ENGT5258 Advanced Solid Mechanics Assignment - De Montfort University, UK
Assignment - Creep and Fatigue
The learning outcomes that are assessed by this coursework are:
1. Creep relaxation calculations, factors affecting creep.
2. Fatigue life methods, cumulative fatigue determination methods.
3. Endurance limit and modifying factors.
Explain and answer the questions.
1. Creep
Q1. Explain and discuss the following in terms of creep with practical examples
1. Stress relaxation
2. Creep rupture strength
3. Creep life
4. Factors affecting creep
Q2. A secondary creep rate is given in table below were obtained from creep tests carried out on Aluminium alloy at 100oC
|
σ, MPa
|
120
|
160
|
210
|
250
|
280
|
300
|
|
∈·s, h-1
|
6.2 x 10-6
|
4.2 x 10-5
|
1.42 x 10-4
|
2.3 x 10-4
|
4.7 x 10-4
|
6.2 x 10-4
|
Determine the parameters of the Norton power law for creep: ∈·s = Aσn
Where ∈·s is the secondary creep rate, σ is stress, and A & n are constants. The result should include MATLAB polyfit with clear steps.
Q3. The secondary creep rates are given in table below obtained from a series of tensile tests as various temperatures under the same load.
|
T, K
|
290
|
300
|
310
|
320
|
330
|
|
∈·s, h-1
|
4.8 x 10-6
|
2.74 x 10-5
|
1.4 x 10-4
|
6.44 x 10-4
|
2.7 x 10-3
|
Consider the material complies with Arrhenius definition: ∈·s = D exp (- Q/RT)
Given the molar gas constant as R = 8.314 Jmol-1K-1. Determine the activation energy and the constant for secondary creep and hence identify the material. The result should include MATLAB polyfit with clear steps.
Q4. In a cylindrical vessel a pressure of 1.5 MPa acts on a circular cover plate. The cover plate has a diameter of 450mm and is held in a position by thirty bolts of 20mm diameter, equally spaced around the rim. Ignoring primary creep but account for elasticity with E = 210GPa and a secondary creep rate of 32.2 x 10-17 σ4h-1, where σ is in MPa: Given that
tm = 1/(AE(n-1)) ((1/σn-1)-(1/σ0n-1))
Where all symbols have their standard meaning, A and n can be found from creep rate. Determine
1. The initial tightening stress in the bolts in order that a safety factor of 1.6 is maintained after 8000hrs of creep relaxation at 500oC.
2. The time when the bolts should be re-tightened to prevent leakage around the plate.
2. Fatigue
Q5. Give a brief descriptions on the following:
1. Explain the three major fatigue life methods and their benefit and limitations.
2. Discuss endurance limit with practical examples, also include endurance limit modifying factors.
3. Briefly explain with examples the meaning of stress concentration and notch sensitivity.
Q6. The fatigue life of various stress levels of machine tool steel is given in the following table. The machine tool is subjected to reversed cycle loading at 120 cycle/day in a continuous sequence.
|
σ, MPa
|
±130 MPa
|
±120 MPa
|
±80 MPa
|
|
Nf, cycles
|
8 x 103
|
104
|
4 x 105
|
Which involves the following three stages:
1. 250 cycles at ±130 MPa
2. 250 cycles at ±120 MPa
3. 250 cycles at ±80 MPa
Estimate the life of the component in days according to
1. Miner's rule
2. A non-linear approach where damage curves D = √R, D = R and D = R2 apply to the semi-stress ranges of 130 MPa, 120 MPa and 80 MPa respectively.
Q7. The reverse stress fatigue limit for low-carbon steel is ±270 MPa, its Ultimate Tensile Strength, UTS is 670 MPa and its yield stress is 260 MPa.
1. Estimate the safe range of stress for a repeated cycle based on the Gerber and Goodman fatigue predictions.
2. Determine the peak stresses and safe range of stress for an alternating tensile cycle with mean stress 185 MPa based upon the Soderberg prediction.
Note - The report should be concisely written with clear steps.