LECTURE # 23
Chapter 7Fatigue Failure Resulting from Variable Loading Dr. A.
Aziz Bazoune
King Fahd University of Petroleum & MineralsMechanical
Engineering DepartmentDr. A. Aziz Bazoune Chapter 7: Fatigue
Failure Resulting from Variable LoadingME 307 Machine Design I
CH-07 LEC 25 Slide 2LECTURE 26Dr. A. Aziz Bazoune Chapter 7:
Fatigue Failure Resulting from Variable LoadingME 307 Machine
Design I It has midrange stress plotted along the abscissa and all
other components of stress plotted on the ordinate, with tension in
the positive direction.The endurance limit, fatigue strength, or
finite-life strength whichever applies, is plotted on the ordinate
above and below the origin.The midrange line is a 45o line from the
origin to the tensile strength of the part.
CH-07 LEC 25 Slide 3
Figure 7-24Modified Goodman diagram showing all the strengths
and the limiting values of all the stress components for a
particular midrange stressModified Goodman DiagramDr. A. Aziz
Bazoune Chapter 7: Fatigue Failure Resulting from Variable
LoadingME 307 Machine Design I CH-07 LEC 25 Slide 4Plot of Fatigue
Failures for Midrange Stresses in both Tensile and Compressive
Regions.Figure 7-25Plot of fatigue failures for midrange stresses
in both tensile and compressive regions. Normalizing the data by
using the ratio of steady strength components to tensile strength
Sm/Sut, steady strength component to compressive strength Sm/Suc,
and strength amplitude component to endurance limit Sa/Se enables a
plot of experimental results for a variety of steels.
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 25 Slide 5Master
Fatigue Diagram.Figure 7-26
Master fatigue diagram for AISI 4340 steel with Sut = 158 Sy =
147 kpsi.
The stress component at A are
min = 20, max = 120, m = 70, o = 50
all in kpsi
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide
6Fluctuating StressesFailure data for Sm in tension and in
compressionCOMPRESSIVE mean stresses are BENEFICIAL (or have no
effect) in fatigue TENSILE mean stresses are DETRIMENTAL for
fatigue behavior
S is for strength2.Representing mean stress effect using
modified Goodman Diagram
Mean Stress Effect (R -1)Dr. A. Aziz Bazoune Chapter 7: Fatigue
Failure Resulting from Variable LoadingME 307 Machine Design I
CH-07 LEC 26 Slide 7In Fig. 7-27, the tensile side of Fig. 7-25 has
been redrawn in terms of strengths, instead of strength ratios,
with the same modified Goodman criterion together with four
additional criteria of failure.Such diagrams are often constructed
for analysis and design purposes; they are easy to use and the
results can be scaled off directly. The early viewpoint expressed
on a diagram was that there existed a locus (sa, sm) diagram was
that there existed a locus which divided safe from unsafe
combinations of (sa, sm) . Ensuing proposals included:The parabola
of Gerber (1874), The Goodman (1890) (straight) line, The Soderberg
(1930) (straight) line.Dr. A. Aziz Bazoune Chapter 7: Fatigue
Failure Resulting from Variable LoadingME 307 Machine Design I
CH-07 LEC 26 Slide 8
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 9 As
more data were generated it became clear that a fatigue criterion,
rather than being a fence, was more like a zone or band wherein the
probability of failure could be estimated. We include the failure
criterion of Goodman becauseIt is a straight line and the algebra
is linear and easy.It is easily graphed, every time for every
problem.It reveals subtleties of insight into fatigue
problems.Answers can be scaled from the diagrams as a check on the
algebra.Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting
from Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 10
Either the fatigue limit Se or the finite-life strength Sf is
plotted on the ordinate of Fig. 7-27. These values will have
already been corrected using the Marin factors of Eq.(7-17). Note
that the yield strength is plotted on the ordinate too.This serves
as a reminder that first-cycle yielding rather than fatigue might
be the criterion of failure.The midrange-stress axis of Fig. 7-27
has the yield strength Syt and the tensile strength plotted along
it. Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 11The
criteria of failure are diagrammed in Fig.7-27:The Soderberg,The
modifiedGoodmanThe GerberThe ASME-ellipticYieldingThe diagram shows
that only the Soderberg criterion guards against any yielding, but
is biased low.Considering the modified Goodman line as a criterion,
point A represents a limiting point with an alternating strength Sa
and midrange strength Sm . The slope of the load line shown is
defined as .
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 12
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 13
BFAILURE CRITERIA (mean stress)1-Modified Goodman Theory
(Germany, 1899)
Factor of SafetyLoad Line slope
n = OA/OBFor infinite life Failure Occurs When:Dr. A. Aziz
Bazoune Chapter 7: Fatigue Failure Resulting from Variable
LoadingME 307 Machine Design I
BCDEFn = OC/OBCH-07 LEC 26 Slide 14FAILURE CRITERIA (mean
stress)2- The Soderberg Theory (USA, 1933)
Factor of SafetyFor infinite life Failure Occurs When:For finite
life fatigue strength Sf = sa replaces Se
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 15Factor
of Safety
BCDEF
n = OF/OBFailure Occurs When: Factor of SafetyFor finite life a
replaces SeFAILURE CRITERIA (mean stress)3- The Gerber Theory
(Germany, 1874) Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure
Resulting from Variable LoadingME 307 Machine Design I CH-07 LEC 26
Slide 16Factor of Safety
BCDEF
n = OE/OBFAILURE CRITERIA (mean stress)4- The ASME Elliptic
Failure Occurs When: Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure
Resulting from Variable LoadingME 307 Machine Design I CH-07 LEC 26
Slide 17Factor of Safety
BCDEF
n = OE/OBFailure Occurs WhenFor finite life sa replaces
SeFAILURE CRITERIA (mean stress)
4- The ASME Elliptic Dr. A. Aziz Bazoune Chapter 7: Fatigue
Failure Resulting from Variable LoadingME 307 Machine Design I
CH-07 LEC 26 Slide 185- The Langer (1st Cycle) Yield LineFAILURE
CRITERIAFailure Occurs WhenFactor of Safety
n = OD/OB
BCDEF
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 19
(7-43) (7-44) (7-45) (7-46) (7-47) Criteria EquationsDr. A. Aziz
Bazoune Chapter 7: Fatigue Failure Resulting from Variable
LoadingME 307 Machine Design I CH-07 LEC 26 Slide 20
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 21The
stresses na and nm can replace Sa and Sm, where n is the design
factor or factor of safety. Then, Eqs. (7-43) to (7-46) become:
(7-48) (7-49) (7-50) (7-51) Dr. A. Aziz Bazoune Chapter 7:
Fatigue Failure Resulting from Variable LoadingME 307 Machine
Design I CH-07 LEC 26 Slide 22We will emphasize the Gerber and
ASME-elliptic for fatigue failure criterion and the Langer for
first-cycle yielding. However, conservative designers often use the
modified Goodman criterion. The design equation for the Langer
first -cycle-yielding is
The failure criteria are used in conjunction with a load line,
Principal intersections are tabulated in Tables 7-9 to 7-11. Formal
expressions for fatigue factor of safety are given in the lower
panel of Tables 7-9 to 7-11. The first row of each table
corresponds to the fatigue criterion, the second row is the static
Langer criterion, and the third row corresponds to the intersection
of the static and fatigue criteria.
(7 *) Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting
from Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide
23The first column gives the intersecting equations and the second
column the intersection coordinates. There are two ways to proceed
with a typical analysis: One method is to assume that fatigue
occurs first and use one of Eqs. (7-48) to (7-51) to determine n or
size, depending on the task. Most often fatigue is the governing
failure mode. Then follow with a static check. If static failure
governs then the analysis is repeated using Langer Static yield
equation.
Alternatively, one could use the tables. Determine the load line
and establish which criterion the load line intersects first and
use the corresponding equations in the tables.Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable LoadingME 307
Machine Design I CH-07 LEC 26 Slide 24
TABLE (7-9)
Amplitude and Steady Coordinates of Strength and Important
Intersections in First Quadrant for Modified Goodman and Langer
Failure Criteria. FatigueCriterionStatic Langer
CriterionIntersection of the Static and Fatigue CriteriaDr. A. Aziz
Bazoune Chapter 7: Fatigue Failure Resulting from Variable
LoadingME 307 Machine Design I CH-07 LEC 26 Slide 25TABLE
(7-10)
Amplitude and Steady Coordinates of Strength and Important
Intersections in First Quadrant for Gerber and Langer Failure
Criteria. GerberLanger Intersection of Gerber and Langer
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 26TABLE
(7-11)
Amplitude and Steady Coordinates of Strength and Important
Intersections in First Quadrant for ASME Elliptic and Langer
Failure Criteria. ASME EllipticLanger Intersection of ASME Elliptic
and Langer
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide
27Special Cases of Fluctuating StressesCase 1: sm fixed
Case 2: sa fixed
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 28Case
3: sa / sm fixed
Case 4: both vary arbitrarily
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I
CH-07 LEC 26 Slide 29
EXAMPLE 7-11 (Textbook)
Solution(7-18) (7-4), p. 329 Dr. A. Aziz Bazoune Chapter 7:
Fatigue Failure Resulting from Variable LoadingME 307 Machine
Design I CH-07 LEC 26 Slide 30EXAMPLE 7-11 (Textbook)
(7-25), p. 331 (7-8), (7-17), p. 325, p. 328 (7-10)Dr. A. Aziz
Bazoune Chapter 7: Fatigue Failure Resulting from Variable
LoadingME 307 Machine Design I CH-07 LEC 26 Slide 31
(7-*)(7-28)(7-10)
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 32
Figure 7-28
Principal points A, B, C, and Don the designers diagram drawn
for Gerber, Langer and load line.Dr. A. Aziz Bazoune Chapter 7:
Fatigue Failure Resulting from Variable LoadingME 307 Machine
Design I CH-07 LEC 26 Slide 33
(7-28)7-10Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure
Resulting from Variable LoadingME 307 Machine Design I CH-07 LEC 26
Slide 34
7-297-11
Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from
Variable LoadingME 307 Machine Design I CH-07 LEC 26 Slide 35
Figure 7-29
Principal points A, B, C, and Don the designers diagram drawn
for ASME Elliptic, Langer and load lines.Dr. A. Aziz Bazoune
Chapter 7: Fatigue Failure Resulting from Variable LoadingME 307
Machine Design I CH-07 LEC 26 Slide 36
7-11Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting
from Variable LoadingME 307 Machine Design I