Fatigue damage of adhesive layers – experiments and models.

1. Fatigue damage of adhesive layers –
experiments and models.
by
Tomas Walander, Alexander Eklind, Thomas
Carlberger, Ulf Stigh
1
Tamonash Jana
001411202019

2. 2
Introduction
Generation of macroscopic cracks due to fatigue.
Use of adhesive materials in Industry.

3. 3
Adhesives
1. DOW Betamate5096
(BM5096)
 A Rubber Based Stiff
Structural Adhesive
 Epoxy Resin
 Nominal Layer
Thickness- 0.3 mm
2. DOW BetaForce
2850 (BF2850)
Polyurethane (PUR)
based Adhesive
Soft modular
Adhesive
Nominal Layer
Thickness- 1 mm

4. 4
Methodology
1st Approach - Paris’ law combined with the Energy
Release Rate G :
For a linear elastic specimen with a single crack tip loaded
with a prescribed load F
(1)
b=width of the specimen, Complience C=Δ/F,
a=Crack length

5. 5
As suggested by Berry(1963)
p,q=Compliance calibration parameters
Now
Substituting dC/da in eqn (1)
⇒
(2)
(3)
(4)

6. 6
 Experimental values of Δ, F, and number of elapsed
Cycles N are obtained.
Using Eqtn (3) and (4), G vs. a is evaluated for each
experiment
Hence the parameters c and n of ‘Paris’ Law’ are
evaluated.
(5)

7. 7
The relation used for determining da/dN
using experimental data is
afit =fitted crack length
(6)

8. 8
2nd Approach - Damage Mechanics Approach :
The damage evolution law is given by
(7)
D=Damage variable, σ= Peel stress, kn= elastic stiffness ;
alternatively
(8)
α, β =Damage law parameters, σth = fatigue threshold value
in stress

9.  The damage laws are implemented as a User Material
subroutine (UMAT) in Abaqus with the cohesive elements to
simulate the experiments.
9
The model does only consider damage in peel loading.

10. 10
Experiment

11.  Specimens are manufactured according to the dimensions
in the table below.
 By repeated experiments, the static stress-deformation
relations for Mode I loading are first determined for each
adhesive.
 For the rubber adhesive, the method of Andersson and
Stigh (2004) is used; for the PUR adhesive, the method of
Tamuzs et al. (2004) is used.
11

12. Stress-deformation relations for Rubber adhesive
12

13. 13
Stress-deformation relations for PUR adhesive

14. A fatigue test rig is developed consisting of a solid bar with
six individual loads cells.
14
The rig is mounted in a servo hydraulic tensile test
machine.
The experiments are controlled with the initial value of
Load ratio=0.1
The experiments are performed at 4 Hz for up to three
million load cycles.

15. 15
Experimental data and simulations of F vs N for
Rubber adhesive

16. Experimental data and simulations of F vs N for PUR
16
adhesive

17. 17
Evaluated a vs. N for Rubber adhesive

18. 18
Evaluated a vs. N for PUR adhesive

19. 19
Evaluated G vs. N for Rubber adhesive

20. 20
Evaluated G vs. N for PUR adhesive

21. 21
Result Analysis and Parameter Identification
The end value of G is used as an engineering estimate of
the threshold value Gth for fatigue crack growth.
The corresponding threshold value in stress σth is
determined as the value of stress corresponding to the point
where G= Gth.
The parameters α and β in Eq. (8) are determined by fitting
results from
numerical simulations to the experimental results in a log-log
plot of (da/dN) vs. G.

22. 22
Parameters obtained by evaluation

23. 23
Conclusion
Fracture mechanics using Paris’ law provides simpler
parameter estimation than damage mechanics approach.
The local modelling of fatigue damage using damage
mechanics provides a more physical model of the fatigue
properties.
The experimental results contain substantial scatter for the
rubber based adhesive. Thus, a large
number of repeated experiments are necessary to give useful
data and properties.

24. 24
Thank You