ENGT5258 Advanced Solid Mechanics: Creep and Fatigue Course Work I

This assignment solution covers creep and fatigue analysis, focusing on creep relaxation calculations, fatigue life methods, and endurance limits. It includes calculations for pressure vessels, initial tightening stress, and time for tightening using Miner’s rule to determine cumulative fatigue. The solution also addresses the safe range of stress using Gerber’s and Goodman’s criteria, along with Soderberg prediction, to determine peak stress and safe stress ranges. The analysis incorporates material properties and cyclic loading conditions to assess fatigue life and structural integrity. Desklib is a platform where you can find this and many other solved assignments and past papers.

Creep and Fatigue 1
CREEP AND FATIGUE
By Name
Course
Instructor
Institution
Location
Date

Creep and Fatigue 2
Q 4
Pressure vessel (p) is given as1.5 Mpa
D:a of the cover plate (D) is given as 450 mm
D:a of bolt (d) = 20mm
Area A = πr2
Which can as well be given as,, Area A = π
4 (D2)
R= 225mm
Number of bolts = 30
Elasticity E = 210×103 Mpa
Area A = π
4 (D2)
A = π
4 (450×450)
A= 159043.12 mm2
Secondary creep rate = 32.2 ×10-17 σ−4h-1
First part
Initial tightening stress in the bolt n is given by
σ = P D2
nd = 1.5× 450 × 450
30 ×20
σ = 303750
600
σ = 506.25Mpa
Second part

Creep and Fatigue 3
Time for tightening
The equation for finding the time for tightening is given below
σ = Pr
t = 1.5× 225
t
506 = 1.5× 225
t
t= 337.5
506.25
t= 0.66 seconds ss
Q 6
From Miner’s rule , failure is witnessed when
n 1
N 1 + n 2
N 2 + ……………………..+ ¿
¿ = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Where ni = number of cycles at ith stress table,
Ni = number of failure links to ith stress relevant. ¿
¿ = damage ratio
Stages
1. 250 cycles at σ 1
2. 250 cycles at σ 2
3. 250 cycle at σ 3

Creep and Fatigue 4
250
8 ×1 03 + 250
8 ×1 04 + 250
8 ×1 05 = C damage
C = 0.056875
When C = 1, life is entirely entrusted
X= 10.056875) = 1
X= 17.5824 repetition needed
Life time left after three stages ( in days)
At 130 MPa, days = 8 ×1 03 × 0.943125
120
= 62.85 days
At 120 Mpa , days = 103 × 0.943125
120
= 78.59 days
At 80Mpa, days = 4 × 105 × 0.943125
120
= 3143.75 days
Q 7
The reverse steel fatigue limit
= ± 270 Mpa = σ max
σ max= +270 Mpa
σ min = -270 Mpa
Endurance limit Se= 0.5 , Sut = 300 Mpa
Sut = 600 Mpa , Sut = 360 Mpa
σ a= σ max+ σ min
2

Creep and Fatigue 5
σ a= 270± 270
2 = 0Mpa
σ m= 0 Mpa
1) The safe range of stress
From Gerbers creteria
Se= 0.5 , sut = 0.5 ×600 = 300 mpa
hσ
se +( nσm
sut )2 = 1 = σa
se = 1 (σ m =0)
Factor of safety n
n = se
σa = 300
270
n= 1.11111
Safe range can easily be obtained from the factor of safety as below;
300-270 = 30
2)
Peak stress and safe range of the stress
From Goodman´s criteria
σa
se + σm
sut = 1
m n= se
σa (σ m =0)
n= 300
270 = 1.11111111
From Soderberg prediction
σa
se + σm
sut = 1
m

Creep and Fatigue 6
σa
300 + 185
260 = 1
m
σ a= σmax−σmin
2 = 86.53
= σ max-σ min = 173.07
σm = σmax+ σmin= 370
σmax= 271.5Mpa
σ min = 98.46 Mpa
Bibliography
Budynas, R., 2014. Shigley's Mechanical Engineering Design. 3rd ed. Hull: CRC.
Ekvall, C., 2011. Statistical Analysis of Fatigue Data. 3rd ed. Hull: ASTM International.
Fonstein, N., 2015. Advanced High Strength Sheet Steels: Physical Metallurgy, Design, Processing, and
Properties. 3rd ed. Chicago: Springer.
Mobley, K., 2012. An Introduction to Predictive Maintenance. 2nd ed. Stoke: Elsevier.
Roberts, N., 2014. Structures Subjected to Repeated Loading: Stability and strength. 2nd ed. Florida: CRC
Press.
Taylor, F., 2014. The Internal-combustion Engine in Theory and Practice: Combustion, fuels, materials,
design. 1st ed. Manchester: MIT Press.