Local Strain Patterns Research Articles

On Technological Uses of Local Strain Patterns of the Commercial Zr-Nb Alloys

Plastic flow localization behaviour has been investigated in commercial Zr alloys used in the nuclear power industry. The type of deformation localization pictures corresponding with the stage preceding material fracture is described. Proposed is a method for assessing the reserve ductility of the metal subjected to deformation in rolling of thin-wall Zr alloy tubes by examining the local strain patterns.

Dislocations and inclusions in prestressed metals

The effect of prestress on dislocation (and inclusion) fields in nonlinear elastic solids is analysed by extending previous solutions by Eshelby and Willis. Using a plane-strain constitutive model (for incompressible incremental nonlinear elasticity) to describe the behaviour of ductile metals ( J 2 -deformation theory of plasticity), we show that when the level of prestress is high enough that shear band formation is approached, strongly localized strain patterns emerge, when a dislocation dipole is emitted by a source. These may explain cascade activation of dislocation clustering along slip band directions.

Tendon motion and strain patterns evaluated with two-dimensional ultrasound elastography

The purpose of this study was to evaluate the use of 2D ultrasound elastography to assess tendon tissue motion and strain under axial loading conditions. Four porcine flexor tendons were cyclically loaded to 4% peak strain using a servo hydraulic test system. An ultrasound transducer was positioned to image a longitudinal cross-section of the tendon during loading. Ultrasound radiofrequency (RF) data were collected at 63 frames per second simultaneously with applied force and crosshead displacement. A grid of nodes was manually positioned on an ultrasound image of the unloaded tendon. Small kernels (2×1mm) centered at each node were then cross-correlated with search regions centered at corresponding nodal locations in the subsequent frame. Frame-to-frame nodal displacements were defined as the values that maximized the normalized cross-correlations. This process was repeated across all frames in the loading cycle, providing a measurement of the 2D trajectories of tissue motion throughout the loading cycle. The high resolution displacement measures along the RF beam direction were spatially differentiated to estimate the transverse (relative to tendon fibers) tissue strains. The nodal displacements obtained using this method were very repeatable, with average along-fiber trajectories that were highly correlated (average r=0.99) with the prescribed crosshead displacements. The elastography transverse strains were also repeatable and were consistent with average transverse strains estimated via changes in tendon width. The apparent Poisson's ratios (0.82–1.64) exceeded the incompressibility limit, but are comparable to values found for tendon in prior experimental and computational studies. The results demonstrate that 2D ultrasound elastography is a promising approach for noninvasively assessing localized tissue motion and strain patterns.

Experimental characterization of the intragranular strain field in columnar ice during transient creep

A digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones.

Design of strain-engineered quantum tunneling devices for topological surface states

Strain-dependent charge and spin transport on a topological insulator (TI) surface are investigated by combining first-principles calculations with quantum tunneling theory. It is shown that the Dirac point of helical surface states can be significantly shifted by applying compressive uniaxial strain. As an example of strain engineering applications based on this effect, a strain-induced quantum tunneling nanostructure is designed, where the tunneling conductance and the spin texture of surface states can be sensitively modulated by strain. Our work suggests that various local strain patterns can be integrated to manipulate surface states in all-TI-based spintronic nanodevices.

Time and depth dependent poisson’s ratio of cartilage explained by an inhomogeneous orthotropic fiber embedded biphasic model

A time- and depth-dependent Poisson’s ratio has been observed during unconfined compression experiments on articular cartilage, but existing cartilage models have not fully addressed these phenomena. The goal of this study was to develop a model which is able to predict and explain these phenomena, while also being able to fit other experimental scenarios on full depth cartilage specimens such as confined and unconfined compressions. A biphasic (poroelastic), fiber-embedded cartilage model was developed. The heterogeneous material properties of the cartilage (aggregate modulus, void ratio tensile modulus) were extracted from reported experiments on individual layers of bovine articular cartilage. The nonlinear permeability material constants were found by fitting the overall response to published experimental data from confined compression. The matrix of the cartilage was modelled as an inhomogeneous isotropic biphasic material with nonlinear strain dependent permeability. Orthotropic layers were added as embedded elements to represent collagen fibers. Material parameters for these layers were derived from tensile tests of different layers of cartilage. With these predefined tensile parameters, the model showed a good fit with multi-step confined and unconfined compression experiments ( R 2=0.984 and 0.977, respectively) and could also predict the depth-dependent Poisson’s ratio ( R 2=0.981). The highlight of the model is the ability to explain the time-depth dependent Poisson's ratio and, by association, the strong effect of material inhomogeneity on local stress and strain patterns within the cartilage layer. This material model’s response may provide valuable new insight into potential initiation of cartilage fibrillation or delamination in whole-joint simulations.

Plastic flow localization in h.c.p. Zr alloys on macro- and microscale levels

The regular features exhibited by plastic strain localization on macro- and microscale levels at the parabolic strain hardening stage are examined for commercial Zr alloys used in nuclear power industry. The plastic flow shows instability, which is manifested as oscillatory variation of space-time distributions of local strain patterns as revealed by speckle interferometry. It is shown that the periodic accumulation of deformation in the flow nuclei enhances the evolution of dislocation structure within the nuclei so that one of them becomes a prefracture zone in which necking would finally occur. The data obtained are discussed within the framework of a synergetic approach to plastic deformation evolution at the final flow stage.

Lanczos potential for the Gödel spacetime

The emergence in the deforming material of local strain patterns (self excited waves), which are ordered in space and evolve with time, has been investigated for a wide range of metals and alloys. The main parameters of these waves, i.e. propagation rate against work hardening coefficient, dispersion law and wavelength against specimen length and grain size, have been defined. The possibility of treating plastic flow localization as a process of plastic flow occurring in a deforming medium is considered. A set of equations has been developed, which is appropriate for the description of the evolution of local strain domains. The changes in the type of local strain pattern observed in the various stages of flow are examined. A model is proposed to account for the large-scale periodicities exhibited by the distribution of localized deformation.

On the waves of plastic flow localization in pure metals and alloys

AbstractThe emergence in the deforming material of local strain patterns (self excited waves), which are ordered in space and evolve with time, has been investigated for a wide range of metals and alloys. The main parameters of these waves, i.e. propagation rate against work hardening coefficient, dispersion law and wavelength against specimen length and grain size, have been defined. The possibility of treating plastic flow localization as a process of plastic flow occurring in a deforming medium is considered. A set of equations has been developed, which is appropriate for the description of the evolution of local strain domains. The changes in the type of local strain pattern observed in the various stages of flow are examined. A model is proposed to account for the large‐scale periodicities exhibited by the distribution of localized deformation.

Non-uniform strain distribution within rat cartilaginous growth plate under uniaxial compression

Growth plates are highly inhomogeneous in morphology and composition. Mechanical loading can modulate longitudinal bone growth, though the mechanisms underlying this mechanobiology are poorly understood. The proximal tibial growth plates of six rats were tested in vitro under uniaxial compression to 5% strain, and confocal microscopy was used to track and capture images of fluorescently labeled cell nuclei with increasing applied strains. The local strain patterns through the growth plate thickness were quantified using texture correlation analysis. The technique of texture correlation analysis was first validated by comparing theoretical simulated strain maps generated from numerically distorted images. The texture correlation algorithm was sensitive to the grid size superimposed on the original image, but remained insensitive to parameters related to the size of the final image mask, which was searched by the correlation algorithm for each grid point of the original image. Within the growth plate, experimental strain distributions were non-uniform in all six specimens. Growth plates were mostly under compression strains. The strain distributions differed among the histomorphological zones of the growth plate, which was most obvious in specimens with regular growth plate shape: higher compressive strains (4–8 times higher than the applied 5% strain) were located mainly in regions overlapping the reserve and hypertrophic zones with lower compressive strains in the proliferative zone. This study documents the non-uniform mechanical behavior of growth plate across its three histological zones when exposed to compression. Further investigation is required to establish the significance of non-uniform strain fields during growth in vivo.

Western Mediterranean Ridge mud belt correlates with active shear strain at the prism-backstop geological contact

A high-resolution swath-mapping survey conducted in the deep waters of the eastern Mediterranean Sea allowed mapping of active faults and mud volcanism along a sizable portion of the Mediterranean Ridge. Active shear is localized at the prism-backstop con- tact, a major dextral flower structure and a site of massive mud expulsion. We investigate the relationship between the mud output rate and horizontal strain rate by combining the mud volume estimate from sea-bottom reflectivity with kinematic modeling based on far- field global positioning system data and local fault and strain patterns. We find a direct correlation between maxima of mud output and maxima of the shear component of strain at the backstop contact. Mud volcanism may reflect the abundance of solid (mud) and fluid (methane) sources combined with a favorable tectonic regime established at the prism-backstop contact in post-Pliocene time, in relation to plate tectonic changes.

Geologic evolution of the Martian dichotomy in the Ismenius area of Mars and implications for plains magnetization

The origin of the Martian dichotomy, which divides highlands from lowlands, is unknown. We examine a section of the dichotomy (50–90E) defined by steep scarps and normal faults. Stratigraphy and age relationships preclude the formation of the 2.5 km high boundary via erosion. The abrupt disappearance of topographic knobs ∼300–500 km to the northeast is interpreted as a buried fault. Alignment of the buried fault with grabens, stratigraphy, and age determinations using crater counts indicate that the lowland bench is down faulted highlands crust. The estimated local strain (3.5%) and fault pattern are broadly consistent with gravitational relaxation of a plateau boundary. Magnetic and gravity anomalies occur on either side of the buried fault. Admittance analysis indicates isostatic compensation. Although nonunique, a model with a 10 km thick intracrustal block under the lowland bench, a 20 km thick block under the plains, and an excess density of 200 kg/m3 provides a good fit to the isostatic anomaly. A good fit to a profile of the magnetic field perpendicular to the dichotomy is produced using uniformly polarized intracrustal blocks 10–20 km thick, an intensity of 6 Am/m, a field inclination of −30°, and gaps aligned with the isostatic anomalies. One interpretation is that high‐density intrusions demagnetized the crust after dynamo cessation and that low‐lying magnetized areas could be down faulted highlands crust. Another model (inclination of 30°) has magnetized crust beneath the isostatic anomalies, separated by gaps. The gaps could result from hydrothermal alteration of the crust along fault zones.

Importance of mitral valve second-order chordae for left ventricular geometry, wall thickening mechanics, and global systolic function.

Mitral valvular-ventricular continuity is important for left ventricular (LV) systolic function, but the specific contributions of the anterior leaflet second-order "strut" chordae are unknown. Eight sheep had radiopaque markers implanted to silhouette the LV, annulus, and papillary muscles (PMs); 3 transmural bead columns were inserted into the mid-lateral wall between the PMs. The strut chordae were encircled with exteriorized wire snares. Three-dimensional marker images and hemodynamic data were acquired before and after chordal cutting. Preload recruitable stroke work (PRSW) and end-systolic elastance (E(es)) were calculated to assess global LV systolic function (n=7). Transmural strains were measured from bead displacements (n=4). Chordal cutting caused global LV dysfunction: E(es) (1.48+/-1.12 versus 0.98+/-1.30 mm Hg/mL, P=0.04) and PRSW (69+/-16 versus 60+/-15 mm Hg, P=0.03) decreased. Although heart rate and time from ED to ES were unchanged, time of mid-ejection was delayed (125+/-18 versus 136+/-19 ms, P=0.01). Globally, the LV apex and posterior PM tip were displaced away from the fibrous annulus and LV base-apex length increased at end-diastole and end-systole (all +1 mm, P<0.05). Locally, subendocardial end-diastolic strains occurred: Longitudinal strain (E22) 0.030+/-0.013 and radial thickening (E33) 0.081+/-0.041 (both P<0.05 versus zero). Subendocardial systolic shear strains were also perturbed: Circumferential-longitudinal "micro-torsion" (E12) (0.099+/-0.035 versus 0.075+/-0.025) and circumferential radial shear (E13) (0.084+/-0.023 versus 0.039+/-0.008, both P<0.05). Cutting second-order chords altered LV geometry, remodeled the myocardium between the PMs, perturbed local systolic strain patterns affecting micro-torsion and wall-thickening, and caused global systolic dysfunction, demonstrating the importance of these chordae for LV structure and function.

Effects of Pore Morphology and Bone Ingrowth on Mechanical Properties of Microporous Titanium as an Orthopaedic Implant Material

Successful bone formation which leads to functional osseointegration is determined by the local mechanical environment around bone-interfacing implants. In this work, a novel porous titanium material is developed and tested and then impact of porosity on mechanical properties as a function of bone ingrowth is studied numerically. A superplastic foaming technique is used to produce CP-Ti material with rounded, interconnected pores of 50% porosity; the pore size and morphology is particularly suitable for bone ingrowth. In order to understand the structure-property relations for this new material, a numerical simulation is performed to study the effect of the porous microstructure and bone ingrowth on the mechanical properties. Using ABAQUS, we create two-dimensional representative microstructures for fully porous samples, as well as samples with partial and full bone ingrowth. We then use the finite element method to predict the macroscopic mechanical properties of the foam, e.g., overall Young's modulus and yield stress, as well as the local stress and strain pattern of both the titanium foam and bone inclusions. The strain-stress curve, stress concentrations and stress shielding caused by the bone-implant modulus mismatch are examined for different microstructures in both elastic and plastic region. The results are compared with experimental data from the porous titanium samples. Based on the finite element predictions, bone ingrowth is predicted to dramatically reduce stress concentrations around the pores. It is shown that the morphology of the implants will influence both macroscopic properties (such as modulus) and localized behavior (such as stress concentrations). Therefore, these studies provide a methodology for the optimal design of porous titanium as an implant material.

Wave phenomena in low-rate plastic flow of solids

An investigation of plastic flow localization patterns (waves) which are ordered in space and evolve with time has been performed for a wide range of metals and alloys. These waves are found to have the following basic features: the dependence of propagation rate on work hardening coefficient, dispersion law and scale effect. The possibility of addressing plastic flow localization as a self-organization process occurring in a deforming medium is considered. A set of equations appropriate for the description of local flow nuclei is discussed. Consideration is given to a change-over from one local strain pattern to another in accordance with the respective stages of flow. Proposed is a model for interpreting the large-scale periodicities exhibited by the distribution of localized strain nuclei.

Wave phenomena in low-rate plastic flow of solids

An investigation of plastic flow localization patterns (waves) which are ordered in space and evolve with time has been performed for a wide range of metals and alloys. These waves are found to have the following basic features: the dependence of propagation rate on work hardening coefficient, dispersion law and scale effect. The possibility of addressing plastic flow localization as a self-organization process occurring in a deforming medium is considered. A set of equations appropriate for the description of local flow nuclei is discussed. Consideration is given to a change-over from one local strain pattern to another in accordance with the respective stages of flow. Proposed is a model for interpreting the large-scale periodicities exhibited by the distribution of localized strain nuclei.

Wave phenomena in low‐rate plastic flow of solids

AbstractAn investigation of plastic flow localization patterns (waves) which are ordered in space and evolve with time has been performed for a wide range of metals and alloys. These waves are found to have the following basic features: the dependence of propagation rate on work hardening coefficient, dispersion law and scale effect. The possibility of addressing plastic flow localization as a self‐organization process occurring in a deforming medium is considered. A set of equations appropriate for the description of local flow nuclei is discussed. Consideration is given to a change‐over from one local strain pattern to another in accordance with the respective stages of flow. Proposed is a model for interpreting the large‐scale periodicities exhibited by the distribution of localized strain nuclei.

Strain compatibility and shear zones: is there a problem?

In analyzing deformation in rocks, it is important to ensure that the solutions obtained satisfy strain compatibility. This creates a challenge to understanding patterns of strain associated with shear zones, in which measured strain may appear incompatible with the strain in the shear zone walls. Flattening strains are common in natural shear zones with locally straight and parallel boundaries: to satisfy compatibility conditions such strains require volume loss across the shear zone or deviations from plane strain, with or without discontinuities between the shear zone and the wall rock. In the case of shear zones for which there is no evidence of volume loss or discontinuities along the shear zone walls, problems of strain compatibility may be resolved if individual shear zones are linked together in an appropriate fashion. Shear zones commonly occur in anastomosing arrays, and simple configurations of such arrays and the strains associated with them are examined. It is shown that local transpression with strain compatibility can be accounted for in this way. Quite complex local strain patterns can develop in simple arrays.

Lateral variations of strain in experimental forced folds

Packages of rock layers, deformed under confining pressure by the uplift and rotation of a steel-block forcing assembly, translate both towards, and away from, the margin of the principal uplifted block. The resulting asymmetric forced folds, and especially their long, planar limbs, exhibit along-layer variations in strain. Alternations of layer elongation and contraction occur along profiles extending away from the antiform/synform couplet. Layer-normal strains are mostly nil, so the longitudinal strains largely equate to volume strains in these plane-strain models. Spaced anomalies in outcrops, indicating either increased cementation, or erosional weakness, may suggest that similar processes operate in nature to produce variations in damage caused during the flexural-slip process. Two, non-exclusive explanations are offered to account for the patterns of strain observed in the experiments: (1) they may be caused by decaying wavetrains of small-scale flexural deflections (and their local strain patterns) related to the bending of the major forced folds; or (2) they may be caused by a `patchy' development of layer-parallel slip, and the consequent spatial variability in displacements.

Characterizing and Modeling Plastic Strain Inhomogeneity in Thin Metallic Sheets

AbstractUsing a newly developed plastic strain measurement technique based on digital image correlation, surface plastic deformation of polycrystalline aluminum alloys in a thin sheet form has been experimentally characterized at a length scale comparable to that of the thickness of the aluminum sheets but much larger than the average size of individual grains. Both static and dynamic local straining patterns in these aluminum alloys have been observed and these strain patterns can not be simulated using the conventional plasticity models. The texture clustering of grains may contribute to the static local plastic strain patterns detected in an Al-Mg alloy. Two distinctive dynamic straining behaviors resulted from the dynamic strain aging of dislocations due to the alloying elements have been experimentally established for 5XXX and 6XXX alloys, respectively. First observation of dynamic strain inhomogeneity is also made in a sheet metal specimen deforming predominately in a plane strain state.