Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

Load-Unload Response Ratio and Accelerating Moment/Energy Release Critical Region Scaling and Earthquake Prediction

The main idea of the Load-Unload Response Ratio (LURR) is that when a system is stable, its response to loading corresponds to its response to unloading, whereas when the system is approaching an unstable state, the response to loading and unloading becomes quite different. High LURR values and observations of Accelerating Moment/Energy Release (AMR/AER) prior to large earthquakes have led different research groups to suggest intermediate-term earthquake prediction is possible and imply that the LURR and AMR/AER observations may have a similar physical origin. To study this possibility, we conducted a retrospective examination of several Australian and Chinese earthquakes with magnitudes ranging from 5.0 to 7.9, including Australia's deadly Newcastle earthquake and the devastating Tangshan earthquake. Both LURR values and best-fit power-law time-to-failure functions were computed using data within a range of distances from the epicenter. Like the best-fit power-law fits in AMR/AER, the LURR value was optimal using data within a certain epicentral distance implying a critical region for LURR. Furthermore, LURR critical region size scales with mainshock magnitude and is similar to the AMR/AER critical region size. These results suggest a common physical origin for both the AMR/AER and LURR observations. Further research may provide clues that yield an understanding of this mechanism and help lead to a solid foundation for intermediate-term earthquake prediction.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Finite Boundary Effects in Problem of a Crack Perpendicular to and Terminating at a Bimaterial Interface

In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731-2755) are discussed also.

Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Conical emission by femtosecond pulses with different spectral bandwidths

Conical emission (CE) has been investigated experimentally by laser pulses with different pulse durations and spectral bandwidths. The results show that the overall CE curve will shift as the varying of spectral bandwidth of pump laser pulse. But for pump laser pulses which have same spectral bandwidth but different pulse duration, the CE angles will be same at the spectral region close to the pump wavelength while will be different at the spectral region far away from the pump wavelength. We have also fitted the measured CE angles with X-wave model. The calculated curves and the measured CE curves match reasonably well. The best fits indicate that the group velocity of the filament pulse may be greatly controlled by controlling the spectral bandwidth of pump laser pulse. (C) 2008 Elsevier B.V. All rights reserved.

Effects on the proton production from explosions of hydrogen clusters subjected to intense femtosecond laser fields

The dependence of the maximum and average energies of protons, which were produced in the interaction of an intense laser pulse (similar to 1 x 10(16) W cm(-2), 65 fs) with hydrogen clusters in a gas jet backed up to 80 bar at liquid nitrogen temperature (similar to 80 K), on the backing pressure has been studied. The general trend of the proton energy dependence on the square of the average cluster radius, which is determined by a calibrated Rayleigh scattering measurement, is similar to that described by theory under the single size approximation. Calculations are made to fit the experimental results under a simplified model by taking into account both a log-normal cluster size distribution and the laser intensity attenuation in the interaction volume. A very good agreement between the experimental proton energy spectra and the calculations is obtained in the high- energy part of the proton energy distributions, but a discrepancy of the fits is revealed in the low-energy part at higher backing pressures which are associated with denser flows. A possible mechanism which would be responsible for this discrepancy is discussed. Finally, from the fits, a variation of the cluster size distributions was revealed to be dependent on the gas backing pressure as well as on the evolving time of the gas flow of clusters.

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America

大尺寸Ce：Lu1.6Y0.4SiO5闪烁晶体的生长和光谱特性

采用中频感应提拉法生长出尺寸为Ф60mm×110mm的Ce：Lu1.6Y0.4SiO5（LYSO）晶体,与LSO晶体相比,LYSO晶体的优势是提高了晶体质量、降低了熔点和原料成本等.在室温下测试了LYSO晶体的透过光谱、激发光谱和发射光谱,结果表明Y的加入使LSO晶体的吸收边向短波方向偏移.Ce^3＋的4f^1→5d^1跃迁吸收导致紫外区产生三个吸收带.发射光谱具有Ce^3＋典型的双峰特征,经Gaussian多峰值拟合,双峰395nm和418nm归属于Ce1发光中心,而435nm的发光峰与Ce2发光中心有

Ce：Lu2Si2O7闪烁晶体的结构和光谱特性

采用中频感应提拉法生长出Ce：Lu：Si2O7(Ce：LPS)晶体．通过x射线粉末衍射分析，晶体结构属单斜晶系的C21m空间群·光学显微镜下可观测到晶体的(110)解理．在室温下测试了Ce：LPS晶体的吸收光谱、激发光谱和发射光谱。结果表明，Ce：LPS晶体的吸收峰只有两个，分别位于302和349nm，且与激发峰的位置一致，归因于Ce^3+的4f^1→5d^1跃迁的特征吸收所致．发射光谱具有Ce^3+典型的双峰特征，经Gaussian多峰值拟合，带状谱是由384和407nm两个发射峰叠加而成，且后者的强度

The growth patterns of juvenile and precocious Chinese mitten crabs, Eriocheir sinensis (Decapoda, Grapsidae), stocked in freshwater lakes of China

Stocking experiments with Eriocheir sinensis were conducted in two small, shallow lakes to study its growth pattern in 1994-1997. For the initially immature crabs, carapace width (CW) increases from 21.2 +/- 0.4 mm (mean +/- s.e.) for females and 22.3 +/- 0.5 mm for males in January, to 65.4 +/- 0.5 mm for females and 66.9 +/- 0.6 mm for males in October. There is no significant difference in CW and carapace length (CL), although there is a large difference in body weight (BW) between sexes in every month from January to August when crabs are juvenile, however, there are significant differences in CW, CL. and BW between sexes after September when the crabs become sexually mature. The growth curve from January to October fits a logistic equation and may be expressed as CW = 75.7 (1 + exp (0.914 - 0.011t))(-1) for females, and CW = 77.5 (1 + exp (0.889 - 0.011t))-1 for males, where CW is in mm, t in days. For precocious crabs (reaching maturity by the first autumn, CW does not change much from January to July, which indicates that precocious crabs stop growing. Like juveniles, the precocious crabs show no differences in CW and CL, but do show a statistically significant difference in BW between sexes.

The field emission properties of nonpolar a-plane n-type GaN films grown on nano-patterned sapphire substrates

Si-doped nonpolar a-plane GaN films were grown on nanopatterned sapphire substrates by a low-pressure metal organic chemical vapor deposition (MOCVD) system. The structure, morphology and field emission properties of the sample were studied by means of high-resolution X-ray diffraction (HRXRD), atomic force microscopy (AFM), and field emission measurement. The XRD analysis shows that the sample is a nonpolar a-plane (11 (2) over bar0) GaN film. The field emission measurement shows that the nonpolar GaN films exhibit excellent field emission properties with a threshold emission field of as low as 10 V/mu m at a current density of 0.63 mu A/cm(2), and a high field emission current density of 74 mA/cm(2) at an applied field of 24 V/mu m. Moreover, the Fowler-Nordheirn plot of the sample fits a near linear relation. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Properties of exchange interaction in Yb3Fe5O12 under extreme conditions

In Yb3Fe5O12, the exchange effective field can be expressed as H-eff = -lambda center dot center dot center dot M-Fe = -lambda chi(eff)center dot center dot center dot H-e = -gamma center dot center dot center dot H-e where gamma is named as the exchange field parameter and H-e is the external magnetic field. Then, in this paper, by the discussions on the characteristics of the exchange field parameter gamma, the properties of exchange interaction in ytterbium iron garnet (Yb3Fe5O12) are analyzed under extreme conditions (high magnetic fields and low temperatures). Our theory suggests that the exchange field parameter gamma is the function of the temperatures under different external magnetic fields, and gamma = a+b center dot center dot center dot T+c center dot center dot center dot T-2, where the coefficients a, b, c are associated with the external magnetic fields and the magnetized directions. Thus, the temperature-dependence, field-dependence and anisotropic characteristics of the exchange interaction in Yb3Fe5O12 are revealed. Also, excellent fits to the available experiments are obtained. (C) 2009 Elsevier B.V. All rights reserved.

Characterization of silicon carbide thin films and their use in colour sensor

A series of hydrogenated amorphous silicon carbide (a-Si1-xCx:H) films were prepared by plasma-enhanced chemical vapour deposition (PECVD) using a gas mixture of silane, methane, and hydrogen as the reactive source. The previous results show that a high excitation frequency, together with a high hydrogen dilution ratio of the reactive gases, allow an easier incorporation of the carbon atoms into the silicon-rich a-Si1-xCx:H film, widen the valence controllability. The data show that films with optical gaps ranging from about 1.9 to 3.6 eV could be produced. In this work the influence of the hydrogen dilution ratio of the reactive gases on the a-Si1-xCx:H film properties was investigated. The microstuctural and photoelectronic properties of the silicon carbide films were characterized by Rutherford backscattering spectrometry (RBS), elastic recoil detection analysis (ERDA), and FT-IR spectrometry. The results show that a higher hydrogen dilution ratio enhances the incorporation of silicon atoms in the amorphous carbon matrix for carbon-rich a-Si1-xCx:H films. One pin structure was prepared by using the a-Si1-xCx:H film as the intrinsic layer. The light spectral response shows that this structure fits the requirement for the top junction of colour sensor. (c) 2004 Elsevier B.V. All rights reserved.