The variation in fatigue crack closure behavior across the thickness of aluminum alloy specimens was investigated. The specimen geometries examined were the middle crack tension M(T) and compact tension C(T). The fatigue crack closure behavior was determined using remote displacement and strain gages, near tip strain gages, and fatigue striations. A hybrid experimental/numerical method was also used to infer the crack opening loads. The results indicate a variation in crack opening load, of 0.2 in the specimen interior to 0.4 to 0.5 at the surface

Dawicke, D. S.

Grandt, A. F., Jr.

Newman, J. C., Jr.

English

NASA Technical Reports Server

t _ Im
NASA TECHNICAL MEMORANDUM 102590
THROUGH-THE-THICKNESS FATIGUE CRACK
CLOSURE BEHAVIOR IN AN ALUMINUM ALLOY
D. S. Dawicke, J. C. Newman, Jr.,
and A. F. Grandt, Jr.
January 1990
National Aeronautics and
Space Administration
Langley Research Center
Hampton, Virginia 23665
(NASA-TM-10)S90) THROUGH-THE-THICKNESS
F^TIGUt CRACK CLGSURE BFHAVIGR tN AN
ALUMINUM ALLCY (NACA) 8 p CSCL 20K
G_/39
N00-20427
Unclas
0771i45
https://ntrs.nasa.gov/search.jsp?R=19900011111 2020-03-19T22:45:00+00:00Z
i# _l
THROUGH-THE-THICKNESS FATIGUE CRACK CLOSURE BEHAVIOR IN
AN ALUMINUM ALLOY
D.S. Dawicke', J.C. Newman, Jr.", A.F. Grandt, Jr.***
The variation in fatigue crack closure behavior across the
thickness of aluminum alloy specimens was investigated. The
specimen geometries examined in this study were the middle
crack tension M(T) and compact tension C(T). The fatigue
crack closure behavior was determined using remote
displacement and swain gages, near tip strain gages, and fatigue
striations. A hybrid experimental/numerical method was also
used to infer the crack opening loads. The results of this study
indicate a variation in crack opening load, in terms of the ratio of
opening load to maximum load, of 0.2 in the specimen interior
to 0.4-0.5 at the surface.
INTRODUCTION
Many of the crack growth analyses of fatigue cracks have been made with the
assumption that the crack front is straight. In reality this is rarely the case, with
even the simplest geometries exhibiting a curved crack front. In many cases, such
as constant amplitude loading, this curvature is essentially trivial because the crack
rapidly assumes a nearly "steady state" shape. For other conditions, such as
overloads and variable amplitude loading, the crack front curvature becomes more
pronounced as the crack growth behavior is affected by the complex interaction
between the stress intensity factor and fatigue crack closure variations through-the-
thickness.
Experimental evidence of a through-the-thickness variation in fatigue crack
closure behavior was observed by Pitoniak et al (1) in their experiments with
polymethylmethacrylate (PMMA), a transparent polymer. The through-the-
thickness fatigue crack closure behavior of polymers was further illustrated in work
by Ray et ai (2-3) and Troha et al (4). A method of obtaining a detailed description
of the through-the-thickness variation in fatigue crack closure behavior of metals
• Analytical Services and Materials, Inc., Hampton, VA 23666
•, NASA Langley Research Center, Hampton, VA 23665
•*, School of Aeronautics and Astronautics, Purdue University, W. Lafayette,
IN 47907
usingfatigue striationswasdevelopedby Sunderet al (5) basedon thework of
Pellouxet al (6). AnandanandSunder(7-8)usedthismethodto obtainadetailed
descriptionof thethrough-the-thicknesscrackopeningloadsfor crackspropagating
from a notch root.
The purpose of this study was to examine the through-the-thickness variation
in fatigue crack closure behavior of 2024-T351 aluminum alloy. The fatigue crack
closure behavior of this alloy was examined experimentally using the "standard"
remote displacement and strain gages, near-tip strain gages, and a fatigue striation
method. A hybrid experimental/numerical method was also used to infer the crack
opening load. The fatigue crack growth tests were conducted under constant stress
amplitude (AS) loading for material characterization and constant stress intensity
factor range (AK) loading for fatigue crack closure behaver fiaeasurement.
CRACK OPENING LOAD MEASUREMENT TECHNIOUE_;
The fatigue crack closure behavior was experimentally described through the
measurement of the crack opening load. The crack opening loads were measured
with near-tip strain gages, fatigue striations, backface strain gages (C(T) only), and
crack opening displacement (COD) gages (M(T) only). The material used in this
study was 9.5mm thick 2024-T351 aluminum. The M(T) and C(T) specimens
were tested under a constant stress intensity factor range of AK=I3.8 MPa m 1/2 and
a stress ratio of R=0.1. One M(T) specimen was tested with a 1.6 overload. The
surface crack lengths were measured optically and the AK was maintained, to
within :i:2%, through load shedding. The details of the experiments and crack
opening load measurement techniques are provided in References 9-10.
The crack opening loads were determined from backface strain gages and
COD gages by recording the load and strain (or displacement) for a complete
loading-unloading cycle. The backface strain (or displacement) against load curve
should (for relatively low loads) be linear for a specimen that has a crack that is
always open. The presence of fatigue crack closure causes the initial portion of the
signal to be non-linear, as part of the load is required to relieve the residual
compressive stresses on the crack surfaces due to closure. The opening load was
found by identifying the load at which the signal became linear. The reduced
displacement (or strain), as defined to be the difference between the actual
displacement and a line fit through the linear portion of the upper unloading curve,
was used to magnify the non-linearity in the measured displacement (or strain)
curve to aid in identifying the crack opening load.
The crack opening loads were determined from near-tip strain gages in a
manner similar to that described above. The near-tip strain gage technique used a
small strain gage placed 0.Smm below and behind the crack tip and oriented to
measure strain perpendicular to the direction of loading. A strain gage oriented in
this manner produced the load/strain behavior shown in Figure 1. The two knees
in the curve were hypothesized to represent the loads at which the crack surfaces
separated in the interior (lower change) and at the surface (upper change).
A techniquebased on the work of Sunder et al (5) was used to determine the
fatigue crack closure behavior from fatigue striations. The method used a special
loadingsequenceto markthefatiguesurfacewith uniquelyspacedfatiguestriations
at different cracklengthsduring thetest. Thesurfacewasmarkedby applyinga
specialloadingsequenceconsistingof 20cycles.Thecyclesin thesequencehada
constantmaximumloadandminimumloadswhich increasedwith eachsucceeding
cycle. Thespacebetweenfatiguestriationsshouldremainconstant,corresponding
to aconstanteffectivestressintensityfactor range,as long asthe minimum load
wasbelow thecrackopeningload. The spacebetweenfatigue striationsshould
decrease,correspondingto a decreasingeffective stressintensity factor range,
whentheminimum loadroseabovethecrackopeningload. The crackopening
load wasobtainedby determiningat which cycle the spacingbetweenfatigue
striations beganto decrease.The fatigue striationswere examinedat several
locationsthrough-the-thicknessof the specimento obtain thevariation in crack
openingload.
HYBRID EXPERIMENTAL/NUMERICAL CRACK OPENING
_ALCULATION
A hybrid experimental/numerical method was developed to infer the crack opening
load behavior at any location through-the-thickness from a measurement of crack
growth rate and a calculated stress intensity factor range at that location on the crack
front. The method relies on the assumption that the material crack growth behavior
can be uniquely described by a relationship between crack growth rate and the
effective stress intensity factor range. This crack growth relationship was
approximated from high stress ratio (R=0.5) constant stress amplitude tests. For
the 2024-T351 alloy, the cracks were assumed to always be open for stress ratios
above R=0.5, thus the effective stress intensity factor range was equal to the
applied stress intensity factor range. The crack growth rate data were represented
well by a simple power law (Equation 1) for the stress intensity ranges of interest.
da -- 3.95x101°(AK_) zs (1)
dN
The effective stress intensity factor range at any point along the crack front
(_)) was determined by measuring the crack growth rate at that location on the
crack front from the fatigue fracture surface, and substituting the rate into Equation
1. The stress intensity factor range for that location (AK(z)) was determined using a
3-D finite element analysis for a curved, through-the-thickness crack. The crack
shape used in the analysis was obtained from examination of the fatigue fracture
surfaces. With the information on AKeg z) and AK(z), the opening load could be
calculated from the customary definition of AKea(z) given by Equation 2.
(2)
RESULTS AND DISCUSSIONS
Crack opening loads determined experimentally and inferred for the same
conditions using the hybrid experimental/numerical calculation technique are shown
in Figures 2-3 for the M(T) and C(T) specimens, respectively. The solid symbols
representheupperandlower kneesof thenear-tipstraingage signal. In Figure 2,
the symbols on the left (2z/B=-l) correspond to the M(T) specimen with the
overload and the symbols on the right (2z/B=I) correspond to the M(T) specimen
without the overload. The symbols were located on the surface where the
measurement was made, even though the lower knee is thought to represent the
crack opening behavior of the interior. The small dashed line in Figures 2 and 3
represents the constant value of crack opening load determined from COD in the
case of the M(T) specimen and backface strain in the case of the CCI') specimen.
The C(T) and M(T) specimens had crack opening loads around 0.4-0.5 at the
surface and 0.2 in the interior, with the C(T) specimens having slightly higher
crack opening loads, as shown in Figures 2 and 3. After crack growth of 0.4 mm
following a 1.6 overload, the M(T) specimen had a crack opening load (Popcn/Pmax)
of 0.6 at the surface and around 0.3 in the interior, as shown in Figure 2. The
lower knee of the near-tip strain gage signals showed good agreement with the
crack opening loads determined from the striations in the specimen interior. The
hybrid experimental/numerical calculation showed good agreement with the crack
opening loads determined from the striations throughout the specimen and the
calculated surface crack opening loads agreed with the upper knee of the near-tip
strain gage signals.
The hybrid experimental/numerical calculation was also used to infer the
crack opening load for a surface crack in a transparent polymer material subjected
to pure bending. The crack opening load through-the-thickness was obtained by
Ray et al (3) through optical interference. The comparison of the experimental
measurements and the hybrid calculation in Figure 4 indicates that the transparent
polymer behaves in a qualitatively similar manner as the aluminum alloy. The large
dashed line represents the minimum applied fatigue load. The load was dropped to
zero, for one cycle, during the optical interference measurements to determine crack
opening loads below the minimum load. The hybrid technique cannot infer crack
opening loads below the applied minimum load, but the location at which the
inferred opening load exceed the minimum fatigue load (_,30 °) agrees quite well
with the optical interference measurements.
CONCLUDING REMARKS
The results of this study indicate that fatigue crack closure behavior varies along the
crack fronts of through-thickness and surface cracks in the materials examined.
Crack opening loads determined by the fatigue striation method, a near-tip strain
gage method, and a hybrid experimental/numerical calculation were consistent with
each other.
SYMBOLS USED
B = specimen thickness (m) R
P = applied load (KN) z
PA_pen -- crack opening load (KN) Pmax
= stress range (MPa) da/dN
AKar = effective stress intensity AK
factor range (MPa m In)
= stress ratio
= distance from mid-plane (m)
= maximum applied load (KN)
= crack growth rate (m/cycle)
= stress intensity factor range
0VlPa m 1_)
(I)
/_EFERENCES
Pitoniak, F.J., Grandt, A.F., Jr., Montulli, L.T., and Packman, P.F.,
Engng Fract. Mech., Vol. 6, 1974, pp. 663-670.
(2) Ray, S.K. and Grandt, A.F., Jr., ASTM STP 982, 1988, pp. 197-213.
(3) Ray, S.K. and Grandt, A.F., Jr., Exp. Mech., Vol. 28, No. 3, September
1988, pp. 273-280.
(4)
(5)
(6)
(7)
(8)
(9)
Troha, W.A., Nicholas, T., and Grandt, A.F., Jr., ASTM STP 982, 1988
pp. 598-616.
Sunder, R., and Dash, P.K., Int. J. Fat., April 1982, pp. 97-105.
Pelloux, R.M., Faral, M. and McGee, W.M., Fat. Engng Mater. Struct.,
Vol. 1, 1979, pp. 21-35.
Anandan, K. and Sunder, R., NAL PDMT 8625, National Aeronautical
Laboratory, Bangalore, India, April 1986.
Anandan, K. and Sunder, R., Int. J. Fat., Vol. 9, No. 3, October 1987.
Dawicke, D.S., Ph. D. Thesis, Purdue University, 1989.
(10) Dawicke, D.S., Grandt, A.F., Jr., and Newman, J.C., Jr., Engng Fract.
Mech., Accepted for Publication.
1.0
0.8
.__e 0.6
emax 0.4
0.2
1.0
0.8
p 0.6
P ax 0.4
0.2
oO • I • I . L . • . l . I . I . I
0.0 -200 -400
Micro Strain
Surface
f V Crack
A Opening
Load
Interlor_
Crack Opening .Z
Load
oo5o'"'...........'
- 0 50
Reduced
Micro Strain
Figure 1. Load-strain and load-reduced strain behavior for a near tip strain
gage.
0.7 0.7
0.5I / 1.6 Overload / 0.5
eopen [_N° Overl°ad _i eopen J
o.l _m o._
-1 0 1 -1 0 1
2_' B 2z/' B
Figure 2. Experimental and calculated
crack opening loads for a
M(T) specimen subjected to
constant AK loading with
and without a 1.6 overload.
Figure 3. Experimental and calculated
crack opening loads for a
C(T) specimen subjected to
constant AK loading.
0.6
Pope O'4
Pax0.
0.0
Figure 4
Symbol Key for Figures 2-4
o Fatigue Striation Measurement
Q Upper Knee in Near-Tip Strain Gage Signal
II Lower Knee in Near-Tip Strain Gage Signal
- - - Displacement Gage Measurement
Minimum
Fatigue
Load _ ltybrid Calculation
Crack epth13
• • ! , --_ 1 • .i •
0 3 0 6 0 9 0 half
0 (degrees) IL. Crack "l
Length
Experimental and calculated crack opening lo,'ds for a surface crack in
a transparent polymer subjected to pure bending.
6
Report Documentation Page
1. Report No
NASA TM- 102590
4. Title and Subtitle
Through-the-Thickness Fatigue Crack Closure Behavior
in an Aluminum Alloy
I 2 Government Accesspon No J 3 RecJpient's Catalog No
1
i 5 Ruport Date
January 1990
I ....
7" Author(s)
D. S. Dawicke*; J. C. Newman, Jr.; and A. F. Grandt, Jr.*
1
9. Performing Organization Name and Address
NASA Langley Research Center
Hampton, VA 23665-5225
-_i-Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, DC 20546
6 Performing Organization Code
8. Performing Organization Report No.
10 Work Unit No
505-6 3-01-05
11 Contract or Grant No
13 Type of Report and Period Covered
Technical Memorandum
I 14 Spr_nsor_ng Agency Code
15. Supplementary Notes
*D. S. Dawicke, Analytical Services and Materials, Inc., Hampton, VA 23666
**A. F. Grandt, Jr., Purdue University, West Lafayette, IN 47907
16, Abstract
The variation in fatigue crack closure behavior across the thickness of aluminum alloy specimens was
investigated. The specimen geometries examined in this study were the middle crack tension M(T) and
compact tension (C(T). The fatigue crack closure behavior was determined using remote displacement a
strain gages, near tip strain gages, and fatigue striations. A hybrid experimental/numerical method was
also used to infer the crack opening loads. The results of this study indicate a variation in crack opening
load, of 0.2 in _he specimen interior to 0.4_0.5 at the surface
17, Key Words (Suggested by Author(s))
Fatigue
Crack closure
Through-the-Thickness
Striations
Near tip strain gage
19, Security Classif. (of this report)
Unclassified
NASA FORM 1626 OCT 86
18 Distribution Statement
Unclassified - Unlimited
Subject Category - 39
20. Security Classif. (of this page)
Unclassified
21. No. of pages
7
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Through-the-thickness fatigue crack closure behavior in an aluminum alloy

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