FLOW STRESS MODELING FOR AERONAUTICAL ALUMINUM ALLOY 7050-T7451 IN HIGH-SPEED CUTTING

The high temperature split Hopkinson pressure bar （SHPB） compression experiment is conducted to obtain the data relationship among strain, strain rate and flow stress from room temperature to 550 C for aeronautical aluminum alloy 7050-T7451. Combined high-speed orthogonal cutting experiments with the cutting process simulations, the data relationship of high temperature, high strain rate and large strain in high-speed cutting is modified. The Johnson-Cook empirical model considering the effects of strain hardening, strain rate hardening and thermal softening is selected to describe the data relationship in high-speed cutting, and the material constants of flow stress constitutive model for aluminum alloy 7050-T7451 are determined. Finally, the constitutive model of aluminum alloy 7050-T7451 is established through experiment and simulation verification in high-speed cutting. The model is proved to be reasonable by matching the measured values of the cutting force with the estimated results from FEM simulations.

Establishment and application of flow stress models of Mg-Y-MM-Zr alloy

The hot working behaviors of Mg-9Y-1MM-0.6Zr （WE91） magnesium alloy were researched in a temperature range of 653 773 K and strain rate range of 0.001 1 s 1 on Gleeble 1500D hot simulator under the maximum deformation degree of 60%. A mathematical model was established to predict the stress—strain curves of this alloy during deformation. The experimental results show that the relationship between stress and strain is obviously affected by the strain rates and deformation temperatures. The flow stress of WE91 magnesium alloy during high temperature deformation can be represented by Zener-Hollomon parameter in the hyperbolic Arrhenius-type equation, and the stress—strain curves obtained by the established model are in good agreement with the experimental results,which prove that the model reflects the real deformation characteristics of the WE91 alloy. The average deformation activation energy is 220 kJ/mol at strain of 0.1. The microstructures of WE91 during deformation processing are influenced by temperature and strain rates.

A FLOW STRESS MODEL FOR AZ61 MAGNESIUM ALLOY

The flow stress behaviors of AZ61 alloy has been investigated at temperature rangefrom 523 to 673K with the strain rates of 0.001-1s^(-1). It is found that the averageactivation energy, strain rate sensitive exponent and stress exponent are different atvarious deformation conditions changing from 143.6 to 176.3kJ/mol, 0.125 to 0.167and 6 to 8 respectively. A flow stress model for AZ61 alloy is derived by analyzingthe stress data based on hot compression test. It is demonstrated that the flow stressmodel including strain hardening exponent and strain softening exponent is suitableto predicate the flow stress. The prediction of the flow stress of AZ61 alloy has shownto be good agreement with the test data. The maximum differences of the peak stressescalculated by the model and obtained by experiment is less than 8%.

FLOW STRESS MODEL FOR HARD MACHINING OF AISI H13 WORK TOOL STEEL

An approach is presented to characterize the stress response of workpiece in hard machining, accounted for the effect of the initial workpiece hardness, temperature, strain and strain rate on flow stress. AISI H13 work tool steel was chosen to verify this methodology. The proposed flow stress model demonstrates a good agreement with data collected from published experiments. Therefore, the proposed model can be used to predict the corresponding flow stress-strain response of AISI H13 work tool steel with variation of the initial workpiece hardness in hard machining.

A new flow stress model based on Arrhenius equation to track hardening and softening behaviors of Ti6Al4V alloy

The conventional Arrhenius-type model was adopted to identify the deformation characteristic of Ti6 A14 V(TC4) titanium alloy based on the stress-strain curves of isothermal compression test. A new flow stress model based on Arrhenius equation was proposed for TC4,which is composed of peak flow stress(PFS) prediction and strain compensation. The predicted PFS is set as a reference to derive the flow stress model at any strain ranging from approximately 0 to 0.7. The predictability and efficiency among the proposed model, conventional model,and an existing physical-based model of TC4 were comparatively evaluated. It is found that the newly proposed model can simultaneously track the hardening and softening behaviors of TC4 through a single expression while the other existing models are only valid in the softening region.Besides, the wider application range and acceptable accuracy of the new model have been achieved by fewer material constants with much-simplified modeling procedure than the other models.

New approach for modeling flow stress of aluminum alloy 6A10 considering temperature variation

The flow stress behavior of aluminum alloy 6A10 was studied by the hot compression tests at temperatures from 350℃ to 550 ℃ and strain rates from 0.1 s^-1 to 10 s^-1 with Gleeble-1500 thermo-mechanical simulator. The result demonstrates that the temperatures of specimen differ from initial ones affected by deformation conditions, and that the softening mechanism is dynamic recovery. A new approach was proposed to analyze the flow stress character directly from actual stress, strain, temperature and strain rate data, without performing any previous flow stress correction caused by temperature variation. Comparisons between the experimental and predicted results confirm that the established flow stress model can give reasonable estimation, indicating that the mentioned approach can be used in flow stress model analysis of the materials that undergo only dynamic recovery based on the data obtained under variable deformation temperature.

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

Research on flow stress in ferrite deformation of a Ti-IF steel

The experiments of the ferrite warm deformation of ultra-low carbon （ULC） Ti-IF steel were carded out on a hot simulator and the influences of deformation temperature, strain, and strain rate on the flow stress were analyzed. New flow stress models suitable to ferrite warm forming of Ti-IF steel were given on the basis of analyzing the influence of deformation technology parameters on the flow stress.

COMPUTATION OF RECIRCULATING SWIRLING FLOW WITH THE GLM REYNOLDS STRESS CLOSURE

A Reynolds stress closure based on the generalized Langevin model (GLM), developed by Haworth and Pope, is applied to the flow calculation with swirl-induced recirculation. The purpose of the work is to assess the performance of this model under the complex flow conditions caused by the presence of strong swirl which gives rise to both unconventional recirculation in the vicinity of the symmetry axis and strong anisotropy in the turbulence field. Comparison of the computational results are made both with the experimental data of Roback and Johnson and the computational results obtained with the typical isotropization of production model (IPM) and the k-∈ type Boussinesq viscosity model.

Development of Flow Stress of AISI H13 Die Steel in Hard Machining

An approach was presented to characterize the stress response of workpiece in hard machining, accounting for the effect of the initial workpiece hardness in addition to temperature, strain and strain rate on flow stress in this paper. AISI H13 die steel was chosen to verify this methodology. The proposed flow stress model demonstrates a good agreement with experimental data. Therefore, the proposed model can be used to predict the corresponding flow stress-strain response ofAISl H13 die steel with variation of the initial workpiece hardness in hard machining.

Simulation of Average Turbulent Pipe Flow: A Three-Equation Model

The aim of this study is to evaluate a three-equation turbulence model applied to pipe flow. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed average pipe flow. The model is based on the Reynolds averaged Navier-Stokes equations. Boussinesq hypothesis is invoked for determining the Reynolds stresses. Three local length scales are solved, based on which the eddy viscosity is calculated. There are two parameters in the model;one accounts for surface roughness and the other is possibly attributed to the fluid. Error in the mean axial velocity and Reynolds stress is found to be negligible.

FLOW STRESS OF STEEL 55SiMnVB AT HIGH TEMPERATURES AND HIGH STRAIN RATES

Based on the analyses of hot-deformation mechanism of the steel,a new constitutive equation describing the flow stress of steels was derived.The flow stress data of steel 55SiMnVB have been determined at 900—1200℃,strain rates of 1—100s^(-1)and true-strain of 0.08—0.8.An available evaluated formula on the flows tress has been obtained by means of non-linear regression.It can express clearly the physical process of hot-deformation.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

AN EXTENDED k-ε MODEL FOR NUMERICAL SIMULATION OF WIND FLOW AROUND BUILDINGS

It is assumed in this paper that for a high Reynolds number nearly homogeneouswind flow, the Reynolds stresses are uniquely related to the mean velocity gradientsand the two independent turbulent scaling parameters k and E. By applying dimensionalanalysis and owing to the Cayley-Hamilton theorem for tensors, a new turbulenceenclosure model so-called the axtended k-ε model has been developed. The coefficientsof the model expression were detemined by the wind tunnel experimental data ofhomogeneous shear turbulent flow. The model was compared with the standard k-εmodel in in composition and the prediction of the Reynold's normal Stresses. Using thenew model the numerical simulation of wind flow around a square cross-section tallbuilding was performed. The results show that the extended k-ε model improves theprediction of wind velocities around the building the building and wind pressures on the buildingenvelope.

A quasi single-phase model for debris flows and its comparison with a two-phase model

A depth-averaged quasi single-phase mixture model is proposed for debris flows over inclined bed slopes based on the shallow water hydrosediment-morphodynamic theory with multi grain sizes. The stresses due to fluctuations are incorporated based on analogy to turbulent flows, as estimated using the depth-averaged k-? turbulence model and a modification component. A fully conservative numerical algorithm, using wellbalanced slope limited centred scheme, is deployed to solve the governing equations. The present quasi single-phase model using four closure relationships for the bed shear stresses is evaluated against USGS experimental debris flow and compared with traditional quasi single-phase models and a recent physically enhanced two-phase model. It is found that the present quasi single-phase model performs much better than the traditional models, and is attractive in terms of computational cost while the two-phase model performs even better appreciably.

Discussion and prediction on decreasing flow stress scale effect

Based on crystal plasticity theory and surface layer model, relation of flow stress to billet dimension and grain size was built, and rationality of derived relation was verified with tensile tests of different size billets. With derived expressions, relation of decreasing flow stress scale effect to billet dimension, grain size as well as billet shape was discussed and predicted. The results show that flow stress is proportional to billet size; with decrease of grain size, flow stress is less influenced by billet dimension. When both cross section area and grain size are same, flow stress decrease of rectangular section billet or sheet is larger than that of circular section billet.

Plastic flow behavior of superalloy GH696 during hot deformation

In order to investigate the hot deformation behavior of superalloy GH696, isothermal compression experiments were carried out at deformation temperatures of 880?1120 °C and strain rates of 0.01?10 s?1. And the deformation amount of all the samples was 50%. The strain rate sensitivity exponent (m) and strain hardening exponent (n) under different deformation conditions were calculated, meanwhile the effects of the processing parameters on the values ofm andn were analyzed. The results show that the flow stress increases with the increase of strain rate and the decrease of deformation temperature. The value ofm increases with the increase of deformation temperature and decreases with the increase of strain rate, while the value ofn decreases with the increase of deformation temperature. A novel flow stress model during hot deformation of superalloy GH696 was also established. And the calculated flow stress of the alloy is in good agreement with the experimental one.

AH36船板钢变形抗力模型研究

通过热模拟压缩试验,获得了AH36船板钢的高温流动应力曲线,分析了变形温度、应变速率及应变对变形抗力的影响。分别采用Arrhenius模型、周纪华-管克智模型、Hensel⁃Spittel模型、美坂佳助改良模型和井上胜郎模型,建立AH36船板钢的变形抗力模型,并对模型进行了比较。研究结果发现,周纪华-管克智模型和Arrhenius模型相对于其他几种模型具有更好的预测精度。

Development and application of coupling model of aluminum thin-gauge high-speed casting

Based on the analyses of aluminum melt flow, solidification, heat transfer during the process of twin-roll casting, a coupling mathematical model of aluminum thin-gauge high-speed casting was developed, which included the casting roller shell. At the same time, Galerkin method was adopted to solve the coupling model. The fluid field and temperature field of aluminum melt in casting zone, the temperature field and thermal stress field of roller shells were simulated by the coupling model. When the casting velocity is 7m/min, and the thickness of strip is 2mm, the circumfluent area comes into being in the casting zone, and the mushy zone dominates the casting zone, while the temperature of melt decreases rapidly as it approaches the rollers. The temperature of the roller shell varies periodically with the rotation of roller, and reaches the highest temperature in the casting zone, while the temperature of roller shell decreases gradually as it leaves the casting zone. The difference of thermal stress between the inner surface and outer surface of the roller shell is very large, and the outer surface suffers tensile-compressive stress.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.