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Surface tracking of diffusion bonding void closure and its application to titanium alloys

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Abstract

Diffusion bonding is a process by which two flat, usually metallic, surfaces are welded together at a high temperature and moderate pressure. Bonding occurs due to a combination of diffusion and power law creep that close the voids formed by microscopic differences between the mating surfaces. While the different process parameters are well understood the effects of surface condition and void shapes during bonding has not been thoroughly researched. In this paper we use measured surface profiles, discretize them, and apply the diffusion and creep equations numerically to the profiles in order to provide insight into the effects of surface geometry on bonding. Using this method the voids can interact with each other and the effects of nearby voids can be computed. Experimental tests are performed to confirm the model and theoretical tests were created to determine what the effects of different surface geometries are on bonding performance. While in most cases the bonding was dominated by power law creep the most optimal void shape was one where the voids had completed the creep stage and were controlled by diffusive processes. It was also found that concentrating the overlap area also increases bonding performance.

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Abbreviations

f 0 :

Initial fraction of bonding

σy :

High temperature yield strength

P :

Bonding pressure

J :

Atomic flux

D :

Diffusion constant

k :

Boltzmann constant

T :

Temperature

Δμ :

Chemical potential

Ω:

Atomic volume

γ s :

Surface energy

κ :

Surface curvature

s :

Void surface length

\( \frac{d{v}_n}{dt} \) :

Surface diffusion nodal velocity

α :

Angle between the x axis and the void surface

κ tip :

Tip curvature

β :

Steady state flux along the bonded boundary

X :

Half length of a boundary

L :

Half length of a void

σ :

Local stress

δ b :

Boundary layer thickness

f :

Current overlap ratio

\( \frac{d{u}_r}{dt} \) :

Change in height of the boundary material

\( \dot{\varepsilon} \) :

Power law creep strain rate

A c :

Creep constant

n :

Creep exponent

G :

High temperature shear modulus

w n :

Slice width at node

x n :

X coordinates at node

σ n :

Stress at node

h n :

Height at node

w bi :

Bond width

y n :

Y coordinates at node

R a :

Arithmetic mean deviation of the surface profile

R z :

Averaged maximum peak to valley height of each sample length in the surface profile

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Acknowledgments

The authors of this paper would like to thank The Boeing Company for providing the diffusion bonded coupons. The analytical work was conducted with the support of Boeing-Pennell Professorship funds. We also sincerely acknowledge the discussions, support and encouragement given by Dr. Daniel G. Sanders, Senior Technical Fellow in The Boeing Company during the investigation.

Funding

This study was funded by The Boeing Company.

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  1. Department of Mechanical Engineering, University of Washington, Box 352600, Seattle, WA, 98195, USA

    Bryan Ferguson & M. Ramulu

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  1. Bryan Ferguson
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Correspondence to M. Ramulu.

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Ferguson, B., Ramulu, M. Surface tracking of diffusion bonding void closure and its application to titanium alloys. Int J Mater Form 13, 517–531 (2020). https://doi.org/10.1007/s12289-019-01489-0

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