← All parts of this equation

Equation 27 · Part 6 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

=

Ps=exp⁡[−V(σσ0)m],P_s = \exp\left[-V\left(\frac{\sigma}{\sigma_0}\right)^{m}\right],
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

If the strength of a brittle body is set by its largest flaw, and flaw populations are random, then strength is a random variable and reporting a mean is an error of category. The standard treatment is the Weibull weakest-link model, in which the probability that a body of volume V survives a uniform stress σ\sigma is Ps=exp⁡[−V(σσ0)m]P_s = \exp\left[-V\left(\frac{\sigma}{\sigma_0}\right)^{m}\right]. with m the Weibull modulus and σ0\sigma_0 a scale parameter. A larger m means tighter scatter. A review of Weibull analysis across ceramics reports moduli of roughly 10 or below for many advanced ceramics such as alumina, hydroxyapatite and silicon carbide, below about 7 for the glass-ceramics and zirconias surveyed, and above 40 for one magnesium-based glass,…

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.