In the study of strength of materials, the compressive strength is the capacity of a
material or structure to withstand loads tending to reduce size.
It can be measured by plotting applied force against deformation in a testing machine.
Some material fracture at their compressive strength limit; others deform irreversibly,
so a given amount of deformation may be considered as the limit for compressive load.
Compressive strength is a key value for design of structures.
Compressive strength is often measured on a universal testing machine; these range from
very small table-top systems to ones with over 53 MN capacity.
Measurements of compressive strength are affected by the specific test method and conditions
of measurement.
Compressive strengths are usually reported in relationship to a specific technical standard.
Introduction
When a specimen of material is loaded in such a way that it extends it is said to be in
tension.
On the other hand if the material compresses and shortens it is said to be in compression.
On an atomic level, the molecules or atoms are forced apart when in tension whereas in
compression they are forced together.
Since atoms in solids always try to find an equilibrium position, and distance between
other atoms, forces arise throughout the entire material which oppose both tension or compression.
The phenomena prevailing on an atomic level are therefore similar.
The "strain" is the relative change in length under applied stress; positive strain characterises
an object under tension load which tends to lengthen it, and a compressive stress that
shortens an object gives negative strain.
Tension tends to pull small sideways deflections back into alignment, while compression tends
to amplify such deflection into buckling.
Compressive strength is measured on materials, components, and structures.
By definition, the ultimate compressive strength of a material is that value of uniaxial compressive
stress reached when the material fails completely.
The compressive strength is usually obtained experimentally by means of a compressive test.
The apparatus used for this experiment is the same as that used in a tensile test.
However, rather than applying a uniaxial tensile load, a uniaxial compressive load is applied.
As can be imagined, the specimen is shortened as well as spread laterally.
A Stress–strain curve is plotted by the instrument and would look similar to the following:
The compressive strength of the material would correspond to the stress at the red point
shown on the curve.
In a compression test, there is a linear region where the material follows Hooke's Law.
Hence for this region where this time E refers to the Young's Modulus for compression.
In this region, the material deforms elastically and returns to its original length when the
stress is removed.
This linear region terminates at what is known as the yield point.
Above this point the material behaves plastically and will not return to its original length
once the load is removed.
There is a difference between the engineering stress and the true stress.
By its basic definition the uniaxial stress is given by:
where, F = Load applied [N], A = Area [m2] As stated, the area of the specimen varies
on compression.
In reality therefore the area is some function of the applied load i.e.
A = f(F).
Indeed, stress is defined as the force divided by the area at the start of the experiment.
This is known as the engineering stress and is defined by,
A0=Original specimen area [m2] Correspondingly, the engineering strain would
be defined by:
where l = current specimen length [m] and l0 = original specimen length [m]
The compressive strength would therefore correspond to the point on the engineering stress strain
curve defined by
where F* = load applied just before crushing and l* = specimen length just before crushing.
Deviation of engineering stress from true stress
In engineering design practice, professionals mostly rely on the engineering stress.
In reality, the true stress is different from the engineering stress.
Hence calculating the compressive strength of a material from the given equations will
not yield an accurate result.
This is because the cross sectional area A0 changes and is some function of load A = φ(F).
The difference in values may therefore be summarized as follows:
On compression, the specimen will shorten.
The material will tend to spread in the lateral direction and hence increase the cross sectional
area.
In a compression test the specimen is clamped at the edges.
For this reason, a frictional force arises which will oppose the lateral spread.
This means that work has to be done to oppose this frictional force hence increasing the
energy consumed during the process.
This results in a slightly inaccurate value of stress which is obtained from the experiment.
As a final note, it should be mentioned that the frictional force mentioned in the second
point is not constant for the entire cross section of the specimen.
It varies from a minimum at the centre to a maximum at the edges.
Due to this a phenomenon known as barrelling occurs where the specimen attains a barrel
shape.
Comparison of compressive and tensile strengths Concrete and ceramics typically have much
higher compressive strengths than tensile strengths.
Composite materials, such as glass fiber epoxy matrix composite, tend to have higher tensile
strengths than compressive strengths.
See also Compression
Box compression test Deformation
Schmidt hammer Tensile strength
References
Mikell P.Groover, Fundamentals of Modern Manufacturing, John Wiley & Sons, 2002 U.S.A, ISBN 0-471-40051-3
Callister W.D.
Jr., Materials Science & Engineering an Introduction, John Wiley & Sons, 2003 U.S.A, ISBN 0-471-22471-5