failure

Document Sample
failure Powered By Docstoc
					Failure & Strength
                        Failure Modes (1)
 Failure Modes
 • Fiber breaking -- tension in fiber direction
 • Fiber buckling -- compression in fiber direction
 • Matrix fracture -- tension in transverse direction
 • Matrix compression failure/matrix crazing --
   compression in transverse direction
 • Other failure modes:
       – Fiber debonding -- fiber-matrix bond fails
       – Delamination -- separation between layers in laminate


ME429: Int. to Composite Materials                               AErklig
                         Failure modes (2)
• 2 failure types related to the 4 modes:
  matrix failure or fiber failure.
      – Fiber failure typically causes composite failure
      – matrix failure may not
• Realistic loading is biaxial or triaxial.




ME429: Int. to Composite Materials                         AErklig
              Laminate Failure Criteria
• Failure criteria for a single ply.
• Failure criteria aim to relate all failure modes with
  a single curve; No reason this should hold.
• Single Mode Failure Criteria
      – Maximum stress criterion
      – Maximum strain criterion
• Interactive Failure Criteria
      – Tsai Hill criterion
      – Tsai Wu criterion
• Fiber-Matrix Failure criteria
      – Hann, Erikson & Tsai failure criterion
      – Hashin failure criterion
ME429: Int. to Composite Materials                        AErklig
                           Strength Values
• F1t=fiber direction tensile strength
• F1c=fiber direction compressive strength
•  F2t = transverse direction tensile strength
• F2c=transverse direction compressive
  strength
• F6= in plane shear strength
• F4, F5= interlaminar shear strength
• f12=biaxial interaction coefficient

ME429: Int. to Composite Materials               AErklig
                   Layer Failure Criteria
• Failure for a single-layer material
• Strength ratio            ultim ate
                                     R
                                           applied


      – R > 1 -- stress is below failure level
      – R < 1 failure is predicted




ME429: Int. to Composite Materials                    AErklig
            Maximum Stress Criterion
• Fracture occurs if any one of the stresses in
  material coordinates is greater than experimental
  strength
• 1> F1t if 1 > 0
• abs(1) > F1c
• 2> F2t if 2 > 0
• abs(2) > F2c if 2 < 0
• Shear stresses
      – abs(4) > F4
      – abs(5) > F5
      – abs(6) > F6


ME429: Int. to Composite Materials                    AErklig
 Stress Criterion -- Strength Ratios
•   Failure occurs for R < 1
•   R1 = F1t/1 if 1 > 0
•   R1 = -F1c/1 if 1 < 0
•   R2=F2t/2 if 2 > 0
•   R2 = -F2c/2 if 2 < 0
•   R4 = F4/abs(4)
•   R5 = F5/abs(5)
•   R6 = F6/abs(6)

ME429: Int. to Composite Materials   AErklig
              Maximum Strain Criteria
•   Most popular failure criterion in industry
•   R1 = e1t/e1 if e1 > 0
•   R1 = -e1c/e1 if e1 < 0
•   R2= e2t/e2 if e2 > 0
•   R2 = -e2c/e2 if e2 < 0
•   R4 = g4u/abs(e4)
•   R5 = g5u/abs(e5)
•   R6 = g6u/abs(e6)

ME429: Int. to Composite Materials               AErklig
              Stress and Strain Criteria
• Even though we are using linear elasticity,
  these criteria vary because of the Poisson
  effect.     stressin 1  direction is
                                1
                           1  [E1e1   21e 2 ]
                                
                             1  12  21
                           wherefailure occursat
                                e1t  e1
                           e2           ( top curve)
                                 21  21
                           e 2  e 2 c   12 e1 (bottom curve)
ME429: Int. to Composite Materials                                  AErklig
Maximum Strain & Stress Criteria




ME429: Int. to Composite Materials   AErklig
                  Tsai-Hill Criterion (1)
• Includes interactions among stress
  components
• Quadratic interaction is introduced
• Similar to Von-Mises stress criteria
• Limitations
      – Mode of failure is not identified
      – Inadequate for materials with different
        tension/compression nonlinearity
  (1 ) 2 (1 f2 ) (f2 ) 2 (f ) 2 (f4 ) 2 (5 ) 2
    f         f                                  f

        2
                 2
                           2
                               62        2
                                                    2
                                                       1  0
  (F1 )     (F1 )     (F2 )    (F6 ) (F4 )     (F5 )

ME429: Int. to Composite Materials                              AErklig
                  Tsai-Hill Criterion (2)
      – Good fit in 1st quadrant will result in poor fit
        (non-conservative prediction) in 2nd quadrant
      – For shear and transverse components only




ME429: Int. to Composite Materials                         AErklig
                              Tsai-Wu Criterion
          – parameters fi and fii are functions of failure
            stresses Fi
          – failure stresses in compression are taken +ve
          – interaction term f12 accounts for
            tension/compression nonlinearity
          – Limitation
                 • does not distinguish matrix and fiber failure

f11  f 2  f2  f11 (1 ) 2  f 22 ( f2 ) 2  2f12 (1  f2 )  f 66 ( f6 ) 2  f 44 ( f4 ) 2  f 55 (5 ) 2  1  0
   f                    f                               f                                                   f


             1
f12 
      2 F1t F1c F2 t F2c


    ME429: Int. to Composite Materials                                                                         AErklig
                 Comparison of Criteria




ME429: Int. to Composite Materials        AErklig
        Fiber-Matrix Failure Criteria
• Hahn, Erikson & Tsai failure Criteria
                  – Quadratic relationships assume smooth transition in failure
                    mode between tension and compression
             fiber failure
             (f111 )R 2  (f11 )R  1  0
                  2


             matrix failure
             (f 22 2  f 666  f 44 2  f 555 )R 2  (f 2 2 )R  1  0
                    2
                             2
                                       4
                                                2



• Hashin Failure Criteria
             fiber failure
             (f111  f 666 )R 2  (f11 )R  1  0
                  2        2


             matrix failure
             (f 22 2  f 666  f 44 2  f 555 )R 2  (f 2 2 )R  1  0
                    2
                             2
                                       4
                                                2


ME429: Int. to Composite Materials                                            AErklig
                        Laminate Strength
• Single Ply failure already described
• Laminate Failure Criteria
      – use single ply theories to predict first ply failure
        (FPF)
      – usually associated with matrix cracking
        (F2t<F1t)
      – each layer is then discounted (or degraded)
        until fiber failure (FF) occurs
• Limitation
      – degraded material constants difficult to define


ME429: Int. to Composite Materials                         AErklig
                  First Ply Failure (FPF)
                              define laminate and BCs;
                                   calculate A,B,D



                                  calculate stresses on
                               top and bottom of each ply



                                 check failure criteria



ME429: Int. to Composite Materials                          AErklig
                  Fiber Failure (FF) -- 1
• First ply failure
      – usually matrix cracks
      – affect transverse and not longitudinal stiffness
• Degradation of layer
      – fd: empirical degradation factor
            •   E1=E10
            •   E2= fd E20
            •   G12= fd G120
            •    12= fd 120
            •   f12= fd f12
            •   0 indicates original, undegraded property

            •   Failure criteria modified to eliminate transverse or shear failure
• New Stress analysis

ME429: Int. to Composite Materials                                               AErklig
                           Fiber Failure (2)
                                define laminate and BCs
                                    calculate A,B,D

                                    calculate stresses on
                                 top and bottom of each ply

                                     check failure criteria

                                     failure      no failure

         degrade material props*                  end of problem

        modify failure criteria*

ME429: Int. to Composite Materials
                                     * see Barbero, Section 7.2    AErklig
                           Fiber Failure (3)




ME429: Int. to Composite Materials             AErklig

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:13
posted:8/4/2011
language:English
pages:21