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Ceramics and glasses

For a ceramic with a Weibull modulus m = 10, specimens of volume V had a characteristic strength of 500 MPa. Using the Weibull volume effect σ₂/σ₁ = (V₁/V₂) to the power 1/m, which value is closest to the characteristic strength of a component of volume 10V made of the same material?

  1. AAbout 50 MPa
  2. BAbout 500 MPa (unchanged)
  3. CAbout 397 MPa
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Answer: C. About 397 MPa

In the weakest-link picture, a larger volume is more likely to contain a large flaw, so strength falls. σ₂ = 500 × (1/10) to the power 0.1 = 500 × 0.794 ≈ 397 MPa. About 50 MPa assumes strength is inversely proportional to volume; in fact it enters through the m-th root, so the drop is gradual. About 500 MPa treats strength as a size-independent material constant, as for metals. Using the bend strength of small specimens directly to design a large component errs on the unsafe side, so the design of ceramic components corrects the strength for differences in effective volume.

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