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Name: Debabrata
Status: student
Grade: 9-12
Country: India
Date: Winter 2013-14

In stress - strain diagram, why stress is plotted in Y-axis and strain is plotted in X-axis?


It might seem that the experiment that produces a stress-strain curve is the application of a certain quantity of force (independent variable) and measuring the amount of deformation that results (strain, dependent variable). And sometimes, that is in fact what is done. However, historically, because stress-strain plots came from an engineering background where it was more important to know how much force was required to deform an object by a certain amount, then the independent variable was the amount of deformation -say 1mm in the x direction- and the question was how much force would be required to produce that deformation -making the stress the dependent variable.

In more recent times, we do both studies, but we have stuck with the historical format - much like we stick with the keyboards that was meant for mechanical typewriters, or some countries drive on the right or left side of the street.

Greg (Roberto Gregorius) Canisius College

This is arbitrary, but the convention is that FORCE (stress) is plotted on the Y axis and STRAIN (dimensional change) is plotted on the X- axis. As far as I know this is strictly arbitrary.

Vince Calder

Traditionally, the independent variable is plotted on the X axis and the Dependent variable on the Y axis. In this case, Strain is the independent variable, and Stress is the dependent. This may be counter-intuitive -- but it is a consequence of how the curves are generated. The machines that are used to generate these curves (usually large hydraulically operated gantries) control the distance moved (strain) and measure the force (stress) observed. Since stress is the key parameter that governs interesting phenomena, like bending and failure, it is the key quantity to be observed. Hence experiments are designed to determine the stress(es) at which these interesting phenomena occur. Thus, it is the dependent variable. Since strain is easily controlled and measured, it is the independent variable.

Hope this helps, Burr Zimmerman

Stress-strain diagrams are generally the result of a mechanical test of a material to determine its stiffness, strength, and other mechanical properties. These tests are normally carried out using displacement control - that is, you control the deformation of the material and measure the resultant force or stress. As such, the independent variable (the variable we 'control') is the strain, and is placed on the x-axis.

Because this is generally the case with mechanical tests, this has become the standard way of representing stress-strain information. It is, of course, quite possible to test a material using a force-controlled test, where a known force is applied to the material and the resultant displacement of the material is measured. Even in such a circumstance, however, the data is normally displayed following the convention of stress on the y-axis and strain on the x-axis.

Another potential reason tied to the choice of stress-strain diagrams is that the slope of this diagram corresponds to the elastic modulus of the material; the slope of the strain-stress diagram would correspond to the inverse of the elastic modulus. Given that people normally discuss the modulus of a material and not its inverse, it makes sense to plot the diagram following the convention rather than the other way around.

Shimon Unterman Ph.D.

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