Finite element simulation and visualization of leaky Rayleigh wavesfor ultrasonic NDE

The generation and propagation properties of transient leaky Rayleigh waves are characterized by a two-dimensional finite element model. The displacement vector is used as the primary variable for the solid medium and a potential scalar, which is a replacement for the pressure, is taken as the fundamental variable for the fluid medium. The coupled system of finite element equations are solved in the time domain by direct integration through the central difference scheme. Three configurations are considered: the conversion of a Rayleigh surface wave into a leaky Rayleigh wave, a focused beam probing a fluid/solid interface at the Rayleigh angle, and the interaction of a defocused wave with the interface. The wave velocity in the fluid (water) is lower than the Rayleigh wave velocity in the solid (aluminum). The wave propagation profile in each case is predicted by the model. The finite element model proves to be an effective tool for surface acoustic device design and ultrasonic NDE     

Finite element simulation and modeling of 2-D arrays for 3-D ultrasonic imaging

Issues of modeling and design of 2-D arrays in three dimensions with finite element code are discussed. These ultrasonic arrays are used for real time dynamic imaging of the heart. Topics include optimization, sensitivity, and performance and methods to speed up the run times required for computer simulations of large three-dimensional models. Empirical results from 45×45 2-D arrays are also presented     

旋转超声磨削钛合金有限元仿真与试验研究

为了研究固结磨粒磨具的磨料粒度对旋转超声磨削钛合金磨削力的影响,采用随机空间平面切割正六面体的方法构建了具有实际磨粒几何特征的不规则多面体磨粒,并基于虚拟格子法建立了磨粒在磨具端面随机分布的多颗磨粒磨具模型。使用Deform-3D软件构建了三维旋转超声磨削钛合金有限元模型,采用拉格朗日增量算法获得了多颗磨粒磨具旋转超声磨削钛合金Ti6Al4V的磨削力仿真值,得到了磨料粒度对磨削力的影响规律,并通过试验进行了验证。结果表明,旋转超声磨削钛合金磨削力随着磨料粒度的增大而减小,且试验结果和仿真结果具有一致性,说明了多颗磨粒磨具模型、旋转超声磨削有限元模型具有一定的准确性,为多颗磨粒磨具旋转超声磨削的相关研究提供了新的方法。     

有限元简化模型应用于超声换能器模拟分析

依据有限元方法的基本物理思想,在某些不需要计算辐射声场的准确声学参数和波束特性的工程应用方面,对流体模型进行充分简化,提出了简化模型处理的有效方法,利用该方法对超声换能器进行模拟分析,并进行了样品的制作和测试,实测结果与模型简化分析处理的结果基本一致。可以证明,用该方法进行换能器的优化设计是可行和高效的。     

圆盘型非接触超声波马达定子的振动模拟与测试

介绍一种圆盘型非接触超声波马达的结构。利用有限元法计算了超声波马达定子在不同振动模态下的固有频率,并用激光测振仪对定子进行了测试,结果两者吻合较好。由于振幅和非接触马达的声辐射压力密切相关,因此通过谐响应分析计算了定子的振幅与定子驱动电压的关系,从而为马达的实验研究提供了理论依据。在最优模态B21下进行转子转速测试,测得最高转速为1600rpm。     

Finite element simulation of piezoelectric transformers

Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design     

Finite element analysis of underwater capacitor micromachined ultrasonic transducers

A simple electromechanical equivalent circuit model is used to predict the behavior of capacitive micromachined ultrasonic transducers (cMUT). The equivalent circuit model of the cMUT lacks important features such as coupling to the substrate and the ability to predict crosstalk between elements of an array of transducers. To overcome these deficiencies, a finite element model of the cMUT is constructed using the commercial code ANSYS(R). Calculation results of the complex load impedance seen by single capacitor cells are presented, then followed by a calculation of the plane wave real load impedance seen by a parallel combination of many cells that are used to make a transducer. Crosstalk between 1-D array elements is found to be due to two main sources: coupling through a Stoneley wave propagating at the transducer-water interface and coupling through Lamb waves propagating in the substrate. To reduce the crosstalk level, the effect of structural variations of the substrate are investigated, which includes a change of its thickness and etched trenches or polymer walls between array elements     

Finite element simulation of microindentation on aluminum

Vickers indentation of 6061-T6 aluminum was modeled using a three-dimensional finite element analysis (FEA) program. Two different work hardening behaviors were assumed. The results were compared with actual indentations using both a static microindenter and a load and depth recording microindenter. The hardness and plastic flow behavior showed excellent agreement, validating the FEA model, and implying that the work hardening of the aluminum decreases past a compressive strain of 0.09. The unloading results were analyzed using Sneddon's solution for the indentation of an elastic half-space by a rigid axisymmetric indenter. The results confirm the validity of applying Sneddon's solution in this case, implying that Bolshakov and Pharr's corrections of Sneddon's solution (which were determined for a conical indenter) are not directly applicable tothe Vickers indenter.     

Finite element simulation of piezoelectric vibrator gyroscopes

A finite element approach to the simulation of piezoelectric vibrator gyroscopes is presented for characteristic prediction. The formulation is given including the effect of Coriolis force due to rotation for a piezoelectric thin plate, which is considered to be two-dimensional in plane vibration. For numerical examples, the gyroscopes of a thin square plate, and a cross-bar and a ring built in the plate are considered, which pave the way for the development of the gyroscopes of monolithic configuration. The effect of the rotation on the modal shapes, the resonant frequencies, and the transmission characteristics are discussed demonstrating the sensing capability against the rotation     

Finite element simulation of elastic-creep growth of a semicircular surface crack

An initially semicircular crack loaded in Mode I tension with a material model similar to 316 SS at 600°C has been simulated using the finite element method. Two techniques have been used to predict creep crack growth. One technique assumes that the rate of crack growth does not effect the crack tip stress and strain rate distributions and that crack growth is determined by the stationary state conditions. A second technique is a more general approach. The crack is extended by the node release technique. Crack growth was predicted throughout on the basis of the C^* contour integral. When the stresses were non-stationary, this is termed C(t) and was used instead of C^* in the creep crack growth rate expression. Stresses, creep strains and displacements are discussed for this simulation.     

Finite dynamic element formulation for a plane triangular element

The higher order dynamic correction terms for the stiffness and inertia matrices associated with a triangular plane stress-strain finite dynamic element are developed in detail. Numerical results presented indicate that the adoption of these matrices along with a suitable quadratic matrix eigenproblem solver effects a significant economy in the free vibration solution of structures when compared with the analysis based on the usual finite element procedure. A FORTRAN IV computer program listing of the various relevant element matrices is also presented in the Appendix.     

Finite element simulation of phase field model for nanoscale martensitic transformation

A finite element framework of a phase field model for nanoscale martensitic transformation is proposed on the basis of time-dependent Ginzburg–Landau kinetic equations. The bulk total free energy consists of the chemical driving energy, the interfacial energy, the elastic energy, the inertial energy (for a dynamic case), the energy due to applied field and the effects of surface energy which need to be considered at the nanoscale. Single-variant and multi-variant martensitic phase transformations in a nano-sized NiAl plate are considered. The numerical results show the effects of each energy item on the phase transformation and the self-accommodating twinned morphologies as the result of strain energy minimization.     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

Finite element simulation of the braiding process for arbitrary mandrel shapes

An approach to simulate the two-dimensional braiding process using a commercial explicit finite element software is presented. Preforms with generic shapes are analyzed. A procedure is given to determine the boundary conditions of the braiding mandrel including the extraction of necessary geometry information. The friction coefficients needed as input parameters are determined in separate tests. The simulation results are processed with an algorithm that derives the braiding angle and the axial spacing of the yarns. For validation, a generic mandrel geometry is overbraided and a method to compare simulation and experiment is presented. The preform is analyzed using an optical sensor. The measurements are filtered and averaged. The simulation model is validated by comparing the braiding angle of simulation and experiment. A good agreement between simulation and experimental results is achieved.     

梯度陶瓷喷嘴残余应力的有限元分析

为了提高喷嘴的抗冲蚀磨损能力,将梯度功能材料理论运用于喷嘴材料的设计中,改传统的均质喷嘴材料为非均质喷嘴材料,提出在梯度陶瓷喷嘴制备中将残余压应力引入喷嘴入口的设计目标.在组成分布指数一定的条件下,针对主要设计参数对梯度陶瓷喷嘴残余应力的影响进行有限元分析,探讨了梯度层厚度、临界梯度层材料组分差对SiC/(W,Ti)C单梯度陶瓷喷嘴残余热应力的影响规律,在组成分布指数取0.5时,优化SiC/(W,Ti)C梯度陶瓷喷嘴梯度层厚和临界梯度层材料组分差.结果表明,残余应力随梯度层厚h及临界梯度层SiC体积组分差的不同产生很大差异,合理设计梯度层厚h及临界梯度层SiC体积组分差可在喷嘴入口形成有效残余压应力,最佳梯度层厚为5mm,临界梯度层SiC组分差小于5%(体积分数).     

带过渡段阶梯形变幅杆的有限元分析

对几组不同变幅比带不同过渡段的阶梯形变幅杆进行了有限元分析,获得了阶梯形变幅杆特性随过渡段形状和尺寸变化的一些规律。利用有限元软件ANSYS算出了每个变幅杆的纵振动模式谐振频率。并用其后处理功能得出了粗细端面的相对位移,由此计算振幅放大系数,得到的结果与已有的关于阶梯形变幅杆的理论以及实验结果符合得较好,计算出的谐振频率与实际测量值也较好地相符。文中还利用该软件计算了变幅杆粗细端分界面上的应力及其分布,数据表明过渡段可以显著改善粗细分界面上的应力集中。最后对导波理论和有限元分析方法的结果做了初步比较,两者亦符合较好。     

Finite element modeling of transient ultrasonic waves in linear viscoelastic media

Linear viscoelasticity offers a minimal framework within which to construct a causal model for wave propagation in absorptive media. Viscoelastic media are often described as media with `fading memory,' that is, the present state of stress is dependent on the present strain and the complete time history of strain convolved with appropriate time-dependent shear and bulk stress relaxation moduli. An axisymmetric, displacement-based finite element method for modeling pulsed ultrasonic waves in linear, homogeneous, and isotropic (LHI) viscoelastic media is developed that does not require storage of the complete time history of displacement at every node. This is accomplished by modeling stress relaxation moduli as discrete or continuous spectra of decaying exponentials and relaxation times. Details of the construction and computation of the time-dependent stiffness matrix are presented. As an application of the finite element method, a finite number of exponentials (amplitudes and relaxation times) are employed to represent a typical model for a continuous relaxation spectrum. It is demonstrated that a small number of discrete exponentials are required to model ultrasonic wave propagation of a typical band-limited pulse in a model material accurately. Previous work has shown this model to be consistent with other analytic models for wave propagation in viscoelastic media     

Finite element simulation of interfacial segregation in dilute alloys

The finite element software Comsol is used to simulate surface or grain boundary segregation in dilute alloys. The model computes simultaneously the evolution of interfacial concentration and diffusion in the bulk. The solute exchange between bulk and interface is governed by Darken’s equation. The model is able to reproduce thermodynamic and kinetic aspects of the phenomenon, in particular the saturation segregation level and the short-time segregation kinetics expressed by the McLean approximation. It is also able to reproduce experimental trends in the case of surface segregation of sulphur in a Ni superalloy. In the case of the grain boundary segregation of impurities (P or S) in engineering alloys, the present approach provides a practical tool, as it can be coupled to other finite element simulations (heat transfer and/or mechanics). Thus, it becomes possible to predict the risk of synergetic segregation and thermomechanical damage during service or processing (forging, welding,...).     

饱和砂土振动注浆的有限元模拟

在有限单元法基础上,考虑大位移大应变情形,采用套叠屈服面模型对饱和砂土振动注浆进行了数值模拟和分析。当振动荷载分别作用在孔底或孔壁上时,同一振动力随振动时间增长,残余孔压和峰值孔压均有所增加。振动力越大,历经同一振动时间的残余孔压和峰值孔压越大。当振动荷载作用持续一段时间,然后再施加注浆压力,发现孔壁中间节点径向位移达到最大值,向两端位移逐渐减小。