Coursework I: Analysis of Creep and Fatigue in Solid Mechanics

This document provides a detailed solution to a solid mechanics assignment, specifically coursework I for the ENGT5258 module. The assignment covers two primary topics: creep and fatigue. The creep section explains stress relaxation, creep rupture strength, creep life, and the factors affecting creep, including stress intensity, loading age, temperature, and material properties. The fatigue section discusses the three major fatigue life methods (stress-life, strain-life, and linear-elastic fracture mechanics), endurance limit, notch sensitivity, and stress concentration. The solution also includes relevant references to support the analysis and concepts discussed. The assignment aims to assess the student's understanding of these critical concepts in solid mechanics, which are essential for designing reliable and durable engineering components. The provided solution offers a comprehensive overview of the subject matter, aiding students in their studies and assignments.

Solid Mechanics:
1) Stress relaxation:
Creep is said to be the increase in the plastic strain by having the stress as the constant factor. A
good contact force could be achieved by having elastic strain with the maximum stress achieved.
The material selected should have the sufficient elastic modulus with the yield strength. The
stress-strain curve could serve as an indication of stress and strain relationship. Creep and stress
relaxation have two similar yet distinct mechanism through which there is an increase of plastic
strain over a period of time.
Stress relaxation is defined as the decrease in stress by having the strain as the constant factor.
The principle of creep could be best understood with the help of the elastic rubber band. When a
rubber band is stretched with the nominal weight then it tends to return back to its original
position. Suppose the rubber band is hung by the weight with the elevated temperature then there
occurs deformation with the occurrence of creep (weight is not varied) [1]. During unloading, the
tendency of the material that fails to come back to its original shape then it is known as the stress
relaxation. During stress relaxation the part remains unchanged. It could partially regain its
position after removing the deflection. Hence it is noted until the load is removed while the stress
relaxation is invisible [2]. The contact performance will decline steadily without any visual
effect.
ii) Creep Rupture Strength:
The stress applied to a material causing it to rupture at a constant temperature within a specified
time is known as creep rupture strength [3]. Similar to the creep test, the rupture test is also
carried out but at a higher stress level until the material fails and the failure time should be noted.
The sufficient chart is also plotted.
iii) Creep Life:
All the components are basically designed based on the reasonable life operation. Creep life is
defined as the life of the material at which the material could sustain above which causes certain
problem and failures.
iv) Factors affecting creep:
The following are the factors that affect the creep that are as follows: (Here the creep nature of
the concrete has been mentioned)
 Intensity of stress
 Loading age
 Temperature
 Coarse aggregate

 Strength
 Volume to surface ratio
 Ambient RH
 Multi-axial loading
5) i)Fatigue:
The three major fatigue life methods and these methods predict fatigue life in number of cycles
to failure for a specified loading level that includes the following:
Stress-life: The high cycle fatigue (>10000) could be addressed well by this method and this
method is not accurate for the low cycle fatigue [4]. It has the following features such as easy to
implement, Contains ample supporting data, high-cycle application is represented adequately.
This is completely based on the stress level. This could be analyzed by stress-number of cycles
to failure curve (S-N curve).
Strain-life: The detailed analysis of the plastic deformation is done at the specified region. This
works well with the low-cycle fatigue application. A few uncertainties persist in the result.
Linear-elastic fracture mechanics: Detects the crack that is also present and it also predicts the
growth of the crack with respect to the stress intensity.
ii) Endurance limit:
Endurance limit is defined as the maximum stress amplitude below which the material will not
fails though there is maximum number of cycles. Endurance limit that is commonly known as the
Fatigue limit, occurs for certain materials such as Ti and Fe. In this case, larger the value of N
the curve becomes horizontal in the S-N curve [5]. Hot Mix Asphalt (HMA) mixtures have been
used to conduct the endurance limit test. The fatigue strength of the material also deals with the
effect of bending and torsion loading along with the influencing factor. These factors include the
following:
 Stress concentration
 Surface condition
 Corrosion fatigue
 Residual stress
 Size of material.
iii) Notch Sensitivity and Stress concentration:
The measure of the sensitivity of the material with the geometric discontinuation is known as the
Notch sensitivity. Notch is known as surface inhomogeneity and this tends to increase the
fracture of the material that leads to a crack or sudden changes in the material. Ductile materials

have low notch sensitivity whereas brittle materials have high notch sensitivity [6]. Certain
materials are not sensitive to notches where the maximum stress is calculated as:
σmax = kf σ0
kf is said to be known as the stress concentration factor that is defined as the ratio of the
endurance limit of un-notched specimen to the ratio of the endurance limit of notched specimen.
References:
[1] R. I. Stephens, A. Fatemi, R. Stephens, and H. O. Fuchs, Metal Fatigue in Engineering,
John Wiley & Sons, New York, NY, USA, 2008.
[2] M. A. Miner, “Cumulative damage in fatigue,” Journal of Applied Mechanics, vol. 12,
pp. A159–A164, 1945. View at Google Scholar
[3] G. Ayoub, M. Naït-Abdelaziz, F. Zaïri, and J. M. Gloaguen, “Multiaxial fatigue life
prediction of rubber-like materials using the continuum damage mechanics approach,”
Procedia Engineering, vol. 2, no. 1, pp. 985–993, 2010. View at Publisher · View at
Google Scholar
[4] J. Schijve, Fatigue of Structures and Materials, Springer Science & Business Media,
2011.
[5] H. F. S. G. Pereira, A. M. P. de Jesus, A. A. Fernandes, and A. S. Ribeiro, “Analysis of
fatigue damage under block loading in a low carbon steel,” Strain, vol. 44, no. 6, pp.
429–439, 2008. View at Publisher · View at Google Scholar · View at Scopus
[6] L. Xi and Z. Songlin, “Strengthening of transmission gear under low-amplitude loads,”
Materials Science and Engineering A, vol. 488, no. 1-2, pp. 55–63, 2008. View at
Publisher · View at Google Scholar · View at Scopus