Weibull Analysis Flashcards
What are the Weibull statistics?
Probability of survival or failure, effect of sample volume, variability or consistency of strength
What are the Weibull parameters m and stress o?
M: Weibull shape parameter or modulus - higher m value = narrower distribution of strength so more confidence of strength across a material, lower m value = lower confidence of strength
Stress o: Weibull scale parameter
What is the effect of specimen volume of distribution of strength?
Smaller specimen of same material - likelihood of having a higher strength as less potential for a large defect
What are V and n in Weibull volume analysis?
V is the volume of a discrete element
N is the number of discrete elements in a specimen
N x V = Total Volume
What does an infinite, zero and 10-25 value of m mean?
Infinite means at a given stress value, all will fail (ideal)
Zero means probability is the same at all stresses (worst case)
10-25 is a good range of m value - percentage confidence of when ceramics will fail
What is zero point stress?
Stress where Ps(V) = 1
What is the Weibull equation and how do you plot it?
Ps(V) = exp(-V (appliedstress - zeropointstress / mean stress of samples)^m)
Double log it then plot it:
Lnln(1/Ps) = ln(V) + m ln(appliedstress - zeropointstress)
Gradient = m
What is time dependent failure?
Fixed load but component still fails over a period of time
Eg. If water formed Silicon Hydroxide with Silicon in a metal, it would increase a crack size until it reaches the critical crack length
What test is used to find the effect of K1 on crack growth velocity?
Double torsion test
What are the two ways of presenting time dependent failure data?
SPT Diagrams (Strength-Probability-Time)
Proof Testing
What is the effect of thermal shock on ceramics?
When temperatures vary rapidly, the change in temp and finite room for thermal expansion leads to stresses that can cause failure.
The surface wants to contract but the hot interior constrains it so tensile stresses appear at surface which can lead to cracking and fracture.
What is the equation for stress related to a temperature change?
Stress = Eatemp change
Temp change is average internal temp minus the environment temp
A = thermal expansion coefficient
What is the equation that gives the temperature change required for fracture?
Temp change for fracture = fracturestressk / Ea
K = thermal conductivity of solid
