# failure

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```					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

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
• 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
– 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
•   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

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 views: 13 posted: 8/4/2011 language: English pages: 21