各向异性复合材料尖劈的应力奇异性次数研究

为了确定各向异性复合材料尖劈的应力奇异性次数,提出了一种确定广义平面应变情况下各向异性弹性接合材料界面端应力奇异性次数的一维特殊有限元法。该方法基于最小势能原理,通过坐标变换和变量分离消除径向坐标,把应力奇异性次数的求解降阶为仅与环向坐标相关的一维问题。采用三节点一维等参数二次单元,对该一维线性领域做网格划分。数值计算结果与理论解比较,表明该方法具有很高的精度和效率。     

Local stiffening effect of 'double deck1 bending strain gauges: part 2

In stress measurement where it is difficult or impossible to access the inside surface of the structure, "double deck" (DD) or "sandwich" bending strain gauges can be used to measure both the membrane and bending strains. A DD gauge consists of a pair of constituent foil gauges which are bonded on the upper and lower surfaces of a plastic base or filling. It is mounted on the external surface of the test specimen to measure the external surface strain, and by extrapolation, the internal surface strain of the. specimen. The. sensitivity of the DD bending gauge increases when the separation between the pair of constituent foil gauges increases. However, this also increases the stiffness of the whole gauge. If the stiffness of the DD gauge is significant compared with that of the plate to which it is attached, the presence of the gauge may cause significant changes in local stiffness and result in errors of strain interpretation. This study is presented in two papers. Part I, appeared in the Feburary 1996 issue of Strain, presented an approximate analytical solution for the local stiffening effect of a DD gauge, and quantifies the errors in the strain measurement. Part 2 (this paper) presents the verification of the. solution using a three-dimensional finite element calculation, a parametric study and a correction method that can be applied easily. The extrapolation errors due to the stiffening effect and random reading noises are also explored. The figure and equation numbers in this part are continuedfrom Part 1, but the reference numbering is specific to Part 2.     

采用SemiLoof型约束条件的薄板矩形广义协调元

本文采用SemiLoof型约束条件,建立一个十二自由度的薄板矩形广义协调元。单元自由度只含角点位移,不含Loof结点位移、单元间的协调条件全部采用点型协调条件,不采用积分型协调条件。此单元吸取广义协调元和SemiLoof元的双重优点,消除其缺点,成为同类低阶薄板单元中的最优单元。     

Finite element analysis of creep fracture initiation in a model superalloy material

Detailed finite element analyses were performed for a single edge-cracked specimen geometry under both plane stress and plane strain constraint for a superalloy material that obeys a power-law creep relationship. The objectives of these analyses were to elucidate the stationary creep crack-tip fields and to provide guidance for the experimental measurement of crack-tip deformations. New results demonstrate that, for both plane stress and plane strain, the angular variations in the creep strain fields do not agree with HRR-type predictions, although the radial variations are in agreement with HRR-type creep strain field predictions in a zone very near the crack tip. Thus, the use of experimental measurement of surface displacement and/or strain data for the location of HRR-type fields may not be possible, unless modifications to the existing HRR-type theory are made. It is also noted that the size of the stress-based HRR-dominance zone is only a fraction of the creep zone size in plane stress, and is very small (especially along =0°) compared to the creep zone size in plane strain. Furthermore, the dominance of the singular strain fields are at least two orders of magnitude smaller than the corresponding stress dominance zones. As such, unless the microstructural features of the material are smaller than the dimensions of the dominance zones, the basis for using stress or strain-based fracture parameters derived from the HRR-type fields for prediction of creep fracture initiation is unclear.     

AN UPPER BOUND FINITE ELEMENT PROCEDURE FOR SOLVING LARGE PLANE STRAIN DEFORMATION

A unique and robust upper bound finite element procedure is developed for the analysis of large plastic deformation problems under plane strain condition. It can consistently treat problems with isotropic strain varying materials. It can also effectively solve problems with any initial ‘guessed’ velocity field, even from an random number generator. To explore and demonstrate the capability of this new approach, strip tension and plane strain compression problems are solved. For validation, the computed results are compared with existing analytical or experimental solutions in good agreement. The phenomenon of shear band formation can be simulated and, as expected, is found to develop more distinctly in strain softening materials than in perfectly plastic and strain hardening materials. © 1997 by John Wiley & Sons, Ltd.     

板坯连铸结晶器内铸坯凝固及变形的热力耦合有限元分析

建立板坯连铸结晶器内凝固坯壳形成及其应力和变形的热力耦合有限元分析模型,采用二维瞬态热传导有限元方法分析温度场,采用二维热弹塑性接触有限元方法计算应力分布。编制了有限元程序,计算分析了三种结晶器锥度、三种拉坯速度和三种保护渣层情况下,结晶器内Q235铸坯凝固坯壳的形成过程。得到凝固坯壳的温度场、厚度、变形、与结晶器壁间的气隙以及应力分布等,得到该三种工艺参数对结果的影响规律。     

Local stiffening effect of 'double deck' bending strain gauges: part 1

In stress measurement where it is difficult or impossible to access the inside surface of the structure, "double deck" (DD) or "sandwich" bending strain gauges can be used to measure both the membrane and bending strains. A DD gauge consists of a pair of constituent foil gauges which are bonded on the upper and lower surfaces of a plastic base or filling. It is mounted on the external surface of the test specimen to measure the external surface strain, and by extrapolation, the internal surface strain of the specimen. The sensitivity of the DD bending gauge increases when the separation between the pair of constituent foil gauges increases. However, this also increases the stiffness of the whole gauge. If the stiffness of the DD gauge is significant compared with that of the plate to which it is attached, the presence of the gauge may cause significant changes in local stiffness and result in errors of strain interpretation. This study is presented in two papers. Part I presents an approximate, analytical solution for the local stiffening effect of a DD gauge and quantifies the errors in the strain measurement. Part 2, to appear subsequently in Strain, will present the verification of the solution using a three dimensional finite element calculation, a parametric study and a correction method that can be applied easily. The extrapolation errors due to the stiffening effect and random reading noises are also explored.     

Heat conduction effects on strain localization in plane-strain tension

The deformation behaviour of a rectangular block under tension is investigated for a rate- and temperature-dependent solid using the finite element method. Isotropic behaviour is assumed and the effect of deformation-induced heat generation is studied in conjunction with heat conduction. Localization into diffuse necking is examined by applying the instability criterion defined for the particular rate-dependent behaviour. The influence of different thermal boundary conditions on the deformation mode considered, is demonstrated by means of parametric studies.     

一种新型厚薄板通用三角形广义协调元

本文提出了一种假设单元剪切应变场的新方法,基于广义协调理论构造了一个只有9个自由度的三角形厚薄板通用单元TCGC-T9.数值算例表明:该单元具有自由度少,精度高,无剪切闭锁现象等特点,适用于从极薄板到厚板较大的范围。     

QUADRATIC TRIANGULAR C0 PLATE BENDING ELEMENT

In this paper, a six-node triangular C⁰ plate bending element is developed by the assumed strain formulation. The sampled transverse shear strains in the element are chosen such that the latter has a favourable constraint index of shear locking and the strains are optimized with respect to a linear pure bending displacement/rotation field. It happens that the optimal strains are the mean strains along the element edges and medians. Numerical examples reveal that the element is free from shear locking and passes all the patch tests for plate bending elements. Moreover, the element accuracy is close to that of a state-of-the-art seven-node assumed strain element. © 1997 by John Wiley & Sons, Ltd.     

Characteristics of three-dimensional stress fields in plates with a through-the-thickness crack

Three-dimensional finite element analyses were performed on plates with a through-the-thickness crack. Global-local finite element technique with sub-modeling was used to achieve the refinement required to obtain an accurate stress field. The existence of a weaker singularity was verified, and a model was proposed to explain the behavior of stresses in the boundary layer. This model is able to account for the competing interaction between the inverse square root singular term and the vertex singular term. The energy release rate was calculated using the modified crack closure method and energy balance. A simple technique without 3-D calculation was suggested for evaluating an approximate 3-D stress intensity factor at the mid-plane. The effect of plate thickness on the size of the three-dimensional region was studied, and the validity of two-dimensional linear elastic fracture mechanics was discussed.     

采用广义协调条件构造具有旋转自由度的四边形膜元

本文根据广义协调的概念[1],通过引进单元结点刚体转角,提出两种具有平面内旋转自由度的四边形膜元。单元列式简单,是能通过任意四边形分片检验的收敛单元。数值计算表明这两种单元无论是位移还是应力都有很高的计算精度。     

Transverse shear and pressurization effects in the bending of plates with reinforced cracks

The authors develop an eigth-order model for bending of transversally isotropic plates and use integral transforms and a collocation method to form a line-spring model for a cracked plate. The eigth-order model allows satisfaction of the three standard plate bending boundary conditions; the normal moment, twisting moment, and transverse shear force, and an additional shear stress resultant that allows analysis of transverse normal stresses near the crack tip. The line-spring model is used to develop geometry correction factors for bending of finite-thickness plates, accounting for transverse shear deformation and pressurization of the plate near the crack tip. The line-spring model is then applied to the problem of a plate with a reinforced crack, and the results are used to validate an interpolation solution based on an energy method. While not explicitly analysed, the models are applicable to many problems, including bending of bonded repairs, fracture and fatigue of composite and layered materials, surface cracks, crack tip plasticity and crack closure or crack face interaction.     

Semi-analytical model based on generalized plane strain assumption for unidirectional composites with matrix micro cracks

Generalized plane strain state is assumed and stress-based finite strip method is formulated for analysis of unidirectional laminates with matrix microcracks. Total complementary potential energy is minimized and fourth-order Euler Lagrange governing equations are presented. This stress-based generalized plane strain approach analyzes general layup and loading conditions. It provides flexibility to control the number of finite strip nodal lines within each lamina; hence, stress behavior can be predicted across each lamina at the desired location of the structure. Along with all of the capabilities which are common with finite strip methodology based on plane strain assumption, this current work has extended the analysis of the cracked laminate. For example, by incorporating behavior of the out of the plane shear stress, boundary conditions including natural boundary conditions are imposed appropriately to solve governing Euler's equations. Results are compared with previously developed displacement-based formulation in the literature for cracked laminates. It has already been shown that a stress-based plane strain approach enhances variation-based cracked laminate analysis where only the case of cross-ply laminate under tension is considered. This current work applies generalized plane strain-based finite strip methodology to carry out analysis under different loading conditions.     

采用面积坐标的四边形厚薄板通用单元

本文采用四边形面积坐标,利用假设剪切应变场方法和广义协调理论构造出一个具有12个自由度的四边形厚薄板通用弯曲单元TACQ。基本思路如下:首先从Mindlin厚板理论出发,独立假设剪应变场和挠度场,而转角场则由挠度场和剪应变场导出;其次,单元剪应变场是先按Timoshenko厚梁理论确定单元各边剪应变,然后在单元内进行合理插值导出;第三,单元挠度场是根据单元角点处挠度的点协调条件以及单元各边挠度和法向转角的平均协调条件导出。这个方法有两个特点,(1)由于满足点协调和边协调的广义协调条件,故能保证收敛;(2)由于在薄板情况剪应变退化为零,故不出现剪切闭锁现象。数值算例表明:该单元具有精度高,收敛性和可靠性好,对网格畸变不敏感,无剪切闭锁现象等优点;适用于从极薄板到厚板较大的范围。     

弯曲凹模形状与受力的有限元分析

在弯曲模设计中,人们对模具形状的设计考虑甚少,而模具形状对模具内部受力状态有重要影响。合理的形状可以大大减少模具内应力,提高模具寿命。本文用有限元法对三种形状的弯曲凹模进行了力学分析。结果表明,不同形状模具的内应力有很大的差异,证明优化模具形状设计是提高模具设计水平的一个重要方面。本文为合理设计模具外形提供了参考依据。