APPLIED J-INTEGRAL IN HY130 TENSILE

PANELS AND IMPLICATIONS FOR

FITNESS FOR SERVICE ASSESSMENT

D. T. Read

National Bureau of Standards

U.S. Department of Commerce

Boulder, CO 80303

July 1982

—Q0—

100

, U56x 82-1670

1982

wC, 2

NBSIR 82-1670

APPLIED J-INTEGRAL IN HY130 TENSILE

PANELS AND IMPLICATIONS FOR

FITNESS FOR SERVICE ASSESSMENT

KATIOHAL BUBKA l QW STANDARDS

UBRaKT

$E? 1 5 1982

not- P)cclC

D. T. Read oc

OSG

\ c\

Fracture and Deformation Division

National Measurement Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, CO 80303

Sponsored by:

Naval Sea Systems Command

David Taylor Naval Ship R&D Center

Annapolis, MD

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1. INTRODUCTION , 1

2. METHOD 2

2.1 Analytical approach 2

2.2 Experimental procedure 4

3. RESULTS AND DISCUSSION 6

3.1 Strain distributions 6

3.2 Strain dependence of J-integral, stress, and crack

mouth opening displacement 8

3.3 Gross section yielding results 10

3.4 Implications of present results for fitness-forservice assessment 12

3.5 Surface flaws 14

4. CONCLUSIONS 17

5. ACKNOWLEDGMENTS 17

6. REFERENCES 18

7. FIGURES 21

8. APPENDIX. APPLIED J-INTEGRAL VALUES IN TENSILE PANELS 102

i i i

APPLIED J-INTEGRAL IN HY130 TENSILE PANELS AND IMPLICATIONS FOR FITNESS FOR SERVICE ASSESSMENT*

D. T. Read

An experimental technique for direct evaluation of the J contour integral

is described. Results are reported and discussed. Some fifteen cracked HY130

tensile panels were tested, including center-cracked, single-edge-cracked,

double-edge-cracked, face-cracked, and part-through-cracked configurations. As crack size increased, the post-yield deformation pattern changed from gross

section yielding, for very small cracks, to net section yielding, for larger

cracks. Net section yielding was associated with much larger O-integral values

than gross section yielding. The product of crack mouth opening displacement

and yield strength was approximately equal to the J-integral for all cases in

the tensile panel geometry used here. The implications of these results for

f i tness-for-service assessment of practical components and structures containing

crack-like defects are discussed. Net section yielding behavior is intolerable

in high-performance applications. Gross section yielding behavior can be

treated using a J-integral estimation curve derived from the present experimental

results. The scatter in the normalized gross section yielding contribution to 0 was high, approximately a factor of 2. This scatter was attributed to specimen

imperfections and experimental problems. The experimentally derived J-integral

estimation curve of the present study fell at the top of the range of previously

reported curves. Applications of this estimation curve to cases of residual

stresses, stress concentrations, and surface cracks are briefly described.

Key words: crack; defect; fi tness-for-service; fracture mechanics; gross section

yielding; J-integral; net section yielding; surface crack; through crack.

1. INTRODUCTION

This report describes experimental evaluation of the J-integral as a function of stress or strain for through and part-through cracks in tensile panels. The principle of the present method is to measure the integrand terms of J at suitable intervals along an appropriate contour and then

evaluate the integral. Because the resulting J value is based directly on the definition of J, no assumptions about the crack size or the behavior of stress-strain fields produced by the action of

the crack tip are necessary. This advantage is crucial in cases of very short cracks, which are

of special interest for structural applications. The present method extends previous direct

experimental evaluations of the J-integral in metals and composites in the elastic range [1-3] and

in rubber [4] to the case of metals in the plastic strain range.

The J contour integral has been applied widely in characterizing the fracture toughness of

metals [5-7]. But its application to evaluation of structural durability requires knowledge of the

material J

c value needed in a cracked, structural element subject to stress and strain. The material

J value needed is the same as the applied J-integral value addressed experimentally in this study.

The present study, therefore, is complementary to current work advancing the use of the J-integral

for materials characterization; it also extends current knowledge of applied J-integral values beyond

Contribution cf U.S. National Bureau of Standards, not subject to copyright.

This report was prepared as part of the Fracture Control Technology Program under the sponsorship of

Dr. H. H. Vanderveldt, Naval Sea Systems Command (SEA 05R15). The effort was directed by

Mr. John P. Gudas, David Taylor Naval Ship R&D Center, under Program Element 62761N, Task Area

SF-61-544 - 504

1
the linear-elastic case where well-known and widely used handbook solutions [8] for the stress

intensity K can be used to calculate the applied J-integral.

2. METHOD

The principle of the present method is to obtain the J integral by measuring its integrand terms

at suitable intervals along an appropriate contour and then evaluating the integral. The analytical

and experimental aspects of the present method for direct experimental evaluation of the J contour

integral are discussed separately below.

2.1 Analytical approach

The definition of the J-integral as given by Rice [9] is:

J = f W dy - T • 3u/8x ds (1)

where W is the strain work density, f is the traction vector, u is the displacement vector, x and

y are Cartesian position coordinates, and s is arc length along the contour. The contour chosen

for direct measurement of the J-integral is indicated in Fig. 1 for single-edge-cracked specimens.

Because of symmetry about the plane of the crack, only half of each specimen was instrumented. The

contour follows specimen free surfaces along the y-direction and traverses the tensile axis at a location away from the crack. For some specimens, one y-direction contour segment was along the

specimen centerline.

Plane stress behavior was assumed all along the contour because no through-thickness applied

stresses were present and because the specimen thickness was small compared with its length and width

[3].

Evaluation of the two terms of Eq. 1, the work density term, Wdy, and the traction-bending term,

f*3u/9x ds, for contour segments DC, CGA, and AB (Fig. 2) is now discussed in detail.

The strain work density W, given as

W = fa

.

-de . , (2

)

where a., is the stress tensor and e.. is the strain tensor, reduces simply to

ij ij K J

W = fo de

yy yy

(3)

along DC and AB because all stress components except a are zero for these contour segments along

free surfaces in plane stress. Below yield, a is given simply by e^/E (where E is Young's

modulus) again because all stresses except a are zero. For the same reason, the yield criterion

becomes, simply, e *E > c^, where is the yield strength, and the stress depends on the strain

e just as the longitudinal stress depends on the longitudinal strain in a simple tensile bar. A stress-strain curve from a smooth-bar tensile test of the specimen material was found to be well

approximated by ari elastic-perfectly-plastic stress strain law. This bilinear stress-strain relation,

in the form

2
= e E, for e < Q m yy yy y

= o , for e > Q m y yy y

( 4 )

was substituted into Eq. 3. The resulting expressions for W,

“ = Ee*

y

/2, for Eyy <o

y/E

“ = »y/2E + »y

U

yy

- °y

E) for cyy<cy

/E ,

( 5 )

were used in the evaluation of the integrand of Eq. 1 along contour segments DC and AB. The traction

vector, f, is zero along contour segments DC and AB because they are on free surfaces, so the second

term of the integrand of Eq. 1 is zero for these segments.

Along segment CGA, dy is zero because this segment is parallel to the x-axis. Therefore the

first term of the integrand of Eq. 1 does not contribute. The traction f at the contour can be

expressed as T^ = n

^

, where n^ is the unit vector outward normal to the contour. Along segment

CGA, n. is the unit vector outward normal to the contour. Alona segment CGA, n = 1 and n = 0 so

j y x T = o and T = a . The shear stress, o , was assumed to be negligible for this contour segment

y yy x xy xy chosen to be away from the crack. The x-component of u along CGA, u , was assumed to be negligible

because no source for such a displacement component was present. Therefore, the integrand in Eq. 1 reduces to T^ • 9uy /9x for contour segment CGA. The traction, T , was calculated from strains

measured by strain gages between C and G and G and A (Fig. 2) using the stress-strain relation of

Eq. 4 above, which applied because all stress components except a ; were insignificant along CGA. yy

The traction, T , all along CG was assumed to be the value calculated from the strain gage between C and G. The bending term, Su^/Sx, all along CG was approximated by

3uy/9x = [ u ( G ) - u (C)]/[x(G)-x(C)] . (6)

The value of u (G) was obtained as half the displacement measured by the linear variable differential

transducer (LVDT) mounted between points G and H. In similar fashion, u

y (C) was obtained from the

LVDT mounted between points C and E. The quantities x(G) and x(C) were simply the x coordinates of

points C and G. The traction-bending term, T^*9u

y /9x, along segment CG was calculated using T

y and

9u /3x obtained as described, and the traction-bending term along segment GA was calculated

simi larly

.

Strain values needed for calculation of the work density, W, were available at only a limited

number of locations along contour segments DC and AB. Therefore the integral of Eq. 1 could only be

evaluated approximately. Two different approximation methods were tried. The first method was

direct numerical integration (no-fit procedure). Segments DC and AB were divided into increments

each containing one strain gage. The contribution of each increment to the integral was taken to be

the product of the strain energy density, calculated from the measured strain value using Eq. 5,

multiplied by the increment length. Because of the sense of the contour integration, increment

lengths along DC were taken to be positive, and those along AB, negative. The second method for

evaluating the integral of Eq. 1 was to fit the measured strain values along segment DC or AB to a polynomial or selected nonlinear function of distance y from the crack plane; the strain values given

by the fitting functions were then used to calculate work density values, using Eq. 5, at

3
many locations along segments DC or AB so that conventional numerical integration could be used to evaluate Eq. 1 along these segments. Functions were selected and evaluated according to how well

they reproduced the observed dependence of strain on position. Strain values from strain gages were available at approximately eight locations along both segments CD and AB. In addition, qualitative

indications of the dependence of strain on position were obtained from brittle lacquer coatings on the specimen surfaces. Third- and-fourth order polynominals expressing strain e ^

as a function of

distance, y, from the crack plane achieved a compromise between fitting the measured strain values

and modeling the qualitative dependence of strain on position. Fifth- and sixth order polynominals

fit the measured values more closely, but introduced spurious maxima and minima into the position

dependence of the strain. The nonlinear functions were chosen to provide a better fit to the measured

strain values without introducing spurious maxima and minima. The functional forms used were: on segments DC,

eyy

= a

l ex P(" d 2

-y

)

+ a 3 +a

4y (7)

and on segments AB,

e yy

= a

i ex P(" z ^/ 2 ) + a 4

+ a

5y

+ V" • (8)

The a^. were coefficients to be fitted and z = (y-a^/a^. These functions allowed modeling of the low

strain region near the crack mouth on contour segment AB and the peak in strain on segment DC where a deformation band emanating from the crack intersected the specimen surface.

The analytical strategy just discussed was applied to experimental data obtained as described

bel ow. 2.2 Experimental procedure

The specimen material used in the present study was HY130 steel; the plate used had a yield

strength of 933 MPa and a tensile strength of 964 MPa. The chemical composition of the plate used is listed in Table 1. Engineering stress-strain curves obtained using round bar tensile specimens with

gage section 6 mm in diameter by 25 mm long, Fig. 3, showed that the specimen material was nearly

el astic-perfectly-pl astic . The stress rose only 2 percent between 1 and 5 percent strain. J-integral

resistance curves (J-R curves) obtained using the unloading compliance technique on side-grooved

compact tensile specimens 25 cm thick are shown in Fig. 4. Also shown for comparison is a J-R curve obtained from a face-cracked tensile panel 25 mm thick by 90 mm wide by 300 mm long, with initial

crack length 4 mm. The difference between J-R curves from the two specimen types is caused by

differences in crack tip constraint, as discussed in a later section. Pin-loaded tensile panels with

gage sections 30-cm long by 9-cm wide by 1-cm thick were used for most tests. Larger-scale tests were performed in wedge-gripped center-cracked panels with gage sections 84 cm long by 56 cm wide by

2.5 cm thick. Saw-cut notches were usually used instead of fatigue cracks to postpone tearing (in

all but the two cases where fatigue precracks were used). Figure 5 indicates the configurations of

the 15 specimens covered in this report. Figures 6 through 12 give details of the instrumentation of sever specimens representati ve of each design. Similar instrumentation was used on the other specimens of each design.

As indicated in Figs. 6 through 12, the strain gages were concentrated near the crack mouths and

on the opposite side of the specimen at a location offset from the crack plane by a distance on the

4
order of the length of the uncracked ligament. These two locations were the sites of significant

features of the strain distribution.

Table 1. Chemical compositions by weight percent and treatment for HY130.

Chemical Composition, weight percent:

Ni Cr Mo V C_ Mn P Si 5.00 0.42 0.53 0.043 0.11 0.76 0.005 0.03

S Cu A1 Co Ti Fe 0.004 0.022 0.021 0.02 0.008 bal

Treatment: Austenitized, quenched, tempered, quenched.

Very small gages (four or five independent gages on a single backing sheet, active length of about

0.75 mm each, gage centers about 1.4 mm apart) were used near the mouth of short cracks. Linear

variable differential transducers (LVDTs) were used to measure relative displacements of the ends of

the gage sections. A clip-on gage was mounted in the crack mouth to measure crack mouth opening

displacement (CM0D). Each specimen was coated with brittle lacquer or photoelastic plastic to reveal

strain patterns. The strain patterns produced were suitable for recording by photography.

A servohydraul ic testing machine with a load capacity of 1 MN was used. The tests were run

in displacement control. An analog-to-digital (A-D) conversion system with a 16-bit resolution

was connected to the strain gages, LVDTs, testing-machine load cell, and CM0D gage. The A-D converter was connected to a minicomputer system. The minicomputer system consisted of a processor,

a dual floppy-disk data-storage unit, a digital plotter, and a printer.

The servohydraul i c testing machine was controlled manually, but the data acquisition, on-line

analysis, storage, printing, and plotting for each data point were controlled by the minicomputer.

For each deformation increment, each sensor was polled and its signal was converted from

electrical to physical units and stored on floppy disk. Then the J-integral was calculated by

direct numerical integration as described above. The J-integral, stress, CM0D, average strain

(defined below), measured displacement, and measured strain values were printed. Finally, each

strain-gage output was plotted on a bar graph, and the calculated J-integral value was plotted

against average strain. (The bar graphs of strain provided real-time indications of proper

functioning of individual strain gages and the yielding of different parts of the specimen, but were not used for data analysis.)

Average strain e, also referred to as gage length strain, was calculated as

i l = (V CE + V GH + V af )/3L = AL/L (9)

where V^ is the displacement measured by the LVDT mounted between points C and E and similarly Vg^

and V^p are displacements measured by the other two LVDTs. L is the y-direction distance between

contour segments CGA and EHF and represents the specimen gage length. The measured displacements, and

therefore e, included both contributions from the strain field of the crack and contributions from

5
the strain that would have existed in the absence of the crack. A consistency check on this calculation of e was made by integrating measured strains along y-direction contours. The two methods gave

identical values at low strains. At high strains, disagreement occurred, usually indicating strain

gage failure.

In the course of a typical test, first the instrumented specimen was mounted in the testing

machine, and all of the instrumentation was connected and checked for proper function. When all the

apparatus was performing properly, a zero-load data point was taken, and the specimen was extended by

a preselected amount. Then the computer was allowed to proceed through the data acquisition-storagecalculation-print-plot procedure described above. The specimen was then extended further and the

procedures repeated. The strain patterns revealed by the brittle lacquer coating were photographed

periodically throughout the test. Tests were terminated for two reasons: specimen tearing or gage

failure. Tearing occurred before strain-gage failure for specimens with large cracks.

About one hundred data points, each consisting of about twenty-five measured strain values,

three displacement values, one CMOD value, and one load value, were obtained during a typical test. The maximum average strain (defined above) attained during a test ranged from around 1.5 times yield

for relatively deep cracks to near 9 times for shallow cracks.

3. RESULTS AND DISCUSSION

The experimental results are presented and discussed in separate sections on: strain distributions; strain dependence of J-integral, crack mouth opening displacement (CMOD), and stress;

detailed discussion of gross section yielding (GSY) results; implications of present results for

f i tness-for-servi ce assessment; and surface flaws. The primary measured quantity in this study was strain as a function of position, obtained from strain gage data. The character of the strain

distributions controlled the behavior of the J-integral. Crack length controlled the form of the

strain distributions. Two general types of strain distributions occurred, resulting in two general

forms of the dependence of J-integral on strain. The quantities measured in this series of experiments allowed study of the strain dependence of J-integral, stress, and CMOD. These data are presented graphically for seven representati ve specimens. The unifying concept for all these

experimental results is that net section yielding (NSY) produces high J-integral values and GSY

produces low values. Because only the GSY case is appropriate to an estimation-curve approach to

fi tness-for-servi ce assessment, the GSY results are discussed separately. Average and upper-bound

curves representing the dependence of J-integral on strain and crack length are extracted from the

data for the one specimen with GSY and the three specimens with combined GSY and NSY. Methods of

applying the upper bound of the present results as a f i tness-for-service assessment curve for through

cracks are discussed. Surface crack behavior is more complex than through-flaw behavior. Yielding

of the ligament behind a surface crack produces an intermediate characteristic dependence of

J-integral on applied stress between contained plasticity and general (gross or net section)

yielding. A three-step procedure for estimating applied J-integral values, which accounts for

contained plasticity, ligament yielding (LY), and GSY is described.

3.1 Strain distributions

Strain distributions in HY130 tensile panels were obtained both from strain gages (quantitative

information) and from brittle lacquer and photoelastic coatings (qualitative information). Strain

distributions measured by the strain gages are plotted in Figs. 13 through 19. These figures show

the longitudinal strains parallel to the tensile axis plotted against distance from the plane of the

6
crack for seven representative specimens. For most specimens, data from three different scans of the

strain gages are plotted, one just before yield, one after some yielding, and one after considerable

yielding. Specific strain levels are indicated in the plots. Two measures of the strain level are given, gage length strain and remote strain. Gage length strain was defined earlier in Eq. 9. It is the change in the gage length divided by the original gage length. Remote strain is the strain

measured by a strain gage remote from the crack. The difference between gage length strain and

remote strain is a measure of the strain concentration introduced by the crack. This strain concentration is significant for plastic strains for specimens with cracks larger than approximately one percent of the cross section.-

In the scans before yield (nominal yield strain for H Y 130 is 0.0045), strain distributions along

contour segments on the uncracked sides are uniform just as would be the case if no cracks were

present. The crack sizes were not large enough to influence the strain distributions away from the

crack for the specimens described by Figs. 13 through 19. The face-cracked

specimen (Figs. 9 and 16) was an exception to this behavior pattern. This crack was sufficiently

deep that bending reduced the strain opposite the crack. On the cracked contour segment "strain

shadows" of the cracks can be seen. A crack forms a free surface perpendicular to the tensile

direction, so the stress in this direction vanishes at the crack mouth. Therefore the strains near

the crack mouth are low. Far away from the crack, the strain has the value it would have had everywhere in the absence of the crack. The strain shadow is localized around the crack mouth. The

extent of the strain shadow varies with the size of the crack. The strain shadow occurs both before

and after yield, as can be seen in Figs. 13 through 19.

In the strain gage scans after yield, a new feature of the strain distribution appears on the

contour segments opposite the crack: a hump or spike of high strain offset from the crack plane by

approximately the length of the uncracked ligament (Figs. 13-19). These strain spikes result from

deformation bands that emanate from the crack tip and extend to the opposite side of the specimen.

The deformation band is a localized region of high strain. In the coordinate system with axes

parallel and perpendicular to the specimen axes, the strain in the deformation band is an extensional

strain along the tensile axis and a compressional strain perpendicular to the tensile axis. The

strain transverse to the axis was not detected by the axial strain gages. Strains transverse to the

tensile axis do not contribute to the J-integral along free surfaces because stresses transverse to the tensile axis are zero at free surfaces. (In some specimens contour segments lying parallel to the tensile axis did not fall along free surfaces. Some transverse strain gages were used in such

cases. These indicated strains small enough so that corrections to the J-integral were not usually

needed. A transverse strain contribution was included in the J-integral for the large,

center-cracked panel with a = 5 mm.) The occurrence of deformation bands for postyield strains was also clearly shown by the brittle lacquer and photoelastic coatings (Figs. 20-26).

Postyield strain patterns for cracked tensile panels have been divided into two general types:

net section yielding (NSY) and gross section yielding (GSY) [10,11]. Panels with NSY have deformation bands, panels with GSY do not. In NSY, the specimen segments outside the deformation bands move

as rigid bodies. Displacements applied at the specimen ends are transmitted fully to the crack

through the deformation bands. The change in CM0D is equal to the change in the relative displ acment

of the specimen ends. The specimen segments outside the deformation bands remain at or below yield

strain, while high strains occur within the deformation bands. This behavior is apparent in most of

the strain distribution plots. Figs (13-19).

If the crack is small enough so that plastic strain is distributed uniformly all along the

specimen length, no deformation band is formed and GSY occurs. Of the through-cracked specimens

7
tested in this program only the single-edge-cracked specimen with a 1-mm crack formed no deformation

band. The strain distributions in this specimen are plotted in Fig. 27; brittle-lacquer representations of its strain patterns are shown in Fig. 28. These figures show that in this specimen no NSY

occurred and that GSY did occur. Experimental problems with this test were caused by the small crack

size and instrumentation malfunctions. But the GSY behavior of this specimen was clear. The singleedge-cracked specimen with a crack length of 2 mm, the double-edge-cracked specimen, and the large

center-cracked specimen with a half-crack length of 5 mm exhibited a combination of NSY and GSY. Jn these specimens deformation bands were formed, but the strains remote from the crack reached levels

well above yield because the cracks were small and the deformation bands strain-hardened enough to compensate for the missing cross-sectional area in the crack plane.

From an examination of data from all tested specimens including those with part-through cracks,

it is concluded that crack area must be restricted to 1 percent or less of total specimen crosssectional area to avoid NSY in HY 130 tensile panels.

3.2 Strain dependence of J-Integral, stress, and crack mouth opening displacement

The strain dependence of the J-integral, stress, and CMOD are presented in Figs. 29 through 35

for seven representative specimens. Each of these figures consists of eleven separate graphs that

present relationships between measured quantities. They are:

a. J-integral plotted against gage length strain

b. J-integral plotted against remote strain

c. J-integral plotted against stress

d. Stress intensity factor plotted against stress

e. Stress plotted against gage length strain

f. Stress plotted against remote strain

g. Gage length strain plotted against remote strain

h. Crack mouth opening displacement plotted against gage length strain

i. Crack mouth opening displacement plotted against remote strain

j. Crack mouth opening displacement plotted against stress

k. J-integral plotted against crack mouth opening displacement

These figures, along with Figs. 6 through 28, provide a very complete and detailed description of the

response of cracked HY130 tensile panels to imposed strains. The key theme that unifies all these

experimental results is the effect of yielding pattern on J and on CMOD. Net section yielding

produces high J and CMOD values, gross section yielding produces low values. The plots are discussed

individually for the first specimen of the series. The remaining specimens all demonstrated similar

behavior.

For each of the seven specimens chosen as typical, a graph of J-integral plotted against gage

length strain (for example. Fig. 29a) is shown. The behavior of these curves is parabolic, at strains below yield, and linear, at strains above yield. The parabolic part below yield is accounted

for by linear elastic fracture mechanics. The linear part at strains above yield is the region of

interest here. This region of the J-integral vs. gage length strain curve is linear for both net and

gross section yielding. To distinguish NSY from GSY, the plot of J-integral vs. remote strain

(Fig. 29b for the center-cracked panel with crack half-length 4 mm) is helpful. Note that in Fig.

27b the remote strain remains near yield while the J-integral increases rapidly. For similar values

of J, the gage length strain reached twice yield. This behavior difference indicates that

displacements imposed at the specimen ends are being transmitted to the crack tip, steadily

8
increasing the J-integral. Because these displacements are not absorbed as plastic strain away form

the crack, the remote strain does not increase. This is the signature of net section yielding. If NSY were to occur in a structure, increases in J-integral could occur at constant strain because the

strain considered in a structure is the remote strain, not the strain at the crack. The imposed

displacement needed to increase J to critical levels is about 1 mm or less, too small to be noticed

i For continuity with linear elastic fracture mechanics, the J-integral can be converted to stress intensity factor in the usual way and plotted against stress, as in Fig. 29d for the first

specimen of the series. This particular specimen had high scatter in its stress intensity factor vs. stress plot, as can be seen by reference to the other plots of these quantities. Figs. 30d through

35d. The results were a linear dependence of stress intensity factor on stress below yield with

experimental error superposed. In Fig. 29d, the theoretical linear elastic stress intesnity factor

is shown as a solid line. The experimental techniques and crack sizes used here were aimed at behavior in the plastic strain range, not at the well-known, well understood linear elastic behavior.

Some significant experimental errors occurred in the elastic range. These errors were lower in the

plastic range, because of the larger and more easily measured strains in the plastic range. These

experimental errors are evident in several of the plots of stress intensity factor against strain.

They were accepted in order to concentrate the experimental effort on understanding the behavior in the plastic strain range. The plots of stress intensity factor against stress show that as stress

approaches yield strength, stress intensity factor increases more rapidly, indicating increasing

plastic zone size.

The plots of stress vs. gage length strain (Fig. 29) for the first specimen of the series)

clearly show the nearly elastic-perfectly-plastic nature of H Y 130 in the strain range considered

here. The plots of stress vs. remote strain (Fig. 29f for the first specimen of the series)

emphasize again that very little remote yielding occurs in NSY. Perhaps the clearest method of

distinguishing GSY from NSY uses a plot of gage length strain against remote strain (Fig. 29g for the

first specimen of the series). For NSY, the two strains increase together in the elastic strain

range; but after yield the gage length strain continues to increase but the remote strain does not,

so the data points form a nearly vertical line. If GSY had occurred, the two strains would continue

to be nearly equal above yield.

For each set of results plotted, it can be seen that the dependences of CMOD on gage length

strain, remote strain, and stress (Figs. 29h-29j for the first specimen of the series) parallel those

of the J-integral. This is not surprising because it is well known that the crack tip opening displacement (CTOD) is closely related to J and is an alternate measure of the driving force for

fracture under plastic strain. In the tensile geometries studied here, CMOD and CTOD seem to be

increasing at the same rate in the plastic strain range. The J-integral J is plotted against CMOD

for the seven typical specimens (Fig. 29k for the first one of the series). For these specimens, it can be seen that the approximation

J -v, ay

• CMOD (10)

holds, where is the material yield strength. A line showing the locus J=a CMOD in Figs. 29k

through 35K shows the accuracy of Eq. 10. This finding improves confidence in the J-integral results

because CMOD is a much simplier quantity to obtain experimentally.

For the case of the edge-hole-cracked specimen, the J-integral should be correlated with the

strain at the hole in the absence of the crack. The presence of the crack prevents measurement of

this strain. It can be calculated by application of Neuber's rule [12], given below in Eq. 14.

9
Plots of J-integral and CMOD against Neuber strain and Neuber stress are given in Fig. 33. The

relationship between the behavior of a crack at a stress concentration and a crack in a tensile panel

in 6SY is discussed later in §3.4.

The spectrum of behavior from NSY for long crack lengths to GSY for short cracks is most fully

illustrated by the five single-edge-cracked specimens [13]. Their J vs. strain behavior is plotted

in Figs. 36 and 37. Note that the increase in crack length from 1 mm to 20 mm did more than simply

raise the J-integral in the plastic strain range: it actually prevented the specimens with cracks

4 mm long and longer from reaching remote strains above yield (Fig. 38). For NSY, J increases with

imposed displacement at a constant level of remote strain. The specimen with the 1 mm crack reached

remote strain levels well above yield with low J-integral values. A similar effect is shown by the

comparison of the large center-cracked panels (Fig. 39). The panel with the 16 mm crack never

reached remote strains above yield. From these results it can be concluded that for a hi gh-performance

component which must survive tensile strains above yield, NSY must be avoided.

3.3 Gross section yielding results

The experimental results for through-cracked specimens with GSY are crucial for formulating a

f i tness-for-service assessment method. Net section yielding must be handled separately and in any case is unacceptable in high performance structures. The single-edge-cracked specimen with a 1-mm

crack was the only specimen with GSY without any NSY. The specimens with combined GSY and NSY were

the single-edge-cracked specimen with a 2-mm crack and the double-edge-cracked specimen with 2-mm

cracks, both 90-mm wide, and the center-cracked-specimen with hal f-crack-1 ength 5 -mm, width 560 mm, and thickness 25 mm. A fi tness-for-service assessment curve was derived from the data from these

specimens. Previous J-integral estimation curves [14-16] plotted normalized J-integral against

normalized strain. The normalization equations used were

and.

Normalized J-Integral = j = EJ/^aCy ),

Normalized strain = e = e/e

y

11a

'lib!

where E is Young's modulus, a is crack length (usual fracture mechanics usage), is material yield

strength, and e^ is the nominal yield strain given by a /E. The key normalization operation in Eq. 11a is that J-integral is divided by crack length; all the other parameters are material

properties independent of crack length or specimen geometry. The appropriate strain for Eq. 11 is remote strain, for GSY. For GSY, the J-integral is proportional to the extent of the strain

shadow around the crack mouth. Because in HY130 the stress is essentially constant above yield, the

strain work density reduces approximately to the product of yield strength and strain for strains

well above yield. The J-integral is the difference between cracked and uncracked sides of the strain

work density integrated over y position, as indicated in Fig. 40. The yield strength factors out, so that J-integral is proportional to the difference between cracked and uncracked sides of strain

integrated over y position. The strain on the uncracked side is simply the remote strain, for a tensile panel; so the J-integral is approximately proportional to the area of the strain shadow on a plot of strain against position.

For purposes of evaluating the J-integral, the strains near the crack mouth for each specimen

were fitted by an exponential function given in Eq. 7 above. To obtain a fi tness-for-service curve

10
representative of all the experiments with GSY, strain data for these specimens was fitted to the

function:

e(y)/'&

r

= 1 - exp(-gy/a) (12)

where e(y) is strain at a distance y from the crack mouth, is remote strain, and g is the fitting

parameter. The parameter g was allowed to vary with e . Normal ization of t was performed according

to Eq. lib. A plot of e(y)/e against y/a for the normalized strain interval from 1.5 to 2 for the

four specimens with GSY and the fitting function of Eq. 12 is shown as Fig. 41. J-integral values were calculated from the strain dependence of Eq. 12 using the definition of J in Eq. 1, with tractionbending terms assumed to be negligible for GSY. The resulting J-integral values were normalized

according to Eq. 11a and plotted against normalized remote strain in Fig. 42. As indicated by Figure 41, the normalized J-integral vs. strain curves for the individual

experiments exhibited a high degree of scatter. Figure 43 shows the behavior of the individual

specimens. The line in Fig. 43 labeled "four-specimen average" is a linear least squares fit to the

postyield data of Fig. 42. The scatter among the data of Fig. 43 might be a result of variability of

specimen material properties and possible experimental error in measured strain values. This scatter

may also be a result of the inadequacy of Eq. 12 to represent the dependence of strain on position

for specimens of two sizes with three crack geometries. Neither solid mechanics calculations nor numerical analysis has successfully calculated the specific form and slope of the normalized

J-integral vs. strain curve for GSY for any crack geometry or specimen size. The data and analysis

of the present study show that a single curve can approximately represent the dependence of applied

J-integral on strain for all crack geometries and specimen sizes in HY130, as long as only GSY occurs. Such a curve should be regarded as a good first-order approximation.

The data for the double-edge-cracked specimen in Fig. 43 form the lower bound of the experimentally observed GSY behavior. This specimen had the largest ratio of crack size to specimen width

of the four through-cracked specimens with GSY. Large relative crack sizes tend to favor NSY. Therefore, one might suspect that the extraction of the GSY J-integral behavior was less accurate for

this specimen than for the others. This data set is lower than any theoretical predictions.

Therefore use of this data set as the basis of a f i tness-for-servi ce assessment curve cannot be

supported at present.

The nature of GSY behavior may be relevant to the scatter of data in Fig. 43. In GSY, the crack

is so small that it does not control the specimen behavior. Other variables such as local variability of flow strength, imperfections in specimen machining, or perturbation of the strain

distribution by the gripping apparatus may be capable of producing variability in applied J values.

Such variability would also occur in practical applications. Previous experimental attempts [17] to verify the Burdekin-Dawes [14] crack opening displacement (COD) design curve have been subject to more scatter than the present study; the experimental method used was totally unrelated to that of

the present study.

The data of Fig. 43 can be compared with previous fi tness-for-servi ce assessment curves[14-16]

.

The f i tness-for-service curve considered representative of the data of Fig. 43 is the experimental

upper bound. Figure 44 shows previous J-integral estimation curves. Quantitative comparison can be

11
made by expressing the upper-bound curve of Fig. 43 as an equation relating normalized J-integral, j, to normalized strain, e:

e<l (13a)

j = 2 + 4 (e-1 ) , e>l (13b)

The key element of these equations is the number that multiplies the term (e-1) in Eq. 13b. This

number gives the rate of increase of normalized J-integral with normalized strain in the plastic

strain range. This rate is the slope of a normalized applied J-integral vs normalized strain plot.

The range of previous estimates [14-16] of this quantity is 2 to 4; see Fig. 45 (Turner's [16] value

of 5 applies only over a narrow strain range). Therefore, the lower bound of the present results is almost as large as the lower bound of previous estimates, the trend of the present results is within

the range of previous estimates, and the upper-bound of the present results is the same as the upper

bound of previous estimates.

The present experimental results provide the upper-bound curve of Fig. 43 as an experimentally

derived J-integral estimation curve for HY130, Fig. 46. This curve is applicable to contained

plasticity and GSY only. Net section yielding cannot be treated using the J-integral estimation

curve of Fig. 46. Net section yielding constitutes a separate failure mode. Structures should be

checked to ensure that this failure mode will not occur. According to the instructions for

application of the COD design curve [18], the need for critical assessment of this failure mode

(yielding due to overloading of remaining cross section, in the terminology of Ref. 18) is most likely to arise in small structural sections.

Once NSY has been excluded, the applied J-integral level for any through-thickness flaw or any

full-width surface flaw can be estimated for any level of applied strain from Fig. 46. The

estimation cgrve of Fig. 46 clearly overestimates applied J-integral where linear elastic fracture

mechanics (LEFM) is adequate and the plastic zone is small compared to the crack size. In such cases LEFM might be used if necessary; the present estimation curve provides for conservative tolerance

levels for the large flaws that would be under consideration in such cases. However near yield

stress the plastic zone size increases rapidly with stress, so that for such stresses the present

estimation is considered to be accurate rather than conservative.

The strain axis should be entered at the applied strain value anticipated in the component in question. The presence of residual stresses or stress concentrations must be accounted for in the

applied strain value. Residual stresses of unknown magnitude should be estimated to be at yield

level. One yield strain unit should be added to the normalized strain before entering the J estimation curve. Stress concentrations in tension can be conservati vely approximated as uniform tensile

strain fields for which the strain level is approximated using the Neuber relation [12]

3,4 Implications of present results for f i tness-for-servi ce assessment

e = KjS , KtS<1 (14a)

(14b)

12
where S is nominal stress divided by yield stress, ct/ct , Ky is the elastic stress concentration

factor, and elastic-perfectly plastic behavior has been assumed. The J-integral estimation curve is then entered at the calculated normalized strain value. The estimated J-integral value is likely to be conservative by a factor of 3 to 10 if the stress concentrator radius is not adequately large

compared with the crack length. For the edge-hole-cracked specimen tested here, the applied

J-integral value was approximately one sixth the value estimated from Fig. 46. For this case the

crack length was 0.15 of the stress concentrator radius. Of course, NSY must be avoided for stress

concentrations

.

The J-integral estimation curve derived here from experimental J measurements provides the value

of applied J-integral divided by crack length after the material yield strength and Young's modulus

are accounted for. Applied J-integral levels greater than some critical level are predictive of

material tearing. If the desired failure criterion is the least detectable tearing at a sharp

fatigue crack, very low critical flaw size levels will be predicted at strains of a few times yield.

A typical Jj

c value for HY130 would be about 230 kN/m (1300 lb/in). For a strain of 3 times yield

the predicted critical flaw size would be 1.6 mm (0.071 in). However the HY130 specimens tested here

at room temperature, including those with fatigue cracks, showed no tendency to macroscopic tearing

at J levels less than around 900 kN/m (5000 lb/in). If a critical J-integral of 900 kN/m were used

instead of 230 kN/m, the predicted critical flaw size would be 7 mm (0.28 in). This

calculation indicates that care must be exercised in adopting an' appropriate critical J-integral

value.

It is well-established that the degree of crack-tip-constraint in a structure or specimen has a major influence on its fracture behavior [19]. This effect is usually discussed in terms of the

dependence of some crack-initiation criteria such as a critical stress intensity factor, K , on specimen thickness. But the constraint effect applies to tearing (R-curve) behavior as well [20-22].

The J-R curves shown previously as Fig. 4 demonstrate this effect. The face-cracked tensile panel

1 cm thick has less constraint than side-grooved compact tensile (CT) specimens 2.5 cm thick by 5 cm wide. Accordingly, the J-R curve for the face-cracked tensile panel lies above that for the compact

speicmen. The J-R curve of through cracked tensile panels 1 cm thick used in this study has not been

specifically measured, but its qualitative behavior has been observed. In accord with expectation

based on consideration of constraint, the J-R-curve for the through-cracked tensile panels 1 cm thick

are even higher than the curve for the face-cracked panel in Fig. 4. This explains why very high

J-integrals were obtained in the tensile panel tests before significant tearing.

The variability of J-R behavior with configuration, coupled with the need that structures be

demonstrated to be as crack tolerant as possible, may require use of configuration-specific J

c values

for crack initiation and propagation. The J

c value chosen controls the flaw size calculated using

the gross-section-yielding J-integral estimation curve. Larger J

c vlaues correspond to larger flaw

sizes.

Use of configuration-specific J values instead of conservative values from CT specimens can be

classified with use of application-specific applied stress and strain values instead of conservative

estimates as refinements to a basic f i tness-for-servi ce assessment proceudre. such refinements allow

demonstration of larger tolerable crack sizes in specific situations, at a cost of additional

information about the application and additional information about the configuration dependence of J values for crack initiation and propagation.

Qualitative use of this configuration dependence of effective fracture toughness is made in some well-known fracture criteria, including through-thickness-yielding, 1 eak-bef ore-break , and

13
ratio-analysis-diagram. Attempts have been made to quantify crack-tip constraint in order to explain

the configuration-dependence of fracture toughness, but no generally applicable method is available.

3.5 Surface flaws

Three surface-cracked HY130 specimens have been tested. Net section and gross section yielding

effects occurred in these specimens. The rule that flaws 1 percent of the cross-sectional area are required for GSY held for surface flaws in HY130 base metal. For the remainder of this section it

will be assumed that NSY has been eliminated from consideration.

Three behavior types, each associated with a specific three-dimensional strain pattern, must be

accounted for in calculating applied crack driving force for surface cracks: elastic, ligament

yielding (LY) and gross section yielding.

Elastic strain

At low stresses, a tensile panel containing a surface crack behaves in a generally elastic

fashion; plastic strains occur only in a very small zone near the crack tip. Applied J-integral can

be evaluated in this stress range using equations reported by Newman and Raju [23]:

J a

2

it h F (15a)

E Q

Q

= 1 + 1.464 /hvl.65

c

(15b)

F

= [Mj + m

2 <T

> 2 + m

3 <T>X (15c)

M

1 = 1. 13 - 0 o o

Jj=y

( 15d)

M

2

= -0 .54 + - 0.89

0.2 + h ( 15g)

c

M

3 = 0.5 - 1.00.65 + hc

+ 14 (1.0 - -) 24

c

( 1 5 f

)

fw

=

t sec (5£/i)] " (15g)

where o is applied stress, h is surface crack depth, c is surface crack half-length, t is plate

thickness, and W is plate width.

Ligament yielding

As stress increases, the crack tip plastic zone extends through the ligament behind the surface

flaw toward the back face of the specimen. This ligament plasticity causes the crack driving force,

measured by applied J-integral or applied CTOD, to increase with applied stress at a higher rate than

before LY. Experimental verification of an analytical model for LY was reported recently by Cheng et

al [24]. According to this study, CTOD resulting from LY is given by

CTOD = 2 (2c + 2r ) [a — -

E where c is crack half-length,

(l-h/t)o7

h is crack depth, t is plate thickness,

(16)

plastic zone size and

14
a is material flow strength. A previously obtained Dugdale solution for the plastic zone size was

given as

. / 7T o C \ sin (2

' 2 w

}

sin (j • 2

d W

/ tt a

= cos

a

1 (17)

where Cp = c + 2 r^, o'/o 1 = 1 - (1 - a/a) • t/h, and W is plate width. A somewhat more rigorous

analytical model was developed by King using a simplified line-spring approach [25]. The crack

driving forces calculated from King's model are practically identical to those from Eq. 16. This

agreement allows increased confidence in the reliability of Eq. 16. The simplified line spring model

also shows that CTOD values can be converted to J-integral values for tensile panels simply by

multiplying CTOD by a . The agreement between the line spring model and experimental ly measured

J-integral values was found to be good (Fig. 45). Another variation of the LY model was reported by

deWit and Smith [26]. Although the mathematical form they reported is slightly different from

Eq. 16, their calculated CTOD values agree well with those from the other models. The mathematical

form used in Ref. 26 was found to be adaptable for graphical evaluation, as discussed below.

Gross section yielding

As the stress is increased, the LY model eventually breaks down because yielding spreads away

from the ligament. After yielding spreads throughout the specimen, GSY behavior occurs (assuming the

absence of NSY). Data obtained to date in this study and the precedent of the British approach [18]

indicate that surface cracks in tensile panels with GSY can be treated in the same general way as through flaws in GSY. That is, the increase in applied J-integral is proportional to the increase in applied strain and the effective crack size a:

AJ ^ a Ae . (18)

Here a depends on crack depth, h, crack half-length, c, and plate thickness, t. It is independent of

plate width and independent of applied strain. The plot of Fig. 46 illustrates the form of the

dependence of a on h and c. This plot was derived by requiring that in cases where the surface crack

reduces to a through crack, the effective crack size should reduce to h or c, as appropriate, and

that a should be zero when c or h is zero. Figure 46 is consistent with the available data, but it has not been critically evaluated at values of c/t above 0.8 and h/t values above 0.12. The

extremely large specimen sizes required for experimental tests of GSY behavior in this range of crack

sizes might make such measurements impractical unless a specific need for the data arises.

Evaluation of total J-integral

The applied J-integral produced by the three mechanisms discussed above can be evaluated as follows. The first step is to determine the stress where LY begins and to obtain an index of the

degree of yielding around the surface crack. According to the models presented above, ligament

yielding begins at an applied stress level, a*, given as:

a* = a (1 - h/t) . (19)

As the stress increases, the degree of LY also increases. The quantity chosen as the surface crack

yielding index is zero for stresses below a* and increases linearly with applied stress. When the

applied stress reaches the material flow strength, the plane of specimen material

15
containing the surface crack has yielded everywhere. The surface crack yielding index is chosen to

be one for this stress level. The surface crack yielding index Y is given mathematically as

o/o - (1 - h/t)

Y = h/t (20)

and can conveniently be evaluated using the graph of Fig. 49. This same graph can also be used to evaluate a*, the stress level at which LY begins. The stress a* is the stress where the line for the

h/t value under consideration intersects the x-axis. Interpolation may be used to locate lines for

h/t values not shown in the figure.

The normalized applied J-integral for the elastic stress range is found by entering the x-axis

of Fig. 50 at either a* or the applied stress, a, whichever is lower, and reading off the indicated

y-axis value. The effective crack size for elastic behavior can be obtained from Fig. 51, allowing

calculation of the absolute value of the elastic part of the applied J-integral.

If the applied stress is greater than a*, additional contributions to the applied J-integral

must be accounted for. The LY contribution to the applied J-integral can be evaluated using Fig. 52,

entering the x-axis at the surface crack yielding index previously obtained from Fig. 49. For the

scaling chosen for the y-axis of Fig. 52, the effective crack size is given by

a = hc/t ,

as noted on the figure. The absolute value of the applied J-integral from LY is added to the

contribution from elastic strain.

The maximum achievable surface crack yielding index occurs at the stress level at which yielding

occurs away from the surface crack. This stress level is indicated by a vertical dashed line in Fig. 49. The value used was obtained from the experimental data of the present study. For applied

strain levels above yield, the maximum surface crack yielding index for the crack under consideration

is used in evaluating the LY contribution to the applied J-integral.

The GSY contribution to the applied J-integral value could be evaluated using the graph of Fig.

53 to obtain normalized J-integral and the effective crack size plot of Fig. 48. As discussed above,

Fig. 48 is only hypothetical for c/t values above 0.8 and h/t values between 0.12 and 1.

Discussion

The concept of a three-step evaluation procedure for applied J-integral is illustrated by

Fig. 54, which may be compared with Fig. 46 for through cracks. Simplification of the evaluation

process illustrated by Fig. 54 awaits advances in understanding of surface flaw behavior.

Probably the most problematic aspect of the procedure described above is the use of the material

flow strength in the evaluation of the LY contribution to the applied J-integral. The flow strength

is based on the idealization of a metal as an elastic-perfectly plastic material. The present

specimen material, HY130 steel, is nearly elastic-perfectly plastic. But GSY cannot occur in an ideally elastic-perfectly plastic tensile panel containing a surface flaw, because the crosssectional area of the crack plane is less than the area away from the crack, so that all the strain

must occur in the plane of the crack. Strain-hardening and three-dimensional geometrical constraint

effects can raise the effective strength of the material surrounding the surface crack to a high

enough level that GSY can occur. Another important effect is overmatching weld metal in specimens

with welds transverse to the tensile axis. The flow strength of an overmatching weld can easily be

higher than the yield strength of the base metal, which would lower the applied J-integral from LY.

16
An additional beneficial effect of overmatching may be to limit applied plastic strain during GSY in

a transverse weld to values below those in the surrounding base plate. Lower applied strain would

mean lower applied J-integral values. The existence of these strengthening effects is demonstrated by

Fig. 55, which shows fractured welded and base metal HY130 specimens containing small surface cracks.

These specimens fractured away from their cracks. But the magnitude of effective strengthening owing

to overmatching, strain hardening, and geometrical constraint must be carefully studied; the ability

of surface cracked specimens or structures to achieve gross section yielding should not be taken for

granted.

4. CONCLUSIONS

As a result of 15 direct experimental measurements of the applied J-integral in HY130 tensile

panels several conclusions have been reached:

1. Applied J-integral is controlled qualitatively by deformation pattern. Net section

yielding produces large applied J-integral values, whereas gross section yielding produces

small applied J-integral values.

2. Fi tness-for-servi ce assessment for contained plasticity and gross section yielding can

be performed using a J-integral estimation curve to obtain applied J-integral as a function of applied strain and crack size.

3. Net section yielding is intolerable in high performance components. This yielding pattern

can be avoided in tensile panels by restricting crack size to 1 percent or less of the

load-bearing cross-sectional area.

4. The J-integral estimation curve for gross section yielding can be used to treat cracks

at stress and strain concentrations. Neuber's rule may be used to estimate applied strain.

A safe (too large) estimate of applied J-integral will be obtained if the crack under

consideration is not sufficiently small compared with the stress concentrator.

5. Estimation of applied J-integral values for surface flaws requires consideration of

ligament yielding as well as contained and gross section yielding. Contributions of each

of these yielding patterns to applied J-integral can be evaluated using estimation curves specific to each yielding pattern.

5.

ACKNOWLEDGMENTS

This report was prepared as part of the Fracture Control Technology program under the sponsorship

of Dr. H. H. Vanderveldt, Naval Sea Systems Command (SEA 05R15). The effort was directed by

Mr. John P. Gudas, David Taylor Naval Ship R&D Center, under Program Element 62761N, Task Area

SF-61-544-504. The contributions of J. D. McColskey as technician on this project are gratefully

acknowledged. Helpful discussions with J. P. Gudas, H. I. McHenry, R. B. King, and Y. W. Cheng,

assistance in data analysis and plotting by P. Campau and B. Gunther, and manuscript preparation by

J. Wilken are appreciated.

17
6. REFERENCES

J. Tirosh and C. A. Berg, Experimental Stress Intensity Factor Measurements in Orthotropic

Composites, Composite Materials: Testing and Design (Third Conference), STP 546 , American

Society for Testing and Materials, Philadelphia, 1974, pp. 663-673.

G. Herrmann and G. S. Kino, Ultrasonic Measurements of Inhomogeneous Stress Fields,

Proceedings of ARPA/AFML Review of Progress in Quantitative NDE , AFML-TR-78-205 , Air Force

Materials Laboratory, 1979, pp. 447-451.

R. B. King and G. Herrmann, Nondestructive Evaluation of the J and M Integrals, Journal of

Appl ied Mechanics 48, 1981, pp. 83-87.

H. L. Oh, A Simple Method for Measuring Tearing Energy of Nickel Rubber Strips, Mechanics of

Crack Growth, STP 590 , American Society for Testing and Materials, Philadelphia, 1976, pp. 104-114.

W. A. Logsdon, Elastic Plastic (Jj ) Fracture Toughness Values: Their Experimental

Determination and Comparison with Conventional Linear Elastic (Kj ) Fracture Toughness

Values for Five Materials, Mechanics of Crack Growth, STP 560 , American Society for Testing

and Materials, Philadelphia, 1976, pp. 43-60.

J. A. Begley and J. D. Landes, The J integral as a Fracture Criterion, Fracture Toughness,

STP 514 , American Society for Testing and Materials, Philadelphia, 1972, pp. 1-20.

J. D. Landes and J. A. Begley, The Effect of Specimen Geometry on Jj , Fracture Toughness,

STP 514 , American Society for Testing and Materials, Philadelphia, 1972, pp. 24-39.

H. Tada, P. Paris, and G. Irwin, The Stress Analysis of Cracks Handbook , Del Research

Corporation, Hellertown, Pennsylvania, 1973.

J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration

by Notches and Cracks, Journal of Applied Mechanics 35, 1968, pp. 379-386.

C. E. Turner, Methods for Post-Yield Fracture Safety Assessment, Post-Yield Fracture

Mechanics

,

edited by D. G. H. Latzko, Applied Science Publishers, London, 1979, pp. 23-210.

W. Soete and R. Denys, Full and General Yield Behavior of Homogeneous Plates with Cracks,

Proceedings of the International Institute of Welding Conference at Bratislava, Doc. X— 921-79 , 1979.

H. Neuber, Theory of Stress Concentration for Shear-strai ned Prismatical Bodies with

Arbitrary Nonlinear stress strain Law, Journal of Applied Mechanics 28 , 1961, pp. 544-550.

D. T. Read, Applied J-Integral Values in Tensile Panels,", Appendix of this report.
[ 14 ] M. G. Dawes, The COD Design Curve, in Advances in Elasto-Plastic Fracture Mechanics , edited

by L. H. Larsson, Applied Science Publishers, London, 1980, pp. 279-300.

[15] J. A. Begley, J. D. Landes, and W. K. Wilson, An Estimation Model for the Application of the

J-Integral, Fracture Analysis, STP 560 , American Society for Testing and Materials, Philadelphia,

1974, pp. 155-169.

[16] C. E. Turner, Elastic-Plastic aspects of fracture stress analysis: methods for other than

standardized test conditions, in Fracture Mechanics in Design and Service, Philosophical

Transactions of the Royal Society of London A299, 1981, pp. 73-92.

[17] J. D. Harrison, M. G. Dawes, G. L. Archer, and M. S. Kamath, The COD Approach and Its Application to Welded Structures, Elastic-Plastic Fracture, STP 668 , American Society for

Testing and Materials, Philadelphia, 1979, pp. 606-631.

[18] British Standards Institution, Guidance on Some Methods for the Derivation of Acceptance

Levels for Defects in Fusion Welded Joints, PD6493 : 1 980 , British Standards Institution,

London, 1980.

[19] S. T. Rolfe and J. M. Barsom, Fracture and Fatigue Control in Structures , Prentice-Hall, New

Jersey, 1977, pp. 372-412.

[20] J. R. Rice, W. J. Drugan, and T-L. Sham, Elastic-Plastic Analysis of Growing Cracks, Fracture

Mechanics, STP 700 , American Society for Testing and Materials, Philadelphia, 1980, pp. 189-221.

[21J M. G. Vassilaros, J. A. Joyce, and J. P. Gudas, Effects of Specimen Geometry on the Jj-R

Curve for ASTM A533B Steel, Fracture Mechanics, STP 700 , American Society for Testing and

Materials, 1980, pp. 251-270.

[22] S. J. Garwood, Measurement of Crack Growth Resistance of A533B Wide Plate Tests, Fracture

Mechanics, STP 700 , American Society for Testing and Materials, 1980, pp. 271-295.

1.23] J. C. Newman, Jr. and I. S. Raju, Analyses of Surface Cracks in Finite Plates under Tension

or Bending Loads, NASA Technical Paper 1578, 1979. Available from NTIS, Springfield,

Virginia.

[24] Y. W. Cheng, H. I. McHenry, and D. T. Read, Crack-opening Displacement of Surface Cracks in Pipeline Steel Plates, Proceedings of the Fourteenth National Symposium on Fracture Mechanics,

June 30-July 2, 1981, Los Angeles, California.

19
[ 25 ] R. B. King. Y. W. Cheng, D. T. Read, and H. I. McHenry, J-Integral Analysis of Surface

Cracks in Pipeline Steel Plates. Proceedings of Second International Symposium on ElasticPlastic Fracture Mechanics, 1981, to be published.

[26] R. deWit and J. H. Smith, Development of Some Analytical Fracture Mechanics Models for

Pipeline Girth Welds, Fracture Mechanics, STP 700 , American Society for Testing and Materials,

Philadelphia, 1980, pp. 513-528.

20
o

S r

o

Specimen

Load

Load

Specimen

with

Contour

J=/

r

Wdy-T-||ds

x,y Position coordinates

W Strain energy density

T Traction vector

JL Partial derivative with

dx respect to x

u Displacement vector

Figure 1. Contour for direct measurement of J-integral in single-edge-cracked specimens.

I

| Small strain gages

1 Strain gages

[j LVDTs

0 CMOD gage

Specimen with

Instrumentation

Figure 2. Instrumentation of single-edge-cracked specimen.

21
STRAIN

Figure 3. Engineering stress-strain curves for the HY130 specimen material

used in the present study.

22

STRESS,

ksi
0.02

DELTA a, in

0.04 0.06 0.08

T

1000r T

800-

5000

- 600^ -J

<

cc(D

Uj 400

200

A Face Cracked

Tensile Panel

A

A

° R o

ftp

fiP D o'

D 0 oo°D

° o osro

jQ

^ ° Compact Tensile Specimens

-4000

3000

-2000

-1000

_L 0.5 1.0 1.5

DELTA a, cm

2.0 2.5

Figure 4. J-integral crack growth resistance curves (J-R-curves) for the HY130 material used in the present study. The lower curves are

for standard 2.5cm thick compact tensile specimens. The upper curve

is for a crack 4mm deep in a tensile panel 25mm thick by

90mm wide by 300mm long.

23

-INTEGRAL,

Sb/in
HY130

Tensile

Panel

Geometries

for

Direct

Measurement

of

J-lntegral

(widths

indicated)

24

Figure

5.

Tensile

panel

geometries

for

direct

measurement

of

J-integral

in

HY130.

Specimen

widths

indicated.

Thickness

of

90

mm

wide

panels

was

10

mm.

Thickness

of

wider

panels

was

25

mm.
HY130 Tensile Panel

Width = 90 mm

Crack-Half-Length = 4 mm

• LVDT attachment point

CMOD Crack mouth opening

displacement gage

Figure 6. Instrumentation layout for center-cracked tensile panel, crack half-length 4 mm.

CMOD Crack mouth opening

displacement gage

Figure 7. Instrumentation layout for single-edge-cracked tensile panel, crack length 4 mm.

25
HY130 Tensile Panel

Width = 90 mm

Crack Length = 2 mm

• LVDT attachment point

CMOD Crack mouth opening

displacement gage

Figure 8. Instrumentation layout for double-edge-cracked tensile panel, crack length 2 mm.

26
HY130 Tensile Panel

Width = 90 mm \ 0

*

LVDT Displacement gages

• LVDT attachment point

CMOD Crack mouth opening

displacement gage

Figure 9. Instrumentation layout for face-cracked tensile panel, crack depth 2 mm.

27
CMOD Crack mouth opening

displacement gage

Figure 10. Instrumentation layout for edge-hole-cracked tensile panel, crack length 2 mm, hole

radius 14 mm.

NOTE: . • LVDT attachment point

All instrumentation on face side is duplicated on back side CMOD Crack mouth opening

displacement gage

Instrumentation layout for wide center-cracked tensile panel, crack half-length 16

panel width 560 mm.

Figure 11.
v°

|j Small strain gages (4)

[] Strain gage

LVDT Displacement gage

• LVDT attachment point

CMOD Crack mouth opening

displacement gage

Figure 12. Instrumentation layout for surface-cracked tensile panel, crack depth 6 mm, crack

length 25 mm.

29
HY130

Tensile

Panel

Center-Cracked

o

*

nivhis

30

DISTANCE

ABOVE

CRACK

PLANE,

cm

'

DISTANCE

ABOVE

CRACK

PLANE,

cm
HY130

Tensile

Panel

Single-Edge-Cracked

Crack

Length

=4

mm.

Specimen

Width

=

90

mm.

Gage

Length

Strain

Remote

Strain

J-Integral

(

kN/m

)

*

cxi o

co on cxi LO LO

r^.

1

11

00 co

01 ^ CO

CO LO LO o o o

o o o

o o o

CO LO LO o co ^ r^. <—

o o .-I o o o

o o o

s~

CD -OE O LO o

lo o

NIVH1S

NlVdlS

31

DISTANCE

ABOVE

CRACK

PLANE,

cm

DISTANCE

ABOVE

CRACK

PLANE,

cm
HY130

Tensile

Pane!

DoubSe-Edge-Cracked

Crack

Length =2

mm.

Specimen

Width =

90

mm.

C

ro

i- CO

r->. Oh o

<3- co CM O O «-H o o o o o o

<dCD

fl3 CD

Sa> -QE

fOo

CO

Oh

O CO CM LO

O

C0

6= o©5owc©Eo©w 8 ? * O C < o c 05

sd

#=> CO

Od

NIVH1S

32

DISTANCE

ABOVE

CRACK

PLANE,

cm

DISTANCE

ABOVE

CRACK

PLANE,

cm
HY130

Tensile

Pane!

Face-Cracked

Crack

Depth =2

mm.

Panel

Width =

90

mm.

33

Figure

16.

Strain

distributions

in

face-cracked

tensile

panel

with

crack

depth 2

mm

at

three

strain

levels.
HY130

Tensile

Panel

Edge-=HoSe~Cracked

Crack

Depth

=2

mm.

Hole

Radius

=

14

mm.

Gage

Length

Strain

Neuber

Strain

J-Integral

(

kN

C

LT>

II

K

^ ro h

kDfON

fO N O

--H kO 'tt

KSD O O

cr» lo

co *-h ro OHO

o o o

Nivais

o o o

LO LO CO H(\J ^ o o o

o o o

o o o

s_ai _QE

d

rou

on

O O C\J fO kD CTi

N8VB1S nivhjjs

34

DISTANCE

ABOVE

CRACK

PLANE,

cm

DISTANCE

ABOVE

CRACK

PLANE,

cm
HY130

Tensile

Panel

Center-Cracked

Specimen

Width

=

560

mm.

Crack

Half-Length

=

16

mm.

VO O

CO LO O o o

O o

CO CO CO O o

CDt VOo o

o o LO

CO o o CO

CSJ o

CO CO o o

o o

o

C\J o o CD

c

•1— S- JZ 03 a) 4-> S- i—

_o CD 4-> ro E c cn S- Z3 (1) CD -K _l c= CD Qj ^ •f— -M 4-> E c aj co o C \ fO CD s- E •—i ^

o ns -M aj 1 oo C_D CO cn •“D Nivais

35

DISTANCE

ABOVE

CRACK

PLANE,

cm

DISTANCE

ABOVE

CRACK

PLANE,

cm
~o0

XL0

03 O1 CDO

CO

CD

CDc

CO CL0

C/) c00

co>1 EEO

CT>

IIC

CDEo

CDQ.

cn E E O

II U)CD -C c 4-> cn o c —

CD -CI

<J CD fo e

S- ro O Cl.

36

DISTANCE

ABOVE

CRACK

PLANE,

cm

DISTANCE

ABOVE

CRACK

PLANE,

cm
37
38

Single-edge-cracked

tensile

panel,

crack

length

4

mm,

with

brittle

lacquer

coating

to
HY130

Tensile

Panel

TD00

CO

i— O1 0

G) o

LLlI0

-QGOQ EE

<N

IIO

CO O EEo

G)

II O£C0Eo0a

co

39

Figure

22.

Double-edge-cracked

tensile

panel,

crack

lengths

2mm,

with

photoelastic

plastic

coating

to

show

strain

distribution,

at

three

strain

levels.
HY130 Tensile Panel

Face-Cracked

Crack Depth = 2 mm.

Panel Width = 90mm.

Scan Number 6

1

Scan Number 7 1

Scan Number Gage Length Strain Remote Strain J-Integral (kN/m)*

40 0.0029 0.0026 12

61 0.0050 0.0041 132

7 1 0.0071 0.0043 7 12

*1 kN/m = 5.71lb/in

Figure 23. Face-cracked tensile panel, crack depth 2 mm, with brittle lacouer coating to show

strain distribution, at three strain levels.

40
HY130 Tensile Panel Edge-Hole-Cracked

Crack Depth = 2 mm. Hole Radius=14 mm.

Scan Number 30 60 92

Gage Length Strain 0.001 5 0.0025 0.0048

Neuber Strain 0.0035 0.0 1 1 9 0.0335

J-Integral (kN/m) * 13 67 440

* 1 k N / m = 5.71 Ib/in

Figure 24. Edge-hoi e-cracked tensile panel, crack length 2 mm, with brittle lacquer coating to show strain distribution, at three strain levels.

41
42

Figure

25.

Center-cracked

wide

tensile

panel,

crack

half-length

16

mm.

with

brittle

lacquer

coating

to

show

strain

distribution

at

the

end

of

the

test.
-O0O0O0O0

M—

i_

rj

CO £E E £ E e e e

10(0 0 °

CM 1-0)

II II II II -C _ 0 £

j- frt +- 0 O)

c: i: co a cd "O c

CO CL s

_l 0 5 Q -s 5C

!c 0 0 o 2 — 8— E CO

COc O o 2 o0 0

h- a?

Q.

CO

O

CO

T—>*X

43

Figure

26.

Surface-cracked

tensile

panel,

crack

depth 6

rnm,

crack

length

25

mm,

with

brittle

lacauer

coating

to

show

strain

distribution

at

three

strain

levels.
HY130

Tensile

Panel

Single-Edge-Cracked

Crack

Length =1

mm.

Specimen

Width =

90

mm. c

Ln ro

r-~ oo

oj r-'.

Lnn

-fc

a> o

co

XJ

a)

Js£ O

(01_oc3

05Co<c

‘<5

+-* CO

Nivais Eo

UJz<

_J0.*o<

CLO

LU>om<

ujoz<

t—COQ

s-O) JOc

(Cu

oo o o

ro lo

0) *gcoo®O

<0

I— O

o»co<c

*-• co o do

nivhjls Eo

ujz

£LO<

QCO

UJ>Om<

ujoz<H

coQ

44

Figure

27.

Strain

distributions

in

single-edge-cracked

tensile

panel

with

crack

length 1

mm

at

three

strain

levels.
HY130 Tensile Panel

Crack Length = 1 mm.

Single-Edge-Cracked

Specimen Width = 90 mm.

Scan Number 30

Gage Length Strainr 0.0058

Remote Strainr 0.0053

J-Integral (kN/m)= 27.5

Final

*1 kN/m = 5.71 Ib/in

Figure 28. Si ngl e-edqe-c racked tensile panel, crack length 1 mm, with brittle

show strain distribution near yield and at the end of the test.

lacquer coating to

45
1000

800-

-* 600-

cn

a) 400-

200 -

Gage Length Strain/Yield Strain

0.5 1 1.5

x i— . 1 HY130 Tensile Panel

Center-Cracked

Crack Half-Length 4mm

ooooo<

6>

CD y

cP

csP

o

o y°

i am)oniTQfl-Ra1 a

0.000 0.002 0.004 0.006 Gage Length Strain

0.008

- 5000

-4000 -

-3000 o

CT>

0)

2000 -5

-1000

0

0.010

Figure 29a. J-integral plotted against gage length strain for center-cracked tensile panel with

crack half-length 4 mm.

Remote Strain/Yield Strain

Figure 29b. J-integral plotted against remote strain for center-cracked tensile panel with crack half-length 4 mm.

46
CD

0>c

I

1000 -

800-

600-

400-

200 -

Stress, ksi

25 50 75

_L 100 HY130 Tensile Panel

Cen t e r — C r acked

Crack Half-Length 4mm

125

_L

Q O

200 o | ooooouom^mnGQ 000''1 ^

400 600 800

Stress, MPa

150

1000

5000

4000 .E

-3000 o

CD

(D

2000

-1000

—1 0 1200

Figure 29c. J-integral plotted against stress for center-cracked tensile panel with crack length

4 mm.

25 50 Stress, ksi

75 100 125 150

c >

V)

CO

Figure 29d. Stress intensity factor plotted against stress for center-cracked tensile panel with

crack half-length 4 mm.

47
1000 -

800-

Gage Length S tr a i n/ Yi e I d Strain

0.5 i 1.5 _i HY130 Tensile Panel

Cen t e r-C r acked

Crack Half-Length 4mm

oQ)o QdO O qjjrr§pcffi5)cDa%

o

Q_

co 600 - cn

Q)

cP

J?

J?

9

400-

200 -

0.000

I 0.002 0.004 0.006 Gage Length Strain

0.008

-150

125

00 -100

00

oo

<D h 75 ^

-50

-25

0.010

Figure 29e. Stress plotted against gage length strain for center-cracked tensile panel with crack

half-length 4 mm.

Remote Strain/Yield Strain

0 0.5 1 1.5 2

150

-125

05 -100 -*

oo" oo

ao 75

in

50

25

~ I | | | 1 \J 0.000 0.002 0.004 0.006 0.008 0.010 Remote Strain

Figure 29f. Stress plotted against remote strain for center-cracked tensile panel with crack length

4 mm.

I2.UU

1000 -

HY130 Tensile Panel

Cen t e r-C r acked

Crack Half-Length 4mm

800- o

CL

(/> 600 - co

a)

in 400-

200 -

48
Remote Strain/Yield Strain

0 0.5 1 1.5 2

cD

in

~o

a> >\cD

00

CDc

_l

d)CDoO

Figure 29g. Gage length strain plotted against remote strain for center-cracked tensile panel with

crack half-length 4 mm.

c

0)£

<1) o

D

Q-

</)

CDcc

o;q. O

<jo

k_ o

Gage Length Strain/Yield Strain

0.5 1.5

- 0.03

- 0.02

- 0.01

c

a>E

<1) O

O

QV)

CDCc

<DQ. O

(JO

0.00 u

0.000 0.002 0.004 0.006 0.008 0.010 Gage Length Strain

Figure 29h. Crack mouth opening displacement plotted against gage length strain for center-cracked

tensile panel with crack half-length 4 mm.

49
2*o

oo

Remote Strain/Yield Strain

0.5 1.5

0 . 8

-

c

a)E

(DO

O

Q.

in 0 . 6

-

05c

c

a)CL O

HY130 Tensile Panel ®

Cen t e r-C r acked

Crack Half-Length 4mm

«

oo

fto

oo

o

0.4-

0 . 2

-

0^00022222

0.000 0.002

o

o

o

(Poo

T

- 0.03

T

0.02

- 0.01

c

a>E

0)O

O

CL

in O

CDcc

<ua. O

CJo

0.00 o

0.004 0.006 Remo t e Strain

0.008 o.oio

Figure 29i . Crack mouth opening displacement plotted against remote strain for center-cracked

tensile panel with crack half-length 4 mm.

c

Cl) E

a)o

o

CL

in

CDc

c

a>CL O

o

D

o

Stress, ksi

25 50 75 100 _L_ I I

I

0 . 8

-

HY130 Tensile Panel

Cen t e r-C r acked

Crack Half-Length 4mm

0 . 6-1 a

0.4-

0 . 2

-

125

o

o%

o

o

o

o

o

o

rj 0, o o o o o OOOOOOOOOOOO COOQOooc^

T "T

150

- 0.03

- 0.02

- 0.01

c

Q)E

a)o

oa

in

CDc

c

a)Q_ o

u

a

0.00 o

200 400 600

Stress, MPa

800 1000 1200

Figure 29j . Crack mouth opening displacement plotted against stress for center cracked tensile

panel with crack half-length 4 mm.

50
0.00 Crack Mouth Opening Displacement, in

0.01 0.02 0.03

Figure 29k. J-integral plotted against crack mouth opening displacement for center-cracked tensile

panel with crack half-length 4 mm.

51

Integral,

Ib/i
-Integral,

kN/m

J—

Integral,

kN/m

Dependence of J-integral , stress, and crack mouth opening displacement on strain

for single-edge-cracked tensile panel with crack length 4 mm.

Gage Length S tr a i n/Yi e I d Strain

Figure 30a.

Remote Strain/Yield Strain

0 0.5 1 1.5 2

Figure 30b.

52

-Integral,

Ib/in

J—

Integral,

Ib/i
Stress

Intensity

Factor,

MPa

Vm

^

Integral,

kN/m

25 Stress, ksi50 75 100 150 2100 -

1800 -

1500 -

1200 -

900 -

600 -

300 -

HY130 Tensile Panel

Single-Edge — Cracked

Crack Length 4mm

< KinooiHMMio m nnf^Q- 0 200

lOOCCC^ mOQQOOfflOO0000'

400 600 800

Stress, MPa

1000

17512000

10000

8000

-6000

4000

2000

cn

a)

-0 1200

Figure 30c.

25 50 Stress, ksi75 100 125 150 175

</)

ui

Figure 30d.

53
Gage Length Strain/Yield Strain

0 0.5 1 1.5 2 2.5 3

Figure 30e.

Remote Strain/Yield Strain

0 0.5 1 1.5 2

Figure 30f.

54

Stress,

ksi
Crack

Mouth

Opening

Displacement,

Remote S tr a i n/ Yi e I d Strain

0 0.5 1 1.5 2

c

D

2.5

1.5

in

“D

a> V\c

o

in

CT> c

0

0-5 ^

oO

Figure 30g.

Gage Length Strain/Yield Strain

Figure 30h.

55

Crack

Mouth

Opening

Displacement,

in
Crack

Mouth

Opening

Displacement,

mm

Crack

Mouth

Opening

Displacement,

Remote Strain/Yield Strain

Figure 30i

.

25 50 Stress, ksi

75 100 125

_=J 150 175

3 . 5

-

2 . 5

-

2

-

0 . 5

-

HY130 Tensile Panel

Single-Edge-Cracked

Crack Length 4mm

itTMTM ni~

l7n -.-o-rio.ooooooooooo 0^000000'^^^

r

400 600 800

Stress, MPa

o 200 1000 1200

Figure 30j

.

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

56

Crack

Mouth

Opening

Displacement,

in

Crack

Mouth

Opening

Displacement,

in
Crack Mouth Opening Displacement, in

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Figure 30k.

57

Integral,

I

b/i
Integral,

kN/m

J—

Integral,

kN/m

Figure 3 1 a - 3 1 k . Dependence of J-integral. stress, end crack mouth opening displacement on strain

for double-edge-cracked tensile panel with crack lengths 2 mm.

Gage Length Strain/Yield Strain

Figure 31a.

Remote Strain/Yield Strain

0 0.5 1 1.5 2 2.5

Figure 31b.

58

Integral,

I

b/i
Stress

Intensity

Factor,

MPaVm

^

Integral,

kN/m

Stress, ksi

30 60 90 120 150 180

Figure 31c.

200

150 -

100 -

30 60 Stress, ksi

90 120 150

200 400 600 800 1000 Stress, MPa

180

1 1 L. HY130 Tensile Panel

i 1 1 r Double-Edge-Cracked g

Crack Lengths 2mm §

o

€

8

o

o

o

o

o

o

o

o

o

o

o

o

CP0

0°

0<*

o

u

0

o o o

o o

o

o o o

o

1

1200

- 150

200

-100

-50

Figure 3 Id

.

59

Stress

Intensity

Factor',

ksivin

J-Integral,

Ib/i
Gage Length Strain/Yield Strain

0 12 3 4 5

Figure 31e.

Remote Strain/Yield Strain

Figure 31f.

60
Crack

Mouth

Opening

Displacement,

Remote S tr a i n/Yi e I d Strain

0 0.5 1 1.5 2 2.5

c

o

00

CDc

a>

a)CDoO

0.025

0.020

0.015

0 . 010 -

0.005-

0.000 -

HY130 Tensile Panel

Double-Edge-Cracked o Crack Lengths 2mm o

o

o

o 1

o

o

o

o /

oO°°°°

-3

c

o

00

T>

<D \c

o

00

-CCDc

0)

a)CDoO

0.000 0.002 0.004 0.006 Remote Strain

0.008

o

o.oio

Figure 3 lg

.

Gage Length Strain/Yield Strain

Figure 31 h

.

61

Crack

Mouth

Opening

Displacement,
Crack

Mouth

Opening

Displacement,

mm

Crack

Mouth

Opening

Displacement,

Remote Strain/Yield Strain

0 0.5 1 1.5 2 2.5

Figure 31 i

.

Stress, ksi

30 60 90 120 150 180 0.025

0.020

0.015

0.010

0.005

0.000

Figure 31j.

62

Crack

Mouth

Opening

Displacement,

in

Crack

Mouth

Opening

Displacement,

in
Crack Mouth Opening Displacement, in

0.000 0.005 0.010 0.015 0.020 0.025

Figure 31k.

63

-Integral,

I

b/i
-Integral,

kN/m

J-Integral,

kN/m

Figure 32a-32k. Dependence of J-integral, stress, and crack mouth opening displacement on strain

for face-cracked tensile panel with crack depth 2 mm. Gage Length Strain/Yield Strain

0 0.25 0.50 0.75 1 1.25 1.50

Figure 32a.

o 1000 4-

800-

Remote Strain/Yield Strain

0.4 0.6 0.8 HY130 Tensile Pane

F ace-C r acked

Crack Depth 2mm

%

-5000

600-

-4000 ._

400-

200

o

o

o

o

-3000 o

CD

CD

-2000 _

-1000

j-irn<-rr>nrTyYTriQOnQQ-)CPoOcPo

(~)^(--) 0 wbogdo aaaDOGOOQ^

tBBi nmi

aP1cPL

=4-0

5.0 *io"

J 0.0 1.0 2.0 3.0 Remote Strain

4.0

Figure 32b.

64
0 25 100 125

cn

CDc

I

1000

800-

600-

400-

200 -

Stress, ksi

50 75 HY130 Tensile Panel

Face-Cracked

Crack Depth 2mm

%

-5000

-4000

-3000

o

o -2000 o

o

oo

0 jtroaoo aanopoeacoonomp. r»n@QnnQ-|CPoOO O

COocP'(P

150 300 450

Stress, MPa

600 750

-1000

+ 0

I £

>o

CL

200 -

150-

Figure 32c.

Stress, ksi

25 50

_L 75 HY130 Tensile Panel

Face-C r acked

Crack Depth 2mm

100 125

o

o

200

150

(/)

100 -

50-

oo

Qo

o

°o O ^nO® °

,o o

O O

° o

On CO CP^

CtePOouo oO

OqoOOO°-“00°

150 300 450 600

Stress, MPa

750

-100

-50

Vo

Figure 32d.

65

Stress

Intensity

Factor,

ksiVin

J-Integral,

Ib/i
Stress,

MPa

Stress,

MPa

750 -

600

450

300 -

150

Gage Length Strain/Yield Strain

0.25 0.50 0.75 1 1.25 1.50 -J —I 1 ' HY130 Tensile Panel

F ace-C r acked

Crack Depth 2mm

,00 0 O OO O O

-125

jP

Jp

J?

s9

Gage Length Strain

-100

-75

-50

-25

i r

i I — I i I | H-o

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

3 *10

Figure 32e.

Remote Strain/Yield Strain

0 0.2 0.4 0.6 0.8 1

Figure 32f.

66

Stress,

ksi

Stress,

ksi
Crack

Mouth

Opening

Displacement,

mm

Gage

Length

Strain

o

*

Remote Strain/Yield Strain

0.2

7.0-

6.0

5.0-

4.0-

3.0-

2 . 0

-

1 . 0

-

0.0

HY130 Tensile Panel

Face-C r acked

Crack Depth 2mm

o.o

cP

<

P

o

o

o

o

oo

o

,CP"

-(P

,cP

L.cP

,cP cP

L

T“

1.0 T

2.0 3.0 Remote Strain

4.0

- 1.50

1.25

- 0.75

- 0.50

- 0.25

1-0 5.0 *io"

3

Figure 32g.

Gage Length Strain/Yield Strain

0.25 0.50 0.75 1 1.25 1.50

- O.O^S

- 0.02

- 0.02

- 0.01

L o.oc

Figure 32h.

67

Crack

Mouth

Opening

Displacement,

in

Gage

Length

Strain/Yield

Strain
Crack

Mouth

Opening

Displacement,

mm

Crack

Mouth

Opening

Displacement,

£

£

i

0.75

0.50

0.25

0

1

0.75

0.50

0.25

0

Remote S tr a i n/Yi e I d Strain

0.2 0.4 0.6 0.8

-L HY130 Tensile Panel

F ace-C r acked

Crack Depth 2mm

oo

o

o

rrmnnocojcoomoocgoo^000SoooaoccoococcD

,oCO 1 L

0.0 1.0 2.0 Remo t e

3.0 Strain

4.0

0.04

- 0.03

- 0.02

- 0.01

-- 0.00

5.0 MO'

3

Figure 32 i

.

25 Stress, ksi50 75 100 —!

HY130 Tensile Panel

F ace-C r acked

Crack Depth 2mm

125

0.04

- 0.03

- 0.02 o

o

oo

o

o

_o

- 0.01

i r-r-rmn mmotupoooooooooooc000000^"i©

<3oOOOO OOOOOOOCO

,o°°

*r 0.00

0 150 300 450 600

Stress, MPa

750

Figure 32 j.

68

Crack

Mouth

Opening

Displacement,

In

Crack

Mouth

Opening

Displacement,

i
0.00

5000

4000

3000

2000

1000

0

Figure 32k.

69

-Integral,

Ib/in
-Integral,

kN/m

J-Integral,

kN/m

Figure 33a- 33g. Dependence of J-integral, stress, and crack mouth opening displacement on strain

for edoe-hol e-cracked tensile panel with crack length 2 mm.

Neuber Strain/Yield Strain

Figure 33a.

250-

200 -

30 Neuber Stress, ks60 90

JL _L

120 HY130 Tensile Panel

Edge-Ho I e-Cracked

Crack Length = 2 mm.

Hole Radius = 14 mm.

150

-1200

150 -

100 -

-900

-600

50 - 1

-300

o +

0

I I

' ^ 200 400 600

Neuber Stress, MPa

T-J-0

800 1000

Figure 33b.

70

-Integral,

Ib/in

J-Int

eg

ra

I,

I

b/in
IE

>o

Q_

CO

200 -

ISO

100 -

50 -

30 «L.

Neuber Stress, ksi

60 90 120 HY130 Tensile Panel

Edge-Ho I e-C racked

Crack Length = 2 mm.

Hole Radius = 14 mm.

200

cP o°

o o° l

I r~

600 800

150

400

Neuber Stress, MPa

200

150

-100

-50

*-0

1000

Figure 33c. 12Neuber Strain/Yield Strain

3 4

V)

(/I

<1) JO

zs

<1)

Figure 33d.

71

Stress

Intensity

Factor,

ksi

Vin
Crack

Mouth

Opening

Displacement,

Neuber Strain/Yield Strain

Figure 33e.

Neuber Stress, ksi

0 30 60 90 120 150 £ 0.30 E

5 0.25 E

0)o

D

a 0.20

V) o

op 0.15 c

Cl O 0.10

=3O2 0.05

o

O

O 0.00 i i i i i 0 200 400 600 800 1000 Neuber Stress, MPa

HY130 Tensile Panel

Edge-Ho le-Cracked

Crack Length = 2 mm.

Hole Radius = 14 mm.

- o.oio

- 0.008

- 0.006

o0O 00000 0 = 0 0000

-°°

- 0.004

- 0.002

JL n nnn

Figure 33f.

Crack

Mouth

Opening

Displacement,

in.

Crack

Mouth

Opening

Displacement,

in
0.000 Crack Mouth Opening Displacement, in.

0.002 0.004 0.006 0.008 0.010

Figure 33g.

73

-Integral,

Ib/in
Integral,

kN/m

J-Integral,

kN/m

Figure 34a-34k. Dependence of J-integrai, stress, and crack mouth opening displacement on strain

for center-cracked tensile panel with width 560 mm and crack half-length 16 mm.

2000

1500

1000

500

0

2000

1500

1000

500

0

Gage Length Strain/Yield Strain

D 0.5 1 1.5 2

1 I I L- HY130 Tensile Panel

Cen t e r — C r acked

Crack Half-Length 16mm

lOOOO,oo° c

0.008

- 12000

-9000

-6000

-3000

0 0.000 0.002 0.004 0.006 0.010 Gage Length Strain

Figure 34a.

Remote Strain/Yield Strain

0.2 0.4 0.6 0.8 HY130 Tensile Panel

Cen t e r-C r acked

Crack Half-Length 16mm

r, c n, ° 2

° ° ‘

'

o o o o o

' i f

» > >- — =|=

1.0 2.0 3.0 Remo t e Strain

-12000

-9000

-6000

-3000

0

5.0 io

" 3 0.0 4.0

Figure 34b.

74

Integral,

Ib/in

J

Integral,

Ib/i
25 Stress, ksi

50 75 100 125

2000

j* 1500

CD

(D 1000

500-

HY130 Tensile Panel o Cen t e r— C r acked

Crack Half-Length 16mm

o

o

o

o

o

o

o

, n onnnnnnOQ 000000000

oo

o °o o

o o

o

200 400 600

Stress, MPa

800

12000

c

9000

^

CD 6000 <D

-3000

L 0

Figure 34c.

E

200-

D

CL

LD

150-

100 -

Stress, ksi

50 75

I

I HY130 Tensile Panel

Cen t e r — C r acked

Crack Half-Length 16mm

50-

o 200 400 600

Stress, MPa

800

200

150

-100

-50

Figure 34d.

75

Stress

Intensity

Factor,

ksiv'in
Gage Length S tr a i n/Yi e I d Strain

0.5

i 1.5

800

HY130 Tensile Panel

Center-Cracked 0

Crack Half-Length 16mm

o o o oq oo

-125

600 -

-100

00 400 -

-75

-50

200 - -25

o'.ooo 0.002 0.004 0.006 Gage Length Strain

t

0.008

- 0 0.010

Figure 34e.

0.2 Remote Strain/Yield Strain0.4 0.6 0.8 1

800 -

HY130 Tensile Panel

Cen t e r — C r acked

Crack Half-Length 16mm

,oo<3»-125

600 -

-100

00 400 -

75

50

200 - -25

0-f©-

0.0 "T1.0 2.0 3.0 Remo t e Strain

4.0 5.0 MCf

'

Figure 34f.

Stress,

ksi

Stress,

ksi
0

0.010 -iRemote Strain/Yield Strain

0.2 0.4 0.6 0.8

-i j_——

i i HY130 Tensile Panel

Cen t e r — C r acked

Crack Half-Length 16mm

-2

0.008 caW 0 . 006 -

CDc

CD

CDCDao

0 . 004 -

0 . 002 -

0.000

0.0

co

1.5

1.0 2.0 3.0 Remote Strain

-i

- 0.5

c

D

in

~o

CD >\c

D

in

CDc

0)

CDCDOO

5.0 M0'

Figure 34g.

Gage Length Strain/Yield Strain

0.5 _L

C

CDE

CDO

O

CL

CD a

CDcC

CDCL o

2

-

HY130 Tensile Panel

Cen t e r — C r acked

Crack Half-Length 16mm

1.5 HP~ 0.16 C

- 0.12

0.08

- 0.04

o

oo

n OQOO°0OOOOOO' ' ,ooO

(

0.000 m0.002

,cP

0.004 0.006 Gage Length Strain

T

0.008

0.00

0.010

Figure 34h.

77

Crack

Mouth

Opening

Displacement,
Crack

Mouth

Opening

Displacement,

mm

Crack

Mouth

Opening

Displacement

o Remote Strain/Yield Strain

4 -

0.2 _L0.4 _L

0.6

_L HY130 Tensile Panel

Cen t e r-C r acked

Crack Half-Length 16mm

0.8 _L *r 0.16

3

- 0.12

- 0.08

- 0.04

0 -4«-

0.0

_Q_n_O_Oj0_O^O O O o o o o O ° °

1.0 2.0 3.0 Remo t e Strain4.0 o.oo

5.0 M0”

Figure 34 i

.

0

4

25 Stress, ksi

50 75 HY130 Tensile Panel

Cen t e r-C r acked

Crack Half-Length 16mm

100

! 125 —L— 0.16

- 0.12

2

-

O

o

o

o

o

- 0.08

1- - 0.04

04-

0

n n n o ooooooooooo o O T T

200 400 600

Stress, MPa

800

o.oo

Figure 34 j.

78

Crack

Mouth

Opening

Displacement,

in

Crack

Mouth

Opening

Displacement,

in
Crack Mouth Opening Displacement, in

0.00 0.04 0.08 0.12 0.16

Crack Mouth Opening Displacement, mm

Figure 34k.

79

Integral,

I

b/i
-Integral,

kN/m

J-Integral,

kN/m

Figure 35a-35k. Dependence of J-integral, stress, and crack mouth opening displacement on strain

for surface-cracked tensile panel with crack depth 6 mm and crack length 25 mm.

Gage Length S tr a i n/Yi e I d Strain

0.3 0.6 1000

800-

600

400

200 -

HY130 Tensile Panel

Su rf ace-C r acked

Crack Depth 6mm

Crack Length 25mm

0.9

_j

1.2 1.5 _L

CCD

cP

cP

0.0 1.0 2.0 3.0 4.0 5.0 Gage Length Strain

6.0

-5000

4000

-300C

-200C

-1000

7.0 *io"

:

Figure 35a.

0.0 1000

800-

600-

400

200 -

Remote Strain/Yield Strain

0.2 0.4 0.6 _i_

HY130 Tensile Panel

Surf ace-C r acked

Crack Depth 6mm

Crack Length 25mm

0.8

_j

-5000

0.0

0-4000

o

c - 3000

co -2000

-1000

oo oooooo'DO cc l

I I 1.0 2.0 3.0 Remote Strain

4.0 * 10

' :

Figure 35b.

80

-Integral,

Ib/in

J-Integral,

Ib/i
Stress, ksi

0 25 50 75 100 125

Figure 35c.

Stress, ksi

0 25 50 75 100 125

Figure 35d.

81
Stress,

MPa

Stress,

MPa

Gage Length Strain/Yield Strain

Figure 35e.

Remote Strain/Yield Strain

0.0 0.2 0.4 0.6 0.8

(/)

00

oo

a)

00

Figure 35f.

82
Crack

Mouth

Opening

Displacement,

mm

Gage

Length

Strain

Remote Strain/Yield Strain

0.0 0.2 0.4 0.6 0.8

Figure 35g.

Gage Length Strain/Yield Strain

0 0.3 0.6 0.9 1.2 1.5

0.05

0.04

0.03

0.02

0.01

0.00

Figure 35h.

83

Crack

Mouth

Opening

Displacement,

in
Crack

Mouth

Opening

Displacement,

mm

Crack

Mouth

Opening

Displacement,

o.o Remote S tr a i n/Yi e I d Strain0.2 0.4 0.6

1 . 2

-

0.8

0.6

0.4-

0 . 2

-

0.4

_l HY130 Tensile Panel

Surface— Cracked

Crack Depth 6mm

Crack Length 25mm

0.8

oooooo

oooo CO cO° cP cP

0.0 —

1.0 2.0 Remo t e Strain3.0 4.0

* 10

'

Figure 35i

.

25 Stress, ksi

50 75 100 125

Figure 35

j

0.05

0.04

0.03

0.02

0.01

0.00

0.05

0.04

0.03

0.02

0.01

0.00

84

Crack

Mouth

Opening

Displacement,

in

Crack

Mouth

Opening

Displacement,

in
0.00 Crack Mouth Opening Displacement, in

0.01 0.02 0.03 0.04 0.05

Figure 35k.

85

Integral,

Ib/i
-Integral,

kN/m

5

J-Integral,

kN/m

o 8 Gage Length Strain/Yield Strain

36. 3-integral plotted against gage length strain for five single-edge-cracked spe

Remote Strain/Yield Strain

Figure 37. J-integral plotted against remote strain for five single-edge-cracked specimens.

86

Integral,

Ib/in

J

J-Integral,

Ib/i
0 Remote 12Strain/Yield Strain

3 4

Figure 38. Gage length strain plotted against remote strain for five single-edge-cracked speci- mens .

Remote Strain/Yield Strain

0 0.5 1 1.5 2 2.5 3

Figure 39. J-integral plotted against remote strain for two wide center-cracked panels.

87
Figure 40. Schematic plot of behavior of strain along direction of tensile axis plotted against

distance from crack plane showing strain shadow.

88
1.2

co

l_ CO

<DO

E

©

OC

o

k. CO

Figure 41.

1-

0. 8

-

0. 6

-

0. 4

-

0. 2

-

Normalized strain from 1.5 to 2.

=r 0 5 10 15 20

Normalized Y-Position

Plot of strain divided by remote strain against distance from crack plane divided by

crack length for normalized remote strain 1.5 to 2 for the 4 specimens with gross section yielding and the fitting function of Eq. 12. For this data the fitted value

of g was 0.29.

o>©

c

~o©

N

o

E

30

25 -

20 -

15 -

10 -

Four-spec i men average of J-integral (GSY)

vs strain

0 1 2 3 4 5 6 7 Normalized Strain

Figure 42. Normalized J-integral from gross section yielding plotted against normalized strain

for the same specimens used for Fig. 39.

89
HY130 Tensile Panels with Through Cracks

Gross and Net Section Yielding

— Double Edge Cracked, a = 2 mm, 2W = 90 mm

o = Center-Cracked, a = 5 mm, 2W = 560 mm

A = S i ng I e— Edge— C r acked, a = 2 mm, W = 90 mm

Gross Section Yielding

+ = Single-Edge-Cracked, a = 1 mm, W = 90 mm

Figure 43. Plot of normalized

showing bounds and

J-integral from gross four-specimen averagesection yielding for individual specimens

90
Normalized

J

-Integral

0 1 2 3 4 5 6 7

Normalized strain

Figure 44. Previous J-integral estimation curves.

91
92

Turner

Turner

Dawes

Dawes

Begley

Present

(low

strain)

(high

strain)

(m

=

1)

(m

=

2)

Study
J—Integral Estimation Curve

Figure 46. Experimentally derived J-integral estimation curve for contained yielding and gross section yielding in HY130 in tension.

93
Stress, ksi

0 25 50 75 100 125

Figure 47. Dependence of applied J-integral on stress for a surface-cracked tensile panel with

crack depth 6mm and crack length 25mm. The curve gives values calculated using the simiplified line spring model with flow strength taken as 975 MPa (141 ksi).

94

-Integral,

Ib/in
o_,

Figure 48. Form of the dependence of effective crack size a on crack depth to thickness ratio h/t and half-length to thickness ratio c/t.

95
Surface

Crack

Yielding

Index

Figure 49. Surface crack yielding index for HY130 plotted against applied stress for several relative crack depths.

96
200 400 600 800 1000

Stress, MPa

Figure 50. Dependence of normalized applied J-integral for HV130 on stress for contained

plasticity for surface flaws.

97
98
Figure 52. Normalized J-integral for ligament yielding plotted against surface crack yieldirc

index.

Normalized post- yield strain

Figure 53. Dependence of normalized J-integral for surface cracks for gross section yielding on normalized applied strain.

99
Surface Cracks

Figure 54. Schematic composite J-integral estimation curve for surface cracks showing contained

yielding, ligament yielding, and gross section yielding behaviors.

100
Figure 55. Photograph showing fractured welded and base metal HY130 specimens containing small surface

cracks. Note that the fractures occurred away from the cracks.

101
APPENDIX

APPLIED J-INTEGRAL VALUES IN TENSILE PANELS

D. T. Read

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

Key Words: f i tness-for-service; fracture mechanics; fracture toughness;

J-integral; nickel steel; yielding.

Contribution of NBS. Not subject to copyright.

This report was prepared as part of the Fracture Control Technology program

under the sponsorship of Dr. H. H. Vanderveldt, Naval Sea Systems Command (SEA

05R15). The effort was directed by Mr. John P. Gudas, David Taylor Naval Ship

R&D Center, under Program Element 62761N, Task Area SF-6 1 -544-504

.

Published in Proceedings of the Second International Symposium on Elastic

Plastic Fracture Mechanics, sponsored by the American Society for Testing and

Materials, Philadelphia, PA, October 6-9, 1981.

102
ABSTRACT

The J contour integral has been applied widely in characterizing

the fracture toughness of metals. In addition, the applied J-integral

can be used to characterize the driving force for fracture in structures.

This use of the J-integral requires knowledge of the dependences of the

applied J integral on stress, strain, and crack size. Results from an

experimental study of the applied J-integral as a function of strain in

tensile panels are discussed in this paper. Variables controlling the

applied J integral are associated with the three observed deformation

patterns: stress controls J for linear elastic strains and contained

yielding, displacement controls J for net section yielding, and strain

controls J for gross section yielding. Experimental results of this

study show that the applied J-integral value for a given strain level is

much higher for net section yielding than for gross section yielding.

The yielding pattern obtained was found to depend on the ratio of crack

length to specimen width. The transition from gross to net section

yielding in the material tested used occurred as the ratio of crack

length to specimen width was raised from about 1 to about 5 percent.

The significance of this transition is twofold; first, a strong increase

in applied J values is produced by a small increase in crack size;

second, this effect occurs at crack sizes that are small compared with

specimen width. The present experimental results resolve ambiguities in

the literature regarding the applicability of different estimation

formulae for J and allow approximate calculation of the applied J-integral

for any crack size or stress level.

103
INTRODUCTION

The J contour integral [1] has been applied widely in characterizing

the fracture toughness of metals [2-4], but its application to evaluation of the durability of structures containing cracks has been delayed

because dependences of the applied J-integral on stress, strain, and

crack size have not been generally well established. In response to

this need, a technique for measurement of the applied J-integral in

tensile panels of HY-130 steel as a function of applied stress, displacement, and strain has been applied to the elastic-plastic strain

range [5]. This technique is applicable to short, as well as long,

cracks, unlike the J-integral evaluation techniques commonly used in

material toughness testing. In this paper, experimental results on the

behavior of the applied J-integral are discussed, and conclusions are

drawn about the factors that control the applied J-integral. Two concepts

central to the development of the arguments in this paper, controlling

variables for J and deformation patterns, are now introduced:

The use of J as a fracture-characterizing parameter requires that J

be related to structural loading. To formulate such relationships, the

structural loading must be appropriately characterized. Some variables

that might be used to characterize structural loading are remote stress,

remote strain, strain over some gage length, and applied displacement.

This choice of a characterizing parameter is not necessary in linear

elastic fracture mechanics (LEFM) because the laws of linear elasticity

enforce consistent relationships among the variables. For example, the

stress and strain, are related through the material elastic constants.

The LEFM stress intensity factor is related unambiguously to either

remote stress or strain. Widespread yielding invalidates the laws of

104
linear elasticity and also the fixed relationships among the loading

variables. Therefore, one may not simply assume that some variable, for

example stress, is the appropriate controlling variable for J in yielding

fracture mechanics; the appropriate controlling variable must be identified.

For some materials power-law hardening occurs over the entire strain

range of interest, and so the various loading parameters may scale with

one another [6], In HY130, however, the stress-strain behavior is

nearly elastic-perfectly plastic, so that deformations above yield can

occur at essentially constant stress. This behavior prevents reliable

scaling of deformations against applied stresses. The criterion for a

proper J-controlling variable characteristic of the deformation state is

that the J-integral must be a single-valued function of the controlling

variable. Variables that change while the J-integral remains constant

or that remain constant while the J-integral changes must obviously be

rejected. A major argument herein is that different variables control J

at different stress and strain levels and crack lengths for HY130 and

possibly for many other materials.

A convenient classification of stress levels and crack lengths is

by deformation patterns [7,8]. Figure 1 depicts deformation patterns

characteristic of different deformation levels in a cracked specimen:

linear elastic, contained yielding, net section yielding, and gross

section yielding. Each of these patterns was observed in the present

study and was important for interpreting the results. In this paper the

appropriate controlling variables for the applied J-integral for the

different deformation patterns are identified and formulas for estimating

J for each region are discussed.

105
EXPERIMENTAL TECHNIQUE

The experimental technique used for measurement of the J-contour

integral for elastic-plastic conditions was described in detail in a

previous paper [5]. The materials tested was HY-130 steel, a 5-Ni

,

0.4-Cr, 0.5-Mo steel with a yield strength of 933 MPa, an ultimate

strength of 964 MPa, and very low strain hardening. Briefly, contours

enclosing crack tips in single-edge-cracked, center-cracked , and surfacecracked specimens of HY-130 steel were instrumented with strain gages

and linear-variable-displacement transducers (LVDTs) to measure the

integrand terms of the J-integral. The integral was then evaluated

numerically. Pin-loaded specimens with a gage section of 300 mm x 90

mm x 10 mm were used. Cracks were simulated by saw-cut notches of 1-,

2-, 4-, 7-, and 20-mm lengths. Some notches were sharpened by fatigue.

Load was measured using the built-in load cell of the 1 MN servohydraul ic

test apparatus. Displacement over the gage length was obtained from the

LVDT outputs. Remote strain was obtained from the strain gages near the

end of the gage section. The experimental uncertainty in the J-integral

in the plastic range was estimated at ± 10%.

RESULTS AND DISCUSSION

Measured values of the J-integral are plotted against gage length

strain in Fig. 2. Gage length strain is defined as the change in the

length of the gage section divided by its length. For most crack lengths,

the J values assume a parabolic dependence on strain for low strain

values and a linear dependence at higher strains. For a given strain

level, J increases with crack length. In short, the general trends of

the data in this figure are in accord with prior observations [9,10].

106
Appropriate controlling variables for J for the different deformation patterns are now considered.

Linear Elastic Strains and Contained Yielding

First, consider loads well below the nominal yield load of the

cracked specimens. For such loads, the plastic zone at the crack tip

is small compared with the length, width, and thickness of the specimen,

so a linear elastic treatment is appropriate. For this situation, the

elastic strain (given by a / E where a is the nominal remote stress and E

is Young's modulus), the gage length strain, and the remote strain are

all approximately the same except near the crack tip because linear

elasticity holds throughout the specimen. Nominal stress is commonly

used as the independent variable in linear elastic fracture mechanics [11]

In the linear elastic region it is clearly most convenient to regard

nominal stress as the controlling parameter. Experimentally derived

values of the applied stress intensity factor, K, are plotted against

nominal stress in Fig. 3. The stress intensity factor data in this

figure were calculated using measured J-integral values and the equation

K = /(JTT 0)

The experimental data of Fig. 3 support the existence of the linear

elastic regime; the stress intensity is proportional to the stress up to

about 700 MPa, which is about 75% of the material yield strength. The

experimental ly measured K values are in agreement with predicted values

from linear elastic fracture mechanics within the experimental uncertainty

For the elastic strain region, linear elastic relationships between

applied stress a, and stress intensity factor, K, for several crack

configurations may be used. These are conveniently collected in Ref. [11]

107
As the load is further increased, the plastic zone expands

rapidly outward from the crack tip. As long as the plastic zone remains

sufficiently small, nominal stress remains the appropriate J-control 1 ing

parameter [12]. This situation is termed contained yielding.

Net Section Yielding

The HY-130 material used in the present study has very little

strain hardening, so a definite limit load is reached when the remaining

ligament adjacent to the crack yields. The plastic zone penetrates to a

free boundary forming a deformation band (Fig. 1). Upon further imposed

displacement, the load no longer increases but the J-integral continues

to increase because the crack continues to open. A plot of experimental ly

measured J-integral values vs. stress. Fig. 4, illustrates this behavior.

After yield, nominal stress is no longer the J-control 1 ing variable

because J increases while stress remains constant. For relatively deep

cracks, the remote strain becomes constant along with the nominal stress,

because all the imposed deformation is transmitted to the deformation

bands while the specimen ends move apart as rigid bodies. Therefore

remote strain is also ineligible for consideration as the controlling

parameter for J for this case. The gage length strain, that is, imposed

displacement divided bv some qaqe lenqth, increases with the J-inteqral,

but it depends on the gage length and so is not unique. The displacement,

that is, the change of the gage length from its original value, increases

along the width J and does not depend strongly on the choice of gage

length, so it is a possible J-controlling variable for deep cracks. This

choice is supported by relationships given by Rice, Paris, and Merkle [13]

for the J-integral in specimens with deep cracks; in these relationships,

J is proportional to the imposed displacement in tensile specimens:

108
J ( 2 ) = - 1 p dP/da d V.

where V is imposed displacement at the load point, P is the load, and a

is crack length. This relationship applies for both elastic and plastic

deformation. In plasticity, P becomes the limit load. For the case of

single-edge-cracked specimens pin-loaded in plane stress, the limit load

is [14]

P = o

f

WB { [ (1 -a/W)

2 + (a/W)2

] 1/2 - a/W} (3)

Here a

^

is the flow stress and W the specimen width. Applying (2),

assuming no strain hardening, the plastic part of J is found:

1 - 2a/W

[(1 -a/W)

2 + (a/W)2

] 172

+ 1}V (4)

where Jp is the part of J associated with plastic deformation and V

p is

the total displacement less the elastic part. Using (4), the normalized

rate of change of J with imposed displacement, M, given by M = AJ/cjy A V,

1-2 a/W

[(l-a/W)

2 + (a/W)

2

] 1/2

+ 1 ,

i s

(5)

This M value is applicable for plastic strains. The flow stress for the

limit load expression may be taken as the average of yield and ultimate

strengths. This value is accurately known for HY-130 because its yield

and ultimate strengths are nearly the same. Experimental data are shown

in Fig. 5. In this figure, experimentally determined values of the

quantity M are plotted against normalized crack length. The net section

yield theory prediction (5) is shown as a broken line.

109
The noteworthy feature of this comparison is that the experimental data

fall away from the theoretical predictions of a/W at values less than

about 0.1. Similar behavior was previously observed for a C-Mn ship

steel [9]. Equation 2 with conventional limit load expressions usually

gives finite J values at a = 0. But a nonzero J value is nonsensical in

the abscence of a crack. Therefore, at some crack length, J must deviate

from the conventional predictions and approach zero as crack length approaches

zero. The data fall approximately on a straight line through the origin,

although the actual behavior is probably more complex. Using the

slope of this line, g, dependence of J on displacement in this short-crack

net-section-yielding region, J sn> can be described approximately by

AJ

$n = g

a a

f

A V/W (6)

The full value of J in this region is given by

J = J e + g a a

f (V-Ve )/W (7)

where J gand v 0 are the J-integral and displacement values at yield.

From the data of Fig. 5, the constant g was evaluated to be about 15.

An extension of the simple theory of Eq. 2, in which a term accounting

for crack tip region constraint (CTRC) was added to the usual expression

for applied load, was used previously to obtain a closer fit to the

data in Fig. 5 [5].

In summary, in net section yielding for both long and short cracks,

imposed displacement controls the applied J value.

110
Gross Section Yielding

For very small crack lengths, the plastic strain is no longer

concentrated by the crack tip in the remaining ligament but instead

spreads throughout the whole specimen. The corresponding deformation

pattern is gross section yielding. Strain is the controlling variable

for the gross yielding region [15-17]. The transition from net section

yielding to gross section yielding is illustrated in Fig. 6. This

figure presents a plot of displacement contributed by strains associated

with the crack (abbreviated crack-related displacement) against remote

strain. The crack-related displacement is the total imposed displacement

less the product of remote strain times gage length. Figure 6 shows

that for the deeper cracks the remote strain remained constant as the

crack-related displacement increased, as would be expected for net

section yielding. But for the 1-mm crack the remote strain continued to

increase and the crack-related displacement showed no steep rise at

yield as in the net section yielding case, indicating that the entire

specimen was yielding, behavior characteristic of gross section yielding.

From this figure, it can be seen that the boundary between net section

yielding and gross section yielding for the HY-130 material used in this

study is located somewhere between the 1-mm crack and the 2-mm crack.

It will be rounded off to a/W = 0.01 for purposes of the next section.

Figure 2 shows that the measured J-integral values for the 1- and 2-mm

cracks were much less than for the longer cracks. This illustrates the

fact that J for the net section yielding is much higher that for gross

section yielding. Relationships between J and strain for gross section

yielding have been proposed previously [15-17]. These are in general

agreement with one another but have not been critically evaluated in

this study.

Ill
Deformation Behavior Map

It has been shown that the proper controlling parameters for J are

stress, imposed displacement, and remote strain, and that each rules in

a specific region of applied stress or strain and crack size; a behavior

map depicting the location of these regions is shown as Fig. 7. Its

ordinate is a logarithmic scale for normalized crack size, a/W. Its

abcissa is normalized stress, a/a , up to a/a

y

= 1 , and then it divides

into separate scales for long and short cracks. For long cracks, the

second part of the abcissa is displacement, and for short cracks, it is

normalized remote strain, e /e . For low nominal stresses, the deformation

rem y

is linear elastic for all crack sizes. With increasing stress, specimens

with long cracks yield first, and eventually as a/a^-* 1 all specimens

yield. The curve extending from the upper left corner of the graph down

to °/°y

= 1> a/W - 0 is the boundary between linear elastic behavior and

contained yielding. The nearly parallel curve forms the boundary between

contained yielding and extensive yielding. Extensive yielding is divided

by a horizontal line into gross section and net section yielding. Here

this line has been placed at a/W = 0.01. High strain hardening or yield

elevation by constraint might raise this line. For small crack lengths

(the gross section yielding region) the controlling parameter for J,

namely, remote strain, is given on the lower abcissa. For larger

cracks (net section yielding), the controlling parameter for J, namely

displacement, is given on the upper abcissa. Within the net section

yielding region, the short crack region is separated from the remainder

by another horizontal line. Displacement is still the controlling

1 1 2
parameter for this region, but the crack-size dependence is different.

Deformation maps like this could be used to depict the effect of material,

part geometry, or deformation type (for example, residual vs applied

stress) on the formation of the different deformation patterns.

The large behavior difference observed between gross and net

section yielding explains why one set of J-vs-di spl acement formulae, of

the type given by Ref. [13], have been used in material toughness tests

of deeply notched specimens, whereas an entirely different family of

relationships between J and strain has been proposed for application to

structures [15-17]. Structures usually have small cracks, which produce

gross section yielding, whereas test specimens are deeply cracked,

producing net section yielding.

Further Research

The present results are, of course, not adequate for general, reliable application to decisions about cracks in real structures. The

most needed experimental extension of the present work is to geometries

that produce yield elevation by constraint and materials with different

stress-strain behaviors; such work is in progress. The two most important

outstanding issues are: (1) the location of the transition from net

section yielding to gross section yielding, and, (2) the dependence

of J on remote strain and crack length for gross section yielding.

Analytical methods, such as finite element analysis, also need to be

developed to allow explanation and, eventually, prediction of the

occurence of the various deformation patterns and their effects on

applied J-integral values [18].

113
The question of the applicability of conventionally measured

fracture toughness values to the variety of deformation patterns

described here is an interesting problem that arises once net and

gross section yielding behaviors have been clearly differentiated.

CONCLUSION

In this study, the variables controlling the applied J-integral in

the linear elastic, contained yielding, net section yielding, and gross

section yielding regions have been identified as stress, displacement,

and remote strain, respectively. Experimental evidence in favor of the

validity of existing relationships between J and stress, J and displacement,

and J and strain in their appropriate regions has been presented, and a

new relationship between J and displacement for the short crack net

section yielding region has been derived from experimental results.

ACKNOWLEDGMENT

This report was prepared as part of the Fracture Control Technology

Program under the sponsorship of Dr. H. H. Vandervel dt , Naval Sea

Systems Command (SEA 05R15). The effort was directed by Mr. John P.

Gudas, David Taylor Naval Ship R&D Center, Under Program Element 62761N,

Task Area SF-61 -544-504.

Technical assistance by J. D. McColskey and helpful discussions

with H. I. McHenry, R. B. King, and R. H. Dodds, Jr. are gratefully

acknowl edged.

114
REFERENCES

1. J. R. Rice, "A Path Independent Integral and the Approximate Analysis

of Strain Concentration by Notches and Cracks," Journal of Applied

Mechanics 35^, 1979, pp. 379-386.

2. J. A. Begley and J. D. Landes, "The J Integral as a Fracture Criterion," Fracture Toughness , ASTM STP 514 , American Society for

Testing and Materials, Philadelphia, 1972, pp. 1-20.

3. J. D. Landes and J. A. Begley, "The Effect of Specimen Geometry on

Jj

c

," Fracture Toughness , ASTM STP 514 , American Society for Testing

and Materials, 1972, pp. 24-39.

4. W. A. Logsdon, "Elastic Plastic (Jj

c

) Fracture Toughness Values:

Their Experimental Determination and Comparison with Conventional

Linear Elastic ( Kj c

) Fracture Toughness Values for Five Materials,"

Mechanics of Crack Growth , ASTM STP 560 , American Society for

Testing and Materials, 1976, pp. 43-60.

5. D. T. Read, "Direct Experimental Evaluation of the J Contour Integral,"

forthcoming.

6. V. Kumar, M. D. German, and C. F. Shi h , "Estimation Technique

for the Prediction of Elastic-Plastic Fracture of Structural

Components of Nuclear Systems," General Electric Report SRD-80-094,

1980.

7. C. E. Turner, "Methods for Post-Yield Fracture Safety Assessment,"

Post-Yield Fracture Mechanics , edited by D. G. H. Latzko, Applied

Science Publishers, London, 1979, pp. 23-210.

8. W. Soete and R. Denys, "Full and General Yield Behavior of Homogeneous Plates with Cracks," Proceedings of the International

Institute of Welding Conference at Bratislava, Doc. X-921-79, 1979.

115
9. D. T. Read and H. I. McHenry, "Strain Dependence of the J-Contour

Integral in Tensile Panels," Advances in Fracture Research , edited

by D. Francois, Pergamon, New York, 1981, pp. 1715-1722.

10. R. J. Bucci, P. C. Paris, J. D. Landes, and J. R. Rice, "J Integral

Estimation Procedures," Fracture Toughness , ASTM STP 514 , American

Society for Testing and Materials, Philadelphia, 1972, pp. 40-69.

11. H. Tada, P. C. Paris, and G. R. Irwin, "The Stress Analysis of

Cracks Handbook," Del Research Corporation, Hellertown, Pennsylvania,

1973.

12. G. R. Irwin and P. C. Paris, "Fundamental Aspects of Crack Growth

and Fracture," in Fracture , An Advanced Treatise , Vol . Ill, edited

by H. Liebowitz, Academic Press, New York, 1971, pp. 1-46.

13. J. R. Rice, P. C. Paris, and J. G. Merkle, "Some Further Results of

J-Integral Analysis and Estimates," Progress in Flaw Growth and

Fracture Toughness Testing , ASTM STP 536 , American Society for

Testing and Materials, Philadelphia, 1973, pp. 231-245.

14. G. G. Chell, "Elastic-Plastic Fracture Mechanics," in Developments

in Fracture Mechanics-! , edited by G. G. Chell, Applied Science,

London, 1979, p. 76.

15. M. G. Dawes, "The COD Design Curve," in Advances in Elasto-Plastic

Fracture Mechanics , edited by L. H. Larsson, Applied Science Publishers,

1980, London, pp. 279-300.

16. J. A. Begley, J. D. Landes, and W. K. Wilson, "An Estimation Model

for the Application of the J-Integral," Fracture Analysis ASTM

STP 560 , American Society for Testing and Materials, Philadelphia, 1974,

pp. 155-169.

116
17. C. E. Turner, "Elastic-Plastic aspects of fracture stress analysis

methods for other than standardized test conditions," in Fracture

Mechanics in Design and Service , Phil. Trans. R. Soc. Lond. A299,

1981, pp. 73-92.

18. R. H. Dodds, Jr., D. T. Read, and G. W. Wellman, "Finite Elment

and Experimental Evaluation of the J-Integral for Short Cracks,"

to be published in Proceedings of the 14th National Symposium on

Fracture, Los Angeles, 1981, sponsored by the American Society for

Testing and Materials.

117
YIELDING PATTERNS

(no bending)

Elastic Strains Yielding Confined to

Everywhere Crack Tip Region

Net Section

Yielding

Gross Section

Yielding

Figure 1. Deformation patterns.
GAGE LENGTH STRAIN

Figure 2. J-integral plotted against gage length strain for several

crack lengths.

119

J-INTEGRAL,

Ib/in
,

MPa

vrrT

Figure 3. Measured stress intensity factor plotted against remote stress

for a single-edge-cracked specimen with a 4-mm crack.

120
J-INTEGRAL,

kN/m

1500

1000 -

500-

0,

HY 130

4 mm Single-Edge Crack

i Up"

iiuiiiiiiuiiiiiiu cxjp cPia

1

) 200 400 600 800

c ##*

3

STRESS, MPa

Figure 4. Measured J-integral plotted against remote stress for

single-edge-cracked specimen with a 4-mm crack.

1000

121

113

OI^qtiaCttDD

Otltttp

CD

D
Figure 5. Net section yielding, theory and experiment. Normalized

slopes of J-integral-vs. -displacement lines and experimental

data.

122
CRACK-RELATED

DISPLACEMENT,

mm

REMOTE STRAIN

Figure 6. Displacement contributed by the strain field of the crack

(crack-related displacement) plotted against remote strain.

123
NORMALIZED

CRACK

LENGTH,

a/W

DISPLACEMENT, V, mm

0 1 2

NORMALIZED

STRESS, cr/<Ty

NORMALIZED

STRAIN, €/€

y

Figure 7. Deformation behavior map for tensile panels of HY130 with

cracks.

i

124
U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 82-1670

2. Performing Organ. Report No. 3. Publ ication Date

August 1982

4. TITLE AND SUBTITLE

APPLIED J-INTEGRAL IN HY130 TENSILE PANELS AND IMPLICATIONS FOR FITNESS FOR

SERVICE ASSESSMENT

5. AUTHOR(S)

D. T. Read

6 . PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

Naval Sea Systems Command

John P. Gudas, Project Monitor

Code DTNSRDC 2814

David Taylor Naval Ship R&D Center

Annapolis Laboratory

Annapolis, Maryland

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached,

11. ABSTRACT (A 200-word or less factual summary of most sign ifi cant information. If document includes a significant

bi bl iography or literature survey, mention it here) An experimental technique for direct evaluation of the J contour integral is described. Results are reported and discussed. Some fifteen cracked HY130 tensile

panels were tested, including center-cracked , single-edge-cracked, double-edgecracked, face-cracked, and part- through-cracked configurations. As crack size

increased, the post-yield deformation pattern changed from gross section yielding,

for very small cracks, to net section yielding, for larger cracks. Net section

yielding was associated with much larger J-integral values than gross section

yielding. The product of crack mouth opening displacement and yield strength

was approximately equal to the J-integral for all cases in the tensile panel geometry

used here. The implications of these results for fi tness-for-service assessment of

practical components and structures containing crack-like defects are discussed. Net

section yielding behavior is intolerable in high-performance applications. Gross

section yielding behavior can be treated using a J-integral estimation curve derived

from the present experimental results. The scatter in the normalized gross section

yielding contribution to J was high, approximately a factor of 2. This scatter was attributed to specimen imperfections and experimental problems. The experimentally

derived J-integral estimation curve of the present study fell at the top of the range

of previously reported curves. Applications of this estimation curve to cases of

residual stresses, stress concentrations, and surface cracks are briefly described.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) crack; defect; fi tness-for-servi ce ; fracture mechanics; gross section yielding;

J-integral; net section yielding; surface crack; through crack.

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