Finding 0.2% offset strain

This one is intended mostly for folks who break things. Specifically, structural engineers who pull on steel (or other ductile metal) bars until they fail. From Wikipedia:

Ductile metals do not have a well defined yield point. The yield strength is typically defined by the "0.2% offset strain". The yield strength at 0.2% offset is determined by finding the intersection of the stress-strain curve with a line parallel to the initial slope of the curve and which intercepts the abscissa at 0.2%.

The question, then, is "Is there an easy way to determine the 0.2% offset strain line, without a calculator handy?" Yes, there is. Shown below is a typical stress-strain curve, in this case for a rolled steel bar.

The first step is to find the slope of the elastic portion of the stress-strain curve. You can do that very easily with the Distance from... command on the Info menu. Ensure that Snap cursor to nearest data point is checked, then drag the mouse from a point near the origin along the initial (hopefully linear) slope:

To avoid retyping (and transcription errors), drag your mouse over the "slope" value, right-click and select "Copy". Now select the Y=f(X) command on the Generate menu. The equation we want is simply (in this case) "21.6569856057*(x-2000)" (2000 microinches/inch = 0.2% strain). For the from X value use 2000 (or any smaller value); for to X use a strain value large enough that the line will be certain to cross the stress-strain curve. You can then zoom in if you overshoot the curve by a lot. The with interval dX entry isn't critical, since you'll be generating a straight line.

Finally, select Find Intersections... on the Info menu. (If this command is disabled you likely need to sort the data points with the Sort command on the Edit menu.) Check the Insert data points... and Add labels at intersections boxes, and you get:

... indicating a yield stress of ~70.5ksi at a strain of ~0.005.

Thanks much to Stephen Rowell for his input on this one.

About this Entry

This page contains a single entry by David Hyde published on June 18, 2009 5:15 PM.

Ternary plot options for rocks was the previous entry in this blog.

Offsetting a curve is the next entry in this blog.

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