Strain Localization Zones Research Articles

Homogenized finite element analysis of distal tibia sections: Achievements and limitations

High-resolution peripheral quantitative computed tomography (HR-pQCT) based micro-finite element (μFE) analysis allows accurate prediction of stiffness and ultimate load of standardised (∼1 cm) distal radius and tibia sections. An alternative homogenized finite element method (hFE) was recently validated to compute the ultimate load of larger (∼2 cm) distal radius sections that include Colles' fracture sites. Since the mechanical integrity of the weight-bearing distal tibia is gaining clinical interest, it has been shown that the same properties can be used to predict the strength of both distal segments of the radius and the tibia. Despite the capacity of hFE to predict structural properties of distal segments of the radius and the tibia, the limitations of such homogenization scheme remain unclear. Therefore, the objective of this study is to build a complete mechanical data set of the compressive behavior of distal segments of the tibia and to compare quantitatively the structural properties with the hFE predictions. As a further aim, it is intended to verify whether hFE is also able to capture the post-yield strain localisation or fracture zones in such a bone section, despite the absence of strain softening in the constitutive model.Twenty-five fresh-frozen distal parts of tibias of human donors were used in this study. Sections were cut corresponding to an in-house triple-stack protocol HR-pQCT scan, lapped, and scanned using micro computed tomography (μCT). The sections were tested in compression until failure, unloaded and scanned again in μCT. Volumetric bone mineral density (vBMD) and bone mineral content (BMC) were correlated to compression test results. hFE analysis was performed in order to compare computational predictions (stiffness, yield load and plastic deformation field pattern) with the compressive experiment. Namely, strain localization was assessed based on digital volume correlation (DVC) results and qualitatively compared to hFE predictions by comparing mid-slices patterns.Bone mineral content (BMC) showed a good correlation with stiffness (R2 = 0.92) and yield (R2 = 0.88). Structural parameters also showed good agreement between the experiment and hFE for both stiffness (R2 = 0.96, slope = 1.05 with 95 % CI [0.97, 1.14]) and yield (R2 = 0.95, slope = 1.04 [0.94, 1.13]). The qualitative comparison between hFE and DVC strain localization patterns allowed the classification of the samples into 3 categories: bad (15 sections), semi (8), and good agreement (2).The good correlations between BMC or hFE and experiment for structural parameters were similar to those obtained previously for the distal part of the radius. The failure zones determined by hFE corresponded to registration only in 8 % of the cases. We attribute these discrepancies to local elastic/plastic buckling effects that are not captured by the continuum-based FE approach exempt from strain softening. A way to improve strain localization hFE prediction would be to use longer distal segments with intact cortical shells, as done for the radius. To conclude, the used hFE scheme captures the elastic and yield response of the tibia sections reliably but not the subsequent failure process.

A damage constitutive model for concrete under uniaxial compression capturing strain localization

This paper presents a damage constitutive equation capturing the feature of strain localization and, on this basis, proposes a novel damage constitutive model for concrete under uniaxial compression. It is found that the proposed model can better simulate the stiffness degradation behavior of concrete under cyclic loading, well reproduce the dependency of the post-peak stress-strain curve on specimen or measuring length under monotonic loading, and provide FE simulation results that are insensitive to mesh size. Influence of the maximum aggregate size on the strain localization zone length is discussed.

Dynamic strength and full-field cracking behaviours of pre-cracked rocks under impact loads

The impact loads have a significant influence on the dynamic strength and cracking behaviours of pre-cracked rocks, which plays a key role in the stability and safety of rock engineering. In this study, impact tests were performed by using a split Hopkinson pressure bar (SHPB) in conjunction with the high-speed photography technique. The dynamic strength of pre-cracked rocks under different strain rates and flaw angles was analysed, and the full-field cracking behaviours were elucidated by the evolution of strain localization zones based on the digital image correlation (DIC) analysis. By means of discrete element method (DEM), the impact tests were numerically reproduced to study the strength enhancement and the cracking processes. The results illustrate that the increase in the strain rate and flaw angle would lead to the increasing dynamic strength, the change of tensile and shear crack number is consistent with the strength variation, implying that the microcracking processes has a significant influence on the rate dependency of dynamic strength. As for the cracking behaviours, the strain localization zones would form around the flaw, and the crack branching phenomenon could be witnessed in dynamic tests. Furthermore, the complexity of cracking patterns becomes larger with the increasing strain rate, while the samples with the large flaw angle are difficult to generate strain localization zones and macroscopic cracks. By using a DIC-based method to analyse the crack initiation mechanisms, three types of stress-induced cracks were identified, i.e., mode I, II, and mixed mode I/II cracks. Among these cracks, the mode II cracks are the dominate type of cracks. Based on the mathematical analysis of Griffith model, the combined action of the tangential stress distribution and sliding deformation might be the reason for the crack initiation, and the rate-dependent strength might be induced by the increase of the maximum tangential stress regarding external stress.

Frictional strength, electrical conductivity, and microstructure of calcite–graphite mixtures sheared at a subseismic slip rate

Calcite is a common mineral found in carbonate-bearing fault zones. Crystalline graphite (Gr) can be generated within calcite-bearing fault zones, which may contribute to their low strength and high electrical conductivity. To investigate the mixed effects of Gr on calcite gouges, a dedicated assembly was employed in a rotary-shear friction experiment, which enabled simultaneous measurement of friction and electrical conductivity. The experiments were conducted on synthetic dry calcite–Gr mixtures with 0–50 wt% Gr under a fixed normal stress of approximately 2 MPa at approximately 20 °C. A constant equivalent slip rate of 1 mm/s was imposed, with displacements ranging from 0.8 to 4.6 m. To resolve the microstructure evolution, four additional displacement-controlled experiments were performed on the 6 wt% Gr-bearing specimens under the same conditions. Following high peak friction, all Gr-bearing mixtures experienced dramatic slip weakening. The steady-state electrical conductivity of the specimens increased by over eight orders of magnitude when the Gr content exceeded 6 wt%. Microstructures indicated that the calcite particles initially formed a strong framework with distributed Gr, followed by the gradual development of conductive strain-localization zones (SLZs) and Gr-lubricated slip surfaces with increasing displacement. Even the mixtures with low-Gr content (< 2.4 vol%) developed smooth slip surfaces, sustaining low-level electrical conductivities throughout the experiments. For specimens with high electrical conductivities (Gr > 5.3 vol%), abundant Gr flakes were present in the SLZs, forming an interconnected structure. Combined with our companion study on quartz-Gr mixtures, we propose that the conductivity and frictional strength trends with displacement for Gr-bearing mixtures are not always consistent. Mineral crystal properties (e.g., hardness and crystal structure) may influence the frictional properties of these mixtures significantly, while the level of electrical conductivity of a fault zone cannot be used to infer its frictional strength.

Unraveling the transformation of ductile damage mechanisms of void evolution and strain localization based on deformation heterogeneity

This study delves into the ductile damage mechanism via exploring the intrinsic nature of the transformation of void and strain localization induced damages. In tandem with this, tensile experiments were conducted by using ductile metals of pure titanium and austenite steel with different grain sizes (d¯) and sample thicknesses (t). Various damage behaviors were generated: the void damage (Dv) in which the damage is induced by voids and their evolution, the strain localization induced damage (Dl) in which damage is controlled by localized deformation, and their mixed mode. Examinations of damage characteristics show a transformation from Dl to Dv with the increase of t/d¯ or hardening. To identify the decisive factor behind the mechanism, crystal plasticity finite element simulations were performed, and the grain-level non-homogeneous deformation was carefully examined. The materials with severe inhomogeneous deformation were found to have fewer voids, while the ones with more uniform deformation possessed evident void growth. Deformation heterogeneity was thus identified as a pivotal factor for the Dl - Dv transformation. The change of micro-defect configuration of void and grain boundary (GB) with deformation heterogeneity was discovered to be the underlying cause. In the Dv case, the large number of strain localization zones penetrating within the bulk promotes void nucleation and growth from vacancies and dislocations. The Dl case, on the other hand, gets more new GBs but smaller number of voids during deformation. The larger continuous strain localization zone facilitates the dislocation-consuming process of GB formation, resulting in the difficulty of void formation. Additionally, a characteristic parameter representing the deformation heterogeneity degree was defined. A Dl - Dv paradigm, which involves the change of damage mode and micro-defect configuration with deformation heterogeneity, and the characteristic parameter was established. The paradigm was validated to have a wide applicability with its efficiency in interpreting extensive damage phenomena. These explorations are expected to add new insights into the understanding of damage mechanism and support the development of a unified damage prediction platform.

Study of cyclic crack‐tip opening displacement of microstructurally small fatigue crack using digital image correlation

AbstractThe current work investigates the relationship between the crack growth rate (CGR) and the cyclic crack‐tip opening displacement (ΔCTOD) of microstructurally small fatigue cracks by using high‐resolution digital image correlation (DIC). Load‐controlled fatigue tests were conducted on small‐scale specimens of 18%Cr body‐centered cubic ferritic stainless steel. Microstructurally small fatigue crack growth was analyzed based on accurate high sample‐rate measurements, starting from a sub‐grain crack length up to seven times the volume‐weighted grain size dv = 224 μm. Under these experimental conditions, the high‐resolution analyses reveal that variation from the otherwise linear relationship between CGR and ΔCTOD on double logarithmic scale is due to the crack‐tip bypassing an inhomogeneous shear strain localization zone. In this zone, ΔCTOD is not able to characterize the behavior of microstructurally small fatigue cracks. Outside the shear strain localization zone, ΔCTOD still is a valid crack driving force parameter.

Combined effects of fault geometry and roadway cross-section shape on the collapse behaviors of twin roadways: An experimental investigation

Natural faults in key areas can significantly affect the stability of underground twin roadways. To assess the combined effect of fault geometry and roadway cross-section shape on the collapse behaviors of twin roadways, a series of uniaxial compression tests were carried out on the double-hole specimens using pre-embedded joints to represent faults. In the experiments, the digital image correlation (DIC) and acoustic emission (AE) techniques were used to monitor the strain field evolution and internal crack development in the specimens. The test results showed that the strain localization zones were mainly generated near the roadways and joint, and the initiation locations and patterns of the induced cracks were directly affected by the roadway cross-section shape and joint inclination (α). According to the collapse paths, the collapse modes of the twin roadways can be divided into three categories for different α: joint lap collapse (α = 0°), quasi-integrity collapse (α = 90°), and through-joint collapse (with α ranging from 30° to 60°). In general, the circular twin roadways were found to be more stable than the square twin roadways. Moreover, as α increased from 0° to 90°, the collapse stress was observed to first decrease to its minimum at α = 45° and then increase. Finally, the detailed stress distributions around the roadways and joint were numerically analyzed to supplement the experimental results. The results from this work can be of great engineering significance for the design and construction of similar underground roadways in jointed rock masses to achieve structural stability and safety.

Characterizing Complex Deformation, Damage, and Fracture in Heterogeneous Shale Using 3D-DIC

Safe drilling and effective fracturing are constant challenges for shale formations. One of the most important influencing factors is the accurate characterization of the deformation and damage caused by inherent lamination and natural fractures. Furthermore, shale formations exhibit fine-scale heterogeneity, which conventional laboratory methods (linear variable differential transformer (LVDT), strain gauges, etc.) cannot distinguish. To overcome these constraints, this research aims to investigate the damage and deformation characteristics of shale samples using three-dimensional digital image correlation (3D-DIC). Under uniaxial and diametrical compression, samples of Wolfcamp, Mancos, and Eagle Ford shale with distinct lamination and natural fractures are evaluated. The 3D-DIC system is utilized for image processing, visualization, and analysis of the shale damage process under varying loads. DIC made quantitative full-field strain maps with load (tension, compression, and shear), showing all the damage process steps and strain localization zones (SLZs). DIC maps are used to quantify damage variables in order to investigate sample damage. Damage variables are used to categorize the damage evolution process of shale specimens into four stages: initial damage, linear elastic, elastic–plastic, and plastic damage. Characterizing shale damage evolution with a strain localization line is more effective because there is more damage there than in the whole sample. Damage variables based on major strain and its standard deviation from the DIC strain map for all tested shale samples follow a similar trend, though diametrical compression variables are greater than uniaxial compression. In both uniaxial and diametrical compression, the Wolfcamp shale was reported to have the highest damage variable, which was measured at 0.37, while the Eagle Ford shale was reported to have the lowest damage variable. This image-based technique is more effective not only for understanding the laminated and naturally fractured rocks but also for predicting the hydraulic fractures that will occur during the stimulation process.

Numerical investigation of plastic strain localization for rock-like materials in the framework of fractional plasticity

The plastic strain localization phenomenon is of critical importance for rock-like materials when undergoing non-homogeneous deformation. This paper presents a fractional plastic framework which is applied to take into account the plastic strain localization of rock-like materials. The novelty of the presented framework lies in the non-coaxial plastic flow that is controlled by the RiemannLiouville (RL) fractional derivative without additional plastic potential. The hardening response is described by a function of the generalized plastic shear strain. The capability of the fractional constitutive model to predict the main mechanical behaviors of rock-like materials is assessed by the conventional triaxial compression test data of Vosges sandstones from the literature. With the help of a MATLAB-based finite element method, several numerical examples (i.e., a plate, a plate with a hole, and a plate with a crack) are implemented, compared and analyzed to demonstrate the effectiveness of the proposed framework and the influence of the fractional order on the strain localization. It can be found from the numerical application of the twin-tunnel that the fractional model is promising to flexibly capture the strain localization zone for rock-like materials.

Strain Localization: Analog Modeling and Anisotropy of Magnetic Susceptibility

AbstractThe majority of the strain in Earth crust and upper mantle is localized to the high strain zones developed at ductile‐to‐brittle condition at kilometer‐to‐micrometer scale. Therefore, they represent the key to understanding the deformation evolution of the lithosphere. The finite strain pattern recorded within these zones has been therefore a subject of research in geology. The methods studying rock magnetism such as the anisotropy of magnetic susceptibility (AMS) are frequently used techniques to characterize and quantify deformation and flow record in rocks. Numerous sedimentary, subsolidus and submagmatic deformation zones exhibit typical evolution of the AMS ellipsoid across the strain gradient suggesting indirect not straightforward correlation between AMS and strain ellipsoids. To document spatiotemporal and internal fabric evolution during strain localization, pure shear, simple shear, and shear zone (SZ) analog experiments were performed using shear‐thinning thixotropic material of plaster of Paris. The experimental results closely resemble the record from natural SZs in sedimentary rock systems but also in subsolidus SZs and submagmatic mushy systems. The magnetic fabric evolution across deformation zones is interpreted to be associated with the intersection and transposition of preexisting primary fabric with shear fabrics and evolution of synkinematic subfabrics. Their development is attributed to localization of deformation at microscale due to the self‐organized slip of anisometric particles forming microshear planes reflecting the symmetry of deformation. The experimental results when confronted with the natural examples implies that the localization and partitioning of deformation is one of the most important factors for the interpretation of AMS in deformation zones.

An investigation on the evolution of strain localization zone in metallic materials based on tensile tests and a 1-D nonlocal model

Abstract Metallic materials exhibit pronounced strain localization during damage and failure, posing a challenge in damage mechanics when predicting the change in the size of the strain localization zone. In this study, uniaxial tensile tests were carried out to observe changes in the size of the strain localization zone during the loading of aluminum and low-carbon steel. The initial and final states of the two metallic materials during deformation localization were compared. The strain localization zone shrank gradually with the increase in the load, which agrees with existing electronic speckle pattern interferometry (ESPI) results. This experimental phenomenon was further analyzed theoretically. By establishing the relationship between the material characteristic length and the damage, the variation of the material characteristic length was revealed, and the form of the nonlocal kernel function with a varying characteristic length was determined. The results demonstrated that within the framework of nonlocal damage theory, the nonlocal kernel function with a varying characteristic length can be used to satisfactorily simulate the gradual shrinkage of the strain localization zone of metallic materials with the damage evolution. Therefore, this study provides an effective theoretical tool for predicting the size of the strain localization zone.

The study of mechanism of localized shear fracture in AlMg6 alloy under dynamic loading on a split Hopkinson pressure bar

This work is devoted to the substantiation of one of the mechanisms of plastic strain localization under conditions of high-rate dynamic loading associated with jump-like processes in the defect structure of materials. The specimen behavior under dynamic loading was investigated using a split Hopkinson pressure bar. In order to identify the characteristic stages of strain localization, we performed in-situ thermodynamical studies of the deformation process by recording temperature fields with the CEDIP Silver 450M high-speed infrared camera. The temperature measurements made in the zone of strain localization do not support the wide-spread idea that the strain localization mechanism is caused by thermoplastic instability. Dynamic tests were carried out for specimens, which were specially designed to study plastic strain localization in AlMg6 alloy under conditions of dynamic loading on the split Hopkinson pressure bar using the StrainMaster strain measurement system. The specimens after the experiment were subjected to microstructural analysis using an optical interferometer-profile meter and a scanning electron microscope. The structural analysis revealed the correlated behavior of defect ensembles, which can be classified as a structural transition facilitating strain localization. Experimental data, examination of deformed specimen structure and data of numerical simulation with consideration for kinetics of microdefect accumulation in the material allow us to infer that one of the mechanisms of plastic strain localization at high loading rates is caused by jump-like processes in the defect ensembles.

Study on the Grayscale Characteristics of Borehole Images of Progressive Failure of Coal Bodies with Different Moisture Contents

The failure process of a coal body around a borehole has progressive characteristics. Image characteristics can visually characterize the stress and failure characteristics of the coal body around a borehole during progressive failure. To investigate the effect of the moisture content on the progressive failure of the coal body around the borehole, an image test system for the deformation and fracture of coal rock was used, and progressive failure tests of coal body specimens with different moisture content conditions around boreholes were performed. We acquired images of the deformation field during the entire process of specimen failure. Based on the grayscale image theory, the variation in the grayscale characteristic parameters of the progressive failure process was analyzed. The results show that throughout the progressive failure of coal bodies with different moisture contents around a borehole, the main specimen failure can be divided into six stages: compression density, elastic deformation, crack initiation and stable extension, crack nonstable extension, post-peak softening, and post-peak failure. With increasing moisture content, the σcd/σf values of the 20%- and 40%-moisture-content specimens were 5.1% and 11.3% lower than those of the dry specimens, respectively, and the maximum uniaxial compressive strength σf was 5.1% and 17.4% lower than those of the dry specimens, respectively. The number of cracks that developed decreased. The grayscale histogram had a reduced grayscale peak at each stage, and the surface distortion diminished. The declining grayscale mean curve indicates a lagging development of stress concentration zones. The declining grayscale entropy curve indicates that macroscopic cracks form. The rising grayscale standard deviation curve indicates the delayed development of strain localization zones and weakening of specimen damage. The study explains the deformation and failure characteristics of the coal body around the borehole and the variation in grayness.

Two‐phase model for the excavation analysis in partially saturated soft soils using the particle finite element method

AbstractA two‐phase velocity‐pressure stabilized formulation is proposed for the numerical analysis of mechanized excavations in partially saturated soft soils using the Particle Finite Element Method (PFEM). The fully coupled formulation is based on the theory of porous media in association with the Soil Water Characteristic Curve and the porosity‐dependent Kozeni‐Carman model for the realistic estimation of the soil permeability. The combination of the PFEM methodology, characterized by a global re‐meshing strategy equipped with a new adaptive mesh refinement scheme for the resolution of strain localization zones in the ground, with a hypoplastic constitutive model for the description of the non‐linear behavior of the deformable soil skeleton, allows for the modeling of very large deformations, as required for excavation simulations. The PFEM model is validated based on selected geotechnical benchmark problems concerned with fully and partially saturated soil specimens. The model is further applied to computational re‐analyses of excavation tests involving a single cutting tool moving in a sandbox. The reaction force‐tool displacement curve for the excavation tool as well as the evolution of the deformed topology of the sand including the formation of shear zones obtained from the computational model are compared with respective experimental observations. Parametric investigations aimed at elucidating the influence of selected geotechnical parameters on the excavation process are also carried out. Finally, the suitability of the proposed PFEM‐based numerical strategy for the modeling of 3D excavation problems is demonstrated by means of 3D PFEM simulations in fully saturated sand.

Localized deformation at initial stages of plastic flow in high-manganese steel

The work is devoted to the study of macroscopic localization of plastic deformation during uniaxial tension of single crystals of the Hadfield steel (Fe – 13 % Mn – 1.03 % C). In the course of studies at the stage of easy sliding, significant differences were found in the nature of macrolocalization of plastic deformation in the single-crystal samples under study. All patterns of deformation localization observed in these cases can be divided into two types. The first type of strain localization corresponds to the initiation at the upper yield point and further propagation of the strain front, which gradually transfers the sample material from undeformed state to deformed one. This manifested itself most clearly in single crystals oriented along the tension axis [377] and [355], where the strain localization pattern appears as a single zone of localized deformation on the yield plateau. Such a deformation front passes through the sample volume only once as a Chernov-Luders band. In this case, the flow of the material is carried out without hardening until all its elements are transferred to the deformed state. Single zones of strain localization were also observed at the stages of easy sliding and yield plateau in the Hadfield steel single crystals oriented along the tension axis [123] and [012]. In the second type of localization, at the stage of easy sliding, synchronous movement along the pattern of several deformation centers occurs. Their movement can be unidirectional and counter, and the speeds are both the same and different from each other. Further deformation of the Hadfield steel single crystals oriented along the tension axis [355] or [012], led to the movement of two deformation localization centers at the stages of easy sliding. In single crystals oriented along [111], the strain localization pattern is respectively represented as four localized strain sites. Consequently, the synchronous movement of deformation fronts occurs along an already deformed, albeit to a small extent, material. As a reason for the difference between the two types of macrostrain localization at stage I (the easy sliding stage and the yield plateau), the number of active sliding systems or tensile twinning in the studied single crystals can be discussed based on crystallographic analysis and metallographic studies.

Fracture evolution and failure behavior around an opening in brittle jointed rocks subjected to uniaxial compression

To investigate the fracture evolution and failure behavior around an opening in brittle jointed rocks, an experimental study was carried out in which cross-jointed samples with granite cavities were uniaxially loaded while the mechanics, acoustics and optics were simultaneously observed. These results were compared and analyzed to better understand the deformation and cracking process. The results show that the presence of cross joints and the change in included angles play a crucial role in influencing the strength and deformation properties of the samples. The peak strength and elastic modulus depend on the included angle and first decrease and then increase with increasing included angle, reaching the minimum values when β equals 45°. A stress fluctuation point generally corresponds to a large acoustic emission (AE) event and a turning point in the accumulated AE count curve. The good correlation of the three observations provided a reasonable holistic picture of the process zone nucleation and the subsequent cracking processes. The cracking behavior around openings and cross joints is significantly affected by the included angle because of drastic changes in the stress distribution surrounding the defects. The highlighted strain localization zones formed near the joint tip and around the chamber interact with each other and jointly dominate the initiation and propagation mode of new cracks, eventually leading to more complex failure patterns and severe fracture degrees. Moreover, there will also be an interaction between the same set of cross joints, and the tips can be connected, showing the characteristics of intensified deformation in local areas. The unstable failure of a sample is primarily dominated by tensile cracks and locally by shear cracks around the cavern and the joint tips. Microcrack zones are regarded as white patches macroscopically, and microcrack nucleation is considered to be the microformation mechanism of a white patch.

Prolonged grain boundary sliding in naturally deformed calcite marble at the middle crustal level

It is generally accepted that grain boundary sliding (GBS) is the dominant deformation mechanism in fine-grained strain localization zones. However, the lifetime of GBS during deformation in monomineralic rocks is hotly debated, as grain growth may inhibit the operation of GBS. In this contribution, recrystallized matrix grains in calcite marbles from the Jinzhou detachment fault zone at the middle crustal level, Liaodong Peninsula, Northeast China, show clear evidence of GBS, e.g., 1) fine grains with sizes of 5–30 μm, nearly equant grain shapes and slightly curved grain boundaries, 2) rare evidence for intracrystalline deformation, 3) existence of four-grain junctions and aligned straight grain boundaries, and 4) weak crystallographic preferred orientations. The existence of high misorientation zones along the margins of the matrix grains, especially at their triple junctions, and differences in cathodoluminescence (CL) characteristics between rims and cores of the grains indicate simultaneous accommodation of GBS by dislocation motion and grain boundary diffusion. The different CL characteristics between rims and cores of calcite matrix grains and the presence of calcite-filled cracks imply fluid activity during deformation. Fluids could dramatically enhance GBS by promoting dislocation motion and grain boundary diffusion. Additionally, the nucleation of fine grains by dynamic recrystallization and cavitation-sealing processes during GBS guaranteed the maintenance of GBS. At the same time, the occurrence of micropores and the existence of second phases also inhibit grain growth. These features make GBS the dominant deformation mechanism in naturally deformed marbles in the middle-upper crust.

The origin and localization of “vermiculite” along the intra‐terrane shear zones in the Bundelkhand Craton, India: Mechanism and implication

Vermiculite, a clay mineral of economic importance, is reported for the first time from the Bundelkhand Craton. The locales of the vermiculite occurrence are mapped within the Bundelkhand granitoids at several places. The identification of the fracture system and the zones of strain localization within Bundelkhand granitoids are critical for targeting the occurrences of vermiculite. A range of studies including meso‐, micro‐, and sub‐microscopic analyses were used to delineate the characteristic features of vermiculite along the brittle/ductile shear zones in the Bundelkhand Craton. SEM‐based EDS, EPMA, and XRD analyses confirm the ubiquitous dominance of vermiculite as fracture infills and/or channel infill materials along the zones of nucleation of ductile shear zones. It is postulated here that the occurrence of vermiculite is a result of supergene alteration of biotite present in the vein material. The parent material of the fracture infills from which the veins crystallized is genetically derived from the host rock (Bundelkhand granitoid), which later healed the fractures and prompted the nucleation of ductile shear zones in the Bundelkhand Craton.

A representation learning framework for detection and characterization of dead versus strain localization zones from pre- to post-failure

Experiments have long shown that zones of near vanishing deformation, so-called “dead zones”, emerge and coexist with strain localization zones inside deforming granular media. To date, a method that can disentangle these dynamically coupled structures from each other, from pre- to post- failure, is lacking. Here we develop a framework that learns a new representation of the kinematic data, based on the complexity of a grain’s neighborhood structure in the kinematic-state-space, as measured by a recently introduced metric called s-LID. Dead zones (DZ) are first distinguished from strain localization zones (SZ) throughout loading history. Next the coupled dynamics of DZ and SZ are characterized using a range of discriminative features representing: local nonaffine deformation, contact topology and force transmission properties. Data came from discrete element simulations of biaxial compression tests. The deformation is found to be essentially dual in nature. DZ and SZ exhibit distinct yet coupled dynamics, with the separation in dynamics increasing in the lead up to failure. Force congestion and plastic deformation mainly concentrate in SZ. Although the 3-core of the contact network is highly prone to damage in SZ, it is robust to pre-failure microbands but is decimated in the shearband, leaving a fragmented 3-core in DZ at failure. We also show how loading condition and rolling resistance influence SZ and DZ differently, thus casting new light on controls on plasticity from the perspective of emergent deformation structures.Graphic abstract

Improved virtual extensometer measurement method in complex multi-fracture situation

To overcome the limitation of the virtual extensometer method in measuring the crack opening displacement (COD) in the process of complex multi-crack propagation of rock, the measurement error of Digital Image Correlation (DIC) local deformation is theoretically analyzed. An improved virtual extensometer method for measuring the COD is proposed, which considers the temporal and spatial characteristics of crack development in the process of complex crack propagation. The accuracy of the proposed method is verified by the strain localization band numerical simulation test and indoor single crack simulation test. Furthermore, the method is applied to the two-dimensional similarity simulation test of simulating complex multi-fractures in rock stratum. The COD obtained by the traditional and improved methods is compared with the measured COD. The results show that in the case of multiple complex cracks, to obtain the COD accurately, the relative distance between the virtual extensometer measuring point and the crack should be greater than half of the sum of the width of the crack strain localization zone and the subset size. With the development of the crack, the relative distance between the virtual extensometer measuring point and the crack should increase with the increase of the width of the crack strain localization zone. The error of the COD measured by the traditional method increases with fracture development, and the maximum is 21.20%. The maximum relative error between the COD measured by the improved method and the measured crack opening is 3.61%. The research results improve the accuracy of the virtual extensometer in measuring the COD under complex multi-crack conditions.