STRESS DISTRIBUTION ALONG INTERFACE AFTER COOLING

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

Simulation restults from Lin’s model 1 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)

The evolution of cohesive traction and energy Case 1: ,

Case 2: ,

Case 3: ,

Case 4: ,

Effect of work of shear separation on force-displacement curve

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

Effect of shear strength on force-displacement curve