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Materials processing and joining

A green compact at 70% relative density is sintered to 95% relative density. Assuming isotropic shrinkage and no change in mass, which value is closest to the linear shrinkage (fractional decrease in length) due to sintering?

  1. AAbout 9.7%
  2. BAbout 26%
  3. CAbout 36%
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Answer: A. About 9.7%

Since the mass does not change, the volume is inversely proportional to the density, so V/V₀ = 0.70/0.95 ≈ 0.737. Because the shrinkage is isotropic, the length ratio is the cube root of the volume ratio, (0.737)^(1/3) ≈ 0.903, and the linear shrinkage is 1 − 0.903 ≈ 9.7%. About 26% is the volume shrinkage 1 − 0.737, and about 36% is the increase in relative density (0.95 − 0.70)/0.70; neither is the fractional decrease in length. When making sintered parts, the die dimensions are made larger to allow for this shrinkage. If the green density varies from place to place, because of friction with the die wall and the like, the shrinkage also varies, causing warping and dimensional scatter after sintering.

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