Axisymmetric Tension Research Articles

Analysis of crack branching morphology in a disk of brittle material under axisymmetric tension by using branching dimension

In order to characterize the complex crack branching patterns observed in the brittle fracture of disk specimens under axisymmetric tension, the branching dimension is newly denned from a power relation between the radius of a circle and the total crack length contained in the circle by using a crack branching law which was introduced in previous research. The branching dimension corresponds to the change of nominal stress with increasing crack length when a power relation is applicable between the nominal stress and the crack length. The branching patterns which were observed both for the flexural tests of disks of brittle materials and the bulge tests of disks coated with brittle materials were well expressed by the branching dimension.

On the evolution of texture and yield loci in axisymmetric deformation of F.C.C. polycrystals

A comprehensive analysis of texture formation and the evolution of macroscopic yield loci in face-centered cubic polycrystalline metals is presented for each of axisymmetric tension and compression, based upon the classic aggregate model of Taylor [1938a]. The nonuniqueness of slip rates corresponding to rate-independent hardening theories is resolved in two alternative ways: the average slip method (Bunge [1970]) and minimum plastic spin (Fuh & Havner [1989]). Calculations to logarithmic strains of 1.61 in tension and compression are carried out for each of four hardening rules: the “simple theory” (Havner & Shalby [1977]), Taylor hardening (Taylor & Elam [1923]), the “P.A.N. tule” (Peirce, Asaro, & Needleman [1982]), and a two-parameter rule (Nakada & Keh [1966]). The results compared with each other, with other computational studies (for both rate-independent theories), and with experimental information on texture.

Axisymmetric Tension Testing of Geomembranes

Abstract The newly developed axisymmetric tension test is useful in evaluating the performance of geomembranes subjected to out-of-plane stress conditions such as those that can develop due to localized subsidence under waste-containment cover and liner systems. In this paper, the equations necessary to describe the geomembrane stresses and strains during testing are derived, and equations used to calculate geomembrane stresses during axisymmetric field loadings are also presented and compared. Finally, the testing equipment and procedures are investigated.

The effect of particle shape and stiffness on the constitutive behavior of metal-matrix composites

This paper deals with the effective constitutive behavior of ductile metals reinforced by aligned spheroidal inclusions with linear-elastic properties. For simplicity, both the matrix and the inclusions are assumed to be incompressible and isotropic, so that the overall constitutive behavior of the metal-matrix composites is incompressible and transversely isotropic. Based on a recently proposed variational method for estimating the effective behavior of nonlinear composites, results are obtained for the initial yield surfaces and overall stress-strain relations in terms of the three essentially distinct loading modes for this class of composites : Axisymmetric tension (relative to the symmetry axis of the inclusions), longitudinal shear (along the symmetry axis) and transverse shear (perpendicular to the symmetry axis). It is found that particle shape has a significant effect on the effective response of the composites, and that this effect is markedly different for the three loading modes. For the axisymmetric mode, oblate and prolate shapes have the largest strengthening effects ; for the transverse mode, oblate shapes are most effective ; and for the longitudinal mode, nearly spherical shapes are best. Particle stiffness also has a strong effect on the initial yielding behavior of the composites, which is magnified for the more severe aspect ratios. On the other hand, the stiffness of the particles does not seem to significantly affect the stress-strain behavior of the composites for strains greater than about five times the yield value.

The effects of rate sensitivity and plastic potential surface curvature on plastic flow localization in porous solids

Plastic flow localization in porous elastic-viscoplastic solids is analyzed with an emphasis on the effects of material rate sensitivity and plastic potential surface curvature. The effect of rate sensitivity is included in a material model that accounts for a change of yield surface curvature in a rate-insensitive porous ductile solid. Shear band formation under plane strain and axisymmetric tension, and localized necking in biaxially stretched sheets are analyzed by using the present material model. The results illustrate the interactions of the effects of void nucleation and growth, material rate sensitivity and plastic potential surface curvature on plastic flow localization. The effects of nonproportional straining paths on localized necking in thin sheets are also demonstrated.

Hydrogen-assisted ductile fracture in spheroidized 1520 steel: Part II. Pure bending

The effects of hydrogen on ductile fracture were investigated in a spheroidized steel similar to AISI 1520, containing negligible amounts of P and S, using notched bend bar tests. The effects of hydrogen were exhibited either in the form of enhanced plastic instability along characteristic slip traces in mode II or of enhanced, strain-controlled, local crack tip processes. The contri-bution of enhanced plastic instability, however, was only apparent under conditions in which flow localization also occurred without hydrogen. The role of plastic instability near the crack tip was found to be dominant in these bend bar tests, whereas it was small or negligible in previous tests in axisymmetric tension. Microstructural effects were rationalized in terms of a critical, local concentration of hydrogen. The intrinsic effect of hydrogen appeared to be the enhancement of strain-controlled fracture processes.

Crack initiation, propagation and branching in a disk of brittle material under axisymmetric tension

The most stable crack nucleation and crack branching patterns in an infinite plate under axisymmetric tension were analysed by using Griffith theory. The analytical results were compared with the experimental results of flexural tests on glass, ceramic, and acryl disks. The strain energy released by nucleation of a star-shaped crack, U, was approximately given by U = (2πσ 2a 2/E)(1 − 1/n) , and the strain energy release rate, G n , by G n = (47πσ 2a/E)(1/n)(1 − 1/n) , were σ is nominal tensile stress, a is crack length, n is crack number, and E is elastic modulus. The energy consideration on the basis of Griffith theory indicated that the most stable crack nucleation shape in a homogeneous brittle material is a line-shaped crack ( n = 2). In addition, the most stable crack length after the ith branching has occurred, a i , is given as: a i = {(2 2i + 1)/(2 i + 1 − 1)}{Eγ/πσ i 2])} , where σ i is the nominal stress at the ith crack branching and γ is the surface energy per unit area. The experimental results of flexural tests on the disk specimens of brittle materials corresponded well to the analytical results.

軸対称引張り荷重を受けるぜい性材料円板におけるき裂分岐形態の分岐次元による解析

In order to quantify the crack branching morphology of brittle materials under axisymmetric tension, the “branching dimension” was defined in the present paper, and the relation between the branching dimension and fracture mechanics parameters was introduced.The branching dimension Db is defined as: Db=d(logLi)/d(logai), where Li is the total crack length after i-th crack branching has occurred and ai is the crack length which corresponds to the distance from crack nucleation point to crack tip. When the nominal stress σi varies with increasing crack length ai according to the relation, σi/σ0=(ai/a0)m, the branching dimension Db can be expressed by:Db=2+2m=2+2·d{log(σi)}/d{log(ai)}where σ0 and a0 are the stress and the crack length at crack initiation. Moreover, Db can be expressed by the change of the number of cracks, n, with increasing crack length, ai:Db=1+d{log(n)}/d{log(ai)}The branching dimension can well characterize the branching patterns obtained from the flexural test of Pyrex glass, ceramic and high strength steel specimens.

Flow Localization Behaviors of Thermo-Elasto-Viscoplastic Cylindrical Bars under Axisymmetric Tension.

Flow Localization Behaviors of Thermo-Elasto-Viscoplastic Cylindrical Bars under Axisymmetric Tension.

A stress ratio parameter for studying the workability of metals—Tension and compression

Axisymmetric tension and compression tests were simulated using the rigid-viscoplastic finite element analysis code ALPID 2.1. The tension test simulations were run for strain rate sensitivity parameters in the range of 0.2–1.1. The compression test simulations were run for 0.2, 0.4, and 0.8 strain rate sensitivity parameters and for 0.0, 0.001, 0.150, and 0.800 friction factors. Variations of the stress ratiog (mean stress/effective stress) in combination with the strain rate and with respect to time have been studied. The rate of change of the square of theg parameter with respect to the log of the strain rate allows a useful description of the material workability within the simulated test specimens during the deformation processes.

The effect of void shape on void growth and ductility in axisymmetric tension tests

The effect of void growth and ductility in axisymmetric tension tests was examined theoretically. The inelastic response of periodic arrays of initially oblate spheroidal voids in a homogeneous isotropically hardening matrix was analyzed for loading histories representative of axisymmetric tension tests. The failure strains were taken as the point where the deformation mode became that of uniaxial strain. All subsequent deformation was localized to ligaments between the voids. The results showed that, for stress states with a low hydrostatic stress component, the void growth rates were governed primarily by the void dimension perpendicular to the tensile axis. They also indicated that the failure strains were proportional to the projected area of the voids onto a plane perpendicular to the tensile direction, in agreement with published experimental results. For stress states with higher triaxiality, the influence of the initial aspect ratio was diminished.

軸対称引張り荷重を受けるぜい性材料円板におけるき裂発生形態

The most stable crack initiation pattern in an infinite plate under axisymmetric tension was analyzed by using Griffith theory. The result was compared with the experimental results of flexural tests using glass and ceramic disks.The strain energy release rate Gn for nucleation or propagation of a star-shaped crack is approximately expressed as Gn=(4πσ2a/E)(1/n)(1-1/n), where a is the crack length, n is the number of cracks, σ is the applied stress, and E is the elastic modulus. The energy consideration on the basis of Griffith theory indicated that the most stable crack uncleation pattern in homogeneous and uniform brittle materials under uniform tension is a line shaped crack (n=2). In addition, even if a star-shaped crack happens to pre-exist in a brittle material, it may propagate only as a line-shaped macro-crack. This theoretical deduction was confirmed by the flexural tests on glass and ceramic disks.

Ductile fracture in spheroidized 1520 steel

Ductile fracture was investigated in a spheroidized steel, similar to AISI 1520, which contained negligible amounts of P and S. The detailed substeps of the ductile fracture process were characterized by careful sectioning studies. It was found that 1. (i) void initiation appeared to be controlled by a criterion involving stress, 2. (ii) void growth was predominantly affected by plastic strain, 3. (iii) additional strain was needed to arrive at final fracture even after the void coalescence stages, comprising microvoid coalescence and macrovoid coalescence, had occurred and 4. (iv) the central crack growth in tension mainly depended on the strain concentration at the crack tip. The effect of localized deformation on fracture could not play a role in axisymmetric tension, due to a high critical strain for shear band formation.

Effect of Yield Surface Curvature on Necking and Failure in Porous Plastic Solids

The effect of material path dependent hardening on neck development and the onset of ductile failure is analyzed numerically. The calculations are carried out using an elastic-viscoplastic constitutive relation that has isotropic hardening and kinematic hardening behaviors as limiting cases and that accounts for the weakening due to the growth of micro-voids. Final material failure is incorporated into the constitutive model by the dependence of the plastic potential on void volume fraction. Results are obtained for both axisymmetric and plane strain tension. Failure is found to initiate by void coalescence at the neck center in axisymmetric tension and within a shear band in plane strain tension. The increased curvature of flow potential surfaces associated with the kinematic hardening solid leads to somewhat more rapid diffuse neck development than occurs for the isotropic hardening solid. However, a much greater difference between the predictions of the two constitutive models is found for the onset of ductile failure.

Crack-growth prediction in axisymmetric pull-out and tension specimens

A methodology is developed which combines the basics of reinforced concrete, three-dimensional plasticity, stress freezing and the shear-difference method and utilizes the maximum-tensile-stress criterion to predict crack locations and their direction of propagation in reinforced axisymmetric specimens. The advantages of using a three-dimensional photoelastic model include: (1) the generation of stress trajectories, (2) the accurate location of singular zones and stress concentrations, and (3) the direct observation of internal cracks.

Axisymmetric Tension of an Infinite Body Containing a Series of Spherical Cavities

The problem of an elastic infinite body containing a series of spherical cavities under tension is treated. It is assumed that several spherical cavities with equal radii are arranged on a line at equal intervals and that the infinite body is subjected to uniform tensile stress in the direction of the line of cavities. The method used in this study is a numerical one in which the general solution of the biharmonic equation in the polar coordinates is recurrently superposed until all boundary conditions at the surface of each cavity are satisfied. Calculated results for the stress concentration factor are indicated in some diagrams for various values of the number of cavities, the ratio between their interval and radius, and Poisson's ratio.

Mechanical behavior of fetal dura mater in axisymmetric biaxial tension

Mechanical behavior of fetal dura mater in axisymmetric biaxial tension

Axisymmetric Tension of an Infinite Body Containing Two Spherical Cavities

A problem of stress concentration in an infinite body which contains two spherical cavities of equal diameter and is subjected to uniform tension in the direction of the row of cavities is treated in this paper. A method of solution is proposed for this problem, in which the solution for an infinite body with one cavity is superposed recurrently on the solution of an infinite body without cavity so that the boundary conditions on the surfaces of two cavities are satisfied. The validity of this method is verified by comparing the calculated results with the solutions obtained by H. Miyamoto and with the results by the finite element method. Numerical results obtained by the present method are shown in some illustrated figures.

Axisymmetric Tension of an Infinite Body Containing Two Spherical Cavities

直径の等しい2球かを持つ無限体が軸対称単軸引張りを受ける問題を解析し,応力集中に関する一連の結果を求めた.解析には,1球かを持つ無限体の問題の解を利用し,両球かの表面に交互に分布荷重を繰返し与えて,球か表面の境界条件を近似的に満たす数値解法を用いた.

The Stress Field in an Elastic Half Space Having a Spheroidal Inhomogeneity Under All-Around Tension Parallel to the Plane Boundary

Stress distributions are evaluated for a semi-infinite elastic body having a spheroidal inhomogeneity under an all-around tension (axisymmetric uniform tension) at infinity. Boussinesq’s potential functions are used for the analysis. A special technique is employed for the traction-free condition on the free surface, where the ordinary Legendre functions are expressed in terms of the Bessel functions in cylindrical coordinates. A closed-form expression for the stress concentration factor is found for a special case of a needlelike inhomogeneity.