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Analytical and Experimental Characterization of Damping in Composite Materials and Structures Ronald F. Gibson Mechanical Engineering Department Advanced.

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Presentation on theme: "Analytical and Experimental Characterization of Damping in Composite Materials and Structures Ronald F. Gibson Mechanical Engineering Department Advanced."— Presentation transcript:

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. studentsMS Students Jimmy HwangRangarajan Thirumalai Joana FineganRajiv Pant Huimin GuanLan 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) S ij (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 S ij complex compliances S ij * (  ) For sinusoidal input strains: elastic moduli C ij complex moduli C ij * (  ) For constant input stresses: elastic compliances S ij creep compliances S ij (t) For constant input strains: elastic moduli C ij relaxation moduli C ij (t)

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

11 Strain energy/finite element method – based on Ungar-Kerwin equation (1962) for loss factor of a system of linear viscoelastic elements where η i = damping loss factor for the ith element in model W i = 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 Specimen Conditioning Amplifier Miniature accelerometer Nylon filament suspension Instrumented hammer Conditioning Amplifier Data acquisition board PC with LabView Impulse – frequency response test apparatus WSU sub-program Rigid support

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

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

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 3D quarter domain single cell finite element model of RVE

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

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

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

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 Modes 1 and 3 are symmetric about midspan Modes 2 and 4 are asymmetric about midspan disbond

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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)

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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 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)

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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 Thermoplastic fibers which form matrix after melting Reinforcing fibers

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 304 mm 264 mm Ribs 6.2 mm x 6.4 mm Skin 1.5 mm thick

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


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