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.

A new hardening law for strain gradient plasticity

A new hardening law of the strain gradient theory is proposed in this paper, which retains the essential structure of the incremental version of conventional J(2) deformation theory and obeys thermodynamic restrictions. The key feature of the new proposal is that the term of strain gradient plasticity is represented as an internal variable to increase the tangent modulus. This feature which is in contrast to several proposed theories, allows the problem of incremental equilibrium equations to be stated without higher-order stress, higher-order strain rates or extra boundary conditions. The general idea is presented and compared with the theory given by Fleck and Hutchinson (Adv. in Appl. Mech. (1997) 295). The new hardening law is demonstrated by two experimental tests i.e. thin wire torsion and ultra-thin beam bending tests. The present theoretical results agree well with the experiment results.

Gal(1-x)Mn(1-x)Sb Grown on GaSb with Mass-Analyzed Low-Energy Dual Ion Beam Deposition

The Ga1-xMnxSb samples were fabricated by the implantation of Mn ions into GaSb (1 0 0) substrate with mass-analyzed low-energy dual ion beam deposition system, and post-annealing. Auger electron spectroscopy depth profile of the Ga1-xMnxSb samples showed

Electron Beam Surface Remelting of AISI D2 Cold-Worked Die Steel

Electron beam surface remelting has been carried out on AISI D2 cold-worked die steel. The microstructure and hardening behavior of the electron beam surface remelted AISI D2 cold-worked die steel have been studied by means of optical microscopy and Vickers hardness testing. It was found that AISI D2 steel can be successfully surface hardened by electron beam surface remelting. This surface hardening effect can be attributed to microstructural refinement following electron beam surface remelting. (C) 2002 Elsevier Science B.V. All rights reserved.

Laminar Plasma Spraying of Metal Wire in Atmosphere

利用层流等离子体射流，以普通工程铁丝为喷涂材料，在Q235基体表面制备金属涂层，并利用喷涂系统的参数可调性研究工艺参数对涂层质量的影响。结果表明，利用层流等离子体射流喷涂可以得到具有典型层状结构、氧化较少的致密涂层。

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.

Numerical Simulation on the Micro-Scale Bending Induced by Pulsed Laser Beam

利用自行研制的含热传导、冲击动力学大、变形有限元程序,模拟了小尺寸梁在脉冲激光加热条件下的变形过程。在此基础上,利用商用程序模拟了冷却及残余应力的产生,研究了激光参数（强度及分布）等对于微弯曲的影响。数值模拟结果与文献中的实验观察相吻合。

Static Study of Cantilever Beam stiction under Electrostatic Force Influence

The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beamsolutions of the loads with different distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation offers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length offers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The effects of dielectric layer thickness and electrostatic voltage on the cantilever beamstiction are studied.The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.

Electron Beam Surface Treatment. Part II: Microstructure Evolution of Stainless Steel and Aluminum Alloy During Electron Beam Rapid Solidification

Surface rapid solidification microstructures of AISI 321 austenitic stainless steel and 2024 aluminum alloy have been investigated by electron beam remelting process and optical microscopy observation. It is indicated that the morphologies of the melted layer of both stainless steel and aluminum alloy change dramatically compared to the original materials. Also, the microstructures were greatly refined after the electron beam irradiation.

Investigation of Mn-Implanted n-Si by Low-Energy Ion Beam Deposition

Mn ions were implanted to n-type Si(0 0 1) single crystal by low-energy ion beam deposition technique with an energy of 1000 eV and a dose of 7.5 x 10^{17} cm^{-2}. The samples were held at room temperature and at 300degreesC during implantation. Auger electron spectroscopy depth profiles of samples indicate that the Mn ions reach deeper in the sample implanted at 300degreesC than in the sample implanted at room temperature. X-ray diffraction measurements show that the structure of the sample implanted at room temperature is amorphous while that of the sample implanted at 300degreesC is crystallized. There are no new phases found except silicon both in the two samples. Atomic force microscopy images of samples indicate that the sample implanted at 300degreesC has island-like humps that cover the sample surface while there is no such kind of characteristic in the sample implanted at room temperature. The magnetic properties of samples were investigated by alternating gradient magnetometer (AGM). The sample implanted at 300degreesC shows ferromagnetic behavior at room temperature.

Thermal fracture characteristics induced by laser beam

The damage mechanism of a cracked material due to laser beam thermal shock is an important problem when the interactions of high power laser beam with materials are studied. The transient thermal stress intensity factors (TSIFs) for a center crack in an infinite plate subjected to laser beam thermal shock are investigated. When the crack is in the heat affected zone, the compressive thermal stress causes the crack surface to come into contact with each other over a certain contact length, but the high tensile stresses around the crack tip tend to open the crack. In this case, the problem may be treated as a pair of embedded cracks problem with a smooth closure condition of the center crack. The TSIFs and the crack contact lengths are calculated with different laser beam spatial shapes. The TSIFs induced by thermal shock are in marked different from those induced by general mechanical loading.

Modified Generalized Beam Lattice Model Associated With Fracture Of Reinforced Fiber/Particle Composites

Lattice-type model can simulate in a straightforward manner heterogeneous brittle media. Mohr-Coulomb failure criterion has recently been involved into the generalized beam (GB) lattice model, and as a result, numerical experiments on concrete under various loading conditions can be conducted. The GB lattice model is further used to investigate the reinforced fiber/particle composites instead of only particle composites as the model did before. Numerical examples are given to show the effectiveness of the modeling procedure, and influences of inclusions (particle, fiber and rebar) on the fracture processes are also discussed. (c) 2008 Elsevier Ltd. All rights reserved.

Thickness And Component Distributions Of Yttrium-Titanium Alloy Films In Electron-Beam Physical Vapor Deposition

Thickness and component distributions of large-area thin films are an issue of international concern in the field of material processing. The present work employs experiments and direct simulation Monte Carlo (DSMC) method to investigate three-dimensional low-density, non-equilibrium jets of yttrium and titanium vapor atoms in an electron-beams physical vapor deposition (EBPVD) system furnished with two or three electron-beams, and obtains their deposition thickness and component distributions onto 4-inch and 6-inch mono-crystal silicon wafers. The DSMC results are found in excellent agreement with our measurements, such as evaporation rates of yttrium and titanium measured in-situ by quartz crystal resonators, deposited film thickness distribution measured by Rutherford backscattering spectrometer (RBS) and surface profilometer and deposited film molar ratio distribution measured by RBS and inductively coupled plasma atomic emission spectrometer (ICP-AES). This can be taken as an indication that a combination of DSMC method with elaborate measurements may be satisfactory for predicting and designing accurately the transport process of EBPVD at the atomic level.

High-power laser beam shaping by inseparable two-dimensional binary-phase gratings for surface modification of stamping dies

For surface modification of stamping dies, an inseparable two-dimensional binary-phase gratings is introduced to implement the wavefront transformation of high-power laser beams. The design and fabrication of the gratings are described in detail. Two-dimensional even sampling encoding scheme is adopted to overcome the limitations of conventional Dammann grating in the design of two-dimensional output patterns. High diffractive efficiency (>70%) can be achieved through the transformation of the Gaussian laser beam into several kinds of two-dimensional arrays in focal plan. The application of the binary-phase gratings in the laser surface modification of ductile iron is investigated, and the results show that the hardness and the wear resistance of the sample surface were improved significantly by using the binary-phase gratings. (C) 2008 Elsevier Ltd. All rights reserved.