1. Sri Harsha Garapati 1 Analysis of Single Fiber Pushout Test of Fiber Reinforced Composite with a Nonhomogeneous Interphase By Sri Harsha Garapati MS Mechanical Engineering University of South Florida Major Professor: Autar Kaw, Ph. D. Committee: Glen Besterfield, Ph. D. Craig Lusk, Ph. D.

2. Sri Harsha Garapati 2 Objective  Modeling a finite element model of fiber reinforced composite with nonhomogeneous interphase  To analyze the effects of critical parameters on the results of single fiber pushout test  To perform a qualitative and quantitative study of these parameters on the results of single fiber pushout test.

3. Sri Harsha Garapati 3 Outline  Single Fiber Pushout Test  Literature Review  Formulation  Finite Element Modeling and Validation  Results and Conclusions

4. Sri Harsha Garapati 4 Single Fiber Pushout Test  The fiber in the specimen is pushed out by the indenter and the interfacial properties are extracted from the load- displacement curve.

5. Sri Harsha Garapati 5 Literature Review Analytical Models Shear Lag Models Boundary Element Method Finite Element Models

6. Sri Harsha Garapati 6 Interphase In polymeric matrix composites, the interphase is formed due to chemical reaction between the fiber and the matrix It is sometimes introduced voluntarily to improve the fracture toughness

7. Sri Harsha Garapati 7 Nonhomogeneous Interphase Interphase might have multiple regions of chemically distinct layers Functionally graded interphases are nonhomogeneous

8. Sri Harsha Garapati 8 Formulation  Geometry  Properties  Continuity Equations  Boundary Conditions

9. Sri Harsha Garapati 9 Geometry

10. Sri Harsha Garapati 10 Properties  Properties of fiber and matrix are taken from the literature  Interphase properties  Properties of the composite are found by using recursive concentric cylinder model developed by Sutcu (1992) Sutcu, M., 1992, "Recursive Concentric Cylinder Model for Composites Containing Coated Fibers," International Journal of Solids and Structures, 29(2) pp. 197.

11. Sri Harsha Garapati 11 Variation of Elastic Moduli in the Interphase Exponential Linear

12. Sri Harsha Garapati 12 Continuity Equations  Radial and axial displacements should be the same at all the interfaces  Radial and shear stresses should be the same at all the interfaces

13. Sri Harsha Garapati 13 Boundary Conditions BC-1BC-2

14. Sri Harsha Garapati 14 Factors for Sensitivity Analysis Type of Indenter (Spherical, Uniform, Flat) Fiber Volume Fraction Thickness of Interphase to Radius of Fiber Ratio (TIRFR) Type of Interphase (Linear, Exponential) Boundary Conditions (BC-1, BC-2)

15. Sri Harsha Garapati 15 Responses for Sensitivity Analysis Load to Contact Depth Ratio (LCDR) Normalized Maximum Interfacial Radial Stress (NMIRS) Normalized Maximum Interfacial Shear Stress (NMISS)

16. Sri Harsha Garapati 16 Loading Spherical indenter loading Uniform pressure indenter loading Flat indenter loading

17. Sri Harsha Garapati 17 Finite Element Modeling

18. Sri Harsha Garapati 18 Contact Elements at the Interfaces

19. Sri Harsha Garapati 19

20. Sri Harsha Garapati 20 Contact Radius Fischer-Cripps, A. C., 1999, "The Hertzian Contact Surface“, Journal of Materials Science, 34(1) pp. 129.

21. Sri Harsha Garapati 21 Verification of Bonded Contact  Interfacial radial and shear stresses on either side of all the interfaces are observed and they differ by less than 1%.  The displacements (both radial and axial) on either side of all the interfaces are found to be the with in 0.1%

22. Sri Harsha Garapati 22 Validation Spherical indenter Uniform indenter Flat indenter

23. Sri Harsha Garapati 23 Validation of the Interfacial Stresses Typical distribution of normalized interfacial radial stress Typical distribution of normalized interfacial shear stress

24. Sri Harsha Garapati 24 Convergence Test MESH DENSITY NMIRSNMISS A1.7108E-071.0312E-06 B1.6380E-071.0252E-06 C1.6378E-071.0241E-06 D1.6376E-071.0241E-06 E1.6376E-071.0241E-06

25. Sri Harsha Garapati 25 Comparison with Huang’s Shear- Lag Model

26. Sri Harsha Garapati 26 DESIGN OF EXPERIMENTS FactorSymbolLevel 1Level 2Level 3 Type of IndenterAUniform Pressure Indenter Spherical Indenter Flat Indenter Fiber Volume FractionB0.50.60.7 Thickness of Interphase to Fiber Radius Ratio C1/201/151/10 Type of InterphaseDLinearExponential_ Boundary ConditionsEBC-1BC-2_

27. Sri Harsha Garapati 27 Results ANSYS parametric design language (APDL) is developed to run all the combinations of the factors. After each run, responses for sensitivity analysis are written to a text file. Matlab Program is used to extract the LCDR,NMIRS and NMISS values from the text files and writes to a excel sheet.

28. Sri Harsha Garapati 28 LCDR LCDR can vary as mush as 20 to 50% depending up on the type of indenter SOURCEPERCENTAGE CONTRIBUTION Loading99.9 LCDR depends only on the type of indenter

29. Sri Harsha Garapati 29 NMIRS differ as much as by 70% with boundary conditions for higher fiber volume fraction and differ as much as by 95% for lower fiber volume fraction. NMIRS differ as much as by 150% with type of interphase for higher fiber volume fraction and differ as much as by 190% for lower fiber volume fraction. NMIRS differ as much as by 32% with type of interphase for higher fiber volume fraction and differ as much as by 93% for lower fiber volume fraction. NMIRS

30. Sri Harsha Garapati 30 SOURCEPERCENTAGE CONTRIBUTION Fiber volume fraction 27.1 Thickness of interphase 19.8 Type of interphase18.6 Boundary conditions17.0 NMIRS

31. Sri Harsha Garapati 31 NMISS differ as much as by 170% with type of interphase for higher fiber volume fraction and differ as much as by 60% for lower fiber volume fraction. NMISS

32. Sri Harsha Garapati 32 SOURCEPERCENTAGE CONTRIBUTION Fiber Volume Fraction57.3 Boundary Conditions30.0 NMISS

33. Sri Harsha Garapati 33 Comparison with Shear-Lag Models Shear-lag models approximate the distributed loading on the entire fiber, but this assumption underestimates the shear modulus of the interphase by the order as much as 1000.

34. Sri Harsha Garapati 34 Conclusions LCDR can differ by as much as 20 to 50% depending up on the type of distribution of load. NMIRS could vary up to 95% depending up on the assumed or applied boundary conditions. NMIRS could vary from 32 to 93% depending upon the thickness of interphase. NMISS could differ by 170% depending up on the boundary conditions

35. Sri Harsha Garapati 35 Conclusions The load-displacement curve is dependent only on type of load distribution. The critical interfacial radial stress is mainly dependent on the fiber volume fraction, type of interphase, thickness of interphase and the boundary conditions. The critical interfacial shear stress is mainly dependent on the fiber volume fraction and the boundary conditions.

36. Sri Harsha Garapati 36 Conclusions Approximating indentor loading as distributed uniformly throughout the fiber can underestimate the extracted property of the shear modulus of the interphase by an order of as much as a 1000.

37. Sri Harsha Garapati 37 Questions ?

38. Sri Harsha Garapati 38 Thank You