Orthotropic Failure Surface - Revision history

Nairnj: /* Failure Surface */

2020-02-21T06:09:48Z

Failure Surface

← Older revision		Revision as of 06:09, 21 February 2020
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	<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>		<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>

	The crack that forms is in the i direction with normal in the <math>~~\vec~~{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} < \tau_{ij,j}^{(c)}</math>, otherwise the crack normal is in the <math>~~\vec~~{\hat i}</math> direction.		The crack that forms is in the i direction with normal in the <math>{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} < \tau_{ij,j}^{(c)}</math>, otherwise the crack normal is in the <math>{\hat i}</math> direction.

	== Damage Law Properties ==		== Damage Law Properties ==

Nairnj: /* Failure Surface */

2020-02-21T06:09:07Z

Failure Surface

← Older revision		Revision as of 06:09, 21 February 2020
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	== Failure Surface ==		== Failure Surface ==

	This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material directions. Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:		This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material directions. Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:

Nairnj: /* Failure Surface */

2020-02-21T06:08:31Z

Failure Surface

← Older revision		Revision as of 06:08, 21 February 2020
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	== Failure Surface ==		== Failure Surface ==

	This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material ~~direction~~ Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:		This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material directions. Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:

Nairnj: /* Failure Surface */

2020-02-21T06:08:08Z

Failure Surface

← Older revision		Revision as of 06:08, 21 February 2020
Line 6:		Line 6:
	== Failure Surface ==		== Failure Surface ==

	This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material ~~direciton~~		This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material direction Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:

	Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:

Nairnj: /* Damage Law Properties */

2020-02-21T06:07:20Z

Damage Law Properties

← Older revision		Revision as of 06:07, 21 February 2020
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	! Property !! Description !! Units !! Default		! Property !! Description !! Units !! Default
	\|-		\|-
	\| ~~sigmacA~~ \|\| Critical stress for failure in the ~~axial~~ direction ~~(output as <tt>sigcA</tt>)~~ \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite		\| sigmaXXc \|\| Critical stress for failure by tension in the material x direction \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
	\|-		\|-
	\| ~~sigmac~~ \|\|Critical ~~transverse tensile strength~~ for ~~tensile~~ failure in the ~~isotropic plane (output as <tt>sigcT</tt>)~~ \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite		\| sigmaYYc \|\| Critical stress for failure by tension in the material y direction \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
	\|-		\|-
	\| ~~taucA~~ \|\| Critical ~~shear~~ stress for failure ~~due to axial shear stress with failure parallel to~~ the ~~axial~~ direction \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite		\| sigmaZZc \|\| Critical stress for failure by tension in the material z direction \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
	\|-		\|-
	\| ~~taucT~~ \|\| Critical ~~shear~~ stress for failure ~~due to axial~~ shear ~~stress~~ with ~~failure through~~ the ~~axial~~ direction \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite		\| tauXY-Xc \|\| Critical stress for failure by shear in the material x-y plane. The crack that forms is in the x direction with normal in the y direction. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
	\|-		\|-
	\| ~~tauc~~ \|\|Critical ~~transverse~~ shear stress for shear failure n the ~~isotropic~~ plane ~~(output as <tt>taucRS</tt>)~~ \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite		\| tauXY-Yc \|\| Critical stress for failure by shear in the material x-y plane. The crack that forms is in the y direction with normal in the x direction. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
			\|-
			\| tauXZ-Xc \|\| Critical stress for failure by shear in the material x-z plane. The crack that forms is in the x direction with normal in the z direction. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
			\|-
			\| tauXZ-Zc \|\| Critical stress for failure by shear in the material x-z plane. The crack that forms is in the z direction with normal in the x direction. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
			\|-
			\| tauYZ-Yc \|\| Critical stress for failure by shear in the material y-z plane. The crack that forms is in the y direction with normal in the z direction. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
			\|-
			\| tauYZ-Zc \|\| Critical stress for failure by shear in the material y-z plane. The crack that forms is in the z direction with normal in the y direction. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| infinite
	\|}		\|}

	Notice this law has two axial shear strengths (<tt>taucA</tt> and <tt>taucT</tt>). If failure occurs by shear in a plane parallel to the axial direction, the failure and crack orientation will be determined by the minimum of taucA and taucT. Even though the maximum value is never used to initiate failure, ~~it is~~ still needed for damage evolution. For example, in wood, <tt>taucA</tt> is called "shear parallel strength", <tt>tauT</tt> is called "shear perpendicular strength", and <tt>tauc</tt> is called "rolling shear strength". For wood, <tt>tauT</tt> is much larger than <tt>taucA</tt>, which means shear failure is by shear cracks parallel to the wood fibers in the axial direction. But, if the ~~wood~~ initiates failure by tension ~~parallel tot he fibers and then is loaded~~ in ~~shear~~, the shear damage evolution will be determined by softening ~~law~~ based on ~~<tt>tauT</tt>~~.		Even though the maximum shear value for each ij plane is never used to initiate failure, they are still needed for damage evolution. For example, if the material initiates failure by tension in the x direction, the shear damage evolution will be determined by softening laws based on shear strengths with the same normal (''i.e.'', tauXY-Yc and tauXZ-Zc) even if they are larger that the other shear strengths for those planes.

Nairnj: /* Failure Surface */

2020-02-21T05:54:13Z

Failure Surface

← Older revision		Revision as of 05:54, 21 February 2020
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	<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>		<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>

	The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} ~~\lt~~ \tau_{ij,j}^{(c)}</math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.		The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} < \tau_{ij,j}^{(c)}</math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.

	== Damage Law Properties ==		== Damage Law Properties ==

Nairnj: /* Failure Surface */

2020-02-21T05:53:52Z

Failure Surface

← Older revision		Revision as of 05:53, 21 February 2020
Line 13:		Line 13:
	<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>		<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>

	The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} \tau_{ij,j}^{(c)}<\math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.		The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} \lt \tau_{ij,j}^{(c)}</math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.

	== Damage Law Properties ==		== Damage Law Properties ==

Nairnj: /* Failure Surface */

2020-02-21T05:53:25Z

Failure Surface

← Older revision		Revision as of 05:53, 21 February 2020
Line 13:		Line 13:
	<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>		<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>

	The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)}<\tau_{ij,j}^{(c)}<\math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.		The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)} \tau_{ij,j}^{(c)}<\math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.

	== Damage Law Properties ==		== Damage Law Properties ==

Nairnj: /* Failure Surface */

2020-02-21T05:52:54Z

Failure Surface

← Older revision		Revision as of 05:52, 21 February 2020
Line 13:		Line 13:
	<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>		<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>

	The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)}~~\lt~~\tau_{ij,j}^{(c)}<\math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.		The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)}<\tau_{ij,j}^{(c)}<\math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.

	== Damage Law Properties ==		== Damage Law Properties ==

Nairnj at 05:52, 21 February 2020

2020-02-21T05:52:22Z

← Older revision		Revision as of 05:52, 21 February 2020
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	This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material direciton		This failure surface has nine failure properties. First, are three tensile strengths <math>\sigma_{ii}^{(c)}</math> where i is x, y, or z that give tensile strength in the three material direciton

	Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz)~~. When shear in one of these reaches this stress, the material initiates damage~~. The second index ~~give~~ the direction of the shear crack in that plane. ~~For example,~~		Second, are six shear strengths <math>\tau_{ij,i}^{(c)}</math> that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:

	<math> \tau_{ij} > \min\bigl(\tau_{ij}^{(i,c)},\tau_{ij~~}^{(j~~,~~c)}\bigr) \ &{\rm with}\~~
	~~\hat{\vec n} = \left\{ \begin{array}{ll}~~		<math>\tau_{ij} > \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr)</math>
	~~\vec{\hat~~ j~~} & {\rm if}\ \tau_{ij~~}^{(i,c)}<\~~tau_{ij}^{(j,c~~)~~} \\~~
	~~\vec{\hat i} & {\rm if}\ \tau_{ij}^{(i,c)}>\tau_{ij}^{(j,c)}~~
	~~\end{array}\right.~~
	</math>

	The ~~first two shear strength are for failure at maximum shear stress~~ in ~~planes parallel to~~ the ~~axial direction. When failure occurs in such a plane, the resulting crack will either be parallel to the axial~~ direction with normal in ~~transverse~~ direction (if <math>\~~tau_A~~ < \~~tau_T</~~math>~~) or parallel to~~ the ~~transverse direction with~~ normal in the ~~axial direction (if~~ <math>\~~tau_T<~~ \~~tau_A~~</math>~~) . The last shear strength is for failure in the isotropic plane, which occurs in the maximum shear stress~~ direction ~~in that plane~~.		The crack that forms is in the i direction with normal in the <math>\vec{\hat j}</math> direction if <math>\tau_{ij,i}^{(c)}\lt\tau_{ij,j}^{(c)}<\math>, otherwise the crack normal is in the <math>\vec{\hat i}</math> direction.

	== Damage Law Properties ==		== Damage Law Properties ==