Analytical cohesive model for Compact Tension specimen
Girona, 22 July 2013
Characterization of the
intralaminar fracture cohesive law
A. Ortega, P. Maimí., E. V. González.
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
Outline
1 – Direct method: analytic model
1.1 – Dugdale’s Condition
1.2 – Validation of the model
2 – Inverse problem
3 – Results
4 – Conclusions
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
Preamble: Why use a cohesive model?
Quasi-brittle materials:
– Exhibit no hardening prior to the material failure.
– Need a relatively high amount of energy to propagate a crack.
– Develop a Fracture Process Zone relatively large compared to other
problem dimensions.
In this scenario, Linear Elastic Fracture Mechanics (LEFM)
cannot be used to predict the crack growth.
– A cohesive model is introduced to take into account the fracture
mechanics at the FPZ.
– The cohesive law is considered to be a material property.
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1 – Direct method
To obtain the load-displacement (P-u) curve of a Compact
Tension (CT) specimen taking into account the cohesive
stresses at the Fracture Process Zone (FPZ).
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1.1 – Dugdale’s Condition: a superposition problem
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Characterization of the intralaminar fracture cohesive law
1.1 – Dugdale’s Condition
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1.1 – Dugdale’s Condition: determination of the
cohesive stresses
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1.1 – Dugdale’s Condition: determination of the
cohesive stresses
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1.1 – Dugdale’s Condition: Inputs and outputs
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Characterization of the intralaminar fracture cohesive law
1.1 – Direct method.
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1.2 – Model validation
Excellent agreement with FEM for a linear cohesive law.
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
1.2 – Model validation
As proven, the analytic model is equivalent to a FEM solution
Advantages of analytic model over FEM:
– Extremely fast computing time (<1s vs ~10min).
– Any random CL shape.
Advantages of FEM over analytic:
– Easier to implement for any geometry.
– Analytic only solved for isotropic material (can be implemented for
orthotropic materials).
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: The FPZ formation
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: The FPZ formation
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: The FPZ formation
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
2 – Inverse problem: Solution algorithm
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
3 – Results
Quasi-isotropic woven glass fabric [(0/45)5]S.
Madrid, 8th April 2015
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
3 – Results
The CL shape depends on the number of points used to do
the fitting.
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
3 – Results
The CL shape depends on the number of points used to do
the fitting.
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
3 – Results
The CL shape depends on the number of points used to do
the fitting.
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Characterization of the intralaminar fracture cohesive law
Madrid, 8th April 2015
3 – Results
The CL shape depends on the number of points used to do
the fitting.
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Characterization of the intralaminar fracture cohesive law
4 – Overview
Madrid, 8th April 2015
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Analytical cohesive model for Compact Tension specimen
Thank you for your
attention.
Girona, 22 July 2013
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Analytical cohesive model for Compact Tension specimen
Girona, 22 July 2013
(33)