growth of a zoned plagioclase porphyroblast in a mylonite zoning patterns in a plagioclase porphyroblast in a blastomylonite derived from lewisian gneiss near loch eriboll northwest scotland suggest that the crystal grew during deformation discontinuities in the concentrations of cao k 2 o and feo mark the boundaries of overgrowths and define a core overgrowth structure the simultaneous changes in concentration of cao and k 2 o are used to construct a qualitative chemical potential diagram that reflects changes in a ca a 2 h and a k a h in the coexisting fluid during growth increases in these activity ratios are believed to have caused supersaturation of the grain boundary fluids with respect to plagioclase the repeated periods of growth indicate repeated overstepping of equilibrium which could have been caused by ion exchange on surfaces newly exposed during deformation these data fit a model that relates cyclic variations of strain rate in fault zones with cyclic periods of crystal growth which in turn could have a major influence on fault rock rheology

microstructures and c axis fabrics indicative of quartz dissolution in sheared quartzites and phyllonites abstract quartzites sheared in low metamorphic grade shear zones that extend along the contact with migmatitic gneissic complexes in the quadrilatere ferifero region southeastern brazil show quartz microstructures indicating deformation by dissolution dissolution occurred adjacent to the foliation planes preferentially in quartz porphyroclasts oriented with their 0001 planes parallel to the foliation dissolution worked as an efficient mechanism to remove porphyroclast edges smoothing foliations and enabling strain accommodation both dissolution and crystal plasticity were competitive crystallographically controlled processes operating in different domains of the evolving microstructure dissolution occurred along the foliation planes while isovolume crystal plasticity and accompanying recrystallization operated essentially in the quartzose domains between folia phyllonites formed in the most strained domains of the shear zones fine grained quartz grains in phyllonites show uncommon c axis fabrics c axis oriented at low angles to the stretching lineation which were interpreted to form either by direct reprecipitation or by residual concentration of grains unfavourably orientated to undergo dissolution domainal c axis fabrics reflect a deformation partitioning path with increasing participation of solution transfer strengthening c axis maxima at low angles with the stretching lineation at the expense of crystal plastic processes during progressive phyllonitization

evolution of mica fish in mylonitic rocks abstract mineral fish are lozenge shaped porphyroclasts single crystals in a finer grained matrix which occur in ductile shear zones and which are commonly used as shear sense indicators mineral fish of biotite tourmaline k feldspar garnet hypersthene and quartz occur in mylonites but most common are white mica fish these mica fish can be subdivided into six morphological groups that develop by different mechanisms determined by different initial shapes and orientations the principal mechanisms of formation are intracrystalline deformation combined with rigid body rotation concomitant selective grain size reduction occurs by recrystallisation cataclastic separation pressure solution and diffusional mass transfer microboudinage has been proposed for the breakdown of large mica fish into smaller ones but many mica fish undergo shortening rather than extension along their long axes evidence is presented for an alternative process in which the tips of mica fish are isoclinally folded and then break off along the hinge of these microfolds all the presented fish shaped porphyroclasts or mineral fish have a specific shape preferred orientation with their long axis at a small antithetic angle with respect to the foliation they represent a special group of objects with a stable orientation due to flow partitioning into narrow shear bands

development of single crystal σ shaped quartz porphyroclasts by dissolution precipitation creep in a calcite marble shear zone abstract within a greenschist facies calcite marble shear zone isolated quartz grains change shape across the shear zone profile whereas quartz grains have a spherical to elongated shape in the coarse grained marble protolith and protomylonite they are asymmetric shaped porphyroclasts with wedge shaped appendages wings in ultramylonites in all cases quartz grains are single crystals they are sometimes twinned but never recrystallized stress induced dissolution precipitation creep is the favourable shape controlling process during deformation providing a relatively undeformed core truncation of pre existing cathodoluminescence cl patterns and syntaxial precipitation of wings the necessary fluids may have been released from fluid inclusions during dynamic recrystallization of the calcite matrix the development of shape is not related to the crystallographic orientation of the quartz porphyroclasts crystallographic orientation analysis by electron backscatter diffraction ebsd and cl analyses exclude crystal plasticity as a shape controlling mechanism of quartz grains during mylonitisation however in ultramylonites quartz clasts have a strong crystallographic preferred orientation cpo with c axes sub parallel to the shear direction this fabric is uncommon for quartz under greenschist facies conditions it might be explained by a strengthening of a pre existing weak cpo during mylonitisation by rigid particle rotation of elongated quartz grains

fabric transitions in the saxony granulite terrain abstract quartz fabric transitions reported from the saxony granulite terrain and from the nearby ore mountains are interesting because of the changes in the pattern types and the variation in the opening angles of the fabric skeletons a short summary is presented of salient features in research documented in the east german literature between 1961 and 1978 the changes in fabric skeleton with decreasing metamorphic grade are proposed as mainly consequent to the deactivation of prism c glide systems as temperature decreases fabrics indicative of the appearance of the c burgers vector might be diagnostic for deformation in regimes of comparatively high temperatures or low strainrates or for deformation under conditions such that there is a relatively high kinetically effective hydroxyl content in the quartz structure

exhumation and doming of the thasos metamorphic core complex s rhodope greece structural and geochronological constraints abstract the thasos island metamorphic core complex s rhodope n aegean sea was generated between 26 and 13 ma progressive extensional tectonics was associated with upwarping of the deeper parts of this core complex to a narrow gneiss dome and with formation of a steep topographic high we present a combined structural microstructural and geochronological study that constrains the deformation time path of progressive extension and exhumation thasos island consists of three superimposed more or less flat lying metamorphic units with downward decreasing geochronologic ages which are separated by two systems of low angle normal detachment surfaces trending nw se the upper unit stayed in supracrustal level since 50 ma representing the upper plate during an early phase of extension not later than 26 23 ma upper levels of the core complex intermediate unit underwent pervasive mylonitization with top to the sw shear from about 21 ma onward the intermediate unit was rigid and top to the sw slip continued at least until 13 8 ma on the discrete detachment surface that separates the core complex from the upper plate yet in the 21 15 ma period deeper levels lower unit still deformed plastically and deformation successively concentrated in zones of high strain and in discrete detachment surfaces that caused decoupling of the lower from the intermediate unit these indicate downdip movements in opposite sense associated with doming of the lower unit at that stage simultaneously the intermediate unit was fragmented on high angle normal faults that sole into the dome bounding detachment surface and roof into the core complex bounding detachment surface these faults confine tilt blocks that are arranged around the lower unit gneiss dome doming of the core complex occurred simultaneously with subsidence of basins located on the upper plate

c slip in quartz from subsolidus deformed granite abstract the slip behaviour of quartz from a granite and granitic veins during subsolidus high temperature conditions 700 800 c of deformation is studied by lattice preferred orientation lpo and microstructural techniques lpos with a point maximum of c axes parallel to the shear direction which is close to the stretching lineation are presented and interpreted with the aid of light and electron microscopy in terms of c as the dominant slip direction during plastic deformation microscopy of such samples reveals the presence of 0001 tilt boundaries and free 0001 burgers vector dislocations in edge orientations a change in lpo in a decreasing temperature environment from c axes parallel to the shear direction to c axes normal to the shear direction documents a fabric transition from the rare c slip to the more common a slip fabric it is concluded that conditions of high temperature and partial pressure of water are required to initiate dominant c slip during deformation at geological strain rates

dissolution and replacement creep a significant deformation mechanism in mid crustal rocks abstract zoning patterns and zoning truncations in metamorphic minerals in a granodioritic orthogneiss indicate that strain and s c fabrics in these rocks were produced by dissolution precipitation and replacement processes even at epidote amphibolite facies metamorphic conditions the metamorphic fabric is defined by alternating layers and folia dominated by quartz feldspars and biotite epidote zoning patterns in most metamorphic plagioclase orthoclase epidote and sphene are truncated at boundaries normal to the shortening direction suggesting dissolution interfaces of relict igneous orthoclase phenocrysts that face the shortening direction are embayed and replaced by biotite epidote and myrmekitic intergrowths of plagioclase and quartz metamorphic plagioclase grains are also replaced by epidote we interpret these microstructures to reflect strain enhanced dissolution the cores of many grains show asymmetric overgrowths with at least two generations of beards all oriented on the ends of grains that face the extension direction we interpret these textures to reflect precipitation of components dissolved by deformation enhanced dissolution while biotite and quartz probably deformed by dislocation creep the overall deformation was accommodated by dissolution perpendicular to the shortening direction and precipitation parallel to it these chemical processes must have been activated at lower stresses than the dislocation creep predicted from extrapolations of data from experiments in dry rocks thus wet crust is likely to be weaker than calculated from these experimental studies

the effect of the basal prism mechanism switch on fabric development during plastic deformation of quartzite abstract blacic described a transition from basal a to prism c dislocation glide systems as temperature increased or strain rate decreased in sequences of experiments involving deformation of single crystals of quartz in this paper theoretical aspects of competition between these systems during plastic deformation are discussed it is concluded that the basal prism mechanism switch should have important consequences for the development of crystallographic fabrics during plastic deformation of quartzite and the taylor bishop hill analysis is used in an attempt to predict expected fabric transitions

the composite floor of the cretaceous back arc basin of south georgia part of an ophiolite sequence and pre jurassic continental basement rocks are remnants of the composite floor of the cretaceous back arc basin system on south georgia the partially preserved ophiolite consists of pillow lavas and breccias inter bedded tuffs basic and silicic dykes and occasional sills it is intruded by a composite gabbro plagiogranite pluton and smaller gabbroic plutons the basement gneisses are intruded by layered gabbros diorites granitic rocks and numerous basic dykes a migmatitic aureole surrounds the plutonic rocks which are fragmented and net veined by remobilized crustal rocks the mafic rocks of the ophiolite sequence and basement complex are geochemically similar and both formed by differentiation of a mantle derived sub alkali tholeiitic magma in a former back arc basin tectonic setting the plagiogranite and silicic dykes and lavas of the ophiolite and some of the silicic rocks within the basement formed by differentiation of the basic magma the remainder of the granitic rocks within the basement are geochemically distinct comprising remobilized basement rocks and a calc alkaline pluton of a remnant magmatic arc the back arc basin formed by emplacement of the tholeiitic magma within pre existing basement rocks up to 80 extension of the continental crust occurred prior to rifting and development of the back arc basin

some garnet microstructures an illustration of the potential of orientation maps and misorientation analysis in microstructural studies the microstructures of two contrasting garnet grains are mapped using automated electron backscatter diffraction in both cases there is a very strong crystallographic preferred orientation with measurements clustered round a single dominant orientation each garnet grain is divided into domains with similar orientations limited by boundaries with misorientations of 2 or more in both samples most of misorientation angles measured across orientation domain boundaries are significantly lower than those measured between random pairs of orientation domains one sample is a deformed garnet that shows considerable distortion within the domains lines of orientation measurements within domains and across domain boundaries show small circle dispersions around rational crystallographic axes the domain boundaries are likely to be subgrain boundaries formed by dislocation creep and recovery the second sample is a porphyroblast in which the domains have no internal distortion and the orientation domain boundaries have random misorientation axes these boundaries probably formed by coalescence of originally separate garnets we suggest that misorientations across these boundaries were reduced by physical relative rotations driven by boundary energy the data illustrate the potential of orientation maps and misorientation analysis in microstructural studies of any crystalline material

processes controlling the shrinkage of porphyroclasts in gabbroic shear zones abstract this paper presents microstructural and geochemical data on amphibole and clinopyroxene porphyroclasts collected in amphibolite facies ultramylonites of the ivrea verbano zone italy the well rounded porphyroclasts show a concentration of defects including 100 twins stacking faults free dislocations subgrains and microcracks within their rims that indicate stress concentrations localised deformation within the margins of porphyroclasts increases reaction kinetics and supports amphibole clinopyroxene replacement reactions and heterogeneous plagioclase nucleation in addition to microcracking and or subgrain rotation these metamorphic reactions lead to a marginal grain size reduction and the shrinkage of porphyroclasts in order to correlate the defect concentration at the rim of porphyroclasts with stresses a finite element inclusion matrix model is used it depends on the degree of bonding between inclusion and matrix whether strong stress concentrations within the rim of the inclusion occur for well coupled two phase systems shear stresses within the rim of the inclusion can reach a magnitude many times the magnitude of the matrix stresses marginal stress concentrations do not evolve if inclusion and matrix are decoupled this may indicate that mechanically decoupled porphyroclasts can survive to very large strains

quartz c axes parallel to stretching directions in very low grade metamorphic rocks abstract quartz preferred orientations with c axes parallel to stretching directions are widespread in slates phyllites and very low grade schists of the south island new zealand in general these rocks lack evidence for plastic deformation of quartz and often preserve the original clastic quartz which naturally tends to be elongate parallel to the c axis the c axis preferred orientation can be explained therefore by mechanical rotation of clastic grains during deformation so that long axes became parallel to the stretching direction plastic deformation does however play a role in some very quartz rich layers which display a preferred orientation due to basal slip with c axes at high angles to the stretching direction solution transfer is important in enhancing the contrasts between pelitic and quartz rich lithologies but its role in producing c axis preferred orientations by competitive anisotropic growth or solution seems important only in slickenfibres and in fibrous quartz veins of shear zones where quartz displays very strong preferred orientations with c axes parallel to the local stretching direction in contrast the non fibrous quartz pressure shadows in some muscovite rich layers display a c axis preferred orientation similar to adjacent quartz rich sand layers and it probably results from nucleation of pressure shadow quartz on pre existing mechanically oriented quartz clasts

silicon diffusion in a natural quartz aggregate constraints on solution transfer diffusion creep abstract silicon bulk diffusion rates were determined in a fine grained 1 2 m diameter natural quartz aggregate novaculite from hot springs ar the diffusion experiments were done at 600 800 c and 150 mpa confining pressure hydrothermal and at 800 1100 c and 1 atm in a stream of dry n2 the technique employed an isotopic tracer 30si and standard step scan analysis using an ion microprobe sims the temperature dependence of silicon bulk diffusion in the novaculite is described by the arrhenius parameters d0 bulk 3 7 10 10 m2 s and q 137 18 kj mol and d0 bulk 6 2 10 9 m2 s and q 178 38 kj mol for the hydrothermal and dry experiments respectively at 800 c the silicon bulk diffusion rate at 150 mpa hydrothermal is about a factor of 10 greater than at 1 atm dry for an assumed effective grain boundary width of 2 nm the silicon grain boundary diffusion rates in novaculite are a factor of two to three less than oxygen diffusion rates for similar hydrothermal conditions and more than 12 orders of magnitude greater than anhydrous silicon volume diffusion rates extrapolated to the temperature of these experiments the results of this study provide valuable constraints on the role of diffusion accommodated deformation in quartz rich rocks

fabric development in experimentally sheared quartzites abstract a fine grained quartzite was deformed under a combination of simple shear and axial compression to varying amounts of shear strain 1 3 to 2 9 the experiments were conducted at 800 c 1500 mpa and an axial strain rate of 10 6 s in the dislocation creep regime shear zone boundaries were oriented at 45 or 30 to the compressior axis the progressive development of deformation microstructures including planar fabrics and c axis preferred orientations was studied as a function of increasing shear strain elongate original grains define a foliation s which rotates from 45 to 0 to the shear zone boundary with increasing strain producing a sigmoidal foliation in a single shear zone a second foliation invariant in orientation is defined by elongate recrystallized grains which lie at about 30 40 to the shear zone boundaries no c surfaces parallel to the shear zone boundaries were observed however extensional crenulation cleavages c defined by parallel zones of recrystallized grains as well as impurity and melt segregations were observed even at low strain lying at approximately 30 to the shear zone boundaries and these could easily be mistaken for c surfaces c axis preferred orientations of original grains define symmetric type i crossed circle girdles at low strain 2 with the greater concentration of c axes in the direction of shear these features are very similar to those observed in natural ductile shear zones

intragranular dynamic recrystallization in naturally deformed calcite marble diffusion accommodated grain boundary sliding as a result of subgrain rotation recrystallization abstract intragranular microshear zones within a greenschist facies calcite marble were studied to try to constrain better the processes of dynamic recrystallization as well as the deformation processes that occur within newly recrystallized grains intragranular recrystallized grains within large twinned calcite porphyroclasts can be related to the host from which they have recrystallized and are the focus of an electron backscatter diffraction study lattice distortions low angle boundaries and some high angle boundaries 15 in the microshears within a porphyroclast have the same misorientation axes suggesting that deformation occurred by climb accommodated dislocation creep involving subgrain rotation recrystallization changes in the ratio of host and twin domain as the deformation zone is entered show that twin boundary migration also occurred recrystallized grains have similar sizes 10 60 m to subgrains suggesting that they formed by subgrain rotation however within the intragranular microshear zones the misorientations between recrystallized grains and porphyroclasts are considerably larger than 15 and misorientation axes are randomly oriented moreover recrystallized grain orientations average around the porphyroclast orientation we suggest that the recrystallized grains once formed are able to deform partly by diffusion accommodated grain boundary sliding which is consistent with predictions made from lab flow laws

the petrological significance of misorientations between grains misorientation analysis quantifies microstructural features in tectonites metamorphic and igneous rocks and allows hypotheses on their formation to be tested the misorientation between two lattices can be expressed by a rotation axis and rotation angle for lattices with symmetry it is conventional to take the minimum angle that enables one lattice to be rotated into the other for a group of lattice measurements two types of misorientation distribution can be calculated selecting random pairs of grains gives the random pair misorientation distribution selecting neighbouring pairs gives the neighbour pair misorientation distribution the forms of both distributions are visualised using histograms or cumulative frequency diagrams they are strongly influenced by any overall crystallographic preferred orientation and by intrinsic crystal symmetry in many rocks the random pair misorientation distribution and neighbour pair misorientation distribution are statistically significantly different quantified using the kolmogorov smirnov test differences between the random pair misorientation distribution and neighbour pair misorientation distribution imply that adjacent grains have physically interacted or are inherited from a precursor microstructure interactions include 1 reduction in surface energy by lattice alignment we show this may have occurred in garnet clusters in schist and olivine in a cumulate it is well known in metals and may be a common geological process 2 nucleation where those nuclei have influenced the orientation of adjacent nuclei 3 mechanical rotations of facetted grains in compacting crystal mushes so that faces become parallel 4 growth twinning inheritance includes 1 subgrain rotation recrystallisation in tectonites deforming by crystal plastic processes 2 mechanical and transformation related twinning 3 domainal microstructures e g where grains have formed from a few large original grains may give rise to spurious correlations when the orientation data cover more than one domain with this proviso misorientation analysis can be used to investigate many important microstructural processes

experimental observations on the effect of interface slip on rotation and stabilisation of rigid particles in simple shear and a comparison with natural mylonites for axial ratios r not vert similar3 porphyroclasts from three mylonites all show a very strong spo with the long axis of the best fit ellipse at an antithetic angle of 5 10 to the shear direction this is more consistent with a stable end orientation than with the transient fabrics predicted by theory for elliptical rigid particles in simple shear the cause of this divergence is investigated in a series of high simple shear strain 15 analogue experiments performed in a ring shear machine couette flow using a linear viscous matrix pdms the rotational behaviour of elongate r not vert similar5 rigid particles with elliptical and rhomboidal shapes comparable with the natural examples is modelled for both coherent and slipping particle matrix interfaces interface slip causes a dramatic reduction in the rotation rate of the elliptical particle compared with theory when the long axis is close to the shear direction but not stabilisation interface slip does result in stabilisation of the rhomboidal particle with the long diagonal oriented at a small antithetic angle to the shear direction for monoclinic particles mirror image shapes referred to here as types 1 and 2 show different rotational behaviour for the type 1 particle with a shape comparable to porphyroclast systems and mica fish the long side rotates asymptotically into parallelism with the shear direction natural examples of type 1 particles such as hornblende and olivine porphyroclasts measured from the finero mylonites southern alps show a very strong preferred orientation for r not vert similar3 with the long side parallel or at a small 5 antithetic angle to the mylonitic foliation for type 2 particles the short side stabilises close to the shear direction or at a small synthetic angle as also observed for sillimanite porphyroclasts from the mont mary mylonites western alps in this natural case stabilisation of the short sides is against an extensional crenulation cleavage rather than the mylonitic foliation the analogue experiments establish that interface slip is one mechanism for stabilisation of elongate rhomboidal particles in natural examples decoupling from the matrix may be affected by extensional crenulation cleavage or c planes in s c fabrics

provenance interpretation of quartz by scanning electron microscope cathodoluminescence fabric analysis we used a cathodoluminescence cl detector attached to a scanning electron microscope sem to study patterns of variable intensity cl in quartz grains from a variety of igneous metamorphic sedimentary and shock deformed meteorite impact rocks distinctive fabrics in quartz grains revealed by sem imaged differential cl include zoning healed fractures complex shears planar features shocked quartz dark cl streaks and patches indistinct mottled texture and nondifferential low contrast cl zoning is common in volcanic quartz and some plutonic quartz zoned plutonic quartz is distinguished from volcanic quartz by the presence of closed fractures and dark cl streaks and patches metamorphic quartz displays either an indistinct mottled texture or nearly uniform nondifferential cl quartz from rocks severely deformed by tectonism displays a complex pattern of multiple small scale shears quartz from meteorite impact sites and some system boundaries is characterized by intricate patterns of planar features presumably created by shock metamorphism thus the sem cl fabric analysis technique provides a rapid method for distinguishing quartz from a variety of source rocks

dynamic recrystallization of feldspar a mechanism for ductile shear zone formation feldspar aggregates experimentally deformed in the dislocation creep regime undergo dynamic recrystallization because recovery is difficult due to the limited climb of dislocations recrystallizing aggregates have a lower strength because of the cyclic production of small strain free grains and they develop a strong preferred orientation consistent with that observed in mylonites thus recrystallization accommodated dislocation creep may be responsible for the grain size reduction and strain softening that lead to the formation of many mylonites and ductile shear zones

texture development of recrystallised quartz polycrystals unravelled by orientation and misorientation characteristics abstract the development of microstructures and textures i e crystallographic preferred orientations during recrystallisation of naturally deformed quartz polycrystals has been studied via electron diffraction techniques in the scanning electron microscope in the investigated sample series of quartz rich rocks originating from different deformation regimes the microstructural and textural changes in quartz have been significantly influenced by dynamic recrystallisation based on microstructural observations paired with orientation and misorientation analyses down to the scale of grains and subgrains criteria could be established which characterise the dominant recrystallisation process and its influence on texture development it is shown that the texture development during dynamic recrystallisation is controlled by a differential activation of slip systems in grains of soft and hard orientations the analyses provide further evidence that specific grain orientations are preferred during crystal plastic deformation recrystallisation and grain growth the influence of twinning after the dauphine law was also investigated observations of a progressive reduction in the population of dauphine twin boundaries during recrystallisation and a penetrative deformation in both hosts and twins indicate a generation prior to deformation and recrystallisation a mechanical origin for twinning and possible influence on texture development was therefore discarded

experimental modelling of mantled porphyroclasts abstract mantled porphyroclasts are commonly used as sense of shear indicators in mylonites analogue experiments have been carried out to model the development of such objects rigid spheres mantled by a viscous plasticene putty mixture with power law behaviour were suspended in an optically transparent newtonian polymer matrix the samples were deformed between two cylinders one placed within the other and with coinciding axes this induces a non coaxial flow between the cylinders and allows the achievement of high finite strain the viscous mantle around the rigid sphere remained undeformed deformed into an ellipsoid or developed wings the final geometry depends mainly on the induced viscosity contrast between the mantle and the matrix which is a function of the flow induced stress on the surface of the mantle winged mantles only develop if the induced viscosity contrast between the mantle and the matrix polymer is sufficiently small if this critical induced viscosity contrast is exceeded the mantled sphere remains undeformed or obtains a stable ellipsoidal shape even at high finite strain shaped winged mantles only develop in simple shear flow if the mantle around a rigid sphere is thin

deformation of garnets in a low grade shear zone elongated shapes of garnets in high grade metamorphic rocks have been explained as a result of plastic crystal flow or anisotropic growth in the case of low to medium grade metamorphic rocks a satisfactory explanation has not been proposed yet for elongated garnets we have studied elongated garnets grown under low grade metamorphic conditions in a shear zone with a composite planar linear fabric garnet shapes in three dimensions define oblate ellipsoids drawing on evidence from compositional x ray maps it can be deduced that growth zoning is truncated along the long borders of grains whereas subcircular garnets show non truncated concentric growth zoning this fact shows that selective dissolution along planes parallel to the foliation and the c surfaces can be claimed to be the main mechanism responsible for the deformation of the garnets under examination here more specifically dislocation enhanced dissolution which occurs at low temperatures and low dislocation mobility is arguably the mechanism responsible for partially dissolving the garnet grains selective dissolution is expected to yield plane strain oblate ellipsoids i e with a volume loss as measured in the elongated garnets however the rock as a whole has been deformed by plastic flow in a simple shear regime as shown by the existence of numerous shear criteria and the strain calculations performed 0 1997 elsevier science ltd