66
Chapter 2
VI. FATIGUE
This section uses materials from [2.10] Faupel and Fisher, Engineering
Design, 2nd Edn (1981) John Wiley and Son Inc. the pages 766-782 and
795-798 are used with the permission of Wiley Liss Inc., a subsidiary of
Wiley and Sons Inc. Revisions and additions have been made to reflect
the uses of probability.
The material is developed to reflect the probability variations in all of
the parameters and to use the concepts in Section V. Authors such as
[2.9,2.17,2.26] and others cited are drawn upon to attempt to apply probability to a semi-empirical approach to fatigue through the use of ~rr-~rm
curves and data concerning the variation of parameters.
The critical loading of a part is in tension under varying loads and
temperatures. When the materials are below their high temperature creep
limits and above the cold transition temperatures for ductility and operating
with a linear stress-strain motion or a reversible one the ~r-C% curves can be
used. The creep limits and cold transition temperatures should be determined for a proposed material as the character Will define the thermal limits
of a part. Conversely thermal maximums and minimums of a design will
define the only materials which can meet the design requirements. The temperatures below the cold transition can be analyzed with ~rr--Crm curves with
proper corrections for temperature. The problem of elastic buckling may
also be considered for the proper fatigue life.
The equations for the fatigue curves are
Soderberg’s law
~r~m + a~ = 1
(2.44)
O’y O"
e
Goodmants law
~r,n + ~rr = 1
(2.45)
O" u
O- e
Gerber’s law
[ \[am] + a~ =
(2.46)
err and ~rm are derived from the loading, the part shape and dimensions. The
unknown values can be solved for but Eqs. (2.44)-(2.46) will allow
one unknown in each equation. Two or more unknowns require as many
equations or an iteration procedure.
If the Soderberg curve, Eq. (2.44), for a simple stress is examined [2.9]
KI ~m g2ar
~m
~r
~
~-~q
~-1
(2.47)
ay
ae
a~/K~ ae/K2
For all three equations (Eqs. (2.44)-(2.46)), Ki factors infl uencing fatigue
Chapter 2
VI. FATIGUE
This section uses materials from [2.10] Faupel and Fisher, Engineering
Design, 2nd Edn (1981) John Wiley and Son Inc. the pages 766-782 and
795-798 are used with the permission of Wiley Liss Inc., a subsidiary of
Wiley and Sons Inc. Revisions and additions have been made to reflect
the uses of probability.
The material is developed to reflect the probability variations in all of
the parameters and to use the concepts in Section V. Authors such as
[2.9,2.17,2.26] and others cited are drawn upon to attempt to apply probability to a semi-empirical approach to fatigue through the use of ~rr-~rm
curves and data concerning the variation of parameters.
The critical loading of a part is in tension under varying loads and
temperatures. When the materials are below their high temperature creep
limits and above the cold transition temperatures for ductility and operating
with a linear stress-strain motion or a reversible one the ~r-C% curves can be
used. The creep limits and cold transition temperatures should be determined for a proposed material as the character Will define the thermal limits
of a part. Conversely thermal maximums and minimums of a design will
define the only materials which can meet the design requirements. The temperatures below the cold transition can be analyzed with ~rr--Crm curves with
proper corrections for temperature. The problem of elastic buckling may
also be considered for the proper fatigue life.
The equations for the fatigue curves are
Soderberg’s law
~r~m + a~ = 1
(2.44)
O’y O"
e
Goodmants law
~r,n + ~rr = 1
(2.45)
O" u
O- e
Gerber’s law
[ \[am] + a~ =
(2.46)
err and ~rm are derived from the loading, the part shape and dimensions. The
unknown values can be solved for but Eqs. (2.44)-(2.46) will allow
one unknown in each equation. Two or more unknowns require as many
equations or an iteration procedure.
If the Soderberg curve, Eq. (2.44), for a simple stress is examined [2.9]
KI ~m g2ar
~m
~r
~
~-~q
~-1
(2.47)
ay
ae
a~/K~ ae/K2
For all three equations (Eqs. (2.44)-(2.46)), Ki factors infl uencing fatigue