High Strain Gradients Research Articles

Combined application of distributed fibre optical and digital image correlation measurements to structural concrete experiments

The combined application of distributed fibre optical strain measurements on reinforcing bars and digital image correlation (DIC) measurements on the concrete surface has a great potential to increase knowledge in many fields of structural concrete. This paper explores the advantages of these measurement techniques for concrete tests and the key aspects to be considered in order to obtain reliable measurements suitable for quantitative analysis. The uncertainty of DIC analysis is highly dependent on the test conditions and user carefulness, and should be assessed for each test. A procedure to quantify the DIC uncertainty in large scale structural tests is presented, showing that it is highly dependent on the quality of the calibration. Comparative tests on distributed fibre optical strain measurements with different fibre coatings show that polyimide-coated fibres capture properly high strain gradients and, therefore, should be used when instrumenting reinforcing bars in RC specimens. Moreover, the measuring noise was found to be dependent on the absolute strain level. Combined plots of crack kinematics and reinforcement strains, stresses and forces are shown for the results of a series of two concrete panel tests subjected to diagonal tension. Crack locations predicted by both measurements match perfectly in these experiments.

Relating Bone Strain to Local Changes in Radius Microstructure Following 12 Months of Axial Forearm Loading in Women.

Work in animal models suggests that bone structure adapts to local bone strain, but this relationship has not been comprehensively studied in humans. Here, we quantified the influence of strain magnitude and gradient on bone adaptation in the forearm of premenopausal women performing compressive forearm loading (n = 11) and nonloading controls (n = 10). High resolution peripheral quantitative computed tomography (HRpQCT) scans of the distal radius acquired at baseline and 12 months of a randomized controlled experiment were used to identify local sites of bone formation and resorption. Bone strain was estimated using validated finite element (FE) models. Trabecular strain magnitude and gradient were higher near (within 200 μm) formation versus resorption (p < 0.05). Trabecular formation and resorption occurred preferentially near very high (>95th percentile) versus low (<5th percentile) strain magnitude and gradient elements, and very low strain elements were more likely to be near resorption than formation (p < 0.05). In the cortical compartment, strain gradient was higher near formation versus resorption (p < 0.05), and both formation and resorption occurred preferentially near very high versus low strain gradient elements (p < 0.05). At most, 54% of very high and low strain elements were near formation or resorption only, and similar trends were observed in the control and load groups. These findings suggest that strain, likely in combination with other physiological factors, influences adaptation under normal loads and in response to a novel loading intervention, and represents an important step toward defining exercise interventions to maximize bone strength.

Lateral Termination of a Cycladic‐Style Detachment System (Hymittos, Greece)

AbstractThe bedrock of Hymittos, Attic peninsula, Greece, exposes a pair of low‐angle crustal‐scale ductile‐then‐brittle detachment faults. The uppermost detachment fault separates sub‐greenschist facies phyllite and marble of a Pelagonian Zone hanging wall, from greenschist facies metasedimentary schist, calc‐schist, and marble correlated to the Cycladic Blueschist Unit. A second, structurally lower detachment fault subdivides the metamorphic rocks of the Cycladic blueschist unit footwall into middle and lower units. There is a marked step in metamorphic grade between the sub‐greenschist facies uppermost package, and the middle‐to‐upper greenschist facies middle and lower packages. A suite of new white mica40Ar/39Ar and zircon (U‐Th)/He dates indicates accommodation of deformation along these faults occurred from the late Oligocene to the late Miocene with both faults active during the middle Miocene. The structures have clear top‐S/SSW kinematics determined from flanking folds, sigmoids, shear bands, stair‐stepping of strain shadows on porphyroclasts, and SCC' fabrics. The ductile‐to‐brittle deformation of the structures, morphology of the massif, and the increase in metamorphic grade suggest these low‐angle structures are part of a major, crustal‐scale extensional complex, located at the northwest end of the West Cycladic Detachment System, that accommodated Miocene bivergent exhumation of Attic‐Cycladic metamorphic core complexes in the central Aegean. Taken together, the above data suggest that multiple coeval detachment branches may form in areas with high strain gradients to accommodate the mechanically necessary termination of Cycladic‐style detachment systems.

Quantifying microscale drivers for fatigue failure via coupled synchrotron X-ray characterization and simulations

During cyclic loading, localization of intragranular deformation due to crystallographic slip acts as a precursor for crack initiation, often at coherent twin boundaries. A suite of high-resolution synchrotron X-ray characterizations, coupled with a crystal plasticity simulation, was conducted on a polycrystalline nickel-based superalloy microstructure near a parent-twin boundary in order to understand the deformation localization behavior of this critical, 3D microstructural configuration. Dark-field X-ray microscopy was spatially linked to high energy X-ray diffraction microscopy and X-ray diffraction contrast tomography in order to quantify, with cutting-edge resolution, an intragranular misorientation and high elastic strain gradients near a twin boundary. These observations quantify the extreme sub-grain scale stress gradients present in polycrystalline microstructures, which often lead to fatigue failure.

Analysis of preliminary local hardening close to the ferrite–martensite interface in dual-phase steel by a combination of finite element simulation and nanoindentation test

This study investigated the local preliminary hardening of ferrite near ferrite–martensite interfaces in dual-phase (DP) steel. Geometrically necessary dislocations (GNDs), generated in the case of interfacial misfit between different phases, may cause preliminary hardening around such interfaces. Firstly, finite-element simulations of nanoindentations were conducted using an ideal cylindrical DP model without preliminary hardening around the ferrite–martensite interface. The simulations indicated gradually decreasing nano-hardness with increasing distance from the ferrite–martensite interface. Second, nano-hardness measurements of ferrite near the ferrite–martensite interface were performed for laboratory-made DP steel containing 10 vol.% martensite. The measurements were consistent with the simulation without preliminary hardening around the interface. That is, interfacial preliminary hardening of ferrite was not indicated by our measurements. The GND density, which has been reported to cause preliminary hardening around the interface, supported this result. The density on ferrite was increased around the interface, but the area was very small compared with the nanoindentation size. We conclude that another hardening mechanism, e.g., GND accumulation under a high strain gradient around the interface, acts as a microstructural local strengthening factor in DP steel deformation.

Prediction of heterogeneous microstructural evolution in cold sprayed copper coatings using local Zener-Hollomon parameter and strain

Cold spray processing is a solid-state coating technique and an emerging method for additive manufacturing, in which metal powder particles are bonded through high-velocity impact-induced deformation. However, the severe plastic deformation of powder particles at extremely high strain rates, high strain gradients, and localized elevated temperatures yields rather complex and heterogeneous microstructures in materials produced in cold sprayed coatings or bulk forms. A good understanding, and even prediction, of such heterogeneous microstructures is essential for determining suitable post-processing conditions as well as the final properties of cold sprayed products. In this study, we employ a cold spray system to deposit copper coatings over a large temperature range (373 K to 873 K) and we systematically investigate the microstructural evolutions of the coatings using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) techniques. Diverse microstructures are observed, including recrystallized grains, annealing twins, shear bands, submicron-sized grains, deformation twins, and nanometer-sized grains. To understand the formation of such complex microstructures, we obtain local strains, strain rates and temperatures of the cold sprayed powder particles using the finite element method (FEM). Based on our experimental and simulation results, we have created the first deformation mechanism map for cold sprayed coatings to interpret and predict the heterogeneous microstructural evolutions in copper using the local Zener-Hollomon (Z) parameter and plastic strain (strain-Z-microstructure map). Such a map can be used to predict and design the microstructures of cold sprayed copper samples based on processing parameters and can also be extended to other severe plastic deformation (SPD) processes, such as cutting, extrusion, solid-phase welding, and other solid-state additive manufacturing processes.

Effects of metallic microstructures on fatigue fracture of Q345 steel

Effects of high-frequency cyclic loading on the banded ferrite–pearlite steel were analyzed through crack initiation and propagation. Interfaces of ferrite and pearlite colony with a small angle deviation from the loading axis were verified to be the most potential sites to fabricate the microcracks caused by the high strain gradient. The initial crack extension inside ferrite grain was driven by shear stress in model II along the direction with a 45° angle to the loading axis. Banded pearlite colony and the high-angle grain boundaries were considered as the dominant factors that promote the fatigue resistance of the material through arousing crack deflection in short crack propagation range and crack branching in long crack propagation range to reduce the crack propagation driving force in the crack tip. P–S–N curves were used to quantify the dispersion of fatigue lifetimes and evaluate the effect of elevated volume content of pearlite colony on the fatigue performance of the material.

Prediction of Heterogeneous Microstructural Evolution in Cold-Sprayed Copper Coatings Using Local Zener-Hollomon Parameter and Strain

Cold spray processing is a solid-state coating technique and an emerging method for additive manufacturing, in which metal powder particles are bonded through high-velocity impact-induced deformation. However, the severe plastic deformation of powder particles at extremely high strain rates, high strain gradients, and localized elevated temperatures yields rather complex and heterogeneous microstructures in materials produced as coatings or bulk forms. A good understanding, and even prediction, of such heterogeneous microstructures is essential for determining the post-processing conditions as well as the final properties of cold-sprayed products. In this study, we employ a cold spray system to deposit copper coatings over a large temperature range from 373 K to 873 K and we systematically investigate the microstructural evolutions of the coatings using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) techniques. Diverse microstructures have been observed, including recrystallized grains, annealing twins, shear bands, submicron grains, deformation twins, and nanometer-sized grains. To understand the formation of such complex microstructures, we obtain local strains, strain rates and temperatures of the cold-sprayed powder particles using the finite element method (FEM). Based on our experimental and simulation results, we created the first deformation mechanism map for cold sprayed coatings to interpret and predict the heterogeneous microstructural evolutions in copper using the local Zener-Hollomon (Z) parameter and plastic strain (strain-Z-microstructure map). Such a map can be used to predict and design the microstructures of cold-sprayed copper samples based on processing parameters and can also be extended to other severe plastic deformation (SPD) processes, such as cutting, extrusion, and solid-phase welding.

Coupled atomistic‐continuum simulation of the mechanical properties of single‐layered graphene sheets

AbstractThe purpose of this work is the multiscale modeling of a single‐layered graphene sheet. The model is divided into three parts. One is an atomistic domain which is simulated with the atomic‐scale finite element method (AFEM). Another is a continuum domain. In this domain, the mechanical properties are investigated by using a finite element based on a nonlocal continuum shell model with a high order strain gradient. To be exact, it is a 4‐node 60‐generalized degree of freedom (DOF) Mindlin–Reissner finite shell element with a second order strain gradient. In the third part, a new transitional finite element is developed for smoothing the transition between the atomistic domain and continuum domain.

Strain Gradient Plasticity in Multiprincipal Element Alloys

The strain gradient plasticity of multiprincipal element alloys, CoCrNi and CoCrFeMnNi, was investigated in work-hardened and annealed conditions using nano-indentation. The hardness of the alloys demonstrated significant dependence on indentation depth, which was explained by geometrically necessary dislocations resulting from the high strain gradients due to the shape of the indenter. The characteristic length-scale of the indentation size effect for the multiprincipal element alloys was found to be larger than pure nickel due to higher friction stress, which constrains the storage volume of geometrically necessary dislocations.

A comparison of seismic response to conventional and face destress blasting during deep tunnel development

Abstract A novel design of development face destress blasting was implemented during the construction of an experimental tunnel at great depth. A second tunnel was developed nearby using conventional blasting as a control. The tunnels were developed parallel to one another and perpendicular to a high sub-horizontal stress. High resolution seismic monitoring was used to record and compare the seismic response generated by each excavation. Analysis of the seismic data from the conventionally blasted tunnel indicated that the seismogenic zone of stress-driven instability extended up to 3.6 m ahead of the face. Destress blasting within the corresponding zone of the adjacent tunnel had the effect of reducing the rock mass stiffness, primarily due to weakening of the pre-existing natural discontinuities. The reduction in rock mass stiffness was inferred from the spatial broadening of the seismogenic zone and associated reduction in the measured spatial density of events, radiated energy and seismic potency ahead of the face. High strain gradients around the unsupported portion of the conventionally blasted excavation were implied by the rate at which the spatial density of seismicity changed with respect to the tunnel face position. In contrast, the change in the spatial density of seismicity around the destressed development face was much more gradual. This was indicative of lower strain gradients in the rock there. A reduction in rock mass stiffness following destress blasting was also indicated by the much wider variety of seismic source mechanisms recorded adjacent to the destressed tunnel. Seismic source mechanisms associated with destress blasting were also more clearly characteristic of compressive overstressing with fracture closure. The source mechanism data also indicated that destress blasting induced instability on all natural joint sets. When compared to conventional development blasting, destress blasting typically reduced violent strain energy release from the rock mass and the associated seismicity, but not always.

Numerical Investigation of the Mechanical and Damage Behaviors of Veined Gneiss During True-Triaxial Stress Path Loading by Simulation of In Situ Conditions

Investigations on the Posiva Olkiluoto spalling experiment (POSE) at the nuclear waste disposal site in Olkiluoto, western Finland, have revealed that the presence of anisotropic veined gneiss (VGN) could affect the evaluation of spalling/damage strength of the host rock. In this study, the mechanical and damage behaviors of anisotropic VGN during complex true-triaxial in situ stress path loading is numerically investigated, considering the lifetime stress evolution of POSE. Overall, the discrete element numerical results show reasonable agreement with those of laboratory experiments for both strength and damage development. Numerical simulations at the microscale showed that the damage is concentrated within the discontinuous foliation bands and at the interfaces between weak and strong bonds when the mineral composition of the foliation bands is heterogeneous. It is possible that the varying stiffnesses of the two materials cause strain concentration at strong segments within the weak foliation bands or high strain gradients at the interfaces between the weak and strong bands, leading to tensile failure of the strong bonds. However, if continuous foliation bonds are employed, fractures mainly propagate within the weak bonds, indicating that the heterogeneity of the foliation bonds is a predominant factor affecting the failure of VGN. After weak bonds and interfaces failure, shear movements occur along the weak bonds, forcing the strong bonds to bear most of the load. The simulations also show that the unloading of σ2 and σ3 triggers microcracks in the early stages, revealing the role of unloading in rock damage. The change in the secant modulus in relation to the foliation angle is generally found to follow a U-shaped anisotropy and obtains the lowest value at 45°. For each test, the modulus gets the minimum value in the damage stage and recovers in the unloading stage, but it cannot reach its original value. Sample strength increases as the foliation orientation angle increases from 0° to 45° in relation to σ2, because the increase in normal stress from σ2 causes the role of the strong foliation bonds to become significant as the bonds strengthen. The damage to the strong bonds leads to a larger reduction in the modulus at the damage stage.

Residual stress in laser cladded rail

Abstract To improve the fatigue life of components subject to loads with high surface strain gradients, it is possible to coat them with an alloy of higher durability. The present study focuses on the effect of cladding high value track components, made of a standard rail steel UIC 900A/grade 260, with a layer of a premium martensitic stainless steel to reduce wear and fatigue. The laser cladding process inevitably generates residual stresses in the clad and parent metal, which could be detrimental to the integrity of the component. Therefore, measurements to determine the residual stress state of cladded rail were performed using semi-destructive centre-hole and deep hole drilling and non-destructive neutron diffraction techniques. Subsequently, the effects of cycling loading and wear, representative of typical service loads, on the redistribution of the residual stress field were investigated. It was observed that laser cladding causes a triaxial compressive residual stress field in the clad and near the interface and a tensile stress field in the parent material. The stress field is shown to change when the first cycle of load is applied but reaches a steady state after only 10 cycles: After the 10th cycle there is no evidence that the clad continues accumulating strain which could indicate that there is low risk of ratcheting. Wear effect on residual stress redistribution was found to be local on the surface of the specimen only.

Application of Digital Image Correlation (DIC) to the Measurement of Strain Concentration of a PVA Dual-Crosslink Hydrogel Under Large Deformation

Hydrogels are a class of soft, highly deformable materials formed by swelling a network of polymer chains in water. With mechanical properties that mimic biological materials, hydrogels are often proposed for load bearing biomedical or other applications in which their deformation and failure properties will be important. To study the failure of such materials a means for the measurement of deformation fields beyond simple uniaxial tension tests is required. As a non-contact, full-field deformation measurement method, Digital Image Correlation (DIC) is a good candidate for such studies. The application of DIC to hydrogels is studied here with the goal of establishing the accuracy of DIC when applied to hydrogels in the presence of large strains and large strain gradients. Experimental details such as how to form a durable speckle pattern on a material that is 90% water are discussed. DIC is used to measure the strain field in tension loaded samples containing a central hole, a circular edge notch and a sharp crack. Using a nonlinear, large deformation constitutive model, these experiments are modeled using the finite element method (FEM). Excellent agreement between FEM and DIC results for all three geometries shows that the DIC measurements are accurate up to strains of over 10, even in the presence of very high strain gradients near a crack tip. The method is then applied to verify a theoretical prediction that the deformation field in a cracked sample under relaxation loading, i.e. constant applied boundary displacement, is stationary in time even as the stress relaxes by a factor of three.

On a family of numerical models for couple stress based flexoelectricity for continua and beams

A family of numerical models for the phenomenological linear flexoelectric theory for continua and their particularisation to the case of three-dimensional beams based on a skew-symmetric couple stress theory is presented. In contrast to the standard strain gradient flexoelectric models which assume coupling between electric polarisation and strain gradients, we postulate an electric enthalpy in terms of linear invariants of curvature and electric field. This is achieved by introducing the axial (mean) curvature vector as a strain gradient measure. The physical implication of this assumption is many-fold. Firstly, analogous to the standard strain gradient models, for isotropic (non-piezoelectric) materials it allows constructing flexoelectric energies without breaking material’s centrosymmetry. Secondly, unlike the standard strain gradient models, nonuniform distribution of volumetric part of strains (volumetric strain gradients) do not generate electric polarisation, as also confirmed by experimental evidence to be the case for some important classes of flexoelectric materials. Thirdly, a state of plane strain generates out of plane deformation through strain gradient effects. Finally, under this theory, extension and shear coupling modes cannot be characterised individually as they contribute to the generation of electric polarisation as a whole. As a first step, a detailed comparison of the developed couple stress based flexoelectric model with the standard strain gradient flexoelectric models is performed for the case of Barium Titanate where a myriad of simple analytical solutions are assumed in order to quantitatively describe the similarities and dissimilarities in effective electromechanical coupling under these two theories. From a physical point of view, the most notable insight gained is that, if the same experimental flexoelectric constants are fitted in to both theories, the presented theory in general, reports up to 200% stronger electromechanical conversion efficiency. From the formulation point of a view, the presented flexoelectric model is also competitively simpler as it eliminates the need for high order strain gradient and coupling tensors and can be characterised by a single flexoelectric coefficient. In addition, three distinct mixed flexoelectric variational principles are presented for both continuum and beam models that facilitate incorporation of strain gradient measures in to a standard finite element scheme while maintaining the C0 continuity. Consequently, a series of low and high order mixed finite element schemes for couple stress based flexoelectricity are presented and thoroughly benchmarked against available closed form solutions in regards to electromechanical coupling efficiency. Finally, nanocompression of a complex flexoelectric conical pyramid for which analytical solution cannot be established is numerically studied where curvature induced necking of the specimen and vorticity around the frustum generate moderate electric polarisation.

Precise Measurement of Steep Residual Strain Gradients Using Neutron Diffraction in Strongly Absorbing Materials with Chemical Compositional Gradients

Abstract A round robin benchmark weldment, denoted TG6, from the European Network on Neutron Techniques Standardization for Structural Integrity (NeT), offers the ability to test the technique of residual stress determination using neutron diffraction to an extreme. This test component comprises a 200 mm by 150 mm by 12 mm rectangular base plate made from Inconel 600 with three passes of Alloy 82 weld metal deposited in a slot of length 76 mm. This not only has large grain issues in the weld region but a large interplanar spacing variation caused by high strain gradients and a change in material composition. Because of the high absorption of neutrons in the Inconel 600 within the gauge volume, there is a large difference between the instrumental gauge volume IGV (which is the volume of space defined by the neutron beam paths through the defining apertures, taking into account properties of the beam) compared with the sampled gauge volume SGV (which is the intersection of the IGV with the sample that takes into account the absorption of the neutrons). The relative shift in position of the center of gravity of measurement (when the gauge volume is fully immersed in the sample) has been observed to be significant, for example, ∼0.3 mm, using 1 by 1 by 5 mm3 defining optics (where 5 mm is the gauge volume height) and increases approximately proportionally with larger gauge volumes dimensions in the horizontal plane. The magnitude of this shift depends upon many parameters. Measuring the sample and rotating 180° and measuring again, taking the average is another way one can eliminate this absorption effect. This novel approach is compared with three neutrons instruments on the same sample.

A parametric study of DIC measurement uncertainties on cracked metals

AbstractDisplacements and strains in the presence of a crack in welded steels have been studied using digital image correlation (DIC) under zero load and selected loading conditions. A parametric study has been carried out to assess the effects of some of the key parameters, including subset size, step size, and the size of the measurement window, on the measurement uncertainties for systematic and random errors. The assessments were carried out a region around the crack tip, where high strain gradients and inhomogeneous deformation present significant challenges for DIC measurements.

FEM Simulation of Influence of Asymmetric Cold Rolling on Through-Thickness Strain Gradient in Low-Carbon Steel Sheets

Grain refinement by severe plastic deformation can make conventional metallic materials several times stronger, but it leads to dramatic loss of their ductility. Gradient structure through the thickness of processed material represents a new strategy for producing a superior combination of high strength and good ductility. In gradient metallic materials the grain size increases gradually from nanoscale at the surface to coarse-grained in the core. Strain gradient can be considered as a mechanism of creating of such microstructures. Providing of predetermined strain gradient in the metallic materials can be achieved by asymmetric rolling (AR), when circumferential speeds of the top and bottom work rolls are different. Since the AR is a continuous process, it has great potential for industrial production of large-scaled sheets. Searching the optimal process parameters which can provide special strain gradients through sheet thickness is very important. This paper presents the distributions of the effective strain through sheet thickness of low-carbon steel AISI 1015 processed by a single-pass AR. Influence of process parameters was investigated by the finite element method with using software DEFORM 2D. Extremely high strain gradient e ≈ 4...8 through sheet thickness during a single-pass AR was found. FE analysis of the deformation characteristics, presented in this study, can be used for optimization of the AR process as a method of fabrication of metallic materials with gradient microstructures.

The effects of Zr level in Ti-Zr-Cu-Ni brazing fillers for brazing Ti-6Al-4V

Microstructure and macro-micro mechanical properties of the joints of Ti-xZr-15Cu-10Ni brazing fillers (mass fraction x=10, 18, 37.5) were studied by in-situ tensile test, SEM, EBSD and EDX. It was found that although the increase in the Zr level lowers the melting point of the brazing materials, which is beneficial to reduce the time of manufacturing and the wear of the equipment, the brazing joints became harder due to solid solution hardening and transformed from a ductile to brittle fracture mode. The microstructural analysis revealed that the increase of Zr level increases the grain size, which leads to high strain gradient across the brazing joints. Thus, high Zr in the brazing joints reduces the ductility of the joints. In this study 10% Zr is found to be the most compatible one with the Ti-6Al-4V matrix. However, in practice, 18Zr is the optimal brazing material for engineering applications due to the balance of the mechanical performance, cost, reliability and applicability.

Designing and Validating Parallel Wire Suspension Bridge Wire Strands for Neutron Diffraction Stress Mapping

Suspension-bridge cables are constructed from strands of galvanized steel wire. They are failure-critical structural members, so a fundamental understanding of their mechanics is imminently important in quantifying suspension bridge safety. The load-carrying capabilities of such strands after local wire failures have been the subject of many theoretical studies utilizing analytical equations and finite-element analysis. Little experimental data, however, exists to validate these models.Over the past five years we have developed a methodology for measuring stress/strain transfer within parallel wire strands of suspension bridge cables using neutron diffraction [1,2]. In this paper we describe the design and verification of parallel cable strands used in our studies. We describe the neutron diffraction strain measurements performed on standard 7-wire and expanded 19-wire models in various configurations at both the Los Alamos National Laboratory Spectrometer for Materials Research at Temperature and Stress (LANL SMARTS) and at the Oak Ridge National Laboratory VULCAN Engineering Materials Diffractometer (ORNL VULCAN). Particular attention is placed on the challenges of aligning and measuring multibody systems with high strain gradients at body-to-body contact points.