Viscoplastic Finite Element Simulation of Microscopic Sintering Behavior

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Viscoplastic Finite Element Simulation of
Microscopic Sintering Behavior

• Donggang Yao
• Instructor Professor Ian Grosse
• University of Massachusetts, Amherst, MA 01003
• May, 1999

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What Is Sintering ?

• Bonding particles together
• Thermal treatment involved
• Occur on microscopic level
• An example is ceramic firing

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Why Sintering ?

• Improve mechanical strength
• A post process for powder injection molded parts

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What drives Sintering ?

• Tendency to lower surface energy
• Smaller the particle higher the energy
• Surface area reduction
• Surface tension
• Sintering stress

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Microscopic Sintering Models

• 1. Isolated closed spherical pore
• 2. Two spherical particles contact together
• 3. One spherical particle surrounded by six

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Why Sintering Simulation?

• Predict microscopic shrinkage
• Determine effect of particle size
• Fundamental understanding of sintering

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How Simulation?

• A unified viscoplastic finite element formulation
• Using the three microscopic models
• Implement in ANSYS

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Anands Viscoplastic Model

• Time-dependent plasticity
• High temperature metal deformation
• Governing equations
• Material parameters

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Finite Element Models

• 1. Isolated closed spherical pore
• 2. Two spherical particles contact together
• 3. One spherical particle surrounded by six

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General Assumptions

• The particles during sintering is viscoplastic
• Under uniform and constant temperature
• Surface tension is uniform

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Program Inputs
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Simulation Procedure

• Transient viscoplastic
• Nonlinear large deformation
• Various load steps on logarithm time scale
• Convergence improvement

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Results and Discussions
Spherical Pore

• 1. Displacement
• Contour plot
• Vector plot
• 2. Effect of pore size
• Radial displacement versus time
• Filled volume versus time

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Results and Discussions, Continue
Two Contacted Particles

• 1. Displacement
• Contour plot
• Vector plot
• 2. Effect of pore size
• Volume shrinkage versus time
• Neck growth versus time

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Results and Discussions, Continue
One Surrounded by Six

• 1. Displacement
• Contour plot
• Vector plot

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Conclusions

• A viscoplastic finite element formulation
  presented
• Three microscopic sintering models simulated
• Microscopic sintering behavior analyzed
• Effect of pore or particle size became clear
• Agreed with classic predictions and experiments
• Fundamental understanding of the sintering
  process

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Future Work

• Viscoplasticity is a good approximation in the
  initial sintering stage under 800 C
• Material becomes more liquid-like at elevated
  temperature
• A combined model in the future work

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Thank you!

• Question?

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Convergence to a Flat Surface
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Sintering Stress
Equivalent normal stress
Sphere under surface tension ?
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Model 1 Spherical Pore
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Model 2 Two contacted Particle
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Model 3 One Surrounded by Six
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Governing Equations
Flow equation
Evolution equation
with
where
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Material Parameters in Anands Model
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Model 1 Spherical Pore
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Model 2 Two contacted Particle
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Model 3 One Surround by Six
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Displacement of the Spherical Pore
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Displacement of the Spherical Pore
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Radial Displacement Versus Time
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Filled Volume versus Time
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Displacement of the Two Contacted Particles
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Displacement of the Two Contacted Particles
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Volume Shrinkage versus Time
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Neck Growth versus Time
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Displacement in One Particle by Six
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Displacement in One Particle by Six