Difference between revisions of "Crack Settings"
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\sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | R(3\cos\theta - 1)\right|</math> | \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | R(3\cos\theta - 1)\right|</math> | ||
where R = K<sub>II</sub>/K<sub>I</sub>. The second term is 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. This method requires K<sub>I</sub> and K<sub>II</sub> which can only be done for isotropic | where R = K<sub>II</sub>/K<sub>I</sub>. The second term is 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. This method requires K<sub>I</sub> and K<sub>II</sub> which can only be done for isotropic (and subclasses), mooney, heisotropic (and subclass), and viscoelastic. All use initial, low strain modulus to calculate stress intensity factos. | ||
in cod hoop direction, the code uses the max energy release rate method, but assumes R = δ<sub>t</sub>/δ<sub>n</sub> or the sliding and opening crack opening displacements. This can be used for any material. | in cod hoop direction, the code uses the max energy release rate method, but assumes R = δ<sub>t</sub>/δ<sub>n</sub> or the sliding and opening crack opening displacements. This can be used for any material. | ||
Revision as of 10:15, 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 term is 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. This method requires KI and KII which can only be done for isotropic (and subclasses), mooney, heisotropic (and subclass), and viscoelastic. All use initial, low strain modulus to calculate stress intensity factos.
in cod hoop direction, the code uses the max energy release rate method, but assumes R = δt/δn or the sliding and opening crack opening displacements. This can be used for any material.