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Modelling Ti-Ti Diffusion Bonding

Modelling Ti-Ti Diffusion Bonding. Andy Kong. What is diffusion bonding?. Solid state joining approach to fuse two materials together through the physics of diffusion. Materials are held together under pressure in a chamber that is filled with Argon gas.

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Modelling Ti-Ti Diffusion Bonding

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  1. Modelling Ti-Ti Diffusion Bonding Andy Kong

  2. What is diffusion bonding? • Solid state joining approach to fuse two materials together through the physics of diffusion. • Materials are held together under pressure in a chamber that is filled with Argon gas. • The chamber is heated to 50-80% of the melting temperature of the lowest melting temperature of the two materials. • The quality of the bond depends on the bonding times, temperature, and pressure used.

  3. Why is it used? • Metals which are difficult to weld by conventional means can be joined by this process. Ex. Titanium • The join where the two materials meet becomes indistinguishable at micrometer scales. • Able to create very complex internal microstructure not capable by conventional machining. • http://www.vpei.com/technologies-processes/diffusion-bonding

  4. Theory • Diffusion is governed by Fick’s second law. • D – diffusion coefficient • C – concentration • For the 1-D case, solution requires an initial condition (initial concentration) and two boundary conditions. Equation given by COMSOL R – reaction rate

  5. Building a model • Testing the times to create a good diffusion bond is both costly (materials) and takes a large amount of time. • Model the diffusion bonding of two pieces of Ti6Al4V each .1mm thick and 64mm diameter. • Model size used was 1mm thick and .18mm tall to shorten computation times. Actual pieces used were 1mm thick and 64mm tall. • Surface asperities are modeled as circles with radius 30e-6 m. • Titanium is in BCC crystal structure Beta form at the temperatures which diffusion bonding is done.

  6. Parameters in the model of the experiment • What parameters I used: • Assume no diffusion at the boundary layers of the materials. • Initial concentration of the surface asperities are 0. • Temperature set to 927 C • Pressure 0.7 – 2MPa • Experimental time of 0.5 – 4 hrs • The diffusion coefficient, the most important parameter of the model. • Diffusion coefficient determined by the Arrhenius equation. A – pre-exponential factor -> 9e-6 m2/s Ea – activation energy -> 153 KJ R – Universal Gas Constant ->8.31J/(molk) T – temperature -> 1220K Gives us k = 2.53e-12 m2/s

  7. Results

  8. 1-D Concentration Graph

  9. When do we stop? • At about 10,000 seconds, able to get 92% bond. This time is within the time scales as shown in the experimentation. • To get to a 95% bond, the model predicts it will take about 20,000 seconds or about 5.5 hours.

  10. Mesh Convergence • Changing the element sizes of the mesh changes nothing until we hit the “very coarse” element sizes in COMSOL. • The “extremely coarse” mesh has only 62 elements giving us maximum element sizes of 6.6e-4m and minimum element sizes of 1e-4m. • The “extra fine” has 834 elements with the smallest element size being 6e-7 meters and the largest element size being 1.34e-4 meters in length on a side

  11. Due to the interpolation of the concentration in COMSOL. The “extremely coarse” mesh has only 62 elements while the “extra fine” has 834 elements.

  12. Time Step Dependence • If we change our time steps, the number of iterations it takes to converge will change. We will also see that the values of the concentration that are interpolated will differ across different time steps. • But the final convergence is the same. That is because of the nature of our study. • 3 options in COMSOL • Free, Intermediate (mid-point), Strict (exact time steps used) • Our values of concentration did not vary much when we varied our mesh, even at the “coarse” levels due to COMSOL’s selection of time steps in calculation of the concentration.

  13. Relative convergence using a time step of starting at 100 seconds. COMSOL actually ignored this input and used .01 seconds as its starting value. Relative convergence using the BDF “Free” time step method. We see that the convergence is more orderly and the convergence is faster, only taking 16 iterations.

  14. Conclusion • Using a very simplistic model with many assumptions…. • The model was able to get similar results with experiment. • Improvements to be made: Make the model more dynamic, account for more physics - pressure correction.

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