Interest in shock-wave phenomena in metals is due both to their wide use in the physics of high pressures and to the ever-greater adoption of explosive and ...
SHOCK-WAVE PROCESSES IN METALS L. A. Merzhievskii and A. D. Resnyanskii
Interest in shock-wave phenomena in metals is due both to their wide use in the physics of high pressures and to the ever-greater adoption of explosive and other impulsive highenergy methods of treatment in technological processes. The ability to predict the behavior of material under the action of brief intense loads is important in studying, and using in practice, the phenomena of welding and strengthening by explosion, hydroexplosive stamping, powder stamping, obtaining new chemical compounds, constructing equations of state, and so on.
Until recently, the study of shock-wave processes in metals was basically experimental in character. At present, sufficient experimental information has been accumulated, and the focus of investigation has shifted toward the construction of models capable of describing the features of the behavior of metals and alloys in the conditions being realized. In a number of cases, traditional models of elastoplastic bodies have been refined and generalized to the given conditions [1-5]; in others, the models are complicated by taking account of the influence of viscosity [6-8]. A special group consists of models taking account of the physical nature of the plastic deformation- its dislocational kinetics [9-15]. These latter models permit a more accurate and detailed description of the behavior of shock waves in metals, including splitting effects of the plastic-wave amplitude in interaction with an overtaking rarefaction wave. Unfortunately, this approach, on account of the lack of experimental data on the kinetics of dislocations in semicrystalline materials, only allows onedimensional nonsteady problems to be considered. In [16], the use of dislocational representations of plastic deformations was proposed for closure of the model of a viscoelastic body of Maxwell type [8]. This allows the advantages of the dislocational model to be combined with the completeness of description achievable in multidimensional formulations. The method of numerical solution of problems within the framework of this model was outlined in detail in [17]. In the present work, solutions of a series of specific one-dimensional shock-wave problems are given, allowing the behavior of the material in given conditions to be analyzed. Comparison of the results of numerical calculations with experimental data offers the possibility of estimating the applicability of the model proposed and the method of calculation for describing the behavior of metals under shock-wave loads. The total closed system of equations of the model employed was given in [8, 16]. the one-dimensional nonsteady case, it takes the form
In
o (Pr~)T-+ a (p~r ~)a~ = O, a (p~r~) Ot
~
a [(p,:" -- ~0 ~1 Or
a[p(E + u2/2)rv] Ot
+ v r v-lt~.,.~ O,
a {[pu (E + u~/2)'-- ,~lul r:} +
c3b 8b a~ + u O r -
Or
v (3 -- ~') u d~ r + -~
0, :
(1) O,
v (v -- t) u + d3 ~O, r OE OE OE E = E ( a , b , c , S ) , c i 1 = p - . ~ a , r = p - g ' g , % ---- P T e ' ac ac a--t + u ~
OE = ~,
d3=b-q,
= poo/exp (a + b + c), T -----9 (a, b, c, S), ds=c--q,
q=t/3.1n(poo/p),
Translated from Fizika Goreniya i Vzryva, Vol. 20, No. 5, pp. 114-122, SeptemberOctober, 1984. Original article submitted December 16, 1983.
580
0010-5082/84/2005-0580508.50
9 1985 Plenum Publishing Corporation
u, m / s e c
0,30
75 50
O, 1525
',
~ 1
0,2 0,4 0,6 n, em
O
Fig. I
0,5
/~O
r, cm
Fig. 2
where Poo, 0, u, E, S, T are the initial and current density, velocity, specific internal energy, entropy, and temperature; oi, i = i, 2, 3, principal stress; t, r, time and spatial variable; a. b, c, logarithms of the rarefaction coefficients of an element of the medium along the coordinate axes; v = 0, i, 2 plane, cylindrical, and spherical cases, respectively; E(a, b, c, S), equation of the elastic energy with a nonspherical deformation tensor; T(a, b, c, S), dependence of the relaxation time of the tangential stress on the parameters of state of the medium. The elastic-energy equation from [18] and the relaxation-time equation from [19] are used to close the system. Collision of Two Plates The problem of the collision of two plates is simpler for numerical solution and easily reproduced experimentally. Comparison of the results of the calculations with the extensive experimental data available allows the adequacy of the model of the real medium employed to be judged. The mathematical problem reduces to finding the functions u, p, a, b, c, E, o~, o2, os, T from Eq. (i) with v = 0 and the following initial data and boundary conditions t=0:
b=c=0
@=po, u = u o , T = T o p=p~, u=u~, T=TI t>O:
ol(-h(t), t)=O,
when
when when
-h(O)~r~H(O),
--h(O) < r < O , O~r~H(O),
(2)
ot(H(t), t ) = O .
Usually, the collision occurs experimentally at a motionless barrier, i.e., uz = O. On the shock adiabatic curves and rarefaction isentropic curves of the metals there are breaks (points of discontinuity of the derivatives) and points of inflection, reflecting the singularities in the behavior of the given materials associated with the presence of elastic interaction forces of the atoms in the crystalline structures. As a result, in a definite range of loading parameters, there is seen the splitting of the shock wave into an elastic precursor, propagating at the velocity of thelongitudinal perturbations and transmitting a load equal to the Hugonoit elastic limit, and a plastic wave. The latter finally transfers the material to a thermodynamic-equilibrium state corresponding to a shock wave of the given intensity. In the plastic wavefront, relaxation of the tangential stress occurs, and as a result the uniaxial deformed state is transformed to a triaxial stress state corresponding to the yield surface. These features of the process are well transmitted in calculating shock-wave propagation. In Figs. 1 and 2, profiles of the mass velocity and maximum shear stress (oI -- o2)/2 at different times in an iron plate are shown, in the case when Po = Px = 7.8 g/cm 3, uo = 0.I km/sec, ul = 0, To = Tx = 300~ h(0) >> H(0) = 1.5 cm. Despite the smoothing of the fronts on account of the approximate viscosity used in the difference scheme, the process in which the elastic precursor separates and a two-wave configuration is established is sufficiently clearly traced. Curve 1 in Fig. 1 shows experimental variation in the amplitude of the elastic precursor as it propagates in Armco iron [i0]. Curve 1 corresponds completely to the theoretical damping of the elastic precursor. Its velocity coincides with good accuracy with the velocity of propagation of elastic perturbations calculated from the wellknown elastic constants of the metal. The dashed curves in Fig. 1 show the propagation of the same wave as calculated from Eq. (i) under the assumption of instantaneous relaxation of the tangential stress to zero (the hydrodynamic approximation). The velocity of propagation of the hydrodynamic and plas581
tic waves and also the final states behind their fronts are the same. The difference in curvature of the fronts agrees with the existing ideas regarding the dynamics of shock transitions in hydrodynamic media and metals. After reaching the free surface, the shock wave is reflected by the rarefaction wave. As follows from Fig. I, the calculation conveys the complex character of the rarefaction wave as well as states from the elastic and plastic sections. It is striking that, whereas precise doubling of the mass velocity realized behind the shock wavefront occurs in the hydrodynamic approximation in the rarefaction wave, the mass velocity behind the rarefaction wave is 5-7% less in the more precise approximation of a viscoelastic body.
Characteristic profiles of the maximum tangential stress, which is the motive force of plastic flow (Fig. 2), are qualitatively different from the analogous profiles calculated within the framework of the dislocatlonal model of [Ii, 13]. The sudden increase on the front of the elastic precursor is followed by a section of further increase (o~ -- s2) with a smaller velocity, and only then does the tangential stress begin to decrease on account of relaxation. Variation in (0, -- oz) of this form is more realistic, since some time is required for the dislocations responsible for plastic flow and hence relaxation to reach their maximum velocity of motion and sufficiently large concentration, and in this period the rate of increase in (o: -- 02) in the shock wavefront will still exceed the relaxation rate. It is interesting to note that the position of the maximum tangential stress corresponds to the position of the hydrodynamic shock wavefront at that time. Damping of Shock Wave The problem of the change in shock-wave amplitude in interaction with rarefaction waves propagating from the back or side surface of the loaded sample is important in understanding the development of shock-wave processes and testing wave phenomena. In practice, it is necessary to be able to describe the damping process in order to predict the variation in strength characteristics of the material under the action of explosive loads [5] and estlmate the parameters in explosive welding and the throwing of plates and shells. The first, not very successful, attempts to consider this problem led to the construction of analytical solutions in the hydrodynamic approximation [22, 23]. Numerical calculations [14] showed that many of the models used to describe shock-wave processes in metals incorrectly convey the character of the shock-wave damping in their interaction with an overtaking rarefaction wave. Analysis of the mechanisms which must be taken into account if modeling adequate to the experimental results is to be possible was undertaken in [24]. In the plane, one-dlmensional case, the problem reduces to solving Eq. (I) with ~ = 0 and the initial and boundary conditions in Eq. (2) up to values of t larger than the time required for the rarefaction wave from the back surface of the colliding plate to overtake the shock wavefront in the sample being loaded. In a series of experimental works, a plane shock wave in a sample was produced by the explosion of a special explosive charge at its surface (a plane wave generator). In this case, the loading conditions are reproduced in the calculatlonby modeling the explosion in an Instantaneous-detonatlon scheme. The material in the region --h(0) ~ r < 0 is assumed to be compressed gas with the corresponding parameters, and its motion is calculated from Eq. (i), taking T(a, b, c, S)EO with the equation of the detonation products of the given explosive. In the simplest case, the shock-wave damping in interaction with an overtaking rarefaction wave is modeled by solving Eq. (i) with the following initial and boundary conditions 9 t = 0: b = c ~ 0, p = Pi, ~ = ui, T = Yi w h e n h ( 0 ) ~ r ~ H ( 0 ) , ti ~ t ~ 0: ~ , [ h ( t ) , t > tt: a l [ h ( t ) ,
t] = ~io, G , [ H ( t ) ,
t] = 0, ~ , [ H ( t ) ,
t] = 0,
(3)
t] = 0,
where ~,o is determined from the shock adiabatic of the material from the collision conditions or from the detonation-wave parameters and t, is the time at which the rarefaction from the back surface overtakes the shock wavefront in the sample, and is easily calculated with known shock adlabatics and compressibility of the materials [25]. The variation in shock-wave parameters on interaction with a rarefaction wave is traced in Fig. 3, where profiles of the mass velocity in iron loaded by a pulse of duration 0.3 ~sec -- the conditions in Eq. (3) with t, = 0.3 Bsec -- at times t = 0.25 (i), 0.5 (2), 0.75 (3), 1.0 (4), and 1.25 (5) ~sec are shown. The calculation conveys the two-wave structure of the rarefaction wave, consisting, llke the compression wave, of elastic and plastic com-
582
U3~ km/$cc u, rtl J sec 1 75-,
50-
25-
0,25
0,50 ~ cm
0
4
8
Y/%
Fig. 4
Fig.
ponents. Circulation of the elastic waves between the fronts of the plastic compression and rarefaction waves, also observed experimentally (see [2], for example), leads to steps in the damping curves of the shock-wave amplitude. Comparison of the experimental and theoretical curves for steel and aluminum and its alloys (corresponding data are given in [24]) shows their good agreement. The discrepancy, not exceeding 5% in terms of the mass velocity, is explained by the incomplete agreement of the equations of state used in the calculations and the dependence of the relaxation time of the tangential stress in the material used in the experiment. It follows from the results of the calculations agreeing with the data of [2, 14] that the hydrodynamic approximation in the given range of shock-wave amplitudes does not provide a satisfactory description of the experimental damping curves. As shown in [24], this is explained by the hydrodynamic model's failure to take account of the relaxational properties of real metals playing a significant role in wave processes. It is interesting to compare the damping of plane shock waves and waves with cylindrical and spherical symmetry. The variation in wave amplitude on interaction with an overtaking rarefaction wave in the case of arbitrary geometry is described by the relation [24] Dgl.
0~1,
Dt -- A T +
C
(4)
B +-'7-
where D d # b--/- = ~ + ( # - - u ) ~ 7
is the derivative along the trajectory of the shock wavefront; ~ * is the stress at the front in the direction of wave propagation; R is the shock-wave velocity; A, B, C are parameters characterizing the 'hydrodynamic," "Maxwellian," and "geometric" damping, respectively. The latter is only present in the case of cylindrical and spherical waves. The variation in the character of damping as a function of the geometry of the process -- plane (I), cylindrical (2), and spherical (3) -- is traced in Fig. 4, where the velocity of the free surface w in aluminum samples loaded by the impact of a "plate" of the same material of thickness ho = 1.5 mm at velocity 1.2 km/sec is shown. In the cylindrical and spherical cases, it is assumed that the impact occurs in a cavity of radius i0 mm. The choice of w as the characteristic of the process is associated with the most widespread experimental method in which it is the motion of the free surface of the loaded sample in a rarefaction wave that is traced. It is significant that, as in the case of Fig. i, deviation of w from double the mass velocity of the material is observed; this is associated with the influence of the strength properties of the material. In contrast to the plane case, the damping curves in the cylindrical and spherical cases are smooth and monotonic, which indicates not only quantitative but also significant qualitative influence of the geometric factor on the given process. The damping is often described using the solution obtained for waves from a strong point explosion in a compressible fluid [26]. For the variation in mass velocity, it gives
ui/Uio = (r,/r) ~/~, w h e r e i = 9 + 1 , r , , Uio a r e t h e i n i t i a l c u r v e s i n F i g . 4 do n o t s a t i s f y Eq. (5)
(5)
coordinate and the corresponding value of u. The for any value of v. At t h e same t i m e , t h e i n f l u e n c e
of the geometric factor on the damping is so strong that the relation following from Eq. (5) 583
u, kmtsec
I
2,0
c'
i
'
!
i
t,A', I
i
I
,,' *
1,5 1,0
o,5 1i 12
3
4
5
:
L
6
i
,
I
0
4
i
I
O, 5
l,O
5
r, crD
Fig. 5
8 t,Nee
Fig. 6 u~./u 8 = ( r / r , ) 1/~
is satisfied with an accuracy of no worse than 5% if the point at which ua = us is chosen as r,. Note also the inapplicability of the formulas developed in [22, 23] for the description of the results obtained. Wave Processes in Laminar Obstacles Obstacles consisting of several layers of different materials are encountered fairly often in practice. One of the interesting physical effects occurring the such systems is the accumulation of shock waves analyzed in the acoustic approximation and observed experimentally in [27]. In the case where the acoustic impedances of the layers decrease in the direction of wave propagation, there is an increase in mass velocity of the barrier material; in the opposite case, there is an increase in the normal component of the stress. In one experimental case [27], an obstacle of copper and aluminum plates (thickness 3 and 1 mm, respectively) was loaded by the impact of a steel plate of thickness 3 mm at a velocity of 1.46 km/sec. In the given model, this corresponds to the solution of Eq. (I) with 9 = 0 and the initial and boundary conditions t = O:
t~>0:
b = c = 0, T = 300 K
when
0~< r~< 0 . 7 c m ,
p = 7.8 g / c m ~ , a = t . 4 6 km/sec
when
0 ~< r < 0 . 3 c m ,
p = 8.9 g/eras, a = 0
when
0.3 ~< r < 0 . 6 c m ,
p = 2.7 g / c m s, a = 0
when " 0.6 ~< r ~ 0.7 cm,
a,(h(t),
t) = o , ( H ( t ) ,
(6)
k12
t) = O.
Comparison of the theoretical wave profiles with parameters determined from the shock adiabatic of the obstacle materials shows that the calculation is of high accuracy in the presence of a few contact boundaries. In the experiments, the velocity of flight of the last plate was measured. As also follows from the estimates of [27], the theoretical flight velocity of the last plate is determined by theacceleration in the rarefaction wave from the rear free surface; the wave reflected from the contact surface between the preceding layers is not able to reach the aluminum plate before it separates. The discrepancy between the theoretical and experimental flight velocities of the plate is less than 1%. In the case of a laminar obstacle, i n w h i c h a layer of small acoustic impedance is placed between two layers of materlals;wlth a large acoustic impedance, multiple impact loading of one of the extreme impact loading of one of the extreme plates on account of multiple relfectlons of the shock waves from the contact boundaries may occur. In this formulation, in experimental investigations [20, 21], the presence of an elastic precursor in the shock waves propagating through a preliminarily compressed material was established. This singularity in the behavior of metals, which passes beyond the bounds of traditional models of an elastoplastlc body, is d i s c e r n e d b y the model used in the present work. Behind the front of the initial shock wave, the tangential stress is practically relaxed and the material is in a state close to hydrostatic compression. In the absence of tangential stress, there is a cessation of the moving dislocations responsible for the plastic deformation, which leads to a sharp increase in the relaxation time of the tangential stress [19]. Wlth repeated loading, the relaxation time continues to be sufficiently large until the tangential stress exceeds the Peierls--Nabarro barrier, the value of which increases under the action of hydrostatic pressure. Until then, the compressed material behaves elastically, 584
and then there begins intense motion and multiplication of the dislocations, leading to a drop in relaxation time characteristic of plastic flow. It is difficult to predict a priori the trend and magnitude of the variation in amplitude of the elastic precursor, since not only the increase in the Peierls--Nabarro barrier under the action of the hydrostatic pressure must be taken into account but also the influence on its magnitude of the heating in the primary shock wave, possible changes of parameters of the kinetic equations of the dislocations, and so on. In the calculations described below, these factors are taken into account. In Fig. 5, the mass-velocity profiles in a barrier of aluminum (thickness 2.5 mm) and copper (thickness 7.5 m m) loaded by the impact of a 7.5-mm copper plate at a velocity of 2 km/sec are shown. The calculation is performed by Eq. (i) with 9 = 0 and initial and boundary conditions analogous to Eqs. (6) and (7). In the copper part of the obstacle (i r ~ 1.75 cm), the primary shock wave is followed by a secondary shock wave, arising as a result of reflection of the wave in aluminum from the contact boundary with the impacting plate. From the viewpoint of the above analysis, region I is most interesting; it is shown enlarged in Fig. i. The given curves (numbered in accordance with increase in time) clearly show the presence of an elastic precursor in the secondary shock wave. In the primary wave, there is no precursor, since with this compression intensity the plastic-wave velocity exceeds the longitudinal sound velocity. Expansion and Compression of Cylindrical Shells The tossing of cylindrical shells, basically by means of explosions, is noteworthy in connection with the need to solve a series of scientific and practical problems. The problems arising here and the current state of the research were considered in detail in the reveiw [28]. In the one-dimensional nonsteady approximation, the shell motion is described by Eq. (i) with ~ = I. Usually, one of the shell surfaces is subjected to the action of an explosive load and is in contact with the detonation products of the explosion. There arises here the problem of modeling the detonation of the explosive. To simplify the calculations, it is often assumed that the detonation occurs instantaneously. For the detonation products, the adiabatic equation of state is assumed to hold p = po(p,/9,o)L
(8)
where Po, P are the initial and current pressure in the detonation products; 0to, 01 are their initial and current densities; y is the adiabatic modulus. The behavior of the detonation products is calculated from Eq. (i) with ~ = 3 under the assumption that T~0. Thus, the calculation region is divided into two: ro(t) ~ r < rt(t), the detonation products; and Ro(t) ~ r ~ R,(t), the shell, which in turn may consist of several layers of different materials. In the case of throwing of the shell (expansion) rt(t)ERo(t). If the explosive completely fills the shell, ro(t)~0. In each of the subregions, initial and boundary conditions similar to Eqs. (6) and (7) are specified. In [29], the given method of modeling the explosive load using Eq. (8) was compared with calculations of shell throwing using more accurate equations in which it is assumed that the detonation products initially have a constant density equal to the initial density of the explosive and a radial velocity W distributed according to the law
W=Wo[r/r~(O)] ~. The pressure in the detonation products is also constant, and equal to Po. The quantities Wo and Po are determined from the energy-balance equation of the detonated explosive. Comparison of the results of the calculations using these methods of modeling the explosive load with the data of special experiments shows that, for sufficiently thick-wailed shells, both give practically identical results describing the experimental data with good accuracy. In the calculations, the linear relation between in Vo and in O is confirmed; here vo is the final velocity of flight of the shell and B is the loading coefficient. The special interest in the compression of cylindrical shells is associated with the high-speed accumulation of cylindrical cumulative coatings [30]. The solution of this problem in the model of a viscoelastic body is made more attractive in that it was concluded in [30] that the viscosity of the material of real shells has the determining influence on the physical features of the process. The formulation of the problem is analogous to the case of throwing; it is only necessary to set ro(t)~Rt(t). Theoretical curves of R1(t) for collapsing copper shells loaded by explosive charges of different thickness are shown in Fig. 6~ 585
In all cases, Ro(0) = 9 mm, R,(0) = 11.7 mm. The explosive used is a 50/50 alloy of TNT and triglycine hexogen, P,o = 1.65 g/cm 3, D = 7.5 km/sec, po = p,oD2/8; the scattering of the products is calculated using Eq. (8). Curves 1-3 correspond to the following thicknesses of the explosive: 8.2, 5.9, 2.4 mm. The points indicate the experimental results of [30]. The good agreement of the theoretical and experimental results obtained without including any data from the given series of experiments in the calculation indicates the effectiveness of applying the model to the solution of the given class of problems. In contrast to the hydrodynamic approximation [30], the wave character of the shell acceleration associated with circulation of rarefaction water in its wall is conveyed, especially in the case of a thin layer of explosive. The calculations confirm the effect of strong heating of a zone adjacent to the internal surface of the shell. Unfortunately, quantitative estimation of the temperature is difficult since the equation of state of [18] used in the calculations has sufficient accuracy in a limited range of temperature variation. Conclusions The model of a viscoelastic body of Maxwellian type formulated in [8] requires, for closure, a nontraditional equation of state in the form of the dependence of the elastic energy in a nonspherical deformation tensor and the dependence of the relaxation time of the tangential stress on the parameters of state of the medium. In [18], a method of constructing the dependence of the elastic energy of a series of metals was proposed and realized. The dependence of the relaxation time is constructed on the basis of dislocational concepts on the mechanism of plastic deformation and experimental data on the dependence of the dynamic yield point on the deformation rate. This completes the total construction of a model suitable, as supposed, for the solution of problems of intense dynamic (including shock-wave) deformation of metals. In view of the unwieldiness of the model for the solution of specific problems, it is necessary to use a computer; this entails the development of a method of numerical solution of the system of equations of the model. Such a method was proposed in [17]. The good agreement of the results of solving a series of one-dimensional nonsteady problems with experimental data found in the present work permits the conclusion that the model and method of numerical calculation used here is applicable for modeling the behavior of metals over a broad range of variation of the intensity of loading, deformation, and deformation rates. LITERATURE CITED i. 2. 3. 4. 5. 6. 7. 8. 9. i0. Ii. 12. 13. 14. 15. 16. 17. 18. 19. 20. 586
M. L. Uilkins, in: Computational Methods in ~ydrodynamics [Russian translation], Mir, Moscow (1967). L. V. Al'tshuler, M. I. Brazhnik, and G. S. Telegin, Zh. Prikl. Mekh. Tekh. Fiz,, No. 6, 157 (1971). I. V. $imonov, Izv. Akad. Nauk. SSSR, Mekh. Tverd. Tela, No. 2, 105 (1974). L. M. Flitman, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tala, No. 2, 97 (1974). A. A. Deribas, F. V. Nesterenko, G. A. Sapozhnikov, et al., Fiz. Goreneniya Vzryva, 15, No. 2, 126 (1979). Yu. Beida, in: Propagation of Elastoplastic Waves [in Russian], Nauka, Alma-Ata (1973). V. N. Kukudzhanov, in: Report on Applied Mathematics [in Russian], VTs Akad. Nauk SSSR, Moscow (1976). S. K. Godunov, Elements of Continuum Mechanics [in Russian], Nauka, Moscow (1978)~ V. L. Idenbom and A. P. Orlov, Usp. Fiz. Nauk, 76, No. 3, 557 (1962). Dzh. U. Teilor, Mekhanika, No. 4, 145 (1966). Dzh. Dzh. Gilman, Mekhanika, No. 2, 96 (1970). J. N. Johnson and L. M. Barker, JAP, 40, No. ii, 4321 (1969), R. I. Nigmatulin and N. N. Kholin, Izv. A~ad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 131 (1974). V. M. Fomin and E. M. Khakimov, Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 114 (1979). G. I. Kanel', Zh. Prikl. Mekh. Fiz., No. 2, 105 (1982). L. A. Merzhievskii, Arch. Mech. Stosow., 30, No. 4-5, 477 (1978). L. A. Merzhievskii, in: Dynamics of a Solid (Continuum Dynamics) [in Russian], No. 45, Novosibirsk (1980). S. K. Godunov, E. I. Romenskii, and N. S. Kozin, Zh. Prlkl. Mekh. Tekh. Fiz., No. 2, 123 (1974). L. A. Merzhievskii and S. A. Shamonin, Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 170 (1980). A. N. Dremln and G. I. Kanel', Zh. Prikl. Mekh. Tekh. Piz., No. 2, 146 (1976).
21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
J. Lipkin and J. R. Asay, JAP, 48, No. I, 182 (1977). V. P. Kozlov, Zh. Tekh. Fiz., 36, No. 7, 1305 (1966). W. E. Drummond, JAP, 28, No. 12, 1437 (1957). L. A. Merzhievskii and A. D. Resnyanskii, Fiz. Goreniya Vzryva, 19, No. i, 99 (1983). L. A. Merzhievskii, Shock Waves in Condensed Media. Educational Test [in Russian], Novosibirsk (1982). L. I. Sedov, Similarity and Dimensionality Methods in Mechanics [In Russian]~ Nauka, Moscow (1977). V. I. Laptev and Yu. A. Trishin, Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 128 (1974). V. A. Odintsov and L. A. Chudov, in: Mechanics. Problems of the Dynamics of Elastoplastic Media [Russian translation], No. 5, Mir, Moscow (1975), p. 85. L. A. Merzhievskii and A. D. Resnyanskii, in: Dynamics of a Fluid with Free Boundaries (Continuum Dynamics) [in Russian], No. 60, Novosibirsk (1983). N. I. Matyushkin and Yu. A. Trishin, Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 99 (1978).
ELECTROMAGNETIC FORECASTING OF THE MECHANICAL PROPERTIES OF EXPLOSIONHARDENED STEEL I. D. Zakharenko, K. E. Milevskii, and V. N. Moskvin
Explosion working designed to improve the mechanical properties is widely used in the production of various steel items [I]. Here it is important to forecast the mechanical properties of the metal produced by the actions of pulsed loads of various amplitudes and durations produced by explosion. Such forecasting is possible on the basis of correlations between the mechanical properties produced by explosion and the characteristics of the physical fields used in nondestructive testing, such as electromagnetic ones. There are detailed discussions [2, 3] of the mechamisms whereby shock waves influence the structures of various materials. However, there are only a few papers on the effect of shock waves on the electrical and magnetic parameters of metals. Information has been given [3] on the effects of explosive working on the resistivity. Studies have also been made [4] on the relation between shock-wave loading and residual magnetic properties for Armco iron and nickel. Steady magnetic fields have been used in various eases to examine magnetic effects in the shock loading of ferromagnetic materials [ 5 ] . Electromagnetic methods are widely used in the nondestructive testing of heat-treated steels [6]. Here we consider the particularly sensitive to signal from the secondary method of forecasting the
effects of shock waves on the electromagnetic characteristics structural changes in ferromagnetic: the higher harmonics in the emf and the Barkhausen noise signal, which together provide a mechanical parameters of St. 60 components in explosive working~
The measurements were made on specimens of St. 60 of size 8 x 8 x I00 mm cut from cases made by deep drawing. The shock waves were provided by the planar collision of a copper plate of thickness 4 mm impelled by a hexogen charge. The thickness of the explosive varied from 5 to 25 mm. The initiation was provided by a detonator and a linear detonation-wave generator (Fig. i). The initial angle ao and the collision parameters were calculated from the data of [1]. Control specimens and ones treated with shock waves were tested on an RM-102 tensile tester in accordance with GOST 1497-73, and also on an impact tester to determine the mechanical properties. Some of the specimens were also submitted for metallographic analysis. A transducer of transformer type was used to measure the Barkhausen noise emf and the amplitude of the third harmonic in the secondary emf in testing the specimens before and after shock-wave treatment. The transducer of length 50 mm had the following design: an ebonite body of internal diameter 12 =~ was wound wiht PEL wire of diameter 0.06 rmm (two windings of 500 turns each connected differentially), above which there was a winding made Novosibirsk. Translated from Fizika Goreniya i Vzryva, Vol. 20, No. 5, pp. 122-125, September-October, 1984. Original article submitted June 26, 1983.
0010-5082/84/2005-0587508.50
9 1985 Plenum Publishing Corporation
587
