Observations of fatigue crack nucleation and early growth are presented. The state of stress/strain was shown to play a significant role in this process. Early growth occurs on planes experiencing the largest range of shear strain (Mode 2) or normal strain (Mode 1) depending on the stress state, strain amplitude, and microstructure. These observations were summarized in a fatigue map for each material. These maps provide regions where one fatigue failure mode dominates the behavior. Each failure mechanism results in a different failure mode. Once the expected failure mode is identified, bulk deformation models based on the cyclic stresses and strains can be used to obtain reliable estimates of fatigue lives for complex loading situations

Socie, Darrell

English

NASA Technical Reports Server

N88-22423
FATIGUE DAMAGE MAPPING
Darrell Socie
Department of Mechanical and Industrial Engineering
University of Illinois at Urbana-Champaign
Observations of fatigue crack nucleation and early growth are presented.
The state of stress/strain has been shown to play a significant role in
this process. Early growth occurs on planes experiencing the largest
range of shear strain (Mode II) or normal strain (Mode I) depending on the
stress state, strain amplitude, and microstructure. These observations
have been summarized in a fatigue damage map for each material. These
maps provide regions where one fatigue failure mode dominates the
behavior. Each failure mechanism results in a different failure mode.
Once the expected failure mode has been identified, bulk deformation
models based on the cyclic stresses and strains can be used to obtain
reliable estimates of fatigue lives for complex loading situations.
Work done under NASA Grant NAG3-465.
3-213
https://ntrs.nasa.gov/search.jsp?R=19880013039 2020-03-20T06:30:13+00:00Z
EXECUTIVE OVERVIEW OF FATIGUE DAMAGE MAPPING 
I I I I I 
A 
LO 
088 
rc 0.6 
7 
z \ 
0'4 
082 
0 
A fatigue damage map for Inconel 718 loaded in cyclic tension is 
given below. The vertical scale is presented in terms of life fraction 
and the horizontal scale in terms of fatigue life. The solid line repre- 
sents the first observation of a surface crack 100 pm long and serves as a 
demarcation between initiation and growth. The dashed line represents the 
demarcation between crack growth on planes of maximum shear strain ampli- 
tude and crack growth on planes of maximum principal strain amplitude. 
Region A is characterized by shear initiation followed by extensive shear 
crack growth with final failure occurring by a linking of shear cracks 
similar to the tearing of perforated paper. Region B is characterized by 
shear initiation followed by crack growth along the principal stress 
direction. A third region is often observed at long lives and small 
strains where there is no observable initiation or shear initiation 
resulting in nonpropagating cracks. A separate damage model is required 
for each region. 
IN-718, Tension 
-Region A  
\ \ . \ Tensile Crack Growth 
Shetar Crack Growth / A  _ - I  
3-214 
EXECUTIVE OVERVIEW OF FATIGUE DAMAGE MAPPING
The damage maps indicate that a shear strain ba_ed theory is most
appropriate for this material for lives below about i0 _ cycles. One such
damage parameter has been proposed by Fatemi and Socie (1985)
0
n]
Oy
Two parameters are considered to cause fatigue damage. The primary damage
is caused by the cyclic shear strains (y). Stresses normal to the cyclic
shear strain tend to open any microcracks and enhance their growth. Hence
the second term can be interpreted as including crack closure effects.
The term also includes effects from any additional cyclic hardening that
is often observed during nonproportional loading. The stress normal to
the shear crack (On) is normalized with the yield strength (o) to retain
the dimensionless _eatures of strain. In this formulationJno fatigue
damage is computed for planes in the material that do not experience
cyclic shear strain. Results are presented for a wide variety of loading
histories including tension, torsion, biaxial tension, and tests with
complex multiaxial mean stresses. Both proportional and nonproportional
tests are included. This degree of correlation is only possible because
the damage mechanism does not change for the variety of tests considered
here.
162
io-3
4-
<_.
I i I I i Illl I I i I I I I1| I
r/=1.0
D
D
x x
I I I I I Ill I I I I I IIII I I I I I I1_
FATIGUE OF INCONEL 718
O TENSION-ToRsION, COMPLETELY REVERSED
TENSION-TORSION, MEAN STRAIN
Q TENSION-ToRsION, OUT-OF-PHASE
• BIAXIAL-TENSION
X UNIAXIAL, SMOOTH SPECIMEN
X XX
• coX x
X X _X
xx
Z_ x x x--re.
I I l J IIII I I I I I IIII
104
I I I I I IIII f t I i trill I I t I II
,o ,o" ,o'
Nf, Cycles
3-215
FATIGUE DAMAGE MAP FOR INCONEL 718
Test data from individual stress states are summarized in the fatigue
damage map for Inconel 718 given below. The vertical axis has now been
plotted in terms of hydrostatic stress normalized by the maximum principal
stress. Torsion, tension and biaxial tension have values of O, i/3, and
2/3, respectively. Regions of similar fatigue failure modes are given.
Little data exists for the case of biaxial tension and these lines are
shown as dashed. The map shows that over a wide range of stress states
and strain amplitudes the primary failure mechanism is one of shear crack
growth. The x symbols in the preceding figure that fall to the right of
the central tendency of the test data represent large compressive mean
stress tests. This type of behavior is expected since the fatigue damage
map shows a transition from shear to tensile dominated behavior at longer
lives. In this failure mode, compressive stresses would retard crack
growth and prolong fatigue lives.
I0
---2/3
f-N
b
_ 1/3-
0
102
IN-718
Region A
i I I IIII]
103
\\ %%. Region C
%%
I I Illllj I , I I IIIIj I I I I I IIIj I I I r I,IfJ_.
10 4 10 5 10 6 10 7
Nf (cycles)
3-216
FATIGUE DAMAGE MAP FOR 304 STAINLESS STEEL
The fatigue damage map for 304 stainless steel is given below. Note
that the region of shear behavior found in Inconel 718 is restricted to a
narrow range in 304 stainless steel. There is a large region of tensile
dominated behavior. It is suggested that a tensile strain based model is
most appropriate here. One such model has been proposed by Smith, et al.
(1970), and has found widespread use in uniaxial fatigue situations.
°max s a
Two parameters are considered
damage. The maximum principal
stress normal to that plane, Omax.
to be the driving force for fatigue
strain amplitude, s a, and the tensile
I0
2/3
b
b
304 Stainless Steel
\
\
\
C
I130 -
102 103 104 105 lO6 I07
Nf (cycles)
3-217
LIFE ESTIMATIONS FOR 304 STAINLESS STEEL
Test data for 304 stainless steel from Socie (1987) for both
proportional and nonproportional tests are given below. This material
cyclically hardens under nonproportional loading to a stable stress level
that is nearly double that of a proportional test. The increase in cyclic
stress is very damaging and must be accounted for in the model. For the
same total strain range, uniaxial loading has the largest plastic strain
range and longest life. Nonproportional loading tests have the smallest
plastic strain range, largest stress range and shortest life.
1
i0
O4
_u
0
E
0
%
0
%
0
J I I I Ill
104
304 Stainless Steel
O0 o
0 00CD o
&
I i i ]liil
105
Nz.o
I I I i i 'lllil
3-218
MULTIAXIAL MEAN STRESS EXAMPLE
Two loading cases that have the same shear damage parameter are given
below. Consider a standard uniaxial test specimen, Case A, tested in zero
to maximum strain cycling. A tensile mean stress o will result. Now
consider a second test, Case B, of a tubular specimen _ested with the same
axial strain range only in completely reversed loading. The magnitude of
the mean stress in the first test is applied as a hoop stress in the
second test. Since the shear damage parameter is the same for both tests
the fatigue lives would be expected to be similar for a material that
fails in a shear mode. Note that the tensile damage parameter for the
second test is much lower since there is no mean stress in the plane
experiencing the largest range of cyclic principal strain. Results for
Inconel 718 are as follows:
a_/2 o Case A Case B
0.0005 2_0 4245 6735
9768 7221
These tests confirm the selection of the damage parameter since the lives
are the same for both tests. The tensile model predicts an increase in
fatigue life for Case B that was not observed experimentally.
Case A
( R = 0 loadingwith Oo
MeanTensile Stress)
G
Case B o
(R =-1 loadingwith Oo
Mean Hoop Stress)
External
Loading
Conditions
2'2
t A_ Ao
o
o
o
Maximum Stress
and Maximum Strain
Amplitude on Shear Plane
/
/
/
G 7//
oo ;
/
/
/
T= (l+v) _'_
2
3-219
/
/
/
/
/
/
/
T= (1+v)"_
2
%°=_2 2 +0°)
Maximum Stress
and Maximum Strain
Amplitude on Tensile Plane
2
o_ax=A.__o+ %2
ornax
E = A-.-_
2
_ax =Aa
2
i" REFERENCES
Fatemi, A., and Socie, D. F. (1987), "A Critical Plane Approach to
Multiaxial Fatigue DamageIncluding Out-of-Phase Loading," accepted for
publication in Fatigue and Fracture Engineering Materials and Structures.
Smith, R. N., Watson, P., and topper, T. H. (1970), "A Stress-Strain
Function for the Fatigue of Metals," Journal of Materials, JMLSA, Vol. 5,
No. 4, pp. 767-778.
Socie, D. F. (1987), "Multiaxial Fatigue Damage Models," Journal of
Engineering Materials and Technology, Vol. 109, No. 4, pp. 293-298.
3-220


Fatigue damage mapping

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server