Editing Compressive strength (section)

== Introduction ==
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|image1=Tension applied.svg
|caption1=[[Tension (physics)|Tension]]
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|image2=Compression applied.svg
|caption2=[[Compression (physics)|Compression]]
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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, molecules or [[atoms]] are forced together when in compression, whereas they are pulled apart when in tension. 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 characterizes 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,<ref>{{Cite journal
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The ultimate compressive strength of a material is the maximum uniaxial [[compressive stress]] that it can withstand before complete failure. This value is typically determined through a compressive test conducted using a [[universal testing machine]]. During the test, a steadily increasing uniaxial compressive load is applied to the test specimen until it fails. The specimen, often cylindrical in shape, experiences both axial shortening and [[geometric terms of location|lateral]] expansion under the load. As the load increases, the machine records the corresponding deformation, plotting a [[Stress–strain curve|stress-strain curve]] that would look similar to the following:[[File:engineering stress strain.svg|thumb|left|True stress-strain curve for a typical specimen]]

The compressive strength of the material corresponds 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\varepsilon,</math> where, this time, {{mvar|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 display="block">\acute\sigma = \frac{F}{A},</math>where {{mvar|F}} is load applied [N] and {{mvar|A}} is 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. {{math|1=''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 display="block">\sigma_e = \frac{F}{A_0},</math>where {{math|''A''<sub>0</sub>}} is the original specimen area [m<sup>2</sup>].

Correspondingly, the engineering [[Strain (materials science)|strain]] is defined by<math display="block">\varepsilon_e = \frac{l -l_0}{l_0},</math>where {{mvar|l}} is the current specimen length [m] and {{math|''l''<sub>0</sub>}} is the original specimen length [m]. True strain, also known as logarithmic strain or natural strain, provides a more accurate measure of large deformations, such as in materials like ductile metals<ref name=":0">{{Cite book |last1=Benham |first1=P. P. |title=Mechanics of Solids and Structures |last2=Warnock |first2=F. V. |publisher=Pitman |year=1973 |isbn=0-273-36191-0}}</ref><math display="block">\acute \epsilon = \ln (l/l_o)=ln(1+\epsilon_e)</math>The compressive strength therefore corresponds to the point on the engineering stress–strain curve <math>\left(\varepsilon_e^*, \sigma_e^*\right)</math> defined by<math display="block">\sigma_e^* = \frac{F^*}{A_0}</math>
<math display="block">\varepsilon_e^* = \frac{l^* - l_0}{l_0},</math>

where {{math|''F''<sup>*</sup>}} is the load applied just before crushing and {{math|''l''<sup>*</sup>}} is the specimen length just before crushing.