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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.
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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.
 
[[File:Army.mil-2007-02-07-153623.jpg| thumb|150 px|Measuring the compressive strength of a steel [[Drum (container)|drum ]]]]
Compressive strength is often measured on a [[universal testing machine]];  these  range from very small table-top systems  to ones with over 53 MN{{Elucidate|date=January 2014}} capacity.<ref>{{Citation
  | last = NIST
  | title = Large Scale Structure Testing Facility
  | url = http://www.nist.gov/bfrl/facilities_instruments/large_scale_struct_testing_fac.cfm
  | accessdate = 04-05-2010 | postscript =.}}</ref> 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 ==
 
[[Image:Tension applied.svg|thumb|30px|right|Tension]][[Image:Compression applied.svg|thumb|30px|right|Compression]]
 
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 [[compression (physical)|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==
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 (usually cylindrical) is shortened as well as spread [[wiktionary:lateral|laterally]]. A [[Stress–strain curve]] is plotted by the instrument and would look similar to the following:
 
[[Image:engineering stress strain.svg|thumb|True Stress-Strain curve for a typical specimen|centre]]
 
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 '''''<math>\sigma=E\epsilon</math>''''' 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 [[Plasticity (physics)| 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:
 
<math>\sigma = \frac{F}{A}</math>
 
where,
F = Load applied [N],
A = Area [m<sup>2</sup>]
 
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,
 
<math>\sigma_e = \frac{F}{A_0}</math>
 
A<sub>0</sub>=Original specimen area [m<sup>2</sup>]
 
Correspondingly, the engineering [[Strain (materials science)|strain]] would be defined by:
 
<math>\epsilon_e = \frac{l-l_0}{l_0}</math>
 
where
l = current specimen length [m] and l<sub>0</sub> = original specimen length [m]
 
The compressive strength would therefore correspond to the point on the engineering stress strain curve <math>(\epsilon_e^*,\sigma_e^*)</math> defined by
 
<math>\sigma_e^* = \frac{F^*}{A_0}</math>
 
<math>\epsilon_e^* = \frac{l^*-l_0}{l_0}</math>
 
where
F<sup>*</sup> = load applied just before crushing and l<sup>*</sup> = specimen length just before crushing.
 
== Deviation of engineering stress from true stress  ==
[[Image:Barelling.svg|75px|thumb|Barrelling]]
 
In engineering design practice they 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 A<sub>0</sub> 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 section (geometry)|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 (physical)]]
*[[Box compression test]]
*[[Deformation (engineering)]]
*[[Schmidt hammer]] (measuring compressive strength of concrete)
*[[Tensile strength]].
 
==References==
{{Reflist}}
 
* 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
 
{{DEFAULTSORT:Compressive Strength}}
[[Category:Materials science]]

Revision as of 20:20, 5 February 2014

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