technical report no. 28
TRANSCRIPT
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TECHNICAL REPORT No. 28
THE EFFECT OF PRESTRAINING UNDER DIFFERENT STRESS STATES ON THE FRACTURE AND FLOW
PROPERTIES OF 2S-0 ALUMINUM
In Cooperation With The Office of Navai Research, U. S. Navy
N6-ONR-273/I Project NR-031-049 SEPTEMBER 1953
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An Investigation of THE EFFECTS OF STRESS CONCENTRATION AND
TRIAXIALITY ON THE PLASTIC FLOW OF METALS
Technical Report No. 28
THE EFFECT OF PRESTRAINING UNDER DIFFERENT STRESS STATES ON THE FRACTURE AND FLOW PROPERTIES OF 2S-0 ALUMINUM
By
I. Rozalsky
Conducted By METALS RESEARCH LABORATORY
DEPARTMENT OF METALLURGICAL ENGINEERING CASE INSTITUTE OF TECHNOLOGY
In Cooperation With
OFFICE OF NAVAL RESEARCH, U.S. NAVY
Contract N6-ONR-273/I Project NR-031-049
Cleveland, Ohio ' October, 1953
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METALS RESEARCH LABORATORY DEPARTMENT OF METALLURGICAL ENGINEERING
CASE INSTITUTE OF TECHNOLOGY
Technical Report No. 28
THE EFFECT OF PRESTRAINING UNDER DIFFERENT STRESS STATES ON THE FRACTURE AND FLOW PROPERTIES OF 2S-0 ALUMINUM
Written by
•f. d&yJUky I. Roz&lsky
Approved by
o\J>f- &6&iJ>i __ (gc) L./rtbert Assistant Task Order Director
W. M. Baldwin, Jr. Task Order Director
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ft
Distribution List for Technical Report
No. 28 Copy No.
Contract N6-onr-273/1 October, 1953
Copy No. 7^5774- Project NR-031-049
1-2
ft
8
Chief of Naval Research Department of the Navy Washington 25, D.C. Attn: Code 423
Commanding Officer Office of Naval Research Branch Office 495 Summer Street Bost<->& 10, Massachusetts
Commanding Officer Office of Naval Research Branch Off'.ce 50 Church Street New York 7, N.Y.
Commanding Officer Office of Naval Research Branch Office The John Crerar Library Bldg. 10th Floor 86 £. Randolph Street Chicago 11, Illinois
Commanding Officer Office of Naval Research Branch Office 801 Donahue Street San Francisco 24, Calif.
Commanding Officer Office of Naval Research Branch Office 1030 Green Street Pasadena, California
Assistant Naval Attache for Research
London, England U. S. Navy FPO #100 New York, N.Y.
/
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Contract Administrator, SE Area, Office of Naval Res. Department of the Navy W» Ington 25, D.C. Att: Mr. K. F. Lynch
Director, Naval Res. Lab. Washington 25, D.C. Att: Technical Information
Officer
Dr. C. S. Smith Institute for the Study of Metal University of Chicago Chicago, Illinois
University of California Engineering Department Berkeley, California Att: Dr. J. E. Dorn
Dr. E. R. Parker
Professor F. A. Biberstein Department of Mech. Engr. Catholic University of America Washington, D.C.
Professor W. Prager School of Applied Mathematics Brown University Providence, Rhode Island
Dr. L. V. Griffis Applied Mechanics Division Armour Research Foundation Chicago, Illinois
Dr. W. C. MacGregor Dept. of Mech. Engr. Massachusetts Last, of Tech. Cambridge, Massachusetts
;...
}
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26 Director David Tayxor Model Basin Washington 7, D. C.
27 Armour Research Foundation Metals Research Division 35 W. 33rd Street Chicago, Illinois Att: W. E. Mahin
28-29 Director, Naval Res. Laboratory Washington 25, D. C. Attn: Code 2500, Metallurgy
Code 2020, Tech, Library
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Technical Library, TD-41(l)
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i
Commanding Officer Naval Air Material Center Naval Base Station Philadelphia, Penna. Attn: Aeronautical Materials
Laboratory
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Technica. Library AD3(i)
39 Superintendent, Naval Gun Factory Washington 20, D. C. Attn: Metallurgical Lab IN910
40 Commanding Officer U. 5. Naval Ordnance Laboratory White Oaks, Maryland
41 Commanding Officer U. S. Naval Ordnance Test Station Inyokern, California
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53 Commanding Officer Watertown Arsenal Watertown, Massachusetts Attn: Laboratory
54 Office of Chief of Engineers Department of the Army Washington 25, D. C. Attn: Research & Development Br.
AIR FORCES 55 U. S. Air Forces
Research and Development Div. The Pentagon Washington 25, D. C.
56-57 Air Materiel Command Wright-Patterson Air Force Base Dayton, Ohio
, Attn: Materials Laboratory MCREXM
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'" 'i :
OTHER GOVERNMENT AGENCIES
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Dr. Henry Eyring School of Mines It Mineral Ind. University of Utah Salt Lake City, Utah
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Dr. D. S. Clark Department of Mech. Engr. California Institute of Tech. Pasadena, California
University of Illinois Urbana, Illinois Att: Dr. N. M. Newmark
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68 Dr. R. M. Brick Department of Metallurgy University of Pennsylvania Philadelphia, Penna.
69 Bureau of Ships Department of the Navy Washington 25, D. C. Attn: Code 692
70 Professor M. Cohen Department of Metallurgy Massachusetts Inst. of Tech. Cambridge 39, Mass.
71 General Electric Company Research Laboratories Schenectady, New York Attn: J. H. Hollomon
72 Dr. Robert Maddin Department of Mech. Engr. Johns Hopkins University- Baltimore, Maryland
73 Dr. R. F. Mehl Director of Metals Research Lab. Carnegie Institute of Tech. Pittsburgh, Penna.
74 Brookhaven National Laboratory Information k Publication Div. Documents Section Upton, New York Attn: Miss Mary E. Waisman
75 Carbide and Carbon Chemicals Div. Plant Records Department Central Files (K-25) P. O. Box P Oak Ridge, Tennessee
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i
77 General Electric Company 85 Technical Services Division Technical Information Group P. O. Box 100 Richland, Washington Attn: Miss M. G. Freidank
78 Iowa State College 86 P. O. Box 14A, Station A Ames, Iowa Attn: Dr. F. H. Spedding
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U. S. Atomic Energy Commission New York Operations Office 90 P. O. Box 30, Ansonia Station New York 23, N. Y. Attn: Division of Tech. Inf. 91 and Declassification Service
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Dr. W. M. Baldwin, Jr. Case Institute of Technology
Dean Elmer Hutchisson Case Institute of Technology
Dr. A. R. Troiano Case Institute of Technology
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THE EFFECT OF PRESTRAINING UNDER DIFFERENT STRESS STATES ON THE FRACTURE AND FLOW
PROPERTIES OF 2S-0 ALUMINUM *
By
I. Rozalsky **
ABSTRACT
The effects of prestrain under conditions of different stress states but identical strain states upon the fracture and flow proper- ties in tension were obtained for commercially pure (2S-0) aluminum.
For prestrains of the same magnitude a prestrain stress state of simple compression results in a higher retained tensile ductility than does a prestrain stress state of biaxial tension. Also a change in prestrain stress state from simple compression to biaxial tension influences the shape of the fracture stress versus prestrain curve but does not affect the shape of the yield strength versus prestrain curve.
* This paper is based upon a portion of a research program conducted in the Metals Research Laboratory, Department of Metallurgical Engineering, Case Institute of Technology, Cleveland, Ohio in cooper- ation with the Office of Naval Research, U. S. Navy.
** Research Associate, Metals Research Laboratory, Case Institute of Technology.
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';>--•* - "•i-frfc
INTRODUCTION
The object of this investigation was & correlation of the prestrain
effects produced under conditions of different stress states but identical
strain states upon the tensile fracture and flow properties of 2S-0
aluminum.
Fig. 1* summarizes some of the possible typ*s of plastic strains
or prestrains that may be followed by a tensile test.
Tensile prestrain in the same direction as that of the subsequent
tensile test may be produced under prestrain conditions of different
stress states but identical strain states.
The conditions represented by Fig. la, the prestrain stress state
of simple tension, have been studied by Liu and Sachs (1)** for 24ST
aluminum and by Ripling and Baldwin (2) and McAdam and his associates
(3) for steel.
Bridgman (4) considered the conditions represented by Fig. lb, the
prestrain stress state of biaxial compression, in his studies of a number
of alloys.
The prestrain stress state of "cross-compressior"*** represented
* The subscripts a, b, and c for each stress (s) and strain (£,) may apply interchangeably to any of the three principal directions.
** Numbers in parentheses refer to the Bibliography at the end of this paper.
*** Compressive prestrain in one principal direction followed by testing in one of the other principal directions (90 degrees removed from the prestrain direction). The "cross-compression" results in a tensile prestrain in the test direction.
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•*•**
by Fig. lc and Id was considered in this paper as another possible means
of obtaining tensile pre at rain.
Compressive prestrain in the same direction as that of the subsequent
tensile test may also be produced under conditions of different stress states
but identical strain states.
The conditions represented by Fig. le, the prestrain stress state of
simple compression, were studied by Liu and Sachs for 24ST aluminum
(1), Ripling and Baldwin (2), McAdam (3) and Koerber and his coworkers
(5) for steel.
The prestrain stress state of biaxial tension represented by Fig. If
was considered in this research as another means of obtaining compressive
prestrain in the same direction as that of the subsequent tensile test.
MATERIAL AND PROCEDURE
The different prestraining conditions were carried out on specimens
cut from a 10 foot by 4 foot by 3/4 inch 2S aluminum plate and annealed at
650°F for 30 minutes.* The methods by which the tests were conducted
are described below:
Final Tensile Test
These specimens were of the dimensions shown in Fig. 2 except for
specimens taken in the normal direction of the plate after compressive
prestrain in the normal direction. Under these conditions, see Fig. le
* In the fully annealed condition the 2S aluminum is designated as 2S-0 aluminum.
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>*#
•
•
and If, the total length of the tensile test specimen was necessarily
decreased; however, the specimen diameter of 0.150 inch was retained.
Each tensile test was made with a crosshead speed of approximately
0.04 inch per minute, with all tests including the prestrains being made at
room temperature. Concentricity of loading during the tensile testing
operation was ensured by the use of a specially constructed fixture (6).
Prestrain According to Fig, la
The type of specimen used for simple tensile prestrain was of the
shape shown in Fig. 2. It was not considered necessary to re-machine
these specimens prior to their being tested in tension. Prestrains of this
type and subsequent tensile tests were mad_» for each of the three principal
directions, i.e., the longitudinal (rolling), transverse, and normal directions
of the aluminum plate. The direction of the tensile prestrain was the same
as the direction of the subsequent tensile test.
Prestrain According to Figs, lc and Id
The type of specimen used for cross-compressive prestrain was a
rectangular parallelepiped of the dimensions 0.72 inch by 0.50 inch by
0.50 inch or 0.72 inch by 2.00 inch by 2.00 inch. The 0.72 inch dimension
was in the normal direction of the «late the dimensions in the longitudinal
and transverse directions being determined by the direction of the subse-
quent tensile test and the magnitude of prestrain.
Specimens were prestrained by compressing them between two flat
parallel plates in a tensile test machine. A commercial preparation of
molybdenum sulfide was used as a lubricant on the plates to decrease
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*•#
flt friction between the plates and the specimen bases. This technique was
also used for simple compressive prestrain, see Fig. le.
For each of the three test directions two sets of data were obtained
by means of cross-compressive prestrain, e.g., for tests in the normal
direction, it was possible to prestrain by compression in either the
longitudinal or transverse direction to obtain a tensile prestrain in the
normal direction.
Prestrain According to Fig, le.
The type of specimen used for pre straining in simple compression
was a cylinder, the axis of which was parallel to the direction of com-
pression and the test direction. Those taken in the normal direction of
M the plate were 0.72 inch in height and 0.50 inch in diameter. The maximum
amount of prestrain was 6^* = -0.60; greater prestrains reduced the length
of the subsequent tensile test specimens to an impractical point. Those
taken in the longitudinal and transverse directions were of two sizes:
0.75 inch in height and 0.50 inch in diameter for compressive prestrains less than £. = -0.60, and
2.00 inch in height and 0.75 inch**in diameter for compressive prestrains greater than £_ = -0.60.
The maximum length of the tensile test specimen taken in the normal
direction that could be machined from the plate after heavy compressive
* o _ . Original Area P Area after Prestrain
** Narrow flats were left on the cylindrical surfaces of these specimens for the plate thickness was only 0.72 inch, see Fig. 4.
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<*-«*
presirain in the normal direction, according to Fig. le or lft was shorter
the greater the prestrain. It was observed that the effect of variation in
gage length upon the fracture and flow properties of the 2S-0 Aluminum
was not significant, except for the yield strength of specimens of exceed-
ingly short gage length.
The aluminum plate used in this investigation was anisotropic as
may be seen in Fig. 3 and 4 by the oval cross-section which originally
circular specimens assumed when compressed.
Prestrain According to Fig. If
Prestraining in biaxial tension was effected by bulging the 2S-0
aluminum plate by hydraulic means on a 1,000,000 pound hold-down press.
While thin sheet has previously been bulged in such presses (7) (8), the
bulging of thick sheet or plate introduces two difficulties:
(a) The bend stresses at the periphery of the bulge are such as to
destroy a simple biaxial stress state for some distance in from the edge.
Consequently, as large a diameter die (6 inch diameter with a specimen
of 10 inch by 10 inch surface dimensions) as could be handled by the press
was used. Tensile test specimens were taken from the center (pole) of
each dome (bulge) normal to the surface of the plate4*.
(b) Even at the pole of the dome a uniform biaxial strain state did
not exist from the inside surface to the outside surface as was evidenced
* Actually a simple biaxial stress state (stresses in the plane of the sheet only) is not achieved in the case of bulging thick plate since here the hydraulic pressure develops some slight stress normal to the plane of the sheet.
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•
by strains measured from 20-lines-to-the-inch grids photographically
applieo (9) to both the outside and inside surfaces.
After bulging, strain distributions on the top and bottom surfaces
of each bulge were plotted, Fig. 5,6, and 7, for the portion of the bulge
in the vicinity of the pole.
The strains were measured from the pole, see Fig. 5, in the longi-
tudinal direction of the plate at the top and bottom surfaces (e^T and e^gi
respectively) and in the transverse direction of the plate at the top and
bottom surfaces (e~.<r> &nd e——, respectively) of the bulge. The bottom
surface of the bulge was denote1, to be the surface in contact with the oil
during the bulging operation.
The first plate was bulged until fracture occurred. By extrapolation
of Thielsch's data for the hydraulic pressure required for fracture versus
thickness of sheet for 2S-0 aluminum (10), it was determined that an
approximate pressure of 6500 psi would be required to fracture 3/4 inch
plate under conditions of balanced* biaxial tension by means of hydraulic
bulging. Actually, it was experimentally determined that a pressure of
7500 psi was required. The difference in hydraulic pressure was perhaps
due in part to the slight triaxiality in stress state involved in the bulging
of the plate.
No tensile test specimens were taken from this bulge which fractured
under hydraulic pressure, because of the excessive non-uniformity of strain
distribution. More aluminum plates were bulged at successively lower
* Using circular bulging die.
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pressures, and from one specimen, see Fig. 5a, to nine specimens, see
W Fig. 7b, were taken from the pole of each bulge, the number of specimens
depending upon the uniformity of strain in the vicinity of the pole. Each
specimen was cut from the bulge so that its axis was perpendicular to the
top bulge surface.
Compressive prestrain in each of these specimens was computed
(a) from thickness measurements made with pointed micrometers and
(b) from the average strains in the plane of the plate taken on both the
inside and outside surfaces by the assumption of constancy of volume,
e> + d-2 + £3 = o
£} being the longitudinal strain, £3 the transverse strain and £3 the normal
strain. The results obtained by both methods for each specimen were almost
Jg identical.
A considerable strain gradient existed between the top and bottom sur-
faces of each bulge, see Pigs. 5, 6, and 7, and concomitantly, between the
bases of the tensile test specimens cut from the pole of each bulge. For low
hydraulic bulging pressures, the strains in the longitudinal and transverse
directions were compressive* at the bottom surface and tensile at the top
surface of the bulge, however, for high pressures, the strains at the top and
bottom surfaces were both tensile but varied greatly in magnitude.
To determine the strain gradient throughout the thickness, Knoop hard-
ness traverses were made on specimens cut from the poles of the bulges,
* The apparently anamalous compressive strains cannot be explained by the author at this time; however, their explanation may lie in the realm of bulge mechanics.
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-...• *9*
•
Fig. 8. The variation in Knoop hardness was essentially linear with
respect to thickness, even after taking into account the minima in these
curves where a transition from compressive to tensile strains occurred
at some distance from the bottom surface of the bulge. The hardness
was assumed proportional to the strain, thus the strain at any depth
could be obtained. Hence, although some of the tensile test specimens
did not fracture at the exact center of the gage length, the magnitude of
the prestrain at the point of fracture in the tensile test specimen could
be determined.
RESULTS
The effect of prestrain (£_) upon various fracture and flow properties
of 2S-0 aluminum in tension are represented in Figs. 9 to 24. The fracture
properties determined were the retained ductility (£f )* and the fracture
stress (Sf )**. The only flow property investigated was the yield strength
(0.2% offset).
Fracture Properties
Retained Ductility
Plots of retained tensile ductility versus prestrain for prestrain stress
states of simole comoression (/. <0). simole tension f£_>0L and cross- .-p •-. . . y,
compression (£p>0) are shown in Fig. 9, 10 and 11 for specimens prestrained
- Area After Prestrain Ap
'h ~ ln Final Area " "Af
Load at Fracture f ~ Area at fracture
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&£ "**
and tested in the normal, longitudinal and transverse directions, re-
spectively.
For each of the three test directions the curves for the prestrain
stress states of simple tension and cross-compression appear to coincide
in a straight line of 45 degree slope.
However, for tests taken in the normal direction, Fig. 9, for large
cross-compressive prestrains in the longitudinal and transverse directions,
there appears to be a tendency for deviation from the 45 degree line in a
manner analagous to the curve for biaxial compression, see Fig. 12. It was
not possible to justify this tendency for deviation from the 45 degree line,
because of experimental difficulties, e.g., prestrain specimen size limita-
tion in the normal direction and buckling tendencies in prestraining re-
stricted the magnitude of the prestrains to those shown in Fig. 9. In this
paper the curves for cross-compressive prestrain will be assumed to lie
along a line of 45 degree slope for all three test directions as shown in
Figs. 9, 10 and 11.
In these plots the following should be noted for each test direction:
The continuous nature of each of the curves from tensile prestrains
(£p>0) through zero prestrain (dp»0) to compressive prestrains (£p<0);
the maximum in the curve at a simple compressive prestrain of small
magnitude; and the subsequent decrease in retained tensile ductility (£{)
at larger compressive prestrains. These features have also been observed
in other investigations (l) (2).
A plot of the retained tensile ductility versus prestrain under a pre-
strain stress state of biaxial tension and a schematic curve of the expected
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^^
retained tensile ductility (4) versus prestrain under the stress state of
biaxial compression are shown in Fig. 12. For compressive prestrain
(biaxial tension), the curve is a straight line of very steep slope, e.g.,
the retained ductility decreases very rapidly with increasing compressive
prestrain. For tensile prestrain (biaxial compression), the curve has a
smaller slope than the curve for simple tension '45 degrees) after exceed-
ing some critical magnitude of prestrain (4).
The curves in Fig. 9, 10 and 11 were combined with similar curves
for 24S-T4 aluminum (l) and SAE 1340 steel* (2) in Fig. 13.
A comparison of the unworked ductilities of 2S-0 aluminum in each
of the three directions of the plate shows that the ductility in the normal
direction is somewhat greater than that in either the longitudinal or trans-
verse direction. At large compressive prestrains, however, the retained
ductility is greater for the longitudinal and transverse directions than for
the normal direction. Of course, for the tensile prestrains, the ductility
in the normal direction for any magnitude of prestrain is greater than that
in the longitudinal or transverse direction because of the relationship be-
tween the unworked ductilities (£ = 0) in the three directions.
The general shapes of the curves for 24S-T4 aluminum and SAE 1340
steel are similar to those for simple tensile or compressive prestrain for
2S-0 aluminum.
Because of the much lower unworked ductilities of 24S-T4 aluminum
and SAE 1340 steel in comparison with that of 2S-0 aluminum, the plots in
* For specimens taken in the longitudinal direction of round bar stock.
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•"Si
f
Fig. 13 are transposed to Fig. 14 where the ratio of retained ductility to
unworked ductility is plotted versus the ratio of prestrair. to unworked
ductility.
The curve for SAE 1340 steel is considerably higher than the other
curves, whereas the curve for 24S-T4 aluminum approximates somewhat
the curve for 2S-0 aluminum prestrained and tested in the longitudinal
direction.
For comparison purposes Fig. 15 was obtained by combining the
curves in Fig. 12 with the curve for the prestrain stress state of simple
compression in the normal direction in Fig. 9.
Fracture Stress
Plots of tensile fracture stress versus prestrain under conditions
of different stress states are shown for the normal direction, Fig. 16,
the longitudinal direction, Fig. 17, and the transverse direction, Fig. 18.
For each of the three principal directions for prestrain in simple
tension, the curve appears to be a horizontal line; however, for prestrain
stress states of simple compression and "cross-compression", each of
the tensile fracture stress curves exhibits a minimum for each of the three
test directions.
Fig. 19 shows plots of tensile fracture stress versus compressive
prestrain for the prestrain stress state of simple compression in each of
the three principal directions and for the prestrain stress state of biaxial
tension in the normal direction. Also included is the curve for 24S-T4
aluminum (l). The curves for simple compressive prestrain for each of
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... '*""*»
three directions in the 2S -O aluminum plate are similar in that each
exhibits a minimum at a relatively low magnitude of prestrain and then
rises; however, the curves for the longitudinal and transverse directions
do show a tendency to flatten out at higher prestrains at a fracture stress
of the order of magnitude of 50,000 psi. The curve for the prestrain stress
state of biaxial tension for 2S-0 aluminum differs in that it is a straight
line of steep slope with no minimum and no propensity towards flattening
out. The curve for 24S-T4 aluminum is a straight line of gentle slope.
The Effect of Prestrain Upon Flow Properties
Yield Strength
Plots of yield strength in tension versus prestrain for different pre-
strain stress states are shown for the normal direction, Fig. 20; the longi-
tudinal direction Fig. 21; and the transverse direction, Fig. 22. For a given
principal direction, there are but slight differences in the yield strength
curves for the various prestrain stress states.
Plots of yield strength in tension versus compressive prestrain for
the prestrain stress state of simple compression in each of the three princi-
pal directions and for the prestrain stress state of biaxial tension in the
normal direction are shown in Fig. 23. Also included is the curve for
24S-T4 aluminum (1). The curves for 2S-0 aluminum for simple com-
pression in the three principal directions are all quite similar. This
similarity can also be shown for the other prestrain stress states. Liu's
curve is of course much higher than those for 2S-0 aluminum, has a
minimum at a very small value of prestrain, and has a much steeper slope
at prestrains of small magnitude.
-12-
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DISCUSSION OF RESULTS
Pre straining in Biaxial Tension
It is apparent in Fig. 5, 6 and 7 that the strain anisotropy in the
bulge at the vicinity of the pole of the bulge is strain dependent; i.e., the
greater the longitudinal and transverse strains in the bulge surfaces, the
greater is the strain anisotropy.
The Effect of Prestrain upon the Retained Ductility
The inherent scatter of the data for the unworked ductility for 2S-0
aluminum in each of the three directions of the plate should be noted in
Figf.. 9, 10 and 11. This characteristic scatter in unworked ductility is
an implicit factor in the scatter of the retained ductility versus prestrain
data for the above curves.
The relatively large scatter in the retained ductility versus prestrain
data for the stress state of biaxial tension, Fig. 12, was probably caused
by a combination of variations in the previously mentioned bend stresses
and by the plate anisotropy. The trend of the dita might have been more
apparent if it had bees possible to obtain larger compressive prestrains
by means of biaxial tension. This condition was not possible with the
material and equipment used in this investigation.
The greater unworked ductility in the normal direction than in the
longitudinal direction of the 2S-0 aluminum plate appears anomalous when
compared with the results in the published literature (11). The discrepancy
cannot be explained at this time.
The differences between the curves for retained tensile ductility versus
13-
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•***§
prestrain in simple compression in the normal direction and in biaxial
tension, Fig. 15, seem to be of fundamental significance. The unknown
mechanism which causes an increase in retained tensile ductility for
small compressive prestrains for a prestrain stress state of simple
compression appears to be inoperative for a prestrain stress state of
balanced biaxial tension.
The absence of a discontinuity in the prestrain curve from simple
compressive to simple tensile prestrain in Fig. 13 possibly indicates
that the small increase in retained ductility for small values of com-
pressive prestrain has only a slight effect upon the fracture mechanism
in tension.
A change in prestrain stress state from simple tension to "cross-
compression" does not affect the retained tensile ductility, see Fig. 9,
10 and 11, but a change in prestrain stress state to simple compression
or biaxial tension, Fig. 15, modifies the retained tensile ductility curve.
From Fig. 1 the prestrain stress state of cross-compression is
apparently intermediate between simple tension and biaxial compression.
The results, however, indicate that for each of the three test directions
the curve for retained tensile ductility versus prestrain in cross-compres-
sion, Figs. 9, 10 and 11, coincides with the curve for simple tension, rather
than lying somewhere between the curves for prestrain in simple tension
and biaxial compression, Fig. 15.
Fracture Stress
Although the retained ductility and fracture stress are both considered
-14-
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to be fracture properties, the change in prestrain stress state from simple
tension to "cross-compression" (for both, £p>0) caused no change in the
retained tensile ductility curve, Figs. 9, 10 and 11, but caused a change in
the shape of the tensile fracture stress curve, Figs. 16, 17 and 18.
These results should be considered from the point of view that the
fracture stress is not a simple phenomenon. The fracture stress of a
metal depends upon the ductility, the strain hardening rate and the yield
strength of the metal. The interrelations between the above variables and
considerations of their relative magnitudes could certainly produce minima
in those curves for tensile fracture ductility when the prestrain stress state
is changed from one of simple tension to simple compression or "cross-
compression", see Figs. 16, 17 and 18, or change the slope of the fracture
stress curve from a horizontal line for a prestrain stress state of simple
tension to a straight line of steep slope for a prestrain stress state of
biaxial tension, see Fig. 16.
The curves for prestrain in simple compression for the three directions
of the 2S-0 aluminum plate exhibit certain similarities, see Fig. 19. There
is a minimum in each of these curves at a small value of compressive pre-
strain. Then the curves for the longitudinal and transverse directions rise,
flattening out at larger prestrains at fracture stress values of about 50,000
psi. It seems possible to expect that the curve for the normal direction
would also have flattened out after rising from the minimum, had it been
possible to obtain larger prestrains in the normal direction.
Liu's curve for 24S-T4 aluminum is of different shape from the above
-15-
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.v S-**
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curves for 2S-0 aluminum. The difference may be explained by the large
difference in ductility between 2S-0 and 24S-T4 aluminum. Koerber (5)
found that the tensile fracture stress for a mild steel consistently decreased
with increasing compressive prestrain. But McAdam (3) reported that with
increasing compressive prestrain, the tensile fracture stress of an annealed
chromium steel first decreased to a minimum and then increased continu-
ously. Complex curves for fracture stress versus prestrain were obtained
by Backofen and his associates (12) under conditions of prestrair in torsion
and testing in tension. It is possible that a difference between the stress
state in prestraining and in testing tends to complicate the horizontal curve
expected when the stress states for prestrain and testing are of the same
type.
The curve for fracture stress versus prestrain in balanced biaxial
tension is significantly different from that for simple compressive prestrain
in the normal direction, F'ig. 19. Apparently, the effect of the balanced
biaxial tensile prestrain is to mask completely those characteristics present
in the curve for simple compressive prestrain and to cause only a rapid
linear decrease in fracture stress with increasing compressive prestrain.
Yield Strength
The evident proximity of the curves for all prestrain stress states,
see Figs. 20 to 23, indicates that a difference in prestrain stress state has
no significant influence upon the effect of prestrain on the yield strength in
tension.
-16-
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.•-*-.
1
t CONCLUSIONS
The fracture properties (stress and strain) of 2S-0 aluminum depend
not only upon the nature and magnitude of the prestrain, but also upon the
stress state under which a given prestrain is effected, see Fig. 24.
Thus, for example, for each test direction for compressive prestrains
of the same magnitude, a prestrain stress state of simple compression re-
sulted in a higher retained tensile ductility than did a prestrain stress state
of biaxial tension.
For tensile prestrains of the same magnitude (after a critical amount
of prestrain) a prestrain stress state of biaxial compression resulted in a
higher retained tensile ductility than did a prestruin stress state of simple
tension.
However, for tensile prestrains of the same magnitude, a prestrain
stress state of simple tension resulted in the same retained tensile duc-
tility as did a A estrain stress state of cross-compression.
For compressive prestrains of the same magnitude, a prestrain stress
state of simple compression resulted in a higher tensile fracture stress
than did a prestrain stress state of biaxial tension.
The shapes of the curves obtained for tensile fracture stress versus
prestrain differed considerably when the prestrain stress state was varied.
No significant changes in the tensile yield strength versus prestrain
curves were obtained by variations in the prestrain stress states.
-17-
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ACKNOWLEDGMENTS
This work was conducted in cooperation with the Office of N&va.
Research, U. S. Navy. The aid and advice of Dr. W. M. Baldwin Jr.,
Mr. L. J. Ebert, Dr. E. J. Ripling and other meiibers of the Metals
Research Laboratory are greatly appreciated.
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BIBLIOGRAPHY
(1) S. I. Liu and G. Sachs, The Flow and Fracture Characteristics of the Aluminum Alloy 24ST after Alternating Tension and Compression, Metals Tech., Vol. 15 (June, 1948), TP2392.
(2) E. J. Ripling and W. M. Baldwin, Jr., Overcoming Rheotropic Brittle- ness: Precompression Versus Pretension, Trans. Am. Soc. Metals, Vol. 44 (1952), p. 1047-1054.
(3) D. J. McAdam, Jr., G. W. Geil and W . D. Jenkins, Influence of Plastic Extension and Compression on the Fracture Stress of Metals, Trans. A.S.T.M., Vol 47 (1947), p. 554-574.
(4) P. W. Bridgman, Studies in Large Plastic Flow and Fracture, McGraw-Hill (1952), p. 293-310.
(5) F. Koerber, A. Eichinger and R. Moeller, The Behavior under Tensile Stress of Metals Deformed by Compression, Mitt. Kaiser-Vfiiheim Inst. Eisenforschung, Duesseldorf, Vol. 26 (1943), p. 71-88.
(6) G. Sachs, J. D. Lubahn and L. J. Ebert, Notched Bar Tensile Tests on Heat Treated Low Alloy Steels, Trans. Am. Soc. Metals, Vol. 31 (1943), p. 136-160.
(7) G. Sachs, G. Espey, and G. B. Kasik, Circular Bulging of Aluminum Alloy Sheet at Room and Elevated Temperatures, Trans. Am. Soc. Mech. Engrs., Vol. 68 (1946), p. 161-173.
(8) W. T. Lankford, A. R. Low and M. Gensamer, The Plastic Flow of Aluminum Alloy Sheet under Combined Loads, Trans. A.I.M.E., Vol. 171 (1947), p. 574-604.
(9) W. F. Brown, Jr. and M. H. Jones, Strain Analysis by Photogrid Method, Iron Age, Vol. 153 (Sept. 12, 1946), p. 50-55.
(10) H. Thielsch, Bulge Testing of Sheet Metal, Metal Progress, Vol. 56 (July, 1949), p. 86-88.
(11) L. J. Klingler and G. Sachs, Fracturing Characteristics of Aluminum- Alloy Plate, Jour, of the Aero. Sciences, Vol. 15, No. 12 (Dec. 1948), p. 731-734.
(12) W. A. Backofen, B. B. Hundy and J. Wulff, The Ductile Fracture of Metals, Tech. Report No. 3, O.N.R. Contr. N5ori-07841, Project No. NR 031-356 tMy 30, 1951), p. 7-8.
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«*JW'WJ£VtrflMfilftHIBBPS
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FIG.I IVARIOUS PRESTRAIN STRESS AND STRAIN STATES UNDER ISOTROPIC CONDITIONS. CLEAR BLOCKS INDICATE SHAPE BEFORE PRESTRAINING.
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![Page 29: TECHNICAL REPORT No. 28](https://reader031.vdocument.in/reader031/viewer/2022020701/61f8aa8374822b1105221162/html5/thumbnails/29.jpg)
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0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 COMPRESSIVE PRESTRAIN -—, €p
Fig. 3: DEPENDENCE OF STRAIN ANISOTROPY UPON COMPRESSIVE PRESTRAIN IN »/4 INCH THICK 2S-0 ALUMINUM PLATE.
$ *—«.•. ii«»,..-i«»»^.\-«w;»o-%.--.. vmifcm&,g&&*ZM8fcZZ?£'2J!2r'Ji- "L'<':':
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(a) Cylindrical Specimens of 2S-0 Aluminum Compressed Various Amounts in the Transverse Direction of the Pl»te. The Normal (N) and Longitudinal (L) Directions of the Plate are Shown.
(b) Cylindrical Specimens of 2S-0 Aluminum Compressed Various Amounts in the Longitudinal (Rolling) Direction of the Plate. The Normal (N) and Transverse (T) Directions are Shown.
FIG. 4: - PLATE ANISOTROPY AS EVIDENCED BY SPECIMENS PRESTRAINED IN SIMPLE COMPRESSION.
![Page 31: TECHNICAL REPORT No. 28](https://reader031.vdocument.in/reader031/viewer/2022020701/61f8aa8374822b1105221162/html5/thumbnails/31.jpg)
cr 8 t
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STATES.
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Fig. iO^EFFECT OF TENSILE (Co > 0) AND COMPRESSIVE (£p*0)PRESTRAIN IN THE LONGITUDINAL DIRECTION Or W THICK 2S-0 ALUMINUM PLATE UPON THE RETAINED TENSILE DUCTILITY jN THE LONGITUDINAL DIRECTION FOR VARIOUS PRfcSTRAIN STRESS
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STATES. STRESS
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![Page 38: TECHNICAL REPORT No. 28](https://reader031.vdocument.in/reader031/viewer/2022020701/61f8aa8374822b1105221162/html5/thumbnails/38.jpg)
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Fig 12: THE EFFECT OF PRESTRAIN IN BIAXIAL TENSION (£p<0)AND IN BIAXIAL COMPRESSION (£p>0}(SCHEMAT!C AFTER BRIDGMAN} UPON THE RETAINED TENSILE DUCTILiTY IN THE NORMAL DIRECTION OF »/4" THICK 2S~0 ALUMINUM PLATE.
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Flg.l3:THE EFFECT OF PRESTRAIN IN SIMPLE COMPRESSION (€P<0)0R IN SIMPLE TENSION (£p > 0) UPON THE RETAINED TENSILE DUCTILITY FOR 8/4-THICK 2S-0 ALUMINUM PLATE FOR EACH OF THE THREE PRINCIPAL DIRECTIONS. THE PRESTRAIN DIRECTION UfAO TUC O AIIC A t> TUC fMOCATIAM /MT TUT »¥m«j mi. winint. #•*<«* ins. UIHLU iivn yr inc.
SUBSEQUENT TENSILE TEST. !
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-
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PRESTRAIN/UNWORKED DUCTILITY—-£ P/£
Fig.:4:THE EFFECT OF PRESTRAIN IN SIMPLE COMPRESSION (£p < 0)0R IN SIMPLE TENSION (£p>0)UPON THE RETAINED TENSILE DUCTILITY FOR W THICK 2S -0 ALUMINUM PLATE FOR EACH OF THE THREE PRINCIPAL DIRECTIONS. THE PRESTRAIN DIRECTION WAS THE SAME AS THE DIRECTION OF THE SUBSEQUENT TENSILE TEST.
,
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FiQ.I5: THE EFFECT OF PRESTRAIN STRESS STATE UPON THE RETAINED TENSILE DUCTILJTY IN THE NORMAL DIRECTION OF »/4 " THICK 2S-0 ALUMINUM PLATE. THE CURVE FOR BIAXIAL GOMPRESSIVE PRESTRAIN IS SCHEMATIC AFTER BRIDGMAN (4j.
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. PRESTRAIN~»lFlg.lf) BIAXIAL TENSION
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40
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PRESTRAIN ~(Flg. I«) SIMPLE COMPRESSION NORMAL DIRECTION
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PRESTRAIN ~*(Flg la) SIMPLE TENSION NORMAL DIRECTION
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ERSE Dlf _. . J
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• 0.4 +0.8 +1.2 +0.4 -0.8 +1.2 PRESTRAIN IN NORMAL DIRECTION —£p
FiQ.16: EFFECT OF VARIOUS PRESTRAIN STRESS STATES UPON THE TENSILE FRACTURE STRESS IN THE NORMAL DIRECTION OF »/4 INCH THICK 2S-0 ALUMINUM PLATE.
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PRESTRAIN-^ (Fig. It) SIMPLE COMPRESSION LONGITUDINAL DIRECTION
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PRESTRAIN —(Flfl. I c) CROSS-COMPRESSION NORMAL DIRECTION
PRESTRAIN «~~» (Fig, I a) SIMPLE TENSION LONGITUDINAL DIRECTION
H.2 0 0.4 f 0.8 1.2
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PRESTRAIN~(F g. I d)_ CROSS-COMPRESSION TRANSVERSE DIRECTION
+ 0.4 f 0.8 + 1.2 0 + 0.4 + 0.8 1.2 PRESTRAIN IN LONGITUDINAL DIRECTION—£p
Fig. 17: EFFECT OF VARIOUS PRESTRAIN STRESS STATES UPON THE TENSILE FRACTURE STRESS IN THE LONGiTUDiNAL DIREC- TION OF 3/4 INCH THICK 2S-0 ALUMINUM PLATE.
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PRESTRAIN ^o(F!fl. la) SIMPLE TENSION TRANSVERSE DIRECTION +0.4 ^UW f.2
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_PRE8TRASN <r^> (Fig. I d) CROSS-COMPRESSION LONOITUDINAL DIRECTION
+ 0.4 +0.8 +1.2 0 +0.4 +0.8 +1.2
PRESTRAIN IN TRANSVERSE DIRECTION <^6p
Fig. 18: EFFECT OF VARIOUS PRESTRAIN STRESS STATES UPON THE TENSILE FRACTURE STRESS !N THE TRANSVERSE DIRECTION OF »/4 INCH THICK 2S-0 ALUMINUM PLATE.
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Fig. 19: COMPARISON OF COMPRESSIVE PRESTRAIN EFFECTS UPON THE FRACTURE STRESS IN TENSION OF 2S-0 ALUMINUM FOR VARIOUS PRESTRAIN STRESS STATES AND PRESTRAIN DIRECTIONS.
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5 J NORMAL DIRECTK O Of—ro<4 -0t8
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CROSS-COMPRESSION LONGITUDINAL DIRECTION
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T_PRESTRAIN ^ (Fig. I d) CROSS-COMPRESSION TRANSVERSE DIRECTION
0 +0.4 +0.8 -H.2 NORMAL DIRECTION «~€p
Flg.20: EFFECT OF VARIOUS PRESTRAIN STRESS STATES UPON THE YIELD STRENGTH(0.2 PER CENT OFFSET) IN TENSION IN THE NORMAL DIRECTION OF */4 INCH THICK 2S-0 ALUMINUM PLATE.
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_PRESTRAIN ~-(Fig. I •). SIMPLE COMPRESSION LONGITUDINAL DIRECTION
PRESTRAIN—(Fig. I a) _ SIMPLE TENSION LONGITUDINAL DIRECTION
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CROSS-COMPRESSION TRANSVERSE DIRECTION
+0.4 +0.8 +1.2 +0.4 +0.8 1.2
PRESTRAIN IN LONGITUDINAL DIRECTION— Ip
Fig2l: EFFECT OF VARIOUS PRESTRAIN STRESS STATES UPON THE YIELD STRENGTH (0 2% OFFSET) !N TENSION IN THE LONGITUDINAL DIRECTION OF 8/4 INCH THICK 2S-0 ALUMINUM PLATE.
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.PRESTRAIN ^—(Flfl. Id)- CROSS-COMPRESSION LONGITUDINAL DIRECTION
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PRESTRAIN IN TRANSVERSE DIRECTION ~6p
Fig. 22: EFFECT OF VARIOUS PRESTRAIN STRESS STATES UPON THE YIELD STREN6H / A A« vrroLI | III i cndiuiM N tin
TRANSVERSE DIRECTION OF 3/4 INCH THICK 2S-0 ALUMINUM PLATE.
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-0.2 -0.4 -0.6 -0.8 -1.0 -12 -1.4 COMPRESSIVE PRESTRAIN^— £p
Fig.23 COMPARISON OF COMPRESSIVE PRESTRAIN EFFECTS UPON THE YIELD STRENGTH (0.2%0FFSET}iN TENSION
A ki rv HI1U FOR8/* INCH THICK 2S-0 ALUMINUM PLATE
24S-T4 ALUMINUM (I) FOR VARIOUS PRESTRAIN STRESS STATES AND DIRECTIONS.THE PRESTRAIN DIRECTION WAS THE SAME AS THE DIRECTION OF THE SUBSEQUENT TENSILE TEST.
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PRESTRAIN ~6P
Fig.24; SCHEMATIC REPRESENTATION OF RETAINED TENSILE DUCTILITY VERSUS PRESTRAIN FOR VARIOUS PRESTRAIN STRESS STATES FOR 2S-0 ALUMINUM PLATE. THE PRESTRAIN DIRECTION IS THE SAME AS THAT OF THE SUBSEQUENT TENSILE TEST. THE MEAN STRESS (Sm)IS GIVEN FOR EACH PRESTRAIN STRESS STATE IN TERMS OF THE YIELD STRENGTH IN TENSION.