The effect of doubly tapered strut morphology on the plastic yield surface of cellular materials

Although the literature on the mechanics of cellular materials is vast, there is no theoretical model to account for the effects of axial yielding of struts aligned to the applied loading direction on the plastic yield surface under multiaxial loading conditions. An anisotropic hexagonal model having tapered strut morphology is developed to show these effects on the plastic yield surface under multiaxial tensile loading condition. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square cellular materials, and three-dimensional (3D) hexagonal and rhombic cellular materials of rod-like columnar structure. A tetrahedral element with tapered strut morphology is also used for a foam model to illustrate these effects on the yield surface under axisymmetric loading condition. Plastic collapse due to bending moment in the inclined struts is a dominant mode. However, under multiaxial tensile loading, the collapse due to axial yielding of struts parallel to the loading direction is found to be an important mode. The shape of plastic yield surface was found to depend not only on relative density but also on the strut morphology.     

THE ELECTROIMPACT COMPACTION OIF POWDERS: MECHANICS, STRUCTURE AND PROPERTIES

An electroimpact compaction method recently developed for powder consolidation is described In terms of the basic principles of electric discharge and dynamic compaction processes. The influence of processing parameters, microstructural characteristics and mechanical properties of preforms obtained are discussed. Mathematical models for the mechanics of compaction, electrical resistance, discharge current variations and comparisons with experimental results are presented. The best set of properties are obtained when electrical discharge is applied to cause interparticle fusion at the instant when dynamic compaction pressure attains its peak level.     

Aspects of the mechanics of driving nails into wood

For nail driving, some aspects of the effect on penetration of the hammer mass, the speed at impact, the nail size and section shape and the driving direction in relation to the wood grain are reported.A 6 in. long, 0·236 in. dia., round nail was strain gauged to show how the strain in the nail varies with time during an impact.An analysis, which reasonably accounts for the experimental results, is developed for predicting the strain pulse in the nail, the amount of penetration by the nail and its time under strain.Maintaining the same kinetic energy input at each blow, it is found that the larger the initial penetration, the smaller is the further penetration.The effect on penetration depth of the material backing to the piece of wood is reported.The variation of the Euler buckling load with the nail penetration for a specific type of wood and nail dimensions is given.     

Large deflexion response of square frames to distributed impulsive loads

A study of the elastic-plastic response of portal and free-free square frames subjected to distributed magnetomotive impulse is made. A finite difference method which reduces the structure to small masses connected with light links is used to solve the equations of motion of the deforming frames. The links are assumed to have the same strength properties as the material of the structure. Another analytical method is also used which assumes rigid-plastic properties and also allows for changes in geometry during the transient response of symmetrically loaded rectangular frames. The instantaneous profiles obtained from the high-speed photographs and the final deflexions substantiated the predictions of both analytical methods.     

固粒击靶的有效摩擦系数

定义一种固粒击靶的有效冲击摩擦系数为粘着项与犁沟项的组合,其中包含表征剪切金属结合点的状态滑动或滚动的状态参数以及表征冲击物在击靶过程中产生犁沟效应的状态参数。研究表明,对于硬钢球斜冲击软钢靶情况,在连续滑移的情况下,只有在计及接触斑点的微粒间的相互作用的一定条件下,粘着项的值才可能接近0.05,这是Hutchings为使一系列数值计算的钢球反弹速度及角度与实验结果一致,在所有计算中所取的调节参数“摩擦系数”值。然而,研究表明,对于著名的Hutchings实验,如果连续犁沟发生,犁沟项则是冲击过程及初始冲击角的函数,就过程平均而言,其值大于0.05。由此,可认为,冲击过程中可滑移界面瞬间的滑移、滚动及犁沟状态的转化使Hutchings实验中的“摩擦系数”约为0.05;一般而言,这些状态的转化使固粒击靶的有效摩擦系数的过程平均值远小于低速简单滑移的摩擦系数。     

Effective elastic constants of two-dimensional cellular materials with deep and thick cell walls

In order to analyse the elastic constants of cellular materials with deep and thick cell walls, finite element analysis using two kinds of unit cell approach (stiffness matrix method and compliance matrix method) is performed which is applicable to any orthotropic cellular materials. Comparison between results from the FEA, the theories presented in this paper and experiments of previous investigators indicate that the elastic constants of cellular materials with thick cell walls depend not only on the relative density but also on the joint stiffening effect. Approximate formulae under generalised plane strain conditions are also presented for the purpose of obtaining the effective elastic constants for cellular materials with deep and thick cell walls. A satisfactory agreement was found with experimental results obtained on a deep and thick cellular material. The results indicate that the previous models in which the wall of cellular materials is treated as a simple beam are not adequate to evaluate the effective elastic constants of cellular materials with deep and thick cell walls. In addition, considerable attention needs for the measurement of effective Young's modulus of square cellular materials in the two soft directions because it is strongly affected by misalignment errors.     

Dynamically loaded variable thickness cantilevers using a magnetomotive impulse

Dynamical equations governing the plastic deformation of a rigid-perfectly plastic, constant-width cantilever whose cross-sectional thickness is a linear function of length, subject to impulsive tip loading, are obtained and the plastic hinge speed and root rotation are predicted.

Six experimental results are given for root rotation vs root thickness to tip thickness ratio when a constant magnetomotive tip impulse is delivered.     

Stress analysis of two-dimensional cellular materials with thick cell struts

Finite element analyses (FEA) were performed to thoroughly validate the collapse criteria of cellular materials presented in our previous companion paper. The maximum stress (von-Mises stress) on the cell strut surface and the plastic collapse stress were computed for two-dimensional (2D) cellular materials with thick cell struts. The results from the FEA were compared with those from theoretical criteria of authors. The FEA results were in good agreement with the theoretical results. The results indicate that when bending moment, axial and shear forces are considered, the maximum stress on the strut surface gives significantly different values in the tensile and compressive parts of the cell wall as well as in the two loading directions. Therefore, for the initial yielding of ductile cellular materials and the fracture of brittle cellular materials, in which the maximum stress on the strut surface is evaluated, it is necessary to consider not only the bending moment but also axial and shear forces. In addition, this study shows that for regular cellular materials with the identical strut geometry for all struts, the initial yielding and the plastic collapse under a biaxial state of stress occur not only in the inclined cell struts but also in the vertical struts. These FEA results support the theoretical conclusion of our previous companion paper that the anisotropic 2D cellular material has a truncated yield surface not only on the compressive quadrant but also on the tensile quadrant.     

A morphological elastic model of general hexagonal columnar structures

A general three-dimensional (3D) anisotropic hexagonal model of columnar structure with non-uniform strut morphology is developed. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square honeycombs, and 3D hexagonal and rhombic cellular materials of rod-like columnar structure. The effective elastic constants are determined taking account of bending, axial, and shear deformations of the struts. Unlike the theoretical work of other investigators for 2D honeycombs, considering bending, axial and shearing deformations of struts, the present model not only produces transverse isotropy for regular hexagonal columnar structure but also provides a consistent Poisson's ratio when applied to a square honeycomb. The effect of tapered strut morphology on the elastic properties of cellular structures is investigated. For the general hexagonal columnar structures, the bending compliance is the dominant function for the in-plane elastic constants of 2D and 3D structures (excluding the in-plane shear modulus of rhombic structures) and the out-of-plane shear moduli of 3D structures, but the axial compliance is dominant for the in-plane shear modulus of 2D and 3D rhombic structures and the out-of-plane Young's modulus of 3D structures. For cellular materials with the same relative density, the presence of taper increases values of the effective Young's and shear moduli for which the bending compliance is dominant, but decreases those for which the axial compliance is dominant. It is found that the effective elastic properties of cellular materials are dependent not only on the relative density but also on strut morphology both in cross-section geometry and its variation along the strut length which the present model takes account of. These results illustrate the importance of the strut morphology in calculating the effective elastic properties of cellular materials.