Plane Strain Tension Tests Research Articles

Geomembrane Response in the Wide Strip Tension Test

The geomembrane wide strip tension test is a performance test that provides test data from which the stress-strain response of a geomembrane may be calculated. However, the volumetric response of the geomembrane must be accounted for when processing the test data to obtain the geomembrane stress-strain properties. This paper presents the results of strain controlled, uniaxial tension tests performed on two common polymeric geomembranes. During the tests, measurements were taken at specific locations on the geomembrane specimen. These measurements, combined with results from photographic analyses, allowed the specimen width and thickness to be determined during the tests. The measured values corresponded well with the theoretical values, assuming that the geomembrane is incompressible. The test results were not sensitive to the aspect ratio of the test specimen. The wide strip tension test should be considered a uniaxial (not a plane strain) tension test. It was also shown that modeling the stress-strain response of polymeric geomembranes with a constant cross sectional area instead of a constant volume significantly underestimates the actual stress-strain response of the geomembrane, particularly at large strains.

５０８３アルミニウム合金板の集合組織と成形性に及ぼす熱間圧延後熱処理の影響

Effects of heat treatments after hot-rolling on subsequent cold-rolling and annealing textures, and formability for 5083 alloy sheets were investigated by means of pole figures measured with X-ray, uniaxial tension, plane strain tension, bulging and deep drawing tests. The influence of the temperature of the heat treatment on precipitation and recrystallization during subsequent annealing after cold-rolling was analysed using transmission electron microscopy and Vickers hardness tests. The following conclusions were obtained: Heat treatments after hot-rolling can make texture components {123}<634> and {112}<111> become stronger, especially for the latter. They also cause {110}<112> to become weaker during the subsequent cold-rolling. During annealing above the recrystallization temperature, the heat treatments can produce a mixed texture with both stronger {112}<111> and {100}<001>, and weaker {110}<112> components. The mixture of textures has caused the limit diameter ratio of deep drawing to increase and in-plane plastic anisotropy to decrease. The improvement of formability of the alloy sheets is ascribed to both the increase of solid solution of Mn and Mg and the decrease of precipitates caused by the heat treatments after hot-rolling, and also to the evolution of textures on subsequent cold-rolling and annealing.

Plane-Strain Tension Tests on Aluminum Alloy Sheet

A simple way of making plane-strain tension tests on sheet specimens has been developed. This method was used to test sheets of aluminum alloy 2008 T4 and the results were analyzed in terms of a high exponent yield criterion and isotropic hardening. Experimentally measured forces agreed with those calculated from strain measurements using uniaxial tension test curves.

アルミニウム薄板の延性の向上に対する変形中の焼なましの影響

Interstage annealing is often employed as a method to increase the forming limit of sheet metals. This paper describes the effect of interstage annealing on the surface roughening and the improvement of limit strain of aluminum sheets. A rigid-plastic finite element simulation of plane strain tension was firstly made to predict how the limit strain could be increased by the interstage annealing and how the surface roughening would develop with plastic strain after the interstage annealing. Uniaxial tension, plane strain tension and hole expansion tests were then carried out to confirm the result of simulation. The simulation and experimental results show that the interstage annealing contributes to the recovery of ductility, but on the contrary, the increase in plastic strain due to the annealing causes the development of the surface roughening which induces a localized necking. As a result of these two effects which oppose each other, the total strain achieved is limited even if the number of interstage annealing is increased.

Numerical Analysis of Plane-Strain Tension Test for Rate-Dependent Solids

The plane-strain tension test is analyzed numerically for a material with strain and strain-rate hardening characteristics. The effect of the prescribed rate of straining is investigated for an additive logarithmic description of the material strain-rate sensitivity. The dependency to the imposed strain rate so introduced is shown to have a significant effect on several features of the load-elongation curve such as the attainment of the load maximum, the onset of localization, and the overall engineering strain.

Plane strain finite element simulation of shear band formation during metal forming

AbstractA plane strain finite element formulation and solution procedure for shear band failure during the plane strain metal forming process are developed and presented. The large strain elastic‐plastic formulation includes a 5‐node 10‐degree‐of‐freedom (d.o.f.) ‘crossed‐triangle’ element, a 4‐node 8‐d.o.f. element with selective reduced integration, an 8‐node 16‐d.o.f. element and a 4‐node 8‐d.o.f. element with an embedded shear band. The formulation includes an elastic‐plastic material model with a modified Gurson yield function and combined isotropic‐kinematic hardening. The solution procedure is based on a Newton–Raphson incremental‐iterative method with an orthogonal projection of zero or negative eigen‐modes when required. Two different examples of plane strain tension test are studied with results compared with available numerical solutions to evaluate the present formulation and solution procedure of the four different elements. The results demonstrate that both types of the 4‐node quadrilaterals are comparable to the 5‐node crossed‐triangle element as well as the 8‐jiode element. To further validate and to demonstrate the predictive capability and practical applicability of the present development, two plane strain metal forming examples are investigated. The first application is a numerical simulation of a sheet‐stretching test with results compared with experimental data for a commercially pure aluminium–magnesium 5182‐O sheet. The load vs. extension history and the through‐thickness strain are compared. The good agreement suggests that it is possible to numerically determine the parameters needed for the modified Gurson yield function. The second application is a numerical simulation of the formation of dead metal zones in the extrusion process. A plane strain extrusion of a short aluminium billet through straight‐sided dies is presented and characteristic features of the formation of dead metal zone are observed.

Thermal aspects of shear localization in microporous viscoplastic solids

AbstractA set of phenomenological state variable constitutive equations for large deformations of isotropic, thermo‐elasto‐viscoplastic, porous materials is considered, and a new semi‐implicit, incrementally objective time‐integration procedure for these constitutive equations is developed. The constitutive equations and the time‐integration procedure are implemented in a finite element program, and used to study the shear band formation and ductile fracture initiation triggered by flow softening due to the combined effects of void growth and deformation heating, in a plane strain tension test.

Influence of precipitate microstructure on flow and forming properties of an aluminum alloy sheet

A 7075 aluminium alloy sheet was cold rolled, solution heat treated and artificially aged to underaged (UA) and overaged (OA) conditions. A careful fabrication and heat treatment procedure was followed in order to obtain UA and OA sheets having the same isotropic crystallographic texture and uniaxial yield strength. Hydraulic bulge tests, plane strain, and uniaxial tension tests were performed to characterize the mechanical behavior of these materials. The forming limit diagram (FLD) was also obtained for these two conditions. Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) were used to characterize the precipitate microstructure, slip line patterns and fracture surfaces. Experimental observations showed that both macroscopic and microscopic responses of the materials to plastic deformation was strongly affected by the precipitate microstructure. FLDs were theoretically computed with the Marciniak and Kuczynski (MK) analysis, using the yield locus calculated with the Taylor/Bishop and Hill (TBH) theory for polycrystalline plasticity and the stress-strain curve corresponding to both UA and OA conditions. The predicted results were in good agreement with experiments for sheet in the OA condition, and they were not for the material in the UA condition. This was explained in terms of yield surface shape, consistent with the slip line characteristics, though differences in fracture behavior may contribute to these observations. The yield surface shape effect was emphasized since it provides, besides fracture, an alternate interpretation of failure mechanism near balanced biaxial tension, and since it can be described fairly well with a simple phenomenological description of plastic behavior.

CBR Strength (Puncture) of Geosynthetics

Abstract While there exist many types of mechanical tests for use on geosynthetics, most seem to be more suitable for one type of system or another. This paper focuses on a test which may have widespread applicability to assess the strength of all types of geosynthetics. It is the forcing of a 50-mm (2.0-in.) diameter plunger through a horizontally fixed geosynthetic of 150-mm (6.0-in.) diameter. Such dimensions are common to the California bearing ratio (CBR) test apparatus used in assessing soil strength for road subgrades. In actuality, the test is not a puncture test, but is an axisymmetric strength test and should be considered as such. The unsupported geosynthetic is indeed in a state of tension. The stress conditions are well defined, which allow for stress and strain to be calculated and compared to the actual value as obtained in a plane strain (wide width) tension test. This approach has been followed in this study wherein a wide range of geosynthetics (geotextiles, geomembranes, geonets, and geocomposites) have been tested for CBR (puncture) strength and then calculations performed to determine stress and strain. These calculated values were then compared to those obtained in wide width tests. Results are interesting in that the average values of percent variation between wide width tensile strength and CBR calculated tensile strength for those geosynthetics tested are as follows: (1) geotextiles ±12%, (2) geomembranes ±33%, (3) geonets ±17%, and (4) geocomposites ±10%. It is felt that this type of test (which is basically an index test) is helpful in a number of situations, not the least of which is in assessing strength changes before and after exposure of various geosynthetic materials to chemical or biological incubation.

Yield locus of 70/30 brass sheet metals

Yield stresses in uniaxial tension, biaxial tension and close to plane-strain tension tests were determined in a 70/30 brass sheet metal. These results were compared to those obtained by Wagoner [ Metall. Trans. A13, 1491 (1982)] and by Vial et al. [ Int. J. Mech. Sci. 25, 899 (1983)]. Biaxial tension yield stress was greater than uniaxial tension yield stress, and it could be predicted with exponents 1.66–1.75 of Hill's (1979) yield criterion. Close to plane-strain tension tests produced lower strain hardening than uniaxial tension tests; both yield stresses became very close at true strains greater than 0.1. This effect required an increase of the exponent of Hill's (1979) yield criterion, to values greater than 2.0. The set of results obtained by the present research could not be adequately described by the simplified form (Case 4) of Hill's (1979) yield criterion. A study of the evolution of crystallographic textures with strain, along different loading paths, should be performed in order to gain a better understanding of the change in shape of the yield locus of 70/30 brass sheet metals.

Development of new workability test techniques

Two new test methods have been developed for determining the suitability of materials for bulk deformation processing such as rolling, forging or tube making. The tests can be performed on any compressive machine (press or hammer), using a pair of rectangular, opposing anvils of w a width and L lenght. In the “partial-width indentatin test” a work-piece of h = L thickness and w = w a + h width is indented, so that the material overhangs the anvils by b = h/2 on each side. On closing the material expelled from between them puts the “ribs” into secondary tension. After thinning down, materials of moderate ductility fracture, and the reduction in height is a measure of workability (and is about one half the reduction of area in the tension test). In the “secondary-tension test” holes are drilled in the slab, and the ribs thus formed are subjected to tension and, finally, fracture by the co-operating anvils. The reduction of area is a measure of work-ability (and agrees well with reduction of area in a plane-strain tension test). As a result of work described here, the test geometry has been standardized to give greatest sensitivity of measurement without undue sensitivity to unintentional variables. Experiments showed the suitability of these tests for evaluating workability for cold as well as hot working, and for studying the effects of inhomogeneities typical of as-cast structures, such as surface defects, segregation, coarse-grain effects and other variables beyond the reach of usual test methods. The simple tooling may be accommodated in production equipment, thus allowing investigations of workability at relevant temperatures and strain rates in an industrial or laboratory environment.

Deformation and fracture behavior of zircaloy-2 deformed at constant strain rate in iodine environment. II. Plane strain tension test.

Deformation and fracture behavior of zircaloy-2 deformed at constant strain rate in iodine environment. II. Plane strain tension test.

Workability of Aluminum Alloy 7075-T6 in Upsetting and Rolling

The workability of aluminum alloy 7075-T6 was investigated in upsetting and rolling at room temperature with reference to occurrence of free-surface cracks. The fracture criterion was established by a plane-strain sheet tension test and an upset test. An improved version of the matrix method was used to obtain the complete solution in upsetting. Then a workability chart was constructed by combining the fracture criterion and the complete solution for various friction conditions and several specimen dimensions. In rolling, a theory for the analysis of spread was utilized to compute the strain history at a point on the free edge surface. With this theory it was possible to predict workability in multipass rolling with reference to edge cracking. The limiting reductions in thickness were given as functions of workpiece dimensions for various friction values. Experimental results demonstrated that the predictions were very good.

Relationship Between Plane-Strain Ductility and KIc for Various Steels

In most structural steels, the critical plane-strain stress-intensity factor, KIc, which represents the inherent ability of the material to resist crack propagation, increases with increasing test temperature. In many steels, the rate of increase of KIc with test temperature increases markedly above a temperature region which is designated the fracture-toughness transition region. Because of this transition behavior with temperature and the inherently high fracture toughness of many steels, very thick specimens must be tested to determine valid KIc values. However, the large size of these specimens and the cost of conducting the tests minimize the usefulness of this procedure as a research tool for analyzing the fracture behavior of steels under plane-strain conditions. Therefore, as part of a long-range program to obtain KIc values from small specimens, the relationship between KIc and the ductility measured in a small plane-strain tension test was investigated. The results showed that the temperature transition of the plane-strain tensile ductility at fracture, εf.ps, paralleled that of the KIc, whereas the temperature transition of the axisymmetric ductility (measured in a conventional round tension specimen) was quite different from that of the KIc. At any temperature, the relationship between these properties for steels ranging in yield strength, σy, from 80 to 250 ksi is approximated by the equation KIc=Aσyε2f.ps where A is a constant for a given steel. This relationship indicates that for certain steels the KIc value approaches an upper limit or shelf value with increasing temperature, because as the test temperature increases, the plane-strain tensile ductility approaches an upper limit and the decrease in yield strength becomes negligible. The existence of a KIc shelf would imply that in thick sections the material could fail suddenly, even at elevated temperatures. However, because of the rapid rate of increase of the plastic-zone size with temperature (and thus the through-thickness plastic flow at the crack lip), steels in conventional thicknesses would lose plane-strain constraint at temperatures approaching that for the KIc shelf, and therefore only ductile behavior would be expected at shelf temperatures.

Sommarî

A two-step approach is proposed to investigate the shear band formation in cold-rolled aluminum alloy sheet during plane strain tension, compression and simple shear tests. In the first step, a finite element model with only one element using Taylor type polycrystal plasticity model is applied to compute the stress-strain curve of the deformation. In the second step, a full scale mesoscopic simulation is applied for a further study of the details of the shear band development for cases with higher possibility of shear band formation as judged from the results in step 1. Systematic studies show that the hardening/softening features of stress-strain curves obtained by one-element method well agree with the extent of macroscale shear bands development in mesoscopic scale simulation: softening or flat stress-strain curves correspond to the formation of severe macroscale shear band in mesoscopic scale simulation, and the stronger the softening is, the more severe the macroscale shear band is, whereas no macroscale shear band is developed when the curves exhibit continuous and obvious hardening. Therefore, when it is needed to investigate probability and features of shear band formation in many samples or loading modes, e.g. loading along different directions, people can use the first step to efficiently estimate the possibility of macroscale shear band development for all the cases concerned, and then apply the full scale mesoscopic simulation only for those cases where stress-strain curves exhibit little hardening or softening features. Our calculations show that the computation efficiency can be substantially improved by the two-step approach.