Geometrical-transformation approach to optical two-dimensional beam shaping: comment

I show that the research reported by Arieli et al. [Appl. Opt. 86, 9129 (1997)] has two serious mistakes: One is that an important factor is lost in the formula used in that study to determine the x-direction coordinate transformation; the other is the conclusion that the geometrical-transformation approach given by Arieli et al. can provide a smooth phase distribution. A potential research direction for obtaining a smooth phase distribution for a generic two-dimensional beam-shaping problem is stated. (C) 1998 Optical Society of America.

Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and its Alloys

alpha-titanium and its alloys with a dual-phase structure (alpha+beta) were deformed dynamically under strain rate of about 10(4) s(-1). The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate (9 x 10(5) s(-1)) deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations in the bands can be constricted and developed into cell structures; the phase transformation from alpha to alpha(2) within the bands was observed, and the transformation products (alpha(2)) had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10 mu m in diameter observed within the bands are proposed to be the results of recrystallization.

A Quantitative Analysis of the Effect of Laser Transformation Hardening on Crack Driving Force in Steels

A mechanical model of a laser transformation hardening specimen with a crack in the middle of the hardened layer is developed to quantify the effects of the residual stress and hardness gradient on crack driving force in terms of J-integral. It is assumed

Martensitic transformation under impact with high strain rate

This paper deals with the quantitative prediction of the volume fraction of martensitic transformation in a austenitic steel that undergoes impact with high strain rate. The coupling relations between strain, stress, strain rate, transformation rate and transformed fraction were derived from the OTC model and modified Bodner-Partom equations, where the impact process was considered as an adiabatic and no entropy-increased process (pressure less than or equal to 20GPa). The one-dimensional results were found to model and predict various experimental results obtained on 304 stainless steel under impact with high strain rate.

Gamma -> Epsilon Martensite Transformation and Twinning Deformation in fcc Cobalt During Surface Mechanical Attrition Treatment

The deformation microstructure of face-centered cubic cobalt subjected to surface mechanical attrition treatment was studied as a function of strain levels. Strain-induced gamma --> epsilon transformation and twinning deformation were evidenced by transmission electron microscopy and were found to progress continuously in ultrafine and nanocrystalline grains as the strain increased.

A Thermodynamic Constitutive Model for Stress Induced Phase Transformation in Shape Memory Alloys

In this paper a thermodynamic constitutive model is developed for stress induced phase transformation in single crystalline and polycrystalline shape memory alloys (SMAs). Volume fractions of different martensite variants are chosen as internal variables to describe the evolution of microstructure state in the material. This model is then used in prediction the transformation behavior of a SMA (Cu-Al-Zn-Mn) under complex thermomechanical load (including complete and incomplete transformation in mechanical cycling, and proportional/non-proportional loading). (C) 2002 Elsevier Science Ltd. All rights reserved.

Numerical Investigation on Laser Transformation Hardening with Different Temporal Pulse Shapes

A 3-D numerical model for pulsed laser transformation hardening (LTH) is developed using the finite element method. In this model, laser spatial and temporal intensity distribution, temperature-dependent thermophysical properties of material, and multi-phase transformations are considered. The influence of laser temporal pulse shape on connectivity of hardened zone, maximum surface temperature of material and hardening depth is numerically investigated at different pulse energy levels. Results indicate that these hardening parameters are strongly dependent on the temporal pulse shape. For the rectangular temporal pulse shape, the temperature field obtained from this model is in excellent agreement with analytical solution, and the predicted hardening depth is favorably compared with experimental one. It should be pointed out that appropriate temporal pulse shape should be selected according to pulse energy level in order to achieve desirable hardening quality under certain laser spatial intensity distribution.

Numerical Simulation of 3D-Thermal Field with Phase Transformation

以激光熔凝表面强韧化处理为背景,应用空间的弹塑性有限单元和高精度的数值算法、同时考虑材料组织性能的变化来模拟材料的温度场。主要研究激光熔凝加工中瞬时温度场数值模拟,同时考虑相变潜热的影响,为第二步热应力场及残余应力的数值模拟做准备。最后用算例验证了模型的正确性,并给出了不同时刻温度场的分布。

Thermodynamics of the displacive mechanism of alpha(1) transformation in a beta

Thermodynamics of the displacive mechanism of plate-shaped phase alpha(1) was analyzed in beta'Cu-Zn alloys. It was proposed that the displacive transformation of the alpha(1) plate took place in the solute-depleted region formed in the parent phase during the incubation period. The thermodynamic analysis indicated that the driving force of alpha(1) transformation, Delta G, increased with the reduction of x(d), the solute concentration of the depleted region. And, Delta G could overcome-the transformation barrier with solute depletion to a certain degree. In addition, x(d) was higher than the equilibrium concentration in the phase diagram. Therefore, the shear formation of alpha(1) plate in the solute-depleted region was thermodynamically supported.

Rapidly solidified nonequilibrium microstructure and phase transformation of laser-synthesized iron-based alloy coating

The rapidly solidified microstructural and compositional features, the precipitation and transformation of carbides during tempering, and the impact wear resistance of an iron-based alloy coating prepared by laser cladding are investigated. The clad coating alloy, a powder mixture of Fe, Cr, W, Ni, and C with a weight ratio of 10:5:1.1.1, is processed using a continuous wave CO, laser. Microstructural studies demonstrate that the coating possesses the hypoeutectic microstructure comprising the primary dendritic gamma-austenite and interdendritic eutectic consisting of gamma-austenite and M7C3 carbides. gamma-Austenite is a non-equilibrium phase with an extended solid solution of alloying elements. During high temperature tempering at 963 K for 1 h, the precipitation of M23C6, MC and M2C carbides in austenite and in situ carbide transformation of M7C3 to M23C6 and M7C3 to M6C respectively are observed. In addition, the microstructure of the laser-clad coating reveals an evident secondary hardening and a superior impact wear resistance.

Phase Transformation Accommodated Plasticity In Nanocrystalline Nickel

Based on detailed x-ray diffraction and transmission electron microscopy we have found body-centered-cubic (bcc) Ni upon room-temperature rolling of nanocrystalline (nc) face-centered-cubic (fcc) Ni. The bcc phase forms via the Kurdjumov-Sachs (KS) martensitic transformation mechanism when the von Mises equivalent strain exceeds similar to 0.3, much higher than accessible in tensile testing. The fcc and bcc phases keep either the KS or the Nishiyama-Wasserman orientation relationship. Our results provide insights into the deformation physics in nc Ni, namely, the fcc-to-bcc phase transformation can also accommodate plasticity at large plastic strains. (C) 2008 American Institute of Physics.

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

Asymptotic analysis of plane-strain mode I steady-state crack growth in transformation toughening ceramics (II)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原