Advanced Solid Mechanics: Stress Relaxation, Creep, Factors Affecting Creep, Fatigue Life Methods, Stress Concentration, Miner's Rule

Advanced Solid Mechanics 1
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Advanced Solid Mechanics 2
QUESTION ONE
Part 1 Stress relaxation
This is reduction in stress which can be observed with accordance to the quantity of deflection
produced in the structure. It is usually true since maintaining a material in a deformed position
for some period of time leads to plastic deformation1. Creep is an increased plastic deformation
in a constant force applied.
Fig 1 illustrate stress-strain graph for material under stress relaxation.
Fig 2 illustrates a rubber band model, the rubber is made to hang on a pin at step A as shown.
The band is then made to stretch in pin 2 as illustrated in fig 2. Pin 2 is abruptly withdrawn and
1 W. Bottega, Engineering Vibrations. Florida: CRC Press, 2013,p.123.
A. Culp, Principles of Energy Conversion. Hull: McGraw-Hill, 2011, p.541.

Advanced Solid Mechanics 3
the band gets its initial shape again as in C.
Fig b showing a rubber band example
Figure 3 illustrates the band after exposure. There is no conspicuous difference between step 3
and step 2 in the second diagram. But, the pin is withdrawn at step 4, and it becomes stable and
observable.
2. Creep rupture strength
This is the force needed to produce a creep fracture experiment in a given time span. It is as well
referred to as the stress which at a specified temperature can make a structure to rapture in a
specified time.
3. Creep life
Blends of materials employed in applications such as blocks experience a bigger
temperature range and stress for fluctuating time during, start up, shut down creep strain, landing
and take-off accrue at these stages and design could presume a worst case scenario, however, this

Advanced Solid Mechanics 4
could result in a weight penalty2. This can also be illustrated by the fraction law which states that
the fraction of rupture equals to unity as shown in the following diagram;
∑ ¿¿+ t 2
tR 2 + t 3
tR 3 ....) = ∑ i ti
tR 1 = ∫ 1
tR dt = 1
4. Factors affecting creep
The below are main factors which affect creep;
i. Load applied
ii. Exposure temperature
iii. Property of material
iv. Time of exposure
2 L. Steinbeisser, Vibration Problems in Structures: Practical Guidelines. London: Birkhäuser, 2012,p.451.
F. Taylor, The Internal-combustion Engine in Theory and Practice: Thermodynamics, fluid flow,
performance. Stoke: MIT Press, 2014,p.431.