Fatigue damage of adhesive layers –

experiments and models.

by

Tomas Walander, Alexander Eklind, Thomas

Carlberger, Ulf Stigh

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Tamonash Jana

001411202019

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Introduction

Generation of macroscopic cracks due to fatigue.

Use of adhesive materials in Industry.

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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

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Methodology1st 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

b=width of the specimen, Complience C=∆/F, a=Crack length

(1)

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As suggested by Berry(1963)

p,q=Compliance calibration parameters

Now

⇒

Substituting dC/da in eqn (1)

(2)

(3)

(4)

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Experimental values of ∆, F, and number of elapsedCycles 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)

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The relation used for determining da/dN using experimental data is

afit =fitted crack length

(6)

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2nd Approach - Damage Mechanics Approach :

The damage evolution law is given by

D=Damage variable, σ= Peel stress, kn= elastic stiffness ;

alternatively

α, β =Damage law parameters, σth = fatigue threshold value in stress

(7)

(8)

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The damage laws are implemented as a User Material subroutine (UMAT) in Abaqus with the cohesive elements to simulate the experiments.

The model does only consider damage in peel loading.

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Experiment

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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.

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Stress-deformation relations for Rubber adhesive

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Stress-deformation relations for PUR adhesive

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A fatigue test rig is developed consisting of a solid bar with six individual loads cells.

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.

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Experimental data and simulations of F vs N for Rubber adhesive

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Experimental data and simulations of F vs N for PUR adhesive

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Evaluated a vs. N for Rubber adhesive

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Evaluated a vs. N for PUR adhesive

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Evaluated G vs. N for Rubber adhesive

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Evaluated G vs. N for PUR adhesive

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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 fromnumerical simulations to the experimental results in a log-log plot of (da/dN) vs. G.

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Parameters obtained by evaluation

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ConclusionFracture mechanics using Paris’ law provides simpler parameter estimation than damage mechanics approach.

The local modelling of fatigue damage using damagemechanics provides a more physical model of the fatigue properties.

The experimental results contain substantial scatter for the rubber based adhesive. Thus, a largenumber of repeated experiments are necessary to give useful data and properties.

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Thank You