Difference between revisions of "Crack Settings"
Jump to navigation
Jump to search
| Line 4: | Line 4: | ||
| | ||
<math>\cos\theta = { | <math>\cos\theta = {3R^2 + \sqrt{1+8R^2} \over 1+9R^2} \quad {\rm and} \quad | ||
\sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | | \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | R(3\cos\theta - 1)\right|</math> | ||
The second terms in negative or positive depending on K<sub>II</sub> being positive or negative. | where R = K<sub>II</sub>/K<sub>I</sub>. The second terms in negative or positive depending on K<sub>II</sub> being positive or negative. In the limit of K<sub>I</sub> to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees. | ||
Revision as of 09:31, 19 September 2013
This section needs writing. Below are some items that will be used or move else where.
In max energy release rate (or max hoop stress), the crack direction is at angle θ (which is ccw from self similar growth) and obeys
[math]\displaystyle{ \cos\theta = {3R^2 + \sqrt{1+8R^2} \over 1+9R^2} \quad {\rm and} \quad \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | R(3\cos\theta - 1)\right| }[/math]
where R = KII/KI. The second terms in negative or positive depending on KII being positive or negative. In the limit of KI to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees.