An Energy-Based Torsional-Shear Fatigue Lifing Method

An energy-based fatigue-life prediction framework for the determination of full-life, remaining-life, and critical-life of in-service structures subjected to torsional-shear loading has been developed. This framework is developed upon the existing foundation of energy-based fatigue models crafted for the axial, uniaxial bending, and transverse-shear loading cases, which state: the total strain energy density accumulated during both a monotonic event and a cumulative cyclic process is the same material property. The modified energy-based torsional-shear fatigue-life prediction framework is composed of the following entities: (1) the development of a torsional-shear fatigue testing procedure capable of assessing strain energy density per cycle in a pure shear stress state and (2) the determination of the remaining-life and critical-life of in-service aluminum (Al) 6061-T6 structures subjected to shear fatigue through the application of the energy-based prediction method. Experimental data was shown to be affected by load-frame misalignment which was estimated and successfully incorporated into the validation results. Close correlation between adjusted experimental results and the full-life and critical-life predictions stemmed from a 3-to-2 shear-to-axial biaxial loading assumption, which was supported by crack path comparisons. Results of the study effectively demonstrated the versatility of the energy-based lifing method.     

An Energy Based Fatigue Life Prediction Framework for In-Service Structural Components

An energy based fatigue life prediction framework has been developed for calculation of remaining fatigue life of in service gas turbine materials. The purpose of the life prediction framework is to account aging effect caused by cyclic loadings on fatigue strength of gas turbine engines structural components which are usually designed for very long life. Previous studies indicate the total strain energy dissipated during a monotonic fracture process and a cyclic process is a material property that can be determined by measuring the area underneath the monotonic true stress-strain curve and the sum of the area within each hysteresis loop in the cyclic process, respectively. The energy-based fatigue life prediction framework consists of the following entities: (1) development of a testing procedure to achieve plastic energy dissipation per life cycle and (2) incorporation of an energy-based fatigue life calculation scheme to determine the remaining fatigue life of in-service gas turbine materials. The accuracy of the remaining fatigue life prediction method was verified by comparison between model approximation and experimental results of Aluminum 6061-T6. The comparison shows promising agreement, thus validating the capability of the framework to produce accurate fatigue life prediction.     

弹塑性微凸体侧向接触相互作用能耗

传统的结合面研究多基于光滑刚性平面与等效粗糙表面接触假设,忽略了结合面上微凸体侧向接触及相邻微凸体之间的相互作用,这导致理论模型与实际结合面存在较大出入.针对承受法向静、动态力的机械结合面,从微观上研究了微凸体侧向接触及相互作用的接触能耗.将法向静、动态力分解为法向分力和切向分力,获取弹性/弹塑性/塑性阶段考虑微凸体侧接触及相互作用的加、卸载法向分力-变形和切向分力-位移的关系.通过力的合成定理,从而获取加、卸载法向合力与总变形之间的关系,由于法向分力产生的塑性变形及切向分力产生的摩擦,导致加载、卸载法向合力-总变形曲线存在迟滞回线.通过对一个加、卸载周期内的法向合力-总变形曲线积分,获得一个周期的微凸体接触能耗,包括应变能耗及摩擦能耗.仿真分析表明:微凸体在3个阶段的能耗均随变形的增大而非线性增大.微凸体侧向接触角度越大,能耗越大,且在弹性阶段最为明显.在弹性阶段,仅存在侧向的摩擦能耗,故结合面在低载荷作用下必须采用双粗糙表面假设.在塑性阶段,由于微凸体接触能耗为应变能耗,且接触角对其能耗影响甚微,故结合面在大载荷作用下可采用单平面假设对其进行研究.相对于KE和Etsion模型,本文提出的模型与Bartier的实验结果更吻合.     

A hybrid dynamic Smagorinsky model for large eddy simulation

A hybrid dynamic subgrid-scale model (HDSM) pertaining to Large-eddy simulation (LES) has been developed. The coefficient obtained by German dynamic Smagorinsky model (DSM) was integrated with a new dynamic coefficient, based on the dynamic subgrid characteristic length and controlled by the subgrid-scale (SGS) motions. In HDSM, the characteristic wave number determining the characteristic length of the dynamic subgrid is calculated from a new energy weighted mean method when the subgrid scale turbulent kinetic energy and the dissipation wave number are known. The dissipation wave-number is derived from the SGS turbulent kinetic energy spectrum equation. The total dissipation rate spectrum equation is based on the Pao energy spectrum and local equilibrium assumption. The dynamic subgrid characteristic length could take into account the rapidly fluctuating small scale behaviours and the spatial variation of turbulent characteristics. HDSM was used to simulate the fully developed channel and turbulent flow past a circular cylinder, and to determine the impact of the dam-break flow on downstream structure. The HDSM is robust in respect to anisotropic mesh and is less sensitive to grid resolution, and would accurately describe the energy transfer from large-scale to SGS fluctuations and capture more fluctuations of turbulence with same meshes compared to the DSM.     

Theoretical investigation of some thermal effects in turbulence modeling

Fluid compressibility effects arising from thermal rather than dynamical aspects are theoretically investigated in the framework of turbulent flows. The Mach number is considered low and not to induce significant compressibility effects which here occur due to a very high thermal gradient within the flowfield. With the use of the Two-Scale Direct Interaction Approximation approach, essential turbulent correlations are derived in a one-point one-time framework. In the low velocity gradient limit, they are shown to directly depend on the temperature gradient, assumed large. The impact of thermal effects onto the transport equations of the turbulent kinetic energy and dissipation rate is also investigated, together with the transport equation for both the density and the internal energy variance.      

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

饱和黏弹性多孔介质中的平面波及能量耗散

研究了流体饱和不可压黏弹性多孔介质中的非均匀平面波及其能量流和能量耗散规律. 在流 相和固相物质微观不可压、固相骨架宏观服从积分型本构关系和小变形的假定下，利用 Helmholtz分解，得到了饱和黏弹性多孔介质中非均匀平面波的一般解以及纵波、横波相速 度和衰减率等的解析表达式，分析了平面波传播矢量和衰减矢量之间的关系. 数值结果表明 孔隙流体与固相骨架间的相互作用以及固相骨架的黏性对波的相速度、衰减率等有着显著的 影响. 同时，得到了饱和黏弹性多孔介质的能量方程，给出了能量流矢量和能量耗散率. 对 非均匀平面纵波和横波，推导了平均能量流矢量和平均能量耗散率的解析表达式.     

钝圆头质量块对简支梁的多次弹塑性撞击

考虑多次局部弹塑性接触变形行为、多次撞击和多次分离过程,提出了1种采用有限差分方法研究柔性结构多次弹塑性撞击问题的MCIS方法,研究了钝圆柱头刚性质量块水平撞击简支梁的过程。研究结果表明,该撞击过程实际上是1个复杂的多次弹塑性撞击过程,一般存在2个以上的明显撞击区,每个撞击区包含了形式多样的复杂的次生撞击过程。其他撞击区的冲量值与第1个撞击区的冲量值相当,其他撞击过程中损失的撞击动能的总和与首次撞击过程中损失的撞击动能相当,因此,多个撞击区和多次撞击过程将对梁的撞击物理行为产生重要影响。研究还发现,小质量块刚性体撞击时,首次撞击过程的撞击动能损失明显。在大质量刚性体撞击时,后续的多次撞击过程的撞击动能损失明显。 更多还原     

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.     

椭圆截面截卵形刚性弹体正贯穿加筋板能量耗散分析

为获得椭圆截面截卵形刚性弹体正贯穿加筋板的剩余速度,根据椭圆截面弹体贯穿靶板的破坏特征,认为贯穿过程中靶板的能量耗散方式主要为塞块剪切变形功与塞块动能、扩孔塑性变形功、花瓣动力功、花瓣弯曲变形功、靶板整体凹陷变形功、加强筋侧向凹陷变形功。推导了每种能量计算方法,计算中定量考虑了靶板扩孔、花瓣弯曲、凹陷变形的应变率效应。根据能量守恒关系,得到了椭圆截面弹体剩余速度和弹道极限速度预测公式。并通过实验结果对模型进行了验证。结果表明:考虑靶板应变硬化、应变率效应的贯穿模型可以准确预测弹体剩余速度;随着椭圆截面弹体长短轴之比的增大,靶板的弹道极限速度近似线性增大;长短轴之比小于3时,加筋板的主要耗能为花瓣弯曲变形能、整体凹陷变形能。     

Thermodynamically consistent phase field approach to dislocation evolution at small and large strains

A thermodynamically consistent, large strain phase field approach to dislocation nucleation and evolution at the nanoscale is developed. Each dislocation is defined by an order parameter, which determines the magnitude of the Burgers vector for the given slip planes and directions. The kinematics is based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions. The relationship between the rates of the plastic deformation gradient and the order parameters is consistent with phenomenological crystal plasticity. Thermodynamic and stability conditions for homogeneous states are formulated and satisfied by the proper choice of the Helmholtz free energy and the order parameter dependence on the Burgers vector. They allow us to reproduce desired lattice instability conditions and a stress-order parameter curve, as well as to obtain a stress-independent equilibrium Burgers vector and to avoid artificial dissipation during elastic deformation. The Ginzburg–Landau equations are obtained as the linear kinetic relations between the rate of change of the order parameters and the conjugate thermodynamic driving forces. A crystalline energy coefficient for dislocations is defined as a periodic step-wise function of the coordinate along the normal to the slip plane, which provides an energy barrier normal to the slip plane and determines the desired, mesh-independent height of the dislocation bands for any slip system orientation. Gradient energy contains an additional term, which excludes the localization of a dislocation within a height smaller than the prescribed height, but it does not produce artificial interface energy. An additional energy term is introduced that penalizes the interaction of different dislocations at the same point. Non-periodic boundary conditions for dislocations are introduced which include the change of the surface energy due to the exit of dislocations from the crystal. Obtained kinematics, thermodynamics, and kinetics of dislocations at large strains are simplified for small strains and rotations, as well.     

Dissipation of Turbulent Kinetic Energy in a Cylinder Wall Junction Flow

The subject of this study is the discussion of the dissipation of turbulent kinetic energy and its Reynolds number scaling in front of a wall-mounted cylinder. We employed highly resolved Large-Eddy Simulation and ensured that the computational grid was fine enough to resolve most of the scales. A perceptible fraction of the total dissipation is modeled. However, this fraction - about one third - is small enough so that the total dissipation suffers only marginally from some potential shortcomings of the turbulence model. Individual terms of the pseudo dissipation tensor and their Reynolds number scaling are discussed and compared. This tensor and thus the turbulent small scale structures are not isotropic at the Reynolds numbers investigated. Furthermore, the near-wall anisotropy under the horseshoe vortex is likely to persist to larger Reynolds numbers as it can be linked to a flapping of the near-wall layer. The turbulent length scale shows a strong spatial variability. In the region of the vortex system in the cylinder front, the distribution reveals a similar shape as the one of the turbulent kinetic energy and its amplitude is in the order of magnitude of the cylinder diameter. In contrast to the region dominated by the approach flow, the turbulent length scale is independent of the Reynolds number in the region dominated by the vortex system. Even though the flow investigated is in non-equilibrium, common a priori estimations and scalings of the Kolmogorov length scale based on macro scales give satisfying results.     

Implementation of physical boundary conditions into computational domain in modelling of oscillatory bottom boundary layers

This paper discusses the importance of realistic implementation of the physical boundary conditions into computational domain for the simulation of the oscillatory turbulent boundary layer flow over smooth and rough flat beds. A mathematical model composed of the Reynolds averaged Navier–Stokes equation, turbulent kinetic energy (k) and dissipation rate of the turbulent kinetic energy (ε) has been developed. Control‐volume approach is used to discretize the governing equations to facilitate the numerical solution. Non‐slip condition is imposed on the bottom surface, and irrotational main flow properties are applied to the upper boundary. The turbulent kinetic energy is zero at the bottom, whereas the dissipation rate is approaching to a constant value, which is proportional to the kinematic viscosity times the second derivative of the turbulent kinetic energy. The output of the model is compared with the available experimental studies conducted in oscillatory tunnels and wave flume. It is observed that the irrotational flow assumption at the upper boundary is not realistic in case of water tunnels. Therefore, new upper boundary conditions are proposed for oscillatory tunnels. The data of wave flume show good agreement with the proposed numerical model. Additionally, several factors such as grid aspect ratio, staggered grid arrangement, time‐marching scheme and convergence criteria that are important to obtain a robust, realistic and stable code are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Characterization of the Dynamic Response of Structures to Damaging Pulse-type Near-fault Ground Motions

The presence of long-period pulses in near-fault records can be considered as an important factor in causing damage due to the transmission of large amounts of energy to the structures in a very short time. Under such circumstances high-energy dissipation demands usually occur, which are likely to concentrate in the weakest parts of the structure. The maximum nonlinear response or collapse often happens at the onset of directivity pulse and fling, and this time is not predicted by the natural structural vibration periods. Nonlinear response leading to collapse may in most cases occur only during one large amplitude pulse of displacement. From the study of the response of both linear and nonlinear SDOF systems, the effects of these distinctive long-period pulses have been assessed by means of : (i) synthetic parameters directly derived from the strong ground motion records, and (ii) elastic and inelastic spectra of both conventional and energy-based seismic demand parameters. SDOF systems have first been subjected to records obtained during recent earthquakes in near-fault areas in forward directivity conditions. The results indicate that long duration pulses strongly affect the inelastic response, with very high energy and displacement demands which may be several times larger than the limit values specified by the majority of codes. In addition, from the recognition of the fundamental importance of velocity and energy-based parameters in the characterization of near-fault signals, idealized pulses equivalent to near-fault signals have been defined on account of such parameters. Equivalent pulses are capable of representing the salient observed features of the response to near-fault recorded ground motions.     

Results of direct numerical simulation of turbulent flow in a pipe of elliptical cross-section

Within the framework of the complete Navier-Stokes equations the turbulent flow in a pipe of elliptical cross-section with semiaxis ratio b/a = 0.5 is directly calculated for the Reynolds number Re = 6000 determined from the mean-flow velocity and the hydraulic diameter. The distribution of the average and pulsatory flow characteristics over the pipe cross-section are obtained. In particular, the secondary flow in the cross-section plane, typical of turbulent flows in noncircular pipes, is calculated. The equation for the longitudinal vorticity which determines the shape and intensity of the secondary flow is analyzed. In the balance equation for the pulsation kinetic energy the behavior of all the terms that characterize energy production, dissipation and redistribution over the pipe cross-section is described.     

A thermodynamic approach to analyze shear localization in semi-solid materials

A theoretical framework of the shear localization analysis was developed for semi-solid materials taking into account a non-equilibrium relationship between viscous deformation, pressure and interfacial surface energy. Considering a shear layer model, the necessary condition of perturbation growth and subsequent shear localization was derived. The results revealed that the localization phenomenon in the semi-solid deformation strongly depends on the difference between irreversible viscous work done on pores and grains and the reversible viscous deformational work stored as the interfacial surface energy. This thermodynamic quantity indicates the possibility of a perturbation growth or decade in terms of the process parameters such as dilatancy, permeability and also the fraction of the solid skeleton.     

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.     

Similarity solutions of vertical plane wall plume based on finite analytic method

The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.     

Dissipation rate correction methods

Dissipation rates of the turbulent kinetic energy and of the scalar variance are underestimated when the measurement resolution of the small scales of a turbulent flow field are insufficient. Results are presented of experiments conducted in a salt-stratified water tunnel (Schmidt number ∼700). Dissipation rates are determined to be underestimated, and thus correction techniques based on velocity structure functions and mixed-moment functions are proposed. Dissipation rates in laboratory experiments of shear-free, grid-generated turbulence are determined from balance calculations of the kinetic energy and scalar variance evolution equations. Comparisons between the structure function and balance estimates of dissipation show that the corrections are O(1) for the kinetic energy dissipation rate, and are O(100) for the scalar variance dissipation rate. This difference is due to the lack of resolution down to the Batchelor scales that is required for a high Schmidt number flow. Simple correction functions based on microscale Reynolds numbers are developed for both turbulent kinetic energy and scalar variance dissipation rates. Application of the technique to the results of laboratory experiments of density stratified turbulence, sheared turbulence, and sheared density stratified turbulence yields successful corrections. It is also demonstrated that the Karman–Howarth equality (and the analogous Yaglom equation) that relates second and third-order structure functions to dissipation rates is valid for both unstrained (decaying grid-generated turbulence) and density stratified and sheared turbulence at least up to the magnitudes of strains of the current experiments Nt∼10, St∼10, respectively. This is helpful for it allows the use of these equations in the analysis of turbulence even when the large scale background profiles of velocity and scalar are unknown.