Fatigue Material: Difference between revisions

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This command is used to construct an impact material object
{{CommandManualMenu}}
 
The fatigue material uses a modified rainflow cycle counting algorithm to accumulate damage in
a material using Miner’s Rule. Element stress/strain relationships become zero when fatigue life
is exhausted.
 


{|  
{|  
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial ImpactMaterial $matTag $K1 $K2 $δy $gap
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial Fatigue $matTag $tag <-E0 $E0> <-m $m> <-min $min> <-max $max> '''
'''
|}
|}


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{|
{|
|  style="width:150px" | '''$matTag ''' || integer tag identifying material
|  style="width:150px" | '''$matTag ''' || integer tag identifying material  
|-
| '''$tag''' || Unique material object integer tag for the material that is being wrapped
|-
|-
| '''$K1''' || initial stiffness
|'''$E0''' || Value of strain at which one cycle will cause failure (default 0.191)
|-
|-
|'''$K2''' || secondary stiffness
|'''$m''' || Slope of Coffin-Manson curve in log-log space (default -0.458)
|-
|-
|'''$δy''' || yield displacement
|'''$min '''|| Global minimum value for strain or deformation (default -1e16)
|-
|-
|'''$gap '''|| initial gap*
|'''$max '''|| Global maximum value for strain or deformation (default 1e16)
|}
|}


NOTES:
== Description ==
 
This material model accounts for the effects of low cycle fatigue. A modified rainflow cycle
This material is implemented as a compression-only gap material. Delta_y and gap should be input as negative values.
counter has been implemented to track strain amplitudes. This cycle counter is used in concert
 
with a linear strain accumulation model (i.e. Miner’s Rule), based on Coffin-Manson log-log
 
relationships describing low cycle fatigue failure. This material wraps around another material
DESCRIPTION:
and does not influence the stress-strain (or force-deformation) relationship of the parent
 
material.
This material is based on an approximation to the Hertz contact model proposed by Muthukumar (See REFERENCES below). The energy dissipated during impact is:
 
E = kh * δm^(n+1) * (1-e^2) / (N+1)
 
where kh is the impact stiffness parameter, with a typical value of EA/L or 25,000 k-in.-3/2; n is typically taken as 3/2 for the exponent associated with the Hertz power rule; e is the coefficient of restitution, with typical values from 0.6-0.8; and δm is the maximum penetration during the pounding event.  The effective stiffness, Keff, is:
 
Keff = kh * sqrt(δm)
 
The yield displacement is:
 
δy = a * δm
 
where a is typically taken as 0.1.  The initial stiffness, K1, and secondary stiffness, K2, are then selected such that the Impact model dissipates an amount of energy during a pounding event that is consistent with the associated energy dissipated in the Hertz model.
 
K1 = Keff + E / (a*δm^2)
 
K2 = Keff - E / ((1-a)*δm^2)


Response of Impact Material during a pounding event.
Once the Fatigue material model reaches a damage level of 1.0, the force (or stress) of the
parent material becomes zero (1.0x10-8 times the call to the material). If failure is triggered in
compression, the material stress is dropped at the next zero-force crossing (i.e. compression
force never drops to zero).


[[Image:ImpactA.gif]]
The Fatigue material assumes that each point is the last point of the history, and tracks damage
with this assumption. If failure is not triggered, this pseudo-peak is discarded.


Response of Impact Material for displacement cycles of increasing amplitude.
The material also has the ability to trigger failure based on a maximum or minimum strain (i.e.
not related to fatigue). The default for these values is set to very large numbers.


[[Image:ImpactB.gif]]
The default values are calibrated parameters from low cycle fatigue tests of European steel
sections Ballio and Castiglioni (1995), for more information about how material was calibrated,
the user is directed to Uriz (2005).


Valid recorder objects for the material are ‘stress’,’tangent’, ‘strain’, ‘stressStrain’, and ‘damage’.
The stress, strain, and tangent recorder options must be available in the material that you are
wrapping.




'''NOTE:''' Here you can find more information of how to create 'damage' recorders: [http://opensees.berkeley.edu/community/viewtopic.php?f=2&t=54193 link]


EXAMPLE:


== Example: ==


''Click to Download''


[[Media:FatigueExample.tcl]]


REFERENCES:  
[[Media:RandomStrainHstory.tcl]]


Muthukumar, S., and DesRoches, R. (2006). “A Hertz Contact Model with Non-linear Damping for Pounding Simulation.” Earthquake Engineering and Structural Dynamics, 35, 811-828.
[[File:DamageExample.jpg]]


Muthukumar, S. (2003). “A Contact Element Approach with Hysteresis Damping for the Analysis and Design of Pounding in Bridges.” PhD Thesis, Georgia Institute of Technology. http://smartech.gatech.edu/
==References:==


Nielson, B. (2005). “Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones.” PhD Thesis, Georgia Institute of Technology. http://smartech.gatech.edu/
Uriz, Patxi (2005) “Towards Earthquake Resistant Design of Concentrically Braced Steel
Structures,” Doctoral Dissertation, Structural Engineering, Mechanics, and Materials,
Department of Civil and Environmental Engineering, University of California, Berkeley,
December 2005


Ballio, G., and Castiglioni, C. A. (1995). "A Unified Approach for the Design of Steel Structures
under Low and/or High Cycle Fatigue." Journal of Constructional Steel Research, 34, 75-101.


----
----


Code Developed by: <span style="color:blue"> Mathew Dryden, UC Berkeley </span>
Code Developed by: <span style="color:blue"> Patxi Uriz, Exponent </span>

Latest revision as of 18:34, 13 July 2012



The fatigue material uses a modified rainflow cycle counting algorithm to accumulate damage in a material using Miner’s Rule. Element stress/strain relationships become zero when fatigue life is exhausted.


uniaxialMaterial Fatigue $matTag $tag <-E0 $E0> <-m $m> <-min $min> <-max $max>
$matTag integer tag identifying material
$tag Unique material object integer tag for the material that is being wrapped
$E0 Value of strain at which one cycle will cause failure (default 0.191)
$m Slope of Coffin-Manson curve in log-log space (default -0.458)
$min Global minimum value for strain or deformation (default -1e16)
$max Global maximum value for strain or deformation (default 1e16)

Description

This material model accounts for the effects of low cycle fatigue. A modified rainflow cycle counter has been implemented to track strain amplitudes. This cycle counter is used in concert with a linear strain accumulation model (i.e. Miner’s Rule), based on Coffin-Manson log-log relationships describing low cycle fatigue failure. This material wraps around another material and does not influence the stress-strain (or force-deformation) relationship of the parent material.

Once the Fatigue material model reaches a damage level of 1.0, the force (or stress) of the parent material becomes zero (1.0x10-8 times the call to the material). If failure is triggered in compression, the material stress is dropped at the next zero-force crossing (i.e. compression force never drops to zero).

The Fatigue material assumes that each point is the last point of the history, and tracks damage with this assumption. If failure is not triggered, this pseudo-peak is discarded.

The material also has the ability to trigger failure based on a maximum or minimum strain (i.e. not related to fatigue). The default for these values is set to very large numbers.

The default values are calibrated parameters from low cycle fatigue tests of European steel sections Ballio and Castiglioni (1995), for more information about how material was calibrated, the user is directed to Uriz (2005).

Valid recorder objects for the material are ‘stress’,’tangent’, ‘strain’, ‘stressStrain’, and ‘damage’. The stress, strain, and tangent recorder options must be available in the material that you are wrapping.


NOTE: Here you can find more information of how to create 'damage' recorders: link


Example:

Click to Download

Media:FatigueExample.tcl

Media:RandomStrainHstory.tcl

References:

Uriz, Patxi (2005) “Towards Earthquake Resistant Design of Concentrically Braced Steel Structures,” Doctoral Dissertation, Structural Engineering, Mechanics, and Materials, Department of Civil and Environmental Engineering, University of California, Berkeley, December 2005

Ballio, G., and Castiglioni, C. A. (1995). "A Unified Approach for the Design of Steel Structures under Low and/or High Cycle Fatigue." Journal of Constructional Steel Research, 34, 75-101.

Code Developed by: Patxi Uriz, Exponent

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