Mechanics of Materials II. UET, Taxila Lecture No. (4&5). Mechanisms of material failure. In order to understand the various approaches to modeling fracture, fatigue and failure, it is helpful to review briefly the features and mechanisms of failure in solids. Failure under monotonic loading.
Lecture No. (4&5)
In order to understand the various approaches to modeling fracture, fatigue and failure, it is helpful to review briefly the features and mechanisms of failure in solids.
If you test a sample of any material under uni-axial tension it will eventually fail. The features of the failure depend on several factors, including:
2-The applied stress state
3- Loading rate
5-Ambient environment (water vapor; or presence of corrosive environments)
Brittle and Ductile failures
Examples of `brittle’ materials include:
ceramics (Oxides, Carbides & Nitrides)
and Cast Iron
1-Very little plastic flow occurs in the specimen prior to failure;
2-The two sides of the fracture surface fit together very well after failure.
4- In many materials, fracture occurs along certain crystallographic planes. In other materials, fracture occurs along grain boundaries
Examples of `ductile’
Tin and lead
FCC metals at all temperatures;
BCC metals at high temperatures;
polymers at relatively high temperature.
Extensive plastic flow occurs in the material prior to fracture.
There is usually evidence of considerable necking in the specimen
The fracture surface has a dimpled appearance – you can see little holes
Of course, some materials have such a complex microstructure (especially composites) that it’s hard to classify them as entirely brittle or entirely ductile.
Brittle fracture occurs as a result of a single crack, propagating through the specimen. Most materials contain pre-existing cracks, in which case fracture is initiated when a large crack in a region of high tensile stress starts to grow.
Ductile fracture occurs as a result of the nucleation, growth and coalescence of voids in the material
Failure is controlled by the rate of nucleation of the voids and their rate of growth.
In the preceding sections it has been suggested that failure of materials occurs when the ultimate strengths have been exceeded.
Creep is the gradual increase of plastic strain in a material with time at constant load.
At elevated temperaturessome materials (most metals) are susceptible to this phenomenon and even under the constant load mentioned, strains can increase continually until fracture.
This form of fracture is particularly relevant to turbine blades, nuclear reactors, furnaces, rocket motors, etc.
The general form of the strain versus time graph or creep curveis shown for two typical operating conditions.
In each case the curve can be considered to exhibit four principal features:
(b) A primary creepregion, during which the creep rate (slope of the graph) diminishes.
(d) A tertiary creep region, during which the creep rate accelerates to final fracture.
It is clearly vital that a material which is susceptible to creep effectsshould only be subjected to stresses which keep it in the secondary (straight line) region throughout its service life.
Definition of Fatigue
Fatigueis the failure of a material under fluctuating stresses each of which is believed to produce minute amounts of plastic strain.
Fatigue is particularly important in components subjected to repeated and often rapid loadfluctuations, e.g. aircraft components, turbine blades, vehicle suspensions, etc.
Fatigue behaviour of materials is usually described by a
fatigue life or S-N curve
in which the number of stress cycles N to produce failure
is plotted against S.
The particularly relevant feature of this curve is the limiting stress Snsince it is assumed that stresses below this value will not produce fatigue failure however many cycles are applied, i.e. there is infinite life.
In the simplest design cases, therefore, there is an aim to keep all stresses below this limiting level.
Determine the stress in each section of the bar shown in next Figure when subjected to an axial tensile load of 20 kN. The central section is 30 mm square cross-section; the other portions are of circular section, their diameters being indicated.
What will be the total extension of the bar? For the bar material E = 210GN/m2.
(a) A 25 mm diameter bar is subjected to an axial tensile load of 100 kN. Under the action of this load a 200mm gauge length is found to extend by the distance:
0.19 x 10-3 mm.
Determine the modulus of elasticity for the bar material.
The load can be assumed to remain constant at 100 kN.
Where: E = 210 GN/m2
and = 0.3
The coupling shown in next Figure is constructed from steel of rectangular cross-section and is designed to transmit a tensile force of 50 kN. If the bolt is of 15 mm diameter calculate:
(b) the direct stress in the plate;
(c) the direct stress in the forked end of the coupling.
(a) The bolt is subjected to double shear, tending to shear it as shown in Figure. There is thus twice the area of the bolt resisting the shear and from equation: