Micromechanics- Fatigue

Question 1

What is fatigue?

Answer 1

The gradual weakening of a material in response to cyclic loading. Failure due to fatigue occurs at a lower stress (σ sub R) than the nominal strength of the material σc. σR is the residual strength

Question 2

Stress range and ratio

Answer 2

Δ σ=σmax-σmin
R=σmin/σmax

Question 3

What do stress-life curves plot?

Answer 3

Cyclic stress (Δ σ) vs number of cycles to failure (Nf). Doesn’t show the underlying damage mechanisms which control composite fatigue

Question 4

Why are composites safer than metals?

Answer 4

Composites have multiple damage mechanisms as opposed to a single catastrophic failure event. Initial imperfections include fibre fracture, matrix fracture, fibre/matrix debonding, delamination, voids. Growth of damage involves these multiple routes which gradually decrease performance. Provide a warning of impending failure compared to metals where the initial imperfection is often a small crack which fails much more abruptly

Question 5

The accumulative stages of progressive damage composites experience under fatigue

Answer 5

1- localised matrix cracking, fibre cracking.
2- coupling of existing cracks, interfacial debonding, fibre cracking.
3- initial delamination and fibre cracking.
4- extensive delamination and fibre cracking.
5- final fracture and ultimate failure of material.
Note fibre fracture occurs in all 5 stages and stages are necessarily independent of each other

Question 6

Damage vs percent of life graph with 5 stages of damage

Answer 6

Concave curve (1), linear shallow (2 then 3), curves up (4) to fracture (5).

Question 7

How does the type of fibre influence fatigue performance?

Answer 7

Carbon and boron fibre composites show excellent fatigue properties as stiffer fibres are capable of supporting cyclic loading.
Glass fibre composites show poorer fatigue performance as less stiff fibres can’t support as much load which results in matrix damage.

Question 8

How does orientation of fibres and ply lay-up effect fatigue performance?

Answer 8

Unidirectional fibre laminates (all 0°) have highest S-N curve. This is higher than cross-ply due to transverse stiffness being very low resulting in matrix damage. Using symmetrical angle ply lay-ups (like + and -45) gives lower S-N curve at start but less steep drop off than cross and all 0° so crosses the cross-ply line. Woven cloths are lower as crimp reduces strength but slow drop off as is 0/90 system. CSM lower and Doug moulding compound lower still (both shallow)

Question 9

Stiffness vs log time for metal and composite under fatigue

Answer 9

Both start high and shallow curve down. Just after going below required stiffness, metal curves down steep and then vertical down to fracture. Composite continues to curve down a bit steeper than before but fractures much later than metal

Question 10

Types of damage for composite fatigue damage modelling

Answer 10

D1- transverse ply cracks
D2- delamination cracks
D3- fibre breaks

Question 11

Modulus vs number of cycles graph for different stress ranges. Which failure modes dominate for Δ σ1, Δ σ2, Δ σ3?

Answer 11

Start high at E0 (undamaged modulus), linear shallow decrease, then curve down to linear steep decrease. The curve down is sooner for greater stress range and delayed for lower stress range.
For Δ σ1<Δ σ3<Δ σ5:
In Δ σ1 the matrix cracks first followed by delamination and ultimately complete failure. In Δ σ5 the matrix cracks first followed by fibre fracture then complete failure. In Δ σ3 situation is somewhere in between, matrix crack then delamination then fibre failure.

Question 12

What does damage growth rate depend on?

Answer 12

Stress range, stress ratio and current value of D
dD/dN=f(Δ σ, R, D)

Question 13

What does damage in composite increase from and to?

Answer 13

Di to Df
Initial to final damage state

Question 14

What can be used as a measure of damage?

Answer 14

Changing modulus
E=E0g(D)
Where E0 is undamaged modulus and
g(D) is some function of damage that is independent of how the damage was produced but related to material properties and lay-up

Question 15

In lay-up sequence notation, what does a subscript s mean?

Answer 15

Symmetric so the next sequence is a mirror of the previous sequence

Question 16

Formula for f(Δ σ, R, D)

Answer 16

f(Δ σ, R, D)=1/(g’(g^-1(E/E0)))(1/E0)dE/dN
Right side of equation can be evaluated for:
A range of Δ σ at constant E/E0 and R
A range of R at constant Δ σ and E/E0
A range of E/E0 at constant R and Δ σ

Question 17

Sequence of events to failure for fatigue testing of carbon fibre epoxy resin quasi-isotropic composite ([45/90/-45/0]s)

Answer 17

Matrix cracks appear in 90 plies followed by 45 plies.
Small delaminations appear between the 90/+-45 plies which grow into large delaminations.
Continued testing leads to failure of the 0 plies

Question 18

Model for the reduction in modulus as a result of delamination

Answer 18

E=E0+(E-E0)A/A0
Where E is the delaminated modulus
A is the delaminated area
A0 is the total interfacial area

Question 19

How does E/E0 vary with A/A0? What can you use this for?

Answer 19

Linear decrease in E/E0 from 1 to a non-zero value from increasing delaminated area (A/A0).
Can then define the function g(D) (for the specific composite).
Then the damage parameter can be defined D=…(1-E/E0).
Then f(Δ σ, R, D) can be written (dD/dN=…)

Question 20

Damage rate vs stress range graph

Answer 20

dD/dN vs Δ σ both on log scale. A power law relation of
dD/dN=…(Δ σ/σbarTS)^6.4 exists.
σ bar sub TS is mean tensile strength. The power law gives a straight diagonal line with positive gradient. At high stresses dD/dN is higher than power law predicts as tensile strength of the material is approached. There is a lower limit to the power law relation below which no damage occurs. Power law agrees with middle range of experimental data

Question 21

Formula for number of cycles to failure (long)

Answer 21

In databook
Nf=3.1x10^4(Δ σ/σbarTS)^-6.4(1.22(1-R/1+R)^p(1-Δ σ/(1-R)σbarTS
Where p is 2.7 for small stress ranges (<250MPa)
Or p is 1.6 for large stress ranges (>250MPa)