1. Analytical and Experimental Characterization of Damping in Composite Materials and Structures
Ronald F. Gibson
Mechanical Engineering Department
Advanced Composites Research Laboratory
Wayne State University
Detroit, MI 48202

2. Objective
Review recent research on analytical and experimental characterization of damping in composite materials and structures at Wayne State University

3. Contributors Ph.D. students MS Students
Jimmy Hwang Rangarajan Thirumalai
Joana Finegan Rajiv Pant
Huimin Guan Lan Gu
Yu Chen
Zhengyu Liu
Hui Zhao
Shuo Yang
Wei-Hung Chen

4. Sponsors U. S. Office of Naval Research Ford Motor Company
Boeing Company
National Center for Manufacturing Sciences
WSU Institute for Manufacturing Research
American Society for Nondestructive Testing

5. Micromechanics Macromechanics Fibers + Matrix Lamina Laminate
Structure

6. Approaches to analytical modeling of damping in linear viscoelastic composites
Closed form elastic solutions modified by using Elastic-Viscoelastic Correspondence Principle
Finite element implementation of Ungar-Kerwin equation (Modal Strain Energy Method)

7. Elastic-viscoelastic correspondence
Boltzmann superposition integral for linear viscoelastic materials
where
i,j = 1,2,…..6 (contracted notation)
Sij(t) = creep compliances

8. Linear viscoelastic material – special cases of Boltzmann superposition integral
1. Sinusoidally varying stresses
2. Constant stresses
Note correspondence with linear elastic Hooke’s Law

9. Elastic-viscoelastic correspondence principle applied to material properties
For sinusoidal input stresses:
elastic compliances Sij complex compliances Sij*()
For sinusoidal input strains:
elastic moduli Cij complex moduli Cij*()
For constant input stresses:
elastic compliances Sij creep compliances Sij(t)
For constant input strains:
elastic moduli Cij relaxation moduli Cij(t)

10. Example of Correspondence Principle applied to micromechanics: Rule of Mixtures for complex longitudinal modulus of unidirectional composite
where
= Complex Young’s modulus of fiber, matrix or interphase, respectively
= frequency
Vf, Vm, Vi = Volume fraction of fiber, matrix or interphase, respectively

11. Strain energy/finite element method – based on Ungar-Kerwin equation (1962) for loss factor of a system of linear viscoelastic elements
where ηi = damping loss factor for the ith element in model
Wi = strain energy stored in the ith element at maximum
vibratory displacement
n = number of elements in model

12. Experimental characterization using impulse-frequency response method

13. Impulse – frequency response test apparatus
Nylon filament suspension
Rigid support
Instrumented hammer
Miniature
accelerometer
Specimen
Conditioning Amplifier
Conditioning
Amplifier
Data acquisition board
PC with LabView
WSU sub-program
Impulse – frequency response test apparatus

14. Modal frequencies
Modal frequencies and loss factors found by curve-fitting to frequency response curve at peak frequencies

15. Single Degree of Freedom Curve Fit to Peak in Frequency Response Curve by Half Power Bandwidth Method
Peak for
nth mode
Amplitude X
0.707 X
Frequency ••
Damping Loss Factor
= natural frequency of nth mode
= bandwidth at half power points

16. Applications to micromechanical studies of damping in composites
Composites with coated fibers/interphases
High temperature composites
Woven fabric-reinforced composites

17. Representative volume element for a square array of circular fibers with coating/interphase

18. RVEs subjected to four different loading and boundary conditions

19. 2D quarter domain single cell finite element model of RVE

20. 2D multicell finite element model 3D multicell finite element model

21. Effect of interphase size on predicted complex moduli of unidirectional graphite/epoxy composite (Hwang and Gibson, 1992)
Moduli vs. interphase size predicted from FEA model
Loss factors vs. interphase size predicted from FEA model

22. Transverse normal loss factor vs. interphase size predicted from
Effect of interphase size on predicted contributions of constituents to total damping loss factor of graphite/epoxy (Hwang and Gibson, 1992)
Transverse normal loss factor vs. interphase size predicted from
FEA model
In-plane shear loss factor vs. interphase size predicted from FEA model

23. Predicted and measured longitudinal storage modulus
and loss factor of PVC-coated copper wires in epoxy matrix
(Finegan and Gibson, 2000)

24. Apparatus for measuring dynamic mechanical properties of
composite and matrix materials at elevated
temperatures (Gibson, Thirumalai and Pant, 1991)

25. Apparatus for measuring dynamic mechanical
properties of fibers at elevated temperatures
(Gibson, Thirumalai and Pant, 1991)

26. Measured and predicted transverse storage modulus and loss factor of SiC/Ti composite at elevated temperatures (Pant and Gibson, 1996)

27. Microstructure of silicon nitride (Woetting and Zielger, 1986)

28. Measured storage modulus and loss factor of silicon carbide
whisker-reinforced silicon nitride at elevated temperatures
(Yang, Gibson, Crosbie and Allor, 1997)

29. Strain energy/finite element modeling of damping
in woven fabric-reinforced polymer matrix composites
(Guan and Gibson, 2001)
3-D finite element
model of woven fabric

30. Predicted and measured extensional loss factors for
woven E-glass/vinylester resin transfer molded composite
(Guan and Gibson, 2001)

31. Applications to studies of damping in composite structures
NDE of adhesively bonded composite structures by using damping measurements
Polymeric interleaves for improved damping and fracture toughness in composite laminates
Composite grid structures with integral passive damping

32. First four free-free flexural modes of adhesively bonded
composite beam with middle surface disbond at midspan
disbond
Modes 1 and 3
are symmetric
about midspan
Modes 2 and 4
are asymmetric
about midspan

34. Zoom on disbond at midspan for Mode 1 (no slip at disbond interfaces)

35. Zoom on disbond at midspan for Mode 4
slip at disbond interface
no slip in bonded regions

36. Damping and natural frequencies for E-glass/vinylester
composite beam with 10% disbond in epoxy adhesive layer at
middle surface (Yang, Gibson, Gu and Chen, 1998)
Note high damping for disbonded
beam in Modes 2 and 4

37. Adhesively bonded SMC hood closure panel
Disbond between frame and
skin along leading edge

38. Apparatus for impulse-frequency response
Testing of composite hood closure panels
(Gibson and Liu, 1998)

39. Comparison of first 8 modal frequencies of bonded and
disbonded hood closure panels (Gibson and Liu, 1998)

40. Comparison of first 8 modal loss factors of bonded and
disbonded hood closure panels (Gibson and Liu, 1998)

43. Conclusions: For lower modes, frequency shifts seem to be more
reliable indicators of damage than shifts in damping, but for higher modes,
shifts in both frequency and damping are good indicators of damage

44. Improvement of damping capacity and fracture toughness in composite laminates by using polymeric interleaves (Gibson, Chen and Zhao, 2001)

45. End notched flexure (ENF) test for Mode II
energy release rate of composite laminate with interleaf

46. Measurement of damping in ENF specimen

47. Mode II fracture toughness vs. interleaf thickness
for ENF specimens (Gibson, Chen and Zhao, 2001)

48. Model for interlaminar crack tip deformation
zone constraint (Hunston, 1994)

49. Loss factor vs. interleaf thickness for
ENF specimens (Gibson, Chen and Zhao, 2001)

50. Composite grid structures with integral passive damping (Chen and Gibson, 2003)

51. MLS Primary Reflector Use of composite grids in spacecraft reflector
(Courtesy of Composite Optics Inc.)

52. CMIS Reflector Use of composite grids in spacecraft reflector
(Courtesy of Composite Optics Inc.)

53. Co-Cured Rib/Skin Structure
Advanced composite grid structure used in missile shroud (Wegner and Higgins, 2002)
Co-Cured Rib/Skin Structure

54. Large (3 m x 3 m) interlocked composite grid structure fabricated from pultruded carbon/epoxy ribs and rib caps (Tsai, 2001)

57. Motivation
Grid-stiffened composite structures are used in several applications where energy absorption under quasi-static and impact loading and damping of vibrations is important
Previous research has considered mechanical behavior under static loading, but not energy absorption and damping under dynamic loading

58. Manufacturing of Specimens
Laboratory sized isogrid panels (305 mm x 264 mm) made from co-mingled E-glass/polypropylene (Twintex® by Vetrotex) and co-mingled carbon/nylon (Cylon® by Cytec Fiberite)
Used a grooved mold thermoplastic stamping process (Goldsworthy and Hiel, 1999)
Co-mingled unidirectional roving used for ribs
Co-mingled woven fabric used for skins
3M ISD 112 acrylic damping layer for damping studies

59. Co-mingled fiber/thermoplastic matrix yarn
Reinforcing fibers
Thermoplastic fibers which
form matrix after melting

60. E-glass/polypropylene Twintex® composite isogrid panel and steel mold

61. Twintex® E-glass/polypropylene composite isogrid without skin

62. Analytical Modeling Approaches
“Exact” finite element models in which ribs and skin are individually modeled – most likely approach to modeling progressive failure, multiple failure modes and rib/skin interface damping
“Equivalent”, or smeared stiffener models in which the stiffnesses of ribs and skin are smeared, or averaged, to give equivalent stiffnesses – more useful for linear elastic analysis

63. Finite Element Model Construction
3-D ABAQUS finite element model with 20 noded solid elements (C3D20) for ribs and skins
Convergence study to establish model size based on first three modal frequencies
Benchmarked against modal frequency test data for single rib aluminum panel

64. 3-D finite element model of isogrid panel
Integral polymeric damping layers at rib/skin interface, 0.25 mm thick
Ribs 6.2 mm x 6.4 mm
Skin 1.5 mm thick
304 mm
264 mm
3-D finite element model of isogrid panel

65. Predicted and measured free-free vibration modal frequencies for the first four modes of a Twintex® glass/PP isogrid panel (maximum scatter for all the measured frequencies is less than 0.5%).

66. Mode shape for composite isogrid panel, Mode 1, 146 Hz
(Note bending-twisting coupling effects)

67. Predicted and measured loss factors for first four free-free vibration modes of a Twintex® glass/PP isogrid panel without integral damping layer

68. Predicted and measured loss factors for first four free-free vibration modes of a Twintex® glass/PP isogrid panel with integral and bonded damping layers.

69. Strain energy density in damping layer along the rib/skin interface for composite isogrid panel in Mode 1 vibration

70. Predicted and measured loss factors for different percentages of damping materials coverage between the ribs and skin for first free- free vibration mode of a Twintex® glass/PP isogrid panel with integral or bonded damping layers of 3M ISD 112 damping material.

71. Conclusions
Damping in undamaged composite materials and structures vibrating at low amplitudes can be predicted with reasonable accuracy using linear viscoelastic models
Improvement and optimization of damping in composites has been demonstrated experimentally and analytically at both the micromechanical and macromechanical levels
Measurements of damping in composite materials and structures are useful not only for validating analytical models but for non-destructive evaluation as well