Line strain representation and shear strain representation of 3D strain states

The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing test apparatus or equipment. The difficulties encountered in the above work would be greatly simplified if strain states could be expressed in a single strain form, namely including only linear or shear strains. As a start, this paper explores the meaning and nature of strain states. Then, based on the hypothesis of small deformations, two strain state expressions, the linear strain expression method (LSEM) and shear strain expression method (SSEM), were established for incompressible materials with only linear strain and shear strain as parameters respectively. Furthermore, conditions, implementation steps and specific forms for the application of SSEM in 1D, 2D and 3D strain states are obtained. As an example, two representations based on tetragonal pyramid and rotating tetrahedron are especially given. Therefore, conventional strain representation methods can be expressed as a combination of line strains in a certain direction or a combination of characteristic shear strains. The results of this paper provide a new way for understanding deformation characteristics, revealing yielding process, establishing constitutive models, and developing testing apparatus or equipment.

Influence of the ECAP Tool Channel Geometry on the Structure and Properties of Al-3%Mg Aluminium Alloy

In this study, commercial Al-3%Mg aluminium alloy was subjected to ECAP processing using two different ECAP die configurations. The first one – conventional and the second one modified in which a part of the exit channel in the ECAP die, causes twist deformation, to impose extra shear strains to the sample. The local changes in microstructure were characterized by Light Microscopy, SEM equipped with an EBSD facility and TEM. Mechanical properties of the ECAP processed samples were compared based on hardness measurement. The results showed that when ECAP with modified die, the greater grain and crystalline refinement is possible. The microstructures exhibit high dislocation density within subgrains with non-equilibrium and Moiré boundaries. Moreover, the mechanical examinations display a significant improvement in hardness and calculated yield strength when the ECAP process is conducted using a modified die.

Parameter Estimation and Application of Anisotropic Yield Criteria for Cylindrical Aluminum Extrusions: Theoretical Developments and StereoDIC Measurements

Theoretical and experimental studies are presented to characterize the anisotropic plastic response under torsion loading of two nominally identical aluminum Al6061-T6 extruded round bars. Theoretical models are developed using isotropic (Von Mises 1913) and anisotropic (Barlat 1991) yield criteria, along with isotropic strain hardening formulae, to model post-yield behavior under simple torsion loading. For the case of simple shear loading, incremental plasticity theory is used to determine the theoretical elastic, plastic, and total shear strains. A set of experiments are performed to calibrate Barlat’s 1991 yield function. Several specimens are extracted at different orientations to the longitudinal direction of each round Al6061-T6 bar and tested under uniaxial tension and simple torsion to optimally determine all anisotropic (Barlat 1991) yield function parameters. During loading, Stereo Digital Image Correlation (DIC) is used to quantify surface deformations for the torsion experiments and a baseline tension specimen to identify and correct measurement anomalies. Results show the isotropic yield model either underestimates or overestimates the experimental shear strains for both extrusions. Conversely, results using the Barlat 1991 anisotropic yield criteria are in excellent agreement with experimental measurements for both extrusions. The presence of significant differences in the anisotropic parameters for nominally similar extrusions confirms that plastic anisotropy is essential for the accurate prediction of mechanical behavior in longitudinally extruded Al6061-T6 bars.

Influence of High-Pressure Torsion on the Microstructure and Microhardness of Additively Manufactured 316L Stainless Steel

High-pressure torsion (HPT) is known as an effective severe plastic deformation (SPD) technique to produce bulk ultrafine-grained (UFG) metals and alloys by the application of combined compressive force and torsional shear strains on thin disk samples. In this study, the microstructures and microhardness evolution of an additively manufactured (AM) 316L stainless steel (316L SS) processed through 5 HPT revolutions are evaluated at the central disk area, where the effective shear strains are relatively low compared to the peripheral regions. Scanning electron microscopy (SEM) analysis showed that the cellular network sub-structures in AM 316L SS were destroyed after 5 HPT revolutions. Transmission electron microscopy (TEM) observations revealed non-equilibrium ultrafine grained (UFG) microstructures (average grain size: ~115 nm) after 5 revolutions. Furthermore, energy dispersive x-ray spectroscopy (EDX) analysis suggested that spherical Cr-based nano-silicates are also found in the as-received condition, which are retained even after HPT processing. Vickers microhardness (HV) measurements indicated significant increase in average hardness values from ~220 HV before HPT processing to ~560 HV after 5 revolutions. Quantitative X-ray diffraction (XRD) patterns exhibit a considerable increase in dislocation density from ~0.7 × 1013 m−2 to ~1.04 × 1015 m−2. The super-high average hardness increment after 5 HPT revolutions is predicted to be attributed to the UFG grain refinement, significant increase in dislocation densities and the presence of the Cr-based nano-silicates, according to the model established based on the linear additive theory.

Self-assembled Epitaxial Ferroelectric Oxide Nano-spring with Super-scalability

Oxide nano-springs have attracted many research interests because of their anti-corrosion, high-temperature tolerance, oxidation resistance, and enhanced-mechanic-response from unique helix structures, enabling various nano-manipulators, nano-motors, nano-switches, sensors, and energy harvesters. However, preparing oxide nano-springs is a challenge for their intrinsic nature of lacking elasticity. Here, we developed an approach for preparing self-assembled, epitaxial, ferroelectric nano-springs with built-in strain due to the lattice mismatch in freestanding La0.7Sr0.3MnO3/BaTiO3 (LSMO/BTO) bilayer heterostructures. We find that these LSMO/BTO nano-springs can be extensively pulled or pushed up to their geometry limits back and forth without breaking, exhibiting super-scalability with full recovery capability. The phase-field simulations reveal that the excellent scalability originates from the continuous ferroelastic domain structures, resulting from twisting under co-existing axial and shear strains. In addition, the oxide hetero-structural springs exhibit strong resilience due to the limited plastic deformation nature and the built-in strain between the bilayers. This discovery provides an alternative way for preparing and operating functional oxide nano-springs that can be applied to various technologies.

Normalized Modulus Reduction and Damping Ratio Curves for Bay of Campeche Calcareous Clay to Carbonate Mud

Equations to calculate the modulus reduction curve (G/Gmax-γ) and material damping ratio curve (D-γ) of calcareous clay and clayey carbonate mud of the Bay of Campeche and Tabasco Coastline are developed. This was achieved using a database of 156 resonant column tests and 468 strain-controlled cyclic direct simple shear tests performed in clays with 10 % ≤ CaCO3 ≤90 %. The effects of carbonate content (CaCO3), mean effective confining pressure (σ′m), plasticity index (PI), and overconsolidation ratio (OCR) on the shape of the modulus reduction and material damping ratio curves are shown based on the available laboratory data and the equations developed to calculate these curves. It is shown that as CaCO3 increases, the normalized shear modulus (G/Gmax) curve tends to shift downward and the damping ratio (D) curve tends to shift upward; as σ′m and PI increase, the G/Gmax curve tends to shift upward and the damping ratio curve tends to shift downward; and the value of OCR has practically no effect on the position of the curves. The validation of the calculated values of G/Gmax and D shows the best predictions are found at low shear strains for G/Gmax and at large shear strains for D, falling within ± 25 % of the measured values, and shows that due to limitations in the model at large strains (γ > 1 %) for G/Gmax and at low strains (γ < 0.05 %) for D, the calculated values fall within ± 50 % of the measured values. The equations developed to calculate the curves of G/Gmax-γ and D-γ of calcareous clay and clayey carbonate mud are recommended for preliminary or perhaps even final seismic site response evaluations. However, considering the scatter of the data points around the curves, the equations should be used with caution, and parametric and sensitivity studies are strongly recommended to assess the importance of this scatter. In large critical projects, direct experimental determinations of G/Gmax and D for the soils of interest are suggested to be more appropriate.

Regional variation of corneal stromal deformation measured by high-frequency ultrasound elastography

The cornea’s mechanical response to intraocular pressure elevations may alter in ectatic diseases such as keratoconus. Regional variations of mechanical deformation in normal and keratoconus eyes during intraocular pressure elevation have not been well-characterized. We applied a high-frequency ultrasound elastography technique to characterize the regional deformation of normal and keratoconus human corneas through the full thickness of corneal stroma. A cross-section centered at the corneal apex in 11 normal and 2 keratoconus human donor eyes was imaged with high-frequency ultrasound during whole globe inflation from 5 to 30 mmHg. An ultrasound speckle tracking algorithm was used to compute local tissue displacements. Radial, tangential, and shear strains were mapped across the imaged cross-section. Strains in the central (1 mm surrounding apex) and paracentral (1 to 4 mm from apex) regions were analyzed in both normal and keratoconus eyes. Additional regional analysis was performed in the eye with severe keratoconus presenting significant thinning and scarring. Our results showed that in normal corneas, the central region had significantly smaller tangential stretch than the paracentral region, and that within the central region, the magnitudes of radial and shear strains were significantly larger than that of tangential strain. The eye with mild keratoconus had similar shear strain but substantially larger radial strains than normal corneas, while the eye with severe keratoconus had similar overall strains as in normal eyes but marked regional heterogeneity and large strains in the cone region. These findings suggested regional variation of mechanical responses to intraocular pressure elevation in both normal and keratoconus corneas, and keratoconus appeared to be associated with mechanical weakening in the cone region, especially in resisting radial compression. Comprehensive characterization of radial, tangential, and shear strains through corneal stroma may provide new insights to understand the biomechanical alterations in keratoconus.

Zircons of fenites of Ilmeno-Vishnevogorsky Complex (Southern Urals)

Research subject. U-Pb zircon dating, as well as a petrological and geochemical study of pyroxene-amphibole-, pyroxeneamphibole- biotite- and biotite-bearing fenites from the Central Alkaline Band Ilmeno-Vishnevogorsky Complex.Methods. The age of zircons was determined by an ion mass spectrometer (SHRIMP II, Centre of Isotopic Research VSEGEI). The content of REE and trace elements was estimated by secondary ion mass spectrometer methods (CAMECA IMS-4F, Valiev Institute of Physics and Technology RAS).Results. The mineralogical and geochemical (U, Th, REE) features of zircons, as well as fenites, reflect their polygenic-polychronous nature. Most zircon crystals have a metastable matrix and are characterized by averaged REE contents between igneous and hydrothermal types. These crystals are distinguished from magmatic zircons by high LREE contents and low values of Ce anomalies, and from hydrothermal zircons – by differentiated REE distribution spectra. Three ages of zircon were established: 2066–1686 (PR1), 425–404 (S2) and 284–266 (P1) Ma. PR1 zircons reflect the primary features and the degree of changes in the fenite substrate. S2 zircons, limited only to the biotite- bearing fenite, correspond to the age of the miaskite formation process. The P1 zircons clearly reflect the metasomatic process of fenitization initiated by late shear deformations. The temperature of the phenitization processes (based on the Ti content in zircons) was estimated at 630–670°C for S2 and ≤ 600°C for P1 fenites, respectively.Conclusions. Central Alkaline Band fenites were formed by the metasomatic process of PR1 substrate fenitization in the late stage (P1) of shear strains, which are widely expressed in the Ilmeno-Vishnevogorsky Complex.