2 a) possible additional sources of error (creep test)

• temperature not constant over time• light (optical strain gages!) may be not constant• humidity (sample affected!) not constant• load or displacement may not be const.• machine/instrument creeping• creeping of strain gage• etc.

(day / night!)

2 b) Analyzing a creep experiment

0 1 2 3 4 5 6 7 80

5

10

15

20

Dis

plac

emen

t [%

]

Time [min]

secondary

tertiary

primary

0 1 2 3 4 5 6 7 80,000

0,001

0,002

0,003

0,004

0,005

Com

plia

nce

D(t

) [1

/MP

a]

Time [min]

0 1 2 3 4 5 6 7 8

1E-3

0,002

0,003

0,004

0,005

Com

plia

nce

D(t

) [1

/MP

a]

Time [min]

𝐷(𝑡)=𝜀(𝑡)𝜎 0

creep compliance

note that the values of e are given in %, so you have to divide them by 100

to evaluate creep compliance is only useful in the secondary region (marked by )D is in the range of 1/MPa

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

2 c) i. time-temperature-shift for master curve at 120°C

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

2 c) i. result: master curve at 120°C

master curve at 120°C

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

master curve at 120°C

2 c) ii. predict compliance after 5 days

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

master curve at 120°C

5 d = 5*24*60 min = 7200 min

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

master curve at 120°C

5 d = 5*24*60 min = 7200 min

D(5 d) ≈ 1/psi

2 c) iii. possible prediction range at 120°C

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

master curve at 120°C

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

10-3 10-1 101 103 105

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

master curve at 120°C

40000 min == 0,9 months == 0,1 years

130°C 125°C 122°C 120°C 115°C 110°C 100°C 90°C

102 104 106 108 1010

10-6

10-5

10-4

10-3

10-2

Time (min)

Com

plia

nce

D(t

) (1

/psi

)

master curve at 90°C

3e+9 min == 70000 months == 5700 years

for comparison: possible prediction range at 90°C

3. Fatigue testing

a) three examples of applications cyclic stress loading

1. wings of airplanes2. turbine blades3. rotor blades

(nicht sehr schwer, wenn zwei davon schon in b) genannt sind)

b) Wöhler curve and estimation of life time

10-1 100 101 102 103 104 105 106 107 108

20

40

60

80

100

120 Stress

Str

ess

[MP

a]

Cycles N

b) Wöhler curve and estimation of life time

10-1 100 101 102 103 104 105 106 107 108

20

40

60

80

100

120 Stress

Str

ess

[MP

a]

Cycles N

i. N(40 MPa) ≈ 9000 ii. N(27 MPa) ≈ 300000

i. N(40 MPa) ≈ 9000 tlife = N/f = 9000 * 1 / 0,5 s = 18000 s = = 5 hours

ii. N(27 MPa) ≈ 300000 tlife = N/f = 300000 * 1 / 1000 s = 300 s = = 5 minutes

(aim: to show that cyclic loaded components must have huge safetyfactors, if fatigue testing is not performed)