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

  • Bryan Ferguson
  • M. RamuluEmail author
Original Research


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.


Diffusion bonding Surface tracking Titanium 



Initial fraction of bonding


High temperature yield strength


Bonding pressure


Atomic flux


Diffusion constant


Boltzmann constant




Chemical potential


Atomic volume


Surface energy


Surface curvature


Void surface length

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

Surface diffusion nodal velocity


Angle between the x axis and the void surface


Tip curvature


Steady state flux along the bonded boundary


Half length of a boundary


Half length of a void


Local stress


Boundary layer thickness


Current overlap ratio

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

Change in height of the boundary material

\( \dot{\varepsilon} \)

Power law creep strain rate


Creep constant


Creep exponent


High temperature shear modulus


Slice width at node


X coordinates at node


Stress at node


Height at node


Bond width


Y coordinates at node


Arithmetic mean deviation of the surface profile


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



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.


This study was funded by The Boeing Company.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of WashingtonSeattleUSA

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