Rolling With Simplified Stream Function Velocity and Strain Rate Vector Inner Product

 The dual-stream function velocity field is reduced in order to analyze two-dimensional plate broadside rolling in roughing. The strain rate vector inner product and integral mean value theorem, as well as co-line vector inner product are used respectively in plastic deformation power, friction losses and shear power. A theoretical solution of roll torque and separating force for the rolling is obtained and the calculated results by the solution are compared with those measured in broadside rolling on-line. It shows that both the force and torque calculated are higher than those of measured, but the maximum relative error between them is no more than 11%.     

A physical approach to the toughness problem: From thermodynamics to kinetics—I. The homogeneous case

The classical equilibrium equation of a crack under stress is reconsidered, introducing the deformation kinetics through a blunting correction to the elastic energy storage term, and a recalculation of the energy dissipation in the plastic zone. Both are expressed in terms of yield stress, strain hardening rate and strain rate sensitivity. The resulting instability criterion exhibits a ductile-brittle transition, and shows the influence of the above physical parameters on the critical stress intensity factor K_C. In addition, the blunting approximation, which neglects the energy dissipation in the plastic zone, is shown to be valid in most cases.     

Thermal stress fracture of refractory lining components: Part III. Analysis of Fracture

The fracture behavior of refractory components heated from one end is simulated using a twodimensional constant heating rate thermoelastic model and the maximum principal tensile stress fracture criterion. Dimensionless graphical relationships that can be used to predict location of fracture and orientation of cracking are presented. Dimensional analysis and the finite element numerical method are used to develop a general solution for the total strain energy. Based on the premise that extent of crack propagation is directly related to available strain energy at fracture and inversely related to the surface energy per unit area, the solution for total strain energy is used to derive a damage resistance parameter useful for the design and selection of refractory components that accounts for material properties, geometry, and heating and cooling rate. Model predictions of location of fracture, orientation of cracking, and extent of crack propagation are in general agreement with experimental results previously reported in the literature. Limitations of the two-dimensional thermoelastic model are discussed.     

Computer simulation of the effect of coherency strain on cluster growth kinetics

To understand clustering behavior under the influence of a coherency strain, Monte Carlo simulations were carried out for both two-dimensional (2-D) square and three-dimensional (3-D) simple cubic lattices. In the Monte Carlo model, each solute was assumed to exert coherency stress owing to a tetragonal misfit strain and to have surface energy when in contact with solvent atoms. To account for the coherency strain of a cluster whose morphology continuously changes during aging, exact expressions for both the self-strain energy and elastic interaction term for rectangular parallelepipeds were derived. Strong elastic interactions among platelike clusters are shown to develop a stabilized structure with a tendency for bridging the clusters at a right angle. In the early stage of evolution, solute atoms were found to diffuse into regions of stress concentration. Morphological changes revealed step movements on the edge of a cluster, and some steps were moving in the direction of dissolution (rather than growth) for the cluster, thus displaying a dynamic nature of step movement. When an initial shape was an elastically unstable one, a large cluster was found to dissolve into its solid solution, while, in the same environment, a cluster of the same size with a stable morphology sustained growth. During dynamic evolution, some clusters showed concave, instead of convex, surfaces, even though the former are highly nonequilibrium shapes. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Physically Based Constitutive Model for Body Centered Cubic Metals with Applications to Iron

A constitutive model is developed in this work to describe the mechanical behavior of body centered cubic metals under a wide range of strain rates and temperatures. The model is based on macromechanical state variables such as stress, strain, and material constants that include threshold and transition temperature as well as micromechanical terms such as mobile dislocation density and burgers vector. The principle of the activation energy and its dependence on temperature, strain rate, and stress is the key point in this proposed model. The model is used to simulate the experimental behavior of pure iron at various temperatures and strain rates in order to obtain the different model parameters. The model shows good capability in capturing the coupling between strain rate and temperature, plastic strain and strain rate, and plastic strain and temperature. The model is used to characterize the hardness of iron at low and high strain rates for a representative strain of 8%.     

7085铝合金的高温压缩流变应力及软化行为

对均匀化炉冷态7085铝合金进行高温压缩实验,研究该合金在变形温度为350~450℃、变形速率为0.001~0.1 s 1和应变量为0~0.6条件下的流变应力及软化行为。结果表明:流变应力在变形初期随着应变的增加而迅速增大,出现峰值后逐渐软化进入稳态流变;随着变形温度的升高和应变速率的降低,峰值流变应力降低。采用包含Zener-Hollomon参数的Arrhenius双曲正弦关系描述合金的流变行为。分析和建立了应变量与本构方程参数(激活能、应力指数和结构因子)的关系,研究发现本构方程参数随应变量的增加而减少。合金的流变行为差异与动态回复再结晶和第二相粒子相关。     

Thermal activation analysis on the plastic deformation satisfied with the Cottrell-Stokes law

The Cottrel-Stokes law is studied at 300 K in copper by using the translating slope of stress relaxation curves expressed as log-log plots of stress and strain rate which is a sensitive indicator for the validity of the law. It becomes evident that the original law gives the infinite translating slope under the condition of the modified law which requires the product of effective stress and activation volume to be constant. The thermal activation analysis on the plastic deformation satisfied exactly with the Cottrell-Stokes law is then made. The change in activation distance due to normal strain rate change and the total activation energy are obtained to be 0.4–0.5 in the Burgers vector unit and 105 kJ/mol, respectively. Finally, it is concluded that the activation distance remains constant during tensile deformation satisfied with the Cottrell-Stokes law at a given strain rate and temperature.     

Deformation and stored energy of polycrystalline bismuth

Stress-strain curves of polycrystalline bismuth deformed in compression were obtained at 78, 193, 243, 273, 298 and 353 K at strain rates of 2.2 × 10^-4, 2.2 × 10^-3 and 2.2 × 10^-2 s^-1. The strain rate sensitivity was measured by strain rate change tests. Activation volumes and activation enthalpies of deformation were determined. The stored energy of cold work was measured by liquid metal solution calorimetry. The flow stress shows a large strain rate dependence except at 78 K; its strain rate sensitivity goes through a maximum in the range of 243 to 273 K. The interpretation of the activation volume and activation enthalpy suggests that the deformation mechanism changes between 193 and 243 K and between 298 and 353 K. The stored energy of cold work increases at first linearly with strain and at a strain of approximately 0.5 levels off to a saturation value of about 420 J .g-atom^-1. The stored energy and the ratio of the stored to the expended energy are unusually large. Some conclusions are drawn regard-ing the deformation mechanism of bismuth.     

复杂应力状态225Cr 1Mo钢的高温低周疲劳裂纹扩展规律

 用带预裂纹的缺口试件研究225Cr 1Mo 钢高温低周疲劳裂纹扩展规律，通过疲劳试验观察裂纹扩展寿命，应用ANSYS计算裂纹尖端应力应变分量和当量弹、塑性应变范围，利用当量J积分范围表征225Cr 1Mo 钢在复杂应力状态下的低周疲劳裂纹扩展速率。结果表明：疲劳裂纹扩展速率da/dN与当量J积分范围ΔJf的关系不受试件缺口型式和加载应变范围的影响，用当量J积分来评价225Cr 1Mo 钢的高温低周疲劳裂纹扩展规律是有效的。     

Displacive Phase Transformation and Surface Effects Associated with Confocal Laser Scanning Microscopy

The influence of the free surface on martensitic transformation was examined by comparing the highest temperature at which martensite forms (M_S), as measured using dilatometry, with surface observations using confocal laser scanning microscopy. It is found that the proximity of the surface during confocal microscopy permits martensitic transformation to occur at a higher temperature with a reduced free energy change. This is because the strain energy from the shape deformation accompanying the growth of martensite is reduced at a free surface. The second observation is that plates of martensite tend to coalesce as they approach the free surface where there is reduced constraint. The general observations are backed by calculating the strain energy caused by a subsurface edge dislocation as a function of the orientation of its Burgers vector relative to the free surface.     

The plastic deformation of anα-Ti alloy and its thermal activation processvs effective stress

This article presents research on the tensile yield stress of anα-Ti alloy at temperatures from 373 to 77 K and strain rates from 10⁻⁴ to 10². The yield stress increases linearly with logarithmic strain rate. An analysis has been made on activation energy with the variation of effective stress which was obtained either by lowering temperature at constant strain rates or by increasing strain rates at constant temperatures. Activation energy is a function of temperature. It does not change when effective stress is increased by increasing strain rates but decreases with lowering temperature and is not influenced by strain rate.     

Nonlinear and nonlocal continuum model of transformation precursors in martensites

An intrinsic mechanism for explaining the origin of the transformation precursors observed above the transition in the parent phase of many materials undergoing a martensitic transformation is proposed. It is based on a nonlinear and nonlocal elastic continuum model for the elastic displacement field describing the parent-product deformation for the two-dimensional analog of a cubic-tetragonal transformation. By minimizing the Landau-Ginzburg free energy functional for the total elastic (strain plus strain gradient) energy a static, possibly stable, continuous, periodically modulated {110}/〈110〉 strain pattern is obtained which corresponds to alternating layers of more and of less transformed material, consistent with experimental observations. This pattern is stabilized by the balance between nonlinear and nonlocal elastic effects. Numerical application to In_1-x XT _x , alloys gives the minimum period of the modulation in the order of nanometers, in agreement with experimental observations.     

齿轮钢SAE8620 H高温变形行为及热加工图

通过高温压缩试验研究齿轮钢SAE8620H在950~1100℃、应变速率0.01~10 s-1条件下的高温变形行为.该合金钢的流动应力符合稳态流变特征,流变应力随变形温度升高以及应变速率降低而减小,其本构方程可以采用双曲正弦方程来描述.基于峰值应力、应变速率和温度相关数据推导出SAE8620H高温变形激活能Q=280359.9 J·mol-1.根据变形量40%和60%下应力构建该齿轮钢的热加工图,通过热加工图中耗散值及流变失稳区确定其热变形工艺参数范围.SAE8620H钢在在变形程度较小时宜选取低的应变速率进行成形,而在变形程度大时则要选取低温低应变速率或者高温高应变速率.      

The activation energy for creep of columbium (Niobium)

The activation energy for creep of nominally pure columbium (niobium) was determined in the temperature range 0.4 to 0.757T_M by measuring strain rate changes induced by temperature shifts at constant stress. A peak in the activation energy vs temperature curve was found with a maximum value of 160 kcal/mole (672 kJ/mole). A pretest heat treatment of 3000F (1922 K) for 30 min (1800 s) resulted in even higher values of activation energy (>600 kcal/mole, 2520 kJ/mole) in this temperature range. The activation energy for the heat-treated columbium (Nb) could not be determined near 0.5T_M because of unusual creep curves involving negligible steady-state creep rates and failure at < 5 pct creep strain. It is suggested that the anomalous activation energy values and the unusual creep behavior in this temperature range are caused by dynamic strain aging involving substitutional atom impurities and that this type of strain aging may be in part responsible for the scatter in previously reported values of activation energy for creep of columbium (Nb) near 0.5TM.     

Two-Dimensional Simulation Model of Sediment Removal and Flow in Rectangular Sedimentation Basin

A steady, two-dimensional numerical model was created to study the hydrodynamics of a rectangular sedimentation basin under turbulent conditions. The strip integral method was used to formulate the flow equations, using a forward marching scheme for solving the governing partial differential equations of continuity, momentum, advection–diffusion, turbulent kinetic energy, and its dissipation. In this way the flow equations were converted to a set of ordinary differential equations (ODEs) in terms of the key physical parameters. These parameters, along with a set of shape functions, describe flow variables including the velocity, the concentration of suspended sediments, and both the kinetic energy and its dissipation rate. Four Gaussian distributions were investigated, one corresponding to each flow parameter. In order to calculate the turbulent shear stresses, a two-equation turbulence model (i.e., k-ε model) was used. A fourth order Runge–Kutta method numerically integrates the set of ODEs. Simulation results were compared with experimental data, and close agreement (generally within 5–10%) was observed.     

铁酸钙与赤铁矿非等温还原动力学

采用非等温热重的方法,在30% CO+70% N₂(体积分数)气氛下,以10 K·min-1升温至1123 K的过程中,比较了铁酸钙与赤铁矿的逐级还原过程及其还原动力学.结果表明:铁酸钙和赤铁矿开始还原温度分别为873 K和623 K;由反应速率与反应度的关系及分阶段X射线衍射物相分析发现,铁酸钙还原过程为两段式反应(CaO·Fe₂O₃→2CaO·Fe₂O₃→Fe),而赤铁矿还原过程为传统的三段式反应(Fe₂O₃→Fe₃O₄→FeO→Fe).通过Freeman-Carroll法计算得知铁酸钙和赤铁矿的还原平均活化能分别为49.88和43.74 kJ·mol-1;铁酸钙还原过程符合随机成核随后生长模型,动力学模式函数为Avrami-Erofeev方程,其积分形式为[-ln (1-α)]n;而赤铁矿还原过程动力学机理分为两部分,在还原度α为0.1~0.5时,为三级化学反应模型,模式函数积分形式为1-(1-α)3;在α为0.5~0.9时,符合二维圆柱形扩散模型,动力学模式函数为Valensi方程,其积分形式为α+(1-α)ln (1-α).      

Hot Deformation Behavior of Beta Titanium Ti-13V-11Cr-3Al Alloy

Hot compression tests were conducted on Ti-13V-11Cr-3Al beta-Ti alloy in the temperature range of 1203 K to 1353 K (930 °C to 1080 °C) and at strain rates between 0.001 and 1 s^?1 The stress–strain curves showed pronounced yield point phenomena at high strain rates and low temperatures. The yield point elongation and flow stresses at the upper and lower yield points were related to the Zener–Hollomon parameter. It was found that dynamic recovery at low strain rates and dynamic recrystallization at high strain rates were the controlling mechanisms of microstructural evolution. The results also showed that strain rate had a stronger influence on the hot deformation behavior than temperature. The microstructural observations and constitutive analysis of flow stress data supported the change in the hot deformation behavior of the studied alloy varies with strain rate. For various applied strain rates, the activation energy for hot deformation was calculated in range of 199.5 to 361.7 kJ/mol. At low strain rates (0.001 and 0.01 s^?1), the value of activation energy was very close to the activation energy for the diffusion of V, Cr, and Al in beta titanium. The higher value of activation energy for deformation at high strain rates (0.1 and 1 s^?1) was attributed to the accumulation of dislocations and the tendency to initiate dynamic recrystallization.     

Modeling the Flow Curve Characteristics of 410 Martensitic Stainless Steel Under Hot Working Condition

The hot deformation behavior of AISI 410 martensitic stainless steel was investigated by conducting hot compression tests between 1173 K (900 °C) and 1423 K (1150 °C) and between strain rates of 0.001 s⁻¹ to 1 s⁻¹. The hyperbolic sine function described the relation well between flow stress at a given strain and the Zener–Hollomon parameter (Z). The variation of flow stress with deformation temperature gave the average value of apparent activation energy as 448 kJ/mol. The strain and stress corresponding to two important points associated with flow curve (i.e., peak strain and the onset of steady-state flow) were related to the Z parameter using power-law equations. A model also was proposed based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation to estimate the fractional softening of dynamic recrystallization at any given strain. This model can be used readily for the prediction of flow stress. The values of n and k, material constants in the JMAK equation, were determined for the studied material. The strains regarding the peak and the onset of steady-state flow were formulated in term of applied strain rate and the constants of the JMAK equation. A good agreement was found between the predicted strains and those obtained by the experimental work.     

Indentation power-law creep of high-purity indium

Using a variety of depth-sensing indentation techniques, the creep response of high-purity indium, from room temperature to 75 °C, was measured. The dependence of the hardness on the variables of indentation strain rate (stress exponent for creep (n)) and temperature (apparent activation energy for creep (Q)) and the existence of a steady-state behavior in an indentation test with a Berkovich indenter were investigated. It was shown for the first time that the indentation strain rate (-este-/h) could be held constant during an experiment using a Berkovich indenter, by maintaining the loading rate divided by the load (-este-/P) constant. The apparent activation energy for indentation creep was found to be 78 kJ/mol, in accord with the activation energy for self-diffusion in the material. Finally, by performing -este-/P change experiments, it was shown that a steady-state path independent of hardness could be reached in an indentation test with a geometrically similar indenter.     

On the hot tensile deformation behavior of an AISI 316LN stainless steel

The hot deformation characteristics of AISI 316LN stainless steel were studied in the temperature range of 1123–1323 K and strain rate range of 10⁻⁴–10⁻¹s⁻¹ by carrying out tensile tests. The flow stress, ultimate tensile stress and percentage elongation were found to be strongly dependent on the temperature and strain rate. The critical strain required for the initiation of dynamic recrystallisation and peak strain were determined at each condition and their variation with temperature and strain rate studied. The deformation behavior was analyzed using a generic model for high temperature deformation and deformation parameters were computed. The variation of the true activation energy with strain for rate controlled high temperature tensile deformation was obtained. Microstructural studies were carried out on tested samples and the results of all the above studies are presented.