Local deformation in thin steel plates upon piercing

Institute of Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. 10, pp. 69–73, October, 1988.     

Waves in charged thin plates

The spectrum of bending waves of a thin conducting plate bearing an electric charge is investigated. It is proved that there exists a critical value of the field upon exceeding which bending instability of the plate occurs.     

Vibration of delaminated thin composite plates

Free vibration tests have been conducted to study the effect of low-velocity impact induced damage consisting of interlaminar delamination accompanied by matrix cracking on the natural frequencies of thin composite laminated circular plates. Local thickening has been identified, for the first time, as one of the important factors that influence the resonant frequencies of a plate after delamination. Two types of finite element models have been developed to simulate the experiments. Results from both the experiments and finite element modelling have been discussed.     

Quasi-static perforation of thin aluminium plates

This paper presents an experimental and numerical investigation on the quasi-static perforation of aluminium plates. In the tests, square plates were mounted in a circular frame and penetrated by a cylindrical punch. A full factorial design was used to investigate the effects of varying plate thickness, boundary conditions, punch diameter and nose shape. Based on the results obtained, both the main and interaction effects on the maximum force, displacement at fracture and energy absorption until perforation were determined. The perforation process was then computer analysed using the nonlinear finite element code LS-DYNA. Simulations with axisymmetric elements, brick elements and shell elements were conducted. Quasi-static, isothermal versions of the Johnson–Cook constitutive relation and fracture criterion were used to model the material behaviour. Good qualitative agreement was in general found between the experimental results and the numerical simulations. However, some quantitative differences were observed, and the reasons for these are discussed.     

Wave propagation in thin pre-stressed elastic plates

The propagation of elastic waves of small amplitude in a pre-stressed plate composed of an isotropic hyperelastic medium with a strain-energy function of general form, is investigated and the dispersion equation is derived. Approximate solutions for long waves are obtained. The implications for stability are discussed and a simple general criterion is established.     

Resonance acoustoelasticity measurement of stress in thin plates

A computer-driven, swept-frequency measurement technique is developed on the basis of resonance birefringence acoustoelasticity to evaluate the stresses in thin plates. The resonance frequency depends on the thickness and the elastic wave velocity; they change with stress because of the Poisson effect and the acoustoelastic effect. The resonance frequency is obtained from the spectral response curve in the electric impedance of the piezoelectric transducer. The frequency displacement induced by acoustically coupling the transducer can be minimized by employing the resonance peak closest to the transducer fundamental frequency. To illustrate the method, the residual stress is measured in butt-welded aluminum alloy plates and is compared with the results of conventional methods.     

Numerical simulation of welding distortion in thin plates

A three-dimensional model based on the finite-element method is developed to simulate the temperature field and stress distribution in the welding and heat-affected zones during fusion welding of thin plates. The governing equations are solved using the SYSWELD program commercial code. The model’s predictions are tested and verified against the experiments. Angular distortion and longitudinal bending are measured, the results are compared with those obtained from the mathematical model, and a relatively good agreement between them is found. The verified model is used to evaluate the effects of various parameters on the temperature and stress distributions in the welding and heat-affected zones of a thin austenitic stainless steel plate.     

The hybrid-stress model for thin plates

The assumed-stress hybrid finite element model is examined for application to the bending analysis of thin plates. A hybrid-stress functional is defined by using a Mindlin-type displacement assumption and including all components of stress. The Euler equations and matrix formulation corresponding to this functional are examined to assess the effects of plate thickness, and a rationale is presented for the selection of stress assumptions so that locking is avoided in the thin plate limit. To illustrate these concepts, a series of linear displacement quadrilateral elements are derived and tested, and the best of these elements is identified for suggested implementation in general-purpose computer programs.     

Analysis of thin plates by the element-free Galerkin method

A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into finite elements. The satisfaction of the C ¹ continuity requirements are easily met by EFG since it requires only C ¹ weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.Dedicated to J. C. Simo     

Scaling flow fields from the impact of thin plates

A dimensional analysis is performed to obtain velocity scaling relationships for the perforation of thin plates. The approach used is an extension of Dienes and Walsh's “late-stage equivalence” and Holsapple and Schmidt's “coupling parameter” concepts, used to simplify velocity scaling of impact phenomena. The coupling parameter C for plate perforation, is shown to have the form C=dU^μδ^ν for the perforation of thick plates and the form C=dU^μδ^ν f(t/d) for the perforation of thin plates (d is the projectile diameter, t is the plate thickness, U is the impact velocity and δ is the projectile density). It is shown that μ=1/2 for momentum scaling and μ=1 for energy scaling, however, from scaled hydrocode output it is found that, for aluminum impacting aluminum, the value of μ is equal to 0.83±0.03, which is neither energy nor momentum scaling. It is also shown that velocity scaling of thick plate perforation, using the same materials in the model and prototype and the same t/d, is not possible. An example of velocity scaling hydrocode output is given where the radial particle velocity wave profiles from the model calculation at U=55.6km/s and t/d=0.675 are similar to those from the prototype calculation with U=100km/s and t/d=1.08.     

Stress intensity factors for cracks in thin plates

This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented.     

Coercivity reduction in thin orthoferrite plates by annealing

High temperature annealing of thin polished plates of rare-earth orthoferrites has been found highly effective in reducing the coercivity resulting from mechanical processing. The annealing atmosphere must be oxygen or an oxygen-inert gas mixture free of reactive contaminants such as water vapor, carbon dioxide, and platinum oxide. Chemical reactions through contact of orthoferrite with other materials must be avoided. Annealing below 1000°C relieves elastic and plastic surface strains and is characterized by an activation energy of 5.8 × 10³cal/mole or 0.25 eV/molecule. Temperatures near 1500°C are required to remove brittle fracture damage. High temperature annealing may also be effective in reducing the coercivity caused by some bulk defects. The annealing process is capable of producing high quality orthoferrite plates suitable for domain propagation devices.     

Regularized BE formulations for the analysis of fracture in thin plates

A boundary integral formulation for the analysis of cracks in thin Kirchhoff plates is presented. The numerical solution of the relevant equations is addressed following three different approaches: two single integration methodologies initially introduced for 2D elastic solids are here reformulated, compared with a third (Galerkin) double integration approach and extended to the analysis of cracks in thin plates. exploiting an analogy with 2D elastic fracture mechanics. Comparative numerical testing, in terms of stress intensity factors, is performed with reference to straight and curved cracks in unbounded domains. This revised version was published online in August 2006 with corrections to the Cover Date.     

频率-波数域的薄铝板缺陷检测研究

文章将频率-波数域成像算法应用于薄铝板内圆形穿孔缺陷的检测。采用PZFlex软件建立多阵元线性阵列仿真模型,在薄铝板内激发出Lamb波,模拟超声相控阵全矩阵捕获功能。实验中使用M2M公司的超声相控阵仪器对带有通孔缺陷的薄铝板进行全矩阵捕获。基于全矩阵数据完成自发自收模式下的频率-波数法损伤重建,对全矩阵数据进行三维傅里叶变换,利用所有阵列的全部信息完成损伤重建。实验结果表明:频率-波数域成像法能够精确地表征出圆孔损伤的大小和形状,对单缺陷及不同大小、距离的双缺陷均具有良好的检测效果。相对于全聚焦成像法,频率-波数域成像法具有更高的分辨率。