Plane Strain Tests Research Articles

An eigenstrain-based model for residual stress arising from transient local surface heating

We present a model for approximating residual stresses arising from thermally induced plasticity and apply it to a simple two-dimensional (plane strain) test problem of transient heating. The model uses stress fields derived from simple eigenstrains to perturb an initially elastic-only solution in a way that mimics plastic flow. The plane strain condition of the test problem gives rise to plastic strains in the out-of-plane direction, owing to constraints on thermal expansion. However, the model is able to cope with the challenges this poses and also encapsulates the time-dependent nature of the problem. We show that the model agrees well with finite-element simulations under moderate strength heat sources provided that appropriate plastic flow rules are used. There exists sufficient generality in the model to allow its extension to more realistic scenarios.

Influence of advanced yield criteria on predictions of plastic anisotropy for aluminium alloy sheets

Extruded aluminium alloy sheets of AA7003-T6 are characterised by performing an experimental programme and numerical simulations. The anisotropic behaviour of the aluminium alloy is investigated using two linear transformation based anisotropic yield criteria Yld2000-2d (Barlat et al. [1]) and Yld2004-18p (Barlat et al. [2]). The yield criteria are calibrated using previously reported measured values of flow stress ratios and strain ratios obtained from uniaxial tensile tests and disc compression tests. The results from the model calibrations show that Yld2004-18p gives improved prediction. The evaluation of the selected yield functions is extended by performing numerical simulations of in-plane shear tests and plane-strain tension tests using the general-purpose non-linear FE code LS-DYNA. The results from the simulations show that the constitutive model based on Yld2000-2d predicts too low strength for the determined model parameters and indicates that the shape of the yield surface is inadequate. Predictions with the constitutive model based on Yld2004-18p gave better agreement with the experiments.

Observations on the extended Matsuoka–Nakai failure criterion

AbstractThe equivalent Mohr–Coulomb (M‐C) friction angle ϕ (J. Geotech. Eng. 1990; 116(6):986–999) of the extended Matsuoka–Nakai (E‐M‐N) criterion has been examined under all possible stress paths. It is shown that ϕ depends only on the ratio of cohesion to confining stress c′/σ and the frictional angle ϕ, where ϕ is the friction angle measured in triaxial compression (or extension) to which the E‐M‐N surface is fitted. It is also shown that ϕ is independent of c′, when σ=0 and of σ when c′=0, with the former representing an upper bound and the latter a lower bound of ϕ for any particular stress path. The closest point projection method has also been implemented successfully with the E‐M‐N criterion, and plane strain and axisymmetric element tests performed to verify some theoretical predictions relating to failure and post‐yielding behavior. Finally, a bearing capacity problem was analyzed using both E‐M‐N and M‐C, highlighting the conservative nature of M‐C for different friction angles. Copyright © 2009 John Wiley & Sons, Ltd.

A note on pseudo-cohesive behavior in quasi-bidimensional brittle fracture

This paper addresses the study of a planar crack in a plate with a slightly curved crack front, as found in most nominally plane strain tests. Rather than trying to make a full three dimensional analysis of the elastic fields, we look for a systematic procedure to project the three-dimensional features on the plane of the plate. This is achieved by though-the-thickness averaging of the stress and displacement fields. It is shown that the resulting fields are pseudo-cohesive, which means that their expressions are formally identical to those corresponding to a traditional cohesive zone. The results for two simple cases are given to illustrate the pseudo-cohesive behavior, although general results are derived as obvious consequences of the averaging process. The general procedure to carry out the analysis for any kind of crack front shape is indicated, and the application to special cases such as fatigue-grown cracks in metals and stably growing cracks in brittle polymers is shortly discussed.

Liquefaction Mapping in Finite-Element Simulations

Recent criteria have been developed to describe the onset of static liquefaction in constitutive models. This paper expands the theory to a finite-element framework in order to predict potentially unstable regions in granular soils at the engineering scale. Example simulations are presented for two plane strain tests and a submarine slope to demonstrate the applicability of a proposed liquefaction criterion to boundary value problems. In addition, loading rate and mesh size effects on the liquefaction prediction are examined. The methodology presented herein shows promise as a means of predicting soil liquefaction based on solid mechanical theory rather than empiricism.

Anisotropy of magnetic susceptibility study of kaolinite matrix subjected to biaxial tests

AbstractThe potential for structural failure of consolidated clay materials, which is of great importance in many applications, typically are assessed by measuring the localized strain bands that develop under anisotropic load stress. Most methods are precluded from providing a full understanding of the strain anisotropy because they only give two-dimensional information about the stressed clay blocks. The purpose of the present study was to investigate three-dimensional strain localization in a kaolinite matrix, caused by strain anisotropy due to a biaxial plane-strain test, using a relatively new method known as Anisotropy of Magnetic Susceptibility (AMS). This method involves induction of magnetism in an oriented sample in different directions and measurement of the induced magnetization in each direction. The AMS analyses were performed on core samples from different parts of the deformed kaolinite matrix. The degree of magnetic anisotropy (P′), which is a measure of the intensity of magnetic fabric and a gauge of strain intensity, was shown to be greater in cores containing shear bands than in those containing none. A threshold value for P′ for the deformed kaolinite matrix was identified, above which shear bands may develop. The comparison of the shape parameter (T), obtained from undeformed and deformed samples, illustrated a superimposition of prolate strain over the original oblate fabric of the kaolinite matrix. The orientation of the principal strain axis revealed that reorientation or rotation of the principal axis occurred along the shear bands.

Effect of Loading Mode on Strain Softening and Instability Behavior of Sand in Plane-Strain Tests

Experimental data to study the effect of loading mode on the strain softening and instability behavior of sand under plane-strain conditions are presented in this paper. A new plane-strain apparatus was adopted to conduct K0 consolidated drained and undrained tests under both deformation-controlled and load-controlled loading modes. The drained behavior of very loose and medium dense sand and the undrained behavior of very loose sand under plane-strain conditions were characterized. The test results show that the loading mode affects the postpeak behavior and controls whether strain softening or instability will occur in the postpeak region. Shear bands occurred in tests conducted on medium dense sand, but not in tests for very loose sand. The failure line and critical state line are not affected by the loading mode. The study also shows that the concept of a unique “ultimate state” for both dense and loose sand as previously established based on conventional drained triaxial tests is not supported by the...

Full-field measurement technique and its application to the analysis of materials behaviour under plane strain mode

The purpose of the paper is to provide a comprehensive experimental and numerical analysis of one of the encountered and critical state modes in sheet metal forming processes. The study is carried out with the help of the full-field measurement techniques. In order to confer some generality to the proposed work, several materials and different specimen shapes are considered that exhibit more or less homogeneous strain field. The proposed experimental study of the plane strain test is completed by a preliminary identification of the material parameters for non-linear behaviour at finite strains, using heterogeneous strain field.

Modified Direct Shear Test for Anisotropic Strength of Sand

This paper presents a simple method to estimate the directional dependency of granular soil strength using a modified shear box and a special specimen preparation procedure. This method is used to investigate the strength anisotropy of granular materials with particle shapes varying from spherical to angular. The experimental results show that the friction angle of granular materials varies with the orientation of shear plane relative to the bedding plane, and the degree of anisotropy is affected by particle shape. Comparison of the data from direct shear tests in this study with those of plane strain and torsional simple shear tests in the literature shows that direct shear using the modified direct shear box can reasonably capture the directional dependency of the friction angle for cohesionless materials.

Capturing strain localization in reinforced soils

Lade’s single hardening soil model with Cosserat rotation embodied in the finite element method is employed to investigate the behavior of geosynthetic reinforced soils with special attention to the development of shear banding. The ability of the finite element model to detect shear banding in a reinforced soil is examined against three high quality small-scale laboratory plane strain tests on Toyoura sand with and without reinforcement. These three tests were chosen because of the clear failure surfaces that developed in the soil during loading. The FEM analyses were able to reasonably simulate the plane strain laboratory tests including both unreinforced and reinforced cases. The FEM analyses gave reasonably good agreement with the experimental results in terms of global stress–strain relationships and shear band occurrences. Furthermore, and based on FE analyses of a hypothetical geosynthetic reinforced soil (GRS) retaining wall, it is shown that the geosynthetic reinforcements are very effective in hindering the formation of shear bands in GRS retaining walls when small spacing between the reinforcement layers was used. When used properly, the geosynthetic reinforcements made the soil behave as a truly reinforced mass of considerable stiffness and strength.

Anisotropy of magnetic susceptibility analysis of deformed kaolinite: implications for evaluating landslides

Plane strain tests were performed on seven kaolinite blocks, each of which developed shear bands. Anisotropy of magnetic susceptibility (AMS) analysis of the kaolinite reveals a threshold degree of magnetic anisotropy (P′) exceeding which shear bands develop. Since P′ is a strain-intensity gauge and soils are known to develop shear bands prior to landsliding, it is concluded that soil in every landslide-prone region must have its unique threshold P′ exceeding which it develops shear bands before failing. Therefore, AMS monitoring of soil in landslide prone regions is proposed as a potential tool in the management of natural hazard zones.

Undrained behaviour of Changi sand in triaxial and plane-strain compression

The results of an experimental study of the undrained behaviour of Changi sand under axisymmetric and plane-strain conditions are presented. K0 consolidated undrained plane-strain tests and K0 or isotropically consolidated triaxial tests on very loose and medium dense specimens were conducted. The undrained behaviour of sand at very loose and medium dense states under plane-strain conditions was characterised and compared with that under axisymmetric conditions. It was observed that the undrained behaviour of very loose and medium dense sand under plane strain is similar to that under axisymmetric conditions. However, because of the formation of shear bands in plane-strain tests, the post-peak behaviour of medium dense sand in plane strain is different from that in triaxial tests. It was also established that an instability line for plane-strain conditions can be defined in a way similar to that for axisymmetric conditions. Using the state parameter, a unified relationship between the normalised slope of instability line and the state parameters can be established for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can be used for plane-strain conditions.

Shear Strength of Jumunjin Sand according to Relative Density

The properties of sands pertaining to shear strength have been studied extensively by plane strain and triaxial tests for relative densities above 40%. Unfortunately, properties of sand have not been comprehensively studied for relative density below 40%. An experimental investigation of the shear strength of Jumunjin sand was carried out using a plane strain, triaxial and direct shear apparatus according to relative density ranges from 0 to 100%. Because of the complexity of the shear tests on coarse materials, correlations were developed that would be useful for practical purposes. This article presents a comparison of strength properties' results and their correlation with relative density.

Strain-softening behaviour of sand in strain path testing under plane-strain conditions

Experimental data are presented in this paper to study the strain-softening behaviour of sand under plane-strain conditions. K0 consolidated strain path tests were conducted using a new plane-strain apparatus. The stress–strain behaviour of medium dense sand under plane-strain conditions was characterized. The test results show that the occurrence of pre-failure strain softening under plane-strain conditions is affected by the void ratio, the strain increment ratio and the initial effective confining stress. This is consistent with previous findings established under axisymmetric conditions. However, a pre-failure strain-softening behaviour in plane-strain tests conducted under high-confining stresses may consist of three stages, namely, material softening, banding softening, and ultimate state. This observation is different from that in triaxial tests where banding softening does not normally occur.

Formability of Aluminum 5182-Polypropylene Sandwich Sheet for Automotive Application

The AA5182/polypropylene/AA5182 (AA/PP/AA) sandwich sheet is the material fabricated by adhering two aluminum skins to one polypropylene core. When it has the same flexural rigidity as a steel sheet, it is 65% lighter than the steel sheet and 30% lighter than an aluminum alloy sheet. Therefore, it is notified exclusively as good substitutive materials for a steel body to improve the fuel efficiency. Through AA/PP/AA sandwich sheet, however, it has relatively lower formability than that of the steel sheet for automotive application. In this study, we developed formability evaluation techniques in order to apply AA/PP/AA sandwich sheet for an automotive parts. For this purpose, newly adopting formability evaluations (using limit dome height and plane strain test) were carried out in order to secure the fundamental data for the measurement of sheet metal forming and the establishment of optimum forming conditions of the sandwich sheet. The results showed that there were in good agreements between the old formability evaluation method and the new one which was more simplified than that of the old one. From the results of these formability evaluations, the formability of sandwich sheet was higher than that of aluminum alloy sheet alone which was the skin component for the sandwich sheet. In addition, it was found that sandwich sheet could reduce the weight and could have the same flexural rigidity simultaneously when it was compared to the automotive steel sheet.

Influence of Membrane and Filter Paper on Plane-Strain Testing of Soft Sedimentary Rock

Abstract It is recognized that the intermediate principal stress plays an important role in the strength and the stress-dilatancy relation of soft sedimentary rock. However, few plane-strain/true triaxial experiments on soft rock have been referenced in literature due to the relatively high strength of geomaterials. With a conventional plane-strain apparatus, equipped with a prefixed plane-strain confining frame, it is difficult to obtain real isotropic consolidation before shearing. On the other hand, it has been found that the influence of the membrane/covering material on a high-strength specimen cannot be ignored. In this study, therefore, an innovative plane-strain test system for soft rock, that can overcome the shortcomings of the conventional type of apparatus, and issues related to specimen preparation are introduced. The results of drained compression tests and drained creep tests, along with theoretical simulations, are reported. The influence of the membrane and the filter paper are illustrated by a simple finite element method. A combination of experimental and theoretical approaches is employed to facilitate the understanding of the mechanical behavior of soft rock.

Plane Strain Test for Metal Sheet Characterization

This article shows the influence of a plane strain test specimen geometry on the measurable strain field and the influence of free edge effects over the stress computation. The experimental strain field distribution is measured over the whole deformable zone of a plane strain test specimen by an optical strain gauge. The chosen material is the DC06 IF steel of 0.8 mm thickness. The stress field is computed for several geometries at different strain levels by a Finite Element (FE) commercial code (Samcef ®). The results show that the stress field is sensitive to the specimen’s geometry and also to the tested material (strain field behavior is independent of material) and, based on results, an optimal specimen geometry is proposed in order to minimized the stress computation error.

Drained behaviour of Changi sand in triaxial and plane-strain compression

Many geotechnical problems are under plane-strain conditions. However, geotechnical designs still rely largely on testing data obtained under axisymmetric conditions. Therefore a good understanding of the similarities and differences between the strength and deformation behaviours of soil under plane-strain and axisymmetric conditions is important. Experimental data obtained from drained triaxial and plane-strain tests on very loose and medium dense sand are presented in this paper. The strength and deformation characteristics of the sand under plane-strain conditions are studied and compared with those under axisymmetric conditions. The results show that the failure envelope on the plane under plane-strain conditions is below that under axisymmetric conditions, although the friction angle under plane-strain conditions is higher than that under axisymmetric conditions. The critical state line and the stress–dilatancy relationship under plane-strain conditions are also different from those under axisymmetric conditions.

Strength of Sands in Wedge Shear, Triaxial Shear, and Shear Box Tests

Abstract Limited tests had indicated peak drained values of angle of internal friction Φ of gravelly sands measured in the cylindrical wedge shear test (cylwest) to be relatively closer to the Φ expected from plane strain tests than from triaxial tests. Such a difference was not obtained between the results of the prismatic wedge shear test (priswest) and the triaxial test on gravels and crushed rock. In this study, six sands with <3.35 mm particles were tested. It was seen that the main reason for the difference between the Φ values from cylwests and priswests was the difference in the angle δ between the shear plane and the bedding planes. Cylwests, in which δ was nearly the same as in triaxial tests, gave results close to those expected from plane strain tests, and almost identical results to those obtained from shear box tests on specimens so prepared as to make δ the same.

P-30 Formability of Aluminum 5182-Polypropylene Sandwich Sheet for Automotive Application

The AA5182/polypropylene/AA5182 (AA/PP/AA) sandwich sheet is the material fabricated by adhering two aluminum skins to one polypropylene core. When it has the same flexural rigidity as a steel sheet, it is 65% lighter than the steel sheet and 30% lighter than an aluminum alloy sheet. Therefore, it is notified exclusively as good substitutive materials for a steel body to improve the fuel efficiency. Through AA/PP/AA sandwich sheet, however, it has relatively lower formability than that of the steel sheet for automotive application. In this study, we developed formability evaluation techniques in order to apply AA/PP/AA sandwich sheet for an automotive parts. For this purpose, newly adopting formability evaluations (using limit dome height and plane strain test) were carried out in order to secure the fundamental data for the measurement of sheet metal forming and the establishment of optimum forming conditions of the sandwich sheet. The results showed that there were in good agreements between the old formability evaluation method and the new one which was more simplified than that of the old one. From the results of these formability evaluations, the formability of sandwich sheet was higher than that of aluminum alloy sheet alone which was the skin component for the sandwich sheet. In addition, it was found that sandwich sheet could reduce the weight and could have the same flexural rigidity simultaneously when it was compared to the automotive steel sheet.