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Fatigue

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									MDA/CERF: Durability Study
Fatigue Task Group

                    John J. Lesko
                Kenneth L. Reifsnider
                  Stephan P. Phifer
                   Charles E. Bakis
                   Anthony Nanni
                      Clem Heil
ASME 2000 International Mechanical Engineering Congress &
               Exposition, November 2000
Fatigue Issue Not Covered
in This Talk


           ?
Fatigue Failure Mechanisms
   Fatigue-Life Diagram proposed by Talreja
Fatigue - Overview
 Material & Processing Effects
  • Failure Mechanisms     • Interface - Sizing
  • Fiber                  • Laminate
  • Matrix                 • Processing
  • Residual Cure Stress
 Environmental & Testing Effects
  • Frequency/Creep        • Temperature
  • Hygrothermal           • Acid/Base/Electrolyte
 Interactive Effects
Material Effects
• Fatigue Failure Mechanisms
• Fiber
   • E-glass, carbon/graphite, Kevlar
• Matrix
   • Brittle, toughened
• Interface
   • Compatible and non-compatible sizings
• Laminate
   • Woven, stitched, and unidirectional
   • Stacking sequence - 0°, ±45 °, 90° plies
• Processing Type
FIBERS - (0/90°)s
                    •   Gathercole,
                        Reiter,Adam,
                        Harris 1994,
                        IJ of Fatigue,
                        v. 16, no. 8,
                        p.523.
    FIBERS - Tensile Stress
    Fatigue E-Glass




•   Demers, Cornelia. E. 1997 The National Seminar on Advanced Composite Material
    Bridges, May 5-7.
   Normalized Fatigue Performance
        of Glass/Vinyl Ester
                                 100
                                  90
                                                                                                        Dry
   % Ultimate Tensile Strength




                                  80
                                                                                                        Salt
                                  70
                                                                                                        Wet
                                  60
                                  50
                                  40
                                        11% UTS                                                   run out
                                  30
                                  20
                                  10                    1 decade
                                   0
                                  1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08
                                                              # cycles
F. McBagonluri, K. Garcia, M. Hayes, N. Verghese, & J. J. Lesko, "Characterization of Fatigue and Combined Environment on
Durability Performance of Glass/Vinyl Ester Composite for Infrastructure Applications" International Journal of Fatigue, Vol. 22,
Issue 1, 2000, pp. 53-64.
                   Glass Composite Fatigue
                                                                         1. Unidirectional glass/epoxy,
                                                                              vf=0.5
                                                                         2. Unidirectional glass/epoxy,
                 1800                                                         vf=0.33
                            Mandell's                                    3. Unidirectional glass/epoxy,
                 1600                                                         vf=0.16
                            As-received Extren                           4. 0°/90° glass
                 1400
Strength (MPa)




                                                                         5. 30-40% glass in
                 1200       Aged Extren (Water)                               poly(hexamethylene
                                                                              adipamide), injection molded
                 1000       Aged Extren (Salt)                           6. 30-40% glass in polycarbonate
                                                                              injection molded
                  800                                                    7. 30-40% glass in
                                                                              polyphenylenesulfide
                  600                                                         injection molded
                  400                             UTS/B =10.7            8. 30-40% glass in poly(amide-
                                                                              imide) injection molded
                  200                                                    9. Chopped-strand mat polyester
                                                                         10. Sheet molding compound
                    0                                                         (smc) of rubber-modified
                                                                              epoxy
                        0              50          100             150   11. SMC, rubber-modified epoxy
                                                                         12. SMC, r50
                                   Slope S-N (MPa/Decade)                13. 0°/±45 ° /90° glass/epoxy
                                                                         14. Chopped-strand mat polyester
          Mandell, J. F., 1978, “Fatigue Behavior of Fibre-Resin
          Composites,” Developments in Reinforced Plastics 2,
          Properties of Laminates, Ed. G. Pritchard.
      Mechanism: Fatigue of
        Glass Composites
• Crack growth in the fiber dominates the
    failure process
•   Accumulation of damage is accounted for in
    crack growth that takes place based on the
    fractional time spent at a damaging stress
    level
             da
                  AK IN      KI  Y a
             dt
                                                          1

                         r    
                               
                                     t
                                        ( t )  
                                                 N
                                                     
                                                         N 2
Glass fiber remaining
strength given a  (t)
                              1  C          dt 
                         ult           
                                     0  ult        
                                                    
Fatigue Simulation & Experiment
                     1.2

                      1                                                                                      UCFR - unidirectional
                                                                                                             continuous fiber/epoxy
Applied Stress/UTS




                     0.8
                                                                                                             UCMFR - unidirectional
                                                                                                             & continuous strand mat
                     0.6                                                                                     fiber/vinyl ester

                     0.4           UCFR
                                   10 Hz (Model)                                                             S-N Slope (%UTS/decade)
                                   5 Hz (Model)                                                              Data: 10.2 and 13
                     0.2           2 Hz (Model)                                                              Predictions: 12 to 14
                                   UCMFR
                      0
                      1.E+00         1.E+02               1.E+04               1.E+06               1.E+08
                                                         # cycles
             F. McBagonluri, G. Foster, S. Case, W. Curtin, & J. Lesko, “ Simulation Of Fatigue Performance Of Polymeric Composites
             For Infrastructure Applications,” Simulation of Fatigue Performance of Polymeric Composites for Infrastructure Applications
             ASME IMECE 98, Anaheim CA, Nov 1998
Matrix & Sizing
   Effects
Matrix Effects -
S-N Curves for E-glass Laminates

                             •   Konur & Matthews
                                 1989, Composites,
                                 V.20, No. 4, July
                                 1989.
Sizing & Matrix
Toughening Effects

              max  A  B  log N10
             A   o  logN10  o  B

                        •   Salvia, Fiore, Fournier &
                            Vincent I.J. of Fatigue,
                            1997,V.19 No.3, p. 253.
Sizing Effects
                  • EP - Epoxy
                    Sizing
                  • MP - Multi-
                    pupose sizing
                  • Epoxy Resin

                  max  A  B  logN10

                  •   Salvia, Fiore, Fournier &
                      Vincent I.J. of Fatigue,
                      1997,V.19 No.3, p. 253.
Pultruded AS-4/Derakane
411-35 LI: Sizing Effect




        Input: R=0.1 Unidirectional Fatigue Data
Processing
  Effects
Process Type Effects

                  • FW - Filament
                      Winding
                  •   PMC - Prepreg
                      Press Molding
                  •   P - Pultrusion

                  A   o  logN10 o  B


                  •   Salvia, Fiore, Fournier &
                      Vincent I.J. of Fatigue,
                      1997,V.19 No.3, p. 253.
    Process & Laminate
    Effects - Pultruded CP, Prepreg CP & Woven
                                    1
     Normalized Laminate Tensile




                                                           Pultrude (0/90°)5T Vinyl Ester

                                                           Pultrude (0/90°)3S Vinyl Ester
                                   0.8
                                                           Mandell (0/90°)S Epoxy
           Fatigue Stress




                                                           Adams (0/90°)S Epoxy
                                   0.6                     Mandell Epoxy 181 Woven


                                   0.4                                                        Laminated

                                   0.2                                                        Stitched
                                                                                              or Woven
                                    0
                                    1.E+03   1.E+04    1.E+05    1.E+06              1.E+07
                                                 Fatigue Cycles (N)
•   Phifer 1998, Thesis Virginia Tech. http://scholar.lib.vt.edu/theses/available/etd-
    013199-185939
Testing & Environmental
Effects

•Testing
 •Mean Stress & R - Ratio
 •Frequency
•Environmental
 •Hygrothermal
 •Temperature
 •pH Effects
Frequency &
Mean Stress
   Effects
Static vs. Dynamic
Fatigue
                • Mandell &
                 Meier 1983
                 ASTM STP
                 813 p.60
    Test Effects: R - ratio




•   Gathercole, Reiter, Adam, Harris 1994, IJ of Fatigue, v. 16, no. 8, p.523.
Test Effects: R - ratio
                  •   Adams, Fernando,
                      Dickson, Reiter &
                      Harris. 1989, IJ of
                      Fatigue, V. 11, no. 4,
                      p.233.
Environmental
   Effects
                          Enviro-mechanical Fatigue
                             of Glass/Vinyl Ester
                          25000
                                                               Sult dry= 30.7 ksi
                                                          Sult wet (water) = 22.9 ksi                     Dry
                          20000                           Sult, wet (NaCl) = 20.9 ksi
    Stress Levels (psi)




                                                                                                          Wet

                          15000                                                                           Salt


                          10000                                                                run outs


                           5000
                                      R = 0.1
                                      freq = 10 Hz
                             0
                             1.E+02    1.E+03        1.E+04      1.E+05           1.E+06           1.E+07           1.E+08
                                                               # cycles
F. McBagonluri, K. Garcia, M. Hayes, N. Verghese, & J. J. Lesko, "Characterization of Fatigue and Combined Environment on
Durability Performance of Glass/Vinyl Ester Composite for Infrastructure Applications" International Journal of Fatigue, Vol. 22,
Issue 1, 2000, pp. 53-64.
    Temperature Effects -
    S-N Curves




•   Branco, Ferreira, Fael & Richardson 1995 Int. J. Fatigue, V. 18, No. 4, p. 255
                              Effect of Temperature Effect on
                              E-Glass FRP Fatigue
                              100
                                                                                                                    20000
                               90          Sult = 20.9 ksi                 Pultruded E-Glass/Vinyl Ester
% Ultimate Tensile Strength




                               80

                               70                                                                                   15000




                                                                                                                            Max stress (psi)
                               60
                                                                                                       4 °C
                               50
                                                                                                                    10000

                               40

                               30                                                            30 °C
                                                                                                                    5000
                               20                                                  65 °C
                                          R = 0.1
                               10         freq = 10 Hz
                                0                                                                                   0
                                    100            1,000     10,000              100,000   1,000,000          10,000,000

                                                                      # cycles
So Where Are the Gaps?

• Combined Conditions
  • Creep & Fatigue
  • Temperature & Fatigue
  • Temp, Moisture & Fatigue
  • Chemistry & Fatigue
  • Spectrum loadings (stress and environment)
• Tools
  • Generalization of Glass Fatigue
  • Remaining strength representations for
    combined loading
     Estimating Remaining Strength
              Degradation Processes
                   •Cycle dependent Geometry
                   damage           Constitutive                               Remaining Strength
Initial Strength




                                                          Stress or Strength
                   •Kinetic

                   •Chemical

                   •Thermodynamic
                                                                                Life       N
                                                     Stress on Critical Element
       Reifsnider & Stinchcomb, “A Critical Element Model of the Residual Strength and Life of
       Fatigue-loaded Composite Coupons,” ASTM STP 907, 1986
AMERICAN SOCIETY FOR
COMPOSITES

16th Annual Technical Conference
CALL FOR PAPERS
September 9-12, 2001
Virginia Tech, Blacksburg, VA
Donaldson Brown Hotel & Conference Center

Abstracts should be submitted no later than January 31, 2001.
M.W. Hyer by e-mail as a pdf file to asc16@vt.edu


                http://www.esm.vt.edu/ASC/
QUESTIONS
Ranking of Importance of
Data for Fatigue Effects
         Application Area      Sustained   Pure Fatigue    Fatigue       Fatigue &    Fatigue &
                                Stress       Loading      And Temp.      Moisture /     Creep
                               Loading                                      Salt
                              A B C        A    B    C    A   B     C   A B C         A   B   C
        Internal Reinforcement
        Rebar                  4   4   2   4    4    2    5   5     1   5   5    1    5   5   1
        External Reinforcement
        Beams                  3   3   1   4    4    3    5   5     1   5   5    1    5   5   1
        Slabs                  3   3   1   4    4    3    5   5     1   5   5    1    5   5   1
        Columns                4   4   1   4    4    1    5   5     1   5   5    1    5   5   1
        Seismic Retrofit
        Columns, piers         3   5   3   4    4    3    3   5     1   3   5    1    3   5   1
        Shear Walls            3   5   3   3    4    2    3   5     1   3   5    1    3   5   1
        Deck Systems
        Conventional           4   4   1   5    5    1    5   5     1   5   5    1    5   5   1
        beams/girders
        Integral/composite     4   5   1   4    5    1    5   5     1   5   5    1    5   5   1
        beams/girders
        Structural Elements
        Wall panels, profiles 3    5   2   5    5    2    5   5     1   5   5    1    5   5   1

Key: A composite                                    Rank          5: Critical, cannot go forward without it
     B composite/substrate interface;                             3: Important
       adhesive (if any)                                          1: Good to have
     C substrate
Ranking of Availability of
Data for Fatigue Effects
         Application Area      Sustained    Pure Fatigue      Fatigue    Fatigue &    Fatigue &
                                Stress      Loading (2)        And       Moisture /   Creep (5)
                              Loading (1)                    Temp.(3)     Salt (4)
                              A B C         A    B    C     A B C       A B C         A   B   C
        Internal Reinforcement
        Rebar                  2   4   2    3    4    2     5   5   1   3   5    1    5   5   1
        External Reinforcement
        Beams                  2   4   2    2    5    3     5   5   1   5   5    1    5   5   1
        Slabs                  2   4   2    1    5    3     5   5   1   5   5    1    5   5   1
        Columns                3   5   3    3    5    3     5   5   1   5   5    1    5   5   1
        Seismic Retrofit
        Columns, piers         3   4   2    3    4    1     5   5   1   5   5    1    5   5   1
        Shear Walls            3   4   2    2    4    2     5   5   1   5   5    1    5   5   1
        Deck Systems
        Conventional           2   5        2    4          5   5   1   5   5    1    5   5   1
        beams/girders
        Integral/composite     2   4        2    4          5   5   1   5   5    1    5   5   1
        beams/girders
        Structural Elements
        Wall panels, profiles 2    4   3    3    4    3     5   5   1   5   5    1    5   5   1

Key: A composite                                     Rank       1: Widely available and validated
     B composite/substrate interface;                           3: Sparse and/or questionable
       adhesive (if any)                                        5: Not available
     C substrate
Overall Ranking of Gaps
for Fatigue Effects
         Application Area      Sustained   Pure Fatigue     Fatigue       Fatigue &     Fatigue &
                                 Stress      Loading       And Temp.      Moisture /      Creep
                                Loading                                      Salt
                              A B C        A    B    C     A    B    C   A B C         A    B    C
        Internal Reinforcement
        Rebar                  6   8   4   7    8    4     10   10   2   8    10   2   10   10   2
        External Reinforcement
        Beams                  5   7   3   6    9    6     10   10   2   10   10   2   10   10   2
        Slabs                  5   7   3   5    9    6     10   10   2   10   10   2   10   10   2
        Columns                7   9   4   7    9    4     10   10   2   10   10   2   10   10   2
        Seismic Retrofit
        Columns, piers         6   9   5   7    8    4     8    10   2   8    10   2   8    10   2
        Shear Walls            6   9   5   5    8    4     8    10   2   8    10   2   8    10   2
        Deck Systems
        Conventional           6   9       9    9          10   10   2   10   10   2   10   10   2
        beams/girders
        Integral/composite     6   9       6    9          10   10   2   10   10   2   10   10   2
        beams/girders
        Structural Elements
        Wall panels, profiles 5    9   5   8    9    5     10   10   2   10   10   2   10   10   2


Key: A composite                                    Rank        2: Widely available and validated
     B composite/substrate interface;                           6: Sparse and/or questionable
       adhesive (if any)                                        10: Not available
     C substrate
MRLife Methodology
                                                                                       1
      “n”                           0° Critical            90° Subcritical                      Off-Axis
    Fatigue                                                                                     Stiffness
    Cycles                                                                                      Reduction
                                                                                                                     n/N

                                       Damage Accumulation                                      Increase in
                                                                                                0° n) CLT
              Xt 0 ° ( n )
                                             Quasi-static
   Fr 0 °                               Strength & Stiffness
              Xt 0 ° ( qs )
                                                                                                          (n )
                                                                                      Fa   0°           0°
                                                                                                    X T 0 ° ( qs )

                                                n
                  Fr0 ° ( n )  Fr0 ° ( 0 )  N
                                                    1  Fa 0° ( n )   J  ( n ) J 1  d ( n )
                                              0                               N                 N
  1                                                                               1
                       Fr 0°                                                                        S-N
                                                                               Fa0°

            n1     Fa0°
                               n2                                                       N2               N1
Fiber Effects                                                 Mandell, J. F. 1982
Normalized Tensile Fatigue



                              1

                             0.8
         Stress




                             0.6
                                       High Mod. Graphite
                             0.4
                                       Low Mod. Graphite
                                       Kevlar
                             0.2
                                       Uni- E-Glass
                                       181 Woven E-Glass
                              0
                              1.E-01     1.E+01      1.E+03    1.E+05    1.E+07

                                                  Fatigue Cycles (N)
Material Effects - Kevlar
Fibers - (0/90°)

                 KFRP   • Jones, Dickson,
                          Adam, Reiter,
                          Harris 1983,
                          Composites, V.
                          14, No.3, July
Material Effects - E-Glass
Fibers - (0/90°)
                       • Jones, Dickson,
                 GRP     Adam, Reiter,
                         Harris 1983,
                         Composites, V.
                         14, No.3, July
Material Effects - Carbon
Fibers - (0/90°)
                         • Gathercole,
                           Reiter,Adam,
                  CFRP     Harris 1994,
                           IJ of Fatigue,
                           v. 16, no. 8,
                           p.523.
    Tensile Fatigue Damage
    Mechanism




•   Kim & Ebert
    1978, J. of
    Composite
    Matl., V. 12,
    April .
Manufacturing Effects

• S-N curves are dependent upon
  manufacturing process( P-pultrusion, FW-
  Filament Winding, PMC-Press Molding of
  Prepreg)
• Variations in resin and fiber sizing. Curve
  fit to  max  A  B  logN10
o & log(N10)o process related
  

          A   o  logN10 o  B
Sizing & Matrix
Toughening Effects

              max  A  B  log N10
             A   o  logN10  o  B

                        • Salvia, Fiore,
                          Fournier &
                          Vincent I.J. of
                          Fatigue,
                          1997,V.19 No.3,
                          p. 253.
Sizing Effects
                  • EP - Epoxy
                    Sizing
                  • MP - Multi-
                    pupose sizing
                  • Epoxy Resin

                  max  A  B  logN10


                  •   Salvia, Fiore, Fournier &
                      Vincent I.J. of Fatigue,
Process Effects

                  • FW - Filament
                      Winding
                  •   PMC - Prepreg
                      Press Molding
                  •   P - Pultrusion

                  A   o  logN10 o  B


                  •   Salvia, Fiore, Fournier &
                      Vincent I.J. of Fatigue,
                      1997,V.19 No.3, p. 253.
Sizing & Matrix
Toughening Effects
                     • Salvia, Fiore,
                       Fournier &
                       Vincent I.J. of
                       Fatigue,
                       1997,V.19 No.3,
                       p. 253.
Summary from Salvia et al.

• Pultrusion yields lower durabilility
  composites than Filament wound or press
  molded
• Resin and sizing strongly affect both A
  and B of  max  A  B  logN10
 o was directly related to accoustic
  emission threshold. o(pultrusion) = 0.0m
Tensile Strain Fatigue

                     • Harris 1977
                         Composites
                         Oct. p. 214.
Tensile Stress Fatigue

                     • Harris 1977
                         Composites
                         Oct. p. 214.
Material Effects - Shear
Fatigue - Mean Stress

                     • Bevan 1977
                       Composites
                       Oct. p. 277.
Fatigue Failure Mechanims
- Fatigue Stiffness Loss/Crack Development
                                  •   Jamison etc.
                                      1984 ASTM STP
                                      836 p38
Fatigue - Failure
Mechanisms




                    •   Konur &
                        Matthews
                        1989,
                        Composites,
                        V.20, No. 4,
                        July 1989.
Fatigue - Fiber Type


 E-glass                    Type I Carbon




                                   •   Konur &
                                       Matthews
                                       1989,
           Type II Carbon              Composites,
                                       V.20, No. 4,
                                       July 1989.
Fatigue - Fiber Type
                        •   Konur & Matthews
                            1989, Composites,
                            V.20, No. 4, July
                            1989.
      Type III Carbon
Environmental Effects-
Frequency
                     •   Mandell & Meier
                         1983 ASTM STP
                         813 p.60
Environmental Effects-
Dynamic Fatigue
                           •    Mandell & McGarry
                                1985 Polymer
                                Composites Vol. 6
                                No. 3 p.168
            Single Fiber - No
            Fiber Interaction


            Fiber Bundle
Environmental Effects-     R ratio

                    •   Mandell & Meier
                        1983 ASTM STP 813
                        p.60
Environmental Effects-
Temperature




•   Ma, Lin, Tai, Wu & Wu 1995, Polymer Composites, V.16, No.3, June.
Environmental Effects-
Hygrothermal Aging

                                         Pooled Fatigue data




•   Ma, Lin, Tai, Wu & Wu 1995, Polymer Composites, V.16, No.3, June.
Environmental Effects R -
ratio
                    •   Adams, Fernando,
                        Dickson, Reiter &
                        Harris. 1989, IJ of
                        Fatigue, V. 11, no. 4,
                        p.233.
Environmental Effects R -
ratio
 f  a /[(1  m )(c  m )]                      •    Adams, Fernando,
                                                     Dickson, Reiter & Harris.
 a  a /t                                          1989, IJ of Fatigue, V.
                                                     11, no. 4, p.233.
 m  m /t
 c  c /t
                            e
 f 
     1  (1  e / fo ) /[1  ln(1  10 AB logN )]       where


e = endurance value of “f” at high N
fo = f value at low N
A and B are curve fit constants needed for the wider range of
R curves
Environmental Effects R -
ratio
                      •   Adams,
                          Fernando,
                          Dickson, Reiter
                          & Harris. 1989,
                          IJ of Fatigue,
                          V. 11, no. 4,
                          p.233.
Environmental Effects R -
ratio
                      •   Adams,
                          Fernando,
                          Dickson, Reiter
                          & Harris. 1989,
                          IJ of Fatigue, V.
                          11, no. 4,
                          p.233.
Environmental Effects R -
ratio




•   Gathercole, Reiter,Adam, Harris 1994, IJ of Fatigue, v. 16, no. 8, p.523.
Environmental Effects R -
ratio




•   Gathercole, Reiter,Adam, Harris 1994, IJ of Fatigue, v. 16, no. 8, p.523.
Environmental Effects R -
ratio
                      •   Schutz & Gerjarz
                          1977, Composites
                          Oct. p. 245
Environmental Effects R -
ratio
                       •   Schutz &
                           Gerjarz 1977,
                           Composites Oct.
                           p. 245
•   Highsmith &
    Reifsnider
    1982, ASTM
    STP 775, p105.
FIBERS - Tensile Strain
Fatigue




                    E-glass
                    Matrix
                    Graphite


                          •   Dharan 1975,
                              J of Matl.
                              Science, V.10,
                              p. 1665.
•   Highsmith &
    Reifsnider
    1982, ASTM
    STP 775, p105.
•   Highsmith &
    Reifsnider
    1982, ASTM
    STP 775, p105.
FIBERS - Shear Stress Fatigue
(±45°) Fibers

                         •   Gathercole,
                             Reiter,Adam,
                             Harris 1994, IJ of
                             Fatigue, v. 16, no.
                             8, p.523.
FIBERS - Torsional Shear Strain
Fatigue - Fiber/Resin

                        •   Phillips & Scott
                            1977 Composites
                            Oct. p. 233.
Material Effects - Sizing
                            •   Shih & Ebert,
                                1987, Comp.
                                Sci. & Tech.,
                                V.28, p.137.
Material Effects - Sizing
                       •    Shih & Ebert,
                            1987, Comp.
                            Sci. & Tech.,
                            V.28, p.137.
Sizing & Matrix
Toughening Effects
                     •   Salvia, Fiore, Fournier &
                         Vincent I.J. of Fatigue,
                         1997,V.19 No.3, p. 253.
    Process & Laminate Effects -
    Extracted Uni from Pultruded CP & QI Laminates vs. Uni
                                    1
                                                      CP2             CP1
         Normalized Uni- Tensile



                                                      QI1             QI2
                                   0.8
                                                      QI2 at 45°      Owen/Corn.
             Fatigue Stress




                                                      Demers          Mandell
                                   0.6

                                   0.4

                                   0.2

                                    0
                                    1.E+03   1.E+04    1.E+05      1.E+06       1.E+07
                                                 Fatigue Cycles (N)
•   Phifer 1998, Thesis Virginia Tech. http://scholar.lib.vt.edu/theses/available/etd-
    013199-185939
FIBERS - Tensile Stress
Fatigue




   E-glass   •   Dharan 1975,     Graphite
                 J of Matl.
                 Science, V.10,
                 p. 1665.
Test Effects: R - ratio
                    •   Adams, Dickson,
                        etc. 1989, IJ of
                        Fatigue, v. 11, no.
                        4, p.233.

								
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