The formation and growth of <Emphasis Type="BoldItalic">echelon</Emphasis> cracks in brittle materials

Cracks subjected to mode III shear loading fragment into numerous daughter cracks. The formation of such patterns—called echelon cracks—is explored in this work through a phase-field model of fracture. It is shown that the phase field method predicts that a crack subjected to mixed-mode I \(+\) III grows along the extension of the parent crack plane, contrary to experimental observations. In order to replicate the experimentally observed fragmentation of crack fronts, defects are introduced in the vicinity of the crack front to trigger fragmentation of the front; examples of successful formation and growth of these echelon cracks is demonstrated in this paper. It is also shown that the intrinsic scale parameter in the phase field model must be very small in comparison to the scale of formation of the echelon cracks.     

Fracture of elastomers under static mixed mode: the strain-energy-density factor

This work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J _c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J _c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S ^min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction.     

Microstructural and surface morphological studies on Co doped ZnS diluted magnetic semiconductor thin films

Microstructural and surface morphological studies of Co (2.5%) doped ZnS thin films deposited at different substrate temperatures (T_S) of 200, 400 and 600 °C by means of pulsed laser deposition are presented. The deposited films are in wurtzite-hexagonal crystal structure as confirmed by X-ray diffraction and Raman spectroscopy techniques. The films deposited at higher T_S show columnar morphology, as evidence by transmission electron microscopy measurements. Images of the surface topography have been taken by atomic force microscopy (AFM) for the film deposited at different T_S. The film deposited at T_S of 200 °C shows cone-like structures while deposited at T_S of 400 and 600 °C show columnar structures. A fractal analysis has been performed on AFM images to understand the microstructure and surface morphology of thin film at different T_S. Fractal analysis also reveals the morphological changes in the film with increasing T_S. The observed ferromagnetism is correlated with columnar growth of the film which can be used as diluted magnetic semiconductor for spintronic applications.     

Experimental Study of the Thermodynamic Properties of Diethyl Ether (DEE) at Saturation

The isochoric heat capacities \({({C_{V1}^{\prime}} ,{C_{V1}^{\prime\prime}},{C_{V2}^{\prime}},{C_{V2}^{\prime\prime}})}\), saturation densities (\({\rho _{\rm S}^{\prime}}\) and \(({\rho_{\rm S}^{\prime\prime})}\)), vapor pressures (P _S), thermal-pressure coefficients \({\gamma_V=\left({\partial P/\partial T}\right)_V}\), and first temperature derivatives of the vapor pressure γ _S = (dP _S/dT) of diethyl ether (DEE) on the liquid–gas coexistence curve near the critical point have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic piezo-calorimeter. The measurements of \({({C_{V1}^{\prime}} ,{C_{V1}^{\prime\prime}},{C_{V2}^{\prime}},{C_{V2}^{\prime\prime}})}\) were made in the liquid and vapor one- and two-phase regions along the coexistence curve. The calorimeter was additionally supplied with a calibrated extensometer to accurately and simultaneously measure the PVT, C _V VT, and thermal-pressure coefficient, γ _V , along the saturation curve. The measurements were carried out in the temperature range from 416 K to 466.845 K (the critical temperature) for 17 liquid and vapor densities from 212.6 kg · m^?3 to 534.6 kg · m^?3. The quasi-static thermo- (reading of PRT, T ? τ plot) and baro-gram (readings of the tensotransducer, P ? τ plot) techniques were used to accurately measure the phase-transition parameters (P _S ,ρ _S ,T _S) and γ _V . The total experimental uncertainty of density (ρ _S), pressure (P _S), temperature (T _S), isochoric heat capacities \({({C_{V1}^{\prime}} ,{C_{V1}^{\prime\prime}},{C_{V2}^{\prime}},{C_{V2}^{\prime\prime}})}\), and thermal-pressure coefficient, γ _V , were estimated to be 0.02 % to 0.05 %, 0.05 %, 15 mK, 2 % to 3 %, and 0.12 % to 1.5 %, respectively. The measured values of saturated caloric \({({C_{V1}^{\prime}} ,{C_{V1}^{\prime\prime}},{C_{V2}^{\prime}},{C_{V2}^{\prime\prime}})}\) and saturated thermal (P _S, ρ _S, T _S) properties were used to calculate other derived thermodynamic properties C _P , C _S, W, K _T , P _int, ΔH _vap, and \({\left({\partial V/\partial T}\right)_P^{\prime}}\) of DEE near the critical point. The second temperature derivatives of the vapor pressure, (d² P _S/dT ²), and chemical potential, (d² μ/dT ²), were also calculated directly from the measured one- and two-phase liquid and vapor isochoric heat capacities \({({C_{V1}^{\prime}} ,{C_{V1}^{\prime\prime}},{C_{V2}^{\prime}},{C_{V2}^{\prime\prime}})}\) near the critical point. The derived values of (d² P _S/dT ²) from calorimetric measurements were compared with values calculated from vapor–pressure equations. The measured and derived thermodynamic properties of DEE near the critical point were interpreted in terms of the “complete scaling” theory of critical phenomena. In particular, the effect of a Yang–Yang anomaly of strength R _μ on the coexistence-curve diameter behavior near the critical point was studied. Extended scaling-type equations for the measured properties P _S (T), ρ _S (T), and \({({C_{V1}^{\prime}} ,{C_{V1}^{\prime\prime}},{C_{V2}^{\prime}},{C_{V2}^{\prime\prime}})}\) as a function of temperature were developed.     

Copper-containing glass polyalkenoate cements based on SiO<Subscript>2</Subscript>–ZnO–CaO–SrO–P<Subscript>2</Subscript>O<Subscript>5</Subscript> glasses: glass characterization,physical and antibacterial properties

A series of copper (Cu)-containing glasses were synthesized and incorporated into a SiO₂–ZnO–CaO–SrO–P₂O₅-based glass system. Additions of 6 and 12 mol% CuO retained the amorphous character, and glasses were processed to possess similar particle sizes and surface areas. Glass characterization using X-ray photoelectron spectroscopy and magic angle spinning nuclear magnetic resonance determined that the addition of 12 mol% CuO increased the fraction of Q⁴-speciation and the concentration of bridging oxygens. Each glass presented solubility profiles for the release of Si⁴⁺ (18–31 mg/L), Ca²⁺ (13–16 mg/L), Zn²⁺ (<3 mg/L) and Sr²⁺(2–10 mg/L); however, no Cu²⁺ or P⁵⁺ were released. Cu-GPCs were formulated, and the working time (T _w) and setting times (T _s) were found to be dependent on both polyacrylic acid concentration and CuO addition. The mechanical properties, i.e. the compressive strength (18–30 MPa) and the adhesive bond strength (0.79–1.32 MPa), were relative low which is likely due to the glass structure. Antibacterial properties were evaluated in E. coli (4 mm), S. epidermidis (10 mm), S. aureus (UMAS-1) and vancomycin resistant S. aureus (2 mm) and presented antibacterial effects in each microbe tested.     

Magnetic,magnetocaloric properties,and critical behavior in a layered perovskite La<Subscript>1.4</Subscript>(Sr<Subscript>0.95</Subscript>Ca<Subscript>0.05</Subscript>)<Subscript>1.6</Subscript>Mn<Subscript>2</Subscript>O<Subscript>7</Subscript>

We report the results of magnetic, magnetocaloric properties, and critical behavior investigation of the double-layered perovskite manganite La_1.4(Sr_0.95Ca_0.05)_1.6Mn₂O₇. The compounds exhibits a paramagnetic (PM) to ferromagnetic (FM) transition at the Curie temperature T _C = 248 K, a Neel transition at T _N = 180 K, and a spin glass behavior below 150 K. To probe the magnetic interactions responsible for the magnetic transitions, we performed a critical exponent analysis in the vicinity of the FM–PM transition range. Magnetic entropy change (??S _M) was estimated from isothermal magnetization data. The critical exponents β and γ, determined by analyzing the Arrott plots, are found to be T _C = 248 K, β = 0.594, γ = 1.048, and δ = 2.764. These values for the critical exponents are close to the mean-field values. In order to estimate the spontaneous magnetization M _S(T) at a given temperature, we use a process based on the analysis, in the mean-field theory, of the magnetic entropy change (??S _M) versus the magnetization data. An excellent agreement is found between the spontaneous magnetization determined from the entropy change [(??S _M) vs. M ²] and the classical extrapolation from the Arrott curves (µ₀H/M vs. M ²), thus confirming that the magnetic entropy is a valid approach to estimate the spontaneous magnetization in this system and in other compounds as well.     

Optical properties of silver containing As–S–Se thin films

The As₃₃S_{67- y} Se _y , where y = 0, 16.75, 33.5, 50.25 and 67, amorphous thin films were prepared by vacuum thermal evaporation technique. Range of the silver content dissoluted in films was x = 0 – 25 at. %. The refractive index increase with increasing silver and selenium content. The difference of the refractive index (Δn) between undoped and silver doped films was ～ 0.4 and between As₃₃S₆₇ and As₃₃Se₆₇ was films ～ 0.42. The values of non-linear refractive index grow with increasing silver and selenium content. The difference of optical bandgap, ΔE _g ^opt , between undoped As₃₃S₆₇ and fully dopped films with Ag and Se was ～ 1 eV.     

Novel nanohybrid biocatalyst: application in the kinetic resolution of secondary alcohols

In this work, a nanohybrid material was developed and used for the first time to the kinetic resolution of secondary alcohols as rac-indanol, rac-1-phenylethanol (rac-1), rac-1-(3-bromophenyl)-1-ethanol (rac-2) and rac-1-(3-methylphenyl)-1-ethanol (rac-3). Chiral indanol is used as a precursor intermediate for the synthesis of enantiomeric drugs, such as (+)-Indatraline, Irindalone, Indinavir, (+)-Sertraline and Rasagiline mesylate. Chiral 1-phenylethanol is used as an ophthalmic preservative, a solvatochromic dye and an inhibitor of cholesterol absorption and as a mild floral fragrance. For this purpose, the ultrasound irradiation was used to couple APTES on the superparamagnetic nanoparticles surface. Then, the system was activated with glutaraldehyde and used as a support for immobilization of lipase from Pseudomonas fluorescens. Thermal stability analysis was performed in buffer and hexane, showing an excellent stability in buffer solution at 60 °C, holding 72% of the initial activity, even after 7 h. In hexane (40 °C), the immobilized enzyme retained 100% of activity with 693 min of half-life time at 50 °C. The high thermal stability is mainly related to the covalent bonding between enzymes and support. Immobilized lipase on magnetic support proved to be a robust biocatalyst in the kinetic resolution, leading to (S)-indanol with high selectivity (e.e.?>?99%, E?>?200) in 1.75 h at 50 °C, being reused five times without significant loss of the activity and selectivity. The kinetic resolution of rac-1, via acetylation reaction, catalyzed by lipase from Pseudomonas fluorescens immobilized on magnetic support, led to (R)-acetate with enantiomeric excess?>?99% and to the remaining (S)-alcohol with enantiomeric excess of 94%, conversion of 49% and E?>?200, after 48 h of reaction at 40 °C. Under the same reactions conditions, rac-2 and rac-3 were slightly less reactive, since the corresponding (R)-acetates were obtained with conversion values of 44%, but with high enantioselectivity (enantiomeric excesses?>?99% and E values?>?200). These results correspond to an important step in heterogeneous catalysis due to the ability to obtain important precursors for the synthesis of enantiomerically pure chiral drugs and other bioactive substances.     

How much is a quantum controller controlled by the controlled system?

We consider unitary transformations on a bipartite system A × B. To what extent entails the ability to transmit information from A to B the ability to transfer information in the converse direction? We prove a dimension-dependent lower bound on the classical channel capacity C(A ← B) in terms of the capacity C(A → B) for the case that the bipartite unitary operation consists of controlled local unitaries on B conditioned on basis states on A. If the local operations are given by the regular representation of a finite group G we have C(A → B) = log |G| and C(A ← B) = log N where N is the sum over the degrees of all inequivalent representations. Hence the information deficit C(A → B) ? C(A ← B) between the forward and the backward capacity depends on the “non-abelianness” of the control group. For regular representations, the ratio between backward and forward capacities cannot be smaller than 1/2. The symmetric group S _n reaches this bound asymptotically. However, for the general case (without group structure) all bounds must depend on the dimensions since it is known that the ratio can tend to zero. Our results can be interpreted as statements on the strength of the inevitable backaction of a quantum system on its controller.     

Effect of Low-Cycle Fatigue on Fracture Mechanics Parameters According to Speckle Interferometry

Evolution of parameters of fracture mechanics at various stages of low-cycle damage is studied. The developed approach is based on elaboration of optical interference measurements of the deformation response to a small crack length increment. Three sequential symmetrical notches simulate the fatigue crack growth process across the cumulative fatigue damage zone caused by low-cycle fatigue. The values of tangential components of displacement that are measured at several points on cut edges by electronic speckle interferometry are initial experimental information. The coefficients of stress intensity (SIC) and T strains are determined on the basis of the Williams solution. Values of opening and coefficients of stress intensity (SIC) and T strains for cracks of different length with fixed values of preloading cycles N_c equal 0, 100, 1000, 1800, 2500, and 3300 are obtained. The dependences of the parameters of fracture mechanics for cracks of the fixed length on N_c are constructed.     

Study of the Magnetic Properties of Ni/Ag Superlattice

Thin multilayer films of alternating ultrathin Ni and Ag layers (L(Ni)=11,15,30 Å, bulk and \(L(\mathrm{Ag})=50~{\AA})\) have been prepared by evaporation in ultrahigh vacuum under controlled conditions and have been studied by the magnetic measurements. The critical temperature T _C is studied as a function of the surface exchange interaction (J _S). The dependence of T _C on the thickness L of the film has been investigated. A critical value of the surface exchange interaction in the film, above which the surface magnetism appears, is obtained. The shift of the critical temperature T _C(L) from the bulk value \([\frac{T_{\mathrm{C}}(\infty )}{T_{\mathrm{C}}(L)}-1]\) can be described by a power law L ^?λ , where \(\lambda =\frac{1}{\nu_{\mathrm{b}}}\) is the inverse of the correlation length’s exponent. The effective critical exponent associated with the magnetization M(β) is deduced for different thicknesses of Ni layers, and the thickness L(Ag) was being kept constant at 50 Å.     

Comparative Experimental and Density Functional Theory (<Emphasis Type="Italic">DFT</Emphasis>) Study of the Physical Properties of MgB<Subscript>2</Subscript> and AlB<Subscript>2</Subscript>

In the present study, we report an intercomparison of various physical and electronic properties of MgB₂ and AlB₂. In particular, the results of phase formation, resistivity ρ(T), thermoelectric power S(T), magnetization M(T), heat capacity (C _P ), and electronic band structure are reported. The original stretched hexagonal lattice with a=3.083 Å, and c=3.524 Å of MgB₂ shrinks in c-direction for AlB₂ with a=3.006 Å, and c=3.254 Å. The resistivity ρ(T), thermoelectric power S(T) and magnetization M(T) measurements exhibited superconductivity at 39 K for MgB₂. Superconductivity is not observed for AlB₂. Interestingly, the sign of S(T) is +ve for MgB₂ the same is ?ve for AlB₂. This is consistent with our band structure plots. We fitted the experimental specific heat of MgB₂ to Debye–Einstein model and estimated the value of Debye temperature (Θ _D) and Sommerfeld constant (γ) for electronic specific heat. Further, from γ, the electronic density of states (DOS) at Fermi level N(E _F) is calculated. From the ratio of experimental N(E _F) and the one being calculated from DFT, we obtained value of λ to be 1.84, thus placing MgB₂ in the strong coupling BCS category. The electronic specific heat of MgB₂ is also fitted below T _c using α-model and found that it is a two gap superconductor. The calculated values of two gaps are in good agreement with earlier reports. Our results clearly demonstrate that the superconductivity of MgB₂ is due to very large phonon contribution from its stretched lattice. The same two effects are obviously missing in AlB₂, and hence it is not superconducting. DFT calculations demonstrated that for MgB₂, the majority of states come from σ and π 2p states of boron on the other hand σ band at Fermi level for AlB₂ is absent. This leads to a weak electron phonon coupling and also to hole deficiency as π bands are known to be of electron type, and hence obviously the AlB₂ is not superconducting. The DFT calculations are consistent with the measured physical properties of the studied borides, i.e., MgB₂ and AlB₂.     

Influence of hydrogen and frequency on fatigue crack growth behavior of Cr-Mo steel

Fatigue tests on Cr-Mo steel quenched at 860°C and tempered at 580°C were carried out under the frequencies of 0.2, 2, and 20 Hz with specimens containing a small artificial hole. An additional test in which the test frequency was alternately switched between 0.02 and 2 Hz was carried out. Hydrogen charging to the specimens was carried out by an immersion method. The fatigue life of the hydrogen-charged specimens remarkably decreased in comparison with that of the uncharged specimens. The fatigue crack growth rate da/dN increased with decreasing the test frequency f. The acceleration of da/dN saturated at \({\Delta K\,<\,17\,{\rm MPa}\sqrt{m}}\) for f ≤ 2 Hz. The presence of the upper bound for the fatigue crack growth acceleration was found with respect to the effects of hydrogen and test frequency in a hydrogen environment. The test switching the frequency between 0.02 and 2 Hz resulted the difference in fatigue crack growth morphology which is presumed to be caused by the difference in hydrogen concentration in the vicinity of crack tip. The particular crack morphology under the low test frequency with hydrogen was the localization of the slip around the crack tip and the linearization of the crack growth path. The hydrogen-enhanced striation formation model which was proposed to explain the effect of hydrogen on the fatigue crack growth for an austenitic stainless steel and low carbon steel can be applied also to the quenched and tempered Cr-Mo steel in this study.     

Determination of the resistance-curve in <Emphasis Type="Italic">Eucalyptus globulus</Emphasis> through double cantilever beam tests

The prediction of the fracture behaviour through reliable and practical criteria in the design of structural timber elements and connections has become of great importance and demands a proper fracture characterization of the material. Eucalyptus globulus Labill is envisioned as a hardwood species with great potential for high performance structural purposes because of its major mechanical and durability properties, being so far mainly used in paper industry. Experimental research on the identification of the resistance curves to derive the critical strain energy release rate in Eucalyptus globulus L. under pure mode I and RL crack propagation system is performed by means of Double Cantilever Beam tests. Three different data reduction schemes are compared: the Modified Experimental Compliance Method; and two approaches of the Compliance Based Beam Method. These methods take into account the non negligible damage mechanisms at the fracture process zone and have the advantage of being based exclusively on the specimen compliance following an equivalent crack concept, for which crack length monitoring during testing is not required. The Compliance Based Beam Method turns out to be the most appropriate data reduction scheme to obtain the critical energy release rate in eucalyptus because of its simplicity. Concerning this, a high average value of 720 J/m² was obtained confirming Eucalyptus globulus L. as a promising hardwood species for timber structural design.     

Fracture in three-dimensional random fuse model: recent advances through high-performance computing

The paper presents the state-of-the-art algorithmic developments for simulating the fracture of disordered quasi-brittle materials using discrete lattice systems. Large scale simulations are often required to obtain accurate scaling laws; however, due to computational complexity, the simulations using the traditional algorithms were limited to small system sizes. In our earlier work, we have developed two algorithms: a multiple sparse Cholesky downdating scheme for simulating 2D random fuse model systems, and a block-circulant preconditioner for simulating 3D random fuse model systems. Using these algorithms, we were able to simulate fracture of largest ever lattice system sizes (L = 1024 in 2D, and L = 64 in 3D) with extensive statistical sampling. Our recent massively parallel simulations on 1024 processors of Cray-XT3 and IBM Blue-Gene/L have further enabled us to explore fracture of 3D lattice systems of size L =  128, which is a significant computational achievement. Based on these large-scale simulations, we analyze the scaling of crack surface roughness.     

Hardness and fracture toughness of thermoelectric La<Subscript>3−<Emphasis Type="Italic">x</Emphasis></Subscript>Te<Subscript>4</Subscript>

Lanthanum telluride (La_3?x Te₄) is a state-of-the-art n-type high temperature thermoelectric material that behaves as a weak and brittle ceramic. Vickers microindentation hardness testing was explored as a rapid analysis technique to characterize the mechanical properties of this material. An indentation size effect was observed with hardness values ranging from 439 ± 31 kgf/mm² (0.01 kgf/10 s contact time) to 335 ± 6 kgf/mm² (0.5 kgf/10 s contact time). The Vickers indentation fracture toughness, K _VIF, based on measurements of crack lengths emanating from the corners of the Vickers indents was 0.70 ± 0.06 MPa m^1/2.     

Synthesis of highly active cobalt molybdenum sulfide nanosheets by a one-step hydrothermal method for use in dye-sensitized solar cells

Cobalt molybdenum sulfide (Co_(1 ? x)Mo_xS₂, x = 2/3, 1/2, 1/3) nanocomposites with hierarchical nanosheet structure are prepared on the flexible titanium foils by a facile hydrothermal method and used as the counter electrode (CE) materials for the dye-sensitized solar cells (DSSCs). It is interesting that the first produced MoS₂ nanosheets play an important role as the template for the continuously growing of the Co_(1 ? x)Mo _x S₂ nanosheets. Otherwise, it will grow up into octahedral CoS₂ in the synthesis system without the Mo source. The Co_(1 ? x)Mo _x S₂ CE demonstrates higher catalytic activity for the reduction of triiodide to iodide than that of the MoS_2, and CoS₂ CEs due to the Co_(1 ? x)Mo _x S₂ CE with thinner hierarchical nanosheets offers more catalytic active sites and exhibits additional synergistic effect of the combination of Mo and Co. The DSSC with Co_1/2Mo_1/2S₂ CE achieves a photovoltaic conversion efficiency of 9.16%, which is higher than that of the MoS₂ (8.27%) and CoS₂ (7.18%) CEs and even higher than that of the platinum CE (8.49%) under full sunlight illumination (100 mW cm^?2, AM1.5 G).     

A new niobate-based CaO–2CuO–Nb<Subscript>2</Subscript>O<Subscript>5</Subscript> microwave dielectric ceramic composite for LTCC applications

A novel CaO–2CuO–Nb₂O₅ (CCN) ceramic composite was prepared by the solid-state reaction method in the temperature range of 810–890 °C. Typically, the CCN sintered at 870 °C exhibited the excellent microwave properties of ε _r ?=?15.7, Q?×?f?=?28,700 GHz, τ _f = ? 38.4 ppm/°C. The τ _f of CCN was turned to be near zero by adding TiO₂, while the ε _r increased slightly and the Q?×?f decreased. The 0.91CCN–0.09TiO₂ ceramic sintered at 920 °C showed modified properties of ε _r ?=?16.9, Q?×?f?=?21,500 GHz, τ _f = ? 1.6 ppm/°C, which shows potential in LTCC applications.     

Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, \(K_{\mathrm{IE},}\) was evaluated numerically as \(K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)\), where \(\upmu \) is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, \(K_{\mathrm{IE,d}}\), was observed to vary as \(K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}\). Consistent with the FEM simulation, experiments conducted using \(12\,\upmu \hbox {m}\) thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of \(\ge \) \(1.85\times 10^{9}\,\hbox {A/m}^{2}\) for \(a/w = 0.5\). Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.     

Magnetic Studies in Sputtered Ni/Ti Multilayers

Magnetic properties of Ni/Ti multilayers, prepared by the DC triode sputtering method, have been studied by magnetic measurements. Both metal layers are crystalline with a (111) fiber structure when they are thicker than 20 Å. The magnetization decreases with a decrease in Ni layer thickness t _Ni and the analysis of the results at 5 K indicates the presence of a dead Ni layer about 13 Å thick. The effective anisotropy K _eff of Ni/Ti multilayers is obtained using a torque magnetometer. Spin-wave theory has been used to explain the temperature dependence of the magnetization. Approximate values for bulk exchange interaction J _b, surface exchange interaction J _S and interlayer coupling strength J _I for various Ni layer thicknesses have been obtained.