Change In Voided Volume Research Articles

Finite element analysis of void growth in elastic-plastic materials

Three-dimensional finite element computations have been carried out for the growth of initially spherical voids in periodic cubic arrays and for initially spherical voids ahead of a blunting mode I plane strain crack tip. The numerical method is based on finite strain theory and the computations are three-dimensional. The void cubic arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear and high triaxial stress. The macroscopic stress-strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field. For the problem of the initial spherical voids directly ahead of a blunting mode I plane strain crack tip, conditions of small scale yielding were assumed. The near tip stress and deformation fields were obtained for different void-size-to-spacing ratios for perfectly plastic materials. The calculations show that the holes spread towards the crack tip and towards each other at a faster rate than they elongate in the tensile direction. The computed void growth rates are compared with previous models for void growth.

Void Growth in Elastic-Plastic Materials

Three-dimensional finite element computations have been done to study the growth of initially spherical voids in periodic cubic arrays. The numerical method is based on finite strain theory and the computations account for the interaction between neighboring voids. The void arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear, and high triaxial stress. The macroscopic stress-strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction, and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field.

てん料の分布状態とシートの性質 ＩＩ シート断面構造に及ぼすてん料の影響

Filler distribution was evaluated for cross sections of different filler loaded papers. The fillers used in this investigation were talc, clay, ground calcium carbonate andtwo types of precipitated calcium carbonate (calcite and alagonite). The results are summarized as follows.(1) The specific gravity and refractive index of the fillers used in this study are similar to each other, so the major differences among these fillers seem to be only in their size, shape and zeta potential.(2) For all filler loaded papers except those loaded with clay, it is clear that the z-directional count and width of filler aggregates increases as the filler particle size dicreases. A good correlation between z-directional count and width was obtained, regardless of filler type, but the correlation for clay loaded papers differs from that obtained for the other fillers.(3) The area fraction of filler aggregates tends to increase as filler particle size decreases. Inspection of different filler loaded papers by a scanning electron microscope or mercury intrusion technique showed that the change in area fraction with filler type may be attributed to a change in void volume of filler aggregates.

Linear elastic materials with voids

A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed. In the two year period between the submission of this manuscript and the receipt of the page proof, there have been some extensions of the results reported here. In the context of the theory described, the classical pressure vessel problems and the problem of the stress distribution around a circular hole in a field have uniaxial tension have been solved [19,22]. The solution given in the present paper for the pure bending of a beam when the rate effect of the theory is absent is extended to case when the rate effect is present in [21]. The various implications of the rate effect in the void volume deformation are pursued all the subsequent works [19,20,21,22].

The significance of the storage parameter in saturated‐unsaturated groundwater flow

An essential feature of transient groundwater movement is the phenomenon of change in groundwater storage. Storage change is governed by three fundamental processes: change in void volume of the skeleton, change in fluid saturation, and change in fluid density. Since the expansivity of water is very small, the phenomenon of change in storage in fully saturated media is dominated by matrix deformation. When the soil is partially saturated it is customarily assumed that the matrix is essentially rigid and desaturation is the only process governing change in storage. While this assumption may be reasonable at relatively low saturations, it may not be valid at high saturations or in the transition zone between the saturated and unsaturated regimes. The key to the understanding of this lies in a proper appreciation of the constitutive relationships that exist between mechanical stresses on the one hand and moisture suction on the other. This paper examines the theoretical as well as the practical consequences of the role of soil deformation in saturated‐unsaturated groundwater flow.

Void Behavior as Influenced by Pressure and Plastic Deformation

Void behavior has a pronounced effect on the properties and soundness of most materials, and is strongly influenced by the magnitude of hydrostatic pressure during plastic deformation. Using the upper bound theorem approach with a model of idealized geometry to simulate a void-material composite, an analytical criterion for the minimum effective pressure necessary to initiate a permanent void volume change is developed. This pressure is called critical pressure, and its absolute value is the same whether for compression and void closure or tension and void opening. A deviation parameter is also defined, and it indicates that voids of a given geometry will start to open faster under tension than they will start to close under compression of the same magnitude. To compare the aforementioned analytical predictions with real material behavior, copper split billets with artificially introduced voids of predetermined geometries were deformed under different magnitudes of hydrostatic pressure: the process of wire drawing for low pressure deformation, and the fluid environment of hydrostatic extrusion for higher pressure deformation. Those characteristics found to lead to significant void volume change are: (a) high void volume fraction, (b) large relative void size, and (c) voids of unity or greater aspect ratio. Experimental data compared well with the analytical curves; thus, the analytical expressions should be useful in explaining and predicting the behavior of voids in some real materials.