An analytical approach and experimental confirmation of dislocation–twin boundary interactions in titanium

The morphology of $ \{ 10\overline{1} 2\} \left\langle {\overline{1} 011} \right\rangle $ { 10 1 ¯ 2 } 〈 1 ¯ 011 〉 deformation twins formed in commercial purity titanium during an initial pass of equal-channel angular pressing was studied by transmission electron microscopy (TEM). The corresponding diffraction patterns show a symmetry line splitting of $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin boundaries (TB) which is related to the presence of interfacial defects. A simple modeling for the interaction between non-screw a-slip lattice dislocations (Burgers vector b =  $ \frac{1}{3}[\overline{1} \overline{1} 20] $ 1 3 [ 1 ¯ 1 ¯ 20 ] ) and the $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin plane is used according to crystallographic geometry and vector conservation. The results show that dislocation dissociation into different Frank partial dislocations on the interfacial plane is more favorable than its transmission to the other side of the interface. The formation of the Frank partials at the TB can produce a small change in the TB misorientation angle and this is consistent with the symmetry line splitting of the $ (10\overline{1} 2) $ ( 10 1 ¯ 2 ) twin boundaries observed by TEM.     

Accurate loading analyses of curved cracks under mixed-mode conditions applying the J-integral

In linear elastic fracture mechanics the path-independent J-integral is a loading quantity equivalent to stress intensity factors (SIF) or the energy release rate. Concerning plane crack problems, $J_k$ J k is a 2-dimensional vector with its components $J_1$ J 1 and $J_2$ J 2 . These two parameters can be related to the mode-I and mode-II SIFs $K_{\mathrm{I}}$ K I and $K_{\mathrm{II}}$ K II . To guarantee path-independence for curved crack geometries, an integration path along the crack faces must be considered. This paper deals with problems occurring at the numerical calculation of the J-integral in connection with the FE-method. Two new methods for accurately calculating values of $J_2$ J 2 for arbitrary cracks are presented.     

Cross-slip on the first order pyramidal plane (10\bar 11) of a-type dislocations [1\bar 210] in the plastic deformation of α-titanium single crystals

The nature of the cross-slip plane was determined by electron microscopy observations of α-titanium single crystal specimens, oriented for single prismatic slip (10 \(\bar 1\) 0) [1 \(\bar 2\) 10]. The occurrence of cross slip on the first order pyramidal plane (10 \(\bar 1\) 1) was proved for a-type dislocations [1 \(\bar 2\) 10]. Furthermore, two types of dislocation configuration due to the double cross-slip were observed: edge dislocation dipoles and loops elongated along the Burger's vector.     

Effect of Localized Microstructure Evolution on Higher Harmonic Generation of Guided Waves

The use of nonlinear ultrasonics to characterize microstructural evolution is investigated with the aim of enabling earlier remaining useful life prediction and thereby greatly improving condition based maintenance. Higher harmonic generation is sensitive to microstructural features, whose evolution is indicative of ongoing damage processes. Localized plastic deformation is controlled in an aluminum sample by varying the notch length, which dictates the extent of the plastic zone. The essentials of higher harmonic generation analysis for ultrasonic guided waves are highlighted to provide a means to select a primary mode that generates a strong higher harmonic. Experimental methods to use magnetostrictive transducers for third harmonic generation measurements are described. Experimental results on aluminum plates indicate that plastic deformation increases the third harmonic by up to a factor of five and that the harmonic amplitude ratio \(A_{3}\) / \(A_{1}^{3}\) is sensitive to the plastic strain magnitude. These initial results show that when the plastic strain is localized, the \(A_{3}\) / \(A_{1}^{3 }\) ratio appears to be proportional to the plastic zone-to-propagation distance ratio.     

Yield criteria of hexagonal symmetry in the π-plane

The theory of plasticity operates with different yield criteria of incompressible behavior for isotropic materials. Mostly known are the criteria of Tresca, Schmidt-Ishlinsky and von Mises. The first two criteria have a hexagonal symmetry, and the criterion of von Mises has a rotational symmetry in the π-plane. All these criteria do not distinguish between tension and compression (no strength differential effect), but numerous problems are treated in the engineering practice using these criteria. Within this paper, the yield criteria with hexagonal symmetry for isotropic incompressible materials are compared. For this purpose, their geometries in the π-plane will be presented in polar coordinates. The radii at the angles of 15^? and 30^? will be related to the radius at 0^?. Based on these two relations, well-known criteria will be shown in one diagram. The extreme shapes of the yield surfaces are restricted by two criteria: the unified yield criterion (UYC) and the multiplicative ansatz criterion (MAC). The examinations of the UYC and MAC depict a linear combination of these extreme yield surfaces. The resulting criterion with two parameters describes all possible convex forms of hexagonal symmetry. On the other hand, this criterion has one disadvantage: It is not possible to solve explicitly the equation for the equivalent stress. Other known criteria (Sokolovsky, Ishlinsky-Ivlev, Dodd-Naruse, Drucker) are depicted in the proposed diagram and compared with the above mentioned criteria. Further criteria are derived from the consideration of solids with orthogonal symmetry planes in the shear stress space. New criteria are introduced for practical applications. The constraints of convexity are established for them. The proposed consideration of the yield criteria simplifies the selection of a proper criterion. The extreme solutions for the analysis of construction parts can be found using these criteria.     

Superfluid Phases of 3He in a Periodic Confined Geometry

Predictions and discoveries of new phases of superfluid ³He in confined geometries, as well as novel topological excitations confined to surfaces and edges of near a bounding surface of ³He, are driving the fields of superfluid ³He infused into porous media, as well as the fabrication of sub-micron to nano-scale devices for controlled studies of quantum fluids. In this report we consider superfluid ³He confined in a periodic geometry, specifically a two-dimensional lattice of square, sub-micron-scale boundaries (“posts”) with translational invariance in the third dimension. The equilibrium phase(s) are inhomogeneous and depend on the microscopic boundary conditions imposed by a periodic array of posts. We present results for the order parameter and phase diagram based on strong pair breaking at the boundaries. The ordered phases are obtained by numerically minimizing the Ginzburg-Landau free energy functional. We report results for the weak-coupling limit, appropriate at ambient pressure, as a function of temperature T, lattice spacing L, and post edge dimension, d. For all d in which a superfluid transition occurs, we find a transition from the normal state to a periodic, inhomogeneous “polar” phase with $T_{c_{1}} < T_{c}$ for bulk superfluid ³He. For fixed lattice spacing, L, there is a critical post dimension, d _c , above which only the periodic polar phase is stable. For d<d _c we find a second, low-temperature phase onsetting at $T_{c_{2}} < T_{c_{1}}$ from the polar phase to a periodic “B-like” phase. The low temperature phase is inhomogeneous, anisotropic and preserves time-reversal symmetry, but unlike the bulk B-phase has only $\mathtt{D}_{\text{4h}}^{\text{L}+\text{S}}$ point symmetry.     

Dislocation structures in a { \bar{1} 104}/��11 \bar{2} 0�� low-angle tilt grain boundary of alumina (��-Al2O3)

An alumina (??-Al₂O₃) bicrystal with a ( $ \bar{1} $ 104)/[11 $ \bar{2} $ 0] 2^o low-angle tilt grain boundary was fabricated by diffusion bonding at 1500 °C in air, and the grain boundary was observed by transmission electron microscopy (TEM). High-resolution TEM observations revealed that the grain boundary consists of at least two kinds of dislocations. One is a perfect dislocation which has a Burgers vector of 1/3[ $ \bar{1} $ 2 $ \bar{1} $ 0]. The other is dissociated into two partial dislocations with a stacking fault on the (0001) plane, and each partial dislocation has a 1/6[ $ \bar{1} $ 101] edge component. It is suggested from structural considerations that the dissociated-dislocation pair originates from a b = 1/3[02 $ \bar{2} $ 1] perfect dislocation (i.e., 1/3[02 $ \bar{2} $ 1] ?? 1/6[02 $ \bar{2} $ 1] + 1/6[02 $ \bar{2} $ 1]). This dissociation produces a stacking fault in the anion sublattice. The stacking fault energy is estimated to be roughly 1.3 Jm^?2 based on the elastic theory. The authors discuss the dislocation structures and the stacking fault formed on the (0001) plane in detail.     

On the error linear complexity spectrum of p^{n}-periodic binary sequences

The error linear complexity spectrum of a periodic sequence is defined to be the ordered list of $k$ -error linear complexities of the sequence. In this paper, we present an algorithm which computes the error linear complexity spectrum for binary sequences with period $p^{n}$ , where $p$ is an odd prime and $2$ is a primitive root modulo $p^{2}$ .     

Density dependent macro-micro behavior of granular materials in general triaxial loading for varying intermediate principal stress using DEM

This study presents the density dependent behavior of granular materials for varying intermediate principal stress $(\sigma _{{{2}}})$ ( σ 2 ) in general triaxial loading using the discrete element method (DEM). The variation of intermediate principal stress is represented by a non-dimensional parameter $b[={(\sigma _{{{2}}}-\sigma _{{{3}}})}/{(\sigma _{{{1}}} -\sigma _{{{3}}})}]$ b [ = ( σ 2 ? σ 3 ) / ( σ 1 ? σ 3 ) ] , where $\sigma _{{{1}}}$ σ 1 and $\sigma _{{{3}}}$ σ 3 are the major and minor principal stresses, respectively. Isotropically compressed dense and loose samples were prepared numerically using the periodic boundaries. The numerical dense and loose samples were subjected to shear deformation under strain controlled condition for different $b$ b values ranging from 0 to 1. The simulated macro results depict that the friction angle increases with $b$ b until it reaches a peak value and beyond the peak, the friction angle decreases with $b$ b regardless of the density of sample. A unique relationship between dilatancy index and equivalent deviatoric strain exists at small strain level for different $b$ b values when dense sample is considered. By contrast, the same relationship for loose sample does not show uniqueness. The relationships among the major, intermediate and minor principal strains depict non-linear behavior. The non-linearity is dominant for loose sample. The fluctuation in the evolution of strain increment vector direction is dominant in loose sample than dense sample. The evolution of different micro results is presented as well. It is noted that a unique relationship exists between the stress ratio and the fabric measure regardless of $b$ b and the density of sample when strong contacts are considered.     

Specific Heat of K_{0.71}Na_{0.29}Fe_2As_2 at Very Low Temperatures

A commercially available calorimeter has been used to investigate the specific heat of a high-quality K $_{0.71}$ Na $_{0.29}$ Fe $_2$ As $_2$ single crystal. The addenda heat capacity of the calorimeter is determined in the temperature range $0.02 \, \mathrm{K} \le T \le 0.54 \, \mathrm{K}$ . The data of the K $_{0.71}$ Na $_{0.29}$ Fe $_2$ As $_2$ crystal imply the presence of a large $T^2$ contribution to the specific heat which gives evidence of $d$ -wave order parameter symmetry in the superconducting state. To improve the measurements, a novel design for a calorimeter with a paramagnetic temperature sensor is presented. It promises a temperature resolution of $\Delta T \approx 0.1 \, \mathrm{\mu K}$ and an addenda heat capacity less than $200 \, \mathrm{pJ/K}$ at $ T < 100 \, \mathrm{mK}$ .     

Characterization of crack tip stress fields in test specimens using mode mixity parameters

The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the $T$ -stress, elastic–plastic stress fields, integration constant $I_{n}$ , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field $I_{n}$ and the $T$ -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the $T$ -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.     

\lambda -Symmetries, isochronicity, and integrating factors of nonlinear ordinary differential equations

We obtain $\lambda $ -symmetries of some second-order equations of the Painlevé–Gambier type and study their relationship with the standard adjoint symmetry equation used for determining the integrating factor of a second-order ordinary differential equation (ODE). This is followed by a brief study of the $\lambda $ -symmetries of certain special types of third-order ODEs. Finally, we indicate a possible connection between $\lambda $ -symmetries and the property of isochronicity for the Liénard equation of the second type.     

Multi-vortex State Induced by Proximity Effects in a Small Superconducting Square

The influence of the different negative values of the deGennes parameter \(b\) in the thermodynamic properties of a superconducting infinitely long prism of square cross section area \(S=9\xi ^{2}(0)\) in the presence of a magnetic field is investigated theoretically by solving numerically the nonlinear Ginzburg-Landau equations; \(\xi (0)\) is the coherent length at zero temperature. We obtain the vorticity, magnetic induction, Cooper pair density, magnetization and phase of the order parameter as functions of the external applied magnetic field and the \(b\) parameter. Our results show that a multi-vortex state appear in the sample choosing a convenient value of \(b<0\) parameter, even for such small system. Also, we study a superconducting parallelepiped of volume \(V=Sd\) by means of true \(3D\) numerical simulations; \(d\) is the height of the parallelepiped. We focused our analysis on the way which the magnetization curves approximate from \(d\) finite to the characteristic curve of \(d\rightarrow \infty \) . This is the case for which the magnetic field and the order parameter are invariant along \(z\) -direction. For a superconductor of size \(S=9\xi ^2(0)\) we find that the limit below which the system should be considered a real three-dimensional sample when is \(d=8\xi \) .     

Simulation of fatigue crack growth with a cyclic cohesive zone model

Fatigue crack growth is simulated for an elastic solid with a cyclic cohesive zone model (CZM). Material degradation and thus separation follows from the current damage state, which represents the amount of maximum transferable traction across the cohesive zone. The traction–separation relation proposed in the cyclic CZM includes non-linear paths for both un- and reloading. This allows a smooth transition from reversible to damaged state. The exponential traction–separation envelope is controlled by two shape parameters. Moreover, a lower bound for damage evolution is introduced by a local damage dependent endurance limit, which enters the damage evolution equation. The cyclic CZM is applied to mode I fatigue crack growth under \(K_{\mathrm{I}}\) -controlled external loading conditions. The influences of the model parameters with respect to static failure load \(K_{\mathrm{0}}\) , threshold load \(\varDelta K_{\mathrm{th}}\) and Paris parameters \(m, C\) are investigated. The study reveals that the proposed endurance limit formulation is well suited to control the ratio \(\varDelta K_{\mathrm{th}}/K_{\mathrm{0}}\) independent of \(m\) and \(C\) . An identification procedure is suggested to identify the cohesive parameters with the help of Wöhler diagrams and fatigue crack growth rate curves.     

The POLARBEAR-2 Experiment

We present an overview of the design and development of the POLARBEAR-2 experiment. The POLARBEAR-2 experiment is a cosmic microwave background polarimetry experiment, which aims to characterize the small angular scale B-mode signal due to gravitational lensing and search for the large angular scale B-mode signal from inflationary gravitational waves. The experiment will have a 365 mm diameter multi-chroic focal plane filled with 7,588 polarization sensitive antenna-coupled Transition Edge Sensor bolometers and will observe at 95 and 150 GHz. The focal plane is cooled to 250 mK. The bolometers will be read-out by SQUIDs with \(32\times \) frequency domain multiplexing. The experiment will utilize high purity alumina lenses and thermal filters to achieve the required high optical throughput. A continuously rotating, cooled half-wave plate will be used to give stringent control over systematic errors. The experiment is designed to achieve a noise equivalent temperature of 5.7  \(\mu \) K \(\sqrt{s}\) , and this allows us to constrain the signal from the inflationary primordial gravitational corresponding to a tensor-to-scalar ratio of \(r = 0.01\) ( \(2\sigma \) ). POLARBEAR-2 will also be able to put a constraint on the sum of neutrino masses to 90 meV ( \(1\sigma \) ) with POLARBEAR-2 data alone and 65 meV ( \(1\sigma \) ) when combined with the Planck satellite. We plan to start observations in 2014 in the Atacama Desert in Chile.     

Reply: On Role of Symmetries in Kelvin Wave Turbulence

In the Ref. (Lebedev and L’vov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0215-2), this issue, two of us (VVL and VSL) considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic, obtained analytically, is not forbidden, as Kosik and Svistunov (KS) expect by naive reasoning. Here we discuss this problem in additional details and show that theoretical objections by KS, presented in Ref. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0242-z), this issue, are irrelevant and their recent numerical simulation, presented in Ref. (Kozik and Svistunov in arXiv:1007.4927v1, 2010) is hardly convincing. There is neither proof of locality nor any refutation of the possibility of linear asymptotic of interaction vertices in the KS texts, Refs. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0242-z; arXiv:1006.0506v1, 2010). Therefore we can state again that we have no reason to doubt in this asymptote, that results in the L’vov–Nazarenko energy spectrum of Kelvin waves.     

Ternary codes from some reflexive uniform subset graphs

We examine the ternary codes \(C_3(A_i+I)\) from matrices \(A_i+I\) where \(A_i\) is an adjacency matrix of a uniform subset graph \(\Gamma (n,3,i)\) of \(3\) -subsets of a set of size \(n\) with adjacency defined by subsets meeting in \(i\) elements of \(\Omega \) , where \(0 \le i \le 2\) . Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the \(C_3(A_i+I)\) are also examined.     

The Magnetically-Tuned Transition-Edge Sensor

We present the first measurements on the proposed magnetically-tuned superconducting transition-edge sensor and compare the modified resistive transition with the theoretical prediction (Sadleir et al., IEEE Trans App Supercond 23:2101405, 2013). A TES’s resistive transition is customarily characterized in terms of the unitless device parameters \(\alpha \) and \(\beta \) corresponding to the resistive response to changes in temperature and current respectively. We present a new relationship between measured IV quantities (sensor current \(I\) and voltage \(V\) ) and the parameters \(\alpha \) and \(\beta \) and use these relations to confirm we have stably biased a TES with negative \(\beta \) parameter with magnetic tuning. Motivated by access to this new unexplored parameter space, we investigate the conditions for bias stability of a TES taking into account both self and externally applied magnetic fields.     

Four-Channel Current-Biased Kinetic Inductance Detectors Using MgB_2 Nanowires for Sensing Pulsed Laser Irradiation

We recently proposed the idea of a novel sort of superconducting detector, i.e., a current-biased kinetic inductance detector (CB-KID). This detector is different from a current-biased transition edge detector studied previously, and is able to sense a change in kinetic inductance \(L_k\) given by \(L_{k} = \Lambda _{k}l/S = m_{s}l/n_{s}{q_{s}}^{2}S\) ( \(\Lambda _{k}\) ; kinetic inductivity, \(m_s\) ; mass of Cooper pair, \(n_s\) ; density of Cooper pairs, \(q_s\) ; charge of Cooper pair, \(l\) ; length of device, \(S\) ; cross sectional area) under a constant dc bias current \(I_b\) . In the present work, we first extend this idea to construct a multi-channel CB-KIDs array made of 200-nm-thick MgB \(_2\) thin-film meanderline with 3- \(\upmu \) m thin wire. We succeeded in observing clear signals for imaging from the four-channel CB-KIDs at 4 K by irradiating focused pulsed laser. A scanning laser spot can be achieved by an XYZ piezo-driven stage and an optical fiber with an aspheric focused lens. We can see typical signals from all 4 channels at 4 K, and obtain the positional dependence of the signal as the contour in XY plane. Our CB-KIDs can be used as neutron detectors by utilizing energy released from a nuclear reaction between \(^{10}\) B and cold neutron.