168 4. RELIABILITY OF A COMPONENT UNDER STATIC LOAD
% The goodness-of-fit test on the data in the excel
% file “Example 4.5.xls”.
X=xlsread('Example4.4');
Q2=fitdist(X,'norm')
h=chi2gof(X,'CDF',Q2)
4.4 MECHANICAL PROPERTIES OF MATERIALS AS
RANDOM VARIABLES
Most material mechanical properties for mechanical component design typically come from two
types of testing: tensile testing and shear (torsion) testing. From tensile testing, we can obtain
four important material mechanical properties: Young’s modulus E, yield strength S
y
, ultimate
strength S
u
, and Poisson ratio . From torsion testing, we can obtain three important material
properties: shear Young’s modulus G, shear yield strength S
sy
, and ultimate shear strength S
su
.
For a set of test specimens with the same dimension and same material, different material
mechanical properties will be obtained from each test; even tests are conducted on the same test
equipment with the same test procedure. erefore, material mechanical properties are random
variables because there are always some slight variations in chemical composition and some vari-
ations in heat treatment and manufacturing process for the same brand name of the material.
Another important cause for this is that there are always some randomly distributed “defects” in-
side materials such as voids and dislocation [2]. After test data of material mechanical properties
are collected, we can determine their types of distributions and corresponding distribution pa-
rameters. Typically, we can use a normal distribution or a log-normal distribution, or a Weibull
distribution to describe material mechanical properties.
Table 4.4 displays mean, standard deviation, and coefficient of variance of Young’s mod-
ulus E, shear Young’s modulus G, and Poisson ratio of some materials from the literature [3].
In this table, Young’s modulus E, shear Young’s modulus G, and Poisson ratio all follow a
normal distribution. In the second row of this table,
X
,
X
, and
X
are the mean, standard
deviation, and coefficient of variance of a normally distributed random variable X , respectively.
e subscript X in the second row can be Young’s modulus E, the shear Young’s modulus G,
and the Poisson ratio .
Dr. E. B. Haugen published a book [4] in 1980 and provided distribution parameters
of yield strength and ultimate strengths of some materials. Following Tables 4.5–4.10 are a
small selected data form this book. In these tables,
S
u
,
S
u
, and
S
u
are the mean, standard
deviation, and coefficient of variance of ultimate strength, respectively.
S
y
,
S
y
, and
S
y
are
the mean, standard deviation, and coefficient of variance of yield strength, respectively. ose
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