JOURNAL OF PETROLOGY
VOLUME 38
NUMBER 12
PAGES 1635–1644
1997
The Brittle–Ductile Transition in High-Level
Granitic Magmas: Material Constraints
DONALD B. DINGWELL∗
¨
BAYERISCHES GEOINSTITUT, UNIVERSITAT BAYREUTH, D-95440 BAYREUTH, GERMANY
RECEIVED JANUARY 1997; ACCEPTED AUGUST 1997
Granitic magmas residing at high levels in the continental crust
may be subjected to stress transients on a wide range of time-scales.
The origins of the stress transients may be internal, deriving from
the volume evolution of the magmatic system, or external such as
the rapid release of stresses during tectonic and volcanically derived
earthquakes. The strain response of the granitic magma is critically
dependent upon its viscosity and the magnitude and time-scale of
the application or release of the stress. The response of the magma
may be either ductile or brittle. Prediction of the expected response
of the magma requires an accurate and reliable method for determining
the location in temperature and time-scale of the transition of the
response of the melt from ductile to brittle by analogy to the glass
transition determined by frequency domain relaxation studies. The
application of the Maxwell criterion, which treats the magma as a
viscoelastic medium in the linear stress–strain regime, provides such
a method. Application of this method requires accurate viscosity and
elastic modulus data for the magma. The consequence of intersecting
the glass transition in a system where the total strains are significant
is brittle failure of the melt phase. Here, the material constraints
on the brittle–ductile transition of granitic magma are reviewed.
The transition of the mechanical response of magma
from ductile to brittle behavior can have enormously
important consequences for heat, mass and momentum
transfer. Despite this observation, and the fact that the
lithologies produced both by eruptive and high-level
intrusive silicic magmas give clear evidence of both types
of deformation, the characterization of this transition and
the quantification of the conditions necessary to achieve
it are not well understood for magmas. Fluid-saturated
granitic magmas residing at high levels in the Earth’s crust
can potentially experience the transition from viscous to
brittle deformation under a variety of sources of transient
stress related to their internal chemical and physical
evolution and the external circumstances of their emplacement and/or eruption (Dingwell, 1995).
Significant experimental progress towards quantification of the conditions necessary for the transition,
and prediction of the material response of the magma
to it, has been achieved in the past few years, chiefly in
the field of experimental deformation of magma. Here
the quantification of the properties of magma which
are chiefly responsible for controlling the mechanical
response of high-level granitic systems is reviewed.
High-level granitic magma is likely to be subject to
transient stresses stemming from a variety of internal and
external stresses. Those stresses may contain volume
and/or shear components. The internal stresses include
those stemming from volume changes associated with
boiling and crystallization phenomena as well as ascent
of the magma as a whole. The external stresses include
sources of transient stresses within the crust such as
tectonic stresses whose release results in earthquakes and
‘volcanic’ transient stresses where co-eruptive microearthquakes signal transient stress release in or below the
volcanic edifice. The combination of silicic melt chemistry
and high-level emplacement enhances the probability of
brittle response of the magma via at least three of several
depth-related factors: (1) at shallow depths, magmatic
degassing strongly increases the magma viscosity via
dehydration, foaming and crystallization; (2) the reduced
temperatures of the magma and host rock enhance
∗Fax: 49 921 55 3769. e-mail: [email protected]
 Oxford University Press 1997
KEY WORDS:
brittle; ductile; glass transition; melt; viscosity
INTRODUCTION
JOURNAL OF PETROLOGY
VOLUME 38
NUMBER 12
DECEMBER 1997
their propensity for brittle response; (3) surface-related
tectonically or volcanically generated gravitational instabilities can generate very high unloading strain rates
for magma at subvolcanic depths, and magma–water
contact in volcanic conduits or at the surface can generate
shock waves associated with explosive interactions.
VISCOELASTICITY AND THE GLASS
TRANSITION IN MAGMA
The response of a largely molten (<30% crystals) granitic
magma to the application of transient stresses is dominated by the behavior of the melt phase. As such, the
most important first step in the quantification of the
mechanical response of high-level silicic granitic magmas
is an adequate characterization of the glass transition in
such magma. Figure 1 illustrates the calorimetric behavior
of a granitic melt in the vicinity of the glass transition. The
transition from solid-like behavior at lower temperature to
liquid-like behavior at higher temperature causes a sharp
increase in the derivative thermodynamic properties of
the melt such as heat capacity and expansivity as relaxation modes involving the polyanionic network structure of the melt are activated by self-diffusion with
increasing temperature (Dingwell, 1990). The zone of
mixed response between the glassy and liquid regimes
corresponds to a partially relaxed viscoelastic response
of the system.
The significance of the glass transition for the mechanical response of magma lies in the aforementioned
phrases ‘solid-like’ and ‘liquid-like’ behavior. Simply put,
the liquid-like response of the melt to the application of
stresses is entirely viscous or ductile whereas the solidlike response is entirely elastic at small strains (i.e. in the
linear stress–strain regime) but brittle at the higher strains
commonly encountered in magmas in nature. It should
be noted that the width of the zone of hysteresis between
the fully glassy and fully liquid responses of the melt
(Fig. 1) is on the order of several tens of degrees. Translated through the temperature dependence of viscosity,
this width corresponds to several log units of viscosity,
which in turn implies that the viscoelastic response of
the melt can span several log units of strain rate in nature.
The experimental deformation of melts at low strain
and variable strain rate demonstrates clearly the width
of the zone of viscoelastic response in silicate melts
(Dingwell & Webb, 1990; Webb & Dingwell, 1995). Such
viscoelasticity data, expressed as the real (strain is in
phase with the applied stress) and imaginary (strain is
out of phase with the applied stress) components of the
viscoelastic response of a calc-alkaline rhyolite to the
application of torsional stresses, are illustrated in Fig. 2.
The width of the peak corresponding to the out-of-phase
component of deformation indicates the width of the
Fig. 1. Variation of heat capacity, C p, as a function of temperature.
The glass transition expresses itself as a sharp increase in the derivative
thermodynamic properties of the melt phase. An example of such a
derivative property is the heat capacity. At low temperatures the heat
capacity values correspond to the solid-like or glassy response of the
melt phase to temperature changes. The melt structure responds in a
disequilibrium fashion to temperature changes whereby the vibrational
component of the melt entropy can vary in thermal equilibrium, but
the configurational component of the entropy does not. This is because
the self-diffusion of the cations and anions is required by the mechanism
of structural reorganization or relaxation to higher-temperature equilibrium states. The diffusivity provides a kinetic threshold which must
be overcome on a specific time-scale of heating rate before metastable
equilibrium can be achieved. At temperatures higher than the glass
transition such a metastable equilibrium, involving both vibrational
and configurational components of structural change with temperature,
is achieved. The addition of the configurational component of the heat
capacity to its glassy component at T g generates much higher metastable
liquid values of the derivative property. The portion of the derivative
property curves near the glass transition temperature is transient, and
is path dependent in nature. The form of the curve in this interval
depends on material properties, the heating rate and (in the case of
heating) on the thermal history (and thus the quenched-in structure)
of the glass. Data for a haplogranitic melt with added B2O3 redrawn
from Knoche et al. (1992).
viscoelastic response of a rhyolite in the linear stress–strain
regime. This result demonstrates that viscoelastic response of a melt can be expected to be 2 log units of
strain rate slower that the relaxation strain rate calculated
by using the Maxwell relation (s=g/M), where s is the
relaxation time, g the viscosity and M the elastic modulus.
NON-NEWTONIAN FLOW AND
BRITTLE FAILURE
This onset of the viscoelastic response of the melt phase
has a corresponding phenomenon in nonlinear experiments where the deformation of the melt is no longer
independent of the deformation rate and the strains
reach much higher values, similar to those anticipated
in magmas in nature. Experiments to define the onset of
the non-Newtonian rheological response of the melt phase
have been conducted using a variety of deformation
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DINGWELL
BRITTLE–DUCTILE TRANSITION IN GRANITIC MAGMAS
onset of non-Newtonian rheology and ultimate brittle
failure of the melt can be accessed through the predicted
relaxation time or strain rate of the Maxwell relation via
incorporation of the constant offset noted above.
PARAMETERIZATION—NEWTONIAN
VISCOSITIES
Fig. 2. The viscoelastic response of a dry calc-alkaline rhyolitic melt.
The sample of remelted, bubble- and crystal-free obsidian was subjected
to torsional stresses in the frequency (x) range of mHz to kHz and the
viscoelastic response to the forced oscillations was recorded. Here, the
shear modulus is plotted against the frequency (normalized to the shear
relaxation time) of the applied torsional stress. The growth of the
imaginary or ‘out-of-phase’ component of the stress–strain relationship
indicates the onset of significant mixed (viscous + elastic), partially
relaxed strain response to the applied stress. The width of the range
of the observable imaginary component is several log units in frequency
or strain rate. This width translates through the activation energy of
the shear stress relaxation time into a width, at a constant frequency,
of several tens of degrees Celsius. These experiments are performed
under conditions of variable strain rate but very low total strains, with
the result that elastic strains or energy storage, rather than brittle
failure, are the consequence. Nevertheless, the location of the onset of
elastic response in time–temperature space is a fairly accurate indicator
of the conditions necessary for the material in question to exhibit nonNewtonian flow and brittle failure in corresponding nonlinear time
domain experiments (see Fig. 3). Redrawn from Webb (1992).
geometries (Li & Uhlmann, 1970; Simmons et al., 1982;
Hessenkemper & Bru¨ckner, 1988; Webb & Dingwell,
1990), and all yield the fundamental type of response
illustrated here in Fig. 3. The strain-rate-independent
viscosity of the melt encountered at low strain rates
begins to deviate from this Newtonian behavior at a
characteristic strain rate ~3·5 log units slower than the
relaxation strain rate calculated from the Maxwell relation. The consequence of this breakdown of the Newtonian flow of the melt is that the apparent viscosity
decreases with increasing strain rate, in a phenomenon
known as shear thinning. The melt cannot shear thin
indefinitely and with sustained application of stress the
melt eventually ‘breaks’ or fails at a point where the
microscopically accumulated strain defects have
weakened the tensile strength of the melt to a value less
than the applied stress.
Despite the small difference between the onset of
significant elastic response of the melt phase in the linear
regime and the onset of non-Newtonian rheology in the
nonlinear regime, the two events appear to be closely
coupled and are generated by the same fundamental
phenomenon, the inability of the melt to relax on the
time-scale of the deformation. Thus the prediction of the
The necessary inputs for the application of the Maxwell
criterion to the prediction of the onset of non-Newtonian
rheology are viscosity and elastic modulus data. Comparison of longitudinal wave propagation data from ultrasonic studies and shear viscosity data from concentric
cylinder viscometry confirms that the shear viscosity
and volume viscosities of silicate melts are similar in
magnitude. Therefore a sufficiently general description
of the P–T–X dependence of the shear viscosity should
suffice for fulfilling the viscosity data needed as input.
Until recently, the database for shear viscosities of rhyolitic melts was not complete enough to justify a general
model because of the strongly nonlinear dependence
of viscosity on water content and reciprocal absolute
temperature. Recent experimental improvements have
now largely filled in the gap of observations (Dingwell et
al., 1996a, 1996b; Richet et al., 1996) for the previously
under-investigated, high-viscosity region, with the result
that Hess & Dingwell (1996) were able to provide a nonArrhenian model for melt viscosity. Figure 4 illustrates the
essential features of the model predictions. The addition of
water generates the well-known nonlinear decrease of
viscosity vs added water content and an increasingly nonArrhenian dependence of the viscosity on temperature.
Both features exert strong controls on the predicted
viscosities and only now is it possible to model the
rheological consequences of degassing of rhyolitic melts
to a reasonable degree of accuracy. For example, at a
strain rate of 10–1·5 s–1, a calc-alkaline rhyolite containing 2
wt % water would experience the onset of non-Newtonian
behavior at a temperature of 800°C.
Many high-level granites may evolve to the situation
where several relatively incompatible elements which are
normally present at trace levels in granitic magmas
achieve minor or even major element concentration levels
of 0·5 to several weight percent in the melt phase. Figure 5
illustrates that several of these elements can also influence
significantly the viscosity of the melt phase. Predictive
models are generally not yet available to incorporate the
combined effects of water and these other elements. As
a general rule, the effects of combinations of enriched
elements on the viscosity of the melt phase are not
expected to be nonlinear or nonadditive. One example
is the combined influence of boron and water on the
viscosity of a granitic melt (Fig. 6). Interestingly, the
viscoelastic response of the melt (see below), although
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NUMBER 12
DECEMBER 1997
Fig. 3.
shifted to much lower temperature by the addition of
components such as boron, phosphorus or fluorine, does
not appear to vary in internal character in the partially
relaxed region (Fig. 7). By analogy, we can conclude that
the onset and path of non-Newtonian viscosity in these
specialized granitic melts will be unaffected except in the
sense that the temperature at which they occur will be
shifted.
CHEMICAL AND PHYSICAL
INFLUENCES ON VISCOELASTICITY
High-level granite magmas, in a volatile-saturated state,
are complex geo-materials consisting of significant volume
fractions of suspended crystals and vesicles. The influence
of the physical incorporation of these phases on the
rheology and glass transition of rhyolitic melts is illustrated
in Fig. 8, where frequency domain data for the viscoelastic
response of a rhyolitic melt with spherical crystals and
vesicles are compared. As was the case for chemically
induced shifts of the rheology, there are no changes in
the internal structure of the partially relaxed behavior,
but the temperature shifts because of the inclusion of
crystals and bubbles are considerable. These results corroborate time domain studies of the viscosity of crystal
and bubble suspensions, and indicate that the physical
influences of suspended bubbles and crystals up to contents of 30 vol. % can shift the viscosity by up to a log
unit.
Under the rapid application of pressure or shear stress
perturbations to be expected to result from transient
stresses in high-level granitic magmas, the bubbles suspended in the vesicular magma may not have sufficient
time to respond by viscous deformation of their shape
as was the case in Fig. 8. In such a situation, the bubbles
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DINGWELL
BRITTLE–DUCTILE TRANSITION IN GRANITIC MAGMAS
Fig. 3. The non-Newtonian response of a dry calc-alkaline rhyolitic melt, a calc-alkaline andesite, a tholeiitic basalt and a synthetic nephelinite.
The sample of remelted, bubble- and crystal-free obsidian was subjected to longitudinal stresses over a range of strain rates and the onset of
non-Newtonian response to the longitudinal stresses was recorded. The deviation of the response of the melt from a constant ratio of stress to
strain-rate or apparent viscosity indicates a partially unrelaxed response of the melt to the applied strain. The difference in time-scale between
the onset of the non-Newtonian response and the calculated relaxation time of the melt phase is ~3·5 log units. This is slightly larger than the
prediction that would be made from the width of the relaxation peak in Fig. 2, but the approximation that the onset of the non-Newtonian
response of the melt phase can be scaled by a constant offset to the calculated relaxation time of the melt remains valid. Thus the viscosity of
the melt, the time-scale of the deformation and the temperature of the system govern the onset of unrelaxed response and non-Newtonian flow
of the melt phase. Redrawn from Webb & Dingwell (1990).
are likely to contribute to a viscosity increase which can
be modeled in a similar fashion to equations used for
crystal suspensions [e.g. the Stokes–Einstein equation and
derivative formulations; see Dingwell et al. (1993) for a
review].
Torsional deformation experiments of the type discussed
above yield shear modulus data in the mHz to kHz region
which are comparable in magnitude. The influence of
water on the elastic moduli of rhyolitic or granitic melts
is not well known. It is unlikely, however, to lead to a
shift in values of the elastic moduli outside of the bounds
presented above.
ELASTIC MODULI
The predictive power of the Maxwell criterion for viscoelastic response of the liquid phase also requires an
adequate description of the unrelaxed elastic moduli
of the melt phase. Experimental measurements of the
longitudinal modulus of silicate melts using MHz ultrasonic techniques yield moduli that vary with melt compositions within the relatively tight bounds of 3–30 GPa.
MAGMA STRENGTH
Given the relatively good constraints on the prediction
of non-Newtonian rheology and eventual brittle failure
of the melt phase provided above, we now turn to the
consideration of the strength or failure criteria for these
melts. The strength of complex materials such as magmas
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Fig. 4. Parameterization of the dependence of the relaxed Newtonian shear viscosity of calc-alkaline rhyolitic melts on water content and
temperature. The influence of pressure on the viscosity of hydrous calc-alkaline rhyolites can be neglected up to pressures of several kilobars.
(a) illustrates the influence of water content on the viscosity of the melt for a series of isotherms. The extremely nonlinear decrease of the melt
viscosity with increasing water content has been parameterized by an exponential function. (b) illustrates the temperature dependence of the
viscosity of hydrous calc-alkaline rhyolitic melts at a series of compositions with constant water content. The significant curvature of the
dependence of melt viscosity on the reciprocal absolute temperature has been parameterized using a Tamann–Vogel–Fulcher, reduced temperature
fit. Using this parameterization of the dependence of viscosity on water content and temperature, the onset of non-Newtonian flow, leading to
brittle failure, can be predicted in time–temperature space. Reproduced after Hess & Dingwell (1996).
Fig. 5. The individual influence of a variety of chemical components commonly enriched in certain granitic and related magmatic to magmatohydrothermal lithologies on viscosity. These data give an indication of the relative viscosities to be expected in the hydrous equivalent melts;
however, the combined influence of water and excess secondary components such as those illustrated here has not yet been sufficiently investigated
to generate a predictive model. The fact that the influence of water is the greatest and that the viscosities of mixtures in silicate melts are in
general highly nonlinear means that simple additions of the viscosity influences of the individual components on the viscosity of a hydrous highly
specialized granitic melt will probably significantly overestimate the viscosity. More data are needed. Reproduced after Dingwell et al. (1997).
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DINGWELL
BRITTLE–DUCTILE TRANSITION IN GRANITIC MAGMAS
Fig. 6. The influence on viscosity (portrayed as an isokom temperature)
of the combination of boron and water added to the composition of a
calc-alkaline granitic melt. The curve of the combined influence of
boron and water was generated for this specific case by considering
the combined influence of (H2O + B2O3)/6. Such a combination cannot
be generalized and the roots of its empirical success lie in the structural
interaction of water and boron in this granite melt. Specific interaction
of other elements with water and each other are likely to require other
parameterizations. Reproduced after Romano et al. (1996).
is highly under-investigated. There are, however, several
starting points from which we can begin to build an
appraisal of magma strength, and these are summarized
below and in Table 1. We are interested primarily in
tensile strength because in complex geo-materials this is
likely to have a value considerably lower than either the
shear or compressive strength.
The theoretical limit of the tensile strength of the melt
phase may be taken as its elastic modulus, here the tensile
or Young’s modulus. For a pure melt the unrelaxed
Young’s modulus has a value of the same order of
magnitude as the equivalent (unrelaxed) shear and bulk
moduli (i.e. several tens of GPa; Bansal & Doremus,
1986). In practice, melts never reach these levels of
cohesion and their tensile breaking strength is 2–3 log
units lower. Fiber elongation experiments on the nonNewtonian flow of rhyolite indicate a tensile strength of
the shear thinned liquid of ~108·5 Pa (Webb & Dingwell,
1990). The fibers employed in those experiments were
annealed at temperatures slightly above the glass transition to a fully relaxed state and subsequently subjected
to tensile stresses that were large enough to drive their
Fig. 7. The influence of chemistry on the viscoelasticity of granitic melts is illustrated with the examples of additions of several weight percent
of the components B2O3, P2O5 and F2O–1 to a calc-alkaline granitic melt. Each of the components shifts the temperature of the onset of the
viscoelastic behavior considerably through the influence on the relaxed shear viscosity. Apart from this shift in the onset temperature, the
viscoelastic response of the melt is little influenced by the addition of these components despite their probably significant influence on melt
structure. On the basis of the results presented here, no significant influence on the viscoelastic response, and, by analogy, the onset of nonNewtonian flow in nonlinear processes, is expected with the addition of water to these melts, apart from the temperature shift caused by the
shift of the relaxed shear viscosity. G/G x represents the ratio of the real and imaginary components of the shear modulus to the value at infinite
frequency. Redrawn from Bagdassarov et al. (1993).
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Fig. 8. The physical influence of bubbles (a) and bubbles + crystals (b) on the viscoelastic response (the shear modulus, G) of a rhyolitic melt.
The presence of bubbles in the rhyolitic melt decreases the viscosity by up to 1 log unit in the frequency range investigated. The viscoelastic
region is shifted accordingly. The addition of crystals to the bubble suspension increases the viscosity by a similar amount and again the
viscoelastic region is shifted accordingly. The primary influence on the viscoelastic response of the rhyolitic melt is through the influence on the
shear viscosity up to the levels of crystals and bubbles illustrated here in the investigated frequency region. Nonlinear flow of vesicular and highly
crystalline rhyolitic melts may generate distinct rheological response. The labels 9/9, 16/16 and 40/40 correspond to the crystallinity/porosity
of the individual samples. Redrawn from Bagdassarov & Dingwell (1993) and Bagdassarov et al. (1994). (See Figs 2 and 7 for definitions of the
plotted variables.)
rheological response into the non-Newtonian regime
outlined above. Because the fiber breakage occurred after
a period of significant deformation via non-Newtonian
flow, the microstructure of the melt phase must have
recorded a cumulative record of the non-Newtonian
deformation which would presumably lead to weakening
of the fiber. The application of stresses in those
experiments was at a relatively low strain rate and it is
possible that crystal- and bubble-free rhyolitic melts in
nature, when rapidly exposed to a transient stress, could
exhibit slightly stronger behavior. The experimental
evidence to date indicates that no significant compositional dependence of the tensile strength of the melt
phase is to be expected.
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BRITTLE–DUCTILE TRANSITION IN GRANITIC MAGMAS
Table 1: Strength estimates for magma
Material
Strength (Pa)
Method
Theory (T) or
Source
experiment (E)
Silicate melt
1010
Elastic moduli
T
1
Rhyolitic melt
108·5
Fiber failure
E
2
Hydrous vesicular melt
106·5
Decrepitation
E
3
Dome lava
106·5
Curvature
T
4
Dome lava
106·5
Fragmentation
E
5
1, Bansal & Doremus (1986); 2, Webb & Dingwell (1990); 3, Romano et al. (1996); 4, Mungall (1995); 5, Alidibirov & Dingwell
(1996a).
The presence of other phases in a granitic magma will
in general contribute to a lowering of the tensile strength
via the production of spatial variations in the strength of
the bulk phase, which, in turn, generate spatial stress
inhomogeneities in the stress field of the magma. Thus
the magma is likely to develop stress concentrations
locally whose relaxation may impose failure conditions
on adjacent areas of the magma. Most crystalline phases
possess a relatively high strength in comparison with that
of the melt phase. Vesicles of fluid phases have, of course,
negligible internal tensile strengths but their nucleation
and growth may lead to compositional gradients in
the liquid envelope surrounding each vesicle. Water
concentration gradients generated during the diffusioncontrolled growth of bubbles in a water-saturated rhyolitic
magma, for example, can lead to significant local spatial
variations in the rheology of the melt phase, thus generating the possibility of stress concentration near the
bubble surfaces.
Very few experimental data are currently available to
quantify these effects in detail. The case for a vesicular
magma with water-filled vesicles has been experimentally
addressed by Romano et al. (1996), who demonstrated
clearly, on the basis of the decrepitation pressures of fluid
inclusions in glasses, that the effective tensile strength of
hydrous granitic melts containing vesicles can be as low
as 2 log units less than that obtained for bubble-free
melts. Mungall et al. (1996) modeled those observations
in terms of the volume stresses distributed throughout
the melt phase during rapid cooling of the vesicular
magma. Water concentration gradients in vesicular
magma cause significant shifts in the rheology of the melt
and create volume stresses via the influence of water on
the molar volume of the melt. Mungall et al. (1996)
concluded that tensile ‘gradient’ stresses in the immediate
vicinity of the vesicles could be generated that would be
large enough to overcome the tensile strength of the melt
phase locally.
In many volcanic dome magmas the geometry of the
vesicles is extremely tortuous, far from the sub-spherical
geometry of the experiments described above. In such
materials, the local embayments of high curvature will
lead to stress concentrations which should further weaken
the magma as a result of purely geometrical constraints
(Mungall, 1995). In addition, if the crystal and vesicle
volume fractions of a magma come into intimate contact,
separated perhaps only by a thin film wetting of the melt
phase, then the strength of the magma may also be
adversely affected (Proussevitch et al., 1993).
The subjection of magmatic samples to well-controlled
transient stresses has recently been placed on a much
more systematic experimental basis by the development
of the so-called ‘fragmentation’ bomb (Alidibirov &
Dingwell, 1996a, 1996b). This device is capable of subjecting magma samples, mechanically equilibrated under
pressures up to 200 bars and temperatures up to 950°C,
to stress transients that overcome the tensile strength of
the magma. Experimental series in which the magnitude
of the stress transient is systematically varied reveal that
highly crystalline and vesiculated magma dome samples
have characteristic tensile strengths in the range of
106−107 Pa. Experiments in which the vesicularity and
crystallinity of the magma are systematically varied are
at present under way.
If the response of the magma is entirely brittle then the
question arises as to the quantification of the production of
surfaces during deformation. A number of formulations
exist for the quantification of the brittle response of
materials (Cook & Pharr, 1990). These include, for example, the so-called ‘fracture toughness’. A sampling of
hydrous natural rhyolites has been studied by Gerth &
Schnapp (1996). The systematic investigation of fracture
toughness for magmatic geomaterials has not yet been
initiated. This remains an important research goal for
the future.
ACKNOWLEDGEMENTS
This overview of the brittle–ductile transition in highlevel granites was stimulated by my interaction with
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several colleagues over the past decade, including S.
Webb, N. Bagdassarov, M. Alidibirov, C. Romano and
J. Mungall. Helpful reviews were provided by A.
Proussevitch and an anonymous reviewer.
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