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Mechanisms of rotational effect in shock-loaded crystalline metallic materials
M. Gutkin, I. Ovid’Ko, Yu. Meshcheryakov
To cite this version:
M. Gutkin, I. Ovid’Ko, Yu. Meshcheryakov. Mechanisms of rotational effect in shock-loaded crystalline metallic materials. Journal de Physique III, EDP Sciences, 1993, 3 (8), pp.1563-1579.
�10.1051/jp3:1993215�. �jpa-00249021�
Classification Physic-s Abst>.acts
61.70 62.50 81.40
Mechanisms of rotational effect in shock-loaded crystalline
metallic materials
M. Yu. Gutkin, I. A. Ovid'ko and Yu. I. Meshcheryakov
Institute of Machine Science Problems, Russian Academy of Sciences, Bolshoj 61, Vasil. Ostrov, St. Petersburg 199178. Russia
(Received II Maj> /992, >.eiised and accepted 3 June J993)
Abstract. Physical models are proposed which describe the rotational effect (formation of local rotated regions) in crystalline metallic materials at some regimes of schock-wave loading. The suggested models treat the rotational effect as being related to a cry~tal-to-glass-to-crystal
transformation induced by an interaction of a shock-wave front with the local stress fields of dislocation pile-ups. In doing so, several variants of the evolution of defect structures in shock- loaded metallic materials are examined which depend on shock-wave parameters. In particular, the
formation of shear bands and microcracks both located within and near boundaries of the rotated regions are considered in detail.
1. Introduction.
Shock-wave deformation of solids is the traditional subject of intensive experimental and theoretical studies in applied physics, e. g. [1, 2]. In recent years, a new effect the rotational
effect under shock-wave deformation has been observed experimentally [3-10]. This effect
occurs in crystalline metallic materials (steels, copper, aluminium- and titanium-based alloys)
and is as follows [4-10]. In shock-loaded metallic crystals the small regions, with dimensions
being 3-100 ~Lm, are formed which are rotated relative to the neighbouring material. The
disorientation of such rotated regions (which hereafter will be called rotation cells (RCS)) relative to the neighbouring material, ranges from units to dozen degrees. The formation of
RCS seems to be a relaxation effect which does not contribute to macroscopic forming of
loaded samples and occurs as a natural stage of the evolution of a defect structure at high-strain
rates.
At present, microscopic mechanisms of the rotational effect are unknown. So, standard mechanisms of the rotational plastic flow in quasistatically deformed metals (e. g., I1-14]) are not suitable, since they do not explain experimentally observed [4-10] basic features of the rotational effect under shock-wave deformation. The features are as follows. (a) Dimensions
of RCS range from 3 to 100 ~Lm. (b) There are two ba~ic types of RCS which are related to
crystallographic and material rotations, respectively. (c) Crystallographic RCS are approxima-
tely spherical. (d) At boundaries of material RCS which have imperfect (but close to spherical)
form there are often microcracks present. (e) RC boundaries are characterized by a high-angle
disorientation. (fl There exists a resonance interval of the shock-load rate, within which the rotational effect occurs. (g) Parameters (density, spatial organization, etc.) of the dislocation
structure within and near RCS range widely for different regimes of shock-wave deformation.
The main purpose of this paper is to suggest physical models which effectively describe the formation of RCS in shock-loaded metallic materials. In doing so, special attention is paid to analysis and explanation of the above features of the rotational effect which occurs under
compressive wave propagation. The suggested models of the effect are based on an idea about shock-wave-induced crystal-to-glass-to-crystal transformations in local regions near disloca- tion pile-ups- This idea has been briefly discussed in a short communication [15].
The paper is organized as follows. There is a brief review of experimental data [3-10]
present in section 2. Section 3 deals with analysis of features of dislocation ensembles in shock-loaded metallic materials. In section 4 models for the formation of crystallographic RCS
are suggested. Section 5 is concerned with models which describe the formation of material RCS. Section 6 contains concluding remarks.
2. The rotational effect in shock-loaded metallic materials (a short review of experimental data).
The possibility of the formation of local rotated regions in shock-loaded steels was first noted
by Pond and Glass [3]. A systematic experimental examination of the rotational effect in
crystalline metallic materials has been carried out by Meshcheryakov and co-workers [4-10]
who have studied RCS by conventional techniques of optical and electron microscopy, X-ray
analysis and so on.
Experiments [4-10] show that there are two basic types of RCS which are material and
crystallographic ones. Their formation mechanisms essentially differ from one another. So, the formation of a material RC entails the mechanical rotation of a local region (cell) as a whole relative to some axis. At the same time, the formation of a crystallographic RC represents a
lattice-orientation transformation in a local region (cell), in which case, proper displacements
of atoms usually are negligible within this region.
Material RCS have been observed in viscous high-strength steels [5-7, 10] aluminium- and
titanium-based alloys [5-8, I01 under shock-wave deformation. Such RCS are mesoscopic-
scale objects with an imperfect form, being close to spherical their diameters range from 3 to
30 ~Lm. Within material RCS, as a rule, there are found to be present fragments and small
subgrains divided by dislocation sub-boundaries. Sometimes, material RCS form chains (lines)
or more complicated configurations (circles, circle fragments, spirals) whose characteristic dimensions are 100-300 ~Lm. So, a circle of material RCS looks like a « bearing » with the RCS being « bearing balls
».
In brittle solids the boundary regions which divide material RCS from the neighbouring
material contain microcracks oriented tangentially to the boundaries (Fig. I).
Crystallographic RCS have been observed in steels, copper, and titanium-based alloys under
shock-wave deformation [7, 9, 101. Such RCS are characterized by perfect spherical form
(Fig. 2a) and dimensions ranging from 3 to 30 ~Lm. These crystallographic RCS formed under
compressive-wave propagation usually unite in chains (lines), in which case the dimensions of the RCS which form a chain non-monotonically vary along this chain (Fig. 2b).
Sometimes, crystallographic RCS have been observed which formed under release-wave (1)
(') A release wave results from a reflection of the initial (compressive) wave from a free surface of a loaded sample.
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a)
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r
b)
Fig. I. Individual material rotational cells in high-strength aluminium-based alloy DIG (2024 ASTM) (a) and in viscous Cr-4Ni-Mo steel [10] (b).
propagation. Such RCS usually are disorderly distributed in the material and characterized by dimensions ranging from lo to 80 ~Lm. Analysis of RCS formed under a release-wave loading
is beyond the scope of the present paper.
An important feature of the rotational effect is that it has a resonance character relative to the shock-load rate. This effect occurs within a certain (narrow) interval of shock-load rate for each material.
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Fig. 2. -Individual crystallographic rotational cells in viscous Cr-4Ni-Mo steel (al and a chain of
crystallographic rotational cells in Cu [9. 10] (b).
3. Formation of dislocation loop pile"ups in shock"loaded metallic crystals.
In constructing physical models for the rotational effect under shock-wave deformation we start from the analysis of real dislocation structures which are formed in shock-loaded metallic
crystalline materials. In doing so, we confine ourselves to consideration of dislocation structures in steels. This is related to two points which are as follows. First, the majority of
experiments [5-7, 9, 10] concerning the rotational effect deal with, namely, steels. Second, dislocation structures in steels, like other metallic materials characterized by low values
(~ 40 MJ/m2) of stacking fault energy II, 2], represent a rather simple subject for quantitative analysis.
In iron and steel materials, after deformation by a shock-wave with an amplitude smaller than 13 GPa, usually straight and parallel rows of screw dislocations are observed which are
oriented along (II I) directions inside grains [1, 2]. Such experimental data allow Hombogen [16] to propose the model which describes characteristic dislocation structure in shock-loaded
steels as being the ensemble of dislocation loops, in which case edge segments of the
dislocation loops move in the shock-wave front, while screw segments of the dislocation loops
are immovable. In this event the length of each screw segment increases parallel with the motion of the edge segments.
It is evident that the aforesaid evolution of the dislocation loop ensemble leads to the formation of the pile-ups consisting of the edge segments of the dislocation loops when such segments are stopped by effective obstacles (grain boundaries, non-metallic particles, etc.) which are present in steels. Usually, dislocation pile-ups essentially influence physico-
mechanical properties of metallic materials. In particular, the nucleation of new phase at phase transition [17] and melting [18] can occur near the head of a dislocation pile-up- This allows us to suggest that, in the discussed situation concerning the rotational effect, the local amorphous phase is formed in the region near the dislocation pile-up head characterized by both high stress
concentration and high latent energy density.
Detailed analysis of the amorphous phase nucleation followed by the rotated region
formation near the dislocation loop pile-up is the subject of the next subsections. Here we shall focus our attention to consideration of the stress-field characteristics of the dislocation pile-up
which cause the pile-up vicinity to be the preferable place for the amorphous phase nucleation.
Let us estimate the value of the local pressure induced by a stopped pile-up of rectangular
dislocation loops within the region with dimensions close to the characteristic dimensions of
the rotated regions. In doing so, we model the dislocation loop pile-up as the loop of
superdislocation with the Burgers vector B
= Nb. Here N denotes the number of dislocation loops being elements of the pile-up, b is the Burgers vector of such a dislocation loop, while
dimensions of the model superdislocation loop are d and 2 a (d » 2 a (Fig. 3). This model is
correct in handling the dislocation stress fields at distances r » f from the pile-up head, if the
length f of the dislocation pile-up obeys inequality : in 2 am d [19].
z
a
~
i
y
a
x
Fig. 3. The pile-up consisting of N rectangle dislocation loops with Burgers vectors b is modelled as the superdislocation loop with Burgers vector B Nb.
To calculate the stress field of the superdislocation loop, the method [20] is suitable, which is the integration of the stress tensor components of an infinitesimal dislocation loop over the
surface bounded by the superdislocation loop. In doing so, after some algebra, we find
GB uz
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'" (Ia)
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'
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«y- =
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l~
~ j ~v~ ll~~
~
i + i
+
/l~z~
~i v II I ~'°
where G denotes the shear module, v the Poisson ratio, u =x-x', u
= y- y', p~=
1<~ + u~ + z~. We are interested in studying the behaviour of the hydrostatic component of the
superdislocation loop stress field in vicinity of the front edge segment (-awx ma, y = 0, z
= 0), I.e. in the medium points with the coordinates x, y, z « d. The component in this vicinity can be deduced from (I) as
«l~«,>+«>.>+«ziZl+i
~~~ii~j~ I' I'
~~~~~~Y~~~~~~/(x-~)~~y~+~~ ~/(x+~~~y~+z~~~ ~~~
Equation (2) determines the hydrostatic stress field near the pile-up head. The hydrostatic
stress maps at the planes (xz, y
=
0) and ~lz, x
=
0) are shown in figure 4. These maps
demonstrate the distribution of the hydrostatic compression over the dislocation sliding plane, that is, for z
~ 0 (2).
Let'us estimate the ratio YIP, where P
= p ii + v)/[3 ii v)] is the external impulse hydrostatic pressure, p is the applied mechanical stress under uniaxial shock deformation.
For doing this, we use the relationship [19]
B
= «(i v)il, (31
where To = 3 P (1 2
v )/ [2 (1 + v )] is the absolute value of the maximum shear stress which acts in the sliding plane of the superdislocation loop. Equation (2) can be rewritten with the
(2) The hydrostatic stress maps are antisymmetric relative to the sliding plane (.ry, z 0).
~«
~
0.03
o.05
5 o-1
0.2
-5 -3 -1
~«
~ 0.03
~
o.05
~ o-1
0.2 3
5 3
yla
Fig. 4.- Maps of spatial distribution of the hydrostatic stress field induced by the w-shaped superdislocation loop with the edge segment length being 2 a. Here we use value of ) ~ ~
as unit
w v a
for the hydrostatic stress field. (a) The section y
=
0. (b) The section ~ 0.
help of (3) as follows
where fix, y, z denotes the non-dimensional function of coordinates x, y, z, which figures in the square brackets in (2) values of this function label the lines with the constant hydrostatic
component of the superdislocation loop in figure 4.
The effective duration of the front of the elastic precursor of the shock wave is
I
m lo- loo ns, while the time needed for the generation of one dislocation loop with the help
of the Frank-Read mechanism is 0.5 ns when the shear stress is r~ w 10~ ~ G [2]. Thus, for the time period I which characterizes the elastic precursor front (with the maximum shear stress level r~, ~~~ - 10~ ~ G), the pile-up consisting of lo-loo dislocation loops can be formed near
some obstacle (e.g., a grain boundary) within a steel material. The length of such a pile-up is
f
m 0. I-I ~Lm which entails from (3) for r~
m 10~ ~ G, N
~ lo- loo, B
= Nb, b
w
3 1,
v w 0.3.
Within the framework of our model of the rotational effect we are interested in the analysis
of the rotated regions with dimensions 2 a. On the other hand, experimental data [4-10]
indicate the rotated regions to be characterized by mesoscopic dimensions, that is,
2 a
m
3-10 ~Lm. In this event the ratio if (2 al
m o-o1-0.3. For such a range of ratio, formula (2)
is correct. Then from (2). (4) one finds YIP
m (0.2-6 lx10~~ f(x, y, z). As a corollary,
within the region in which the formation of the local amorphous phase can occur, the
hydrostatic field of the dislocation loop pile-up ranges from 4-40 fb (near the pile-up, where
f(x
=
0, y
=
0, z
=
0. I a)
w 20 ; see Fig. 4a) to 0.1-3 fb (in regions distant by 2 a from the
pile-up, where f(.<, y, z)
m 0.5 see Fig. 4) is the value of P.
It should be noted that the plastic front of the shock wave induces new dislocations to join to the dislocation pile-up stopped by obstacles. In this event the value of
« increases due to the increase of both the pile-up length f and « external » pressure P. The qualitative picture of the
formation of the local regions with increased pressure is shown in figure 5.
Po, P, «
Po P
«
o
d d
~
Fig. 5. Local excitations of the shock-wave front near dislocation pile-ups (schematically). Here the axis D intersects the head of the dislocation pile-ups and is oriented along the wave propagation direction.
Fo denotes the mean pressure at the shock-wave front, P the effective local pressure, « the local pressure field induced by the dislocation loop pile-ups, 2a the length of edge segments (which are perpendicular to axis Di of the dislocation loops being elements of the dislocation pile-ups, d the mean
distance between the dislocation pile-ups.
