Users:General FEM Analysis/Materials Reference/Tsai-Wu Failure Criterion

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== General Description ==
 
== General Description ==
  
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It is a practically simple failure criterion which takes interaction of stresses in different directions into account by making use of strength tensors. It is considerably cheaper in computational effort compared to Puck criterion especially in 3D stress states. A drawback of this criterion is that it is based on von Mises criterion which is more suitable for ductile materials. 2D and 3D formulations are implemented into Carat++. As it can not distinguish between different fracture modes, Tsai-Wu Criterion returns one failure index for corresponding failure analysis.
+
Tsai-Wu Failure Criterion
 +
<ref>
 +
S. W. Tsai and E. M. Wu. A General Theory of Strength for Anisotropic Materials. Journal of
 +
Composite Materials, 5(1):58–80, January 1971.
 +
</ref>
 +
is a practically simple failure criterion which takes interaction of stresses in different directions into account by making use of strength tensors. It is considerably cheaper in computational effort compared to Puck criterion especially in 3D stress states. A drawback of this criterion is that it is based on von Mises criterion which is more suitable for ductile materials. 2D and 3D formulations are implemented into Carat++. As it can not distinguish between different fracture modes, Tsai-Wu Criterion returns one failure index for corresponding failure analysis.
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 +
 
 +
== Tsai-Wu Fracture Condition Function ==
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 +
 
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[[File:Tsai-wu fracture condition function.png|350px]]
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 +
 
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== Tsai-Wu in 2D ==
 +
 
 +
=== Strength Analysis ===
 +
 
 +
Fracture envelope for a 2D failure analysis:
 +
<ref>
 +
Altug Emiroglu, Master Thesis: Comparative Study of Puck and Tsai-Wu Failure Criteria, Technische Universität München, 2013.
 +
</ref>
 +
 
 +
[[File:tsai-wu_2D.png|400px]]
  
 
=== Parameter Description ===
 
=== Parameter Description ===
  
 
{| border="1" cellpadding="3" cellspacing="0"
 
{| border="1" cellpadding="3" cellspacing="0"
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|colspan="3" style="background:#efefef;"|  '''Tsai-Wu Parameters (2D)'''
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|-
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|colspan="3" style="background:#efefef;"| Compulsory Parameters
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|-
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!Parameter
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!Values, Default(*)
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!Description
 +
|-
 +
!T11
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|real
 +
|Resistance to longitudinal tension (Direction 1)
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|-
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!C11
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|real
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|Resistance to longitudinal compression (Direction 1)
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|-
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!T22
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|real
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|Resistance to transverse tension (Direction 2)
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|-
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!C22
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|real 
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|Resistance to transverse compression (Direction 2)
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|-
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!S12
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|real
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|Resistance to longitudinal shear
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|-
 +
         
 +
 
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|colspan="3" style="background:#efefef;"| Optional Parameters
 +
|-
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!Parameter
 +
!Values, Default(*)
 +
!Description
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|-
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!STRESS TYPE
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|2D, 3D
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|Indicates what kind of stress state should be used to calculate the failure condition. When not given, related element’s stress type is taken.
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|-
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!T33
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|real
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|Resistance to tension in thickness direction (Direction 3) (''De f ault'' = T22)
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|-
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!C33
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|real
 +
|Resistance to compression in thickness direction (Direction 3) (''De f ault'' = C22)
 +
|-
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!S13
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|real
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|Resistance to longitudinal shear (''De f ault'' = S 12)
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|-
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!FS12
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|real
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|Coefficient, necessary for calculation of F12. (''De f ault'' = -0.5)
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|-
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!F12
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|real
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|F<sub>12</sub> component of strength tensor; F<sub>ij</sub>. When not given, it is calculated using FS12.
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|-
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!P
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|real
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|Strength value, necessary for calculation of F12. See Section 3.2.3
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|-
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!U
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|real
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|Strength value, necessary for calculation of F12. See Section 3.2.3
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|-
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!V
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|real
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|Strength value, necessary for calculation of F12. See Section 3.2.3
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|-
 +
|-
 +
|-
 +
|}
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 +
 +
== Tsai-Wu in 3D ==
 +
 +
=== Strength Analysis ===
 +
 +
Fracture envelopes for a 3D failure analysis:
 +
<ref>
 +
Altug Emiroglu, Master Thesis: Comparative Study of Puck and Tsai-Wu Failure Criteria, Technische Universität München, 2013.
 +
</ref>
 +
 +
[[File:tsai-wu_3D.png|800px]]
 +
 +
=== Parameter Description ===
 +
 +
 +
{| border="1" cellpadding="3" cellspacing="0"
 +
|colspan="3" style="background:#efefef;"|  '''Tsai-Wu Parameters (3D)'''
 +
|-
 
|colspan="3" style="background:#efefef;"| Compulsory Parameters
 
|colspan="3" style="background:#efefef;"| Compulsory Parameters
 
|-
 
|-
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!F12
 
!F12
 
|real
 
|real
−
|F12 component of strength tensor; Fi j. When not given, it is calculated using FS12.
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|F<sub>12</sub> component of strength tensor; F<sub>ij</sub>. When not given, it is calculated using FS12.
 
|-
 
|-
 
!P  
 
!P  
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!F13
 
!F13
 
|real
 
|real
−
|F12 component of strength tensor; Fi j. When not given, it is calculated using FS13.
+
|F<sub>12</sub> component of strength tensor; F<sub>ij</sub>. When not given, it is calculated using FS13.
 
|-
 
|-
 
!FS23
 
!FS23
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!F23
 
!F23
 
|real
 
|real
−
|F12 component of strength tensor; Fi j. When not given, it is calculated using FS23.
+
|F<sub>12</sub> component of strength tensor; F<sub>ij</sub>. When not given, it is calculated using FS23.
 
|-
 
|-
 
|-
 
|-
 
|-
 
|-
 
|}
 
|}
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 +
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== Example of a Complete Input Block ==
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[[File:input_tsai-wu.png|500px]]
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== References ==
 +
<references/>

Latest revision as of 10:07, 15 February 2013

Contents

General Description

Tsai-Wu Failure Criterion [1] is a practically simple failure criterion which takes interaction of stresses in different directions into account by making use of strength tensors. It is considerably cheaper in computational effort compared to Puck criterion especially in 3D stress states. A drawback of this criterion is that it is based on von Mises criterion which is more suitable for ductile materials. 2D and 3D formulations are implemented into Carat++. As it can not distinguish between different fracture modes, Tsai-Wu Criterion returns one failure index for corresponding failure analysis.


Tsai-Wu Fracture Condition Function

Tsai-wu fracture condition function.png


Tsai-Wu in 2D

Strength Analysis

Fracture envelope for a 2D failure analysis: [2]

Tsai-wu 2D.png

Parameter Description

Tsai-Wu Parameters (2D)
Compulsory Parameters
Parameter Values, Default(*) Description
T11 real Resistance to longitudinal tension (Direction 1)
C11 real Resistance to longitudinal compression (Direction 1)
T22 real Resistance to transverse tension (Direction 2)
C22 real Resistance to transverse compression (Direction 2)
S12 real Resistance to longitudinal shear
Optional Parameters
Parameter Values, Default(*) Description
STRESS TYPE 2D, 3D Indicates what kind of stress state should be used to calculate the failure condition. When not given, related element’s stress type is taken.
T33 real Resistance to tension in thickness direction (Direction 3) (De f ault = T22)
C33 real Resistance to compression in thickness direction (Direction 3) (De f ault = C22)
S13 real Resistance to longitudinal shear (De f ault = S 12)
FS12 real Coefficient, necessary for calculation of F12. (De f ault = -0.5)
F12 real F12 component of strength tensor; Fij. When not given, it is calculated using FS12.
P real Strength value, necessary for calculation of F12. See Section 3.2.3
U real Strength value, necessary for calculation of F12. See Section 3.2.3
V real Strength value, necessary for calculation of F12. See Section 3.2.3


Tsai-Wu in 3D

Strength Analysis

Fracture envelopes for a 3D failure analysis: [3]

Tsai-wu 3D.png

Parameter Description

Tsai-Wu Parameters (3D)
Compulsory Parameters
Parameter Values, Default(*) Description
T11 real Resistance to longitudinal tension (Direction 1)
C11 real Resistance to longitudinal compression (Direction 1)
T22 real Resistance to transverse tension (Direction 2)
C22 real Resistance to transverse compression (Direction 2)
S12 real Resistance to longitudinal shear
S23 real Resistance to transverse shear
Optional Parameters
Parameter Values, Default(*) Description
STRESS TYPE 2D, 3D Indicates what kind of stress state should be used to calculate the failure condition. When not given, related element’s stress type is taken.
T33 real Resistance to tension in thickness direction (Direction 3) (De f ault = T22)
C33 real Resistance to compression in thickness direction (Direction 3) (De f ault = C22)
S13 real Resistance to longitudinal shear (De f ault = S 12)
FS12 real Coefficient, necessary for calculation of F12. (De f ault = -0.5)
F12 real F12 component of strength tensor; Fij. When not given, it is calculated using FS12.
P real Strength value, necessary for calculation of F12. See Section 3.2.3
U real Strength value, necessary for calculation of F12. See Section 3.2.3
V real Strength value, necessary for calculation of F12. See Section 3.2.3
FS13 real Coefficient, necessary for calculation of F13. (De f ault = -0.5)
F13 real F12 component of strength tensor; Fij. When not given, it is calculated using FS13.
FS23 real Coefficient, necessary for calculation of F23.(De f ault = -0.5)
F23 real F12 component of strength tensor; Fij. When not given, it is calculated using FS23.


Example of a Complete Input Block

Input tsai-wu.png

References

  1. ↑ S. W. Tsai and E. M. Wu. A General Theory of Strength for Anisotropic Materials. Journal of Composite Materials, 5(1):58–80, January 1971.
  2. ↑ Altug Emiroglu, Master Thesis: Comparative Study of Puck and Tsai-Wu Failure Criteria, Technische Universität München, 2013.
  3. ↑ Altug Emiroglu, Master Thesis: Comparative Study of Puck and Tsai-Wu Failure Criteria, Technische Universität München, 2013.




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