Thermoplastic damage of a stretched plane caused by a moving energy source

A thermoplastic stress and strain calculation is made to analyze the energy distribution around an energy source traveling in a prestretched panel. The technique of finite element is applied such that the motion of the energy source is discretized into a finite number of time increments. Remeshing of the grid pattern is carried out for every time increment.The energy source may represent a welding torch or laser beam with a high local intensity that causes the material to deform beyond its elastic limit and experience permanent damage by evaporation. This reduces the local stiffness and can lead to global instability. The failure analysis is based on the application of the strain energy density theory which is into the incremental theory of thermoplasticity. The specific example involves examining the experimental data of a 7075-T651 aluminum panel subjected to tensile loading. The energy source is assumed to have a finite radius and travels along the line of symmetry being normal to the direction of applied tension. The possible failure location is predicted for each time increment by analyzing the fluctuation of the local strain energy density field. A critical point corresponding to incipient fracture is found. The panel has a width of 45.72 cm and length of 55.88 cm. The prediction is consistent with the experimental observation.     

The synthesis of 2,3-dinorprostacyclin metabolites—a new approach to spirolactone hemiacetals

The major human urinary metabolites of prostacyclin and 6-keto-PGF₁ have been synthesized by a direct route, involving three-carbon homologation of bicyclic lactone intermediates and spontaneous spirolactonization of the products. The fact that these 2,3-dinor-6-oxo metabolites exist almost exclusively as spirolactone hemiacetals under acidic conditions (pH 5 and below) may explain the reported difficulties in derivatizing samples of biological origin. Several 19,19,20,20-d₄ metabolites have also been synthesized.     

Concurrence of mass and energy density for conservative and dissipative systems

The falling body velocity is 00000 when mass and energy are interdependent. The overestimated 00000 prevails when mass and energy are separately independent. The falling time is found to be greater by a factor of 00000. A consistent account of the laws of motion from Galileo to Newton is made possible by using E = mv ² for conservative and dissipative systems. By the same token, the equivalence of energy and mass can be used for the mathematical assessment of gravitational waves at any velocities and not just at the speed of light. The personalized units should be replaced by the “energy density unit” to avoid ambiguities. The key step is the application of the Hookean “force” in conjunction with the work done as energy. The equivalence of mass and energy at any velocity were derived by using Ideomechanics, which is a mathematized verion of I-Ching. Gravitational waves are intimately related to the entanglement of multi-atom space-time.     

Axisymmetric elastodynamic response from normal and radial impact of layered composites with embedded penny-shaped cracks

A method is developed for the dynamic stress analysis of a layered composite containing an embedded penny-shaped crack and subjected to normal and radial impact. Quantitatively, the timedependent stresses near the crack border can be described by the dynamic stress intensity factors. Their magnitude depends on time, on the material properties of the composite and on the relative size of the crack compared to the composite local geometry. Results obtained show that, for the same material properties and geometry of the composite, the dynamic stress intensity factors for an embedded (pennyshaped) crack reach their peak values within a shorter period of time and with a lower magnitude than the corresponding dynamic stress factors for a through-crack.     

Growth of crack caused by temperature gradients with change in surface insulation

This work is concerned with thermoelastic stress and failure analysis of a centrally cracked panel subjected to temperature gradients while the insulation on the crack surface is varied. The corresponding temperature and thermoelastic stress fields are obtained by application of the finite element method. According to the strain energy density criterion, the crack grows incrementally when the maximum of the minimum strain energy density function reaches a critical value for a given material. Crack growth resistance curves involving plots of the strain energy density factor S versus the half crack length a are developed for crack surfaces with varying degree of heat resistance. The resulting curves are straight lines satisfying the condition dS/da = const. and useful for determining combined influence of thermal loading and structural geometry that lead to global instability.     

Mesofracture mechanics: a necessary link

Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates different characteristic lengths for describing different geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the definitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimplified. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two different scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full field solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No definite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The specification of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be first identified with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully, “mesofracture mechanics” could serve as the link to bring macrofracture mechanics closer to microfracture mechanics.     

Dicopper complexes catalyzed coupling/cyclization of 2‐bromobenzoic acids with amidines leading to quinazolinones

Dicopper(I) complexes {Cu₂(bpnp)(CH₃CN)₄}(PF₆)₂] ( 2 ), [{Cu₂(bpnp)(CH₃CN)₄}(BAr₄^F)₂] ( 3 ) and [Cu₂(bpnp)Cl₂] ( 4 ) were prepared from the complexation of [Cu(CH₃CN)₄](PF₆) with 2,7‐bis(2‐pyridyl)‐1,8‐naphthyridine (bpnp) followed by anion metathesis and treatment of chloride sequentially. The X‐ray structural analysis of 4 indicates the molecule to have a twofold axis passing through the Cu₂Cl₂ core, which has the shape of a butterfly, and that the Cu atom is tetrahedrally coordinated with in a Cl₂N₂ donor set. In preliminary experiments 2 was found to be an effective catalyst in the coupling/cyclization of 2‐bromobenzoic acids with amidines, providing the corresponding quinazolinones in good yields. Copyright © 2014 John Wiley & Sons, Ltd.     

Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation

The three-dimensional field equations can in general be regarded as the sum of in-plane and out-of-plane deformation. The method for the general solution is the same for both although the boundary conditions could make a difference. If a particular solution in exact form may be found for the out-of-plane case, the same may not hold for the in-plane case. Hence, there may be a good reason for discussing the out-of-plane crack problem in certain situations that should be emphasized. Otherwise, the reason may lie in the exploration of possible application to the in-plane problem, a direct solution of which would have required a considerable effort. The contribution of this work rests on the new findings for the case of poling parallel to the crack in a magnetoelectroelastic composite made of BaTiO₃–CoFe₂O₄. The inclusions are BaTiO₃ and the matrix is CoFe₂O₄. Several new features of the solution were not expected before hand.Unlike in-plane deformation with poling normal to the crack plane, maximum crack growth enhancement is found to occur in the BaTiO₃–CoFe₂O₄ composite for a volume fraction of about 50%. Crack retardation increases as the volume fraction of the inclusions either increase or decrease. The occurrence of this same phenomenon in Mode I and II remain to be investigated. Poling direction of magnetic and electric field for line defects can have a significant effect on crack growth for magnetoelectroelastic materials. The foregoing conclusions are based on predictions made from the strain energy density criterion.