Intrapartum fetal stimulation tests are moderately useful for predicting the presence or absence of fetal acidemia – meta-analysis

EngineeringFracture Mechanics Printed in the U.S.A.

Vol. 21, No. I, pp. 3148.

0013-7944/85 $3.00 + .oo Pergamon Press Ltd.

1985

FRACTURE CHARACTERISTICS OF THREE METALS SUBJECTED TO VARIOUS STRAINS, STRAIN RATES, TEMPERATURES AND PRESSURES Honeywell

GORDON R. JOHNSON Inc., Defense Systems Division, Edina, MN 55436, U.S.A. and

Air Force Armament

WILLIAM H. COOK Laboratory, Eghn Air Force Base, FL 32542, U.S.A.

Ahstrac-This paper considers fracture characteristics of OFHC copper, Armco iron and 4340 steel. The materials are subjected to torsion tests over a range of strain rates, Hopkinson bar tests over a range of temperatures, and quasi-static tensile tests with various notch geometries. A cumulative-damage fracture model is introduced which expresses the strain to fracture as a function of the strain rate, temperature and pressure. The model is evaluated by comparing computed results with cylinder impact tests and biaxial (torsion-tension) tests.

INTRODUCTION WHENMATERIALS are subjected to dynamic loading conditions such as high velocity impact, explosive detonation or metal forming operations, a wide range of strains, strain rates, temperatures and pressures may be experienced. In some instances there has been a tendency to distinguish “dynamic” material properties from “static” material properties. The underlying assumption is that the differences between the “dynamic” and “static” properties must be due to strain rate effects only. Often associated with high strain rates, however, are large strains, high temperatures and high pressures. Therefore, it is important that the effects of each variable be properly assessed, rather than assuming all distinguishing characteristics are due to strain rate alone. This paper considers fracture characteristics of OFHC copper, Armco iron and 4340 steel. A series of laboratory tests has been performed to determine the effects of strain rate, temperature and pressure on the strain to fracture. A cumulative-damage fracture model is developed and evaluated with an independent series of tests and computations. TEST DATA A description of the three materials is given in Table 1. All of the test specimens were fabricated from the same material stock and the heat treatment was always as specified in Table 1. The torsion test data are shown in Fig. 1. The torsion tester is described in Ref. [I] and the procedure for analyzing the data is given in Ref. [2]. Data for a wide range of other materials are presented in Refq. [3] and [4]. For the data in Fig. 1 the average shear strain, 7, is assumed to occur only in the thin test section, and to occur uniformly along that section. At the higher strain rates, however, there may be some localizations of strain due to adiabatic heating[2]. The average shear strains at fracture are clearly shown for the Armco iron and the 4340 steel. None of the OFHC copper specimens in Fig. 1 fractured due to rotational limitations of the torsion tester. Another shorter-gage, OFHC copper specimen was tested at 3 = 0.008 s-’ and it fractured at 7 = 8.7. Metallographic sections of three torsion specimens are shown in Fig. 2. The OFHC copper specimen appears to exhibit a strain localization near the center of the gage section. There are no voids evident in any of the sections. The tensile Hopkinson bar data are shown in Fig. 3. A representative Hopkinson bar apparatus and data for various materials are presented in [5]. The specific Hopkinson bar used for the data of Fig. 3 is located at the Air Force Armament Laboratory (AFATL) at Eglin Air Force Base. The elevated temperatures were obtained by surrounding the in-place test specimen by an oven such that the temperatures were applied for several minutes prior to testing. The true tensile strain in Fig. 3 is based on the assumption that there is uniform axial strain in the tensile specimen. The stress-strain data are shown only for relatively small strains because they 31

32

G. R. JOHNSON Table

I. Physical

properties

and W. H. COOK

of OFHC

copper,

Armco

iron and 4340 steel

HEAT TREATMENT tK)

TEMPERATURE -__

TIME

(MINUTES)

AT TEMPERATURE

e-

HARDNESS GRAIN ELASTIC

SIZE

(mm1

___~

j F-30

~OCKWELL~

j

0.060-0.090

-__

F-72

o.D%-0.150 d

c -30 < 0.010

PROPERTIES

ELASTIC MODULUS, POISSON’S

(GPaJ

E

RATIO, Y

0.34

SHEAR ~DULUS,

E/2(1 + VI

IGPal

BULK MODULUS.

E/3(1 -2 Y i _”

(GPa)

I

207

200

0.29

0.29

THERMAL PROPERTIES DENSITY.

ikqlm3)

CONDUCTIVITY, SPECIFIC DiFFUSiViN, EXPANSION

k

(W/ml0 UlkqKI

HEAT, cp

h2id

k/pi+, COEF.

NOL. ). a

MELTING TEMPERATURE,

TMELT

(K-l 1 (K) -.

cannot be accurately evaluated after necking occurs in the tensile specimen. While these data can be helpful in examining strength characteristics, fracture characteristics can be determined only by examining post-tested specimens as shown in Fig. 4. The photographs of Fig. 4 and the metallographic sections of Fig. 5 both show the relatively ductile fracture of the OFHC copper and Armco iron, when compared to the 4340 steel. In Fig. 5, voids are most evident in the Armco iron and some are present in the OFHC copper. The 4340 steel also shows some void formation at elevated temperatures. Quasi-static tensile data are shown in Fig. 6. The notched geometry specimens are identical to those used elsewhere and give a concentration of hydrostatic tension in the test specimen [6]. This is clearly shown in the data of Fig. 6. For a specified true strain, the stress (including hydrostatic tension) increases as the notch becomes more severe. It can also be seen that the presence of the hydrostatic tension significantly decreases the strain at which the material fractures. Figure 7 shows metallographic sections of the quasi-static tensile test specimens. The OFHC copper and Armco iron fail in a more ductile manner than the 4340 steel, as expected. The formation of voids is apparent in the unnotched OFHC specimen and all of the Armco iron specimens. No voids are evident in the 4340 steel specimens. DATA

ANALYSIS

AND MODEL

DEVELOPMENT

The test data are analyzed to show the effect of various parameters on the strain to fracture. This is accomplished by developing a cumulative-damage fracture model which attempts to isolate the effects of strain rate, temperature and pressure. Prior to the fracture model development, a strength model and data are briefly described. Strength model

A strength model and data have recently been presented for metals subjected to large strains, high strain rates and high temperatures[7]. Although the focus of this paper is on fracture characteristics, a strength model is necessary to perform computations to evaluate the fracture model.

Fracture characteristics of three metals

33

AVERAGE STRAIN RATES. 7 IS-'1

;/

MJTE: NON

OF THE SPECIMNS

2

I

3

FRACTURED

4

5

6

7

a

STRAIN, ?-R&L

AVERAGE SHAR 600

ARMCO

5w

IRON

c?400 2 c 2 ;

300

z s 1Y z 2w

AVERAGE

NOTE: SPECIMN 1W

STRAIN RATES, 7 (S-l,

DID NOT

FRACTURE AT 7 - 495-I

0 "

1

2

3 AVERAGE SHAR

4 5 STRAIN, ?.Rb'/L

6

7

a

12w

4340

MM-

ii5

STEEL

8W-

I. $ 1.1

117

200 -

AVERAGE STRAIN RATES, 7 IS-')

0

, 0

.25

.50

.75 AVERAGE

Fig. 1. Stress-strain

1.00 SHAR

1.25

1.50

1.75

STRAIN, ?-R8lL

data for torsion tests at various

strain

rates.

2.00

34

G. R. JOHNSON

and W. H. COOK

T”=.292

-

i? 6OOc e

ARMCO

IRON

zi z

I OO

.05

.lO

1

I

(15

.20

I

Fig. 3. Stress-strain

data

for Hopkinson

1

.25

TRUE TENSILE STRAIN.

2tn

.30

.35

.40

Idold)

bar tests at various

temperatures.

The model for the von Mises tensile flow stress, g, is expressed as d = [A + I&“][1 -I- cini *I[1 - T*“]

(1)

where t is the equivalent plastic strain, i* = i/i,, is the dimensionless plastic strain i, = 1.0 SK’, and T* is the homologous temperature. The five material constants are A, m. The expression in the first set of brackets gives the stress as a function of strain for and T* = 0. The expressions in the second and third sets of brackets represent the effects

4340 STEEL

1800 t

OFHC

0.5

1.0 TRUE

Fig. 6. Stress-strain

data for quasi-static

COPPER

STRAIN,

1.5

2.0

2.5

2.I?r;id,ld)

tensile tests using notched

and unnotched

test specimens.

rate for B, n, C,

i* = 1.0 of strain

Fracture characteristics of three metals

cc-_-

I*\\ 1 \

SECTION

OF

SPECIMEN

--

\ 1

\

i 1’

CAGE

CFHC

t i :

-_-_ COPPER

;ii=

83.1

‘5=

14%3-’

L_--__--

Fig. 2. Metallographic sections of the torsion specimens.

35

36

G. R. JOHNSON

OFliC

and W. H. COOK

COPPER

Fig. 4. Photographs

of the fracture

surfaces

on the Hopkinson

bar specimens

ARMCO

IRON

T$=

lo’=

0.410

Fig. 5. Metalio~ap~c

OFHC

COPPER

UWXOTCWED

0.133

T+Y

239

sections of the Hopkinson bar specimens.

AAMCO

IRON

UNUOTCHEO

‘E’

NOTCN

‘E’

NOTCH

‘f’

‘6’

NOTCH

‘8’

NOTCH

‘6%’ NOTCII

NOTCH

Fig. 7. Metallographic sections of the tension specimens.

38

G. R. JOHNSON

OFHC

ARMCO

COPPER

v=190

and W. i-1. COOK

4340

IRON

STEEL

w-343

MIS

Fig. 17. Photographs

4340

of the ends of the impacted

STEEL

Fig. 18. MetalIographic

CL’=343

sections

cylinders.

MIS)

of the impacted

cylinders.

MIS

Fracture characteristics of three metals

39

Table 2. Summary of strength and fracture constants OFHC

STRENGTH a-[A

CONSTAMS Bc"][l+

l

4340

ARK0

COPPER

IRON

STEEL

FOR c Pnlql-vm]

A

(MPd

90

175

792

B

Wa)

292

380

510

”

a31

a32

0.26

C

a 025

0.060

0.014

m

1.09

0.55

1.03

0.54

-2.20

4.89

5.43

3.44

-3.03

-0.47

-2.12

a014

a016

0.w2

FRACTURE

CONSTANTS

cf-[qt

FOR

DpxpD3ql

+ D4hiql+q

Dl Dz D3 D4 D5 SPALL STRESS IMW,

uSPALL

1.12

a 63

_

_

am

0.61 -

‘min d-

urn lti FOR i;l.OS

V-(/i,

-1

T*-IT-T~~~~I~(T~,~-T~~~)

rate and temperature, respectively. The basic form of the model is readily adaptable to most computer codes since it uses variables (c, i *, T*) which are available in the codes. The procedures used to extract the appropriate constants from the test data of Figs. 1, 3 and 6 are presented in [7]. The specific constants are listed in Table 2. The resulting adiabatic stress-strain relationships at various strain rates are shown in Fig. 8. The temperature for the adiabatic condition is due to the plastic work of deformation. In all cases, the adiabatic stresses

“, 2

ARK0

800 -

t,

IRON Q = [175 + 380d2][l+

.060h?][l-

T*.55]

z STRAIN RATE.:(S",_

U

0 0

= [90+292c3'][l+

1

1

I

I

0.5

1.0

1,5

2.0

.025bni*][l-

2.5

TRUE TENSILE STRAIN.<

Fig. 8. Adiabatic stress-strain

relationships.

T*1.09]

I

1

3.0

3.5

4.0

40

G. R. JOHNSON

and W. H. COOK

reach a maximum and then decrease with increasing strain. The point of maximum stress is important inasmuch as it represents the strain at which localized instabilities may begin to occur. Fracture model The fracture model is intended to show the relative effects of various parameters. It also attempts to account for path dependency by accumulating damage as the deformation proceeds. Unlike more complicated Nucleation and Growth (NAG) models[8], the model presented herein uses a limited number of constants and is primarily dependent on the strain, strain rate, temperature and pressure. The basic form of the fracture model developed here was first presented in Ref. [9]. The damage to an element is defined

where At is the increment of equivalent plastic strain which occurs during an integration cycle, and L/ is the equivalent strain to fracture, under the current conditions of strain rate, temperature, pressure and equivalent stress. Fracture is then allowed to occur when D = 1.0. The general expression for the strain at fracture is given by

d = [D, + D, exp Dla*]

[1 + D, In ;*][I

+ D,T*]

(3)

for constant values of the variables (a *, i *, T*) and for CJ* I 1.5. The dimensionless pressure-stress ratio is defined as D* = o,,,/c where o,,, is the average of the three normal stresses and 5 is the von Mises equivalent stress. The dimensionless strain rate, i*, and homologous temperature, T*, are identical to those used in the strength model of eqn (1). The five constants are D, . . . D,. The expression in the first set of brackets follows the form presented by Hancock and Mackenzie[lO]. It essentially says that the strain to fracture decreases as the hydrostatic tension, grn, increases. The expression in the second set of brackets represents the effect of strain rate, and that in the third set of brackets represents the effect of temperature. For high values of hydrostatic tension (a * > 1.5) a different relationship is used; it will be presented later. Since this fracture model is based on fracture strains at constant o*, i* and T*, it is accurate under constant conditions to the extent that the equivalent stress, 5, equivalent strain, E, and stress and strain relationships. equivalent strain rate, i*, can represent the more complicated

a= i=

J J ;

2

5

[(a,

.

-

[(q -

%I2

+

cc2

-

03)’

+

(“3

-

gJ21

i,)* + (4 - iJ2 + (i3 - i,)‘]

where (T,, 02, c3, are the principal stresses and i,, i2, i,, are the principal strain rates. Although simple, the model is rational and should provide an improvement over other fracture models based only on plastic strain or the current condition of other variables. Furthermore, from a computational viewpoint it is attractive since it requires little additional computational time and only one additional element array to store the accumulated damage. The first step required to obtain the material constants is to determine the effect of the dimensionless pressure-stress ratio, 0 *. This can be done by considering the quasi-static tensile data of Fig. 6 and the torsion fracture data of Fig. 9. Numerical simulations, using the EPIC-2 code, are performed on the tensile specimens as shown in Fig. 10. An average pressure for each group of four “crossed” triangles is used to eliminate any excessive stiffness due to the triangular element formulation [ Ill.

Fracture

ARK0

characteristics

41

of three metals

A

IRON A

-A

A

-

--

----

A

NOTE:

ut = 8.7 AT

7 =.008S-1FOR A SHORTER

GAGE COPPER SPECIMEN

m

4340 STEEL l-

__---m

__--

I___----

n

_

ul I001

.Ol

,1

1

10

100

1000

AVERAGE SHEAR STRAIN RATE, 7 (S-l)

Fig. 9. Average

shear strains

at fracture

for the torsion

tests.

Figure 11 shows the computed pressure-stress ratio as a function of the equivalent strain in the center of the specimen. The results for the unnotched specimens show good agreement with the Bridgman data[l2], which are for a range of materials. For the “E” notch specimens, g* tends to increase as 6 increases. For the “B” notched specimens, however, U* decreases as 6 increases. Figure 12 shows the strain to fracture as a function of the pressure-stress ratio for quasi-static conditions. The data at cr* = 0 are from the torsion tests. For the OFHC copper and Armco iron, the torsion tests provide fracture strains greater than those of the tension tests. This is as expected, based on the trend of the tension data in Fig. 11 and similar data reported elsewhere[3,6, lo]. For the 4340 steel, however, the fracture strain obtained from the torsion test is much lower than expected. The reason for this apparent discrepancy is not clear. It may be due to anisotropic characteristics of the material. For the purpose of extracting fracture constants for the 4340 steel, the torsional fracture data will be ignored. The analytic expressions through the data are obtained by varying the appropriate constants until D x 1.0 at fracture for the three tension tests and the torsion tests. The three constants for each material in Fig. 12 are proportional to D,, D,, 4, and need only be adjusted to correspond to a strain rate of i * = 1.O. Figure 12 shows the effect of strain rate and temperature on the strain to fracture. The fracture strains are expressed as the ratio of the Hopkinson bar fracture strains divided by the quasi-static tensile fracture strains. The Hopkinson bar fracture strains are approximately determined by measuring the cross-sectional area of the post-tested specimens as shown in Fig. 4. The temperatures for each test range from the initial temperature at the beginning of the test to the computed temperature at the strain where fracture occurs. The straight lines drawn through the data are “least squares” fits to the midpoints of the range of temperatures. Due to the approximate nature of the data and the rather poor linear fit to the data, the temperature effects cannot be determined with a high degree of accuracy. It is clear, however, that elevated temperatures do indeed increase the ductility of the materials. The effect of the strain rate can be isolated from the temperature effect by considering the ratio of the fracture strains at T* = 0. For all three materials, the ratio is greater than 1.0 at T* = 0,

G.

42

R. JOHNSON and W. Ii. COOK

OFHC

GEWETRY

COPPER

-I

‘E’ NOTCH 1 /

STEEL

ARMCOIRON

4340

STEEL

AAMCOIRON

4340

STEEL

c AVE

SYM#AETRY BOUNDARY ~OND~ION

INlTtAt

4340

= 1.88

I

I

INITIAL ‘8’

NOTE’

GEOMETRY

OFHC COf’PER

NOTCH

CAVE

= Z&&da/d)

Fig. 10. Computedshapes of the tensile specimens at fracture. indicating that the strain to fracture increases slightly as the strain rate increases. This same trend is verified by the fracture data of Fig. 3 and by that of other materialsf3,43. Now the fracture constants can be determined. The strain rate constant, Dd, is obtained from the data of Fig. 13 at T* = 0.The constants related to the pressure-stress ratio (Dl, D2, D3) are those of Fig. 12, adjusted from quasi-static conditions (2 x 0.002 s-l) to i* = 1.0. Finally, the temperature constant, Ds, is obtained from the data of Fig. 13. The resulting relationships are shown in Fig. 14 and the fracture constants are listed in Table 2. It would appear that the pressure-stress ratio is of primary importance. As the hydrostatic tension is increased, the strain to fracture decreases rapidly. The strain rate and temperature effects appear to be less important. Although the work reported herein does not s~cifically address spa11 fracture, it is necessary to provide for a transition from ductite fracture at large strains to spa11 fracture at much smaller strains. Figure 15 shows the relationship which can be used for large values of the pressure-stress ratio (g* > 1.5). The fracture strain varies in a linear manner, from 6* = 1.5 to G,*,,! at E&,. The and the minimum fracture strain, &. The dimensionless input parameters are the spa11stress, ~~~~~~ D$,, is computed from fl,pall,and the current value of the von Mises flow stress, 3. It is recognized that other models may be better adapted to the spa11fracture regime. Some of these are presented in Ref. [13].

Fracture

characteristics

of three metals

43

1.3 -

-\

R*.254Chl

t

1.2 -

'8'

‘6’ NOTCH 1.1 -

'E' W"'iT;r( R..634CM

1.0 b ---___ + .9 -

f

BRIDGWN

\

_--

.B -

.6 -

-0FHC

COPPER

-------ARK0

IRON

---_

STEEL

.4 6 1

.30

.4

I

.B EQUIVALENT

Fig.

11. Pressure-stress

PLASTIC STRAIN

ratio vs equivalent

plastic

(TORSION

TORSION

DATA

I

1.6

1.2

DATA

I

2.0

2.4

strain

for the tensile specimens.

IGNORED)

IGNORED

FOR 4340 STEEL I -.2

0

.2 PRESSURE

Fig. 12. Fracture

strain

2.8

Al CENlER. c

I

.4

.6

- STRESS

vs pressure-stress

.B

RATIO, u“.

ratio

1.0

1.2

1.4

urn/ B

for isothermal

quasi-static

conditions.

44

G. R. JOHNSON and W. H. COOK

Or8

L

I

,

0

,l

.2 DIMENSIONLESS

,3

.4

TEMPERATURE.

I

I

,5

,6

,!

T'

Fig. 13. Effects of strain rate and temperature on the strain to fracture.

Model evaluation

The relationships of Fig. 14 show the effect of various parameters on the strain to fracture. The next step is to evaluate the relationships to extended regions of the parameters. The effect of complicated loading paths is also of interest. A series of cylinder impact tests has been performed to evaluate the strength model[7] and the fracture model. The upper portion of Fig. 16 shows a comparison of the computed deformed shapes and the corresponding test data. The strength model and data are as defined in eqn (11, Fig. 8 and Table 2. The computations were performed with the EPIC-2 code, Again, an average pressure is used for each set of adjacent triangular elements to eliminate any excessive stiffness[l I]. The agreement between the computed shapes and the test data is generally good. It should be emphasized that the results of the cylinder impact tests have not been incorporated into the data, and they represent a totally independent check case for both the strength and fracture models. Additional comparisons for lower impact velocities are given in [7]. The cylinder impact tests of Fig. 16 can also be used to provide an independent check of the fracture model. Figure 17 shows photographs of the ends of the impacted cylinders. For the OFHC copper impact at I’ = 190 m/s and the Armco impact at Y = 279 m/s, there are some localized fractures around the periphery of each of the cylinders. Looking at the metallographic sections in Fig. 18, however, there is no evidence of the void formation which exists in some of the fractured tensile specimens. Therefore, there may be some uncertainty about the actual fracture status of these tests. Figure 16 shovs plastic strain contours and damage contours for three of the impacted cylinders. In all cases the strain is much higher at the center of the impacted end than at the periphery. The damage, however, is more uniform along the bottom of the cylinder. This trend is in the right direction since the lower-strained edge is generally under more hydrostatic tension than is the higher-strained center. Time history responses of several variables in the OFHC copper cylinder are given in Fig. 19. Unfortunately, the damage at the edge of the OFHC copper and Armco iron cylinders is significantly less than the 1.0 required for fracture. The reasons for the apparent discrepancy are not clear. It co&d be that the damage does not accumulate in the manner specified by the model. It could also be that the model and/or data do not extrapolate into the more extreme regions of strain rate, temperature and/or pressure. Also, the fracture status of the OFHC copper and Armco iron cylinder of Fig. 17 is uncertain. Another possibility involves complications associated with the computations. For the actual tests the cylinders were impacted against a high-strength steel anvil. For the computations,

Fracture

characteristics

45

of three metals

OFHC

COPPER

.25 ) = .50

& --------ARMCO

IRON

\

Ef=[-2.20

+ 5.43ExP-.47r

‘][I

+ .OlbPni’][l

+ .b3 T’]

PRESSURE

Fig. 14. Fracture

strains

as functions

of strain

rate, temperature

and the pressure-stress

ratio.

46

G. R. JOHNSON

and W. H. COOK

1.5 PRESSURE-STRESS

Fig. 15. Definition

of fracture

RAT1O.r’

strains

P&

= -%w

P

at large tensile pressure-stress

ratios.

however, a rigid surface is assumed. The rigid surface assumption amplifies the magnitude of the compressive and tensile waves which propagate throughout the cylinder shortly after impact. It can be seen from Fig. 19 that approximately half the strain and half the damage occur during the initial 2.0 to 3.0 ps. The pressure-stress ratio and fracture strain oscillate radically during this time period. Preliminary computations indicated the damage was very sensitive to the assumed values of crspa,, and t/mi”for G* > 1.5. Due to the uncertainty of the model in this range, and the unknown effect ARMGO v=279

OFHC COPPER v=190 M/S

IRON M/S

4340 STEEL v= 343 MIS

r---i

PLASTIC

STRAIN

CONTOURS

r---7

JJz-I&

i

E = .96

-<=225

-E=l

?-&

06

DAMAGE

‘mm Dz 3

1

‘-D:

’

33

-t

-cm222

‘-5:

123

CONTOURS

/( D=49

D=40

= 79

L D-60

--D-51

NOTES. - PLASTIC

STRAIN

- DAMAGE

CONTOURS

TEST

DATA

Fig. 16. Computed

CONTOURS

DENOTED

strain

SHOWN

SHOWN

AT INTERVALS

AT INTERVALS

BY DOTS

and damage

(0

l

OF 0

Of

0 5

1

0)

contours

for the cylinder

impact

tests.

Fracture

characteristics

of three metals

I.0

1.5

/:-: 0 6

LOG(10) STRAIN RATE 4

1.: HOMOLOGOUS

TEMPERATURE

L?

0 1

0,

I

PRESSURE-STRESS

RATIO

r

;:,

5

-’

0: A

.2 -

DAMAGE

/

o-

0

Fig. 19. Time history

data for the lower edge of an OFHC copper cylinder surface at 190m/s.

impacted

against

a rigid

of the rigid surface assumption, it was decided to simply set &, to the fracture strain which existed at g* = 1.5. The damage contours shown in Fig. 16 are based on this approach. A series of quasi-static biaxial tests was also performed to evaluate the model and the data. Unfortunately, there is also some uncertainty associated with these results. The biaxial test consists of a torsion specimen subjected to a torsional strain, followed by tensile strain until fracture occurs. A thin-wall specimen, as opposed to a solid specimen, was selected so the maximum damage due to both torsion and tension would occur in the same location. A solid specimen was not selected because the maximum torsional damage would occur at the outer radius, and the maximum tensile damage would occur at the center of the specimen. The major problem associated with this approach is that it is not possible to accurately measure tensile strain in the specimen. Results for the OFHC copper tests are shown in Fig. 20. The tensile strains are estimated from the post-tested cross-sectional areas of the fractured surfaces. In some instances, the OFHC copper specimens provided smooth enough fracture surfaces to make reasonable measurements. The Armco iron fractured in a ductile, tearing mode and could not be accurately measured. The 4340 steel fractures were nonuniform and occurred in the shoulder area of the specimen. The results of Fig. 20 show an additive effect of torsional and tensile damage. The damage is always less than unity at fracture, however, and this is consistent with the cylinder impact results.

48

G. R. JOHNSON

and W. H. COOK

‘;I.I::‘:

\

\

\

\

\

4

\

TORSIONAL DAMAGE

/ TENSILE DAMAGE

0.2

0.4

0.6

1.0

0.8

INITIAL DAMAGE DUE TO TORSION

Fig. 20. Accumulated

damage

for the torsional

SUMMARY

and tensile portions tests.

of the OFHC

copper

biaxial

AND CONCLUSIONS

A series of tests has been performed to determine fracture characteristics of OFHC copper, Armco iron and 4340 steel. These data have then been used to develop a cumulative-damage fracture model. The results indicate fracture is very dependent on the state of hydrostatic pressure, and less dependent on the strain rate and temperature. The fracture model has been evaluated with an independent series of cylinder-impact and biaxial tests. Although there is some uncertainty associated with the evaluation tests, it appears that fracture occurs earlier than predicted by the model. Acknowledgements-This Independent Development

work was funded Program.

by Contract

F08635-81-C-0179

from the U.S. Air Force,

and a Honeywell

REFERENCES [I] U. S. Lindholm, [2] [3] [4] [5] [6] [7]

[8] [9] [IO] [I I]

[12] [13]

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