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Fatigue experiments and finite element analysis of bolted/bonded double lap joints

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Abstracts

High-strength steel hybrid joints that combine adhesive and bolts have been studied both experimentally and numerically. The fatigue strength of the double lap joint has been experimentally measured under completely reversed cyclic loading. Finite element analysis was used to estimate the stress state at the contact interface of the lap joint. The fatigue strength of bonded and clamped interfaces which have previously been characterized using napkin ring specimens has been combined with the finite element results. The region of the double lap joint which showed fretting damage corresponded well with the region estimated to have significant damage based on the assessment. The resulting fatigue strength assessment was conservative with respect to the experimental results.

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Abbreviations

d :

Loading level interval between subsequent fatigue tests in the small sample staircase series

D :

Damage variable of the cohesive interface model

E :

Young’s modulus

F :

Longitudinal load applied to the double lap joint specimen

\( {\mathit{\mathsf{F}}}_{\mathsf{a}} \) :

Load amplitude applied during the double lap joint experiment

\( {\mathit{\mathsf{F}}}_{\mathsf{a},0} \) :

First load amplitude level of the staircase sequence

\( {\mathit{\mathsf{F}}}_{\mathsf{a},\mathsf{f}} \) :

Load amplitude corresponding to the estimated fatigue strength

\( {\mathit{\mathsf{G}}}_{\mathit{\mathsf{c}}} \) :

Fracture energy

k :

Parameter based on the staircase sequence

\( {\mathit{\mathsf{K}}}_{\mathsf{nn}},{\mathit{\mathsf{K}}}_{\mathsf{ss}},{\mathit{\mathsf{K}}}_{\mathsf{tt}} \) :

Cohesive stiffness component in the normal and in the two shear directions, respectively

\( {\mathit{\mathsf{N}}}_{\mathsf{f}} \) :

Number of cycles to failure

P :

Longitudinal load applied to the double lap joint finite element model as surface pressure

\( {\mathit{\mathsf{P}}}_{\max } \) :

Maximum load during the double lap joint simulation

\( {\mathit{\mathsf{P}}}_{\min } \) :

Minimum load during the double lap joint simulation, maximum compressive load

q :

Static normal stress on the interface of the modified napkin ring specimen

\( {\mathit{\mathsf{t}}}_{\mathsf{n}},{\mathit{\mathsf{t}}}_{\mathsf{s}},{\mathit{\mathsf{t}}}_{\mathsf{t}} \) :

Cohesive traction in the normal and in the two shear directions, respectively

\( {\overline{\mathit{\mathsf{t}}}}_{\mathsf{n}},{\overline{\mathit{\mathsf{t}}}}_{\mathsf{s}},{\overline{\mathit{\mathsf{t}}}}_{\mathsf{t}} \) :

Elastic traction without damage in the normal and in the two shear directions, respectively

\( {\mathit{\mathsf{t}}}_{\mathsf{n}}^0,{\mathit{\mathsf{t}}}_{\mathsf{s}}^0,{\mathit{\mathsf{t}}}_{\mathsf{t}}^0 \) :

Critical cohesive traction in the normal and in the two shear directions, respectively

α :

Coefficient of the exponential damage evolution model

Δ :

Interface relative displacement during a modified napkin ring experiment

\( {\varDelta}_{\mathsf{gap}} \) :

Displacement measured by the clip-on gage during the double lap joint test

\( {\varDelta}_{\mathsf{tot}} \) :

Total displacement measured by the built-in sensor during the double lap joint test

\( {\delta}_{\mathsf{n}},{\delta}_{\mathsf{s}},{\delta}_{\mathsf{t}} \) :

Cohesive relative displacement in the normal and in the two shear directions, respectively

\( {\delta}_{\mathit{\mathsf{m}}} \) :

Effective separation

\( {\delta}_{\mathit{\mathsf{m}}}^0 \) :

Effective separation at onset of damage

\( {\delta}_{\mathit{\mathsf{m}}}^{\mathsf{f}} \) :

Effective separation at full cohesive fracture

\( {\delta}_{\mathit{\mathsf{m}}}^{\max } \) :

Maximum effective separation attained during the loading history

μ :

Coefficient of friction

ν :

Poisson’s ratio

σ 2 :

Calculated contact pressure on the interface

τ 1 :

Calculated interface shear stress along the global 1-direction

\( {\tau}_{\mathit{\mathsf{II}}} \) :

Measured shear stress during a modified napkin ring experiment

\( {\tau}_{\mathsf{f}} \) :

Shear stress amplitude corresponding to the estimated fatigue strength of the bonded and clamped interfaces

CZM:

Cohesive zone modelling

DLJ:

Double lap joint

FEM:

Finite element method

HSS:

High-strength steel

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Acknowledgments

This work was supported by the Finnish Graduate School in Engineering Mechanics. Partial support was also provided by Ruukki Metals Oy and the Finnish Metals and Engineering Competence Cluster (FIMECC). CSC—IT Center for Science Ltd. is acknowledged for the allocation of computational resources.

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Authors and Affiliations

  1. Department of Applied Mechanics, Aalto University, P.O. Box 14300, 00076, Aalto, Finland

    S. Hurme & G. Marquis

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  1. S. Hurme
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  2. G. Marquis
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Correspondence to S. Hurme.

Additional information

Doc. IIW-2472, recommended for publication by Commission XVI “Polymer Joining and Adhesive Technology.”

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Hurme, S., Marquis, G. Fatigue experiments and finite element analysis of bolted/bonded double lap joints. Weld World 58, 771–785 (2014). https://doi.org/10.1007/s40194-014-0157-4

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