Localized melting at separation of AISI 4340 steel tensile samples

Localized melting at separation of AISI 4340 steel tensile samples

Materials Science and Engineering, A142 ( 1991 ) 107-114 107 Localized melting at separation of AISI 4340 steel tensile samples David D. Makei and H...

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Materials Science and Engineering, A142 ( 1991 ) 107-114

107

Localized melting at separation of AISI 4340 steel tensile samples David D. Makei and H. G. F. Wilsdorf Department of Materials Science, University of Virginia, Charlottesville, VA 22903-2442 (U.S.A.)

(Received November 19, 1990)

Abstract Localized melting due to plastic deformation during the separation of tensile samples has previously been investigated in three commercial titanium alloys. In the present study similar melting accompanied by radial cracking has been observed in AISI 4340 steel tensile samples tested at quasi-static strain rates. However, localized melting and radial cracking are absent in samples strained at high strain rates and samples fractured using an ultrasoft test system in which a large spring is placed in series with the tensile sample. Analysis of the results shows that the suppression of radial cracking and localized melting occurs because high rate plastic deformation prior to separation causes the neck region to be adiabatically heated above the ductile-brittle transition temperature range, causing the material to fail in a fully ductile manner.

1. Introduction

Localized melting due to the heat energy caused by plastic deformation has been commonly observed in materials which undergo high rate shear strain, particularly in the cases of friction and adiabatic shear. Recent investigations of certain titanium alloys [1-6] have shown that localized melting also occurs during the final separation of tensile samples. Titanium alloys are particularly prone to adiabatic heating since their high strength, low heat capacity and low thermal conductivity make for high heat production rates and low heat dissipation rates. Fracture surface features which have been associated with localized melting at separation in titanium alloy tensile samples are shown in Fig. l(a) and defined in Fig. l(b). These unusual fracture surface features fall into three general categories, "open surface shear zones", "transition dimples" and mixed mode spheroidized dimples with associated spheroidized surface debris. All these features are found in areas of shear, typically on shear lips, and the surfaces of the melted regions and transition dimples are finely textured, a feature called "microroughening" [3-6]. Sections cut through the locally melted regions accentuate the role of localized shear in the melt0921-5093/91/$3.50

ing process. Highly localized shear is found directly below the melted regions, an example of which is shown in Fig. 2 for Ti-8Mn heat treated to an acicular a platelet microstructure. The localized shear and the substantial temperature increase realized in these areas suggest a role of adiabatic shear. If this is so, this would indicate adiabatic shear resulting from applied tensile forces, not the shear and compressive forces with which it has previously been associated. An interesting result of the temperatures required for melting is the emission of visible light. Photographs of the separation of Ti-6AI-4V tensile samples taken with high speed film [3-5] clearly show that the origins of light emission correspond to the regions of localized melting. In a recent study of the effect of microstructure on localized melting in Ti-6AI-4V it has been shown that localized melting at separation can be suppressed by heat treating to an a colony microstructure [6]. This agrees with the results of a model calculation that a dominant feature required for localized melting is the high rate of dislocation production [7]. Also, the a colony microstructure reduces the size of the smooth areas of shear on the fracture surfaces and decreases the crack propagation rate by increasing the tortuosity of the crack path. These results © Elsevier Sequoia/Printed in The Netherlands

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Fig. 2. This micrograph shows a section below a region of localized melting on the shear lip of a Ti-8Mn tensile sample fracture surface. The deflection of acicular a platelets clearly shows the localized shear directly below the unusual surface features.

(b), Fig. 1. (a) This micrograph of a Ti-6AI-4V tensile sample contains examples of the three major fracture surface features associated with localized melting during separation: an open surface shear zone, transition dimples and mixed mode spheroidized dimples with associated spheroidized surface debris. (b) This is a schematic diagram which defines the locations in (a) of (A) the open-surface shear zone, (B) mixed mode spheroidized dimples with associated spheroidized surface debris and (C) transition dimples.

emphasize the need for a high separation rate and large-scale shear surfaces for local melting to Occur.

2. Experimental procedure T h e material used in the present study was AISI 4340 ultrahigh strength steel. Cylindrical tensile samples with a gauge diameter of 3.4 mm and a gauge length of 12 mm were machined with the tensile axis parallel to the final rolling direction. Heat treatment of the samples started with a 1 h austenitization in sealed quartz capsules filled with argon, after which the capsules were broken

and the samples quenched in stirred oil. Tempering was done at 435 °C in a tube furnace purged with argon, after which the samples were air cooled in the argon-purged tube. T h r e e types of tensile tests were conducted: normal quasi-static tests with an applied strain rate of 8.3 x 10 -4 s - l ; high rate tests conducted at the Fraunhofer Institute in Bremen, F.R.G. at rates between approximately 80 and 3000 s -~ using a flywheel device; and ultrasoft tests, which were similar to the quasi-static tests except that a large spring was placed between the cross-head of the testing machine and the sample, reducing the stiffness of the test system from about 2.5 x 107 N m-1 to approximately 4.8 x 104 N m-1. T h e ultrasoft tests were designed to study the effect of increased stored elastic energy on separation. A profile projector was used to make x 100 tracings of both pieces of the post-fractured tensile samples. T h e s e tracings could then be used to "reconstruct" the shape of the samples just prior to separation. This facilitated the estimation of the volumes included in the sample necks. 3. Experimental results

3.1. Tensile results T h e quasi-static mechanical properties of the samples are summarized in Table 1. These results agree with previous results of AISI 4340 heat treated to a 435 °C temper [8]. High rate tests

109 TABLE 1 Quasi-static tensile results (average of two tests) for AISI 4340 steel (435 °C temper) Ultimate tensile stress 0.2% Offset yield stress Elongation at UTS Elongation at fracture

1320 MPa 1230 MPa 1.02 mm 2.25 m m p e r 12 mm

performed at the Fraunhofer Institute in Bremen, ER.G. indicate a slight increase in ultimate tensile strength (UTS) and yield strength with increasing rate, but elastic wave effects make these results difficult to interpret. Non-linearities in the elastic portion of the load-elongation curve introduced by the large spring used in the ultrasoft device make yield stress and elongation determinations difficult, but the measured UTS values agree with those of the quasi-static tests.

3.2. Low magnification scanning electron microscopy (SEM) results At magnifications of × 24 the fracture surfaces of the normal quasi-static test samples, as shown in Fig. 3(a), contain three distinct regions: a central fibrous area surrounded by an annulus of radial cracking and an outer annulus of shear lip. Examples of fracture surfaces of the high rate and ultrasoft test samples are shown in Figs. 3(b) and 3(c) respectively. Although the surfaces of the high rate samples tend to be slightly less regular than those of the ultrasoft samples, both types of surfaces contain only central fibrous cracking areas surrounded by shear lips. The absence of radial cracking on the high rate and ultrasoft sample surfaces is an important characteristic which will be discussed later.

3.3. High magnification SEM results Fracture surfaces were carefully inspected at higher magnifications for indications of localized melting. The first samples investigated were those from the high rate tests and these surfaces showed no signs of melting to the resolution limit of the microscope (approximately 100 A). Likewise, the ultrasoft test samples showed no signs of melting and, except for being slightly rougher in the central fibrous areas, the surfaces were generally indistinguishable from those of the high rate tests. Surfaces resulting from the normal quasi-static tests were considerably different. Besides the already mentioned presence of radial cracking in

the central crack area, at numerous points near the outside of the shear lip areas these surfaces contained regions which were similar in character to the locally melted regions found in the earlier titanium studies. These areas stand out clearly at moderate magnifications (on the order of × 3000) because, as in the case of the melting in the titanium samples, the locally roughened areas are brighter than the surrounding material on the SEM screen and the micrographs. Figure 4(a) shows a shear lip of one of the normal quasi-static test samples, with the arrow indicating the position of the area shown in Fig. 4(b). Figure 4(b) contains locally melted areas indicated by arrows, one of which is shown at higher magnification in Fig. 4(c). The regions of melting in the steel samples are in some ways different from those in titanium, as shown in Fig. 1, but they bear important similarities. In both cases the locally melted regions are made up of spheroidized dimple walls surrounded by shear dimples. The melted material appears different from the surrounding material not only because of the spheroidized features but also because the spheroidized dimples do not appear to have formed by shear separation. This makes the melted areas different in character from the shear dimples typically found at the borders of the shear lip areas. Also, in both these samples and the earlier titanium samples the melted features are adjacent to smoothly sheared areas, typically in the form of bands. On the titanium sample fracture surfaces these opensurface shear zones are almost completely dimple free, as can be seen in Fig. 1, while in the steel sample fracture surfaces the sheared areas are smoother than the surrounding material but frequently contain holes, making them identical to "holey smeared" regions which have previously been associated with the initiation of adiabatic shear in high rate pure shear experiments on 4340 steel [9-11]. An example of an opensurface shear zone on a 4340 fracture surface can be seen directly above the spheroidized region in Figs. 4(b) and 4(c). 4. Discussion

4.1. Radial cracking The first question which arises from the results is "why do fracture surfaces of the quasi-static test samples contain radial cracks while the radial cracks are absent in the high rate and ultrasoft

110

m

Fig. 3. (a) Low magnification micrograph of the fracture surface of a quasi-static AISI 4340 steel tensile sample with a 435 °C temper showing a well-defined shear lip and a region of radial cracking surrounding the central area of fibrous fracture. (b) Low magnification micrograph of the fracture surface of a high strain rate (applied rate 8.3 x 10 z s-~) AISI 4340 steel tensile sample with a 435 °C temper. Note the total absence of radial cracking. (c) Low magnification micrograph of the fracture surface of an AISI 4340 steel tensile sample fractured using an ultrasoft set-up in which a large spring is placed in series with the sample, decreasing the

Fig. 4. (a) Micrograph of a portion of the shear lip of a quasistatic AISI 4340 (435 °C temper) tensile sample which contains regions of localized melting (arrow indicates region contained in (b)). (b) Higher magnification micrograph of a portion of the shear lip shown in (a) which contains regions of localized melting (indicated by arrows). (c) High magnification micrograph of one of the regions of localized melting shown in (b) which is directly below a smoother-than-normal hand, which is an example of an open-surface shear zone on a 4340 steel fracture surface.

machine stiffness by a factor of approximately 500. Note the absence of radial cracking as in the high rate sample surface shown in (b).

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test samples?". Radial cracking in steels has been extensively investigated, not only in tensile samples but also in various types of service failures [12-14], and it has clearly been shown to result from rapid crack growth. It is frequently the dominant fracture surface feature on surfaces which result from high rate failures such as those caused by impact and explosive loading. This might imply that radial cracking should be expected in the high rate and ultrasofl test samples, where the elongation rate immediately prior to separation is much greater than in the quasi-static tests, but this is not the case. The reason why the radial cracks are found only in the normal quasi-static test samples is that a higher applied strain rate does not necessarily cause a higher crack propagation rate. In a test system such as the one used in this study the elastic energy stored in the loading train (load frame, load cell, grips and sample) results in elastic deformation in the direction of the tensile axis which is large compared to the amount of axial displacement which occurs during actual separation. In our normal quasi-static test system (without the large spring in series with the sample) the stiffness of the total loading train is about 2.5 x 107 N m - 1. Since separation occurs very rapidly even for quasi-static tests, the decrease in load with elongation due to elastic relaxation is obviously less than the decrease in load-bearing capacity with elongation during separation. Under conditions such as this, where the driving force for crack propagation comes primarily from elastic energy stored in the test system, the crack propagation rate is basically controlled by the amount of localized ductility at the tip of an advancing crack, i.e. in the "process" and plastic zones of the crack tip, n o t by the applied strain rate (cross-head speed). Crack tip ductility is the basic mechanism responsible for the ductile-brittle transition with temperature, and the increase in ductility with ambient temperature is a key to understanding the suppression of radial cracking found in the high rate and ultrasoft tests. Studies of AISI 4340 Charpy V-notch samples show that the fracture toughness, as measured by absorbed impact energy, increases dramatically as the ambient temperature increases through the ductile-brittle transformation temperature range [15]. Similarly, fracture surfaces of AISI 4340 tensile samples show that at temperatures below the ductilebrittle transformation temperature range radial

cracking makes up the majority of the central crack area [13, 14], and as the temperature increases through the ductile-brittle transformation temperature range, the percentage of central crack area displaying radial cracking continuously decreases until the radial cracks completely disappear above the transition range. When metals undergo plastic deformation, a very large percentage of the energy of deformation is non-conservative and, by means of drag forces generated by the interactions of dislocations with phonons, electrons and other dislocations, this energy takes the form of heat. In a study of various metals Farren and Taylor [16] found that in certain steels approximately 86.5% of the total work of tensile deformation is evolved as heat. As the strain rate of a deforming system increases, heat losses through conduction become less significant in the calculation of temperature rise, and at high enough rates these losses become negligible and the system behavior is essentially adiabatic. If the strain rate is high enough that phonon drag forces and elastic wave interactions are significant, however, the quasistatic approximation of material behavior becomes inaccurate and dynamic effects must be considered. In between the strain rates where heat conduction or dynamic effects are significant there is a window of rates for which nearly quasistatic and adiabatic conditions exist. This window of strain rates depends on the size and materials properties of the deforming volume and can be approximated by K

17

(1)

where ~ is the strain rate, 17is the flow stress, K is the thermal diffusivity, L is the characteristic length of the deforming region, p is the density and G is the shear modulus [17]. Using the values given in Table 2 for our 4340 steel samples, eqn. TABLE 2 Physical constants of AISI 4340 steel used for calculations Density a 7.83 x 106 kg m -3 [21] Thermal conductivity" 37.5 J m s - J m 2 oC i [21] Thermal diffusivity 1.07 x 10 -5 m 2 s Shear modulus a 7.58 × 104 MPa [22] Specific heat a 4.48 x 102 J kg-1 °C-J [21] ~Room temperature values.

112 (1) places the approximate strain rate limits for quasi-static adiabaticity between 0.074 and 4.1x 103s -1 in the overall gauge length and between 0.32 and 8.5 x 103 s- 1 in the neck. The lower end of the high strain rate tests (where the applied rates are between approximately 80 and 3 x 103 s -1) falls within these limits, as do the post-UTS strain rates of the ultrasoft tensile tests, where neck formation and fracture occur in well under 1 s. Assuming quasi-static adiabatic conditions and also assuming that 86.5% of the energy input into the sample during uniform elongation is converted into heat, the approximate adiabatic temperature rise at a particular value of plastic strain ef can be computed using the equation f,

AT _0.865

f

pc Jo Oy

dep

(2)

where A T is the temperature rise, Oyis the yield stress, ep is the plastic strain, p is the density and c is the specific heat. If we assume that the true stress-true strain behavior of the samples can be approximated by the Holloman strain-hardening relationship [18]

a=Ke"

(3)

then the adiabatic temperature rise equation reduces to AT = _

K

cp(1 +n)

(ef)1+"

(4)

where n and K are the experimentally determined work-hardening coefficients. Unfortunately, these mathematically simple analyses require a true stress-true strain curve which can be accurately fitted using the Holloman relationship. In the case of our tests the extensive post-UTS elongation makes true stress-true strain information difficult to ascertain. The standard method of approximating post-UTS stress-strain information involves the assumption of the von Mises yield criterion [19], resulting in the Bridgeman correction [20]. This analysis, however, also assumes a neck shape which can be approximated by a section from the center of a toroid, i.e. a portion of a doughnut hole, and the profiles of our post-fractured samples show that this is not nearly the case. To more accurately determine the approximate energy of plastic deformation in our tests, the

load-elongation curves which resulted directly from the testing were divided into three different regions: the elastic regions prior to plastic deformation; the uniform elongation regions prior to neck initiation; and the post UTS region which represented the formation of the neck to fracture. Integration of the areas contained in the two plastic deformation regions gives a good approximation of the strain energy put into the samples during straining. It should be noted that this analysis assumes that the load-elongation curves for the quasi-static tests are approximately the same as those for the high strain rate and ultrasoft tests, which are not available. The similar shape of all of the samples after fracture is a relatively good indication that this is a reasonable assumption, and any differences which might occur are probably not significant to the accuracy of this model. To approximate the temperature rise resulting from plastic deformation, we also needed to know the volumes of the deforming regions. Calculating the gauge volume of the samples is obviously trivial, but the volume of the neck is not so straightforward. Using the profile projector, the profiles on both sides of the sample necks were graphically reassembled to approximate the neck shapes at the point of separation. These shapes were then numerically integrated to give approximate values of the total neck volumes. When approximate plastic deformation energy values and approximate deforming volume values are known, a simplified version of eqn. (2) can be used to estimate the temperature rise:

A T= 0.865 Ep

cpV

(5)

There are two different cases for the temperature rise calculations: the high strain rate samples and the ultrasoft samples. The difference occurs because while the high strain rate samples deform completely under nearly adiabatic conditions, the ultrasoft samples are only nearly adiabatic after UTS, i.e. during neck formation. In the calculations this means that the temperature rise of the high strain rate samples is the sum of the uniform and post-UTS increases while the temperature increase for the ultrasoft samples is only that generated during post-UTS deformation. Using load-elongation information from one of the quasi-static samples, the uniform deformation plastic work energy was estimated to be

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about 5.75 J while the post-UTS plastic work energy was about 12.2 J. Volume calculations of the same sample yielded an estimate of the gauge volume of about 119 m m 3 and of the neck volume of about 41 mm 3. Using these values with eqn. (5) yields an approximate temperature rise of 12 °C during uniform elongation and of approximately 74 °C during necking. This makes the total temperature rise at the center of the neck about 86 °C for the high strain rate samples and about 74°C f o r the ultrasoft samples. These calculations are in general agreement with in situ temperature measurements of steel tensile samples made using a high speed IR thermometer [23]. While a temperature rise of between 74 and 86 °C might cause a small amount of thermal softening in most structural metals, this temperature increase is particularly important for the 4340 tensile samples used in this study because the ductile-brittle transformation temperature range is near room temperature. Experiments conducted at various ambient test temperatures have shown that the transformation temperature range for AISI 4340 steel with a 435 °C temper lies between - 160 and approximately 60 °C [14]. Herein lies the explanation of why the radial cracking is absent in the high rate and ultrasoft tests, since the increased temperature in the neck prior to separation causes the material to fracture in a purely ductile manner, while in the quasistatic tests the separating material temperature falls within the ductile-brittle transformation range and the material fractures in a partially brittle manner.

4.2. Localized melting Although adiabatic heating during general gauge deformation and necking can cause an important temperature increase, it is not the mechanism by which localized melting occurs at separation, as shown in these experiments in which the samples which adiabatically heated during overall straining were not the samples which contained locally melted surface areas. The appearance of localized melting in the shear lip areas of 4340 samples is in many ways similar to that of titanium alloys. Spheroidized dimple walls and surface debris are found in patches surrounded by shear dimples, as seen in Fig. 4(b). These patches of local melting are also typically adjacent to relatively smooth surfaces, as seen in Fig. 4(c), which are by all appearances

identical to "holey smeared" regions which have been associated with the initiation of adiabatic shear in high strain rate shear tests of 4340 steel [9-11]. Signs of possible adiabatic shear are not unexpected since highly localized and possibly adiabatic shear has been found to accompany the localized melting in both Ti-8Mn and Ti-6A1-4V tensile samples. A significant difference between the localized melting found on the 4340 sample surfaces and that found on the surface of the titanium alloys is that the melted areas of the 4340 samples occur over smaller local areas (typically by a factor of approximately 3-5); the melted 4340 dimples are typically smaller by a similar factor, and melted areas of the 4340 samples occur less frequently than those of the titanium alloys. The general difference in the size of the melted areas and the included dimples is demonstrated by the scales of Figs. l(a) and 4(c). The parallel between localized melting and radial cracking is of great interest since it emphasizes the need for high crack propagation rates. This is in agreement with a recent study in which localized melting in Ti-6A1-4V tensile samples was suppressed by heat treating to an a colony microstructure, apparently because of an increase in crack path tortuosity and a resultant decrease in crack propagation rate [6]. A recent computer model of heating at a moving crack tip [7] has shown that dislocation production rates are critical in achieving high crack tip temperatures and it may be a lowering of these production rates that inhibits localized melting. An important point to note is that the radial cracking indicates rapid crack propagation in the central crack portion of the sample while the melting is found in the shear lip. This is an indication that, as might be expected, the separation rate of the central crack influences the shear lip formation and separation rate. High crack propagation rates have two major effects on local temperature rise, both of which result from an increase in the local strain rate. First, the shorter time of deformation decreases the amount of heat conducted away from the separating surface, making the conditions more nearly adiabatic. Secondly, increases in strain rate, especially at the high rates which occur during separation, cause an increase in the instantaneous yield stress, thereby increasing the amount of energy resulting from the same amount of strain.

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It should be noted that general heating of the gauge volume, localized heating of the neck and heating during localized and possibly adiabatic shear all predicate the heating at final separation which occurs during the rupture of the ligaments which surround the growing voids. Rupture of these ligaments occurs at extremely high strain rates and the total plastic strain involved is very large, making the local energy density of the ligaments during rupture very high. Temperature increases in the separating ligaments must be, once again, added to the prior temperature increases. Taking this into consideration, it appears that high strain rates and high ambient local temperatures in the immediate vicinity of the separating ligaments are the critical conditions for localized melting at final separation. 5. Conclusions (1) Under certain conditions, specifically those which cause high crack propagation rates, localized melting occurs on the shear lips during the separation of 4340 steel tensile samples. (2) Localized melting can be suppressed by increasing the ambient temperature of the separating volume above the ductile-brittle temperature transformation range. In this study the temperature increase was caused by adiabatic heating of the gauge and neck volumes during elongation. (3) In the 4340 samples used in this study the presence of locally melted regions has been shown to accompany radial cracking, indicating that the mechanisms responsible for the local melting are also associated with rapid crack prop~igation through the central portion of the sample. Acknowledgments This research was supported by the U.S. Office of Naval Research (Grant N00014-88-K-0111), Dr. George Yoder program director. We would like to thank Dr. Yoder for his encouragement and insight. Thanks are also due to Professor Dr. Hans-D. Kunze, Dr. L. W. Meyer and B. O. Reinders at the Fraunhofer-Institut fiir Angewandte Materialforschung for conducting the high rate tests on the 4340 steel samples. The authors also acknowledge the award of a

travel grant from the NATO Scientific Affairs Division, Brussels, Belgium. References 1 J. D. Bryant, D. D. Makel and H. G. E Wilsdorf, in L. E. Murr, K. P. Standhammer and M. A. Meyers (eds.), Metallurgical Applications of Shock-wave and Highstrain-rate Phenomena, Marcel Dekker, 1986, pp. 723-739. 2 J. D. Bryant, D. D. Makel and H. G. E Wilsdorf, Mater. Sci. Eng., 77(1987) 85-93. 3 D. D. Makel, Ph.D. Dissertation, University of Virginia, 1987. 4 D. D. Makel and H. G. F. Wilsdorf, in C. Y. Chiem, H.-D. Kunze and L. W. Meyer (eds.), Impact Loading and Dynamic Behaviour of Materials, Vol. 2, DGM Informationsgesellschaft, 1988, pp. 587-594. 5 D. D. Makel and H. G. E Wilsdorf, Scr. Metall., 21 (1987) 1229-1234. 6 D. D. Makel and D. Eylon, Metall. Trans. A, 21 (1990) 3127-3136. 7 K. Jagannadham and H. G. F. Wilsdorf, Z. Metallk., 80 (10) (1989) 698-709. 8 V. Weiss and J. G. Sessler (eds.), Aerospace Structural Metals Handbook, Vol. I, Syracuse University Press, 1963, Code 1206, pp. 6, 7. 9 J. H. Giovanola, in C. Y. Chiem, H.-D. Kunze and L. W. Meyer (eds.), Impact Loading and Dynamic Behaviour of Materials, Vol. 2, DGM Informationsgesellschaft, 1988, pp. 705-710. 10 J.H. Giovanola, Mech. Mater., 7(1988) 59-71. 11 J.H. Giovanola, Mech. Mater., 7(1988) 73-87. 12 E R. Larson and F. L. Carr, Met. Prog,, (March 1964) 75-79. 13 E R. Larson and F. L. Carr, Met. Prog., (February 1964) 26-30. 14 F. L. Carr and E R. Larson, J. Mater., JMLSA, 4 (4) (1969) 865-875. 15 T. D. Moore (ed.), Structural Alloys Handbook, Vol. I, Battelle's Columbus Laboratories, Columbus, OH, 1980, 4340 Steel section, pp. 70, 71. 16 W. S. Farren and G. I. Taylor, Proc. R. Soc. A, 25 (1925) 422. 17 G. B. Olsen, J. F. Mescall and M. Azrin, in Shock Waves and High-strain-rate Phenomena in Metals, Plenum, New York, 1981, p. 221. 18 J.H. Holloman, Trans. AIME, 162(1945) 268. 19. R. yon Mises, Gfttinger Nachr. Math. Phys. Klasse, (1913) 582. 20 P. W. Bridgeman, Tram. Am. Soc. Met., 32 (1944) 553-574. 21 V. Weiss and J. G. Sessler (eds.), Aerospace Structural Metals Handbook, Vol. I, Syracuse University Press, 1963, Code 1206, p. 2. 22 T. D. Moore (ed.), Structural Alloys Handbook, Vol. I, Battelle's Columbus Laboratories, Columbus, OH, 1980, 4340 Steel section, p. 4. 23 A. K. Sachedev and J. E. Hunter, Metall. Tram. A, 13 (1982) 1063.