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

  • Bryan Ferguson
  • M. RamuluEmail author
Original Research
  • 13 Downloads

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.

Keywords

Diffusion bonding Surface tracking Titanium 

Abbreviation

f0

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

γs

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

κtip

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

δb

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

Ac

Creep constant

n

Creep exponent

G

High temperature shear modulus

wn

Slice width at node

xn

X coordinates at node

σn

Stress at node

hn

Height at node

wbi

Bond width

yn

Y coordinates at node

Ra

Arithmetic mean deviation of the surface profile

Rz

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

Notes

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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Sanders DG, Ramulu M (2004) Examination of superplastic forming combined with diffusion bonding for titanium: perspective from experience. J Mater Eng Perform 13(6):744–752.  https://doi.org/10.1361/10599490421574 CrossRefGoogle Scholar
  2. 2.
    Hamilton CH (1973) Pressure requirements for diffusion bonding titanium. Titanium Science and Technology:625–648Google Scholar
  3. 3.
    Garmong G, Paton NE, Argon AS (1975) Attainment of full interfacial contact during diffusion bonding. Metall Trans A 6(6):1269–1279CrossRefGoogle Scholar
  4. 4.
    Derby B, Wallach ER (1984) Diffusion bonding: development of theoretical model. Metal Science 18(9):427–431Google Scholar
  5. 5.
    Derby B, Wallach ER (1984) Diffusion bonds in copper. J Mater Sci 19(10):3140–3148CrossRefGoogle Scholar
  6. 6.
    Derby B, Wallach ER (1982) Theoretical model for diffusion bonding. Metal Science 16(1):49–56Google Scholar
  7. 7.
    Hill A, Wallach E (1989) Modelling solid-state diffusion bonding. Acta Metall 37(9):2425–2437CrossRefGoogle Scholar
  8. 8.
    Pilling J, Livesey DW, Hawkyard JB, Ridley N (1984) Solid state bonding in superplastic Ti-6Al-4V. Metal Science 18(3):117–122Google Scholar
  9. 9.
    Pilling J (1988) The kinetics of isostatic diffusion bonding in superplastic materials. Mater Sci Eng 100:137–144CrossRefGoogle Scholar
  10. 10.
    Salehi MT, Pilling J, Ridley N, Hamilton DL (1992) Isostatic diffusion bonding of superplastic Ti-6Al-4V. Mater Sci Eng A 150(1):1–6CrossRefGoogle Scholar
  11. 11.
    Orhan N, Aksoy M, Eroglu M (1999) A new model for diffusion bonding and its application to duplex alloys. Mater Sci Eng A 271(1-2):458–468CrossRefGoogle Scholar
  12. 12.
    Ma R, Li M, Li H, Yu W (2012) Modeling of void closure in diffusion bonding process based on dynamic conditions. Sci China Technol Sci 55(9):2420–2431.  https://doi.org/10.1007/s11431-012-4927-1 CrossRefGoogle Scholar
  13. 13.
    Li H, Li MQ, Kang PJ (2016) Void shrinking process and mechanisms of the diffusion bonded Ti–6Al–4V alloy with different surface roughness. Appl Phys A Mater Sci Process 122(1).  https://doi.org/10.1007/s00339-015-9546-9
  14. 14.
    Guo ZX, Ridley N (1987) Modelling of diffusion bonding of metals. Mater Sci Technol 3(11):945–953CrossRefGoogle Scholar
  15. 15.
    Takahashi Y, Inoue K (1992) Recent void shrinkage models and their applicability to diffusion bonding. Mater Sci Technol 8(11):953–964CrossRefGoogle Scholar
  16. 16.
    Li S-X, Tu S-T, Xuan F-Z (2005) A probabilistic model for prediction of bonding time in diffusion bonding. Mater Sci Eng A 407(1-2):250–255.  https://doi.org/10.1016/j.msea.2005.07.003 CrossRefGoogle Scholar
  17. 17.
    Kulkarni N, Ramulu M, Sanders DG (2016) Modeling of diffusion bonding time in dissimilar titanium alloys: preliminary results. J Manuf Sci Eng 138(12):121010CrossRefGoogle Scholar
  18. 18.
    Islam MF, Pilling J, Ridley N (1997) Effect of surface finish and sheet thickness on isostatic diffusion bonding of superplastic Ti-6Al-4V. Mater Sci Technol 13(12):1045–1050.  https://doi.org/10.1179/mst.1997.13.12.1045 CrossRefGoogle Scholar
  19. 19.
    Wang A, Ohashi O, Ueno K (2006) Effect of surface asperity on diffusion bonding. Mater Trans 47(1):179–184.  https://doi.org/10.2320/matertrans.47.179 CrossRefGoogle Scholar
  20. 20.
    Shao X, Guo X, Han Y et al (1980-2015) (2015) characterization of the diffusion bonding behavior of pure Ti and Ni with different surface roughness during hot pressing. Mater Des 65:1001–1010.  https://doi.org/10.1016/j.matdes.2014.09.071 CrossRefGoogle Scholar
  21. 21.
    Guo Y, Wang Y, Gao B et al (2016) Rapid diffusion bonding of WC-co cemented carbide to 40Cr steel with Ni interlayer: effect of surface roughness and interlayer thickness. Ceram Int 42(15):16729–16737.  https://doi.org/10.1016/j.ceramint.2016.07.145 CrossRefGoogle Scholar
  22. 22.
    Zhang C, Li H, Li M (2017) Role of surface finish on interface grain boundary migration in vacuum diffusion bonding. Vacuum 137:49–55.  https://doi.org/10.1016/j.vacuum.2016.12.021 CrossRefGoogle Scholar
  23. 23.
    Zuruzi AS, Li H, Dong G (1999) Effects of surface roughness on the diffusion bonding of Al alloy 6061 in air. Mater Sci Eng A 270(2):244–248.  https://doi.org/10.1016/S0921-5093(99)00188-4 CrossRefGoogle Scholar
  24. 24.
    Somekawa H, Higashi K (2003) The optimal surface roughness condition on diffusion bonding. Mater Trans 44(8):1640–1643.  https://doi.org/10.2320/matertrans.44.1640 CrossRefGoogle Scholar
  25. 25.
    Huang P, Li Z, Sun J (2002) Shrinkage and splitting of microcracks under pressure simulated by the finite-element method. Metall Mater Trans A 33(4):1117–1124.  https://doi.org/10.1007/s11661-002-0213-3 CrossRefGoogle Scholar
  26. 26.
    Huang PZ, Sun J, Li ZH, Gao H (2003) Morphological healing evolution of intragranular penny-shaped microcracks by surface diffusion: part I. Simulation. Metall Mater Trans A 34(2):277–285.  https://doi.org/10.1007/s11661-003-0329-0 CrossRefGoogle Scholar
  27. 27.
    Huang P, Sun J (2004) A numerical analysis of intergranular penny-shaped microcrack shrinkage controlled by coupled surface and interface diffusion. Metall Mater Trans A 35(4):1301–1309.  https://doi.org/10.1007/s11661-004-0304-4 CrossRefGoogle Scholar
  28. 28.
    Pharr GM, Nix WD (1979) A numerical study of cavity growth controlled by surface diffusion. Acta Metall 27(10):1615–1631.  https://doi.org/10.1016/0001-6160(79)90044-0 CrossRefGoogle Scholar
  29. 29.
    Chuang T-J, Kagawa KI, Rice JR, Sills LB (1979) Overview no. 2: non-equilibrium models for diffusive cavitation of grain interfaces. Acta Metall 27(3):265–284.  https://doi.org/10.1016/0001-6160(79)90021-X CrossRefGoogle Scholar
  30. 30.
    Needleman A, Rice JR (1980) Plastic creep flow effects in the diffusive cavitation of grain boundaries. Acta Metall 28(10):1315–1332.  https://doi.org/10.1016/0001-6160(80)90001-2 CrossRefGoogle Scholar
  31. 31.
    Martinez L, Nix WD (1982) A numerical study of cavity growth controlled by coupled surface and grain boundary diffusion. Metall Trans A 13(3):427–437CrossRefGoogle Scholar
  32. 32.
    Wang H, Li Z (2004) The three-dimensional analysis for diffusive shrinkage of a grain-boundary void in stressed solid. J Mater Sci 39(10):3425–3432.  https://doi.org/10.1023/B:JMSC.0000026945.89767.25 MathSciNetCrossRefGoogle Scholar
  33. 33.
    Takahashi Y, Takahashi K, Nishiguchi K (1991) A numerical analysis of void shrinkage processes controlled by coupled surface and interface diffusion. Acta Metall Mater 39(12):3199–3216CrossRefGoogle Scholar
  34. 34.
    Takahashi Y, Ueno F, Nishiguchi K (1988) A numerical analysis of the void-shrinkage process controlled by surface-diffusion. Acta Metall 36(11):3007–3018CrossRefGoogle Scholar

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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