Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

A test case for predicting the rheological properties of polymeric liquids: the multiple coupled Maxwell modes model

In this work, the behavior of the multiple coupled Maxwell modes (MCMM) model is examined with regard to the rheological properties of polymer melts in diverse flow fields, including (i) transient, (ii) steady-state shear flow, (iii) small-amplitude oscillatory shear flow, and (iv) transient uniaxial elongational flow. This model is specialized to the case of pair-wise coupling, i.e., each mode interacts with only one other mode. Consequently, each pair of modes acts independently of the others. For a typical polymer melt of industrial interest, a simple optimization technique is developed for determining the number of independent mode pairs, as well as precise values for the corresponding parameters.The goal of this ongoing study is to fit the parameters of various rheological models using a limited number of simple, standard experiments, and then to see whether or not the models can predict data taken from more complicated experiments. In this paper, only the first step is taken in this direction: we examine for one particularly promising rheological model, the MCMM model (but herein restricted to pair-wise coupling), whether or not it can achieve this goal. This restricted model is chosen because it mimics the effect of pair-wise coupling between relaxation modes that is prevalent in current rheological models. Using this model as a test case allows the optimization technique and analytical methodology for achieving the overall goal to be developed. The outcome of this study with regard to developing the methodology was successful, but the particular model chosen, written in terms of coupled Maxwell modes with pair-wise coupling, is not general enough to predict well typical polymer melt rheological behavior.     

On the coupled system performance of transcritical CO2 heat pump and rankine cycle

As one of the natural refrigerants, CO₂ is a potential substitute for synthesized refrigerants with favorable environmental properties. In order to improve the performance of rankine cycle (RankC), the coupled system cycle (CSC) was designed and the performance was analyzed in this paper, which the CSC is combined by the RankC and the transcritical CO₂ heat pump cycle with an expander. Based on thermodynamic principles, the performance analysis platform was designed and the performance analysis was employed. The results show that the average efficiency of the RankC is about 30 %, and the extraction cycle is about 32 %, while the CSC is about 39 %, and the last one is better than the others at the same parameters. With increasing of the boiler feed water temperature, the efficiencies of the three kinds of cycles show increasing trend. With increasing of pressure in conderser–evaporator or outlet temperature of gas cooler, the efficiency of the CSC shows a downward trend. Some fundamental data were obtained for increasing the RankC efficiency by waste heat recovery, and play an active role in improvement the efficiency of power plants.     

Nonlinear normal modes in multi-mode models of an inertially coupled elastic structure

Nonlinear normal modes for elastic structures have been studied extensively in the literature. Most studies have been limited to small nonlinear motions and to structures with geometric nonlinearities. This work investigates the nonlinear normal modes in elastic structures that contain essential inertial nonlinearities. For such structures, based on the works of Crespo da Silva and Meirovitch, a general methodology is developed for obtaining multi-degree-of-freedom discretized models for structures in planar motion. The motion of each substructure is represented by a finite number of substructure admissible functions in a way that the geometric compatibility conditions are automatically assured. The multi degree-of-freedom reduced-order models capture the essential dynamics of the system and also retain explicit dependence on important physical parameters such that parametric studies can be conducted. The specific structure considered is a 3-beam elastic structure with a tip mass. Internal resonance conditions between different linear modes of the structure are identified. For the case of 1:2 internal resonance between two global modes of the structure, a two-mode nonlinear model is then developed and nonlinear normal modes for the structure are studied by the method of multiple time scales as well as by a numerical shooting technique. Bifurcations in the nonlinear normal modes are shown to arise as a function of the internal mistuning that represents variations in the tip mass in the structure. The results of the two techniques are also compared.     

The effect of gas motion on the reaction kinetics of vibrationally excited molecules

The effect is considered of gas motion on the kinetics of reactions whose energy threshold is overcome as the result of vibrational excitation of the reactant molecules. The conditions are determined for which such an effect may be realized. An expression is obtained for the rate of thermal dissociation of diatomic molecules considered as harmonic oscillators representing a small impurity in a monoatomic inert gas; the expression depends explicitly and nonlinearly on the divergence of the flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–105, November–December, 1984.     

Generalization of the Clausius-Clapeyron equation in a coupled thermomechanical model

Several modifications of the Clausius-Clapeyron equation for deformable media, including solid-phase transformations which depend on the change of additional parameters, are proposed. A model of the medium with tensor concentrations of the components for which the unique Clausius-Clapeyron equation is also valid is proposed. The tensor analog of the transition heat is introduced, and an expression for the total transition heat related to the energies of chemical bonds in the crystal lattice is obtained. At least for slow processes, the fundamental possibility of determining the self transition heat in the experiment is shown analytically. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 103–111, November–December, 1999.     

A lattice-based model of the kinetics of twin boundary motion

In this paper we derive a macroscopic kinetic law for twin boundary motion from a lattice dynamical model. The model is developed for compound and type-1 twins and it is explicitly illustrated for a Cu-Al-Ni shape memory alloy. The governing multiple-well energy is calculated using an effective interatomic potential; a Frenkel-Kontorowa type model is developed for the dynamics at the lattice scale; and a quasi-continuum approximation is used to determine the continuum-scale kinetics. The model predicts that compound twins in the Cu-Al-Ni shape memory alloy are an order of magnitude more mobile than type-1 twins which is consistent with experimental observations.     

混凝土材料损伤耦合的非线性粘弹性本构关系

根据不可逆热力学原理和推广的Onsager原理建立了内变量演化的非线性方程;采用迭代方法得到了非线性方程的迭代解,并根据Lipschitz条件给出了迭代解的收敛条件。由此,建立了一维应力条件下的非线性粘弹性本构关系。将这一本构关系推广至三维应力情况,并考虑了状态方程和损伤演化,在剪切诱导材料粘性的前提下建立了混凝土损伤耦合的非线性粘弹性本构关系。在该关系式中：损伤演化方程与混凝土的粘性应变积累相关;状态方程服从三次多项式的形式。实验结果表明：此模型能够比较好地表征混凝土材料在达到强度极限前后的强化与软化的特征。     

Crack separation energy-rates for the DBCS model under biaxial modes of loading

A Modified version of the Dugdale-Bilby-Cottrell-Swinden (DBCS) model simulating the effect of plasticity at the tip of a crack in an infinite region was used by kfouri and rice (1978) to calculate the crack separation energy-rate G^Δ corresponding to a finite crack growth step Δa during plane strain mode I crack extension. The loading consisted of a remote uniaxial tension σp applied normally to the plane of the crack. Using Rice's path-independent integral J to characterize the applied load in the crack tip region, and assuming the length R of the crack tip plastic zone to be small compared with the length of the crack, an analytical expression was derived relating the ratios (J/G^Δ) and (2a/R) for small values of (2a/R). The analytical solution was incomplete in itself in that the value assumed in the plastic region of the DBCS model for the normal stress Y acting on the extending crack surfaces was the product of the yield stress in uniaxial tension σ_Y and an unknown parameter C, the value of which depends on the effect of the local hydrostatic stresses in the case of plane strain conditions. The analytical solution was compared with a numerical solution obtained from a plane strain elastic-plastic finite element analysis on a centre-cracked plate (CCP) of material obeying the von Mises yield criterion. The value used for the yield stress was 310 MN/m² and moderate isotropic linear hardening was applied with a tangent modulus of 4830 MN/m². A uniaxial tension σp was applied on the two appropriate sides of the plate. The comparisons showed that the analytical and finite element solutions were mutually consistent and they enabled the value of C to be established at 1.91. In the present paper similar comparisons are made between the analytical solution and the finite element solutions for the CCP of the same material under different biaxial modes of loading. By assuming further that the form of the analytical solution does not depend on the details of the geometry and of the loading at remote boundaries, a comparison has also been made with the results of a finite element analysis on a compact tension specimen (CTS) made of the same material as the CCP. The different values of C obtained in each case are consistent with investigations by other authors on the effect of load biaxiality on crack tip plasticity.     

Choice of turbulence model for calculating gas dynamic CO2 lasers with selective thermal excitation

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 163–168, Septebmar–October, 1990.     

Three-dimensional coupled numerical model of creeping flow of viscous fluid

A three-dimensional coupled numerical model is developed to describe creeping flow in a computational domain that consists of a thick viscous layer overlaid with a thin multilayered viscous sheet. The density of the sheet is assumed to be lower than that of the layer. The model couples the Stokes equations describing the flow in the layer and the Reynolds equations describing the flow in the sheet. We investigate the long-time behavior of the flow in the sheet by using an asymptotic method and derive an ordinary differential equation for the sheet boundary displacements and the velocities at the interface between the sheet and the layer. The Stokes and Reynolds equations are coupled by applying the resulting equation as an internal boundary condition. Numerical implementation is based on a modified finite element method combined with the projection gradient method. The computational domain is discretized into rectangular hexahedra. Piecewise square basis functions are used. The model proposed enables different-type hydrodynamic equations to be coupled without any iterative improvements. As a result, the computational costs are reduced significantly in comparison with available coupled models. Numerical experiments confirm that the three-dimensional coupled model developed is of good accuracy.     

Coupled conductive radiative transfer in CO2 with narrow band statistical model and Monte-Carlo simulation

This paper describes an approach in order to determine the radiative source term and the temperature fields in a coupled conductive and radiative transfer. We consider an emitting and absorbing gas (carbon dioxide) enclosed between two horizontal and parallel reflecting plates. The medium is in local thermodynamic equilibrium (LTE). Only radiative and conductive exchanges are considered. An implicit finite difference technique is used to solve the energy conservation equation, and the narrow band statistical model (NBSM) with the Monte Carlo method (MCM) are used for simulation of radiative transfer equation in a coupled manner. This study of coupled conductive-radiative shows many phenomenons: The interaction radiation conduction in an emitting and absorbing gas is sensitive to the molar fraction of gas and the emissivities of walls. Received on 6 July 1999