Users:General FEM Analysis/Materials Reference/Puck Failure Criterion

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== General Description ==
 
== General Description ==
  
−
It is based on Mohr‘s fracture hypothesis which is appropriate for brittle fracture behaviour of composite materials. It can distinguish between fibre fracture and different inter-fibre fracture. Both 2D and 3D formulations are implemented into Carat++.
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Puck Failure Criterion
 +
<ref>
 +
A. Puck: Festigkeitsanalyse von Faser-Matrix-Laminaten. Hanser, 1996. ISBN 3-446-18194-6
 +
</ref>
 +
<ref>
 +
H. Deuschle. 3D failure analysis of UD fibre reinforced composites: Puck’s theory within FEA.
 +
Phd thesis, Universität Stuttgart, 2010.
 +
</ref>
 +
<ref>
 +
M. Knops. Analysis of Failure in Fiber Polymer Laminates. Springer Berlin Heidelberg, Berlin,
 +
Heidelberg, 2008.
 +
</ref>
 +
is based on Mohr‘s fracture hypothesis
 +
<ref>
 +
O. Mohr. Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials?
 +
(German). Zeitschrift des Vereins deutscher Ingenieure, 24:1524 ff, 1900.
 +
</ref>
 +
which is appropriate for brittle fracture behaviour of composite materials. It can distinguish between fibre fracture and different inter-fibre fracture. Both 2D and 3D formulations are implemented into Carat++.
 
Available fracture modes for 2D Puck Criterion are:
 
Available fracture modes for 2D Puck Criterion are:
 
* Fibre Fracture (FF)
 
* Fibre Fracture (FF)
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* Inter Fibre Fracture (IFF)
 
* Inter Fibre Fracture (IFF)
  
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=== Parameter Description ===
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== Stresses on the Fracture Plane ==
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 +
[[File:formel3.1.png|300px]]
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[[File:formel3.2.png|150px]]
 +
 
 +
[[File:formel3.3_2.png|150px]]
 +
 
 +
[[File:Figure 3.4.png|500px]]
 +
 
 +
Stresses of the action plane
 +
<ref>
 +
M. Knops. Analysis of Failure in Fiber Polymer Laminates. Springer Berlin Heidelberg, Berlin,
 +
Heidelberg, 2008.
 +
</ref>
 +
 
 +
 
 +
== Strength Analysis ==
 +
 
 +
In order to judge if a stress vector on the stress spce is leading to damage, a mathematical expression is needed.
 +
This expression is called ''fracture condition'' an is written as the following general form:
 +
 
 +
 
 +
[[File:Formel3.4.png|150px]]
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 +
 
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[[File:sigma_i.png|15px]] : Components of stress vector
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 +
R<sub>i</sub>.  : Strengths under corresponding stresses
 +
 
 +
F : Fracture function
 +
 
 +
 
 +
There are 6 main strengths that should be related to the occurring stress state:
 +
 
 +
[[File:6main_strengths.png|350px]]
 +
 
 +
The general form of fracture condition can also be rewritten as following:
 +
 
 +
[[File:Formel3.5.png|350px]]
 +
 
 +
F < 1 : no fracture
 +
 
 +
F = 1 : fracture limit reached and fracture occurs
 +
 
 +
F > 1 : fracture limit exceeded
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 +
with F [[File:Element.png|10px]] [0,[[File:unendlich.png|18px]])
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 +
[[File:puck.png|1000px]]
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<ref>
 +
Altug Emiroglu, Master Thesis: Comparative Study of Puck and Tsai-Wu Failure Criteria, Technische Universität München, 2013.
 +
</ref>
 +
 
 +
 
 +
== Parameter Description ==
  
 
{| border="1" cellpadding="3" cellspacing="0"
 
{| border="1" cellpadding="3" cellspacing="0"
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!PTTL
 
!PTTL
 
|real
 
|real
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|Inclination parameter, [[File:Pt.png]]
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|Inclination parameter,[[File:pt.png|25px]]  
 
|-
 
|-
 
!PCTL  
 
!PCTL  
 
|real
 
|real
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|Inclination parameter, p
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|Inclination parameter,[[File:pc.png|25px]]
 
|-
 
|-
 
    
 
    
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!S, M   
 
!S, M   
 
|real
 
|real
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|Parameters necessary for calculation of weakening due to X<sub>1</sub> (''De f ault'' = S = M = 0.5)
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|Parameters necessary for calculation of weakening due to [[File:sigma.png|20px]] (''De f ault'' = S = M = 0.5)
 
|-
 
|-
 
!PTT  
 
!PTT  
 
|real
 
|real
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|Inclination parameter p??. When not given, calculated using the strength values. See Section 3.1.2.3
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|Inclination parameter [[File:p.png|25px]]. When not given, calculated using the strength values. See Section 3.1.2.3
 
|-
 
|-
 
!WEAKENING
 
!WEAKENING
 
|int
 
|int
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|Switch for calculation of weakening due to _1.
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|Switch for calculation of weakening due to [[File:sigma.png|20px]].
 
* 0 = OFF
 
* 0 = OFF
 
* 1* = ON
 
* 1* = ON
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|-
 
|-
 
|}
 
|}
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 +
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=== Example of a Complete Input Block ===
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[[File:input_puck.png|500px]]
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 +
 +
== References ==
 +
<references/>

Latest revision as of 10:05, 15 February 2013

Contents

General Description

Puck Failure Criterion [1] [2] [3] is based on Mohr‘s fracture hypothesis [4] which is appropriate for brittle fracture behaviour of composite materials. It can distinguish between fibre fracture and different inter-fibre fracture. Both 2D and 3D formulations are implemented into Carat++. Available fracture modes for 2D Puck Criterion are:

  • Fibre Fracture (FF)
  • Inter Fibre Fracture Mode A (IFF A)
  • Inter Fibre Fracture Mode B (IFF B)
  • Inter Fibre Fracture Mode C (IFF C)

Available fracture modes for 3D Puck Criterion are:

  • Fibre Fracture (FF)
  • Inter Fibre Fracture (IFF)

Stresses on the Fracture Plane

Formel3.1.png

Formel3.2.png

Formel3.3 2.png

Figure 3.4.png

Stresses of the action plane [5]


Strength Analysis

In order to judge if a stress vector on the stress spce is leading to damage, a mathematical expression is needed. This expression is called fracture condition an is written as the following general form:


Formel3.4.png


Sigma i.png : Components of stress vector

Ri.  : Strengths under corresponding stresses

F : Fracture function


There are 6 main strengths that should be related to the occurring stress state:

6main strengths.png

The general form of fracture condition can also be rewritten as following:

Formel3.5.png

F < 1 : no fracture

F = 1 : fracture limit reached and fracture occurs

F > 1 : fracture limit exceeded

with F Element.png [0,Unendlich.png)

Puck.png [6]


Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
EF real Elasticity modulus of the fibres
RTL real Resistance to longitudinal tension (Direction 1)
RCL real Resistance to longitudinal compression (Direction 1)
RTT real Resistance to transverse tension (Direction 2)
RCT real Resistance to transverse compression (Direction 2)
RSL real Resistance to longitudinal shear
VFF real Volume fraction of the fibres
PTTL real Inclination parameter,Pt.png
PCTL real Inclination parameter,Pc.png
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.
NUE12F real Poisson’s ratio for fibres. (De f ault = 0.2)
MGF real Amplification factor (De f ault = 1.2)
S, M real Parameters necessary for calculation of weakening due to Sigma.png (De f ault = S = M = 0.5)
PTT real Inclination parameter P.png. When not given, calculated using the strength values. See Section 3.1.2.3
WEAKENING int Switch for calculation of weakening due to Sigma.png.
  • 0 = OFF
  • 1* = ON
FPS SWS*, GSS Switch for fracture plane search algorithm.
  • SWS* = Stepwise Search Algorithm
  • GSS = Golden Section Search Algorithm
FPS_SWS_SIZE real Step size for step-wise fracture plane search


Example of a Complete Input Block

Input puck.png


References

  1. ↑ A. Puck: Festigkeitsanalyse von Faser-Matrix-Laminaten. Hanser, 1996. ISBN 3-446-18194-6
  2. ↑ H. Deuschle. 3D failure analysis of UD fibre reinforced composites: Puck’s theory within FEA. Phd thesis, Universität Stuttgart, 2010.
  3. ↑ M. Knops. Analysis of Failure in Fiber Polymer Laminates. Springer Berlin Heidelberg, Berlin, Heidelberg, 2008.
  4. ↑ O. Mohr. Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials? (German). Zeitschrift des Vereins deutscher Ingenieure, 24:1524 ff, 1900.
  5. ↑ M. Knops. Analysis of Failure in Fiber Polymer Laminates. Springer Berlin Heidelberg, Berlin, Heidelberg, 2008.
  6. ↑ Altug Emiroglu, Master Thesis: Comparative Study of Puck and Tsai-Wu Failure Criteria, Technische Universität München, 2013.




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