Failure

1
Failure Strength
2
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

3
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.

4
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

5
Strength Values

• F1tfiber direction tensile strength
• F1cfiber direction compressive strength
• F2t transverse direction tensile strength
• F2ctransverse direction compressive strength
• F6 in plane shear strength
• F4, F5 interlaminar shear strength
• f12biaxial interaction coefficient

6
Layer Failure Criteria

• Failure for a single-layer material
• Strength ratio
• R gt 1 -- stress is below failure level
• R lt 1 failure is predicted

7
Maximum Stress Criterion

• Fracture occurs if any one of the stresses in
  principal material coordinates is greater than
  respective strength 
• s1gt F1t if s1 gt 0
• abs(s1) gt F1c
• s2gt F2t if s2 gt 0
• abs(s2) gt F2c if s2 lt 0
• Shear stresses
• abs(s4) gt F4
• abs(s5) gt F5
• abs(s6) gt F6

8
Stress Criterion -- Strength Ratios

• Failure occurs for R lt 1
• R1 F1t/s1 if s1 gt 0
• R1 -F1c/s1 if s1 lt 0
• R2F2t/s2 if s2 gt 0
• R2 -F2c/s2 if s2 lt 0
• R4 F4/abs(s4)
• R5 F5/abs(s5)
• R6 F6/abs(s6)

9
Maximum Strain Criteria

• Most popular failure criterion in industry
• R1 e1t/e1 if e1 gt 0
• R1 -e1c/e1 if e1 lt 0
• R2 e2t/e2 if e2 gt 0
• R2 -e2c/e2 if e2 lt 0
• R4 g4u/abs(e4)
• R5 g5u/abs(e5)
• R6 g6u/abs(e6)

10
Stress and Strain Criteria

• Even though we are using linear elasticity, these
  criteria vary because of the Poisson effect.

11
Maximum Strain Stress Criteria
12
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

13
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

14
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

15
Comparison of Criteria
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Fiber-Matrix Failure Criteria

• Hahn, Erikson Tsai failure Criteria
• Quadratic relationships assume smooth transition
  in failure mode between tension and compression
• Hashin Failure Criteria

17
Laminate Strength

• Single Ply failure already described
• Laminate Failure Criteria
• use single ply theories to predict first ply
  failure (FPF)
• usually associated w/ matrix cracking (F2tltF1t)
• each layer is then discounted (or degraded) until
  fiber failure (FF) occurs
• Limitation
• degraded material constants difficult to define

18
First Ply Failure (FPF)
define laminate and BCs calculate A,B,D
calculate stresses on top and bottom of each ply
check failure criteria
19
Fiber Failure (FF) -- 1

• First ply failure
• usually matrix cracks
• affect transverse and not longitudinal stiffness
• Degradation of layer
• fd empirical degradation factor
• E1E10
• E2 fd E20
• G12 fd G120
• n12 fd n120
• f12 fd f12
• 0 indicates original, undegraded property
• Failure criteria modified to eliminate transverse
  or shear failure
• New Stress analysis

20
Fiber Failure (2)
define laminate and BCs calculate A,B,D
calculate stresses on top and bottom of each ply
check failure criteria
no failure
failure
degrade material props
end of problem
modify failure criteria
see Barbero, Section 7.2
21
Fiber Failure (3)
22
Carpet Plot Design for Failure
23
Stress Concentrations (1)
Stress concentration near a hole failure occurs
when stress at a distance d0 from edge of
discontinuity equals the unnotched strength F0
24
Stress Concentrations (2)

• Stress Concentration Factor
• Ktsmax/sn 7.50
• where smax maximum stress around notch or hole
• sn nominal stress
• fully sensitive to notches
• for unidirectional lamina loaded in tension
  transverse to fibers
• sn, fail F2t / Kt 7.51
• Effective stress concentration, Ke
• quasi-isotropic laminates can withstand greater
  nominal stresses than predicted from eq, 7.51, we
  therefore introduce the concept of notch
  sensitivity.
• q(Ke-1)/ (Kt-1)
• where q notch sensitivity 0,1
• if q1 -- fully sensitive to notches

25
Stress Concentrations (2)
Stress concentration near a notch aradius of
hole
26
Stress Concentrations (3)
q(Ke-1)/ (Kt-1) failure occurs when stress at a
distance d0 from edge of discontinuity equals the
unnotched strength F0
27
Fracture Toughness (1)
28
Fracture Toughness (2)

• Sharp cracks analyzed using fracture mechanics --
  Griffith theory
• Calculate stress intensity factor KI with
  critical stress intensity factor KIC

29
Take-home messages

• Composites have multiple failure patterns
• Compression
• Tension
• First ply failure
• Final failure
• Different failure criteria are appropriate
  depending on your loading mode
• a conservative choice is often appropriate
• Uniaxial, multi-axial, and distinction of
  fiber/matrix failure
• Cracks create stress concentrations, but
  composites are generally good at resisting crack
  propogation