How would you calculate the strain of a specimen?

Question

1, How would you calculate the strain of a specimen?

2, What are the units of strain?

3, how would i Sketch a typical stress versus strain graph for a brittle material?

any ideas? please help?

Answer 1

1.
(a) Strain e = change of length of a specimen under stress divided by its original length. Therefore, if you know its original length, and you can measure its change of length, you have its strain.

(b) Alternatively, the material's Modulus of Elasticity E is related to Stress f and Strain e by the equation:
E = f/e
Hence e = f/E
Therefore, if you know E and f, you can calculate the strain.

2. Strain is the ratio of two lengths. Therefore it is dimensionless.

3. The Stress/Strain curve of a brittle material is a straight line during the short elastic period, a very small drop off at the top, followed by failure. There is little or no plastic deformation before failure, depending on the brittleness of the specimen.

Answer 2

1. measure the change in length of the specimen under stress, versus the length under no stress. Take that delta (a very small length) and divide it by the length of the specimen. Example: a 1.00000 meter rod of steel is pulled with a tension and its length increases to 1.00001 meters. The strain would be 10 micrometers per meter, also called 10 micro-strain.

2. Strain is a dimensionless unit.

3. For most materials, stress (y-axis) versus strain (x-axis) is a linear relationship (straight line with a slope), up to a certain point, and then it changes shape depending on the material. Some materials will go "plastic" and the line will "flatten out"

Here is an example of a brittle material (bone) being compressed (strain also works in compression, not just tension):
http://depts.washington.edu/bonebio/ASBMRed/biomecha/bio.swf


NOTE: you generally don't calculate strain based on taking length measurements, you use a strain gauge attached to the specimen.

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Answer 3

There are laboratory machines to measure strain on prepared metal samples. Perhaps the simplest device is a Berry strain gage that mechanically magnifies the strain (elongation) between two points on the sample. The units of strain are inches/inch (and cancel). For example if you have a 1,000 inch rubber cable and stretch it one inch, the strain will be 1 inch per 1000 inches (0.001). The graph for strain in a brittle sample should be linear up to complete failure.