CLOSURE OF FATIGUE CRACKS AT HIGH STRAINS by Nagaraja S. Iyyer Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of APPROVED: J. N. Reddy MASTER OF SCIENCE in Engineering N. E. Dowling, Chairman September, 1985 Blacksburg, Virginia C. W. th
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CLOSURE OF FATIGUE CRACKS AT HIGH STRAINS
by
Nagaraja S. Iyyer
Thesis submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
APPROVED:
J. N. Reddy
MASTER OF SCIENCE
in
Engineering ~echanics
N. E. Dowling, Chairman
September, 1985 Blacksburg, Virginia
C. W. Sm~ th
CLOSURE OF FATIGUE CRACKS AT HIGH STRAINS
by
Nagaraja S. Iyyer
{ABSTRACT)
Experiments were conducted on smooth specimens to study the
closure behavior of short cracks at high cyclic strains under
completely reversed cycling. Testing procedures and methodology, and
closure measurement techniques, are described in detail. The strain
~cvels chosen for the study cover from predominantly elastic to
grossly plastic strains. Crack closure measurements were made at
different crack lengths. The study reveals that, at high strains,
cracks close only as the lowest stress level in the cycle is
approached. The crack opening was observed to occur in the
compressive part of the loading cycle. The applied stress needed to
open a short crack, under high strain was found to be less than for
cracks under small scale yielding. For increased plastic
deformations, the value of a0 p/amax is observed to decrease and
approaches the value of R. Comparison of the experimental results
with existing analysis has been made and indicates the limitations of
the small scale yielding aporoach where gross plastic deformation
behavior occurs.
ACKNOWLEDGEMENTS
The author would like to thank his committee chairman, Or. N. E.
Dowling, for imparting knowledge and valuable guidance during the
course of this study. In particular, his patience, helpful
criticisms, suggestions and constant encouragement throughout this
study is deeply appreciated. The author would also like to
acknowledge the guidance and suggestions of Professor J. N. Reddy and
Professor C. W. Smith in the preparation of this thesis.
The author thanks Mr. Robert F. Davis, Mr. Kenneth McCauley and
Mr. George C. Lough for their constant help and assistance while
conducting experiments. A warm and sincere thanks is also extended
to Ms. Paula Lee and the secretari~~ staff of Engineering Science and
Mechanics Department.
A very special thanks to Mr. Tom W. Orange of NASA Lewis
Research Center who was the technical monitor of this study.
Financial support of NASA Lewis Research Center uner grant no. NAG-3-
438 is acknowledged.
( i i i )
Chapter
Abstract
TABLE OF CONTENTS
Page
( i i )
List of Figures......................................... (vi)
List of Tables •..•..............•...••.................. (viii)
1 Introduction and Literature Review
1.1 Short Cracks and Their Importance............. 1
Crack surface displacements and stress distributions (26)
Schematic diagram of roughness induced closure
Schematic diagram of oxide induced closure
Monotonic and cyclic stress-strain curve for AISI 4340 steel [411
Strain life curve for AISI 4340 steel (40)
Specimen geometry
Hydraulic actuator with the stiffener
Assembled view of the grip
Details of the grip
Deflection control testing with t~o clip gauges
(a) Schematic diagram of strain measurements (b) Correlation between plastic strains
Strain control testing with the clip gauge mounted across the grip ends.
A typical measurement of cack length vs cycles
da/dn vs ~K for AISI 4340 steel (40)
Schema:ic diagram of closure measJrement
Typical crack at varic~s stress levels in one ccmp1ete cycle
( v i )
Fig. 20-38: Crack opening displacements measured in one complete cycle
Fig. 39:
Fig. 40:
Fig. 41:
Fig. 42:
Fig. 43:
Fig. 44:
Fig. 45:
(a) Load displacement loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
(b) Crack opening displacement during increasing (loading) and decreasing strain (unloading) at different points along the crack length. Different stress (strain) levels correspond to the points shown in load displacement loop.
(c) Crack opening displacement as a function of stress at different points along the crack length during increasing and decreasing strain.
(d) Crack opening displacement as a function of strain at different points along the crack length during increasing and decreasing strain.
Loading and unloading paths in a typical coo vs stress, and COD vs. strain plots.
Typical measurement of the crack opening stress level (cop).
Crack opening stress level as a function of crack length
Crack opening strain level as a function of crack length
Crack opening stress level as a function of t'.J
Crack opening stress level as a function of R
Schematic diagram of the real crack behavior at high strains and corresponding ideal crack behavior.
('I i i )
LIST OF TABLES
TABLE 1: Chemical Composition
TABLE 2: Mechanical Properties
(viii)
CHAPTER 1
INTRODUCTION ANO LITERATURE REVIEW
The present day concern of fracture mechanics is the study of
critical crack sizes which have a significant effect on the life of a
component. The failure of a structure or a component is often due to
the presence of a crack of critical size. Fatigue, which causes
failure of materials by the incipient growth of flaws, is the most
important cause. Thus, understanding the behavior of microcracking
and growth of small cracks in fatigue leads to the development of
improved methods of predicting lives of components.
Failure of materials under fatigue involves Ill the following:
1. Initial cyclic damage (cyclic hardening or softening)
2. Formation of initial microscopic flaws (microcrack initiation)
3. Microcrack coalescence to form a propagating flaw (microcrack
growth)
4. Macroscopic propagation of this flaw (macrocrack growth)
5. Failure instability
Often steps 1 and 2 described above are referred to as crack
initiation, 3 and 4 as crack propagation.
1.1 SHORT CRACKS ANO THEIR IMPORTANCE
The definition of a short crack depends on the nature of tne
problem being considerec. Reference 2 lists various considerations
for defining short cracks, such as the following:
2
1. Relative size of the crack with respect to the microsructure
(grain size etc., 0.4 x 10-6 in to 2 x 10-3 in.)
2. Relative size of the crack with respect to the plastic zone
(typically 0.004 in. in high strength materials, or 0.04 in. to
0.4 in. in low strength materials, and varying with stress level)
3. Size of the crack with respect to thickness (constraint)
4. Size of the crack with respect to the applicability of linear
elastic fracture mechanics, LEFM.
5. Crack detecting capability i.e., cracks that are so small that
they are difficult to find (0.004 in. to 0.04 in.)
Thus, an exact definition of a short crack cannot be made. The
size of a crack to be considered as short (small) depends on the
perspective of the problem that one is faced with.
A reasonable and improved estimate of the life of a comoone~t
can be made by the study of short crack initiation and growth. Since
most service failures are caused by cyclically varying stresses which
cause progressive failure of a component, the short crack problem in
fatigue is of major concern. Advances in the understanding of short
crack growth have enabled increasing~y quantitative studies to be
pursued into the soecific mechanisms that affect initiation and
growth. Manufacturing related problems associated with small cracks
that affect the lives of structural components have been identified
[31. References [4,5,61 discuss the ;mportance of the short cracK
problem.
3
Since the similitude relative to the metallurgical structure
breaks down for short cracks, the local effects will be dominant in
the materials response. Material inhomogenieties, such as crack
front irregularities, second phase particles or inclusions, and grain
boundaries play a vital part in affecting the local stress field and
hence the materials response. In the case of long cracks, all these
effects are integrated and averaged over many grains. But in the
short crack case, the following are important: applied stress, yield
stress and yield properties, crystallographic anisotropy,
homogeneity, and environment.
The behavior of short cracks as to their propagation is
different from that of long cracks, which can be generally handled by
LEFM. The literature indicates that study of short cracks should
If the crack is assumed to have a residual displacement
of 5r appended to its surfaces, then the crack closure can be assumed
to occur at the tip to get a lower bound on (KcloslKmax)• when
o - M - 5R = 0
Normalizing with respect to crack tip opening displacement, 50
a M 6 R -----=O 60 00 60
Observing the crack tip displacement, at n2 0 i.e., when o=a , 0
1 M aR 0 - - - - =
60 00
fK - K ) 2 , ' max , cl os - l 2Eay g(x/tlw)J
(19)
(20)
(21)
(22)
30
Since g(x/6w)lx=O =1 we get
66 = 1 (l _ Kclos)2 60 2 Kmax
(23)
Equation (13) becomes
1 1 - 2 ( 1 0 (24)
or K l 6R
C OS = 1 - 12(1 - ~) Kmax 60
(25)
This closure level is for the crack tip, but first contact of cracks
may occur behind the crack tip, as is the case in Budiansky and
Hutchinson's [251 analysis. A similar form of the equation for the
first contacL closure level has been shown [25,271 to be
K clos Km ax
(26)
During the reloading process, the crack starts opening, and the value
if Kopen when the crack has been fully opened up has been calculated
as for R=O loading as [251
K ~ 0.557 K max
(27)
The above equations have been derived based on the assumptions of
small scale yielding, ideally plastic materials, and plane stress
situations.
From equations (25) and (26) it is observed that the K leve~ at
the contact in the crack ~iD regicn and at first contact anywhere are
31
different. In their analysis, Budiansky and Hutchinson showed that
first contact occurs behind the crack tip. Contrary to this, it has
been observed that in our study, within the resolution experimentally
possible, that contact of cracks occurs first at the tip, in
agreement with the analysis of Newman [ 26]. It was a 1 so observed in
one case only that the crack front irregularities enabled the crack
to close behind the crack tip in a manner consistent with roughness
induced closure.
3.2.2 MODELS OF NEWMAN AND OF NAKAI
An analytical fatigue crack closure model was develooed by
Newman [26] "'hi ch is based on the Dugdale model, but modified to
leave plastically deformed material in the waKe of the advancing
crack tip. A fatigue crack growth analysis program (FASTRAN)
developed by Newman calculates the crack opening stresses under
simulated plane stress and plane strain conditions. The model
developed cannot handle general yielding conditions but is quite
representative of small scale yielding conditions. A simulated plane
strain situation is chosen and the results of Newman's analysis are
shown in Fig. 43.
Recently Nakai et.al. [28] extended Budiansky and Hutchinson's
analysis to short cracks growing from notches under small scale
yielding conditions, and they ar~ived at an equation for ooening the
stress as
32
where ~ = ~w/w is the reversed plastic zone ratio at Kmin'
h=i/w, 1, being the crack length, and R is the ratio of the minimum
stress level to the maximum stress level. The term I{/___!i__h} is a ~-
first order elliptical integral, which is read from mathematical
tables. The reversed plastic zone ratio, ~ at Kmin has been obtained
[27] from Budiansky-Hutchinson's analysis. Such as
1 ~ n-h 112 R = - 2 ~ ((~-n)n) dn
1 l + - J
"!T ~
1/2 1/2 ( 1-h ) l rn 11 + {1-1) I dn (n-~)n 2 1 - (l-1)1/2 (29)
Solving this equation numerically for~ for representative cases
similar to the crack size and plastic zone sizes in our study, the
results are depicted in the crack opening map of Fig. 43. It is to
be noted that the above equations are obtained for small scale
yielding and for cracks growing from nothces where closure cannot
occur over the notch.
Along with these results, values obtained from Elber's estimated
empirical relation (equation 2) is also shown in Fig. 43. The
results from the present study are also indicated in the same fig.
43.
33
3.2.3 COMPARISON OF EXPERIMENTAL RESULTS WITH EXISTING MODELS
The effective stress intensity opening ratio, U, has been found
to increase as the crack length becomes shorter and approaches
unity. When the crack is open throughout the unloading part of the
cycle, closing only at the minumum stress level, the the effective
stress intensity range, defined by
U oK (30)
becomes equal to oK, the overall stress-intensity range. From our
present experimental results, conducted at R=-1 at different strain
levels, it is observed that the crack closes first at the lowest
stress in the cycle, c . , and remains closed for a part of the min loading cycle till it opens at a value J (c > c . ) . This can op op min be seen from the Figures 20-38. If we apply these results to the
equation for crack closure obtained earlier in equation (26) Ne
observe that
K clos K max
. 2 1 - ,, 1 - (~)
~o ( 31)
since sR/5 0 ·1 as R·l, and ~R/S 0 ·0 as R·-n, a reasonable choice for
the estimate of sR/c 0 coLl1d not be made from our present study, since
closure of the cracks was first observed at : . , corresponding to min Kmin· (For R=O loaaings, Budiansky and Hutchinson [25l have
estimated the sR value as 0.856 0 ).
34
Crack closure and opening stress level analysis for cracks
subjected to stress beyond the yield stress does not exist in the
literature. Following the elastic, small scale yielding analysis
gives inconsistent results. This is observed in fig. 43 where the
present data is pictured along with the analytical results.
Our observation that crack closure occurs only at ~ . , suggests mm
that 6R/6 0 =-1, (from eqn. 25) which is not meaningful. If cR taken
to be zero then,
since u Kclos
1 -K-max (---,,.-------=--1 - R 1 (32)
Thus, for short cracks ~hich are subjected to stresses beyond yield,
the crack closure level which occurs at 0 . , and the crack opening mm
level, ~ , may both have significant effects on the growth behavior op of the crack. Since the crack tip advances only in the loading part
of the cycle, the crack opening level, :op' may ~e relatively more
important. If we define the effective stress intensity as
(33)
where, U' is defined as
u-1 - K /K op max 1
1 - R (34)
then, we observe that :he i~creasea plastic deformations, the value
of K0 p/Kmax decreases and approaches the value of R making the va'ue
of J' to approach uni:;. •rom this aefinition of effective stress
35
intensity we observe that for shorter cracks, under large scale
deformations, the value of the effective stress intensity, 6Keff' is
significantly different from the earlier definition of the effective
stress intensity.
From our present results it is observed in most of the cases
that the crack opened in the compressive part of the loading cycle.
This revealed the significant difference in the crack closure and
opening levels, and these do not occur at the same stress level as
assumed in some studies.
From the crack opening displacement versus strain plots in
Figures 20-38, it is also noted that the cracks do not open and close
at the same strain levels. Hence, at high stress-strain levels where
significant plstic strain is involved, the available analysis on
closure/opening of fatigue cracks is insufficient.
CHAPTER 4
GENERAL DISCUSSION
Figure 41 illustrates the crack opening stresses normalized with
respect to the maximum stress, as a function of the crack length at
different strain levels. Since at each strain level, 3 or more crack
length measurements were made, lines are fitted to the data points
representing each strain level. It is observed that at higher strain
levels, as the crack length increases, this relative opening level
increases only slightly with the crack length. At lower strain
levels, the relative opening level is higher for any given crack
length and found to increase more with the crack length.
The corresponding strain level for crack opening, s , normal-op ized with respect to the maximum strain level, E , as a function of max the crack length is shown in Fig. 42 for different levels of strain
amplitude. Here also it is observed that, at higher cyclic strain
levels, the crack opens very early in its loading path, and the crack
opening is delayed more for the lower cyclic strain levels. It is to
be noticed that at low strain amolitude cycling, the crack ooening
level increases ~ith crack lengtn.
It is observed that the stress or the strain opening level is
dependent upon the point along tne crack length where the observa-
tions are made. The difference can De attributec to the irregular
crack front, the ~easurement ~ecnnique, and other microstructural
36
37
features. Stress and strain opening levels in this study are made
considering points which are relatively near the crack tip, typically
0.004 in. Though it would be desirable to measure the crack opening
displacements right at the crack tip, this is not feasible because of
the limitations of the measuring techniques.
Figure 43 describes the variation of crack opening stress level
as a function of 6J. 6J has been calculated without considering
closure effects, but considering plastic strain effects, using the
formula obtained by Dowling [40)
2 (0.714) 2a[• J.EJ + 8.59 Lc6EPJ (35)
where 2a is the crack length, E is the elastic modulus, u~ is the
stress range and 6E is the plastic strain range. p
The data shown in Figure 43 do not indicate a clear correlation
of the trends of the behavior with ~J. Thus no significant
interpretations could be made from this figure. A larger numoer of
tests covering the entire range would be helpful in describing the
behavior with modifications to ~J accounting for closure effec:s.
It is expected that, for an ideal rigid-plastic material, Nhen
the crack opens during the loading part of the cycle, the cracK never
closes unless a compressive strain is imoosed which exceeds the ten-
sile strain reached. This sets one limit and is shown by the solid
line in Fig. 43. For cases where oredominately elastic loading is
38
applied to the specimen, as is done in the usual fracture specimens
under R > 0 loadings, there exists a crack opening level, obtained
from different analyses [26,28] as illustrated in Fig. 43. All the
earlier analyses on crack closure/opening have been done for the case
of small s~ale yielding situations.
Extending the same small scale yielding analyses to R = -1 load-
ing for smooth specimens, as done in our tests, where there are large
scale deformations, the results seems to be not meaningful enough to
describe the phenomenon observed.
Thus we observe that the analysis existing in the literature is
limited to only special cases. We believe that cracks under large
scale yielding conditions behave more similarly to an iaeal crack
with no wake effects and with no contact. Figure 45 illustrates the
behavior of real (fatigue) crack behavior under large scale yielding
conditions. Also shown in the figure is the behavior of an ideal
linear elastic crack with no wake effect. As can be observed from
Fig. 45, the closure level is lower than the opening level. Also it
is to be noticed that the ideal crack closes and opens at ,, = 0.
This behavior of a ideal elastic crack sets one bound, while the
other bound for large scale yielding situations is still to be
analytically investigated.
It is also illus:rated in the Fig. 45, in a manner qualitatively
consistent with the present eperimental results, hew the opening
behavior of a real cracK varies from large scale yielding to smal 1
39
scale yielding conditions. This needs to be investigated and mathe-
matical analysis and modelling done. Such an effort would aid in
bridging the gap between the growth behavior of small microscopic
flaws and that of long cracks.
It ·is observed that in the analysis [25,281 existing in the
literature that the residual displacement, 6R' is assumed to be con-
stant. But this may not be so, since the residual displacements near
the tip of the crack may be different from that of the residual dis-
placements behind the crack tip. This stems from the argument that,
because the contact stress may exceed negative yield, the residual
displacements are changed considerably as the crack front grows far
beyond a given point.
Note that under compressive loading, the crack tip starts
closing and the apparent crack tip recedes. This makes the crack tip
singularity, such as of the type ;r in elastic analysis, to become
weaker and vanish when the crack is fully closed. Considering the
ideal rigid, perfectly plastic behavior of the material, it may be
assumed that the apparent crack tip at any point during. the compres-
sive loading starts receding only when the contact stresses ahead,
between the original crack surfaces, exceed the yield stress. Thus,
a residual compressive deformation of the material exists along the
original crack surface. Exte~ding the same analogy to cyclic loading
situations, it is believed that these contact stresses between the
crack surfaces resulting in compressive residual deformation are
40
responsible for the observed 'no closure' effect in large scale
deformations in R = -1 loading situations, as in our study. Since
these residual deformations must be overcome during reloading, the
crack opening is delayed and as observed takes place at a stress
level a0 p > a .• min It is thus observed that linear residual displacements, as done
in earlier analysis [25,26!, holds if the maximum state fulfils small
scale yielding conditions. This is the case if the monotonic plastic
zone is small compared to the crack length. In the case of a real
fatigue crack under large strains, the above analyses fails to
predict the crack growth behavior accompanied by crack
closure/opening.
Another aspect that is to be noted is the three dimensional
nature of fatigue cracks. The 2-D analyses are only ideal and are
only appropriate for thin sheets. Since the plastic zone ahead of
the crack in a plane strain region is small compared to the plane
stress zone, closure of cracks is less significant in plane strain
situations. The crack closure measured by electric potential [381,
ultrasonic [43j, or compliance [441 methods reveal only an average
obtained at the specimen surface and interior, with stress interac-
tion effects being less significant in the interior. There exists in
the literature [461 data from tne measurement of closure behavior of
cracks under pure plane strain conditions. But in that study also,
the remote load level was gradually decreased as the crack propagated
41
to maintain the small scale yielding situations.
Other factors to be considered while studying crack
closure/opening analysis are the effects of loading condition and
specimen geometry. Dowling and Begley [14] applied the J-integral to
e1astic-plastic and general yield conditions and obtained a good cor-
relation between the crack growth rate and the range of the J-
integral, (uJ). The application of this J-integral to fatigue crack
growth studies at high cyclic stresses and strains at different R
ratios to observe the crack closure/opening phenomenon is planned to
be investigated.
CHAPTER 5
CONCLUSIONS AND SCOPE FOR FURTHER STUDY
The observed closure/opening behavior of cracks reveals the
limitations of the existing elastic-plastic fracture mechanics
approach to the study of crack growth behavior. There exist no
closed form solutions for the redistribution of stresses and
displacements in a cracked body under any general elastic-plastic
conditions. Assumptions made in several analyses just simplify the
problem to a very special case of elastic-plastic fracture
mechanics. The use of the Dugdale model is one such approximation.
In this model, the size of the plastic zone ahead of the crack tip is
completely ignored, and so is the elastic field surrounding it. The
model can be applied to thin sheets under plane stress, where only
the entire strip along the crack axis in front of the crack undergoes
plastic deformation. In real crack situations, the Dugdale model
fails to explain the observed behavior in totality, and in general
cannot be extended to all cases.
An energy balance investigation (model) may be a suitable
approach, thereby the plastic dissipative work within the plastic
zone can be fully considered with the bounded elastic zone in a
cyclic hardening or softening material. The early approach by Rice
[7] to problems of fatigue cracks is to use deformation theory of
plasticity, which is difficult to use for nonlinear cases such as
42
43
crack closure and an extending crack, even under small scale yielding
situations.
Thus, the discrepancies observed between the experimental
observations and the analytical models are because of both mechanics
related factors and material related factors.
The mechanics related factors are:
(1) Re-distribution of stress and displacements in cracked
bodies
(2) Material deformation behavior
(3)
(4)
(5)
Local closure and contact stress effects
Macroscopic closure due to residual stress and deformation
Anisotropic effects and homogeneity
(6) Three dimensional nature of crack
Some of the material related factors are:
(1) Differences in cracking process
(2) Characteristic length comparisons, such as crack length
versus the microstructural dimensions of the material
(3) Transient effects due to grain boundaries, inclusions, grain
to grain non-orientations, etc.
Because of the complexities involved in fatigue crack growth, it
is impossible to single out any one of the factors as a major
controlling parameter. Thus, further research is needed in :his area
to critically analyze the most important parameter (mater~a 1 and/or
geometric) related to plastic strains for the closure behavior of
44
cracks in fatigue.
Further research in this area includes conducting tests at
different R ratios such as -0.5, 0 and 0.7, and examining the
validity of existing analyses of the closure behavior of cracks in
fatigue. This includes various parameters such as different strain
levels, crack lengths, and different specimen geometries. Tests are
being conducted, and the results are expected to provide a good
understanding of this subject. Also, it is planned to carry out
tests on different grain sizes, to expose the effects of grain size,
thus checking the limitations of the continuum mechanics approach
also.
We are at present conducting tests of 2-0 cases on flat
specimens to examine the effects of various parameters on the closure
behavior of cracks. This is expected to bring results leading to
differentiating among the actual mechanism of crack growth and its
closure in fatigue in 2-0 and 3-0 situations. The variables that are
being included in this study are the load ratio, maximum load,
plastic strain level, and crack growth rate. The data will be
analyzed based on J-integral, ard new analysis of the closure of
short cracks will be attempted.
Further work is also aimed at developing a model ~hich describes
the crack tip stresses and displacements, and hence redistributions
of the stresses and displacements, under general elastic-plastic
conditions, which are in :urn expected to help in a better
45
understanding of the crack growth behavior over all strain ranges
from gross plastic to elastic deformation.
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17. Leis. B. N., ''Fatigue Crack Propagation Through Inelastic Gradient Fields," Int. J. of Pressure Vessels and Piping, vol. 10, 1982.
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19. Ohuchida, H., Usami, S., and Nishioka, A. "Fatigue Limit of Steel with Cracks' bulletin of JSME, vol. 18, no. 125, 1975.
20. Elber, W., "Fatigue Crack Closure under Cyclic Tension,'' Engg. Fracture Mechanics, vol. 2, no. 1, 1970.
21. Elber, W., "The Significance of Fatigue Crack Closure," Damage Tolerance in Aircraft Structures, ASTM, STP, 590, i976.
22. Katcher, M., and Kalpan, M., in Fracture Toughness and Slow Stable Cracking ASTM, STP, 559, 1974.
23. Bell, P. D., and Creager, M., in Crack Growth Analysis for Arbitrary Spectrum Loading, AFEDL-TR-74-129, 1974.
25. Budiansk;, B., and Hutchinson, J. W., ''Prnalysis of Closure in Fatigue :rack Growth," J. of App. Mechanics, vol. 45, 1978.
48
26. Newman, J. C., Jr. "A Nonlinear Fracture Mechanics Approach to the Growth of Small Cracks," Proc. of the 55th meeting of the AGARD Structural and Materials Panel on Behavior of Short Cracks in Airframe Components, Toronto, Canada, Sept. 1982.
27. Sehitoglu, H., "Crack Opening and Closure in Fatigue," Report of the University of Illinois-Urbana, 1984.
28. Nakai, Y., Tanaka, and Yamashita, M., "Analysis of Closure Behavior of Small Fatigue Cracks," J. of Society of Materials Science, Japan, Jan. 1983.
29. Dill, H. 0., and Saff, C.R., "Spectrum Crack Growth Prediction Method based on Crack Surface Displacements and Contact Analysis," Fatigue Crack Growth Under Spectrum Loads, ASTM, STP, 595, 1976.
30. Dill, H. 0., and Saff, C.R., "Analysis of Crack Growth Following Compressive High Loads Based on Crack Surface Displacements and Contact Analysis," MCAIR-76-006, Report of McDonnel Aircraft Company, 1976.
31. Newmann, J. C. Jr., "Prediction of Fatigue Crack Growth under Variable Amplitude and Spectrum Loading Using a Closure Model," NASA Technical Memorandum, Jan. 1981.
32. Newman, J. C. Jr., "A Crack Closure Model Predicting Fatigue Crack Growth under Aircraft Spectrum Loading," NASA Technical Memorandum, Jan. 1981.
33. Ohji, K., Ogura, K., and Ohkubo, Y., "Cyclic Analysis of a Propagating Crack and its Corre 1 at ion ·..;ith Fatigue Crack Growtn, '' Engg. Fracture Mechanics, vol. 7, 1975.
34. Ogura, K., and Kohji, K., "FEM Analysis of Crack Closure and Delay Effects in Fatigue Crack Growth Under Variable Amplitude Loading," Engg. Fracture Mechanics, vol. 9, 1977.
35. Suresh, S., and Ritchie, R. 0, "A Geometric Model for Fatigue Crack C 1 osure by Fracture Surf ace Roughness," Met. Trans. vo 1. 13A, 1982.
36. Mccarver, J. F., and Ritchie, R. 0., ''Fatigue Crack Propagation Thresholds for Long and Short Cracks in Rene 95 Nickel Base Superalloy," Mater. Sci. Eng., '101. 55, 1982.
37. Morris, \~. L., James, ~. R., and Buck, 0., "A Simple Model of
49
Stress Intensity Range Threshold and Crack Closure Stress," Engg. Fracture Mechanics, vol. 14, 1982.
38. Gangloff, R. P., ''Electric Potential Monitoring of the Formation and Growth of Small fatigue Cracks in Embrittling Environments".
39. Murakami, Y., Harada, S.S., Endo, T., Taniishi, H., and Fukushima, Y., "Correlations Among Growth Law and Applicability of Miners Rule," Engg. Frcture Mechanics, vol. 18, no. 5, 1983.
40. Dowling, N. E., "Growth of Short Fatigue Cracks in an Alloy Steel," Paper for the ASME, 4th National Congress on Pressure Vessels and Piping Technology, June, 1983, Portland, Oregon, Also Scientific Paper no. 82-107-STINE-P2, Westinghouse R&O Center, Pittsburg, Pa., Dec. 1982.
41. Dowling, N. E., Private Communication
42. Di l lner, C. W., "A Crack Closure Study of High Carbon Steel," Report of Dept. of Theoretical and Applied Mechanics, University of Illinois, Urbana, 1984.
43. Shih, T. T., and Wei, R. P., in Engineering fracture Mechanics, vol. 6, 1974.
44. Heubaum, F., and Fine, M. E., "Short Fatigue Crack Growth Behavior in a High Strength Low Alloy Steel,'' Scripta Metallurgica, vol. 18, 1984.
45. Kikukawa, M., Jana, ,\1., and Hora, H., "Fatigue Crack Propagation and Closure Behavior Under Plane Strain Condition," Report of the Dept. of Mechanical Engg., Osaka UniversitJ, Japan.
46. Gray, G. T., III, and Luetjering, G., ''The Influence of Crack Closure on the Fatigue Crack Propagation of Ti-6Al-4V and Ti-8-6Al", Fatigue, 1984.
47. Macha, D. E., Corbly, D. M., and Jones, J. '..J., "On the Variation of Fatigue crack 1Jpening Load with Measurement Location," Experimenta 1 Meehan i cs, vol. 19, 1979.
' i
I c Ni
i
1.89 I I 0.38 !
Heat Treatment:
s
TABLE 1
CHEMICAL COMPOSITION
AISI 4340 Steel
I p Si Mn
0.052 0.012 0.29 o.77
I Mo I Cr I
0.21 0.83
1. Austenitize at 1560°F, 5 hours to temperature; hold 3 hours; oil quench.
2. Temper at 1225°F, 4 hours to temperature; hold 8 hours; air cool.
Fig. 8: Strain life curve for Arsr 4340 steel (40)
I m I
0 0 .. Q
IO
l'l 0
C\i 0
lL . \
0 l'l IO
t
60
I u.
', LtJ 0: U1 CD
ct IO
0
0 0
I() 0 0
0 0 0 d
(I) _..
I
0 ct
0 ~ + ~
U1 o
O
U1 0
oo
O
c)
...----q 0 (I)
.ff I
0 ct
0 ~·
>,
1-...., (lJ E 0 (lJ O
l
c r• E u (lJ 0
. V
l
.. (]"I . Ol
61
;; I~ I~ I 5 , 1.
0 Ii: " I'' '·
. • a -~ ii ,, I ~ ~I ·• 1 ~
= •I
~ .
~I 0
SPAC£R '\
LOCICN> RINGS
@:GREASE FTTTlNGS TO BE AOOED.
SLEEVE
.._~~~~~~~~~~~~~1ooocu.-~~~~~~~~~~~~~~
Fi'j. lU: Hy<Jraulic dCtuator wit11 the stittner
62
0 I
4•
5
-Part No. Part Name No. Reqd. Material Hardness
1 Universal AF-123 2 (supplied) Co 11 et 2 Cover 2 cc 450SS RC 42
3 Collet Holder .
2 cc 450SS ilr 42
4 3/8-16 Sock Hd Cap Screws 16 (std. bolting) SAE Grade 8, 1.25 in. lonq 5 Housing 2 cc 450SS RC 42
Fig. ll: Assembled view of the grip
0.90001A I el •-a I 0.0005 I REF. DIMENSION GRIND AT FINAl. ASSY 10 FIT COL.LET, SO ™AT ASSEMBLED GRIP WILL ACCEPT O.!lOO DIA ROD
1.35
2.00D
G
Fig. 12 (a) Details of the grip - Cover
All dimensions in inches
5.~ •0001 lei •-a I 0.0005 I
8 HOLES EQUALLY SPM:ED 45° APART 04060IA, C BORE 05940 0325 DEEP AS SHOWN CLEARENCE FOR ll•-16 SOC. HO. CAP SCREWS WITHIN 0.~ OF TRUE POSITION ON 4 5 OIA
075
2.00
0.91
I. 2 5 l r '·---..,;:--,,...,_
~
64
• THO
4 SLOTS 90• APllRT
ORILL a TAP 0.375-16 0.75 OEEP Tl40 8 HOLES 45• APART EOUAU.Y SPACED ON 4.~ DIA. WITMH 0.005 OF TRUE POSITION DRl.L 0.8~ DEEP
Fig. 12 (b) Details of the grtp - Housing
2.995 • 0.001 I e!A-e!o 0005!
3.~
0 0° RING GROOVE 0.22 WIDE
65
/
I 864 & 0.001 lelA-810 00051
TO FIT PRP-33• TO HOLD PR 3000 PSI
0 10•0.00t
i= 0.2 ...1._._
r 0.910 •O 001 --1
I 1Et!.f.-8!ooo<nl 14)/_i_ '0.125. 0 001 -r-
45° CHAMFER
Fig. 12 (c) Details of the grip - Collet Holder
66
Fig. 13: Deflection control testing with 2 clip gauges
,... a.. UJ
N I
w
(T)
<' r-~ _J_ UJ Q
'q' I
w
(a)
I .E-4
Fig. 14:
67
f--
I I I I I I I I I I I I
I ~ I ~I
~ 1f I
I ~
,iu
<:~ v I
I/ I I
I I I I I I / I I
I I I 11 v I I I 111
~} I.I J I
I .Li J9 11 I ~
I 11 I I 11
I 1. E-3 1 .E-2 l . E- I
DELTA EP2
(a) Schematic diagram of strain measurements (b) Correlation between plastic strains
Fig. 15:
68
Strain control testing with the clip gauge mounted across the grip ends.
c ...... -..r::; -0) c Cl)
~ u .,, I.. u
0 -
OJ 0 . 0
c.o 0 . 0
~ 0 0
N 0 . 0
0 0 . 9J.oo
69
~e_eciinen No: 61?-1 Strain amµlitude. € =U.UU~4 a
d' /
/ 20.00 40.00
cycles to failure
1 .i
I
(!)
(!)
I
60.00 z 80.00 100.00 *10
Fig. 16: a typical measurement of cack length vs cycles
70
Hr' AISI 4340 .P++ ++-;* S :700 MPa u
+ ~~ i o·' R =-1 ... : ~ Iii .~~~ u >- :.:~C) v u
i o·· -e e 6 C) ~~ 1i1· : ffiPo + -
......... f!J ~_p IO e::: .i::. i a·' ~ 0 ..... ~
.!!J * ->' u ;. + IO '- 1 a·• 0 u 00 Short Cracks. & 0 z ~ Long Cracks 0 0. 0047 -IO
CJ 0. 0066 . ~
t c·' ):{ Ctr. Hole ~ 0.010 x DEN ¢ 0.018 + Compact + 0. 029
i a·• -~-ut l O' ut tJ<. Stress Intensity Range. MPa rm
Fig. 17: da/dn vs ~K for AISI 4340 steel (40)
Fig. 18:
71
,
C~CK (oPC:U) ( E > £"WI\.)
( C:C1), ~) s'" e
CRAC.IC (CLOSED)
( e'-,..,.i11.)
Schematic Diagram of closure measurement
66. 63 ksi A
-54. 60 ksi Y
72
·f.:.
<!...,.,,,.,, = 74 .8 ksi specimen no . 617-5 strain amplitude= 0. 0066 Nl200R 2a=0 . 0171 in
44. 13 ksi A
Fig. 19: Typical crack at various stress levels in one complete cycle
Crack opening displacements measured in one complete cycle (a) Load disolacernent loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
74
c:: ·~ ( a) Increasin:, Strain .., c:: 9::! '/
Qi \ u ·'ti
:i vi
"':l
:;> c:: c:: Cl) :i 0
~
u 'ti '-u
=i '::> :..;
~
~ I I
o~ ~
0.GO 0.25 a.so 0.75 I .CO
0 x/2a, Relative Position
0 61 c::
r ·~
j ( b) Decreasiny strain .... I c:
Cl)
I = Qj 5 u J "
I '° \ ..-1 VI
"O g; :n ~t c: c: Cl) "'.l. rr 0
'I ' ....:: [ ,, " u f ' '° 'X '-w IX-
:::i 8u ::> 8 :.J
g .::· r- : n~
0.CJO o.zs n c:.n o. 75 I . ::i
x/C.a, .'<elative Position (b) CracK OiJenin~ disjJlace:nent aur111:,i rncreasin:, ( loadiny) and aecreasin~ Strdin (unloaain::i) at dinert:?nt 1-1oints alon::1 the cracK ·1en~th. Different stress (strain) levels corresµond to the ~oints shmvn in load ais11lacement IOOjJ.
= ·~
....,
~ Cl) u ~
1
"' "O
"J> c: c: Cl) :l. 0
.:.(.
u ~ L
'....)
'.:::l "::l u
= ...., c: J)
1 VI
0
8 0
0 .,, 8 0 0
§ l 0 0 -100.JC
0 0 0 0
0
:g r 8
_;") a
·~
c :lJ 1
0
~ -:i "....)
0
8 8 ~ h• 0 -100.C
75
(a) Increasing Strain
,.... " '
+ x b
J.C
stress, ksi
(D) Uecreasing strain
x $
+ 0
0 0
O"", stress, ksi
x
C)
x + 0
C)
x + 0
:cc .0
C)
~
-t
x
~
x( in)
0.0039
0.0076
0.0133
0.0284
0.0315
(c) Crack openin'.J displacement as a function of stress at aifterent points alon; the crack len~tn auring increasiny ana decreasiny strdih.
x/2a
0.01114
0.02171
0.380
0.8114
0.9
c: ·~
....., c: ~ a; u ·U
1 VI
"'O
::-i ;::
c: a; 1 0
~ u tU '-u
......, s :._.)
0 V1
8 0
76
(a) Increasing Strain
x <5 6.
x
+ 0
0
~
+ x
<;)
§8.l~~~t='+-~~~~---~~~~~~~ - C6 ~ ~ ,...,
0 -0.0ISJO
~ 8 0
0 V1 0 0 0
0
0
§ l •I
0 --0 .0 I 500
a.cocoa £,strain
(D) uecreasing Strain
v ......
l, strain
x + 0
x .J_
I
x C) 0 ~
6.
C)
o.c:::::;o 8.JtS'J
x(in) x/2a
0.0039 0.01114
0.0076 0.02171
0.0133 0.380
0.0284 0.8114
0.0315 0.9
(d) Crack openin::J disiJlacement as a function ot strain at Llitferent µoints alon':1 tne crao~ len':1tn aurrn'j increasin~ and aecreasiny strJin.
Crack opening displacements measured in one ccmp 1 ete cycle (a) Load dis~lace~ent loop as obtained frcm c1'~ gauge mo~nted across the grip ends and :ne aoints (correspondiig stress ara strain levels shewn in tab'e) where closure ooservaticns were made.
~I 10 a~·~-+:o....--==;..t==-=""'=~==~~~~~~;:;--'.~ 0o. uo 0 . 25 0 . so 0. "5 l . ~;J
x/2a, Kelative Position (b) Crack o~enin~ displacement durin~ increasiny (loaainy) ana aecreasin~ strain tunloadins) at aifrerent points alony the crack len:;ith. lJifterent stress (strain) leve Is correspona to tne points snown in load aiSjJlacement loo..,.
Crack opening displacements measured in one ccmolete cycie (a) Load disalacement :ccp as obtaine1 fr8m clip gauge mounted acrJss the grip enas and :he Joints (ccrresoonding stress arc strain levels src~n ~n tab~e) where c~osure Jbservaticrs ~ere ~ade.
82
~ o'
i:::: I
i \ a) Increasin~ Strain + ...., \ i::::
~ li u ~
.::::...
~./ 3
~I Vl
'O
::;') §1 .::: .-o' i:::: Q) ..., 0
2 ~~ ~ 3 o I '
:::
...., i::::
~ lJ u ~
.::::... •/1
";:J
:;\ ::: i:::: Q) g-
c • ~ ' ', c:i 0.00
0 .,, 8 0 0
1 o.zs a.so o. cs
x/2a, Relative Position
I .CO
I I
(o} Decredsin'::l strain 1
/s .,, N 0 8t 0 , _ _,__~6~--------~:
7
8
x/Zd, Relative Position (::i) Crack opening displacement durin.g increasing (loading) and decreasing strain (unloading) at different points along the craci< length. Oifferent stress (strain) levels correspona to tne poi'ltS snown 1f1 loaa a1spldce111ent loop.
(c) Crack opening displacement dS a function of stress ar. r. different points alon 9 the crdCK length during increasing and decreasing strain.
84
0 "' § 0
= x (in) x/2a (a) Increasing )t:rain
;...) e> 0.00093 0.0512j = ~
ii 6 0.0032 0 .1778 u 'U
.::i... + 0.0153 0.85
Vl
"' ··-"' . -:: 8
=' ~~ 0 ! c:
x x 0.01746 0.97
~
·-= 11 x .::i... 0
~
u I 'U r...
'._.)
t ....., ~ 0 t '._.) a ;
§ ' a -0.01500 o.:cc:o
"' 0 t strain 0 Q
c::i I = tD) uecreasing strain ._; r = I }:! I lJ t u t 'U
.::i... I Vl
"' I ' -:: ~ . :;-, cs_
0 i • c: I ~
6 ' , ,, ~
6 )< ~ u
,..._, v
~ A r... '-. ....) x --J ;::::: •
-~ ........ ;-----c':~.~~~~~~~~~~~~~~~~~
-J . :; : sea :J .::::::.a : ."": : c:::
(c) Crack opening displacement dS a functiun of stress at different points a1on 9 the crdCK length during increasing and decreasing strain.
85
[(\, = 0.0125 617-3. NSOOF 2a= 0.06 in
--~~-- --
Fig. 23:
---···------ -
----·- Stress Strain ----- Cksi>
1 -59.27 -0.0115
2 - 7.07 -0.0095
3 44.98 -0.0055
4 75.97 0.00435
5 42.44 0.0105
6 -21.22 0.007
7 -59.27 0.0013
8 -81.34 -0.0089
Crack opening displacements measured in one complete cycle (a) Load displacement loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) ~here closure observations were made.
x/~a, Kelative Position (b) Crack openin~ aisplacement duriny increasiny (loaainyJ ana aecreasin~ strain lunloaain~) at aitferent ~oints alun~ the cracK len~tt1. Uirterent stress (strain) levels corresµona tv tn~ points st10M1 in I udCl ai StJ I ace111ent I ooµ.
(c) Crack Ot-1enin:i aist-1lac~1!1ent d::i a function ut stress at airterent ~oint~·alon~ tne cracK len~tn Jurin~ increasin~ and aecreasin~ strain.
..
c
...., ~ a:; u IU
:l. VI
0
::'l
·-= 'lJ :l. 0
.:,,:. u
"' t.. ._, :::::l ~ ._,
c ·-...., c ~ a:; u "' .:l. VI ·-0
':;> c ·-'lJ ~
::>
-""' u 'O t.. ._, =i ::i '....)
88
8' "' 8 0 x (in) x/2a
\ a) Increasin':l )train 0 0.00506 J.0844
5! 8 0
~ 0.01133 0.1888 ....__ __ + 0.01546 0.2577
+ 8 8 x 0
x 0.0433 0.7217 '1
0.04946 0.8243 0 ' c
0
~ § I + 0.05667 0.9445
0 ~ ~ ~
t m C) I
0 -0.0ISCO o.cccco o.01s:::i
&. ' strain 0
"' 0 0 0
\ b) lJecreasin':l strain
0 ~
8 ... 0
+ 8 x 8 0
,,, ~
~ 0
~ ~ El
~I ~ L)
C) 't-4-
8' ~ o I 0 -o. o 1 sea o.cccc::i c.01s:;
[, strain
(a) CraCi< oµenin::i uistJlace;11ent as a tunction ot strain at ditferent f)uints alun':l the cracK len~tn uurin':J increasin:;, and oecreasin~ strain.
Crack ope~ing disJlace~erts measured in one c:mo1ete cycle (a) Load disJlaceme1t lccp as obtained ~ram :lip gauge mounted across :~e 3rio erds and the ooints (ccrrescondjng s:~ess ard stra'n levels shewn in tan"e) N~ere c'osure J~se~~atians ~ere mace.
! I
90 8 8
::::: 0 I (a) Increas i n':t ~train
µ c:: ~ lJ u "O
1 Vl
"O ~ i :n §I ~ 0 c:: <lJ 1 0
;;,,: u "O '-
'....)
.:i x '=> :....> 8 § I .~ . .,.._ 1 0 v
0.00 0.2S a.so 0. 7S I .:'J
CJ
"' x/La, Relative Position
§ 0
c:: (b) lJecreasin~ strain
µ
~ ii u 'O
1 Vl
'::::J .,., ~
lJ 1 :i
.:.: u "O '-
'....)
::::i ':l 0 ....) §1
0 0 a.co a .~s a.SJ a.~s I .CJ
x/La, Relative Position
(D) Crack openin':J dis,ilace•nent Jurin':! increasin':i ( loauiny) and uecreasin':J strain l~nioadin':j) at different points alon':i tt1e cracK len':itri. Uitrerent stress (strain) levels corres;Jonu to tne ;JOlnts shown in loaa ais;Jlctce111ent loop.
c: .... ...., c: ~ a'.i u ,,, ..... ::i.. Ill
"'O
:n c: c: a> i 0
-~ u ,,, L.. :J
c: .... ...., c: ~ a:; u ,,, 1 VI
-::I. ,., c:
-11 ..., 0
.:>It. u ,,, L..
:..J
:::i :::> '..J
8 8 0
0
~ 0
Ill
§ 0
Ill
"' ~ 0
~ ::-.t,.:<
0 ..,,~
91
(a) Increasiny Strain
)~ ._.
' 0
o.c . i:r, stress, ks i
(o) Uecreasin~ strain
+ 6
+ x
+
!C9 9x . -
I x(in) x/2a
I 0 0.0025 0.0694 i i 6 0.0062 0.1889
+ 0.0246 0.6833
+ x 0.0288 0.8 6
(6
:oo.oo
·ICO.O ").C ICO.O
:f, stress, ksi
(c) Crack oµenin':J diSiJldce111ent as a tunction ot stress at dirferent ~oints alun~ the crack len~tn aurin~ incredsin':J an.a decreasin~ strain.
:.-
= ...., ~ 1i u 'i:l
1 <JI
0
";'> = ·~ = JJ -i. 0
.;,,'. u ~
'-'....)
'::l ~
·.:l
c
..... c ~ CJ u ~
1
"" 0
::"I c
JJ 1 0
.;,,'. u ~
'-'...)
92
3 8~~~~~~~~~~~~~~~~~~~-0
x(in) x/2a (aJ Increasin':J ~train
0 0.0025 0.0694
6 0.0062 0.1889
+ 0.0246 0.6833 0
"' 8 0
x 0.0288 0.8 0 '
I g g §~ 0 -0.0ISGO o.c:cco O.CISCO
"' E, ' § strain 0
( b) uecreasin'::l strain
' '
6
~ I + 6 ci + x
Li.\ 6 c x 0 ~ c
[, strain
(a) Crack Of.!en i n:i ai SiJ I acc::nent as a tunct ion or stra i ri at aitterent ,.,oints alun:i tne crack len:it11 aurin:i iricreasin':J dnd uecrcasin~ strain.
Crack opening displacements measured in one complete cycle (a) Load displacement loop as obtained from clip gauge mounted across ~he grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
c:
...., c: ~
:ii u 'U
:i VI
':>
:n c: c: lJ :i 0
o.! u 'U t...
:...>
94 0 ./) 0 8 0
"' N 0 8 0
'
(a) Increasin~ Strain 4 I
3
~
I I I
3 § I ~~"'~~=2:::=======<=>.,;,,,~~~~~~E;-~-=:;--. 6~.:_:i::;::::;:
2 ~ 1 =
O.GO 0.25 o.:o 0. -:OS I .CO
0 x/);i_ KPliltive Position 0
c: 0
( b) uecreasin~ strain ...., c: 5 ~ <1J u
"' :i VI
-0 "' N c ' ::;> 81 c:
·~ 0 = 'lJ
:i 0
.:.t! u
"' t... :...>
--":> :...> 0
0 r 0
8 ! "" -· . / 0 a.co 0.25 a.so 0.75 I .C:J
x/~a, Kelative ~osition
(0) Crack openin~ uisiJiacernent durin~ increasin~ ( loadinlj) and decreasin~ strain (unluaain~) at different iJOints alony tne cracK len~th. Oifferent stress (strain) levels corresµond to the iJOi nts sno1 ... n in I Odd i..l i SiJ I a cement l OOf.!.
(c) Crack uµenin-:J aist-1lacc:~nent as a tunctiun u!' stress at dit'terent ~oints alun':i me crac:<. l~n':itn <Jurin'j incr2asin~ and aecreasin':i strdin.
.
(d) Crack Of-lenin::i aisf)lace111ent as a tunct1on of strain at dirferent µoints alun:; the craci< len:;t11 aur1n~ increasin~ and decreasin~ strain.
Fig. 26: Crack cpening displace~ents measured in one complete cycle (a) Lead displace~ent loop as obtained from clip gauge mountec acrcss the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
98
0
c:: la) lncreas in~ '.:ltra in
~ 4 c::
~ ' ~ u ~
a. "' " 71
= <lJ ::i.. 0
=
::::> c:: c:: lJ
G
! . 16--= 8, g ~;...._____~
2 .I
1 0 a.co o . zs o. so o . 75
"' x/~a, Kelative Position
0 0 0
0 i l (b) Decreasin:J strain
0 g '.
I. :a
g . / 8 ·---'----------------0 O.CJ 0.2S 0. SJ
x/~a. Kelative ~osi:ion I.::
(b) Craci<. CJµenin~ uis~lacernent aurin'::J increasin<:, ( loadin':J) ana decreas1n~ stroin \unluaJ1n~) at a1rrerent ~oints alon'::J trJ e c r au 1 e 'l ~ tri • 0 1 ~ re re r 1 t st res s ~ st r a i n ) I eve l s corre::; 1;unu to tri~ ,Joi11ts sno· .. 1n in load d1Sf.11Jce:nerit loo,.;.
c:
.µ c: ~ li u ~
1 <J)
"'O
~ c: ·~
ClJ
0
-"" u ~ L
'._)
ClJ 1 0
99
§ a
la) Increasin~ ::itrain tS '
I x (in) x/2a ~
C) 0.0016 0.0272' ~ (2)
'. 0.00746 0.1271 6
<) + 0.01546 0.2635 I
~ -"' N a 8
L. x: x 0.02106 0.3590 a
0 '-' () 0.0273 0.6357 ·-X: .,. 0.04413 0.7521
~ 0.05093 0.8680 x ...... \.:..,
,,.,. --50.~0 o.:o so.cu
'J, stress, ksi
(;:)) Oecreasiny strain
a 8 t
g~I~~~.-;;:~·~~~~~~~~~~~~~~~~~ 0 -100 co -50.:0 o.:o s:.:a :co.~
(), stress, r<. s 1
(c) Crdei<. OJJenin~ uis,.,lacerr;ent as a 1'unct1on or stress at <..11rrerent ;.;01nts atun"' rne cracr<. leri"'Ch aur1n" 1ncreas1n" and uecr~dsin~ str~1n.
= .., c::: ~ .l) u
"' '.::l..
"' "":)
:::> c::: ·~
;:: '.l.J 1 ~
.:..: u
"' ~ '...)
:::i -=-:....;
c: ·~
:J U1
8 0 0
U1
"' 0 8 0
8 CJ I 8 0 -0.01
U1
"'' 0.
81 0
ol
~~
100
(a) lncreasin::1 Strain
,. c .. ,
a.co strain
2S
(b) lJecreasin::1 strain
9'. ..J_ ,::,.
<'.> C:.
x (5 4' ? C)
x (in) x/2a
C) 0.0016 0.0272. . 6 0.00746 0.1271
+ 0.01546 I 0.2635
x 0.02106 0.3590
¢ 0.0273 0.6357 ·-+ 0.04413 0.7521
i;c:: 0.05093 0.8680
~
+ <::;> A
C)
8 t 0 ___ :,;,.·---------------~ 0 -0.01 a. :o a.01
('., strain
( d) Cr a.Cr< o,.;eri in~ l1 is,..; I dce1;:ent as a runct i 0ri or st ra 1 n at dltterent f)uints alonJ tt1e craCi<. len::1tn aurin;j 1ncrea.s1n;i ana aecreasin'::J strain.
101
.:: 0 ('- = 0. 0066 •• I I I I; I
. ~ ! . I I ' l : 1 111" 1 ' ; · 11 . I ; : : ~ I 1 .;Jj;;: ; 6.1.Z~S. N l 200F 2a= 0. 0325 ; n
. . . . . . . . •••••I I
t '. ! : ; i 1 ! : • • • • • • • I . '
• • t t ••I
I 1' ! : 'I I .. ' · 1 • . '•' t I ,.J' . t. I I I'. t
; : I:? l?:: ii ·~~··· ~ I 1 l '1: : ; 1
·1::::::::-: . . ....... . . . . . . ....... .
o .. I I t t 4 t e • 1. ~·: '~ •• ......... • . • • t •••• . . . . . . . . . ........... • o • • • t • I 41
Crack opening displacements measured in one complete cycle (a) Load displacement loop as obtained from clip gauge mounted across t1e grip ends and the points (corresponding stress and strain levels sho~n in table) where closure observations were made.
U1 0
102
8.,..--~~~~~~~~~~~~~~~~~~~~
c <1J 1 0
c
0
::;'\ 0 c
= lJ 1 0
la) Increasin~ ~tra1n
a .zs a . so n • ;5 I .CO
x/~a. Kelative Position
l D) uecreasing strain
0. ZS 0. SJ 0 · ''3
x/2a, ~elative Jos1tion
:i) Crack OiJen1n::1 ais,.ilacement Gurin:; increas1'1'J "i·.:..ac11::• ana decreasin':i sr;:.i1ri \'Jnloaain:;1) at Jl~~er !lC ;.io1nts aion::1 :~e cracK len~::n. J1~ferent s::ress (strain 1eve;s :Jrres,.ior.a ::o :~e ;,G i ~ns sr:own ~ n 1 J.la Ji s.., ace:ne'l: , oo;.;.
c:::
.... c::: ~ :v u IQ
1 <II
"'O
::n c::: c::: <1J 1 0
.:.c u IQ '-:....J
~ ':> w
c::: ..... .... c::: ~ Cii u ~
·1 <II
-0
::n c::: c::: <1J .:i.. 0
.:.c u IQ '-:..> ~
~ :::> u
103
~ 0
( a) Increasin~ Strain x (in} x/2a
C) 0.0045 0.1384 -· 6 0.0087 0.2673
+ 0.0234 0.72 "' "' § 0
>'< x 0.0262 0.806
* 6
¢ ¢ ~ 0.0293!-i 0.9015 C)
C)
::(- 8 0 0 e ¢
§ (T"'\ ~
0 -100.CO -SO.CO a.co so.co ICO.C.0
'.If
8 <r, stress, ks i
0 0
( D) Decreasin~ strain
"' "' + § x 0 e
6 C)
Cs + x 6 ~ + ¢ ® ¢
8 0 0 0 ~
0 -100.00 -SO.CO a.co so.co ICJ.OO
<J, stress, KSi
(c) Crack oµenin~ dis~lacement as a tunction ot stress at ditferent points alon',j tt1e crack lenljth durin::i increasiri~ and decreasiny strain.
'
c::
..... c:: ilJ
Q) u ~
1 "' 'O
.:-1 c:: c:: Q) 1 0
""" u IU t..
:...>
:::i ".:) :...>
c::
..... c:: 9:! li u IU
~
VI
"O
:n c
c:: Q) 1 0
-"" u IU t.. u
-=i '::> u
104
"' § 0
(a) Increasin~ Strain x (in) x/2a
0 0.0045 0.1384 ~-
I 6 0.0087 0.2573
+ 0.0234 0.72 "' N 0 0 0 0
...J.... x I
..i... x 0.0252 0.805 ~ 6
<1> ¢ 0.0293!) 0.9015 <1> C)
~ 8 C)
0 8 e <1>
g (T'\
0 -0.CC750 o.::::o O.C07SO
"' £, , strain 0
8 0
( b) Uecreasin'j strain
"' + N 0 0 x 0
!" B 6 C) ...J....
+ c x 6 ~ + 0 ® <1>
0 g 0 0 0 -0 .007SO a.o:;::o 0.CUiS
£' strain
(d) Crack oµenin~ displacement as a tunctiun of strain at aitterent µ01nts aton'j tne crac~ ten'jtn aur1n~ increasinJ anu aecreasin'j strain.
105
Lt\.-: 0. 0066 61 7-5 • N 1 1 OOF 2a= 0.027 in
stress Strain Cksi>
1 -29.42 -0.0052
2 26.59 -0.0027
3 58.71 0.0009
~,,_ 4 69.03 0.0036
5 55.17 0.006
6 17.83 0.0032
Fig. 28:
7 -72.85 -0.0047
Crack opening displacements measured in one complete cycle (a) Load displacement loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels sho~n in table) where closure observations were made.
=
=
c:
......, c: ~ l) u ~
::i... <ll
"";::)
:n = c: l) ~
'::)
.;,,t. u ~ ....
:._)
~ -s :._)
106
la) Increasin:; Strain
/ g 1~ ,;k:--' -----=-1 -~ 8 !' <"' o.oo
0 I 0 CJ ! 0 0 0 0 co
0.25 a.so 0.75
x/2a, Relative Position
(DJ uecreasin:; scra1r1
7 o.~s 0. SJ o. ~s
x;ia. ~e1ative ~usition
I .CO
I .:C'
(o) Craci<. oµeninj uisrilace!1;ent aurin'::J increasin:; ( ludain'::J) ana aecreasrn'::J strain (unluadin:1) at dltferent ,JOlntS alon:i the crac~ len~tn. uitrerent stress lstrainj levels curreSf!Ona to the iJO l ns snown in I uao a i sri I ac.:1ile'1t I OOiJ.
= ·~
...., = ~ .ii u ru
=-<J'I
-a ~
c lJ -0
~ ·...; '1J ~
'....)
,....,
-~
=
107 O•
8 0 0
(a) Increasin~ ~train x (in) x/2a
C) 0.002 0.0278
.!. 0.0051 0.1834
+ 0.0072 0.2589 ~I ' g t of . - x 0.0213 0.7661 0 '
t ¢ 0.0238 0.8581
' I
f i ... 0.0261 0.9382 i I
t i
g l c gr 0 -100.::a -SO.CO o.co so.:o ::c. ;:
~ T, stress, Ksi
0 0
(D) L.Jecrectsin':j strairi
6
6 x ~
ti tT\ '--' ~
~
§1 g~(. .. 0 :-~~~~~~~~~~~~~~~~-
- .~:.:o -so.:o o.:o so.:J ,:;:.:a
~. s -c re s s , i< s i
1 c) Craci< Jue~in= ~is~iacc~en: as d f~nc:ion of s'C~ess at dif~c:rent ,.;oin:s atun'::J :ne crac:< 1en:i'Cr1 uuriri:; inc~c::sin~ ~no Jec~eas1n:i s:ra1n.
:::
..., ::: ~ ·li u ,,, -:i.. /JI
-0
°' ::: ::: 'lJ 1 0
.;,,: u ,,, L.
:....>
'O
::n ·~
::: <lJ 1 0
:::i
108
"' 8 0 0
l a) Increasin'::l )train
0
¥ + ~ x ~
+ ~ <> §I 0 C) ~
'T'
x
¢
....
0 a. ~ § ~l ___ -o;;· 0- ...... ~~~~~~--+~~~~~~~~~~
(a) ·rr·acK OiJenin"' aisi-1lace•nerit as a tunction of st:ra1n at aitrerent r1u1nts alon'::I t:ie cracK len'::lt11 auriri"::I increasin'::I ana aecreas1n'::I strain.
F' g. 29: Crack opening di:claceme~ts measured in one comple~~ cycle (a) Lead displacement loop as obtained •ram clip g~~se mcunteo across the grip ends and the ooints (corresponc~ng stress a~d strain 'eve1s sno~n i~ t~c'.e) M~ere closure ooser1aticns Nere mace.
110
Uo 0 8
c 0
(a) lncreasin'j )train ...., c ~ iii u
"' 1 Vl
"'O ~ 1 ~ §i c . -0 c aJ
0
.;,,:. u
"' I.. :...>
:::::i
~ I '=:> :...>
2
a· (") a.co 0.25 a.so 0. 7S I .CO
Lil
8 x/Za, ~elative Position
a 0
c (b) uecreasin'::! strctin
...., c ~ Cii u "' 1 Vl
Lil "::) § i ...,., c 0
c li :i.. ~
:.L u 'l:l I.. '_)
~ ::i g. '_) s:
0 O.C8
I . ' .
x/ ~d, .-<t: I at l ve J-'o:, lt l •Jrl
(b) CracK Of-!enin-:J ais,.ilaceinent ourin"' incrertsin'::i ( loaain~) and aecreasin'::i strain (unloaa1n~) at aitterent ~oints alon'::i tne cracK len~tn. Difterent stress (strain) levels currespona to the ,.,oints shown in loaa aisplacement looµ.
,, 0 8 0
c:
...., c: ~ lJ u 11:)
'1 VI
"' "'O N
8 ~
0
c: 0
c: lJ 1 0
.:.<'. u "O L
'....)
:::l '.:) 0 '....) 0
0 0 0 0 -100.00
"' 0 8 0
c:
...., c: 9:! CJ u 11:)
::i. V'I "' N
"-:J 0 0 0
-:> 0 c: c: <1J 1 :::> ~ u "O L
'....)
~ -:i 0
0 ...) 0 I 8 I
0 -100.00
~;
111
(a) Increasin'.:f )train
+
-SO. 00 a.ca so.ca
~. stress, ksi
(D) Uecreasin~ strain
I z ?
+ 6
~
6
+
+ C)
!
I ' I I
JOG .~J
-SO. DO a.~n 50.:J ICU.:..O
(), stress, ksi
x( in) x/2a -
0 0.0037 0.1491
6 0.0062 0.2742
+ 0.0183 0.7379
x 0.0206 0.8306
( c) CracK Of!en in~ •Ji s~ I acet11ent as a function or str~s s at different µoints alon'.:f me cracK len.,_,t11 aurin'.:f increasin::i and decreasin~ str3in.
= ...., c: ~ ii u 'O
~ <JI
"::l
~ = c: '1J ~ c ~ u ,, '-
'....)
~
~ ._,
= ._, c: ;,! ii u <1:l
~ ../>
~
.::-> = c: ~
c
°"" :...J 'O '-~
~
~
112
"' 8 0 0
( a) lncreasinlj Strain x(in) x/2a ' i 0 0.0037 0.1491 '
6
i 6. 0.0062 0.2742 I
+ 0.0183 I 0.7379 ' "' N
§ x 0.0206 0.8306 0 C)
+ 6 x 0
& 6 x 8· 0 • gi
0 -0.01 a.co 0.01
"' E , strain g 0 0 I
t l l D) uecreasin'j strain I • t
"'' "'' 0 • c' ~~ 0 6
' -r-
6 9
! ~ m '-' x ol
<;? ~ c ; "7 0 22;
--J .Cl a.co J.JI
[, Strain
(a: ~rac~ J~en1n~ J1S~iaceme": as a r~~c:~~~ 0f str31n a: a1r7erent ~01nts alun~ tne crac~ len~tn c~r~nj increas1n~ ana Jec~~as1n~ str~1n.
.... ;:: :,u1: 1~~:1 1l!Hlj~~~ : : '. '. i i ! ; i : ! ! j j j; : d ~ I~~ ~. :;;:·:::i ·;r•11··· 1l·11··j ; •.• 1· 1 • I : I • ' i f I • ' • 1 • • . • • : • • I • I • • • . I I • , I
- . ..
Stress strain Cksi>
1 -41.02 -0.0058
2 - 0.28 -0.004
3 44.13 -0.0011
4 66.33 0.0037
5 52.48 0.0061
6 14.71 0.00464
7 -54.60 -0.00052
8 -74.27 -0.005
Fig. 30: Crack opening displacements measured in one complete cycle (a) Load displacement loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were maae.
c
...... c ~
~ u ~
1 V'I
"'O
:n = = 1J :i ::>
.:.!. u '" t... :.....>
~ ~ :.....>
c
......
~ 1J u 'O
1 •./)
'::;J
~ c = lJ i ::>
"" u 'O t...
:.....>
=i ~ ...)
114
Ul
8 0 0
l a) Increasi n'::i ::itrain
Ul
"' § 0
4
I
i I ----.:,
' ~,
' 2 '~! 8 ''\ I + 0 1 ""'-· ' 0 0 0 a.co
X/ .:'.a, t<elative Position "' 8 0 0
lb) Uecreasin1:; strain
5 :"\ ?
~I ~
~l 0
. I I
~ I I
\ I I
7 I 0 -~ o, 8~ 8 '
"'-.~ ! o· 0 '= o.:o a .~s 0.50 a. 75 I .:'.l
x/C.a, r<elative Position
(D) Crack ofJenin:i aisul.:icement aurin'::i increasin':; ( loaain':J) ana aecreas1n:J strain \unloaa1n'::i) at a1rrerent iJOlnts alon':i tne crac( len:Jtn. Different stress (strain) levels corresiJona to the µoints shown in loaa uisiJlace:11ent loop.
(d) Crack oµenin'::I ais,;lcice1rrent as a function ot strain at aifferent µoints alon'::I tne cracK len~tn aur1n~ increasinj ana aecreasin'::I strain.
Fig. 31:
117
Stress strain Cksi)
1 -29.42 -0.0052
2 25.74 -0.0027
3 58.71 0.0009
4 69.03 0.0036
5 55.17 0.006
6 17.83 0.0032
7 -22.35 0.0027
8 -72.99 -0.0047
Crack opening displacements measured in one c0mplete cycle (a) Load displacement loop as obtained from clip gauge mounted across the grip erds and the points (corresponaing stress and strain ~evels shown in table) where closure observations were made.
118 "' § 0
I ::::: ( a) Increasiny '.:>train I I .....,
I ::::: CJ 4 E I } l.J +-"''
I u tO
1 3 l/l '/ I
" / i I ::;') c ::::: CJ 1 0
.:¥. u tO r-. u
~ 0 2 ,..,..., u 0 -0 ... ,.,.:', g, -r.-- -·
C)
o.co 0.2S O.SU 0.75 I .~O
x/ 2a, f<elative Position
c:: ( D) lJecreasin':J strain
....., ~ c::
~ > ';-<._ l.J u tO
::'.l. l/l
I
~
::;')
c:: c:: :1.' -, 0 7
.:¥. -~-u / \ :o r-. ~ L u
.::i J "::> ;...) ol
01 8 c· O' 0 a.co O.<S o.sa 0.7S I .~0
x/ (a, Kelative rlosition
(D) Crau Of.lenin 0 diScJlace111ent durin':J incre:isin::i ( loaainy) ana aecreas1n~ strain \Jnloaain~) at aitterent rloints alon~ the cracK len~t~. Oitterent stress (strain) levels corres~om1 to tne cJO i nts snown i 11 I oaa a i si-1 I aceli1ent I oo~.
c: ·~
c: lJ
5
c:
<J
"' 0
119
8~-----------------~ 0
(a) Increasin::i ~train
b x I I I I I
Li: C)X
0 g 0
0 .;..· -----+--·•'---.-..--0 .. ,.,,
C)
~
+
x
-1co.oo -so.c::i a.co so.co IGC .C.J
\J, stress, ksi
§~------------------~ 01 ( b) Decreas i ny strain
+
x
({, stress, KSl
x 3:
x( in) ! x/2a '
0.0012 0.0784
0.0027 0.1764
0.0138 0.9019
0.0146 0.9477
( c) Crack OJJt:ni n:J ai S,J 1 ace:nent as a function ot stress at dltterent ;Joints alon'j the cracK len'::ith durin" increasin'j and decreasiri'j strain.
...... ~ 'lJ u ·'U
1 Vl
" ~ c c lJ 1 0
;,,(_ u 'U t...
'.._)
.:::i =i '.._)
~ 0 8 ! 0
0 0 :::l D G I
'· 0 ......
120
(a) Increas i n':J ~train
x
~ x
S, strain
(b) Oecreasiny strain
+
6 12)
6X
x z
C)
~
+
x
x(in) ! 0.0012
0.0027
0.0138
0.0146
x/2a
0.0784
0.1764
0.9019
o. 9477
-0. CG7SO
r, strain
(d) CraCK OfJenin:i uis..,Jace;;1ent as a function or strctin at llirterent. ;.;01nts alon:i me craCK len':Jt.n durin:i increct:>Hl:i and uecrectsin:J strdin.
121
t.~ = 0. 0042 S17-1. NSSOOR 2a= 0. 029 in
Fig. 32: Crack opening displacements measured in one complete cycle (a) Load displacement loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
( c) Crack OiJen i n'j ui s,; I ace111ent as a function of stress at ditferent ~oints alon'j tne crack len'jtn aurin':J increasin'j ana decreasin~ str~in.
I
c ·~
...... c ~ :jj u ~
..,._
"' ~
"::'I ::: -~ c di 0.. 0
~ u ~ L..
:.....>
c
...... c ~ Qj u ~
'1
"' "O ,, c c l) '1 ·:)
~ u ~ L..
:....>
:::i '.:) '..)
128 e. 8 ci
0
"' §
( a) Increasin'::I Strain
I
x (in) x/2a ¢
0 0.0024 0.053
x 6 0.004 0.0889
4- i~ 0.0056 0. 1244 "" A '
I x 0.00746 0.1657 0 6 ¢ 0.0117 0.26
~ c... '
4- ... 0.03 0.6667 l<: 0 I ·~ 0.0362 0.8044 s .. ·.
A .-., 1-~ ~ F' :;,, I Z 0.0424 0.9424
"- -~ I
~ ...... e I ~ I ,.:...
0 -0.00500 (I .IJi)C,::0
l, strain o.c:::::o
8 "
(o) Uecreasiny strain
0 ~ ,. ~ 0
* 4-~ * 4- l<: 6
§ 8, 0
~ + ~ ~
°;!;"
$ 8 (j ~ ~ _.
6 = IT\
-0.00500 o.occco 0.0050
&, strain (d) CracK o~enin':i aistJlace111e11t dS a function ot strain at ditrerent points alon'::I tne cracK len:;tn aurin":i increasin'::I and decreasin'::I strain.
~ o 7 ~I :::> () :..; 8~:_.;.:c__~:::._...:::..~::::.....~~~~~~~~~~~~~I
Cl a.co 0.25 o.so o. ""5 I .CJ
x/La, ~elative Posi~iun
(D) CracK O,Jenin':J dis~lacernent uuriny increasin:J \ loaain'.:j) ana decreasin'J strain (unloauin':i) at aifferent ,;oin::s alon;, tne crack len~tn. Uifferent stress (strain) levels corresµona to tne ~oi nts snown 1 n I oaa 1.11 s~ I acernent I ooµ.
c: ..... ...., c: (1) = ai u ~
'1 Vl
-c ::n c: ..... = (JJ :i 0
~ u ~ I... u
".::) '::l u
=
c: (1) :::>.. 0
N
8 a a
~ a ~ ... a
§ I I a
-IGO.OQ
131
(a) lncreasi il'::J Strrii n
+
x ' + x 6 x C)
/\ 0 + (,i
§ c.
-SO. CO o .:J
<r, st res s , kc: i
x
+
x 6 C)
+ (b) uecreasin~ strain
0
.0.
+
x
1~: .:.s
'._) a I 01 g: 0 _, -----,.'.:,------....,.....----------0 -IC8.~0
c
-SO.C:J O.C:J SJ .CO
'1"', stress. i<.si
x(in) x/2a
0.00173 0.0715
0.00406 0.1678
0.00586 0.2421
0.0233 0.9628
(jf) CraCK oµenin~ aisf)lacen:ent as a function ot strain at oittere~t points alon'.J tne crac1< len~th aurin~ increasin-;; anu aecreasinj s~ra1n.
c:
...., c: ~ a:; u 'U
1
"" -:l
:::" c: c: ;JJ ~
0
.:»{. u 'U I... u
~
·::::S
.l /l
132
N
§ 0
( d) lncreasin':! :::it: rain I
' " '
' 6 i
+ I
+ 0 c; • a: 01 x 0
x
+ + x 6 x 0
6 0 + 8 * o' - '
~ . c :5 . 0-v .CGSCO o.cc::::::o 0.SCSC8
E, ' strain
(b) Decreasin~ strain
' L; T
x 6
x 0 ~i 3~~~~__.;;.:..:_~~~~~~~~~~~~~~-0 -V.~CSCO
t, strain o.:c;.::
x (in) x/2a
0.00173 0.0715
0.00406 0 .1678
0.00586 0.2421
0.0233 0.9628
(d..) '.:nc< 8L.Je'1i.-:"' ·:is;:;ia.:e!:ient as a t· .. rnc:~on or s:ress at: a1n::rent . .Joints :il0n'j :ne crac:< l~n'jrn uur:'l'J incre:JS1n'j ana Jecreas1n~ s:rain.
I
Fig. 35:
133
stress strain <ksi>
1 -46.54 -0.00356 -
2000 lbs 2 -14.28 -0.00239
3 16.97 -0.00106
4 41.16 0.00032
5 60.97 0.00264
6 40. 31 0.00296
7 4.10 0.00126
8 -27.72 0.00016
9 -48.24 -0.0013
10 -61. 82 -0.00410
Crack opening displacements measured in one ccmplete cycle (a) Load displacement loop as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
c:: <lJ 1 0
~
u ·'O "-~ i ~ I "3..;...
3 ~~. ~?I"_ .... ~ 8 -J. ,""!l'l.'00
CD I I
134
(a) Increasing Strain
x/2a, Relative Position
(b) Decreasin~ strain
6/tb ! /. 7
//(a :n c:: c:: 11 1 0
~ u 'O "-~
.zji I I / ti ~
' I Y. i 91 i I
§ y 10 ~ ,..._ .
x/~a, ~elative Position
(::>) CracK uf'enin~ uist-'lace:11e~n: Jurin'::> increasin':::> ( loaain::;) ana aecreasin~ strain \u11luaai;1;,) at airierent 1-'oints alon':::> tne crac~ len':::>tn. Uifferent stress (strain) levels corr'=Sf10nu to tne 1-'uints sn0v111 in loaa aist-'1ace1;1ent loot-'.
c::
=
c::
...... c:: g,i
ii u
"' ::i..
"' "':J
:n c:: c:: QJ 1 0
~ u "' t.. • .....>
:::::i -:i :...i
g 0 0 0 0 -100.00
"' g 0 0 0
\ a) Increasin~ )train
6
~ C)
"'""" '=' '-' -SO.OD a.co
cr-, stre!:>s, ks i
135
. ~
I ! x (in) x/2a
0 0.00013 0.0083 6 C)
6 0.00133 0.0838
C)
I I
so.co ICC.:JO
( b) Oecreasin'.:! strain
0 0 0 0 0 0 -iC0.20
6
C)
6
C)
t;;;: -SO .:'J o.:o SO.C.J tCO. :J
'J, !:>tress, ksi (c) CracK Of!en1n':J dis,.ilacement dS a tunctiun ot stress at ditterent ~01nts dlun~ tne crack lenjtn uurinj increas1n~ ana decreasin~ strain.
c lJ 1 0
= ....., c lJ
li u -.:I ..., "' "::l
:n c ·~
= <lJ
0
.><: u -.:I (....
'.....)
~ -=i '.....)
~ 0
( a)
8 ~
.---~ § 0
-0.CGSOO
a> 0 0
8 0
136
lncreasin':J :::itra in
6
C)
6
A G \..../
a .oscoo
£.., strain
( b) Deere as i ny stra; n
G
0 0 c '°I ,... 6~ -o .~:::sea o.~:::.::co
[, strain
. x (in} x/2a
0 0.00013 0.0083 0
6 0.00133 0.0838
I
I ! - -
a. :::s.~~
(d) Craci< openin':J dis,.;lace111ent as a function ot strain at d1rferent ,.;oints aion':J cne cracK len':Jtn dur1n':J increasin':J and uecr2asin':J strdin.
f;~ = 0. 0024 617-23.N42234 2a= 0.029 in
----2a---
1 ')., ·~'
1
2
3
4
5
6
7
8
9
stress Strain Cksi>
-43.28 I -0.001925
-26.44 -0.00132
7.64 -0.0002
33.94 0.00083
49.22 0.00165
47.24 I 0.002
- 7.07 0.00018
-26.87 -0.00062
-59.54 I -0.002-::::
Crack opening displace~ents ~easured in one complete cycle (a) Load displace~ent loop as obtained from clip gauge mounted across the grio ends and the points (corresponding s:ress and strain levels sho~n in :~ble) where closure observations Nere ~aae.
I
I
lJ 1 0
0 a.co
138
x
(b) 8ecreasiny strain
6
0.25 C.~D
x/~a. Kelative Position
0. 7S I .CD
(D) Crctci< OiJenin::J disi->lace1nent ~urin':J increasin::J ( loadin':J) ano aecreasin':J strain (unloaoin'j) at oitrerent ;Joints alun"' tt1e crctci< len'.Jtn. Different stress (strain) levels correSiJOnu to tne ;.ioi nts snovin in I uaa a is~ 1 ace111ent l OOiJ.
c::
..... c:: ~ iii u
"' '.1 Ill
"'O
:;"I c:: c:: a.I :::i. 0
~ u
"' ~ :.....J
:::::i :::i :.....J
c::
..... c:: ~ a.I u
"' :::i. :/)
"O
=' c:: c:: l! .... 0 .;,,:. u "' ~
:.....J
~
:'.) :.....J
"' 0 0 8 0
8 c 0 ~ 0
- 75.CO
"' 0 0 0 0 0
~ 0 I 0 0 '=' - 75.CO
139
x (in} x/2a (a) Increas i n1:1 Strain
0 0.0028 0.0965
6 0.0204 0.7034
a.co 75. ::J '1, stress, ksi
(D) uecreasin'j strain
C)
o.:~
o-, stress, Ksi 75.~c
(c) CracK oµenin~ dis~lacement as a function of stress at ditterent ~oints alon~ the cracK lenytn aurin~ increasin0 and decreasin~ strain.
140
x(in) x/2a
0 0.0028 0.0965
6 0.0204 0.7034
O.C:JZSO
(d) CraCK ol-'enin::J cis,..,leicc'llent as a function ut strain at ditterent iJOints alon'.J me craci< len'::itn llurin::1 increasin'::i arHl c:ecreasin·J strctin.
• l I •
Fi'::J. 37:
~.-:.. = 0. 0024 617-23.N32S20 2a= 0. 02i in
-..
141
1
2
3
4
5
6
7
8
9
Stress strain <ksi>
-44.28 -0.00185
-21. 64 -0.00125
0.00 -0.0005
24.05 0.0004
42.72 0.00128
39.60 0.0018
5.65 0.00065
-28.28 0.00066
-55.16 -0.00192
CracK OiJenin':J aisiJlacements rneasurea in one cornf-llde cycle \a) LOdO a1sf-llace1;1ent loot-! as ootainetl trur;, ClliJ ::iau::ie :nountea across tne 'fi,., entls ana me ,.;oints \corresf-lonain':J stress ana strain levels snuwn in taDle) ~.nere closure ooserva-t-i uns were :naue.
'.,D) CrciCk o,.;enin'j uis,.ilace1lient Jurin'.;! increasin:; ( loadin~) anu decreasin':l strarn lunloauin'j) at airterent ,.ioints alon.3
tne cracK ler1':Jtn. Uirrerent stress (strain) levels correStJOnu tu tne ,.;oints snown iri loaa oisrilace1;1ent loori.
c:
....., c: ~ di u IQ
'1
"' "O
::n c: c: ~ 1 0
.:.t. u IQ '-
'...)
=i -::> '...)
c: ·-....., c: Q) E Q) u IQ
:1
"'
143
~ 0
( a) x (in) x/2a Increasin':::I Strain
0 0.0024 0.1091
6 0.0054 0.3545 -
+ 0.0203 0.9227
6 6 6
+ + +
+ g §
0 0 ~ C)
a ,..._ '-'
g c:/ O· 00 , stress, l<si 75.GJ
8.-~~~~~~~~~~~~~~~~~ 0
(D) Decreasin':::I strain
+
<r, stress. ksi
6
+
\c) Crack oµenin9 dis~lacement as a function of stress at different ~oints alon':::I tne cracK len':::ltn durin~ increasin':::I anu decreas1n~ strJin.
-
i= ·-.µ i=
~ Qi u tO
:1 Ill
'O
::n i=
i= (IJ -:i.. 0
~ u ~ L.
:,,,)
:::::l -:i w
i= ·-.µ i= ~ <= iii u tO
:1 Ill
'O
-n i= ·-::: .l) 1 0
~ u tO L. ._, ::i -:i ._,
144
§ 0 ci
(a) Increasi n':J Strain
+ + +
+
~ I;_;; ci
~ ~ ~ ~ ,..... '--'
-0.00250 o.oocco
"' a § c ' strain a
( D) Oecreasin':J strain
+ 0 8 8.i.--e a -0 .00250 0 .CCGCO
f, strain
~
+
C)
~ -+
O.O:JZ50
x(in) x/2a
0.0024 0 .1091
0.0054 0.3545
0.0203 0.9227
(d) Crack OfleninJ dis~laceinent as a fu:iction of strain at different f)Oints alon~ tne crack len~th durin~ increasin~ 3nd decreasiny strain.
Fig. 38:
En. = 0.0024 617-23.N29760 2a= 0.0181 in
L --s
·1
-= i :::::::-
t=,.
145
1
2
3
4
5
6
7
8
:r ., I
T
Stress strain Cksi)
-45.26 -0.001925
-19.80 -0.00117
21. 21 0.0003
49.50 0.00172
32.53 0.00150
4. 24 0.0005
-18.38 0.00025
-53.74 -0.00195
Crack opening displacements measured in one comolete cycle (a) Load displacement looo as obtained from clip gauge mounted across the grip ends and the points (corresponding stress and strain levels shown in table) where closure observations were made.
c:
...... c: ~ Qj u "=' a.. <l'l
-0
:n c: c: ll 1 0
~ u "=' '--
:...>
~ :J :._)
c:
...., c: ~ ii u "=' 1 <l'l
"O
:n c: c: a; '.l.
':>
~ u "=' '--:...>
~ "'.:) :...>
"' § ~ I
0 o.~o
"' ':J 8 0 01
0 ' ~ .L 0 a.co
146
(a) Increasin~ Strain 4
2
1 n. ~s 0.50 0. 75
x/ca, f<elative fJ_gsition
l D) Uecrea::. in':J strain
8
0 .:s O .. ,.5
x/ca, Ke/ative ~ositinn
/ .. I I
I .CO
(D) Crack oµenin·::i aisi-ilacement aurin':J increasin::i ( loaain'j) ana aecreasin::i strain l~nloaoin':J) at aitterent 1-'oints alonj tile crack len':ltn. uirterent stress (strain) levels corresi-iona to tne ,.io1nts snown in loao ais,.ilace1~ent looµ.
1r, stress, ksi ( c) Crdck open in-:; ai sri I aceH1ent as a runct ion or stress at airterent f!Olnts alun':J tne crao. len::ith d'Jrin-:; increasin'::l ~nu aecreasin-:; strctin.
-
c:: <li ~
0
:::;> c:: c:: <li :i.. 0
148
~....-----___ _ 0
la) lncreasin~ Strain 0
A
+
+
~ ,.~ C) ci~E:S~~~~~~_,_~~~~~~~~~--'
-0.00250 0.CCCC8 o.c:~5C
0
c, strain
(b) Uecreasin~ strain
6 + +
6 T
0 §I ~ o..._~~'='-'--~~~~~-+-.;._~-'-~~~~~~~__J
-0. 00250 0. :::cJ o. :~25J
c, strain
x (in) x/2a
0.0024 0.1326
0.0056 0.3093
0.0178 0.9834
(a) CrdcK Of)enin':i aisf.llacement as a function ot strain at airterent f)Oints alon~ the crack len~tn aurin~ increasin~ ana decreasin~ strctin.
.. g c -i.. '-c:
...., c: ~ ii u ·~
:i.. II')
'O
:n = c: lJ .:i.. 0
.:..! u ~ ~
:..>
r-.. ,-,.... v c ')(. '-
= ...., c: ~ 1i u "' :i.. IJ')
'O
::;') c: c lJ ~
:)
.:..! :.J 'Q ~
:..>
::i '::l :..>
Fig.
~
:1 0
rt! ~
0 .N 0
0
0
8 0 -100.00
::i Jl ~
0 ~ 0
r· 0 CTl
0
0 N
0
0
0
8 0 -0.15
39:
,'
STRAIN
149
o.o
I
/ /
I
oo
/'
.10·1
')(.,distance as measured from crack tip, in
, I
€9 0 .00133
0.00606
100.00
0.15
Loading and unloading paths in a typical and E plots.