Marble bowing: comparative studies of three different public building facades

The veneer cladding of the Oeconomicum (OEC, Göttingen), the State Theatre of Darmstadt (STD, Darmstadt) and of the State and University Library (SUB, Göttingen) is characterised by pronounced bowing after a short time of exposure. Direct comparison of bowing data related to measurements from 2000 to 2003 at the SUB clearly show that the amplitude in bowing had significantly increased. The bowing is different in intensity and orientation (concave, convex). The cladding material (Peccia marble, Rosa Estremoz marble and Carrara marble) are different in lattice preferred orientation, grain size distribution and grain interlocking. Depending on the bowing, panels may show cracks mostly initiated at the dowels. The percentage of visible cracks and breakouts increases with the amplitude of bowing except for the STD. Repetitive heating–cooling under dry conditions leads to considerable inelastic residual strain only after the first or second thermal cycle. The residual strain continuously increases again if water is present, whereby the moisture content after a thermal cycle has a certain impact on the decay rate. The water-enhanced thermal dilatation strongly correlates with the deterioration rate obtained from the laboratory bow test. Detailed petrophysical investigations provide evidence that with increasing bowing a decrease of mechanical properties (flexural strength or breaking load at dowel hole) occur. Marble degradation is also connected with the increase in porosity and a general shift of the maximum pore radii to larger pore sizes. On-site damage analyses were combined with laboratory tests of the bowing potential to constrain factors that may influence the risk failure. The experimental bowing data clearly demonstrate that after 40 heating cycles combined with the effect of moisture a certain impact on the decay rate is observed. In the case of demounted panels the bowing tests show that already strongly deformed panels from the building exhibit a lower bowing potential than those with lower amplitudes of bowing. This is not the general case for all marble types. Finally, the artificial bowing causes a significant reduction of the flexural strength and the breaking load at the dowel hole. The strength loss of the experimentally aged claddings combined with on-site damage analyses led to conclusions concerning risk assessment and the predicted lifetime of the investigated marble claddings.     

Strain investigations on calcite marbles using neutron time-of-flight diffraction

In order to describe and explain the effect of bowing of marble facade panels, neutron time-of-flight diffraction was applied to determine residual macro- and microstrain on the calcite mineral phase. The measurements were combined with investigations of the crystallographic preferred orientation (texture) measurements by neutron diffraction, macroscopic measuring of the bowing on marble building stones, as well as microfabric analyses. Three samples were investigated to explain the bowing effect: a fresh broken sample, a good conditioned facade panel and a strongly deformed facade panel. Residual intracrystalline strain was detected in all investigated samples, which differed in the degree of bowing. For the first time, the preferred orientation and the residual strain were found to be related. The results show that different strain magnitudes are reflected by residual strains, which differ significantly in magnitude and direction. Furthermore, different Bragg peak widths have been detected as an indication of microscopic strain. The observed residual strain values in the samples are related with the grain shape and texture properties.     

Bowing of dimensional granitic stones

Bowing is a well-known phenomenon seen in marbles used as building veneers. This form of rock weathering occurs as a result of external factors such as temperature, humidity, the system for anchoring the marble slabs or the panel dimensions. Under the same external conditions, many factors will determine the degree of deformation including petrography, thermal properties and residual locked stresses. The usual way to solve the problem of bowed marble slabs is to replace them with other materials, such as granites, in which the deformation still exists but is less common. In this study, eight ornamental granites with different mineralogy, grain size, grain shape, porosity and fabric were tested in a laboratory to assess their susceptibility to bowing. Three slabs of granite, each cut with a different orientation, were studied under different conditions of temperature (90 and 120°C) and water saturation (dry and wet) to investigate the influence of these factors together with that of anisotropy. At 90°C, only the granite with the coarsest grain size and low porosity exhibited deformation under wet conditions. At 120°C and wet conditions, three of the granites showed evident signs of bowing. Again, the granite with the coarsest grain size was the most deformed. It was concluded that the wide grain size distribution influences microcracking more than other expected factors, such as the quartz content of the rock. Also, mineral shape-preferred orientation and porosity play an important role in the bowing of the studied granites.     

Marble decay induced by thermal strains: simulations and experiments

Thermoelastic behavior of different marble types was analyzed using computational modeling and experimental measurements. Eight marble samples with different composition, grain size, grain boundary geometry, and texture were investigated. Calcitic and dolomitic marbles were considered. The average grain size varies from 75 μm to 1.75 mm; grain boundary geometry differs from nearly equigranular straight grain boundaries to inequigranular-interlobate grain boundaries. Four typical marble texture types were observed by EBSD measurements: weak texture; strong texture; girdle texture and high-temperature texture. These crystallographic orientations were used in conjunction with microstructure-based finite element analysis to compute the thermoelastic responses of marble upon heating. Microstructural response maps highlight regions and conditions in the marble fabric that are susceptible to degradation phenomena. This behavior was compared to the measured thermal expansion behavior, which shows increasing residual strains upon repetitive heating–cooling cycles. The thermal expansion behavior as a function of temperature changes can be classified into four categories: (a) isotropic thermal expansion with small or no residual strain; (b) anisotropic thermal expansion with small or no residual strain; (c) isotropic thermal expansion with a residual strain; and (d) anisotropic thermal expansion with residual strain. Thermal expansion coefficients were calculated for both simulated and experimental data and also modeled from the texture using the MTEX software. Fabric parameters control the amount and directional dependence of the thermal expansion. Marbles with strong texture show higher directional dependence of the thermal expansion coefficients and have smaller microstructural values of the maximum principal stress and strain energy density, the main precursors of microcracking throughout the marble fabric. In contrast, marbles with weak texture show isotropic thermal expansion behavior, have a higher propensity to microcracking, and exhibit higher values of maximum principal stress and strain energy density. Good agreement between the experimental and computational results is observed, demonstrating that microstructure-based finite-element simulations are an excellent tool for elucidating influences of rock fabric on thermoelastic behavior.     

Laboratory and case studies of thermal cycling and stored strain on the stability of selected marbles

Studies of marble panels from the exterior of two buildings document the processes leading to bowing of the material. Bowing of panels is most extensive in those areas that are exposed to direct or reflected thermal energy. The thermal anisotropic behavior of calcite results in grain-boundary separation, grain sliding and microfracturing. The resulting loss of strength is one factor leading to bowing. The development of bows further reduces the panel strength as the outer portions elongate by inelastic deformation mechanisms. Laboratory experiments cycling marble samples for over 200 cycles at three temperatures up to 107°C above room conditions show similar strength losses as the natural situation. The second factor contributing to the bowing process is the release of residual elastic strain. The strain is in part stored in the marble from its geologic history, but may also be accumulated during thermal cycling due to the properties of calcite. Marble panels have been found to bow when stored outside, but not attached to any framework, indicating that the release of residual strain is a critical factor in producing the bows.     

The bowing potential of granitic rocks: rock fabrics, thermal properties and residual strain

The bowing of natural stone panels is especially known for marble slabs. The bowing of granite is mainly known from tombstones in subtropical humid climate. Field inspections in combination with laboratory investigations with respect to the thermal expansion and the bowing potential was performed on two different granitoids (Cezlak granodiorite and Flossenbürg granite) which differ in the composition and rock fabrics. In addition, to describe and explain the effect of bowing of granitoid facade panels, neutron time-of-flight diffraction was applied to determine residual macro- and microstrain. The measurements were combined with investigations of the crystallographic preferred orientation of quartz and biotite. Both samples show a significant bowing as a function of panel thickness and destination temperature. In comparison to marbles the effect of bowing is more pronounced in granitoids at temperatures of 120°C. The bowing as well as the thermal expansion of the Cezlak sample is also anisotropic with respect to the rock fabrics. A quantitative estimate was performed based on the observed textures. The effect of the locked-in stresses may also have a control on the bowing together with the thermal stresses related to the different volume expansion of the rock-forming minerals.     

Influence of shape fabric and crystal texture on marble degradation phenomena: simulations

Microstructure-based finite element simulations were used to study the influence of grain shape fabric and crystal texture on thermoelastic responses related to marble degradation phenomena. Calcite was used as an illustrative example for studying extremes of shape preferred orientation (SPO) in shape fabric and lattice preferred orientation (LPO) in crystal texture. Three SPOs were analyzed: equiaxed grains, elongated grains, and a mixture of equiaxed and elongated grains. Three LPOs were considered: a random orientation distribution function and two degrees of strong directional crystal texture. Finally, the correlation between the direction of the LPO with respect to that of the SPO was examined. Results show that certain combinations of SPO, LPO, and their directional relationship have significant influence on the thermomechanical behavior of marble. For instance, while there is no major dependence of the elastic strain energy density and the maximum principal stress on SPO for randomly textured microstructures, there is a strong synergy between LPO and its directional relationship with respect to the SPO direction. Microcracking precursors, elastic strain energy density, and maximum principal stress, decrease when the crystalline c-axes have fiber texture perpendicular to the SPO direction, but increase significantly when the c-axes have fiber texture parallel to the SPO direction. Moreover, the microstructural variability increases dramatically for these latter configurations. In general, the influence of LPO was as expected, namely, the strain energy density and the maximum principal stress decreased with more crystal texture, apart from for the exception noted above. Spatial variations of these precursors indicated regions in the microstructure with a propensity for microcracking. Unexpectedly, important variables were the microstructural standard deviations of the spatial distributions of the microcracking indicators. These microstructural standard deviations were as large as or larger than the variables themselves. The elastic misfit-strain contributions to the coefficients of thermal expansion were also calculated, but their dependence was as expected.     

Bowing of marble slabs: can the phenomenon be arrested and prevented by inorganic treatments?

Bowing of thin marble slabs is a phenomenon affecting both historic monuments and modern buildings. In spite of the ubiquity and destructiveness of this phenomenon, no fully satisfactory treatment is currently available to arrest and/or prevent bowing. In this study, a treatment based on formation of hydroxyapatite (HAP) was investigated as a possible route to arrest and possibly prevent bowing of Carrara marble slabs. Four different formulations of the HAP treatment were tested and compared to ammonium oxalate and ethyl silicate (widely used in the practice of marble conservation). The treatments were applied onto pre-weathered and unweathered specimens to investigate their ability to arrest and prevent bowing, respectively. Marble behavior was studied in terms of residual strain and bowing after thermal cycles up to 90 °C in dry and wet conditions. Marble cohesion was assessed before and after the thermal cycles by ultrasound. The HAP treatments exhibited promising results, as the residual strain and the bowing after the cycles were always lower or equal to the untreated references, while marble cohesion was always higher. Surprisingly, ammonium oxalate caused marked worsening of marble thermal behavior. In the case of ethyl silicate, most of the initial benefit after consolidation was lost after the thermal cycles. In general, the results of the study point out the importance of evaluating marble thermal behavior to assess the suitability of any conservation treatment and suggest that treatments able to strengthen marble without causing excessive pore occlusion and stiffening are preferable to enhance durability to thermal cycles.     

Physical weathering of marbles caused by anisotropic thermal expansion

 Marbles as building stones as well as in their natural environments show complex weathering phenomena. The most important damage scenario is based on the highly anisotropic thermal expansion coefficient α of calcite, i.e. extreme expansion parallel and contraction normal to the crystallographic c-axis. Therefore, the rock fabric and especially the lattice-preferred orientation (texture) of calcite and/or dolomite as the predominant mineral phases in marbles have a significant influence on the mechanical weathering. The textures of marbles from five different locations vary from a more or less perfect prolate to moderate oblate shape of the [006] pole figure tensor. Accordingly, the texture-derived bulk thermal dilatation anisotropy covers a broad range from –0.048 to 0.680. The modelled thermal dilatations correlate with those obtained from experimental measurements. The difference in magnitude is basically explained by the microcrack fabrics which was not considered in the computations. All samples show a deterioration due to thermal treatment regardless of the strength of texture. The directional dependence of (a) the total magnitude of the thermal dilatation coefficient and (b) of the residual strain is highest in marbles with a strong texture, whereas the Carrara marble with a weak texture exhibits a uniform crack formation. The progressive loss of cohesion along grain boundaries due to dilatancy may serve as an example for the initial stage of physical weathering. Received: 10 February 1999 / Accepted: 16 October 1999     

Microcracking in calcite and dolomite marble: microstructural influences and effects on properties

Microstructure‐based finite-element analysis with a microcracking algorithm was used to simulate an actual degradation phenomenon of marble structures, i.e., microcracking. Both microcrack initiation and crack propagation were characterized, as were their dependence on lattice preferred orientation (LPO), grain shape preferred orientation (SPO), grain size, marble composition (calcite and dolomite) and grain‐boundary fracture toughness. Two LPOs were analyzed: a random orientation distribution function and an orientation distribution function with strong directional crystalline texture generated from a March–Dollase distribution. Three SPOs were considered: equiaxed grains; elongated grains and a mixture of equiaxed and elongated grains. Three different grain sizes were considered: fine grains of order 200 μm (only calcitic marble); medium size grains of order 1 mm (calcitic and dolomitic marbles); and large grains of order 2 mm (only dolomitic marble). The fracture surface energy for the grain boundaries, γ_ig, was chosen to be 20 and 40 % of the fracture surface energy of a grain, γ_xtal, so that both intergranular and transgranular fracture were possible. Studies were performed on these idealized marble microstructures to elucidate the range of microcracking responses. Simulations were performed for both heating and cooling by 50 °C in steps of 1 °C. Microcracking results were correlated with the thermoelastic responses, which are indicators related to degradation. The results indicate that certain combinations of LPO, SPO, grain size, grain‐boundary fracture toughness and marble composition have a significant influence on the thermal-elastic response of marble. Microstructure with the smallest grain size and the highest degree of SPO and LPO had less of a tendency to microcrack. Additionally, with increasing SPO and LPO microcracking becomes more spatially anisotropic. A significant observation for all microstructures was an asymmetry in microcracking upon heating and cooling: more microcracking was observed upon cooling than upon heating. Given an identical microstructure and crystallographic texture, calcite showed larger thermal stresses than dolomite, had an earlier onset of microcracking upon heating and cooling, and a greater microcracked area at a given temperature differential. Thermal expansion coefficients with and without microcracking were also determined.     

Single-layer folding in marble and limestone: An experimental study

Folding experiments have been carried out on single-layers of Carrara marble and Solnhofen limestone at a confining pressure of 275 bars, temperature of 400°C, and strain rates of 5.5×10⁻⁷ to 8.2×10⁻⁷. The marble and limestone layers were embedded in a rock-salt matrix and in a matrix of a mixture of 60% fine-grained halite and 40% fine-grained calcite, respectively, and deformed to different percentages of bulk shortening. Aspect ratios of the layers varied between 11.25 and 15. The stress-strain relationship reveals that strain increased with a very small increment in compressive stresses, once folding was initiated.With progressive deformation the bulk strain is compensated by folding along one fold hinge. The resulting folds are concentric and a combination of class 1a, 1b and 3 type. The changes in the arc length, layer thickness, limb dip and wavelength with progressive folding in marble layers, are discussed.The microstructure and texture of the folded marble and limestone layers have been investigated optically and by means of an X-ray texture goniometer. The inner fold arc exhibits a strong preferred orientation, whereas in the outer fold are the preferred orientation is poorly developed. Differences in the fabric in medium-grained marble and fine-grained limestone layers have been attributed to the difference in mechanism of deformation.     

The effects of strain rate and saturation on a micro-cracked marble

It is well known rock masses contain several types of weakness planes varying from micro-fissure to fault in size. The fracture frequency, degree of saturation and time are the basic rock parameters affecting its behaviour. However, in most cases, it is practically difficult to test heavily fractured rock in laboratory environment. In this study, the effects of micro cracks, strain rate and water saturation on strength are discussed using a small-scale physical experiments. It is attempted to detach the grain boundaries of coarse-grained rock specimens of the Mu?la marble by thermal treatment that would serve as a small-scale physical simulation of fractures in rock masses and enable a discussion of the variations in time dependent mechanical behaviour. An experimental study was conducted on marble specimens induced thermally by micro-cracks in different frequencies. The thermal treatment periods being 24 h in inert atmospheric condition were varied for each test specimen except categories A and G. Effective porosity increased up to 2.4% after the last thermal cycle of category F. Then conventional compression tests with different strain rates were carried out using a servo-controlled testing machine on both dry and saturated specimens. It is concluded that both lowering strain rates and increasing porosity related with thermally induced micro cracks have important effects on strength and failure path. The progressive failure entirely occurs along the grain boundaries fissured by cyclical treatment and inter-granular deformation depends upon degree of thermal influence. The small-scaled laboratory model enabled to demonstrate that parameters such as joint frequency, time and saturation have a significant effect on mechanical behaviour of rock masses.     

Influence of Marble’s Texture on its Mechanical Behavior

This research work studied the influence of texture on the mechanical properties of crystalline rocks at the scale of the laboratory sample. The experiments were performed on a marble varying in texture, so that the study was conducted on homogeneous (entirely xenoblastic or totally granoblastic) and heterogeneous (mix of the two textures) specimens. The mechanical behavior of the homogeneous and heterogeneous samples was investigated with static and dynamic, destructive and nondestructive tests, in natural conditions, at the laboratory temperature, and at higher temperatures. The specimens were heated to 100, 200, and 300 °C, in order to examine the effect of heating temperature on the elastic modulus and P-waves velocity. As a result, the pure granoblastic marble exhibits values of the elastic modulus, P-waves velocity, and strengths, both in natural conditions and on heated specimens, lower than xenoblastic samples. Such different behavior can be explained by a higher grain boundaries porosity of the granoblastic marble. On heterogeneous samples, only the Rock Impact Hardness Number (RIHN) appears able to highlight the dependence of the mechanical properties on the rock texture. In particular, the impact strength improves with increasing the percentage of xenoblastic texture inside the specimen.     

Thermal expansion of granitoids

The thermal rock properties are particularly important for natural stones whenever a temperature change may occur, which becomes particularly important when different materials are combined on any architectural structure. The thermal expansion of a rock is dependent on the coefficients of the expansion of the individual rock-forming minerals and the rock fabric. A systematic study on 65 different stones, mostly granitoids and others magmatic rocks, most of them are often used as dimensional building stones, was performed. Temperature and moisture are very important parameters in the natural environment. Therefore, the thermal expansion, and in addition the thermohygric expansion on selected examples, was measured. The data were also discussed considering the effect of the mineralogy and the temperature. A modeling approach was introduced to show how the mineralogy and the related single crystal properties affect the thermal properties and how good a simple calculation can help to characterize the measured thermal expansion of a rock. The directional dependence of the thermal expansion was also discussed and explained based on detailed rock fabric measurements. In this study, the bowing of granitoid samples was tested and compared with bowing phenomena of granitoid facade panels. The slabs were cut in different directions and were studied under different conditions of temperatures and water saturation. It could be clearly documented that the temperature and the moisture have a control on the bowing behavior. The implication of our data is that thermal expansion depends greatly on wetting and drying, i.e., the thermal cracking is characterized by the residual strain observed after cooling to room temperature. The sensitivity to the thermal cracking has a significant control on the application in architectural constructions.     

Quartz and calcite microfabric transitions in a pressure and temperature gradient,Sivrihisar, Turkey

Interlayered quartzite and marble in the southern Sivrihisar Massif, Turkey, record metamorphic conditions ranging from high-pressure/low-temperature through a Barrovian overprint from chlorite- to sillimanite-zone conditions. This sequence was exhumed under transtension, producing macroscopic constrictional fabrics (L-tectonites) during crustal thinning. Quartz microstructures consist of dynamically recrystallized aggregates in the dislocation creep regime dominated by grain boundary migration. Quartz microstructures are relatively constant across the high metamorphic gradient, and crystallographic fabric patterns transition from plane strain to constriction strain. Calcite fabrics are characterized by progressive overprinting of a columnar texture inherited from the high-pressure polymorph aragonite. In the low-temperature Barrovian domain (<400?°C), shearing of calcite rods produced a very strong c-axis point maximum. At moderate temperature, calcite rods were partially to totally recrystallized and the strong preferred orientation maintained. At temperature >500?°C and high constriction strain, marble has no crystallographic fabric, likely reflecting a transition from dislocation creep to diffusion creep. Phengite in high-pressure/low-temperature marble and quartzite yields relatively simple age spectra with Late Cretaceous (88–82 Ma) ⁴⁰Ar/³⁹Ar ages. Barrovian muscovite records significantly younger ages (63–55 Ma). The transtension system and associated metamorphism may have occurred above a subduction zone in Paleocene–Eocene time as a precursor to intrusion of Eocene (~53 Ma) arc plutons.     

Quartz [0001]-axes preferred orientation, Bluff, New Zealand: Origin elucidated by grain-size measurements

Permian volcanic sediments at Bluff have been strained and thermally metamorphosed by Permian intrusives to metasediments of hornblende—hornfels facies. Quartz, which crystallised as a secondary mineral during metamorphism, has an unusual preferred orientation with c-axes either forming paired maxima in the plane containing the lineation (=maximum principal strain axis = direction of extension) and the perpendicular to schistosity (=minimum principal strain axis = shortening direction) or a broad maximum parallel to the lineation; the paired maxima are approximately 30° either side of the lineation. Some quartz grains are markedly elongate parallel to the lineation, and according to hypotheses of preferred orientation involving crystal plasticity, there should be some correlation between the shape of such grains and their c-axis orientations. Grain-size and shape analysis of Bluff quartz demonstrate that no such correlation exists; the analyses show that the preferred orientation results from oriented nucleation in the residual stress field immediately following the bulk straining of the rocks, with the distribution of c-axes as predicted by Kamb's hypothesis (1959). The time relationships of rock deformation, thermal metamorphism, and nucleation and growth of quartz are discussed.     

Fabric anisotropy and its influence on physical weathering of different types of Carrara marbles

To evaluate the texture-controlled part on the thermally induced degradation of marbles, the anisotropic thermal dilatation was calculated from texture analyses of four exemplary samples from the Carrara area in Italy and compared to experimentally measured dilatation coefficients. The thermal dilatation as determined in the experiment is controlled by an intrinsic part (anisotropic single crystal properties and texture) and an extrinsic part (e.g. thermally induced microcracks). As expected from theoretical calculations, there is a correlation between the strongest dilatation and the c-axis maxima and the weakest dilatation and the a-axis maxima according to the single crystal data of calcite. However, a quantitative correlation could not be established. Obviously, other fabric parameters like the grain size, grain shape anisotropies, grain boundary geometries and microcrack formation during heating modify the texture-controlled part significantly. After thermal treatment up to 130°C, all samples show a residual strain. However, the magnitude and directional dependence is remarkably different and is unequivocally correlated to both the microstructure and the texture. Since the number of parameters controlling the physical weathering is very large, a comprehensive quantification of fabrics is indispensible for the understanding of thermally controlled degradation processes of physical weathering in marbles.     

Evolution of a calcite marble shear zone complex on Thassos Island, Greece: microstructural and textural fabrics and their kinematic significance

The deformation history of a monophase calcite marble shear zone complex on Thassos Island, Northern Greece, is reconstructed by detailed geometric studies of the textural and microstructural patterns relative to a fixed reference system (shear zone boundary, SZB). Strain localization within the massive marble complex is linked to decreasing P–T conditions during the exhumation process of the metamorphic core complex. Solvus thermometry indicates that temperatures of 300–350°C prevailed during part of the shear zone deformation history. The coarse-grained marble protolith outside the shear zone is characterized by symmetrically oriented twin sets due to early coaxial deformation. A component of heterogeneous non-coaxial deformation is first recorded within the adjacent protomylonite. Enhanced strain weakening by dynamic recrystallization promoted strong localization of plastic deformation in the ultramylonite of the calcite shear zone, where high strain was accommodated by non-coaxial flow. This study demonstrates that both a pure shear and a simple shear strain path can result in similar crystallographic preferred orientations (single c-axis maximum perpendicular to the SZB) by different dominant deformation mechanisms. Separated a-axis pole figures (+a- and −a-axis) show different density distributions with orthorhombic texture symmetry in the protolith marble and monoclinic symmetry in the ultramylonite marble consistently with the observed grain fabric symmetry.     

Plagioclase preferred orientation, Foreshore Group metasediments, Bluff, New Zealand

Recrystallised plagioclase in volcanic metasediments of the Foreshore Group (hornblende-hornfels facies) has a strong preferred orientation with crystal a-axes [100] lying parallel to bedding and with a maximum parallel to a lineation (= maximum principal strain axis or axis of greatest elongation); composition varies widely from bed to bed from oligoclase to anorthite. The preferred orientation is interpreted to result from the mechanical rotation of elongate plagioclase ejecta in the original unconsolidated tuff during strain caused by intrusion of the adjacent Bluff igneous complex. Evidence for such an orienting mechanism is found in the preferred orientation of large unrecrystallised plagioclase ejecta. Matrix plagioclase is generally recrystallised to form granoblastic mosaics; this texture represents a mimetic recrystallisation which reduced grainboundary energy in the fine-grained matrix during the thermal event immediately succeeding deformation.