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Ab2013_Filipe

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Filipe Chaves

on 27 April 2014

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Transcript of Ab2013_Filipe

Predict the structure toughness
motivation
Joint mechanical behavior
Strain energy release rate
in mode I and mode II and
mixed-mode I + II
Fernlund G, Spelt JK. Compos Sci Technol (1994), vol. 50 pp. 441–449
Double cantilever beam (DCB)
specimen
difficult to read the crack length
neglects the Fracture Process Zone (FPZ)
crack tip
V. Richter-Trummer et al. , Mat.-wiss. u.Werkstofftech. 2011, 42, No. 5
where D is the flexural rigidity per unit width of the adherends given by
and a is the crack length
Fernlund and Spelt
where:
trying to overcome these problems a Compliance Based Beam Method (CBBM) was used defining an equivalent crack length accounting for the FPZ
Using the Timoshenko beam theory, the strain energy of the specimen due to
bending and including shear effects is
M is the bending moment
subscripts 1 and 2 stand for upper and lower adherends
T refers to the total bonded beam (of thickness 2h)
E and G are the longitudinal and shear modulus
B is the specimen bond width
I is the second moment of area of the indicated section
The shear stresses induced by transverse loading of beams are given by
c is the beam half-thickness
V is transverse load, on each arm for 0 ≤ x ≤ a, and on total bonded beam for a ≤ x ≤ 2L
Using the Castigliano’s theorem
P is the applied load

is the resulting displacement at the same point
Loading scheme
mode partition
compliance
same as DCB
when L = L is the same as ENF
1
(loaded at mid-span)
solving the following equation
where
keeping the real solution allows to obtain
where
the equivalent crack length for mode II is directly obtained from the Compliance equation (C )
II
these equivalent crack lengths take into account the
FPZ
Irwin-Kies equation allows to obtain the strain energy release rate components
strain energy release rate in mode II
strain energy release rate in mode I
NEXT STEP
Numerical validation using ABAQUS with cohesive elements
R
mesh and boundary conditions used in the numerical analysis
elastic and cohesive properties used in the numerical analysis
problem size and model elements
3600 plane strain 8-node quadrilateral elements (adherends)

280 6-node interface elements with null thickness placed at the mid-plane (adhesive)
interface elements
cohesive zone mixed-mode I+II damage model
trapezoidal softening law for pure and mixed-mode cohesive damage model
a quadratic stress criterion is used to identify damage initiation
scenarios
constant FPZ
G
I
G
II
self similar crack propagation
and
st
validation
imposed linear energetic criterion
nd
validation
Classical Compliance Calibration Method (CCM)
this method is easy to apply numerically, since the crack length can be straightforwardly monitored, which does not happen experimentally
although the CCM is a function of a, the a was used to provide better comparison between the two methods
e
CBBM
CCM
envelope validation
experimental validation
3 representative loading cases:

- mode I predominant (phase angle = 0º)


- mixed ratio (phase angle = 20º)


- mode II predominant (phase angle = 85º)
(phase angle = 0º)
(phase angle = 20º)
(phase angle = 85º)
s1=40 mm , s2 =120 mm , s3=160 mm and s4 = -120 mm
s1=60 mm , s2 =100 mm , s3=160 mm and s4 = 80 mm
s1=80 mm, s2 =60 mm, s3=140 mm and s4 = 100 mm
experimental envelope
"classical" DCB
vs.
SPELT (phase angle = 0º)
footnote
the method is based on specimen compliance, beam theory and crack equivalent concept
does not require crack length monitoring during the test
the presence of an eventual non-negligible fracture process zone is accounted
It was verified that R-curves present a steady plateau in conformity with a constant fracture process zone length, thus revealing the conditions of self-similar crack propagation which are fundamental to a rigorous fracture characterization
excellent agreement with Compliance Calibration Method (CCM)
experimental results returned values in accordance with the adhesive properties
experimental results agreed with numerical model simulations
this could be a good tool for adhesive joint design, because it allows an easier test, improving the usability and data computation to obtain expedite results.
Conclusions
mixed-mode I + II
Acknowledgments
The authors would like to acknowledge the support provided to Virginia Tech by the National Science Foundation (DMR NSF 0415840) in the development of a dual actuator load frame capable of facilitating mixed mode fracture studies.

The authors would also like to thank the ‘‘Fundação Luso-Americana para o Desenvolvimento’’ (FLAD) for the support through project 314/06, 2007 and Instituto de Engenharia Mecânica (IDMEC).
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