Pr 32.413/3:1829
NATIONAL DEFENSE RESEARCH COMMITTEE ARMOR AND ORDNANCE REPORT NO. A-217 (OSRD NO. 1829) DIVISION 2
DISCUSSION OF ENERGY MEASUREMENTS IN TENSION IMPACT TESTS
AT THE CALIFORNIA INSTITUTE OF TECHNOLOGY
by
P. E. Duwez, D. S. Clark
and D. S. Wood
LIBRARY
UNIVERSITY OF WASHINGTON
NOV 14 1950
Copy No.
97NATIONAL DEFENSE RESEARCH COMMITTEE ARMOR AND ORDNANCE REPORT NO. A-217 (OSRD NO. 1829)
DIVISION 2
DISCUSSION OF ENERGY MEASUREMENTS' IN TENSION DA PACT TESTS
AT THE CALIFORNIA INSTITUTE OF TECHNOLOGY
by
P. E. Duwez, D. S. Clark
and D. S. Wood
■ ’ •' •
Approved on September 9> 1 9h3	£'2222222^
for submission to the Division Chief	... _ -	-
D. S. Clark5 Offi cial Investi
gator for Contract OEMsr-3b8
Merit P. White} Secretary
Division 2
Approved on September 1^, 19h3 for submission to the Committee
UW
'/c'fi-'''-'"1
> o
'John E. Burchard, Chief
Division 2
Structural Defense and Offen


/







Preface
' The work described in this report is pertinent to the projects designated by the Navy Department Liaison Officer as NO-11 and NS-1O9 and to Division 2 project P2-3O3.
This work was carried out and reported by the California Institute of Technology under Contract OEMsr-3h8.
No. 3h to C. to No. 35 to C. to
Initial distribution of copies of this report
Nos. 1 to 25, inclusive3 to the Office of the Secretary of the Committee for distribution in the usual manner;
No. 26 to R. C. Tolman, Vice Chairman, NDRC;
No. 27 to R. Adams, Member, NDRC;
No. 23 to F. B. Jewett, Member, NDRC;
No. 29 to J. E. Burchard, Chief, Division 2;
No. 30 to W. Bleakney, Deputy Chief, Division 2;
No. 31 to V. F. Davidson, Office of the Chairman, ’NDRC;
No. ’32 to R. A. Beth, Member, Division 2;
No. 33 to H. L. Bowman, Member, Division 2;
Curtis, Member, Division 2;
Lampson, Member, Division 2;
No. 36 to W. E. Lawson, Member, Division 2;
No. 37 to H. P. Robertson, Member, Division 2;
No, 38 to F. Seitz, -Jr-., Member, Division-2;
No. 39 to A. H-. Taub, Member, Division 2;
No... to. to E. B. Wilson, Jr., Member, Division^;
Nos. hi and h2 to R. J. Slutz, Technical Aide, Division 2;
No. h3 to the Army Air Forces (Brig. Gen. B. W. Chidlaw);
Nos. hh and h5 to the Corps of Engineers (Col. J. H. Stratton, Lt. Col. F. S. Besson, Jr.);
No. h6 to the Ordnance. Department (Col. S. B. Ritchie);
No. h7 ho M. P. White, Technical Aide, Division 2;
No. h8 to Watertown Arsenal (Col. H. H. Zornig);
No. h9 to Frankford Arsenal (Lt. Col. C. H. Greenall);
Nos. 50 and 51 to Aberdeen Proving Ground (R. H. Kent,
0. Veblen);Nos. 52 and 53 to Bureau of Ordnance (Lt. Comdr. T. J. Flynn, A. Wertheimer);
No. 51 to Naval proving Ground (Lt. Comdr. R. A. Sawyer);
No. 55 to David Taylor Model Basin (Capt. W. P. Roop);
Nos. 56 and 57 to Bureau of Ships (Lt. Comdr. R. W. Goranson, E. Rassman);
No. 56 to Bureau of Yards and Docks (Par plans Division);
No. 59 to Naval Research Laboratory (R. Gunn);
No. 60 to Rear Adm. R. S. Holmes, California Institute of Technology;' •
No. 61 to H. F. Bohnenbiust, Consultant, Division 2;
No. 62 to J. G. Kirkwood, Consultant, 'Division 2;'
No. 63 to N. M. Newmark, Consultant, Division 2;
No. 61 to D. S. Clark, Consultant, Division 2;
No. 65 to Th. von Karman, Consultant, Division 2;
No. 66 to A. Nadai, Consultant, Division 2;
No. 67 to P. W. Bridgman, Consultant, Division'2.'
The NDRC technical,reports section for armor and ordnance edited this report and prepared it for duplication.'CONTENTS
Abstract ........
Section
Page
1
1.	Introduction ........................................  1
2.	General theoretical considerations .................. i|
3.	Impact velocities	below	the	critical	velocity	....	U
h.	Impact velocities	above	the	critical	velocity	....	11
9. An approximate evaluation of the difference
between the impulses at the moving end and at the fixed end of the specimen at the beginning of
impac t 			11 13
6.	The response of the dynamometer 		
7.	Accuracy and reproducibility of experimental results 				18
8.	Conclusions 		2h
	List of Figures	
Figure		Page
1 .	Schematic force—time diagram for a specimen 8 in. long 							7
2,3.	Computed stress-time diagrams for SAE 1020 cold^ rolled and SAE 2380 steels 		7
M-	Computed stress-time diagrams for annealed copper specimens at impact velocities of 112 and 129 ^ti/sec 		8
6.	Dynamometer mounting 		19
7.	Stress-strain diagram for SAE 1020 cold-rolled steel 		19 16
8.	Stress-time diagram at the fixed end of 8-in. specimen at an impact velocity of 190 ft/sec ....	
9.	Recorded force-time diagram for SAE 1020 cold-rolled steel 						16
10,11.	Reproducibility tests for SAE 1020 annealed steel and for SAE 1020 cold-rolled steel 		22*DISCUSSION OF ENERGY MEASUREMENTS IN TENSION IMPACT TESTS
AT THE CALIFORNIA INSTITUTE OF TECHNOLOGY
Abstract
........
This report is submitted for the purpose of clarifying and justifying the manner in which ultimate strength and energy are measured under dynamic conditions in the Impact Testing Laboratory of the California Institute of
■ Technology. Evidence is presented to show (i) that the force-time diagram recorded at the fixed end of the specimen has the form predicted by theory, (ii) that for most metals the energy given oy a fixed-end dynamometer may be taken as reliable, (iii) that in any case a correction may be applied such that the energy corresponding to the impulse measured at tne fixed end of the specimen will not be in error by more than 10 percent'' and (iv) that the experimental error in the measurement of energy as judged by reproducibility is not more than + 10 percent.
1.	Introduction
Over the past'five or six years, considerable effort has been expended in the study of the influence of impact' velocity on the tensile properties of metals and alloys. In some cases, only the
total energy required to rupture a, tension specimen has been
1,2/
determined as a function of velocity^— On the other hand, some investigators have employed various means of determining the force
1/ H. C. Mann, ASTM 36, 85' (1236),
"High velocity tension impact tests," proc.
2 / H. C . test specimens
Mann, "A fundamental ," Proc. ASTM 37, 102
study of the diagram of impact (1937).- 2 -
„ „ ,	+. r + * 31,5/	„
specimen as a function of time--- or of average
acting on a
• 6// strain?
The method used at the California Institute of Technology
consists of recording an effective force-time diagram derived from
a resistance-sensitive strain gage which is referred to as a
"dynamometer." The equipment and procedure have been used in 7-11/
securing the results presented in previous reports-;----- The dyna-
mometer is rigidly fixed to a heavy base of the testing machine; the specimen.is then screwed into the dynamometer. Hence, the dynamometer is said to beat the fixed end of the specimen. The velocity of the moving end of the specimen, taken as the velocity of the-.impacting jaws, is determined by a stroboscopic method.
The energy required to'fracture the specimen has been computed by
<

3/ D. S. Clark and G. Datwyler, "Stress-strain' relations under tension impact loading," Proc. ASTM 3d, 98 (1938).
U/ D. S. Clark, "The influence of impact velocity on the tensile characteristics of some aircraft metals and alloys," NACA technical note, No. 868, Oct. 19h2.
$/ Deforest, MacGregor and Anderson, "Rapid tension 'tests using the two-load method," Metals Technology, Dec. 19h1,- p. 1.
6/ M. J. Manjoine and A. Nadai, "High speed tension tests at elevated temperatures," Proc. ASTM hO, 822 (19h0); Trans. ASMS;
J. App. Mechanics, June 19h1, p. A77.
!_/ P. E. Duwez, D. S. Wood and D. S. Clark, The propagation of plastic strain in tension, NDRC Report A-99 (OSRD No. 931).	’
8/ P. E. Duwez, D. S. Wood and D. S. Clark, The influence of specimen length on strain propagation in tension, NDRC Report A~W£~(OSHD No. 957).	’
9/ P. E. Duwez, D. S. Wood, D. S. Clark and J. V. Charyk,
The effect of stopped impact and reflection on the propagation of
plastic strain in tension, NDRC Report A-108 (OSRD No. 986).
10/ P. E. Duwez, D,' S'. Wood and D. S. Clark, The influence of impact velocity on the tensile properties of plain~carbon steels
and of a cast steel armor plate, NDRC Report a-158 (OSRD No. 12?U).
11/ P. E. Duwez, D. S. wood and D. S. Clark, Dynamic tests of the tensile properties of SAE 1020 steels, armco iron and 17ST
i- 3 -
multiplying the area under the force-time diagram by the impact velocity. This may be expressed by the relation,
nt
W =	/ r F(t)dt,	(1)
w'o
in which Vx is the impact velocity3 F(t) is the force-time relation and t is the time elapsed from the instant of impact to the instant at which F returns to zero.
The purpose of this report is to present an analysis of the significance and of the accuracy of the values of the energy obtained by this method. The discussion is presented in two parts which cover, .respectively, the theoretical and the experimental aspects of the question. The energy required for rupture should be measured at the moving end. Accordingly, the first step in the theoretical development is concerned with the correction that must be added to the impulse at the fixed end to obtain the value at the moving end. The evaluation of this correction is obtained from the theory of the propagation ol plastic strain. Also a method is presented by which an adequate.approximation of this value can be determined more simply. Finally, the influence of the vibrations of the dynamometer on the measurements is analyzed. It is shown that they influence the shape of the recorded stresstime diagram, but not essentially the value of the impulse.
Finally, this report deals with the accuracy of the experimental results and their reproducibility. Of the two measurements involved, the accuracy of the impulse measurement is discussed in detail and the accuracy of the velocity measurement is high enough to be of little importance in this discussion. However, it may be said that just before the impact the velocity of the impacting jaws is measured within 1 percent. The velocity during the impact can be assumed to be constant since the energy of the rotating jaws is 91,000 ft lb at a velocity of 2> ft/sec, and the energy absorbed by the specimen is of the order of 2000 ft lb.- h -
2,	General theoretical considerations
----------- ----..................
The energy required to fracture the specimen is taken in this discussion to be the impulse at the moving end multiplied by the impact velocity. This impulse corresponds to the area under the force-time diagram up to the instant at which the force first returns to zero. In the first part of this discussion, it will be assumed that the dynamometer is perfect and, therefore, will indicate the true force-time relation. As indicated in the introduction , the dynamometer is attached to the fixed end of the specimen. The impulse computed from the force-time relation is not correct owing to the difference between the forces at the two ends of the specimen. -This difference, and therefore the difference in the impulses at the fixed end and at the moving end, can be determined theoretically, as will be shown in Sec. 3. Such a method is admittedly indirect. It is justified, however, by the fact that
the theory has been verified to give fairly accurate results.
12/
particularly for the computation of the stress-time diagram—'and by the fact that the difference between the values of the impulses is small in comparison with the impulse values.. The difference between, the. theoretical values will thus be .assumed to be the difference between the true values.
The' comparison of the stresses at the two ends of the specimen will be -given in two steps. The first step v.-ill refer to the conditions at the beginning of the impact up to the instant at which necking and rupture occur. The second step will deal with the behavior during necking and rupture of tho specimen. Two cases . must be distinguished depending on whether the impact velocity is smaller or larger than the critical velocity. A complete discussion can be given only for the first case.
3,	Impact velocities below the critical velocity
From the principles given dy von Karman, the impulses at the fixed and the moving ends of the specimen can be computed. The
12/ Reference 9.afore-mentioned principles and the details of such computations
have been presented in other reportsg
For purposes of
comparison, the schematic force-time relations for both the moving and fixed ends of a specimen 8 in. -long are given in Fig. 1. The impulse at each end is ootained by taking the- areas under the corresponding curve. Theoretically, the diagram at the moving end starts at time t = 0 with a stress depending on the impact velocity Then the stress increases to its maximum value	After necking
and rupture have occurred, the stress finally drops to zero. The diagram at the fixed.end differs from the one at the moving end in that the stress remains at zero during the time it takes the elastic wave to travel the length of the specimen. Then, at' a given time, the stress jumps to a value determined by the reflec- 1 tion of the elastic wave from the fixed end. The stress then increases progressively, finally reaching the maximum value. g* . Eventually,/the stress drops to zero. The time at which the dynamometer at the fixed end indicates rupture is not the same as would-, be indicated by a dynamometer at the moving end. This will
be ..discussed, in detail in Sec. 3(b).	.1.1 ............ ...
!
The difference between the impulses at the moving and fixed ends is the difference between the areas under the two curves of Fig. T, or the algebraic sum of areas 1, 2, 3 and h. The difference AQX in impulse at the beginning of the impact is (area 1)
- (area 2) +• (area 3)1 The difference at the ;termination of the impact is - (area 1). As shown in Sec. 3(b), this area could in -some cases be -positive.	- -
.  . .  . ; . .. ... . „ , . . .................. ................
■ ‘	13/ 'Th. von-Karman, The propagation of plastic deformation
in solids, NDRC Report a-29 (OSRD No. 363).
1 h/ Th. von Karman, H. F. Bohnenblust and D. H. Flyers, The propagation of plastic waves in tension specimens of finite length,
NDRC Report A-103' (OSRD No. 9h6).	"
13/ H. F. Bohnenblust, J. V, Charyk and D. H. Hyers, Graphical solutions for problems of strain propagation in tension!- 6 -
(a) Conditions at the beginning of the impact. — The theoretical stress-time diagrams at the fixed end and at the moving end of the specimen have been computed for three different metals. the specimens were taken as 8 in. long and 0.3 in. in diameter.
The shape of the force-time diagram is greatly dependent upon the ratio of the ultimate stress to the elastic limit. Therefore, the three metals are chosen in order to cover the widest possible range'for this ratio. The first portion of the stress-time diagrams both at the moving end and at the fixed end of the specimen as computed for these metals is given in Figs. 3, h and 5. The differences between the impulses at the moving end and at the fixed end at the beginning of the impact as determined from these curves are given in Table I.
Table I. Difference between impulses at moving and at fixed ends of the specimen at the beginning of impact for several metals.
Metal	Approximate Ratio of Ultimate Strength to Proportional Limit	Impact Velocity (ft/sec)	Difference Between Impulses at Moving and Fixed Ends AQ-, (lb sec)
Annealed copper	6	112	Area 1 - area 2 + area 3
(Fig. b)			= 0.28
Annealed copper	6	199	Area 1 - area 2 = 0.77
(Fig. £)			
SAE 23bO steel, 31	1.6	100	Area 1 - area 2 + area 3
Rockwell C (Fig. 3)			= 0.3b
SAE 1020 cold-rolled	1 .2	70	Area 1 - area 2 - 0.2b
steel (Fig. 2)			
(b) Conditions at the end of impact. — At the end of the impact, the diagrams at the fixed end and at the moving end will generally differ, and the.difference between them will depend upon the position along the specimen at which rupture occurs. If it takes place at a-point located at-a distance x from the fixed end, the time taken by the unloading elastic wave to go from the rupture%
%
£7‘g./. Jebe/no/ic force-dime diagram for
& S/oec/mer? a in. iorg^—fixed end,-moving
end.
J'/re^Qo4/b//d)
			tt	
				
	r.			
				
				
				
				
o	o./	o.z
Timefmii/isec)
f/g 2. Computed a/rejs~ Time diagram fordAE/ozo co/d- roi/ed ^e ei&
Time (millisec)
Fig. 4-. Computed s/re$$ - /irr?e diagram for anneafed copper specimen a/ an impac/ ue/oci/y of nz ff/aec-
fixed endp-——mouing end.
Pug.s. Comp u fed ^sfr ess-dime diagram for annea/ed copper specimen af an impacf ue/ocifg of /<W ff/aec ---fix ed end,— — —m o xing en d.
\e»t- 9 -
point to a dynamometer at the fixed end is given by x/c , in which
c0 is the velocity of propagation of the elastic wave. During
that time, the load on the dynamometer 'remains <r A , in whicri A m 0 ., °
is the initial cross-sectional area of. the specimen and <r is the m ■
maximum apparent stress. Therefore, the impulse indicated by an ideal fixed-end dynamometer from the time rupture occurs to the time the load becomes zero is Aq x/c . In the same manner, the impulse indicated at the moving end after rupture occurs is’
<S^Ao (L - x)/cq. The difference between the impulses recorded’ at the moving and the
fixed ends is, therefore
_ tr a — = y A
c	m o c m o c
O	O	n
(2)
If the rupture takes place at the fixed end, x = 0 and the difference in impulses between the two dynamometers is <r A l/c .■ If
m o ' o
rupture takes place in the middle ol the specimen,, x — L and ’ the difrerence between the two impulses is zero. If rupture takes■ place at tne moving end, x = L and the difference between the two impulses is - (y Aq L/c^. M. P. A'hite : has called attention to the fact that this simple formula does not correspond to the propagation of the stopping effect after rupture. The time-lag between the instant
mometer registers a
x c
o
where
of rupture and the instant at which the dyna-decroase in stress is	;
x - 1	x - 2 i
------° + 2_________J
+ 2
(3)
2 p c m o
t =
0	"H1. V
’ i
and where the sum is extended to the first negative term* It is
JjV M. P, White, "The behavior of tensile impact specimens during and after rupture at impact velocities below the critical velocity," unpublished NDRC memorandum, July 1, T . Available
«	in the files of Division 2.
j.he symbol vj denotes the velocity of the point in the f	specimen at which, it ruptures.Table II. Comparison of Impulses at fixed and moving end of specimen.
		„	_					 Approximate Evaluation of Comparison -with True Evaluation	, ~ °oW fenpuA onap pp poodsog qppi aoaag oSnpuooaoj	- 10 - vo co o o vo o- O\ _u O O V\ Ov ' 1	CO Ov O. 1 1	cm co • • T i	i i i i
	(oos qp) % = sov + fov + % 6©spudup popooaaoQ	_V O v- co V— in CM Ov o V, n r-	T— MO- CM O T—	V- j .	-V CM ■ OV nV in in	co VO x— co CM x-
	(OOS qp) eov + ?ov	_V O r- b-vO O CM O O O V- O 1	X~	OV O nV- x~ C' 1	nv co -V o o’ I	CO VO r- CM o’
	(oos qp^ s c/ta^ = idv fUOppO9UJO0	cm cm o- t— CO CO in m O ' ‘	*	vO vO CM CM o’	CO CO T—	V— o’	Ov CM co m o’
Ci O •H •P g- rH1 g O E-i	00 L X ~(96/0V) fespndup poanseoyi jo aeaag ©Supuooaoj	OV C— o in o’ o’ O* VO v-	b— | 1	1	Ov vO OV co 1	CM CM Ov O 1	i i i i 1
	(oos qp) 07 + 9o = fQspndmp snap	O vO x— co ’— _V _V V- vO in co cm	cm r— CM o T	r- Ov o nv vo in	i 1 I 1
	(oos qp) Qh fospndwg pug-poxpg poansnopi Appupuowpaodxg	in in O O IV V CM CM		•u\ v\ • • V\ 1A	O x- • • Cd t—
	(oes qp') e0V + 'T0V = OV fooueaejjpQ pupop	O - V x- co VO O -V r- O O r- o 1	Ov x— O : _V T- O’ 1	in. o o 1	1 1 I 1
	(oes qp) e^oV fq.oedwp jo pug; pe oouoaejjpq ©spudup	CM CM nV _V co CO vO vO o’’’.. 1 1	in m b— r— o’ i	vQ vO CM CM o’ J	v0 vo CM CM O 1 I
	(oes qp) ^7 fpondrag jo psapg pu eoueaejjpQ ©spndiup	CO CO b— C— CM CM O- l>~ O*	nV co co o’	m in CM CM o’	I 1 :	i j
j	(oes/pj)	: fZppoopoA pond up	OJ Cd G\ C\ v— t— O\ O\ V— V		V	 V—	o o o o	o o b- n-	o o in o x— CM
	« sanooQ quoag qopqM pu pug;	Fixed Moving : Fixed Moving	fcuO Vj Ci •H C1 s	bo vi ci 8 ’£ •H O	bO bfl ci ci •£ ■£ c o fc=rv kxM	j j
T?WI		aeddco popeeuuy	0 ppoojoop fpoeps once a VS	/pTOOpOA puopppao J-Aopog poops pop OSO I	ZpTOOpOA j pnopppao 1 QAoqy poa-ppco SYSseen that for steel specimens at the impact velocities investigated this formula reduces to the first term. For copper specimens} more terms must be considered.
The difference AQ2 between the two impulses at the termination of the impact has been computed according to these formulas for the metals already considered under two conditions, namely, that rupture takes place at the moving end and at the fixed end. The results are given in Table II. The total difference AQX + AQ2‘ between the two impulses at the moving end and at the fixed end is also given in Table II, assuming that rupture takes place at either end. This difference is then added algebraically to the impulse measured experimentally at the fixed end of the specimen. The percentage difference between the impulse at the fixed and moving ends is given in Table II. In tests made on steel below the critical velocity and on annealed copper below 112 ft/sec this difference does not exceed 10 percent. However, .for annealed copper at 200 ft/sec, the difference is of the order of 70 percent. This Is due to the particular shape of the stress-time curve of this material.
h. Impact velocities above the critical velocity
The impulse recorded at the fixed end of a specimen when the impact velocity is above the critical value is theoretically zero, since the specimen should break very near the moving end and no wave should travel along the specimen. The impulse at the moving end should also be very small since the force would be applied during the very short time it takes to rupture the specimen. Practically, because of the necking, the rupture does not take place instantaneously and some impulse is always indicated by the fixed-end dynamometer.
5. An approximate evaluation of th. difference between the impulses
at the moving end and at the fixed 3nd of the specimen at the
beginning of impact	r
The analysis presented in the previous sections requires the = computation of the stress-time diagrams at the fixed and moving12. -
ends of the specimen. The following analysis may be used as an approximation in- order to avoid such computation. The -error made at the beginning of impact by measuring the impulse at the fixed end of the specimen is
(h)
where v is the velocity of a particle at a particular point w is the weight of' the specimen and g is the acceleration due to gravity. If a linear velocity -distribution along the specimen from the impact velocity to 0 is assumed, then this error can be approximated- by computing the quantity,
w V-l
g “
(5)
Therefore, this represents approximately the difference between the impulses recorded at the fixed and the moving ends at the beginning of impact. The value of has been computed for the three metals. As shown in Table II, does not differ very much from the true correction AQX. The correction AQ2 previously computed for the end of impact combined with AQ-[ gives an approximate value of the total difference between the impulses at the moving and fixed ends. If these quantities are added to the measured impulse, the percentage error from the true value is below 10 percent even in.the case of annealed copper at 200 ft/sec. In view of the other results given in this report, it is seen that the approximate evaluation of the correction is adequate.

This correction may also be applied to impact velocities above the critical value, In this case, Eq. (>) would give a value probably too large because the mass actually accelerated is only a fraction of the total mass of the specimen, since the necking always takes place very near the moving end. Therefore, if the correction given, by Eq. (f>) combined with AQ2 is added to the measured impulse, the new value obtained is probably' larger than the true impulse, and is certainly so if 2AQ{ is added instead of
}
- 13 -
<
The response of the dynamometer
In the following section, a discussion is presented in which the force-time diagram recorded by a dynamometer of the type used at the California Institute of Technology is compared with the true force-time diagram obtained with a hypothetical dynamometer of infinite rigidity, which would record the stress without influencing its value.
<
The mounting of the actual dynamometer is represented in Fig. 6(a). The part of the dynamometer to which the strain gage is attached is a tube of 2-in. inside diameter and 13/16-in. outside diameter. The dynamometer is screwed into a heavy steel block. The study of the wave propagation in the dynamometer mounting, represented in Fig. 6(a), would be..very complicated. In order to simplify the computation, an almost equivalent mechanical system has been considered and is presented, in Fig. 6(b). The dynamometer is replaced by a cylinder of equivalent cross-sectional area, and its length is the length of the tubular part to which the strain gage is attached.
Computations of theoretical stress-time diagrams have been made for cold-rolled steel specimens 0.300 in. in diameter and 8 in. long for an impact velocity of 1p0 f't/sec. Curve 1 of Fig. 7 is the static stress-strain curve for such a specimen. The plastic range of this curve has been approximated in curve 2 of Fig. 7 by two straight lines. Wo different stress-time diagrams have been computed. The first one, curve 1 of Fig. 8, is the stress-time relation that an ideal, infinitely rigid dynamometer would record at the fixed end of the specimen; this diagram consists of two horizontal steps that are due to the shape of the approximate stress-strain curve taken for the computation. The second stresstime diagram, curve 2 of Fig. 8, has been computed upon the basis of a dynamometer mounted as represented in Fig. 6(b); the block to which the dynamometer is fastened is very long' compared with the length of the dynamometer.- 1h -
The computation of the wave propagation in such a mechanical system is^made by employing the principles explained in previous reports'?- From these computations, curve 2 of Fig. 8 is derived.
The ordinate of this curve is the force on the dynamometer expressed in terms of the apparent stress in the specimen. The force is zero from time t = 0 up to the time at which the elastic wave reaches the front end of the dynamometer (point A). From this time on, the force increases proportionally up to the time it takes for the elastic wave to travel the length of the dynamometer (portion-AR of the curve). At B, the elastic wave is partially reflected by the block to which the dynamometer is attached,' and the load 'increases to point- G, where an unloading wave originates at the front end of■the dynamometer,■thus decreasing the load to ' point E. - This process is repeated-and produces a vibration that is progressively damped by the successive imperfect reflections of waves.	■	•	■	•
The oscillation finally disappears, and the stress during the time from H to I on the diagram is theoretically slightly lower than the true value that would be-indicated by an ideal dynamometer, curve 2 of Fig. 8. After a time, the plastic wave reaches the ’ fixed end of the dynamometer, and the force On the dynamometer ' oscillates again as'in the previous case.
In order to compare the impulse indicated by an ideal and an actual dynamometer, the two force—time diagrams, curves 1 and 2 of Fig. 8, were integrated from point A to point H, which includes the region of greatest oscillation. The values so obtained were 0.323 and 0.306 lb sec for the ideal and actual dynamometer, respectively. These do not differ by more than 6 percent. If the integration is made from point £ to a point corresponding to a later time, the difference decreases.
1
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of Fig. 8. In comparing the actual diagram with the computed one, it should be borne in mind that the stress-strain curve has been approximated by straight lines. The general shape of the experimental diagram bears some similarity to the theoretical diagram, curve 2 of Fig. 8. The peak in stress recorded at the beginning, of the diagram is obviously due to the reflection of the elastic wave in the dynamometer. Therefore, the stress computed from this peak will' not be a measurement of the dynamic proportional limit or yield point of the metal. After the first peak, .the amplitude of the oscillation on the diagram (Fig. 9) decreases for a time and then increases again. This increase in amplitude is due to a plastic wave reaching the front end of the dynamometer.
The ultimate stress reached in the experimental diagram is higher than that in the computed diagram. This might be attributed to one of two causes, namely, that the dynamic stress-strain diagram is higher than the static stress-strain diagram on which the computations are based, or that the dynamic force-calibration of the dynamometer differs from the static calibration. The dynamometer operates within the elastic limit, and there is no reason to believe that the modulus of elasticity is affected by the rate of strain. Furthermore, experimental results with two metals having approximately the same ultimate strength, such as SAE 1020 annealed steel and 17ST aluminum alloy, do not show the same proportional increase of ultimate strength. Therefore, it appears that the difference between the maximum stress in the experimental and theoretical stress-time diagrams is due to a rise of the stress-strain diagram under dynamic conditions.
This discussion shows that the shape of the dynamic stresstime diagram recorded by the dynamometer used is explained on theoretical grounds. The value of the ultimate stress is significant, but not the value at the first peak.18 -
7. Accuracy and reproducibility of experimental results
The accuracy of the force-time diagram recorded by a resistance-sensitive strain gage dynamometer cannot yet be determined exactly. The force scale is established by a static calibration within 1 percent. This calibration can be considered reliable since it is improbable that Young's modulus is influenced by the rate of strain.
A possible uncertainty lies in the fact that the response of the electric circuit might be different for the force-time diagram and the calibration line. The time scale of the oscillator now in use has been calibrated, but its stability is questionable. A crystal oscillator will be built in the near future in order to improve the time measurement. Reproducibility tests have been made in order to obtain some indication of the consistency of the recording device.
In previous reports, there has been some scatter in the data on which were based the curves of energy to produce rupture versus impact velocity. Likewise, there has been a scatter in the values
ultimate strength* Since these data are obtained from the
s»

oscillographic record, the reproducibility tests should indicate whether or not the scatter is due to the performance of the dynamometer.
In order to investigate the scatter of the results obtained with a resistance—sensitive dynamometer, tensile impact tests were made on specimens of SAE 1020 cold-drawn steel and SAE 1020 annealed steel. The specimens were 0.300 in. in diameter and had a gage length of 8 in. Six specimens of the cold-drawn steel were tested at an impact velocity of 30 ft/sec, and six more specimens "were tested at an impact velocity of 130 ft/sec. These velocities are
below and above the critical velocity, respectively, for this material as shown in a previous report-?-7 Six specimens of the
annealed steel were tested at 73 ft/sec and six at 173 ft/sec,
values, which are below and above the critical velocity, resnec-. 18/
tively,'as previously reported-?- All tests were made in the manner
previously described.
«- 19 -
The results of these tests are given in Tables III and IV. Values omitted in these tables correspond to experiments in which some failure in the apparatus made it impossible to obtain a record. The values of ultimate strength, percentage elongation in 8 in., and energy per unit volume to produce rupture are presented in Figs. 10 and 11. In these tests, only the accuracy of the elongation measurement is known. The change in length of the specimen after rupture is measured with an error of less than 0.2£ percent. Consequently, the variation observed in the percentage elongation values from one specimen to another tested at the same impact velocity is not due to measurement inaccuracy.
It is probable that the necking of the specimen in a dynamic test does not occur consistently at exactly the same time during each test. Any delay in the occurrence of necking allows a greater uniform strain to take place along the specimen and a greater percentage elongation is therefore measured.
The values of the ultimate strength given in Tables III and IV have a maximum variation from the average of 11.5 percent for one- specimen. For most specimens, it is smaller than 5" percent.
The ultimate strength is determined from the force-time diagram recorded by the dynamometer by selecting the average stress in the latter portion of the diagram. The vertical scale of the forcetime diagram is calibrated immediately after each test by inserting in the oscillograph circuit a known resistance in place of the resistance of the dynamometer. It is difficult to give an estimate of what part of the scatter is due to differences between specimens and what part is due to experimental error. An experimental error of ± 5 percent on the force scale of the oscillograph seems to be
a safe estimate. This estimate is corroborated by comparing 67
.	19/
experiments— made on SAE 1020 cold-rolled steel specimens in which the gage length ranged from 1 to 10 in. and in which the Impact velocities ranged from 2p to 200 ft/sec. The test results- .20 -
Table III. Reproducibility tests and general results for SAE 1020 annealed steel.
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’able IV. Reproducibility tests and general results for SAE 1020 cold-draw steel.
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Imp act veto city 73 ft/sec
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Impact velocity n£ft/sec
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n


- 23 -
did not show any systematic variation with the impact velocity.
The maximum deviation was 12 percent3 out the standard deviation was £ percent.
As has been explained in Sec. 3(b) of this report., the time computed from the measured elongation and the impact velocity is not exactly equal -to the time recorded in the diagram. The difference between the two times can be estimated theoretically, but in some cases the experimental value is much greater than the value predicted by the theory. For example} in the results reported in Table IV for specimen No. 2U, the percentage elongation measured on the specimen after rupture was 9.6 percent, whereas the elongation computed by means of the time scale of the diagram was 11.0 percent. For other steels previously tested, this inconsistency has been even greater and cannot be accounted for by the stopping effect. These results show that the timing device is not at present accurate enough to consider the distinction between the actual time elapsed from the beginning of the impact to the moment of rupture and the time during which the force is applied to the dynamometer. It is, therefore, superfluous to take into account the influence of the stopping effect on the force-time diagram.
This erratic behavior of' the time scale influences the measurement of the energy. To minimize this, the impulse determined from the force-time diagram recorded at the fixed end has been corrected as follows. If 1^ is the measured impulse, if is the percentage elongation measured on the specimen after rupture by means of the comparator and if is the percentage elongation computed from the time scale of the diagram, the corrected impulse Ic is taken as
I = I h /%. c med
(6)
This correction is approximate and in many cases important. Furthermore, the results obtained are so altered that the exact
corrections discussed in this report are no longer logically
applicable^ therefore} it seems superfluous to compute them. If
in the future, however, a more accurate time scale is developed,
the corrections given in the first part of the report will be
applied.
This discussion can be summarized as follows. When several tensile impact tests are made on identical specimens at the same impact velocity, tne elongation may vary by as much as 20 percent around the average value. This scattering is not due to experimental error, but is inherent in the dynamic process. Furthermore, the force recorded at the fixed end of the specimen, and, in particular, the ultimate strength, varies about 10 percent around the average. A. part of this variation, amounting to 5- percent, is probably due to experimental error, while the other part is .due to possible, differences in structure from one .specimen to another. .
Also, the energy, absorbed by a specimen may differ from the average
value by as much as 20 percent. This range of. scatter is the	h
logical result of the scatter in elongation and in ultimate
strength.	I
8. Conclusions
It has been shown that at velocities below the critical value the correction to be applied to a fixed-end dynamometer to obtain the correct value of energy can be established by means of theoretical stress-time diagrams. This correction has been found to be less than 10 percent for tests made on steel specimens and as high as 70 percent for annealed copper at high velocity. An approximate method of computing this correction has been presented which may be in error by 10 percent at most. This means that if an approximate correction is applied to the energy measured directly by a fixed-end dynamometer, the value s.o obtained will not be in error from the true value by more than 10 percent.
At velocities above the critical value, it has been shown that
n
an appropriate correction gives a value of energy that is larger
b- 25' -
than the true value. If such a correction is applied to the curves of energy versus impact velocity presented in previous reports, the drop in energy above the critical velocity still remains.
By the application of the theory of wave propagation, an analysis of the dynamometer response has been presented. It has been shown that a dynamometer mounted at the fixed end of a specimen gives a stress-time diagram of reliable form. Furthermore, the impulse obtained by integrating the force-time diagram is within ± 2 percent of the true value provided the time scale is precise. The nature of the vibrations presented in the force-time diagram has been analyzed, and it has shown that the first peak in the curve bears no relation to the proportional limit or yield point of the specimen.
By means of a series of tests on identical specimens, it has been shown that the elongation may vary by as much as 20 percent around an average value. This variation is shown to be due entirely to the variation of the time at which fracture occurs under dynamic conditions. In these same tests, the ultimate strength has been found to vary by as much as 10 percent around an average value. It is probable that the error involved in the force measurement is about + 5' percent. The variation in elongation produces a corresponding variation in the value of the energy. Variations of as much as 20 percent are observed^ part of them are to be attributed to experimental errors .
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