Stress

Stress is force per unit area.

In MKS this is Newtons per square meter.

N = \dfrac {kg \: m}{s^2}

\dfrac {N} {m^2} = \dfrac {kg \: m} {s^2} \dfrac {1}{m^2} = \dfrac {kg}{m \: s^2}

A material may be tested for tensile stress building a sample with known dimensions and pulling it. The instrument is built to pull at a constant speed and it measures the force.

The distance the machine has moved is compare to the length of the sample in the direction of the pull. If a sample with a length of 2 cm has been stretched 2 mm we call that a strain of 10%. It should make sense that if the sample had a length of 3 cm then we would be at the same strain when it has been pulled 3 mm.

Assume our sample has a width of one cm and a thickness of 2 mm. We need to convert this to square meters:

1 cm * 2 mm * \dfrac {1 m}{100 cm} * \dfrac {1 m }{1000 mm} = 0.00002 m^2

If the load cell of the Instron tells us that the force was 20 N, then the stress was 1,000,000 N/m^2.

It is typical to use units of Pascals for pressure:

1 Pa = 1 \dfrac {N}{m^2}

For testing a polymer such as PMMA, a graph of stress vs. strain is a straight line at first. The value for the slope of this line is Young’s Modulus.