Crack Propagation Commands - Revision history

Nairnj: /* References */

2026-03-28T02:23:37Z

References

← Older revision		Revision as of 02:23, 28 March 2026
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	== References ==		== References ==
	<references>		<references>
	<ref name="icracks">J. A. Nairn and Y. E. Aimene, "Modeling Multiple Crack Propagation in the Material Point Method by J-Integral Methods Accounting for Other Cracks Intersecting the J Contour," ''Engineering Fracture Mechanics'', '''322''', 111143 (2025).</ref>		<ref name="icracks">J. A. Nairn and Y. E. Aimene, "Modeling Multiple Crack Propagation in the Material Point Method by J-Integral Methods Accounting for Other Cracks Intersecting the J Contour," ''Engineering Fracture Mechanics'', '''322''', 111143 (2025). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/InteractingCracks.pdf See PDF])</ref>

	<ref name="hoop">F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” ''ASME Journal of Basic Engineering,'' '''85''', 519–527 (1963).</ref>		<ref name="hoop">F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” ''ASME Journal of Basic Engineering,'' '''85''', 519–527 (1963).</ref>

Nairnj: /* Crack Propagation Criterion */

2026-03-28T02:18:23Z

Crack Propagation Criterion

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	=== Crack Propagation Criterion ===		=== Crack Propagation Criterion ===

	The crack propagation is controlled by crack tip [[#Crack Tip Materials\|material fracture properties]] and by one of the following fracture criteria (which can be set by number or name, although <tt>XML</tt> files must use a number). Note that any method that ses energy releae rate or stress intensity factors finds those terms using J integral methods. A unique feature is that CRAMP methods can find J integral even for interacting cracks in which the J contour intersects other cracks <ref name="~~icrack~~"/>.		The crack propagation is controlled by crack tip [[#Crack Tip Materials\|material fracture properties]] and by one of the following fracture criteria (which can be set by number or name, although <tt>XML</tt> files must use a number). Note that any method that ses energy releae rate or stress intensity factors finds those terms using J integral methods. A unique feature is that CRAMP methods can find J integral even for interacting cracks in which the J contour intersects other cracks <ref name="icracks"/>.

	<ul>		<ul>

Nairnj: /* Crack Propagation Criterion */

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Crack Propagation Criterion

← Older revision		Revision as of 02:17, 28 March 2026
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	=== Crack Propagation Criterion ===		=== Crack Propagation Criterion ===

	The crack propagation is controlled by crack tip [[#Crack Tip Materials\|material fracture properties]] and by one of the following fracture criteria (which can be set by number or name, although <tt>XML</tt> files must use a number). Note that any method that ses energy releae rate or stress intensity factors finds those terms using J integral methods. A unique feature is that CRAMP methods can find J integral even for interacting cracks in which the ~~Jj countour~~ intersects other cracks.		The crack propagation is controlled by crack tip [[#Crack Tip Materials\|material fracture properties]] and by one of the following fracture criteria (which can be set by number or name, although <tt>XML</tt> files must use a number). Note that any method that ses energy releae rate or stress intensity factors finds those terms using J integral methods. A unique feature is that CRAMP methods can find J integral even for interacting cracks in which the J contour intersects other cracks <ref name="icrack"/>.

	<ul>		<ul>

Nairnj: /* References */

2026-03-28T02:15:38Z

References

← Older revision		Revision as of 02:15, 28 March 2026
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	== References ==		== References ==
	<references>		<references>
			<ref name="icracks">J. A. Nairn and Y. E. Aimene, "Modeling Multiple Crack Propagation in the Material Point Method by J-Integral Methods Accounting for Other Cracks Intersecting the J Contour," ''Engineering Fracture Mechanics'', '''322''', 111143 (2025).</ref>

	<ref name="hoop">F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” ''ASME Journal of Basic Engineering,'' '''85''', 519–527 (1963).</ref>		<ref name="hoop">F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” ''ASME Journal of Basic Engineering,'' '''85''', 519–527 (1963).</ref>

Nairnj: /* Crack Propagation Criterion */

2026-03-28T02:14:25Z

Crack Propagation Criterion

← Older revision		Revision as of 02:14, 28 March 2026
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	=== Crack Propagation Criterion ===		=== Crack Propagation Criterion ===

	The crack propagation is controlled by crack tip [[#Crack Tip Materials\|material fracture properties]] and by one of the following fracture criteria (which can be set by number or name, although <tt>XML</tt> files must use a number):		The crack propagation is controlled by crack tip [[#Crack Tip Materials\|material fracture properties]] and by one of the following fracture criteria (which can be set by number or name, although <tt>XML</tt> files must use a number). Note that any method that ses energy releae rate or stress intensity factors finds those terms using J integral methods. A unique feature is that CRAMP methods can find J integral even for interacting cracks in which the Jj countour intersects other cracks.

	<ul>		<ul>

Nairnj: /* Crack Propagation Criterion */

2023-11-09T00:40:03Z

Crack Propagation Criterion

← Older revision		Revision as of 00:40, 9 November 2023
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	<br><br>		<br><br>

	<math>K_{I}^{(max)} = K_I \cos^3\frac{\theta}{2} - \frac{3}{2}\cos\frac{\theta}{2}\sin\theta \ge K_{Ic}</math>		<math>K_{I}^{(max)} = K_I \cos^3\frac{\theta}{2} - \frac{3}{2}K_{II}\cos\frac{\theta}{2}\sin\theta \ge K_{Ic}</math>
	<br><br>		<br><br>
	where K<sub>I</sub> and K<sub>II</sub> and the partitioned stress intensity factors for the current crack tip <ref name="hoop"/>. This criterion requires an [[#tipmat\|isotropic crack tip material]] because calculation of maximum K<sub>I</sub> and hoop stress direction assumes isotropic crack tip stresses.		where K<sub>I</sub> and K<sub>II</sub> and the partitioned stress intensity factors for the current crack tip <ref name="hoop"/>. This criterion requires an [[#tipmat\|isotropic crack tip material]] because calculation of maximum K<sub>I</sub> and hoop stress direction assumes isotropic crack tip stresses.

Nairnj: /* Maximum Hoop Stress Direction */

2023-11-03T21:06:49Z

Maximum Hoop Stress Direction

← Older revision		Revision as of 21:06, 3 November 2023
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	<math>\tan {\theta\over 2} = {1\over 4}\left({1\over R} \mp \sqrt{{1\over R^2} + 8}\right)</math>		<math>\tan {\theta\over 2} = {1\over 4}\left({1\over R} \mp \sqrt{{1\over R^2} + 8}\right)</math>

	where the sign on the square root is determined by sign of K<sub>II</sub>. This equation gives identical results to the equation above. Because the crack propagation needs to know the ~~normal~~ vector (cos θ, sin θ), however, coding is more efficient to get them directly from the previous equations than ~~to use~~ this alternate form.		where the sign on the square root is determined by sign of K<sub>II</sub>. This equation gives identical results to the equation above. Because the crack propagation needs to know the propagation direction unit vector (cos θ, sin θ), however, coding is more efficient to get them directly from the previous equations rather than this alternate form.

	==== Minimum Strain Energy Density Direction ====		==== Minimum Strain Energy Density Direction ====

Nairnj: /* Maximum Hoop Stress Direction */

2023-11-03T21:05:45Z

Maximum Hoop Stress Direction

← Older revision		Revision as of 21:05, 3 November 2023
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	<math>\tan {\theta\over 2} = {1\over 4}\left({1\over R} \mp \sqrt{{1\over R^2} + 8}\right)</math>		<math>\tan {\theta\over 2} = {1\over 4}\left({1\over R} \mp \sqrt{{1\over R^2} + 8}\right)</math>

	where the sign on the square root is determined by sign of K<sub>II</sub>. This equation gives identical results to the equation above. Because the crack propagation ~~only~~ needs to know the normal vector (cos θ, sin θ), however, it is more efficient to ~~evaluate~~ them directly than to use ~~one triginometric equation to find θ followed by more trigonometric functions to find the unit vector~~.		where the sign on the square root is determined by sign of K<sub>II</sub>. This equation gives identical results to the equation above. Because the crack propagation needs to know the normal vector (cos θ, sin θ), however, coding is more efficient to get them directly from the previous equations than to use this alternate form.

	==== Minimum Strain Energy Density Direction ====		==== Minimum Strain Energy Density Direction ====

Nairnj: /* Maximum Hoop Stress Direction */

2023-11-03T21:03:53Z

Maximum Hoop Stress Direction

← Older revision		Revision as of 21:03, 3 November 2023
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	\sin\theta = - R(3\cos\theta - 1)</math>		\sin\theta = - R(3\cos\theta - 1)</math>

	where R = K<sub>II</sub>/abs(K<sub>I</sub>). In other words, the crack growth is along the vector (cos θ, sin θ) relative to the crack tip coordinate system with $\theta$ the clockwise rotation angle. In the limit of K<sub>I</sub> to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees. In the limit of K<sub>II</sub> to zero, cos θ = 1 for crack direction 0 or self-similar crack propagation. This method requires K<sub>I</sub> and K<sub>II</sub> which can only be done for [[#tipmat\|isotropic materials]]. For anisotropic materials, a variant of the maximum hoop direction is the [[#Crack Propagation Direction\|"<tt>cod hoop</tt>"]] method, which uses the same approach except that R is calculated from R = δ<sub>t</sub>/abs(δ<sub>n</sub>). The following figure ~~defines~~ crack growth ~~angle and plot that~~ angle as a function of R.		where R = K<sub>II</sub>/abs(K<sub>I</sub>). In other words, the crack growth is along the vector (cos θ, sin θ) relative to the crack tip coordinate system with $\theta$ the clockwise rotation angle. In the limit of K<sub>I</sub> to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees. In the limit of K<sub>II</sub> to zero, cos θ = 1 for crack direction 0 or self-similar crack propagation. This method requires K<sub>I</sub> and K<sub>II</sub> which can only be done for [[#tipmat\|isotropic materials]]. For anisotropic materials, a variant of the maximum hoop direction is the [[#Crack Propagation Direction\|"<tt>cod hoop</tt>"]] method, which uses the same approach except that R is calculated from R = δ<sub>t</sub>/abs(δ<sub>n</sub>). The following figure plots crack growth angle as a function of R.

	[[File:Hoopdir.png\|center]]		[[File:Hoopdir.png\|center]]

Nairnj: /* Maximum Hoop Stress Direction */

2023-11-03T21:02:44Z

Maximum Hoop Stress Direction

← Older revision		Revision as of 21:02, 3 November 2023
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	\sin\theta = - R(3\cos\theta - 1)</math>		\sin\theta = - R(3\cos\theta - 1)</math>

	where R = K<sub>II</sub>/abs(K<sub>I</sub>). In other words, the crack growth is along the vector (cos θ, sin θ) relative to the crack tip coordinate system. In the limit of K<sub>I</sub> to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees. In the limit of K<sub>II</sub> to zero, cos θ = 1 for crack direction 0 or self-similar crack propagation. This method requires K<sub>I</sub> and K<sub>II</sub> which can only be done for [[#tipmat\|isotropic materials]]. For anisotropic materials, a variant of the maximum hoop direction is the [[#Crack Propagation Direction\|"<tt>cod hoop</tt>"]] method, which uses the same approach except that R is calculated from R = δ<sub>t</sub>/abs(δ<sub>n</sub>). The following figure defines crack growth angle and plot that angle as a function of R.		where R = K<sub>II</sub>/abs(K<sub>I</sub>). In other words, the crack growth is along the vector (cos θ, sin θ) relative to the crack tip coordinate system with $\theta$ the clockwise rotation angle. In the limit of K<sub>I</sub> to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees. In the limit of K<sub>II</sub> to zero, cos θ = 1 for crack direction 0 or self-similar crack propagation. This method requires K<sub>I</sub> and K<sub>II</sub> which can only be done for [[#tipmat\|isotropic materials]]. For anisotropic materials, a variant of the maximum hoop direction is the [[#Crack Propagation Direction\|"<tt>cod hoop</tt>"]] method, which uses the same approach except that R is calculated from R = δ<sub>t</sub>/abs(δ<sub>n</sub>). The following figure defines crack growth angle and plot that angle as a function of R.

	[[File:Hoopdir.png\|center]]		[[File:Hoopdir.png\|center]]