Cent. Eur. J. Eng. " 1(3) " 2011 " 217-233
DOI: 10.2478/s13531-011-0024-7
Central European Journal of Engineering
Physical Concept of Shear Fracture Mesomechanism
and its Applications
Vision article
Edward S. Dzidowski"
Wroclaw University of Technology, Faculty of Mechanical Engineering, 25 Smoluchowskiego Str., PL 50-372, Wroclaw, Poland
Received 08 February 2011; accepted 26 May 2011
Abstract: The key objective of the present paper is an attempt to create an interface between the existing inconsistent views
on the microscopic and macroscopic aspects of the mechanism of plastic deformation and shear fracture. This
will be enabled by a focus on the course and effects of the evolution of dislocation structure, and will consist in
considering an indirect, i.e. a mesoscopic scale of the discussed phenomena. Thanks to this, a synergy between
the mechanisms of deformation and fracture of materials will be proven, which will provide an opportunity for a
smooth transfer from the microscopic, through mesoscopic, to macroscopic scale of the analysed phenomena.
This in turn will offer an opportunity to define and use the new criteria for controlling the mechanism of shear
fracture. These criteria will be applicable to the complete range of temperatures and strain rates which are
typical of metal working processes. Some examples of how these criteria may be applied in order to optimise
the parameters of metal working will also be provided. These examples have made it possible to prove that the
physical approach to shear fracture mesomechanism offers much broader cognitive and utilitarian opportunities
than the existing purely mathematical methods. This is due to the fact that the physical approach allows for a
deeper understanding of shear fracture meso- and macromechanism, and generates new criteria controlling this
mechanism.
Keywords: Shear fracture " Mesomechanism " Macromechanism " Synergy " Control " Criteria " Applications
� Versita Sp. z o.o.
of materials during metal working processes. The most
1. Introduction
acute problem is lack of capacity to control the course of
fracture which in many cases involves no danger but is
essential to metal working processes including shearing
off, die shearing, or machining.
The fracture of materials is a primary restriction for the ef-
fective use of metal working processes. The above problem
Therefore, the key objective of the present paper is an
is intensified by the lack of a coherent theory of deforma-
attempt to create an interface between the existing incon-
tion and fracture resulting from large plastic deformation.
sistent views on the microscopic and macroscopic aspects
This state of affairs impedes the analysis of cause and
of the mechanism of plastic deformation and shear fracture.
effect relationships and consequently affects the predic-
This will be enabled by a focus on the course and effects
tion, prevention and/or control of the course of fracture
of the evolution of dislocation structure, and will consist
in considering an indirect, i.e. a mesoscopic scale of the
"
E-mail: [e-mail] discussed phenomena. Thanks to this, a synergy between
217
Physical Concept of Shear Fracture Mesomechanism and its Applications
the mechanisms of deformation and fracture of materials
will be proven, which will provide an opportunity for a
smooth transfer from the microscopic, through mesoscopic,
to macroscopic scale of the analysed phenomena. This in
turn will offer an opportunity to define and use the new
criteria for controlling the mechanism of shear fracture.
These criteria will be applicable to the complete range of
temperatures and strain rates which are typical of metal
working processes. Some examples of how these criteria
may be applied in order to optimise the parameters of cold
and hot metal working will also be provided.
Moreover, the usefulness of mesoscopic fracture concept
will be presented with a view to revise the existing opin-
ions on the forming limit diagram for sheet metal forming
processes, as well as the views on the mechanisms of the
formation of various chip types in the course of machin-
ing. Another example of the application of those criteria
will be to prove the usefulness of mesomechanics for the
interpretation of the reasons for the degradation of the
Figure 1. Macroscopic concepts of shear process: a) shear stages
properties of materials which are to be used in increased
according to slip line theory (I-IV) and effect of clamp Q on
shape of slip velocity discontinuity line as likely fracture
temperatures. The issue discussed here is the degradation
trajectory (V-VI); b) shear stages according to transition
of useful properties resulting from cold metal working. To
zone theory (XI-XIV); c) distribution of slip lines for shear
provide an example, the above refers to the pipe bending with flat (VII-VIII) and sharp-pointed (IX-X) stress concen-
trator. Based on [1] and [2].
process applied in the construction of pipelines in heat
and power generating plants, and other similar facilities.
The perspective of further development and wider usage
of the mesoscopic concept of failure and fracture of mate-
rials accompanying large plastic deformation will also be
ally done by pressing the sheared material against the
indicated.
cutting tool (Fig. 1a, V-VI). With this the possibilities of
the method are exhausted. The fact that shear strain de-
termined by this method approaches infinity poses an ad-
2. Hitherto existing views on the
ditional problem. The problem has been partially solved
by the development of the theory of transitional zones.
mechanisms of fracture of materials
The introduction of the theory of transitional zones
2.1. Macroscopic views on the mechanism of
(Fig. 1b) made the values and distribution of strain in
shear fracture
the final stage of shearing real [2]. This means that in-
stead of a line (a surface) with zero thickness (Fig 1a, IV),
The earlier macroscopic methods of the analysis of the
an area having the shape of a biconvex lens is considered
development of strains and fracture in processes based
(Fig. 1b, XI-XII). The beginning of the formation of this
on shear were based mainly on the slip line field theory
area is identified with conditions corresponding to the ac-
and the theory of transition zones. Both theories have
tion of an absolute stress concentrator (Fig. 1c, VII-X). But
serious limitations. According to the slip line field the-
it is not known when and why such a significant change in
ory (Fig. 1a), the plastic sinking of the cutting tool in the
the stress concentration conditions occurs. Moreover, it is
sheared material first causes gradual widening and then
assumed that once the lens is formed, it does not change
narrowing of the plastic strain area [1]. Characteristically,
its shape but only diminishes as the displacement of the
this area finally assumes the shape and dimensions of a
cutting tool increases (Fig. 1c, XIII-XIV).
line (a plane) with zero thickness (Fig. 1a, IV). The line
defines the location of slip velocity discontinuity and it To sum up, the above macroscopic theories do not explain
is identified with the presumed trajectory of fracture. It clearly enough the mechanism and causes of the fracture
is thought that the only way in which the shape of the of a material during its shearing. This makes the control
fracture trajectory can be changed is by eliminating the and optimisation of shear-based processes (machining, die
rotation (bending) of the sheared material, which is usu- shearing, etc.) difficult.
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E. S. Dzidowski
Figure 2. Mechanisms of brittle fracture: a) type 2, b) type 3, c) type
Figure 3. Mechanisms of non-brittle fracture: a) ductile, b) rupture,
1, d) definition of the three type of brittle fracture. Based
c) fracture mechanism map, d) intergranular creep frac-
on [3 6].
ture. Based on [3 6].
2.2. Microscopic views on the mechanism of
e.g., the precision of die shearing and similar technological
fracture
processes, arise. Neither is the problem of shear fracture
trajectory control solved by the theory of adiabatic shear
Typical views on fracture mechanisms are presented on
bands (Fig. 4).
maps of fracture mechanisms (Figs. 2 and 3).
As the figures show, the brittle fracture mechanisms
(Fig. 2a, b) and the ductile fracture ones are explained 2.3. Maps of deformation mechanisms
quite differently even though both require preceding
Figure 4 shows the location of the areas in which adiabatic
plastic deformation. The brittle fracture mechanism is
shear bands occur depending on the kind of material, the
explained by the effects of a flat pile-up of disloca-
rate of its deformation, the temperature and the magnitude
tions (Fig. 2a,b), whereas the ductile fracture mechanism
of the strains (not shown on the map) grey area in Fig. 4.
(Fig. 3a) is explained by the nucleation and development
According to Fig. 4, adiabatic shear bands (ASB) occur
of voids around inclusions and separations. This means
during cold deformation. The presence of adiabatic shear
that two different theories of fracture are applied here:
bands is equated with thermal softening which takes place
the theory of dislocations in the case of brittle fracture
in the region of the dislocation mechanism of deformation
and a modified theory of the porous body in the case of
(blackened area on Fig. 4). Adiabatic shear bands ap-
ductile fracture [3 6].
pear only after critical strain ł and critical strain rate
Problem. Due to the lack of cohesion between the above
"
ł are exceeded. Moreover, their appearance largely de-
theories the causes of the transition from ductility to brit-
pends on temperature. In some cases, the temperature is
tleness (Fig. 2d) cannot be clearly explained. Moreover,
very low, e.g. for aluminium it is about about 200 degrees
the above model of the ductile fracture mechanism does
centigrade below zero.
not explain the fracture of pure metals or the fracture of
monophase metal alloys. Neither does this model gener- Problem. The theory of adiabatic shear bands does not
explain the mechanism of shear fracture which occurs at
ate any criteria for the control of the trajectory of shear
"
strain rates lower than the critical ones (ł Ą ł ).
fracture. Since it is not possible to control the trajectory of
shear fracture, several technical problems, connected with, Therefore one can conclude that the shear fracture prob-
219
Physical Concept of Shear Fracture Mesomechanism and its Applications
three main areas separated from each other by thick lines.
The upper limit of the first area marks the strain mea-
sured at the end of the yield threshold ( ). The upper
limit of the second area is marked by uniform strains ( ).
The boundaries of the third area are marked by failure
strains ( ).
Against the background of the three areas the bound-
aries of subareas, corresponding to the successive stages
in the evolution of the dislocation structures, can be dis-
tinguished. No complete coincidence of the boundaries
of the subareas and those of the three main areas is ob-
served, however this poses no problem for the approach
adopted below. The present author proposes to focus on
the subarea with strongly disoriented cellular structure
(the shaded subarea in Fig. 5). In the author s opinion
this subarea is closely linked to the shear fracture mech-
anism.
Problem. The above subarea of strongly disoriented cellu-
lar structure is not contiguous with the failure strain ( )
curve. In other words, there is still no clear connection be-
tween the evolution of dislocation structures and ductile
fracture, and particularly shear fracture.
This is due to, among other things, the fact that a cellular
structure belongs to low-energy structures, and as such
does not explain the causes of the fracture.
3. Basic problems, restrictions and
paradoxes resulting from the applica-
tion of the hitherto existing theories of
strain localization and fracture
3.1. Problems of chip formation mechanism
modeling
The condition and surface properties of a machined mate-
rial and the wear and life of the tools depend on the type
Figure 4. Strain rate/homologous temperature deformation maps.
of chip formed during machining. The type of chip also
Based on [7, 8].
significantly affects the operation of the machine tools,
especially numerically controlled ones.
Although there are only three basic types of chip (discon-
lem still is not fully correlated with the dislocation mech-
tinuous, segmental and continuous) [10 12], no physical
anism of plastic deformation, although the research on the
model exists which would explain why and how a chip of
evolution of dislocation structures seems to be quite ad-
one type changes into a chip of a different type. Due
vanced (Fig. 5).
to the lack of such a model, the effective control of the
machining process is still unattainable. One should note
that according to the current machinability criteria [13] no
2.4. Maps of dislocation structures
improvement in the machinability of monophase materials
Figure 5 shows a map of the evolution of dislocation struc- is possible.
tures depending on temperature and the magnitude of The modelling of chip formation has been the subject of in-
strain. Characteristic strain values divide the map into tensive researches for a long time. Although many models
220
E. S. Dzidowski
Figure 5. Map of dislocation structure evolution. Based on [9].
have been created, some of the first models, i.e. Pispanen s formed and what should determine the boundaries of their
model (1937) and Merchant s model (1945) - Fig. 6a, are occurrence on maps of deformation mechanisms (Fig. 6b)
most often found in textbooks [14 16]. This is due to the [26] still remain unanswered. According to Fig. 6b, the
fact that none of the more advanced models (Fig. 6a) [17 rate of deformation is not a clear-cut criterion for such
20] explains the formation of more than one type of chip demarcation, especially as the occurrence of the particu-
and usually the stabilized stage in the formation of a ho- lar types of chip is not accompanied by a change in the
mogeneous chip is modelled. plastic strain mechanism (the shaded areas in Fig. 6b).
The basic reason for this state of affairs is the limitations
All of this discourages a search for new physical chip for-
of continuous medium mechanics due to which the com-
mation models and purely numerical models are used in-
monly used models do not generate fracture criteria and
stead (Fig. 6c) [27 30]. There are no indications that nu-
thus are unable to account for the other types of chip.
merical models represent a viable alternative since they
The least questionable are sawtooth chip models. They
do not generate any more physics than the one already
are probably the only models which are physically and
contributed by the previously made assumptions based on
theoretically well-grounded, since this type of chip can
the current knowledge about machining.
be easily linked to the presence of adiabatic shear bands
(Fig. 6b) [21 24]. This, however, does not mean that This means that the modelling of the mechanism of chip
each sawtooth chip is connected with adiabatic shear [25]. formation and change of one type of chip into another still
Moreover the questions of how chips of the other types are remain out of reach.
221
Physical Concept of Shear Fracture Mesomechanism and its Applications
Figure 6. Synthetic illustration of problems related to chip formation mechanism modelling.
3.2. Problems and paradoxes of the hitherto more, different strain localization criteria have to be used
for different states of strain (the problem of LSCs left and
existing limit strain curve concept
right side) - Fig. 7b,d. In the author s opinion, identifying
Strain localization and fracture are generally regarded to strain localization exclusively with local thinning of the
be the phenomena which ultimately delimit sheet metal material ignores the physical sense of this phenomenon
forming (Fig. 7a). and blurs its close link to fracture.
The use of necking as a strain localization criterion and
Limit strain curves (LSCs) are most commonly used to de-
the treatment of sheet metal fracture as a sort of refer-
termine limit strains relating to the above two limitations.
ence point for the experimental determination of LCSs
Although the curves are used to determine the values of
(Fig. 7g) is a source of fallacious notions about the strain
both kinds of limit strains, strain-localization LSCs are
localization-fracture relationship (Fig. 7i).
still regarded to be superior. The appearance of a fur-
row - strong local thinning of the formed material - is In the author s opinion the view that in certain strain in-
thought to be a tangible sign of strain localization. This tervals fracture occurs without strain localization (Fig. 7i)
strain localization criterion is purely geometric. Further- is paradoxical. This view concerns the forming of sheet
222
E. S. Dzidowski
Figure 7. Synthetic illustration of problems related to limit strain curves (LSCs) construction.
223
Physical Concept of Shear Fracture Mesomechanism and its Applications
metal by close to pure (cup) drawing (the left side of LSCs D1) and it consists in the loss of cohesion between the
- paradox 1) and forming close-to-uniform biaxial tension particular layers of the material. As the fracture reaches
(the right side of LSCs - paradox 2) - Fig. 7i. This leads points 2 and 3, the fracture mechanism changes. From
to false notions about the relationships between strain now on the fracture propagates only along the defective
localization and sheet metal fracture in different states of grain boundaries (Fig. 9b, line 2-3 and Fig. 9a, boundary
strain, and to incorrect estimates of the limit strains. GB2).
Hence the final shape of fracture surface A-2-3-4 and that
of surface A1-2-3-4 depend on the shape and width of the
4. Mesoscopic-macroscopic con-
lenticular strain localization zone and on the magnitude
cept of fracture of materials accom-
of the displacements along the defective grain boundaries
(Fig. 9 a, b). This means that the fracture initially prop-
panying large plastic deformation
agates along the boundaries and then across the strain
localization zone formed by the shear bands (Fig. 9b,
The mesoscopic-macroscopic concept of the shearing pro-
c). Characteristically, the strain localization zone shrinks
cess, proposed by the author of this paper, is illustrated in
from top and bottom and eventually widens as a result
Figs. 8 and 9 [31, 32]. According to this concept, the onset
of intercrystalline displacements of the material. Immedi-
(Fig. 8b) and then the development of strain localization
ately before the total separation of the sheared material
in mesoscopic shear bands (Fig. 9a) are of key importance.
into two parts, the zone assumes a shape similar to par-
Here a case of strain localization in quasi-isothermal,
allelogram BCE1F1 (Fig. 9b, blackened area). The above
mesoscopic shear bands (SB) is considered. The develop-
shear fracture mechanism model relates fracture not only
ment of shear bands manifests itself in the appearance of
to the properties (misorientation) of the material s sub-
a lenticular strain localization zone (Fig. 8b). The begin-
structure within shear bands, but also to transverse (acting
ning of strain localization in the mesoscopic shear bands
puts an end to the displacements of the free surface: U transversely to the direction in which shear bands (SBs)
develop) tensile stresses. Such stresses may arise nat-
= U (Fig. 8a, b). The moment when shear bands
urally or be artificially generated as in shear with ten-
appear and the free surface displacements are inhibited
sion. One should note here that the effective value of
can be easily predicted. It is enough to know the rela-
artificially generated tensile stresses amounts to about
tionship between limiting strain U and strain-hardening
0.25 of the yield point value (�0 2). Conventional shear-
coefficient n [33, 34]. Strain (displacement) U is limiting
ing (Fig. 9) is an example of the natural generation of
from the strain localization point of view. The development
transverse tensile stresses. The stresses arise because of
and properties of the dislocation structure within shear
interaction between SBs and the original grain bound-
bands (Fig. 8 h, i, j) determine the susceptibility of the
aries (see Fig. 9a, GB2). The development of shear bands
material to fracturing along the shear bands. The origi-
results in strong flattening and rotation of the grains and
nal grain boundaries become defective as a result of the
in the formation of characteristic laminar lenticular strain
interaction between them and the shear bands (Fig. 9a,
localization zones (SLZ). This may be accompanied by the
boundary GB2). This means that the course and effects
formation of wedge-shaped discontinuities along the orig-
of the shearing process depend here only on the synergy
inal grain boundaries (see Fig. 9a, GB2). The tendency
between the strain localization mechanism and the mech-
to form such discontinuities depends to a large degree
anism of fracture along mesoscopic shear bands.
on the condition of the original grain boundaries. One
The macroscopic course of fracture depends on the
of the factors conducive to the lamination of the origi-
shape of the boundaries of the strain localization zone
nal grain boundaries may be adsorption of foreign atoms.
(Fig. 8b, 9b) and the magnitude of the displacements of
The defective grain boundaries become similar to inclined
the material along the defective grain boundaries (Fig. 9a).
planes whereby the sheared portions of material move and
separate along the SBs (Fig. 9a, shear bands SB1-SB4
and the next ones). The separation is the most complete
5. Mesoscopic-macroscopic model
near the boundaries of SLZs, i.e. at the places where
of shear fracture mechanism
displacement (non-dilatational strain) gradients are the
steepest (see Fig. 9 a and b). To sum up, the shape of
As Fig. 9 shows, the fracture of the sheared material con- shear fracture trajectories depends here on: the way in
sists in its separation along mesoscopic shear bands SB which shear bands develop, the properties of the shear
(Fig. 9a, separation "L)). Initially the fracture propagates bands, the condition of the original GBs and the shape of
along the shear bands (Fig. 6b, trajectories A-B and E1- the SLZ formed by the mesoscopic SBs. This means that
224
E. S. Dzidowski
Figure 8. Mesoscopic-macroscopic concept of shearing. According to E.S. Dzidowski. Description in text.
by properly changing the properties and direction of de- within the shear bands. Depending on the needs, stack-
velopment of shear bands and the way in which transverse ing fault energy, the strain hardening ability of the ma-
tensile stresses are generated one can change the shape terial, the angle of disorientation of the substructure
of the shear fracture trajectories or totally eliminate the formed within the shear bands, the direction in which the
fracture. shear bands propagate, the original condition of the grain
boundaries, the location of the strain localization zone and
so on can be such a criterion. Selected examples illus-
trating the possibilities of controlling the shearing process
6. Criteria and principles of frac-
are shown in Fig. 10.
ture control resulting from the meso-
scopic concept of shear fracture
6.1. General mesoscopic-macroscopic crite-
ria and principles of fracture control in pro-
The presented mesoscopic-macroscopic concept of the
cesses based on material shearing
physical modelling of the shearing process generates cri-
teria for the effective control of processes based on the
shearing of materials. The criteria include everything Figure 10 shows mainly the influence of: the length of
which affects strain localization in mesoscopic shear bands the material s cropped part, the additional state of stress,
and the properties of the dislocation structure formed and the properties of the shear bands on the course and
225
Physical Concept of Shear Fracture Mesomechanism and its Applications
Figure 9. Model of shear fracture mechanism (b) and scanning electron microscopy results which validate it (a, c). According to E.S. Dzidowski.
Description in text.
effects of shear fracture. According to figure 10, a change solely on the properties of the substructure which
in the length of the cropped part leads to a change in the forms within shear bands.
kind of process. In the considered case, the processes are
cropping and orthogonal cutting (machining). They differ
Further to the above, the issue arises on how the proper-
only in the shape of the macroscopic strain localization
ties of the substructure may be changed within the meso-
zone (MSLZ) and the way in which the latter develops.
scopic shear bands.
In the case of cropping, the zone assumes the shape of
a biconvex lens whose axis is parallel to the direction of
6.2. Stacking fault energy as a criterion
shearing. In the case of machining, the MSLZ assumes the
for controlling the mesoscopic-macroscopic
shape of a half-lens whose axis is skew to the direction of
mechanism of formation of various chip types
shearing. Because of the skewness of the axis machining
is a process of cyclic formation of countless MSLZs, owing
In the mesoscopic-macroscopic concept of shear fracture
to which a chip forms.
mechanism presented above, the chip type depends on the
The type of chip depends solely on the properties of the
tendency of the material to fracture along the boundary of
substructure forming within mesoscopic shear bands. This
the macroscopic zone of strain localisation. At the same
means that:
time, the tendency for shear fracture is itself dependent
" the same phenomenon, the localization of strains in
on the course and effects of the evolution of dislocation
mesoscopic shear bands, underlies both processes;
structures. One may conclude that the method to change
the chip type may consist in changing the stacking fault
" the direction of development and shape of the frac-
energy. This is due to the fact that the course of the
ture trajectory depend on the shape of the MSLZ
evolution of dislocation structures depends on the stacking
and the way in which the transverse tensile stresses
fault energy, which is shown in figure 11. The research
are generated;
conducted by the author of the aforementioned paper in
" the material s tendency to shear fracture depends collaboration with his co-worker indeed confirmed such
226
E. S. Dzidowski
Figure 10. Examples of interpretation possibilities of mesoscopic-macroscopic model of shear mechanism (according to E. S. Dzidowski).
227
Physical Concept of Shear Fracture Mesomechanism and its Applications
Figure 11. Dependence of dislocation cell size and tendency for cross-slip and dissociation of dislocations on stacking fault energy in copper and
silver alloys. Based on Swann 1963.
Figure 12. Influence of stacking fault energy on the type of chip (according to Dzidowski, Chruscielski).
228
E. S. Dzidowski
possibility, which is illustrated in the figure below [33]. tion in shear bands. The way in which shear bands de-
velop determines only the macroscopic course of strain
As figure 12 shows, reducing the stacking fault energy
localization and the prior-to-fracture strain values. The
(SFE) leads to a change in the type of chip from continu-
maximum shear stress criterion, which defines the shape
ous (Fig. 12a) to segmental (Fig. 12b) and discontinuous
of the strain-localization limit strain curve (SLLSC), was
chip (Fig. 12c). It should be noted that the chips formed
during intense shear fracture (segmental and discontinu- adopted as the strain localization onset criterion. The
ous chips) have been obtained in the materials more plas- fracture limit strain curve (FLSC) is situated above SLLSC
for the whole range of stress. The distance between the
tic (Cu + 37.4% Zn), or as plastic as (Cu + 7.2% Al) plain
two curves depends mainly on the way in which strain lo-
copper (see figure 12: values A5 and A10). This means
that the equals sign currently put between the discontin- calization develops, i.e. on the concentrated or dispersed
development of shear bands. The fracture mechanism is
uous chip and the brittleness of the machined material, or
closely bound up with the development of shear bands.
the presence of brittle particles [13], shall be deemed as
dramatically inefficient or even incorrect, as brittle frac- The mode of fracture is determined by the local state of
stress and as a result, by the state of strain (Fig. 14).
ture has been confirmed in none of the examined materials
(Fig. 12). This also means that the stacking fault energy
Experiments were carried out [34] to validate the assump-
may become a new and effective criterion for controlling
tions of the above LSC conception, to determine the mech-
the mesoscopic mechanism of chip formation during the
anism and mode of strain localization development de-
machining, as well as for other similar processes, includ- pending on the state of strain and to establish the re-
ing abrasive wear.
lationship between the investigated phenomena and limit
strain values. Scanning microscopy was employed. The
mechanisms and modes of the development of the phe-
6.3. The way of developing shear bands as
nomena were determined by examining the development
a criterion for the modification of the existing
of shear bands and by fractography.
shape of the diagram of metal sheet limit defor-
The results of the investigations challenge the universality
mation
and meaning of the  furrow strain localization criterion.
It has been found that an occurrence of strain localization
Identifying strain localization exclusively with local thin-
does not necessarily entail the appearance of a  furrow
ning of the material ignores the physical sense of this phe-
or apparent disturbance of the sheet metal forming pro-
nomenon and blurs its close link to fracture. This leads to
cess. Shear bands can develop in both concentrated and
false notions about the relationships between strain local-
dispersed mode. Thus the mode in which shear bands de-
ization and sheet metal fracture in different states of strain
velop determines the macroscopic manifestations of strain
and to incorrect estimates of the limit strains (Fig. 7i). The
localization and the critical strain values as regards frac-
author s analysis of the problem and the results of his in-
ture. This means that by  dispersing the development of
vestigations into the strain localization mechanism and
shear bands one can prevent the appearance of a  furrow
the fracture mechanism under large plastic strains have
and to increase the fracture related critical strains. In
led him to the following conclusions:
this way the strain localization-fracture relationships for
1. It is possible to apply one criterion valid for the whole
the right side of LSC have been explained and thus the
range of strain. This criterion should define only the con-
dilemma arising from the inapplicability of the Hill crite-
ditions for the onset of strain localization understood as
rion [35] and the limitations of the Marciniak-Kuczyński
an intramaterial phenomenon.
theory [36] for this side of LSC has been solved.
2. Shear fracture of cold-formed sheet metal cannot occur
without prior strain localization.
3. The critical strain value for fracture is always higher
7. The prospects for development
than the one for the onset of strain localization and the
difference between them depends on the mode in which
and further application of mesome-
strain localization develops. The above theses were in-
chanics of failure and fracture of ma-
corporated into a new conception of the limit strain curve
terials
(Fig. 13).
This conception is based on the assumption that the strain
localization and fracture mechanisms in sheet metal have The abovementioned examples of the application of the
a common origin and there is a synergy between them. mesoscopic-macroscopic shear fracture concept and model
In fact, according to the proposed conception, there is do not fully exhaust all the possible applications of this
only one strain localization mechanism: strain localiza- model. This is due to the fact that this model gener-
229
Physical Concept of Shear Fracture Mesomechanism and its Applications
Figure 13. Proposed new, mesoscopic concept of limit diagram for metal sheet forming.
Figure 14. Effect of state of strain on mode and morphology of sheet metal fracture.
ates both the criteria for predicting the commencement plastic deformations occur as a result of the development
of fracture, and the criteria for controlling the course of of mesoscopic isothermal shear bands [37, 38]. These ex-
and/or the criteria for preventing shear fracture. Conse- amples have made it possible to prove that the physical
quently, this model may be applied wherever large local approach to shear fracture mesomechanism offers much
230
E. S. Dzidowski
broader cognitive and utilitarian opportunities than the [13] Higgins R.A., Engineering Metallurgy. Part I Applied
existing purely mathematical methods, as presented e.g. Physical Metallurgy, Edward Arnold, A division of
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