Takeji Abe

Relation between damage due to circular holes and local deformation of perforated sheets

In the present paper, we propose a new method using the voronoi tessellation and the stereology to evaluate the local damage state due to voids during ductile fracture process. The damage tensor component is calculated based on a representative unit cell obtained from distribution function of line segments of voronoi polygons. Perforated sheets were set up as the plane models of damaged materials and were examined under the condition of uniaxial tension, where the deformation of circular holes is measured. The experimental results show that the distribution of damage tensor components obtained here corresponds well to the fracture pattern of model specimens. It is also shown that the local plastic deformation, i.e. the deformation of each hole is closely related to the damage tensor.

Observation of Microscopic Plastic Deformation of Polycrystalline Aluminum during Uniaxial Tension by Confocal Laser-Scanning Microscope

Microscopic plastic deformation behavior of aluminum sheet during uniaxial tension is experimentally investigated by a confocal laser-scanning microscope. The surface roughening is closely related to the inhomogeneity of polycrystalline metals, that is, to the inhomogeneous plastic deformation of respective grains. Image measuring method of rigid rotation of grain is proposed. It is shown that the averaged grain rotation on the surface plane is much less than the averaged grain rotation out of the surface plane. The averaged grain rotation, the grain-area strain and the mean size strain and the standard deviations of these parameters increase statistically in proportion to the applied strain. The grain rotation in the material is less than that on the surface, thus it is considered that deformation inhomogeneity of grains in the material is less than that of grains on the surface of the material. This fact may indicate that the surface roughness is mainly affected by inhomogeneous deformation of the surface layer. Discussions are made on the grain rotation, the inhomogeneous deformation of the grains and the free surface roughening mechanism. Introduction Almost all metals used in the industries are polycrystalline, and microscopic deformation behaviour of polycrystalline metals is important for estimating macroscopic deformation behavior and strength. Free surface of polycrystalline metal becomes roughened after plastic deformation. It is known that the surface roughening is closely related to the inhomogeneity of polycrystalline metals, that is, to the inhomogeneous plastic deformation of respective grains [1-6] as well as that in the grains [5-10]. Therefore, the experimental study of the surface roughening is also important for the understanding of microscopic deformation behavior of polycrystalline metals. In the present paper, the inhomogeneous deformation on the free surface of polycrystalline aluminum specimen during uniaxial tension is studied. The inhomogeneous deformation of grains in the central area of the free surface of specimen is observed by a confocal laser-scanning microscope (CLSM). The confocal laser-scanning microscope is convenient, which can be used to observe in the atmosphere, and the scanning distance in z-direction is larger than that of the normal optical microscope. The relation between the strain in respective grains and the shape of free surface roughness curve caused by tensile plastic strain is investigated. Discussions are also made on the relation among the variations of strain in each grain, the wavelength of the profile and the surface roughness due to the applied strain. Experimental Method Specimen. The material used in this work is polycrystalline pure aluminum for industrial use (Al 99.5% by weight). The shape of tensile specimen is shown in Fig. 1. The z-axis is the normal Key Engineering Materials Online: 2004-10-15 ISSN: 1662-9795, Vols. 274-276, pp 337-342 doi:10.4028/www.scientific.net/KEM.274-276.337

Quantitative Description of Microscopic Plastic Deformation of Polycrystalline Aluminum Using Laser-Scanning Microscope

The mi c ros copi c pl as t i c de format ion behavior of pol yc r ys t al l ine aluminum shee t dur ing uni axi al t ens ion i s exper iment al l y inves t iga t ed b y a confoc al l a s e r - s canning mi c ros cope. The gr ain rot at ion i s me asur ed f rom images of spec imen sur fa c e be fore and a f t e r deformat ion i s propos ed. Digi t al image proc es s ing t e chnique i s appl i ed to the sur f a c e gr ain image t aken by the CCD c ame ra . The exper iment al dat a obt ained f rom man y gr a ins a re s t a t i c al l y proce s s ed. I t i s shown that the gr ain rot at ion i s l a rge when the shape of gr ain i s clos e to a ci r cl e. Di s cus s ions a r e made on the r el at ion be twe en gra in rot at ion, s t ra ins of gr ains and va r ious f a ctor s af f e ct ing them, such as gr ain s i z e, gra in shape and s l ip- l ine angl e.

Surface Roughening and Formability in Sheet Metal Forming of Polycrystalline Metal

The r–value is defined as the ratio of the width strain to the thickness strain under the uniaxial tensile test of the sheet metal. Based on r-value of grains, a model of plastic deformation of polycrystalline metal and surface roughening after plastic deformation was proposed in the previous paper. Meanwhile, Marciniak and Kuczynski proposed the so-called M-K model which give the analytical estimation of the formability of sheet metal under biaxial stretching considering a certain irregularity of the thickness of the sheet metal. Yamaguchi et al showed that the experimentally measured surface roughness may correspond to the surface irregularity suggested in the M-K model. In the present paper, the formability of sheet metal under biaxial stretching is analyzed based on the previous analysis of surface roughening caused by the difference of the r-value in the sheet metal.

FEM analysis on elastic-plastic deformation of perforated sheets

The influence of distribution and growth of voids on macroscopic mechanical properties are important issues in the ductile fracture of metals. In the present paper, we consider perforated sheets with regularly distributed holes as a simple model for void containg materials. Elastic-Plastic deformation of perforated sheet, where circular holes are distributed regularly, was analyzed numerically under the plane stress condition by means of finite element method introducing the periodic boundary conditions. It is shown that the deformation behavior depends highly on the distribution and arrangement of holes. This results in anisotropy of yield stresses of perforated sheets, which is related to the stress concentration near the holes. It is also shown that the plastic region in perforated sheets does not develop simply in the direction to adjacent holes.

Characteristics of surface roughening during plane strain compression of polycrystalline iron

Roughening behavior of the free surface of polycrystalline iron during plane strain compression is investigated experimentally. The changes in the shape of the free surface, which is roughened during plastic deformation, are observed in the three-dimensions. It is found that the mountains and the valleys of the roughened shape tend to elongate in the constrained direction for the specimen with isotropic grain shape. The shapes of the roughness curves in the loading direction and in the constrained direction are compared. The normalized height distribution of the roughness curve in the constrained direction is symmetric, while that of the roughness curve in the loading direction is asymmetric and positively skew during plane strain compression. Based on a simple simulation of the roughness curves by a random midpoint displacement method, this difference is supposed to be caused by the constraint of the material flow under plane strain condition.

SURFACE BIFURCATION AND SURFACE ROUGHENING OF INHOMOGENEOUS MATERIAL DURING PLASTIC DEFORMATION

The roughening of free surface of metallic materials during plastic deformation is analysed by using plane model of inhomogeneous material and finite strain version of elastic-plastic finite element method. The J2- deformation theory is used as constitutive equation. It is shown that the surface roughening caused by both material inhomogeneity and surface bifurcation is larger in compressive deformation than in tension.

On the Role of Grains in Plastic Deformation and Low Cycle Fatigue of Polycrystalline Metal

In the previous papers, the author discussed the role of r-value (anisotropic parameter in plasticity) on the surface roughening after plastic deformation. In the present paper, discussion is made on the effects of mutual constraint of deformation between neighboring grains at the grain boundary on the surface roughening. A characteristic parameter called constraint ratio is introduced to express the degree of the mutual restriction between grains. The well-known Coffin-Manson relation in low cycle fatigue is deduced considering to the surface roughening after cyclic deformation.

On the Relation between R-Value of a Grain and the Operating Slip Systems of the Grain

The r-value is defined as the ratio of the width strain to the thickness strain under uniaxial tensile loading. The r-value can be defined for each grain in polycrystalline metal during plastic deformation. It was pointed out that r-value of a grain affects the surface roughening of polycrystalline metal, and hence also affects the formability of thin sheet metal. On the other hand, it was shown that by using a rate-type constitutive relation for crystal slips the effect of the number of active slip systems on the yield curves is clarified. In the present paper, the relation between r-value of a grain and its operating slip systems in polycrystalline metals is studied.

Roughening of Contact Surface During Plane Strain Compressive Plastic Deformation of Polycrystalline Copper.

Changes in surface roughness and three-dimensional microscopic shapes of contact surface of polycrystalline copper during plane strain compressive plastic deformation are studied. The roughening of contact surface is measured with a stylus instrument. The microscopic change in surface shape is also observed with a scanning electron microscope. The roughness of contact surface measured in the free direction is larger than that measured in the constrained direction for the specimen having transverse contact surface. Meanwhile, the roughness of contact surface measured in the loading direction of the specimen having longitudinal contact surface is a little larger than that measured in the free direction. From the observation by a scanning electron microscope, it is seen that the mountains and the valleys which appear on the free surface are sharp, while those on the contact surface are relatively rounded.