Yu.I. Mescheryakov, S.A. Atroshenko, M.V. Sil'nikov, N.I. Zhigacheva
Institute of the Mechanical Engineering Problems
Russian Academy of Sciences, Special Materials LTD.
Bolshoi 61, Vas. Ostrov
St. Petersburg, 199178, Russia
fax: (812) 217 8614
e-mail: ymesch@impact.ipme.ru


Nucleation of unusual shear bands inside shock-loaded copper, Cr-Ni-Mo steel, and Cu-MN alloy has been investigated. The formations revealed are plane disks of a round shape, the dimensions of which range within 5-2000 µm in diameter and 1-5 µm thick. On a grain structure background, they look like small round mirrors and lie in the planes perpendicular to the free surface of the plane target. Their nanocrystalline internal structure results from the dynamic recrystallization of the metals during the shock wave passage. The conditions for dynamic recrystallization are estimated to be provided by a unique combination of high local values of strain (>2.9), strain rate (107s-1), and temperature (0.5 Th). Where satisfied, these conditions appear to be sufficient for a local superplasticity of material initiated in the shear bands. Owing to the superplasticity, the material inside the shear band has time to be constrained by surface tension into a round disk, an ideal shape that permits minimum entropy.


Sufficient experimental and theoretical evidence exists to show that shear bands in shock loaded solids are related to the local overheating and softening of materials due to an intensive short-time loading and /or low thermal conductivity (Swegle et al. 1985).

Under certain strain and temperature conditions, this overheating can be accompanied by local structural rearrangements, one effective mechanism of which is dynamic recrystallization. Besides a sufficiently high value of strain rate (> 107 s-1), the necessary conditions for dynamic recrystallization include a high value of plastic deformation (>2.9) and a temperature of the order of 0.4 Th (Th is the homologous temperature) (Meyers et al. 1990).

In this paper, dynamically initiated recrystallization accompanied by a temporary loss of crystal stability and by a local superplasticity is considered in detail. Under moderate shock loading, the nucleation of unusual regions of shear localization has been revealed. All the formations are round disks ranging from tens to hundreds of microns in diameter and between 1-5 µm thick. Careful examination of the interior of these disks by TEM and X-ray analysis revealed a unique nanostructure in these regions, while the rest of the matrix had a typical grain structure.

Conditions for Round Shear Band Formation

Round plane surfaces of shear localization have been revealed in specimens after shock loading in the following way: Specimens are cut in an arbitrary plane along the wave propagation direction. After polishing and etching, the non-etched mirror spots stand out against the background of the grain structure. It should be emphasized that no similar formations were found in the analogous sections of nondeformed materials. Furthermore, when target cuts are made along the planes parallel to the free surface target, no regions of shear localization are found even in deformed materials. The disk's ideal round form is similar to an oil spot on a water surface. This shape results from surface tension, which tends to decrease the free energy of the system. The similar form of the disks undoubtedly has a thermodynamic origin. They may be formed only when the surface tension is greater than the ductile resistance of the material inside the shear bands. Although only the spheroid is known to provide a minimum of free energy for the free liquid, this form cannot be realized herein since the shear banding in solids is an exclusively two-dimensional process. In this situation, the next geometrical form providing a minimum of free energy is the round plane.

Round shear band (RSB) formation is a result of the interaction of compressive waves reflected off the free surfaces of the impactor and the target. The position of the shear region in a longitudinal section of the target can be determined by considering a phase x-t diagram where the wave propagation and interaction processes can be represented in the form of characteristics. As an example, consider the characteristic pattern where a compressed region 800 µm in size nucleates patterns a distance of 4.1 mm from the free surface of the target after a collision between a 1 mm steel impactor and a 5 mm copper target. In Fig. 9.1, the compressed region is restricted by polygon PQRS. According to the diagram, at the instant of collision (x = 0, t = 0), elastic and plastic waves begin to move toward the free surfaces of the target and the impactor simultaneously. During the first reflection from the free surfaces of the impactor and the target, compressive waves transform into release waves whose interaction is known to result in spallation. The region of possible spallation is indicated by dash-lines AA' and BB'. During the second reflection, the release waves transform backward into compressive waves whose interactions just result in the appearance of the local compressive region. This region is restricted by a set of characteristics corresponding to real elastic-plastic waves. For example, the local region indicated in Fig. 9.1 is formed by interactions of compressive waves propagating with velocities between 3.9 x 105 cm/s and 4.8 x 105 cm/s. In the x-t diagram, this region is indicated by shading. The intersection of these regions forms the compressive zone restricted by figure PQRS. The compressive state for this region is limited by the interval of deltat = QS = 150 ns. An analogous pattern for the interaction of compressive waves can be drawn for any RSB.

Fig. 9.1. Phase x-t diagram.

Dynamic compression inside the PQRS-region is a necessary but not a sufficient condition for nucleating the RSB. The second condition is a local longitudinal shear initiated by the particle velocity distribution in the shock loaded material. That distribution results in a shearing of microvolumes relative to each other. For the nature of shock-induced shear banding to be clarified, the stress state of nonuniform material subjected to uniaxial strain must be considered.

Stress State Analysis

During the high velocity collision of plane disks, the so-called "state of uniaxial strain" is obtained for a few microseconds until the lateral rarefaction waves from the edges of the target arrive to complicate the strain pattern. The only non-zero component of total deformation sumxx coincides with the wave propagation direction. The off-diagonal components of the stress tensor sigmaij vanish, and the diagonal components sigmaxx, sigmayy, and sigmazz are non-zero.

As a rule, the only measured dynamic variable during uniaxial straining is the mean stress component coinciding with the wave propagation direction. This value can be expressed in terms of hydrostatic pressure p and mean shear stress t_over as follows:
sigmaxx = p + 3/4 t_over            (1)

Here the shear stress t_over as well as the normal stress sigmaxx are the volume averaged values that are linked with appropriate mean particle velocities by the equations:
sigmaxx (t) = p C1 U_overx (t)       (2)
t_over (t)=pCsumh U_oversumh (t)       (3)
where C1 is the longitudinal sound velocity and Csumh is the shear wave velocity.

The normal component of the average particle velocity U_overx(t) is commonly measured by means of velocity gauges. As for the mean shear component U_oversumh(t), special shock experiments providing oblique plate collisions must be carried out (Abou-Sayed 1975). On the other hand, for steady shock waves, the mean shear stress proves to be equal to a maximum difference between the stress value on the Rayleigh line and the value on the hydrostatic compression curve (Swegle et al. 1985). For concave sigma/sum diagrams, the mean shear stress does not usually exceed 1/20 of the normal stress. For example, in a 6061-T6-aluminum alloy, a maximum shear stress of 0.5 GPa corresponds to a normal stress of 10 GPa (Grady et al. 1987).

Knowledge of the average stress state enables one to describe only the uniform strain, which is commonly done in continuum mechanics. In reality, however, dynamic deformation is not uniform. Under certain threshold strain and/or strain rate conditions, an intensive heterogenization of plastic flow occurs. Basic reasons for that are both the metallurgical nonuniformity of the material and the dynamic strain localization due to the non-linearity of the deformation process itself. It implies that instead of a uniform dynamic deformation with a mean particle velocity U_overp(t), heterogeneity can occur on several structure levels. In general, this kind of nonuniform dynamic straining may be characterized by some distribution function f (r_over,v_over, t) in velocity (or strain-rate) space. A similar function characterizes the kinetics of the inner structure in dynamically deformed solids. However, its experimental determination is not yet possible in reality. From the standpoint of practical applications, however, the more admissible characteristics of structure kinetics seem to be the statistical moments of distribution functions (see Fig. 9.2). The first statistical moment is the average particle velocity U_overp(t), and the second is the particle velocity distribution width deltaUp(t) (or the square root of the particle velocity dispersion). As distinct from the average particle velocity, delta U_overp(t), which is a macroscopic dynamic variable of the deformation process, the particle velocity distribution width (DW) describes the kinetics of the microstructure. When applied to uniaxial strain conditions, it characterizes, statistically, the relative local velocities of microvolumes. Local shear stresses in the wave propagation direction t1(t) and in the particle velocity distribution width deltaUp(t) are linked by the equation:
t1(t) = pCp deltaUp(t)       (4)

Thus, with regard for the heterogeneity of dynamic deformation, the uniaxial strain state of the material can be characterized by the mean normal stress sigmaxx(t), mean shear stress t_over (t) parallel to the planes of maximum resolved stress, and the local shear stress t1(t) in the wave direction. In uniaxial strain experiments during a single shock loading, the mean normal particle velocity deltaU_overp(t) and the particle velocity distribution width deltaUp(t) can be determined simultaneously.

Fig. 9.2. Distribution function.

Then, by using Grady et al. (1987) and Swegle et al. (1985), the mean normal and the local shear stresses can be determined as well. Take as an example that the mean particle velocity and the particle velocity distribution width are equal to 146 m/s and 31 m/s, respectively. Normal stress sigmax counted from Grady (1987) is approximately equal to 6 GPa. This corresponds to the mean shear stress value of 0.3 GPa (1/20 of normal stress). However, local shear stress can be calculated to be 1.22 GPa, which is four times greater than the average shear stress.

Thus, shock loading provides, for short periods of time, conditions for a unique combination of high hydrostatic pressure and longitudinal shear stress. This combination is known to result in a structurally unstable state of the material (Zhorin et al. 1981).

Microstructure Investigations

The microstructure of round shear bands and the adjacent regions were explored using optical, SEM, and TEM techniques and a local X-ray analysis. All the results presented have been carried out in a "Camscan" scanning microscope with "Link-860" equipment for X-ray analysis and an "EM-400T" transmission electron microscope.

Ductile 2Cr-2Ni-Mo-V steel and MO copper were chosen for the microstructure investigation of the inner structure of the shear bands. TEM-objects for the analysis of the fine structure of the shear regions were prepared as follows: from the metallographic sections containing RSB, half-finished products in the form of disks 3 mm in diameter and 0.5 mm thick were cut in such a way that the center of the RSB was situated approximately in the center of the half-finished product. The latter was made thinner from the side opposite the one containing the RSB. This operation was carried out in two stages: first by machining it down to a thickness of 0.15 mm and then by using an electrolytic method to obtain the thin foils transparent for electrons. To reveal the possible artifacts introduced during the foil preparation, one controlled experiment was carried out with initially nondeformed material. It was directed toward studying the fine structure of MO copper foils prepared by the one-side polishing technique described above.

Scanning Microscopy

In Fig. 9.3, the micrographs of typical round shear bands in MO copper and 2Cr-2Ni-Mo-V steel obtained by scanning microscopy is presented. RSB regions look like mirror non-etched plane circular areas. The thickness of those regions was determined by two techniques: by measuring the height of steps appearing on the circle boundaries after intensive etching, and by measuring the cross-section of RSB. The first technique results in an RSB thickness of 1-5 µm. SEM investigation of the cross-sections reveals that under each RSB there exists a region 250 µm thick in which the etching did not reveal initial grain structure. The main feature of this region is the presence of many bands parallel to the section plane. Their thickness is approximately equal to 1-2 µm and the widest of them (3-5 µm) is the evident cross-section of the shear band of interest.

Fig. 9.3. SEM micrographs of copper (a) and steel (b).

No difference in the chemical composition of the RSB and the adjacent regions was found by methods of local X-ray analysis. SEM-investigations of RSB in the "Camscan" microscope with a "Link" X-ray spectrometer and a "Geigerflex-D-max C" diffractometer show that the composition of RSB practically does not differ from the rest of the matrix.


2Cr-2N1-Mo-V steel. In the initial nondeformed state, this steel has a structure of low-tempered martensite with colony sizes within 1-5 µm and lath size on the order of 0.1-0.2 µm. In the inner volume of the lath, a uniformly spread dislocation and needle precipitations of the carbide phase of 0.05-0.2 µm in diameter are clearly seen as well. The fine structure of RBS, which appears in optical metallography mirror non-etching circles, differs from the initial structure very much. The RSB structure is a totality of ultrafine fragments, the mean dimensions of which are equal to L = 72 nm and d = 47 nm. The inner volume of the fragments is practically free from dislocations. The carbide phase is found neither in the volume of fragments nor on their boundaries. It should be noted that the fine structure of RSB has a morphology identical to that inside the adiabatic shear bands which are formed in steels of the ferrite-pearlite class during a high-rate strain, for example in explosive welding.

MO copper. Its initial structure in a nondeformed state contains equal-axis grains with a practically perfect interior. Dynamic loading of MO-copper specimens results in the nucleation of the RSB regions, the fine structure of which is oblong-shaped fragments with mean dimensions of L = 130 nm and d = 97 nm (see Fig. 9.4a). The inner structure of the fragments appears to be without defect while outside the RSB region there is a weak-disoriented cellular dislocation structure with twins in {111} planes.

Microdiffraction patterns from an area of 1 µm2 of RSB are entirely round (see Fig. 9.4b), which testifies that fragments are separated by large-angle boundaries whose orientation vectors are spread chaotically. As a whole, the structure described is similar to that in 2Cr-2Ni-Mo-V steel. The only distinctive feature of MO-copper is a nucleation, over the background of the fine RSB-structure, of the separate fragments of somewhat larger dimension on the order of 0.25-0.4 µm, of equal-axis form.

In the MO-copper specimen loaded under an impact velocity of 183 m/s, round shear bands were also found to be of interest. After annealing at 500°C for one hour in vacuum conditions, the dimensions of previous nanocrystalline fragments increased up to approximately 1-2 µm while outside the RSB regions, the grain size of' the matrix is not changed (280 µm).

Fig. 9.4. (a) Fine structure of RSB in copper and (b) electron diffraction pattern of RSB in copper from square cong2.

Conditions for Recrystallization

The local strain rate during the shearing process is equal to lambda = deltaUp/a where a is the thickness of the shear band. As previously stated, optical measurements show that a = 5 µm. This value needed, however, also includes the region surrounding a, following thermal relaxation, and is therefore greater than the actual shear zone during the passage of the shock wave. To estimate the actual value of a, one can use the expression obtained from Swegle et al. (1985) for the adiabatic shear band thickness, that includes the effect of thermal diffusivity. This will result in a value of a = 9 µm. The total shear strain is given by the local strain rate times the time during which the shearing is taking place. This latter parameter is determined from the time-resolved profile of deltaUp, and is found to be ~60 ns. Therefore, the total shear strain would be 1.8, a value too small to satisfy the recrystallization conditions of Meyers (1990). However, if one uses the particle velocities at the high end of the Gaussian distribution of velocities, one can obtain a local total shear strain of lambda = 3, which is sufficient for recrystallization.

Finally, the temperature rise may be estimated by taking into account that 0.9 of the total plastic work in the shear band converts into heat. The analysis carried out above allows us to deduce that shear localization provides a high value for shear strain, lambda=3, a strain rate of the order of 3 x 107 /s, and an associated temperature rise (although insufficient for melting). For example, the temperature required for recrystallizaation of steel is 721 K. These values of strain, strain rate, and temperature rise are sufficient for dynamic recrystallization of material. This implies that one may expect an intensive recrystallization process in the shear bands, as has actually been observed in our experiments. It is, on the one hand, an interesting deformation process, reminiscent of the well known adiabatic band formation. On the other hand, the difference from this process is in the unusual round form of the shear bands. This forms as a consequence of the surface tension exceeding the ductile friction. Although the mechanism of the structure formation proposed here still requires further exploration, the known mechanical and physical facts fit this interpretation reasonably well.


Abou-Sayed, A.S., R.J. Clifton, and L. Hermann. 1976. J. Experimental Mech. 16:127.

Grady, D.E. and M.E. Kipp. 1987. J. Mech. Phys. Sol. 35:95.

Mescheryakov, Yu.I., and A.K. Divakov. 1994. J. Dymat. 1, no. 4, p. 271.

Meyers, M.A., and A.H. Chokshi. 1990. Scripta. Met. 24:605.

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Published: August 1997; WTEC Hyper-Librarian