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An impact test was conducted on a single crystal of an Fe–3mass%Al alloy with a bcc structure. Microstructural changes in the sheared regions resulting from the impact test were examined. Deformation twinning was observed, with the twinning plane K 1 = { 332 } and the twinning shear direction η 1 = ⟨ 11 3 ¯ ⟩. The conjugate twinning direction η 2 of this mode was discussed. Considering the shear direction required to induce deformation twinning, it can be concluded that η 2 = ⟨ 110 ⟩ is appropriate for the twinning mode in the Fe–3mass%Al. [ABSTRACT FROM AUTHOR]

Slip transmission between neighbouring grains is needed for the occurrence of plastic deformation in polycrystals. A geometric factor defined for a pair of grains with a certain orientation relationship is used to determine the slip transmission. Two slip transmission factors are calculated for randomly oriented grains. One is the slip transmission factor averaged for randomly oriented grains and the other is the minimum of the transmission factors among all possible orientation relationships. The possible number of slip systems in a grain varies for different metals and alloys. The effects of the number of slip systems on the transmission factors are discussed. [ABSTRACT FROM AUTHOR]

Many atolls in tropical oceans are under the threat of sea‐level rise. Mitigation planning requires reliable estimates of increasing wave runup in response to sea‐level rise and changes in wave climate. However, shoreline dynamics on reef‐lined coasts, particularly the effect of low‐frequency waves, are not yet fully understood. Herein, we present a field study on the southernmost atoll of the Maldives to clarify the variability of shoreline water levels driven by waves and tides. The atoll is located just south of the equator and has a moderate wave climate; it is occasionally impacted by long‐distance swells from the South Indian Ocean. Wave evolution on a reef‐lined coast was observed in situ for a period of seven months. The shallow water depth tightly constrains reef‐flat waves under normal wave conditions; however, this constraint is broken under extreme conditions by low‐frequency waves generated from long‐period swells. Particularly, very low‐frequency waves (<0.005 Hz) are amplified via wave resonance over the reef platform and significantly contribute to shoreline motions. Our observation of shoreline motions confirmed that, under energetic conditions, extreme wave run‐ups are characterized by swell run‐ups riding on crests of low‐frequency waves. A combined approach of observations and analytical modeling revealed the long‐term variability of shoreline water levels, highlighting the stochastic nature of extreme water levels influenced by a joint probability of far‐field swells and high tides. Our results suggested that extreme shoreline water levels would increase at a significantly higher rate than sea‐level rise in the future. Plain Language Summary: An atoll is a ring‐shaped coral reef on which a series of islands (having ground elevations of less than a few meters) have formed. Inhabited atolls in tropical oceans are, therefore, considered to be one of the most vulnerable areas to global sea‐level rise, because this rise will exacerbate wave‐induced flooding in island communities. Adaptation strategies require reliable estimates of increasing wave impacts; however, it is often difficult to assess shoreline water levels driven by waves and tides over actual reef topography of diverse forms. This study investigated wave processes on the southernmost atoll of the Maldives, where there is a strong influence from waves traveling from the South Indian Ocean. Our wave observations revealed that extreme shoreline water levels were driven by short waves riding on crests of relatively long waves that developed over the reef platform. The long‐period waves are generated from a group of high swells over the outer reef platform and are significantly amplified when their period coincides with the natural period of the reef water. The study clarified the shoreline dynamics on the reef‐lined coast and demonstrated that extreme shoreline water levels would increase at a higher rate than sea‐level rise in the future. Key Points: A combination of observations and analytical modeling clarified the variability of shoreline water levels on the atoll of the MaldivesWave runup under energetic conditions is characterized by swell runup modulated by dominant very low‐frequency waves (<0.005 Hz)Extreme shoreline water levels on the reef‐lined coast occur with a joint probability of far‐field energetic swells and high tides [ABSTRACT FROM AUTHOR]

Orientation relationships of grains in tricrystals are discussed. Disorientation angles among grains are evaluated and a constrained condition of these around a triple junction is shown. Probability densities of the disorientation angles are obtained for randomly oriented grains by numerical calculations. A disorientation-angle diagram for tricrystal is proposed to characterize the orientation relationships of grains around the triple junctions. [ABSTRACT FROM AUTHOR]

The well-known problem of determining the maximum possible disorientation angle of two cubes is extended to groups of three to six cubes. This problem is considered here to allow identification of specific arrangements of grains with a cubic structure at triple-line or quadruple junctions in polycrystals. The minimum disorientation angle between cubes in the group is defined as the characteristic disorientation angle θ c d of the group. The maximum values of θ c d and the arrangements of cubes giving the maximum θ c d are determined for groups of three to six cubes. [ABSTRACT FROM AUTHOR]

Orientation changes are important factors when considering microstructural changes in materials caused by plastic deformation because these are related to the arrangement and density of dislocations. The three elements of a logarithm of a rotation matrix are called log angles, which compose a rotation vector that can be used as a parameter to represent crystal orientations. Herein, approximate expressions of a rotation vector are derived for a product of two small-angle rotations. The degrees of the first-order, second-order and third-order approximations are discussed. The non-commutativity of two rotations is graphically illustrated using the approximate expressions. Experimental results of orientation changes in a cold-rolled Cu bicrystal are considered to evaluate the validity of the approximate expressions. It is shown that a linear approximation for the product of rotation vectors is valid to treat small-angle orientation changes in plastically deformed crystals with dislocation structures. [ABSTRACT FROM AUTHOR]

Crystal orientation is an important factor when we consider microstructures in materials. With respect to a reference frame, certain crystal orientation can be expressed by a rotation angle $$\Phi $$ around a unit vector $$\mathbf{n}=\left( {h,\hbox { }k,\hbox { }l} \right) $$ . Partitioning of $$\Phi $$ into rotation components around coordinate axes of the reference frame is discussed. For a rotation matrix $$\mathbf{R}$$ corresponding to the axis/angle pair, its logarithm $$\ln \mathbf{R}$$ is a skew symmetric tensor with three independent elements, $$h\Phi , k\Phi $$ and $$l\Phi $$ . It is shown that these elements can be interpreted to be sums of the divided rotation angles around the coordinate axes. The elements $$h\Phi , k\Phi $$ and $$l\Phi $$ of $$\ln \mathbf{R}$$ called the log angles can be used as the rotation components to evaluate crystal orientation in materials. [ABSTRACT FROM AUTHOR]

Using scanning electron microscopy, we investigated how the microstructure of a Cu single crystal with a {15 12 9}〈9 10 3〉 orientation evolved from cold rolling. The first 50 % rolling caused its crystal orientation to rotate to {211}〈111〉. Although orientation splitting occurred near the surface of the single crystal, band-like regions with near-{211}〈111〉 orientations were still present after the fourth 50 % rolling. We measured the spread of crystal orientation in the near-{211}〈111〉 regions as a function of the total plastic equivalent strain induced by all rolling steps. When 50 % rolling was performed less than twice, the spread of crystal orientation was proportional to the square root of the plastic equivalent strain. Based on our results, we discussed the relationship between the spread of crystal orientation and the plastic equivalent strain generated by rolling. [ABSTRACT FROM AUTHOR]

Al single crystals oriented for single slip were cyclically deformed under constant plastic strain amplitudes between 1 × 10−3and 5 × 10−2at 77 K. Al single crystals showed hardening to saturation at all applied shear stress amplitudes. The resultant cyclic stress–strain curve (CSSC) showed a stress plateau in a range of plastic strain amplitude from 2 × 10−3to 2 × 10−2. Surface observation revealed that multiple slip systems were active even at the strain amplitude in the plateau region. At plastic strain amplitudes corresponding to the plateau of the CSSC, persistent slip bands (PSBs) were formed parallel to the primary slip plane. In the PSBs, well-developed dislocation walls parallel to the {100} planes were observed. The microstructure in the PSBs was explained by the fact of multiple activation of the primary and critical slip systems. The above results indicate that the high stacking fault energy of Al is an important factor affecting the fatigue behaviour even at 77 K. [ABSTRACT FROM PUBLISHER]

Using an x-y-z coordinate system, the equations of the superspheres have been extended to describe intermediate shapes between a sphere and various convex polyhedra. Near-polyhedral shapes composed of {100}, {111} and {110} surfaces with round edges are treated in the present study, where {100}, {111} and {110} are the Miller indices of crystals with cubic structures. The three parameters p, a and b are included to describe the {100}- {111}-{110} near-polyhedral shapes, where p describes the degree to which the shape is a polyhedron and a and b determine the ratios of the {100}, {111} and {110} surfaces. [ABSTRACT FROM AUTHOR]

Onaka has shown (2010) that the Hencky equivalent strain is the appropriate quantity to represent the degree of severe plastic deformation based on simple-shear deformation. In a recent paper, Shrivastava et al. have criticized (2011) the Onaka paper and stated that the Hencky formulation does not apply to large simple-shear deformation. In this response, it is shown that this claim of Shrivastava et al. is not consistent with recent accepted knowledge on the Hencky strain. [ABSTRACT FROM PUBLISHER]

Small crystalline particles are often formed comprising near-polyhedral shapes with round edges. When near-polyhedral shapes are analyzed and discussed, it is convenient if these shapes can be expressed by equations with simple parameters. Superspheres are solids expressing various shapes between those of polyhedra and spheres. The superspherical-shape approximation is used in this study to consider the morphology of cubic crystal structure particles. Various near-polyhedral shapes composed of {100}, {111} and {110} planes are described using a simple equation with three shape-related parameters. It is shown that the superspherical-shape approximation is a useful geometrical tool for evaluating the morphology of small crystalline particles. [ABSTRACT FROM AUTHOR]

Effects of Si addition on mechanical properties of severely deformed copper by accumulative roll-bonding (ARB) have been investigated. Tensile tests and strain-rate jump tests have been carried out at room temperature. For annealed coarse-grained polycrystals, the difference in yield stress σ between pure copper and a Cu-1.64at.%Si alloy was only about 15 MPa while the difference became 170 MPa after the ARB process by six cycles. The strain-rate sensitivity m of pure copper increased with increasing the number N of the ARB cycles for N ≥ 5. However, the increase in m becomes less significant for Cu-Si alloys. These findings have been discussed in terms of thermally activated dislocation processes. [ABSTRACT FROM AUTHOR]

Tensile tests and strain-rate jump tests were carried out at several temperatures below room temperature on Cu processed by accumulative roll-bonding (ARB). The temperature dependences of the flow stress and the activation volume were determined. In contrast to conventional coarse-grained materials where the activation volume increases with increasing temperature, the ARB processed copper by 8 cycles with ultrafine-grains showed inverse temperature dependence of activation volume, i.e., decreased activation volume with increasing temperature. This inverse temperature dependence of the activation volume is discussed in terms of thermally activated dislocation bow-out from grain-boundaries. [ABSTRACT FROM AUTHOR]

Using a single crystal of a Cu-6 mass% Ag alloy aged at 723 K for various times, nano-sized Ag precipitates in a Cu matrix were observed by conventional and ultra high-voltage transmission electron microscopes. The nano-sized Ag precipitates with a radius of about 5 nm had a nearly spherical shape. The shape change from the nearly spherical shape to the {111} octahedral shape occurred with increasing the size of the Ag precipitates to 11 nm. Elastic states of the Ag precipitates were evaluated by observing moiré fringes formed between the Ag precipitates and the Cu matrix. The origin of the shape change of the nano-sized Ag precipitates was discussed by considering the sum of elastic strain energy and interfacial energy. [ABSTRACT FROM AUTHOR]

The Hencky strain is an appropriate measure for large deformation where principal directions of strains rotate. In this study, the equivalent strain in large simple shear deformation is re-examined using the Hencky strain. When the amount of simple shear is γ, the equivalent strain of the Hencky strain becomes a logarithmic function of γ, which is the same as the result given by Eichinger [Festigkeitstheoretische untersuchungen, in Handbuch der Werkstoffprufung, E. Siebel, ed., 2nd ed., Springer, Berlin, 1955, p.715]. [ABSTRACT FROM AUTHOR]

Small crystalline particles or precipitates are often formed comprising near polyhedral shapes with round edges. Using the anisotropy of the surface energy given by a simple broken-bond model for fcc crystals, a geometrical analysis is performed to consider the particle-shape dependence of surface energy. Polyhedral and nearly polyhedral particles composed of {100} and {111} planes are treated as examples. The effect of round edges on the variation of surface energy of the nearly polyhedral particles is discussed. [ABSTRACT FROM AUTHOR]

Simple equations are derived that give the shapes of various convex polyhedra. The five regular polyhedra, called Platonic solids (the tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and polyhedra composed of crystallographically low-index planes are treated. The equations also give shapes that are nearly polyhedral with round edges, or intermediate shapes between a sphere and convex polyhedra, and which are observed as the shapes of small particles or precipitates in materials. [ABSTRACT FROM AUTHOR]

The averaged Eshelby tensors that relate uniform eigenstrains and average total strains in doughnut-like inclusions are obtained. These are compared with the Eshelby tensors of oblate spheroidal and rod-like inclusions. We show that the averaged Eshelby tensors of the doughnut-like inclusions on a plane are almost the same as the average of the Eshelby tensors of randomly oriented rod-like inclusions on the same plane. This is satisfied for both 'fat' and 'thin' doughnut-like inclusions. [ABSTRACT FROM AUTHOR]

A shape described by (x[sup 2]1)[sup p/2] + (x[sup 2]2) [sup p/2] + (x[sup 2]3) [sup p/2] 1 (p2) may be called a supersphere. This shape becomes a sphere and a cuboid when p = 2 and p respectively. Shape changes of some precipitates in solid materials are well approximated by the variation in p of the supersphere. Here the elastic states of an infinitely extended material containing a superspherical inclusion Ω with uniform eigenstrains are examined. A case where Ω has the same isotropic elastic moduli as those of the remainder is treated. The averaged Eshelby tensor < S[sub ijkl] > of the superspherical Ω is calculated as a function of p . Using < Sijkl > the elastic strain energy of the material containing the superspherical Ω and its change with transitions of the Ω shape from spherical to cuboidal are discussed. [ABSTRACT FROM AUTHOR]

For an ellipsoidal inclusion with uniform eigenstrains in an infinitely extended material, the total strains in the inclusion are given by the well known Eshelby tensor S[sub ijkl]. A general relationship S[sub 1111]+S[sub 2222]+S[sub 3333]+2(S[sub 1212]+S [sub 2323]+S[sub 3131]) = 3 among the components of the Eshelby tensor and its physical meaning are reported. It is shown that the relationship can be extended to an inclusion with any shape in a material with any anisotropic elastic moduli. [ABSTRACT FROM AUTHOR]

The average Young's moduli are calculated under a plane strain condition for composites containing second phases aligned perpendicular or parallel to an applied uniaxial stress. The Mori-Tanaka concept of 'average stress' together with the equivalent inclusion idea of Eshelby are used. The variation of the average Young's moduli with the transitions of second-phase shape is discussed. When both the Poisson's ratios of the matrix and second phase are zero, the average Young's modulus of the composites monotonically increases with increasing aspect ratio of the second phase. However, when the Poisson's ratios of the matrix and second phase are different from each other, the second-phase shape dependence of the average Young's modulus is not always simple. Maps are derived to show the Poisson's ratio effect. For certain combinations of the Young's moduli and Poisson's ratios of the matrix and second phase, the mixture rule gives the lower bound of the average Young's modulus among those of composites containing a second phase with various shapes. It is also possible that the average Young's moduli of the composites become larger than those of the matrix and second phase. [ABSTRACT FROM AUTHOR]

A copper alloy containing amorphous B2O3 dispersed particles is made by internal oxidation of a dilute Cu-B solid-solution alloy. Although the B2O3 particles behave as plastically non-deformable particles at room temperature, these become liquid particles in the solid Cu matrix at high temperatures. Cu single crystals containing the B2O3 particles are tensile tested at high temperatures. The shape change of the liquid particles due to the plastic deformation of the Cu matrix is observed with electron imcroscopy. The occurrence of relaxation by the diffusion of the Cu atoms along the Cu/B2O3 interface affects the shape change. The kinetics of the diffusional relaxation is discussed on the basis of the results of observations of the particle shape. [ABSTRACT FROM AUTHOR]

Steady-state sliding of grain boundaries is discussed by taking into account the change in the potential energy of an applied stress, when the sliding occurs by diffusional accommodation. The present analysis enables us to derive the sliding rates at boundaries of various shapes in a simple manner without knowing local stress fields. Sliding rate of a boundary containing second phase particles is also derived by similar calculations. The results are compared with previous calculations by other investigators, and it is found that the resultant expressions for the sliding rates are essentially identical to those derived from more complex analyses. [ABSTRACT FROM AUTHOR]

Ultra-fine-grained (UFG) Cu shows little total elongation in tensile tests because simple shear deformation is concentrated in narrow regions during the initial stage of plastic deformation. Here, we attempted to improve the total elongation of UFG Cu obtained by equal-channel angular pressing. By making shallow dents on the side surfaces of the plate-like specimens, this induced pure shear deformation and increased their total elongation. During the tensile tests, we observed the overall and local deformation of the dented and undented UFG Cu specimens. Using three-dimensional digital image correlation, we found that the dented specimens showed suppression of thickness reduction and delay in fracture by enhancement of pure shear deformation. However, the dented and undented specimens had the same ultimate tensile strength. These results provide us a new concept to increase total elongation of UFG materials. [ABSTRACT FROM AUTHOR]