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Determining the effect of loading rates on rock mechanical properties and deformation behavior is of vital importance for underground engineering with high-intensity excavation. In this study, uniaxial compression experiments with the digital image correlation technique were conducted to investigate the mechanical properties, failure modes, and apparent strain fields of the sandstone samples under different quasi-static loading rates. The loading rate effect on the characteristics of strain localization and energy was subsequently analyzed. Results show that with increasing loading rates, both the elastic modulus and uniaxial compressive strength increase logarithmically, and the failure mode changes from shear failure to tensile failure. Meanwhile, there are relationships between the initiation and development of strain localization and the loading rates. As the loading rate increases, the stress and stress level of strain localization initiation and the expansion rate of strain localization at most time increase gradually, while the duration from strain localization initiation to macro-failure decreases. The expansion area of strain localization has no obvious change pattern. In addition, the increase of loading rates enhances the energy absorption, storage, and dissipation properties of the samples, resulting in a higher energy state. It is the essential reason for the differences in mechanical behavior and strain localization of sandstone under different loading rates. [ABSTRACT FROM AUTHOR]

Enhancing the strength and ductility of metallic materials simultaneously is crucial for numerous industrial applications, yet it remains a formidable challenge due to the typical trade-off between these two properties. This study introduces an innovative approach to surmount this challenge by employing a composite bar design that leverages necking inhibition mechanisms for simultaneous improvements in both strength and ductility. The composite bars, comprising aluminum cores reinforced with spirally wound fiber-reinforced polymer (FRP) strands, were fabricated in various configurations to investigate different necking behaviors. Through uniaxial testing, the composite bars exhibited notable increases in both strength and ductility, attributed to the strategic design of the FRP winding angle and FRP content. This design effectively modulates the necking behavior, thereby enhancing the composite bars' mechanical properties. Analysis of the strain distribution further elucidated the role of the spiral FRP strands in necking prevention. The composite bar design method outlined in this study offers a viable strategy for enhancing the mechanical performance of metallic materials, significantly reducing the risk of abrupt failure under high loads and deformations. [ABSTRACT FROM AUTHOR]

The onset of brittle failure in rocks includes dilatancy and strain localization. To better understand this nucleation process, we analyze the evolution of the local three‐dimensional strain tensor using X‐ray tomograms acquired during triaxial compression experiments on granite and sandstone. The onset of the localization of the compaction, dilation, and shear strain occurs when ∼65% of the rock volume experiences dilation. Tracking the locations of the high strains throughout loading suggests that the deformation that occurs early in loading influences the location of the system‐sized fracture network that produces macroscopic failure. This influence is larger in the sandstone experiments than the granite experiments, likely due to the microstructure of the sandstone. These results have important implications for detecting precursors to catastrophic failure. Plain Language Summary: We investigate the fundamental processes that lead to brittle failure in rocks. We deform two common types of crustal rocks, granite and sandstone, under upper crustal stress conditions. As the stress applied to the rock increases, the rock tends to expand (dilate) more than compact, particularly as it approaches catastrophic, macroscopic failure. A larger portion of the rock undergoes dilation when the strain field starts to localize, indicating that accelerating dilation is a precursor to macroscopic failure. We observe different localization patterns in the rocks: in sandstone, strain localization progresses monotonically with increasing stress, whereas phases of delocalization can occur in the granite. Two competing models describe the development of the system‐sized fracture network that produces macroscopic failure: the network develops from (a) the coalescence of fractures that form early in loading, or from (b) the propagation of a process zone of interacting fractures through relatively intact rock. We find that the high strain events persist at the same location throughout the experiments more than expected by chance, particularly in experiments on sandstone. The results provide perhaps the most robust experimental confirmation yet that the fracture network that causes macroscopic failure evolves from the deformation that occurs earlier in loading. Key Points: X‐ray tomography quantifies the evolving spatial evolution of high strain events during brittle failureAt the onset of strain localization, on average 65% of the volume of the rock cores undergo dilationLocalized zones of high strain events persist in space from the onset of loading [ABSTRACT FROM AUTHOR]

Background: Stereo-digital image correlation (DIC) measurements can be challenging when working with small specimens. Achieving high-precision data requires careful selection of hardware, stereo-rig design, illumination, speckling, calibration, and minimization of noise levels. Objective: This study presents an optimized stereo-DIC setup based on parfocal zoom lenses for full-field measurements at magnifications ranging from 0.5× (14.3 × 16.9 mm2) to 2× (3.5 × 4.2 mm2). Methods: The advantages of using parfocal zoom lenses over fixed-focal-length lenses (and extension tubes) for full-field measurements at small fields of view (FOVs) are demonstrated through quantitative comparisons of the temporal evolution of pseudo-strains and null strain analysis from rigid body translation experiments. The optimal speckling parameters for each magnification are determined by analyzing gray-level histograms, mean intensity gradient ( ∇ G ¯ ), and subset size. The challenges of calibration at high magnifications are discussed, along with strategies for obtaining acceptable results. Results: The accuracy of the presented stereo-DIC setup is evaluated through the study of localized phase transformation on a 1 mm diameter superelastic NiTi wire under tension, column buckling, and compression deformations. The presented setup provides highly consistent full-field data over the 0.5–2× magnification range. Conclusion: The results highlight the benefits of using parfocal zoom lenses for stereo-DIC measurements over a range of small FOVs. [ABSTRACT FROM AUTHOR]

A large number of structures in the United States and worldwide include nonductile reinforced concrete (RC) frames with columns and beams that are prone to shear failure. Due to the brittle nature of shear failures, accurate simulation of RC structures with shear-critical members is essential to predicting their overall capacity under severe loading scenarios (e.g., earthquakes) and designing effective retrofits and upgrades. In this paper, a previously developed gradient inelastic (GI) force-based (FB) beam-column element formulation capable of capturing axial-flexural interaction and predicting flexural failures is extended to account for axial-flexural-shear interactions in RC members in order to predict shear failures. The proposed shear-enhanced GI FB element formulation advances the original GI FB element formulation by developing higher-order cross section kinematics, i.e., beyond the plane sections assumption, and by developing a 3D concrete constitutive model. The higher-order cross section kinematics can simulate strain distribution of the cross section more accurately while using 3D concrete constitutive models at the element's cross sections permits simulation of axial-flexural-shear interactions. To incorporate the confinement effects of transverse steel reinforcement, through-the-depth stress equilibrium is strictly enforced in the transverse directions of the member's cross section. To eliminate strain localization phenomena, new gradient nonlocality relationships are introduced in addition to those of the original GI FB formulation. The proposed element formulation is implemented in the OpenSees structural analysis software and is shown to maintain continuous macroscopic section strain distributions over the element length during softening and discretization convergent responses, thereby eliminating the strain localization phenomena. In addition, the predictions of the shear-enhanced GI FB element formulation are compared with data available from experiments on RC beams and columns. [ABSTRACT FROM AUTHOR]

Abstract Thin film nanoindentation has increased interest due to its usage in various applications. It is virtually impossible to measure thin film elastic modulus without the substrate influence. Several different methods exist to obtain the true thin film’s elastic modulus with no attention given to investigate what parameters can improve insight into thin film mechanical property measurement. A key parameter is the tip radius. This work is aimed at quantifying the influence of the tip radius on the strain field under the indenter. Three Berkovich indentation tips with different tip radii were used for thin multilayer nanoindentation with numerical modelling. The results confirm the existence of the large elastically deformed zone, with a strong localization under the tip. Comparison between the experiments and numerical model shows direct connection between the tip radius and strain localization affecting the experiment, emphasizing importance of knowing the tip radius.

In this study, a novel localized selective remelting technique was proposed to treat the welding interface regions on the top and bottom surfaces of the AZ31 friction stir welded joint. Compared with the untreated joint, the treated joint achieved a favorable combination of strength (ultimate tensile strength of 238 MPa) and ductility (elongation of 13.3%). Digital image correlation (DIC) characterization revealed that the high strain-hardening ability primarily stemmed from the substantial mitigation of strain localization, which was caused by a comprehensive factor, including reduced SF value fluctuation between weld micro-zones, low residual dislocation density, and numerous extension twinning activation in the nugget zone.

AbstractThe mechanical behavior of carbon dioxide (CO2)-containing sediments is crucial for the implementation of carbon dioxide storage in the ocean. Current research overlooks the effects of non-uniform deformation on the evaluation of mechanical properties in triaxial tests. In this study, a triaxial testing system equipped with digital image technology of the specimen global surface was used to test the triaxial behaviors of Bohai sand containing CO2 - CO2 hydrates. On this basis, the strain localization, shear band formation, and evolution behavior of the CO2-bearing sediments were analyzed, according to the surface deformation of the triaxial specimens. The results show that the mean values of axial strain, lateral strain, and volumetric strain of CDBS specimens are higher than the global values. The local destructive stress and the local effective internal friction angle φ of the specimens are smaller than the global values. The sample’s shear bands may be generated multiple times and are negatively correlated with the mean stress σm. This study concluded that the global stress-strain curves overestimated the strength of the CDBS samples and underestimated the deformation of the samples. This was due to the inhomogeneous deformation of the samples. [ABSTRACT FROM AUTHOR]

EN-GJS-400-15U nodular cast iron intended to be used as load-bearing element in long-term geological disposal canisters containing spent nuclear fuel in Finland and Sweden was studied for static strain aging (SSA). Tensile test specimens manufactured from the nodular cast iron were pre-strained to 1%, 2% and 3% nominal plastic strains. The pre-strained specimens were aged at different temperatures ranging from room temperature to 400 °C for varying times. The aged specimens were tested with conventional tensile testing using constant cross-head speed of 0.016 mm/s. Additionally, four specimens were studied with digital image correlation (DIC) during the tensile testing to obtain full-field strain measurements. SSA resulted in elevated pronounced yield point in all the conditions, while the as-received material showed continuous yielding behavior. SSA reduced the elongation to fracture. DIC tests showed more localized yielding behavior in the SSA specimens. Over-aging effect was observed at 400 °C where increasing pre-strain did not increase the yield stress more. For 1-day aging time, the highest yield stress increment was found after aging at 200°C. The yield stress of the material was almost identical after aging in 100°C and 200°C. [ABSTRACT FROM AUTHOR]

Rift initiation within cold, thick, strong lithosphere and the evolving linkage to form a contiguous plate boundary remains debated in part owing to the lack of time–space constraints on kinematics of basement‐involved faults. Different rift sectors initiate diachronously and may eventually link to produce a jigsaw spatial pattern, as in the East African rift, and along the Atlantic Ocean margins. The space–time distribution of earthquakes illuminates the geometry and kinematics of fault zones within the crystalline crust, as well as areas with pressurized magma bodies. We use seismicity and Global Navigation System Satellites (GNSS) data from the Turkana Rift Array Investigating Lithospheric Structure (TRAILS) project in East Africa and a new digital compilation of faults and eruptive centres to evaluate models for the kinematic linkage of two initially separate rift sectors: the Main Ethiopian Rift (MER) and the Eastern rift (ER). The ca. 300 km wide zone of linkage includes failed basins and linkage zones; seismicity outlines active structures. Models of GNSS data indicate that the ca. 250 km‐wide zone of seismically active en echelon basins north of the Turkana Depression is a zone, or block, of distributed strain with small counterclockwise rotation that serves to connect the Main Ethiopian and Eastern rifts. Its western boundary is poorly defined owing to data gaps in South Sudan. Strain across the northern and southern boundaries of this block, and an ca. 50 km‐wide kink in the southern Turkana rift is accommodated by en echelon normal faults linked by short strike‐slip faults in crystalline basement, and relay ramps at the surface. Short segments of obliquely oriented basement structures facilitate across‐rift linkage of faults, but basement shear zones and Mesozoic rift faults are not actively straining. This configuration has existed for at least 2–5 My without the development of localized shear zones or transform faults, documenting the importance of distributed deformation in continental rift tectonics. [ABSTRACT FROM AUTHOR]

Shear strain localization refers to the phenomenon of accumulation of material deformation in narrow slip zones. Many materials exhibit strain localization under different spatial and temporal scales, particularly rocks, metals, soils, and concrete. In the Earth's crust, irreversible deformation can occur in brittle as well as in ductile regimes. Modeling of shear zones is essential in the geodynamic framework. Numerical modeling of strain localization remains challenging due to the non‐linearity and multi‐scale nature of the problem. We develop a numerical approach based on graphical processing units (GPU) to resolve the strain localization in two and three dimensions of a (visco)‐hypoelastic‐perfectly plastic medium. Our approach allows modeling both the compressible and incompressible visco‐elasto‐plastic flows. In contrast to symmetric shear bands frequently observed in the literature, we demonstrate that using sufficiently small strain or strain rate increments, a non‐symmetric strain localization pattern is resolved in two‐ and three‐dimensions, highlighting the importance of high spatial and temporal resolution. We show that elasto‐plastic and visco‐plastic models yield similar strain localization patterns for material properties relevant to applications in geodynamics. We achieve fast computations using three‐dimensional high‐resolution models involving more than 1.3 billion degrees of freedom. We propose a new physics‐based approach explaining spontaneous stress drops in a deforming medium. Plain Language Summary: Strain localization is the accumulation of strain in narrow regions of rocks and other materials like metals, soils, and concrete, occurring at different scales. The strength of most geomaterials, particularly rocks, is strongly pressure‐dependent, with strength increasing with increasing pressure. We developed efficient numerical algorithms using High‐Performance Computing (HPC) and graphical processing units (GPUs) to model strain localization in 2D and 3D for applications in geodynamics and earthquake physics. Unlike previous models, our method reveals non‐symmetrical patterns by using very small strain increments, highlighting the need for high‐detail modeling. We found that elasto‐plastic and visco‐plastic models show similar strain patterns for relevant materials. Our method also achieves fast, detailed computations with over 1.3 billion variables and offers a new explanation for sudden stress drops in deforming materials. Key Points: We resolve material instability during deformation resulting in a non‐symmetric pattern of strain localizationWe demonstrate the similarity in patterns of strain localization between frictional and time‐dependent plasticity modelsWe achieve fast numerical simulations in high‐resolution model setups in three dimensions involving more than 500 million degrees of freedom [ABSTRACT FROM AUTHOR]

We combined novel laboratory techniques and numerical modeling to investigate (a)seismic preparatory processes associated with deformation localization during a triaxial failure test on a dry sample of Berea sandstone. Laboratory observations were quantified by measuring strain localization on the sample surface with a distributed strain sensing (DSS) array, utilizing optical fibers, in conjunction with both passive and active acoustic emission (AE) techniques. A physics-based computational model was subsequently employed to understand the underlying physics of these observations and to establish a spatio-temporal correlation between the laboratory and modeling results. These simulations revealed three distinct stages of preparatory processes: (i) highly dissipative fronts propagated towards the middle of the sample correlating with the observed acoustic emission locations; (ii) dissipative regions were individuated in the middle of the sample and could be linked to a discernible decrease of the P-wave velocities; (iii) a system of conjugate bands formed, coalesced into a single band that grew from the center towards the sample surface and was interpreted to be representative for the preparation of a weak plane. Dilatative lobes at the process zones of the weak plane extended outwards and grew to the surface, causing strain localization and an acceleration of the simulated deformation prior to failure. This was also observed during the experiment with the strain rate measurements and spatio-temporally correlated with an increase of the seismicity rate in a similar rock volume. The combined approach of such laboratory and numerical techniques provides an enriched view of (a)seismic preparatory processes preceding the mainshock. Highlights: The combination of novel laboratory and numerical techniques allowed us to detect preparatory processes prior to failure. The employment of distributed strain sensing with optical fibers was successful in imaging strain localization preceding failure. The simulated dissipation of mechanical energy correlated with the observations of strain localization occurring during the experiment. [ABSTRACT FROM AUTHOR]

Due to its good conductive properties, unalloyed (pure) aluminum, such as EN AW-1050A H24, finds new fields of application in electromobility. To optimize components, the cyclic material behavior must be understood and described precisely as a foundation of a proper fatigue life estimation. Various cyclic tests were performed to not only derive the cyclic parameters to describe the material but also to find the most suitable procedure to deal with the challenges faced during the experiments. The main point of interest is the comparison between a surface-mounted clip-on extensometer and an optical system both used for strain control in cyclic tests. For the analysis of the anisotropic behavior of EN AW-1050A H24, un-notched flat specimens were extracted from sheet metal lengthways and crossways in respect to the rolling direction. While the cyclic material behavior for specimens of both directions of extraction is characterized by cyclic softening in general, the specimens extracted crossways show a strain-amplitude-dependent cyclic softening with strong strain localization especially at the contact points of the knives of the clip-on extensometer leading to an increased quantity of invalid experiments as well as sudden fractures. In the study, it was possible to show the benefits of a contactless optical strain control system when dealing with very soft metallic materials such as EN AW-1050A H24. [ABSTRACT FROM AUTHOR]

Abstract The onset of brittle failure in rocks includes dilatancy and strain localization. To better understand this nucleation process, we analyze the evolution of the local three‐dimensional strain tensor using X‐ray tomograms acquired during triaxial compression experiments on granite and sandstone. The onset of the localization of the compaction, dilation, and shear strain occurs when ∼65% of the rock volume experiences dilation. Tracking the locations of the high strains throughout loading suggests that the deformation that occurs early in loading influences the location of the system‐sized fracture network that produces macroscopic failure. This influence is larger in the sandstone experiments than the granite experiments, likely due to the microstructure of the sandstone. These results have important implications for detecting precursors to catastrophic failure.

High strength metastable β titanium alloys are widely employed in the aircraft industry due to their outstanding strength-to-weight ratio. While components can endure complex in-service mechanical loading, the anisotropy in tensile properties has been the subject of limited attention. In this study, its origin was investigated focusing on the role played by millimeter scale β grains as they were recently identified as a source of heterogeneous deformation. Tensile properties of Ti-10V-2Fe-3Al processed via different thermomechanical routes were assessed using multiple sampling directions. In particular, elongation values were observed to vary significantly depending on the testing direction. A combination of SEM, EBSD, µ-CT and in-situ DIC during tensile tests was employed to clarify the underlying causes of this behavior. Substantial differences in strain heterogeneity and localization were found related to features of β grains, including their crystallographic and morphologic orientations. Furthermore, multiple fracture mechanisms were observed to derive from the differences in deformation behavior, and eventually compete to trigger specimen failure. Elongation values are then determined by both the degree of strain heterogeneity and the operating fracture mechanisms. These findings provide a new understanding of the role of the microstructure in the tensile behavior of high strength metastable β titanium alloys.

Recent explosions have prompted researchers to investigate the vulnerability of civil structures, leading to an increased demand for blast-resistant buildings. Laminated glass (LG) panels in glazed facades boost resilience, yet understanding glass fragment interaction with interlayers remains incomplete. This paper presents an integrated experimental-computational study on strain localization in LG polymeric interlayers to accurately simulate their response, addressing this gap. Uniaxial tensile tests were performed on the polymeric interlayer materials polyvinyl butyral (PVB) and SentryGlas® (SG), commonly used in the design of LG in blast-resistant glazing systems. Digital image correlation was used to characterize strain localization within the material. The experimental results were used to calibrate material model parameters to be used in the modeling of LG systems. A three-network viscoplastic (TNV) material model for SG interlayer was calibrated using PolymerFEM software. Yeoh hyperelastic material model parameters were calibrated for the quasistatic response of PVB. A finite element computational model was developed using Ansys LS-DYNA software and validated with experimental data. The study results showcase finite element modeling's ability to accurately predict both the hyperelastic response of PVB and the post-peak large strain behavior of SG interlayer materials by 8% and 3.6%, respectively.

Constrained groove pressing using conventional dies with groove angle of 45° imparts shear deformation within the material and repetitive pressings leads to the development of fine-grained structure. However, the usage of conventional dies leads to strain localization within the sample and also leaves strong impressions on the surface thereby generating microcracks with repeated number of passes. The present work was carried out numerically as well as experimentally to analyze the strain distribution by altering the die profile to sinusoidal form. AA2014 samples pressed using sinusoidal die profile had lesser strain inhomogeneity as compared to samples pressed using 45° groove angle die. The surface texture was observed to be improved, and a total of 40 passes were possible using a sinusoidal die as compared to 4 passes in 45° groove angle die. [ABSTRACT FROM AUTHOR]

In the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated that FEM×DEM approach naturally captures the discrete and anisotropic nature of granular materials. Despite its advantages, FEM×DEM with classical FEM, suffers from mesh dependency, especially when material enters softening phase and exhibits strain localization. To overcome this limitation, FEM×DEM model has been enriched by incorporating a local second gradient model. Nevertheless, the existence of multiple possible solutions is observed. In this paper, we study the variability and loss of uniqueness of numerical solutions to a boundary value problem. Different VEs with equivalent mechanical properties are generated and used to model the pressuremeter tests by means of FEM×DEM. The modeling results show a great variability of the numerical results, both in shape of borehole and in different modes of shear bands. For the same VE, the loss of uniqueness of numerical solutions is evidenced by a slight modification of loading history at the level of the internal pressure applied to the borehole. Finally, we show that when a certain heterogeneity is introduced by using different VEs within the same BVP, even if the uniqueness of the solution is not guaranteed, the set of possible solutions seems more restrained. [ABSTRACT FROM AUTHOR]

Strain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized version of the MCC model, is implemented. It has been recognized, nonetheless, that without resorting to the regularization mechanism, the standard finite element method (FEM) or the second‐order cone programming optimized finite element method (FEM‐SOCP) often experiences instability or interruption of calculating the hardening‐softening responses of overconsolidated soils. To resolve the aforementioned difficulty, the UH model is developed and implemented in the framework of FEM‐SOCP based on the micropolar continuum (mpcFEM‐SOCP) to predict strain localizations of overconsolidated soils. Furthermore, to obviate non‐convexity of mpcFEM‐SOCP induced by material softening, an effective composite update scheme of hardening variable pc, which refers to the implicit variable (IV) scheme for the hardening stage and then refers to the explicit variable (EV) scheme for the softening stage, is proposed. Based on one biaxial compression problem and one rigid strip footing problem, numerical analyses disclose that by applying mpcFEM‐SOCP in conjunction with the composite update scheme of pc, the UH model of micropolar continuum can effectively predict the strain localization behavior of overconsolidated soil during its failure stage, and the stable hardening‐softening responses of overconsolidated soils can be readily attained. [ABSTRACT FROM AUTHOR]

Mesh size dependency caused by strain localization is an ongoing problem in numerical simulations using the finite element method. In order to solve this problem, the concept of including the characteristic element length for regularization is used in the literature. The estimation of the characteristic element length is not a straightforward task since normally the characteristic element length differs from one element to another in the simulation and depends not only on element geometry but also on fracture plane orientation and material orientation. In this paper, an innovative method is proposed to estimate the characteristic element length which works on the orthogonal projection of elements on the fracture plane. The method is implemented in Abaqus/Explicit finite element solver and is verified using simple and more complex load cases such as tensile specimens, open hole specimens, and low-velocity impact. A good correlation between the numerical and experimental results in all of the studied cases was achieved and the proposed method proved to be effective in reducing mesh sensitivity. The use of the volumetric method from the literature for the simulation of open-hole tensile specimens led to more than 25% increase in the estimation of specimen strength while similar values of strength for different element aspect ratios were achieved with the proposed method. [ABSTRACT FROM AUTHOR]

Abstract The deformation behavior of Ti-6Al-4V titanium alloy is significantly influenced by slip localized within crystallographic slip bands. Experimental observations reveal that intense slip bands in Ti-6Al-4V form at strains well below the macroscopic yield strain and may serially propagate across grain boundaries, resulting in long-range localization that percolates through the microstructure. These connected, localized slip bands serve as potential sites for crack initiation. Although slip localization in Ti-6Al-4V is known to be influenced by various factors, an investigation of optimal microstructures that limit localization remains lacking. In this work, we develop a novel strategy that integrates an explicit slip band crystal plasticity technique, graph networks, and neural network models to identify Ti-6Al-4V microstructures that reduce the propensity for strain localization. Simulations are conducted on a dataset of 3D polycrystals, each represented as a graph to account for grain neighborhood and connectivity. The results are then used to train neural network surrogate models that accurately predict localization-based properties of a polycrystal, given its microstructure. These properties include the ratio of slip accumulated in the band to that in the matrix, fraction of total applied strain accommodated by slip bands, and spatial connectivity of slip bands throughout the microstructure. The initial dataset is enriched by synthetic data generated by the surrogate models, and a grid search optimization is subsequently performed to find optimal microstructures. Describing a 3D polycrystal with only a few features and a combination of graph and neural network models offer robustness compared to the alternative approaches without compromising accuracy. We show that while each material property is optimized through a unique microstructure solution, elongated grain shape emerges as a recurring feature among all optimal microstructures. This finding suggests that designing microstructures with elongated grains could potentially mitigate strain localization without compromising strength.

Constraining strain localization and the growth of shear fabrics within brittle fault zones at sub‐seismic slip rates is important for understanding fault strength and frictional stability. We conducted direct shear experiments on simulated sandstone‐derived fault gouges at an effective normal stress of 40 MPa, a pore pressure of 15 MPa, and a temperature of 100°C. Using a passive strain marker and X‐ray Computed Tomography, we analyzed the spatial distribution of deformation in gouges deformed in the strain‐hardening, subsequent strain‐softening, and then steady‐state regimes at displacement rates of 1, 30, and 1,000 µm/s. We developed a machine‐learning‐based automatic boundary detection method to recognize the shear fabrics and quantify displacement partitioning between each fabric element. Our results show fabrics oriented along R1 and Y (including boundary) shears are the two major fabric elements. At rates of 1 and 30 µm/s, the relative amount of displacement on R1 shears is displacement dependent, increasing to ∼20% of the total displacement up to the strain‐softening stage, then decreasing to ∼10%–18% at the steady state. This trend is absent at the high rate where ∼18% of the displacement occurs on R1 shears throughout all investigated stages. At all rates, the relative amount of displacement on Y shears increases linearly with displacement to a total of larger than 50% at the steady state. Our study provides constraints on the development of the active slip zone, which is an important factor controlling heating and weakening associated with small‐magnitude earthquakes with limited displacement (mm‐dm), such as induced seismicity. Plain Language Summary: In the past few decades, several studies have focused on the mechanical behavior of simulated fault zones to understand earthquake nucleation. However, minor attention has been paid to the microstructural characterization of fault‐zone gouges due to the difficulties in quantifying deformation. An understanding of brittle fault‐zone fabrics and their development provides crucial constraints on the mechanical strength and stability of faults. We conducted laboratory experiments on simulated sandstone‐derived fault gouges with a passive strain marker under the conditions relevant to earthquake nucleation to explore the development and evolution of shear zone fabrics and their relations to fault strength. We combined X‐ray Computed Tomography (XCT) and a custom‐designed machine‐learning‐based automatic boundary detection method to analyze the spatial distribution of gouge deformation and to quantify displacement partitioning between deformation features. The results show that our samples have similar evolution of the shear fabrics, partitioning of displacement, and mechanical response with increasing shear strain at all tested nucleation velocities. The evolution of the mechanical behavior from strain‐hardening, to softening, to steady‐state stages is related to the transformation of R1 to shear‐parallel shear bands. Up to 50% of the total displacement can be accommodated within shear‐parallel shear bands, facilitating strain weakening of the materials. Key Points: We performed 3‐D analyses on the evolution of shear zone fabrics within sandstone‐derived fault gouges utilizing the X‐ray CT techniqueOur samples show similar evolution of shear fabrics, slip partitioning, and mechanical response with shear strain at all tested velocitiesUp to 50% of the total imposed displacement can be accommodated within shear‐parallel shear bands during earthquake nucleation [ABSTRACT FROM AUTHOR]

Underground coal mining in China has gradually moved into deeper seams in recent years, which results in a higher ambient temperature in the mining space and significantly affects the mechanical behavior of coal. In this study, dehydrated coal samples were obtained at different temperatures ranging from 30 ∘ to 70 ∘ , and the mechanical behavior of the dehydrated coal was investigated through compressive loading tests. The digital image correlation (DIC) method was used to acquire the strain field of coal, and a multifractal analysis was conducted to characterize the strain evolution of coal. The findings suggest that the increasing temperatures result in higher moisture desorption rates and greater volumetric contraction strain in coal. Furthermore, coal with higher moisture desorption exhibits higher peak stress and peak strains when subjected to compressive loading. The multifractal analysis of the inhomogeneous strain evolution indicates a gradual decrease in the parameter Δ α under compressive loading, followed by a sudden increase before reaching the failure point due to strain localization. The multifractal mechanism was further investigated, revealing that the inhomogeneous strain field of coal is inherently affected by the microstructure of coal. In addition, a mathematical model was proposed to elucidate the relationship between the inhomogeneous coal strain and the microstructure of coal. The result indicates that the inhomogeneity of the coal strain is directly associated with the multifractal singularity of the coal microstructure. Finally, the feasibility of using the multifractal parameter Δ α to identify coal strain localization has been demonstrated, indicating its potential value in aiding engineers to determine the SLZ in deep coal mines. [ABSTRACT FROM AUTHOR]

A less prominent N-S oriented continental-scale strike-slip shear zone occurs within the Babouri-Figuil Magmatic Complex (BFMC). Studies have shown that such shallow to middle crustal levels shear zones often display long-lasting deformation, physical expression of strain localization, and mineralization. However, until dates, deformation evolution and structural mineralization of this ~ 8 km long shear zone in Babouri-Figuil remain enigmatic, which prompted its investigation. A combined structural study supported by U-Pb zircon dating on the sheared granitoids is reported. Biotite granite sampled near Sorawel village yielded zircon U-Pb concordia age of 606 ± 6 Ma, whereas hornblende-biotite granite sampled at the western corner of the Ribao massif yielded zircon U-Pb concordia age of 601 ± 2 Ma. These granites were emplaced in a transpressive tectonic regime shortly after a regional thickening event < 620 Ma. The studied microstructures demonstrate a typical transition from protomylonite to extremely deformed mylonite marked with decreased mineral sizes. On thin sections, two main zones are identified: "zone A" (low-strain zone) and "zone B" (high-strain zone). Core-mantle K-feldspar porphyroclasts within the mylonite show dislocation creep deformation, whereas recrystallized to neocrystallized aggregates indicate plastic flow by viscous grain boundary sliding. Shear sense indicators revealed both early dextral and late sinistral shearing. In all, the results revealed that the Guider-Sorawel shear zone (GSSZ) experienced ductile deformation probably under medium to high temperature conditions. The double shearing is possible during the switch of the regional maximum principal stress from N-S (~ 585 Ma) to NW-SE (< 580 Ma). The obtained dates are syn-collisional and are consistent with D2 deformation phase in other parts of Cameroon. Also, the dates marked the final tectonic college between the north Cameroon domain and the southwest Chad domain, which probably might have induced the SZ. The construction of these adjacent domains probably resulted to a sort of increased temperature and strain localization that led to the initiation of a rheologically weaken mechanical zone via which the magma generated flows to near surface crustal level. [ABSTRACT FROM AUTHOR]

The present experimental study is focused on quantifying the initiation and propagation of desiccation cracking and strain localization in lime-treated compacted expansive soils subjected to controlled temperature and relative humidity conditions. Two bench-scale experimental setups were designed and developed in this study to capture the desiccation cracking and strain localization in soil specimens using digital image processing (DIA) and digital image correlation (DIC) techniques, respectively. A Python program was also developed for autodetection of optimum threshold intensity for crack segmentation, which considerably reduced the chances of noise in DIA and allowed accurate batch processing of multiple images. An open-source software Ncorr was used for two-dimensional DIC analysis to obtain strain localization plots during the desiccation process of soil. The effectiveness of the lime treatment technique for the stabilization of expansive soil was evaluated by considering the major issues of expansive soils such as swelling, shrinkage, unconfined compressive (UC) strength, and desiccation cracking. The results revealed that the lime treatment was ineffective in controlling the desiccation cracking of expansive soil. Only a small percentage of lime (2% or less) was found to slightly reduce the desiccation cracking. However, such small quantities of lime were not found enough to fully sway the swelling and shrinkage nature of the soil. A significant change in the crack pattern was observed in specimens treated with 3% or higher amount of lime. The total length of cracks increased up to 75% due to the addition of 6% lime compared with untreated soil. Similarly, more localized deformation zones were observed in strain localization plots of specimens treated with 3% or higher amounts of lime. [ABSTRACT FROM AUTHOR]

In the presence of softening section constitutive relations, classical beam theories predict erroneous strain singularities, and the corresponding force/flexibility-based (FB) beam-column element formulations result in strain localization and loss of response objectivity, i.e., divergence, rather than convergence, with progressive mesh refinements. To address this challenge, various FB element formulations have been proposed in the literature. One of these formulations is the so-called "gradient inelastic" (GI) FB formulation, which is a two-node element formulation that eliminates the strain localization and achieves response objectivity through strain gradient nonlocality relations. Although a single two-node GI element can effectively simulate an entire beam or column, simulating such a member via multiple two-node GI elements in series (e.g., to apply intermediate point loads, to more accurately capture geometric nonlinearities, or to represent cross-section variation) would not lead to accurate response predictions. This is because, in a model with multiple two-node GI elements in series, the nonlocality relations are not enforced at the intermediate/connection nodes between adjacent elements. Instead, end member boundary conditions (BCs) are enforced at those connection nodes because the two-node GI formulation has been designed to simulate an entire member. To tackle this shortcoming, this paper proposes an innovative multinode GI FB element formulation. To enforce the nonlocality relations at the connection nodes, two different sets of mathematically admissible section strain compatibility conditions (CCs) are adopted. The multinode formulations using both sets of CCs are evaluated through several simulation examples, including beams and columns subjected to various loads. The evaluations demonstrate the ability of both element formulations to produce objective softening responses, while one set of CCs is found to more closely predict the responses of previously tested RC beams under midspan loading. [ABSTRACT FROM AUTHOR]

Polycarbonate (PC) is a thermoplastic polymer used in many engineering applications such as safety devices and aerospace components. However, the unique behavior of PC under tensile load and its effects on the estimation of its constitutive curve are often overlooked in the literature, neglecting to consider crucial aspects of the characterization process. This work carries out a comprehensive analysis of the mechanical behavior of PC to understand the key points for accurate constitutive modeling and simulation of its static tensile performance, including its unconventional deformation mechanisms. The work starts from the accurate analysis of a representative experimental static tensile test on a rectangular section PC specimen and the evaluation of its true stress-strain curve. This analysis, carried out considering the classic length-based approach and the more accurate area-based approach, makes it possible to evaluate in detail the peculiar tensile behavior of this material. The mathematical form of the PC true stress-strain curve is then justified and the coincidence of the obtained length-based and area-based estimates of the same is demonstrated. Then, based on the in-depth understanding of the dynamics underlying the mechanical behavior of PC and making use of FEM simulations, the key points for obtaining its constitutive curve are defined. It is demonstrated that the constitutive curve is able to completely determine the behavior of PC, including its peculiar deformation mechanism. It is also highlighted which specific characteristics of the constitutive curve are critical in affecting various aspects of the material's behavior. The final constitutive curve of PC at hand is then obtained with an inverse approach, capable of accurately simulating all aspects of its tensile behavior. The validity of the proposed modelling key points is then confirmed, effectively explaining the underlying phenomena controlling the tensile behavior of PC and massively reducing uncertainty in the estimation of its constitutive curve starting from its area-based true curve.

The stress drop and strain localization behaviors of Ti–6Al–4V titanium alloy under the action of single pulse were investigated using electrically-assisted (EA) tension tests in this study. It is found that the flow stress drop gradually increases with the increase of current density and pulse width during EA tension. The digital image correlation (DIC) technology was adopted to analyze the strain distribution evolution and fracture regulation in EA micro-tension process. It turn out that the EA tensile sample will suddenly form two new intersecting high-strain bands at the moment of applying a pulse. With the increase of strain, the two high-strain bands converge toward the center and gradually evolve into a crossed localized flow zone, which makes the EA tensile sample exhibit a high local plastic deformation compared with room temperature tension. Furthermore, with the increase of current density, the temperature gradient in the tensile direction of the sample increases gradually, resulting in the narrowing of localized flow zone. The transformation of the localized flow zone eventually leads to the increase of fracture angle and the formation of a sawtooth shape fracture morphology. Finally, a material flow model for the single-pulse EA tension process was established. The calculation results show that about 11 % of the stress drop comes from the contribution of non-thermal electroplastic, the main mechanism of stress drop is thermal softening and thermal expansion induced by Joule heat during EA tension.

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Background: The evaluation of the formability for aluminum alloy under complex loading conditions is particularly significant. Based on the characteristics of conveniently achieving multiple strain path states, the cruciform specimen has been widely used in the experiment of evaluating formability. But there is no general specimen design scheme to realize proportional strain path history in initial fracture point. Objective: This paper was aiming at obtaining the equi-proportional strain path history and exploring the ultimate fracture strain of AA5052 aluminum alloy sheets under the equi-biaxial tension. Methods: Firstly, two cruciform specimen schemes suitable for 1.2 mm sheet materials were proposed. The strain localization characteristics were estimated and thinning critical value in the central region was determined by simulations. Subsequently, through the 3D digital image correlation (DIC) test system, the strain path history of the initial fracture point was obtained. Finally, the fracture morphology characteristics were observed through SEM. Results: The results showed that the initial fracture point could be located in the center of the specimen in both designs (Design-straight and Design-flaring). The specimens with slits showed a smaller strain gradient existed in the central region. Meanwhile, the initial point of fracture was closer to the equi-biaxial tensile strain path, and the strain limit was larger. Conclusions: The two design methods could optimize forming limit value and realize the equi-proportional strain path history in central fracture point. The Design-straight and Design-flaring was more suitable for the AA5052-O and AA5052-H material respectively. It was related to the local stress concentration effect of the material. [ABSTRACT FROM AUTHOR]

White etching area (WEA) is a primary damage in rolling contact fatigue (RCF) of bearing steels. In spite of extensive investigations, there is a large discrepancy in the existing mechanisms of WEA formation. We attempt to unify the mechanisms from the perspective of shear localization and plastic damage accumulation based on ductile damage. RCF tests were conducted to generate WEAs with various microstructures and compositions. A thermodynamically consistent model of the ductile damage evolution from an inclusion was established by developing the phase field damage coupled with the crystal elastic‐viscoplastic constitutive relationship under RCF. The model was implemented into the FE framework through a user materials subroutine. The results indicated that the WEA is the shear band resulting from shear localization. The large inhomogeneity and scatter in WEA's microstructure are due to the influence of the crystal orientation. The development and orientation of SBs predicted by the model and the experimental observation of the WEA are in good agreement. The large micro‐shear strain in the WEA provides the driving force for mechanically controlled austenite phase transformation. The shear band center, which has the largest strain and the least stress, is where cracks initiate. This demonstrates that contrary to earlier reports that WEA is induced by previously formed crack faces friction, cracks actually initiate from the interior of the WEA. Highlights: WEA presents the form of shear band as a result of shear localization.WEA's orientation is significantly influenced by the crystal orientation.Large micro‐shear strain in WEA is the driving force for phase transformation.Instead of WEA being induced by friction of crack faces, cracks begin in WEA. [ABSTRACT FROM AUTHOR]

We propose a phase-field model of shear fractures using the deviatoric stress decomposition. This choice allows us to use general three-dimensional Mohr–Coulomb's failure function for formulating the relations and evaluating peak and residual stresses. We apply the model to a few benchmark problems of shear fracture and strain localization and report remarkable performance. Our model is able to capture conjugate failure modes under biaxial compression test and for the slope stability problem, a challenging task for most models of geomechanics. [ABSTRACT FROM AUTHOR]

The 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. Highlights: Crack tip opening displacement range ΔCTOD and CGR show mostly linear relationship.ΔCTOD and CGR relationship becomes non‐linear if shear strain accumulation is present.If the crack tip penetrates the hardened region, CGR decreases.Strain accumulation is influenced by grain orientation and grain size. [ABSTRACT FROM AUTHOR]

In this work, a desirable combination of mechanical properties is achieved at 550 °C by tailoring the boundary microstructure between the primary α phase (αp) and the transformed β structure (βtrans) in a dual-phase Ti-6242s titanium alloy. The αp/βtrans boundary is displaced by a transition region that consists of β nano-plates or nanoprecipitates gradually penetrating into the αp in a particular semi-equiaxed microstructure (S-ES). The results show that the αp/βtrans boundary, where strain concentration easily occurs during deformation in the equiaxed microstructure (ES), induces recrystallization softening in the α phase. However, the transition region in the S-ES alleviates the strain localization and thus effectively inhibits the recrystallization softening that occurred in the α phase with concentrated strain. These β plates/precipitates in this region in turn enable an appropriate accumulation of dislocations. Significant improvement in the high-temperature strength, ∼240 MPa for the yield strength, is obtained for the S-ES relative to the ES. This work provides a new strategy for achieving outstanding strength at high temperature by designing special boundary architecture in dual-phase titanium alloys.

Strain hardening remains challenging for maintaining the plasticity of metals, especially those of high strength. The hetero-deformation induced (HDI) stress can effectively alleviate the problem, specifically with a large mechanical response mismatch. Accordingly, the strain localization and hardening in dual-phase steel consisting of ductile ferrite (F) and almost undeformed bainite (B) were investigated by calculating HDI stress (σh) based on the tensile load-unload-reload (LUR) hysteresis loop and modified equation. Of particular note is that strain localization first appears in the ferrite, and then transfers to the F/B interface during tensile LUR. The generated σh by the accumulation of geometrically necessary dislocations (GNDs) inhibits the mobile dislocation, thereby reducing the strain difference, which promotes the transfer of strain localization. The transformation of strain localization changes the hardening behavior from ferrite hardening to F/B interfacial hardening. The results state clearly that the σh enhances strain hardening while induced strain localization maintains tensile plasticity. Eventually, with the increase σh, the failure of dual-phase steel tends to transition from initial ductile fracture to brittle fracture.

The production of prismatic dislocation loops in nuclear reactor core materials results in hardening because the loops impede dislocation motion. Yielding often occurs by a localised clearing of the loops through interactions with gliding dislocations called channeling. The cleared channels represent a softer material within which most of the subsequent deformation is localized. Channeling is often associated with hypothetical dislocation pileup and intergranular cracking in reactor components although the channels themselves do not amplify stress as one would expect from a pileup. The channels are often similar in appearance to twins leading to the possibility that twins are sometimes mistakenly identified as channels. Neither twins nor dislocation channels, which are bulk shears, produce the same stress conditions as a pileup on a single plane. At high doses, when cavities are produced (either He-stabilised bubbles at low temperatures or voids at high temperatures), there can be reduced ductility because the material is already in an equivalent advanced stage of microscopic necking. He-stabilised cavities form preferentially on grain boundaries and at precipitate or incoherent twin/ε-martensite interfaces. The higher planar density of the cavities, coupled with the incompatibility at the interface, results in a preferential failure known as He embrittlement. Strain localisation and inter- or intragranular failure are dependent on many factors that are ultimately microstructural in nature. The mechanisms are described and discussed in relation to reactor core materials.

This is a review of the papers written by the author with co-researchers, which have been published in Soils & Foundations and related publications. The contents of the papers are related to experimental and theoretical aspects of geomechanics, namely, the constitutive modeling of cohesive and sandy soils, the governing equations of three-phase materials, and analyses of the behavior of geomaterials and grounds. The following topics are included in the papers: effective stress, skeleton stress, constitutive models of clayey and sandy soils and soft rocks, material instability, strain localization, consolidation, bearing capacity, excavation problems, governing equations of multi-phase geomaterials, liquefaction, unsaturated soil, seepage-deformation coupled analysis, gas hydrate-contained soil, internal erosion, the material point method (MPM), and X-ray CT for geomaterials.

The transition point of the crack length to a microstructurally small crack is necessary for predicting crack extension behavior. The conventional criterion is the crack length smaller than the grain size and is a probabilistic criterion. This criterion does not consider the metal's crystallite plasticity property discrepancy (CPPD). However, CPPD determines crack extension behavior for recently developed advanced materials with complex microstructures. Therefore, the authors propose a deterministic judgment method for microstructurally small cracks considering crystallite plasticity based on a physics‐based crystal plasticity finite element model with strain localization. The proposed method is based on the difference value of the crack tip opening displacement varying with the ratio between the crack length and grain size with the change in the grain orientation ahead of the crack tip. A case study for copper is performed, and the results show that the novel method can be applied to define the microstructurally small crack. [ABSTRACT FROM AUTHOR]

Strain localization in soils causes the failure of slopes and foundations. Shear strength is an important factor that affects strain localization in soils. It is well known that the shear strength of natural clay is highly anisotropic due to the internal soil structure. An anisotropic failure criterion for natural clay is presented in which an anisotropic variable is used to describe the relative orientation between the stress directions and soil fabric. The failure criterion is employed in a Drucker–Prager model that considers the strain softening of natural clay. The effect of anisotropic strength on strain localization in clay is analyzed by two examples, including an undrained slope stability analysis and a simulation of a hollow cylinder test of Boom clay. It is found that the shear strength anisotropy affects both the strain localization pattern and factor of safety for the undrained slope. Simulation of the tests on Boom clay shows that the model with the anisotropic yield criterion yields an eye-shaped strain localization pattern that cannot be obtained by the model with the isotropic yield criterion. [ABSTRACT FROM AUTHOR]