Statistical variation of material properties

In practice, material properties are seldom homogenous, as they are sensitive to variations in parameter such as :

Composition, heat treatment & processing condition.

Others that influence material behavior

Surface roughness, internal stress, sharp corners and stress raiser.

Variation in material properties can be solved by choosing factor of safety.

Factor of safety accommodates unknown influences that affect the life of component under service condition.

Statistical variation of material properties

Material properties can be statistically described by mean value, standard derivation and coefficient of variation.

Experiment data obtained from large number of samples, material properties follow a normal distribution.

It is possible to estimate statistical data from non-statistical sources that give range or tolerance limits.

In this case the standard deviation S is approx. given by :

S = (max. value of property – min. value)/6 …… ( 1.1 )

Statistical variation of material properties

Example

If the range of strength of an alloy is given as 800 – 1200 MPa, and the mean value can be taken as 1000 MPa

The standard deviation S can be estimate as

S = ( 1200 – 800 )/6 = 66.67 MPa

The coefficient of variation v is then

v = 66.67/1000 = 0.0667

•If sample is about 25 test eq. 1.1 is to divide by 4

•A sample of about 5 to divide by 2