Plane Strain Tests Research Articles

Performance review of various uncoupled fracture criteria for TRIP steel sheet

The exact numerical description of ductile fracture for advanced high strength steel (AHSS) sheets, particularly for different deformation modes, is an ongoing issue for the sheet metal research community at large. Although, in the last few decades, several research groups have proposed different fracture criteria, there is no consensus on suitability of one particular criterion especially for AHSS sheets. Hence, in the present work, the performance of six important fracture criteria was assessed for TRIP1180 sheet deformed under different loading conditions. Mechanical tests that induce different loading conditions – uniaxial tension, bulge, shear, hole-expansion, plane strain and 3-point bending tests, were conducted. A finite element study was performed using a commercial explicit finite element solver integrated with an appropriate material subroutine. The constitutive equations and material parameters were taken from a previous work carried out on the same TRIP1180 sheet. Finally, six uncoupled fracture criteria were applied to describe the fracture in numerical simulations. The study showed that traditional uncoupled fracture criteria describe the fracture reasonably well. Results also revealed that a high number of fracture coefficients are no guarantee for improved fracture prediction under different loading conditions.

Feasibility Study of a Combined Tension-Torsion Hopkinson Bar

The increasing interest to improve the description of the plastic behavior and the fracture prediction for ductile materials under complex loading conditions conducted the researchers to overcome the J2 plasticity theory. To do this more sophisticated plasticity model base on ductile damage have been implemented. Material model parameters must be identified by means of proper testing and calibration procedures requiring different loading conditions. Different types of tests must be performed, imposing multiaxial stress paths to the specimens. Tensile tests on smooth and round notched bars, plane strain tests, torsion tests, compression and combined tension–torsion tests on hollow and solid cylindrical bars must be executed. While multiple works are present in literature for model assessment and validation in quasi-static conditions, nothing can be found at high strain rate in biaxial conditions (tension-torsion). Biaxial tests in dynamic conditions are very difficult to carry out especially if you are interested to register the entire story of stress and strain. In this work, analytical and numerical study to evaluate the feasibility to carry out dynamic tension, dynamic torsion, dynamic torsion-static tension/compression and dynamic tension–dynamic torsion tests is discussed. The tests will be performed using a properly designed Split Hopkinson Bar.

Micromechanical modelling of ductile fracture in pipeline steel using a bifurcation-enriched porous plasticity model

In this paper, we investigate the possibility of predicting ductile fracture of pipeline steel by using the Gurson–Tvergaard–Needleman (GTN) model where the onset of void coalescence is determined based on in situ bifurcation analyses. To this end, three variants of the GTN model, one of which includes in situ bifurcation, are calibrated for a pipeline steel grade X65 using uniaxial and notch tension tests. Then plane-strain tension tests and Kahn tear tests of the same material are used for assessment of the credibility of the three models. Explicit finite element simulations are carried out for all tests using the three variants of the GTN model, and the results are compared to the experimental data. The capability of the simulation models to capture onset of fracture and crack propagation in the pipeline steel is evaluated. It is found that the use of in situ bifurcation as a criterion for onset of void coalescence in each element makes the GTN model easier to calibrate with less free parameters, all the while obtaining similar or even better predictions as other widely used formulations of the GTN model over a wide range of different stress states.

Effect of Loading Boundary Conditions in Plane Strain Mechanical Response and Local Deformations in Sand Specimens

AbstractThis study investigates the effect of loading boundary conditions on the mechanical behavior of cuboidal sand specimens during plane strain (PS) testing. Deformation-controlled PS compressi...

Mechanical behaviour of granular media in flexible boundary plane strain conditions: experiment and level-set discrete element modelling

This article presents the results of level-set (LS) discrete element method (DEM) simulations with experimental comparisons of flexible boundary plane strain tests in granular media. The grain-scale micromechanics at the particle level is captured well with LS-DEM, while the overall macroscopic response of the specimen is in quite good agreement with the simulation results. Onset and evolution of localized zones of shear strain accompanied by a significant amount of grain rotation could be well apprehended in the simulations, while the bulging of the specimen could be noticed in the experimental findings as well as in the model predictions. Multiple zones of shear strain accumulation in conjugate arrays were also observed on subsequent biaxial shearing of the sand specimen. The computational results furnish a quantitative estimate of the evolution of force chains and grain fabric orientation. Initially, these force chains were isotropic which on further deformation oriented in the direction of loading, and the grains aligned themselves in their preferred fabric orientation and remained in that fashion till the end of biaxial loading.

Shear Band Characterization of Clayey Soils with Particle Image Velocimetry

Identifying the spatial distribution of deformation and shear band characteristics is important for accurately modeling soil behavior and ensuring the safety of nearby geotechnical structures. However, most research on the shear behavior of soils has focused on granular soil and clay-rich rocks, with little focus on clayey soil, and the entire shearing process from the initial state to failure has not been observed. This study evaluated the spatial distribution and evolution of deformation in clayey soils from the initial state to the post-failure state and the shear band characteristics. Plane strain tests were performed on normally consolidated and over-consolidated clay specimens, and digital images were captured through a transparent side wall for particle image velocimetry (PIV) analysis. PIV was performed to evaluate the displacement and deformation of soil particles. The results show that the shear-strain behaviors of two clays during the shearing process could be divided into four stages: initial, peak, softening, and steady state. Shear bands were observed to form in the softening stage, and the shear band slopes were compared to values in the literature. These results can be used to characterize shear bands in clay as well as predict failure behavior and guide reinforcement at actual sites with soft ground.

Constitutive modelling of LZ91 magnesium-lithium alloy sheet by uniaxial tension loading tests

Magnesium-lithium (Mg-Li) alloy is a kind of ultra-lightweight metallic materials with much lower density than those of conventional magnesium alloy or aluminum alloy. Here, the mechanical behavior of LZ91 Mg-Li alloy sheet was investigated by uniaxial tension loading tests, including standardized uniaxial tension tests and plane strain tests, in which the strain field was measured by 2D digital image correlation (DIC). Firstly, the true stress-true strain curves along the rolling and transverse directions are higher than that along the diagonal direction. The Hocket-Sherby hardening model is more accurate to represent the true stress-true strain curve of LZ91 Mg-Li alloy sheet. Then, the anisotropic coefficients increase with the plastic strain increasing up to about 10%. After that, the anisotropic coefficients become stable, and the ones along the rolling and transverse directions are below 1 while the ones along the diagonal direction is above 1. At last, the yielding stresses in the plane strain tests along the rolling and transverse directions were adopted instead of equi-biaxial yield stress and anisotropic coefficient to simplify the experimental procedures for parameter identification of Yld2000-2d yield function. By comparison of the predicted and experimental results, the Yld2000-2d yield function was validated to describe the anisotropic yielding behavior of LZ91 Mg-Li alloy sheet.

A novel coupled FDM‐DEM modelling method for flexible membrane boundary in laboratory tests

SUMMARYDifficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress‐strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM‐DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.

Applicability of compact tension specimens for evaluation of the plane-strain fracture toughness of steel

AbstractThe plane-strain fracture toughness test method enables the determination of the plane-strain fracture toughness (KIC) of metallic materials by tests using a variety of precracked specimens, such as bend, compact tension (CT), arc-shaped, disk-shaped specimens. In this study, to determine the effect of the heat treatment process on the specimen thickness required for a valid plane-strain test in accordance with the ASTM standard, fracture tests are performed by using CT specimens made of AISI 1040 carbon steel. Furthermore, by taking into consideration the effect of residual stress caused by heat treatment in the vicinity of the notch, additional fracture tests are also performed. The specimens are machined from rolled plates in the L-T rolling direction (crack plane is perpendicular to the rolling direction). Having performed experimental analyses, the applicability of the plane-strain fracture toughness tests using CT specimen made of AISI 1040 steel is investigated.

Theoretical and experimental bifurcation analysis of rock under plane strain compression

A new plane strain apparatus for rock testing was designed and built, and a series of plane strain tests on sandstone was performed. The formation and orientation of localization in sandstone were studied theoretically within the framework of equilibrium bifurcation theory. Corresponding elastoplastic constitutive models with nonlinear yield and potential functions were developed and fitted on the plane strain test data. The inclination of the shear band and the bifurcation point were predicted using the acoustic tensor method. The comparison of the computational and experimental results indicates that the initiation of a shear band predicted by a two-dimensional model could occur within the strain hardening region (i.e. prior to the peak stress), and the predicted orientations of the shear bands agreed qualitatively with those measured.

A bounding surface model of gas-hydrate-bearing sediments

Gas hydrates are a very promising energy source, but its exploitation also faces some challenges in marine geotechnics. The dissociation and formation of hydrates can significantly change the mechanical properties of sediment layers. Large-scale extraction of natural gas hydrate may trigger submarine landslides; therefore, an appropriate constitutive model is necessary for the safe exploitation of natural gas hydrates. In this paper, a bounding surface model of gas-hydrate-bearing sediments (GHBSs) is developed based on the modified Cam-clay model. The size of the bounding surface is related to hydrate saturation by introducing an additional hardening parameter. It is assumed that the additional hardening parameter is related to the hydrate saturation level and plastic volumetric strain. The method for determining the model parameters is given. The model is used to simulate the triaxial compression drainage test of GHBS under different test conditions. It is demonstrated that the model can adequately capture the main deformation characteristics of GHBS. The proposed model is implemented into a finite-element method software program, and finite-element modelling of the plane strain test is carried out. The comparison of results shows the validity of the model.

Measurement of Restitution and Friction Coefficients for Granular Particles and Discrete Element Simulation for the Tests of Glass Beads.

A slant plate flat throw test system for measuring the restitution coefficient of granular materials and a sliding friction test instrument for measuring the friction coefficient between discrete particles and continuum boundary surface materials are developed. The restitution coefficients of the glass bead particles, the glass beads relative to the glass plate, the composite of glass plate and the rubber membrane and the friction coefficients between the glass beads and the rubber film and the filter paper are measured by the designed methods. Based on the measured restitution coefficient and friction coefficient, the discrete element numerical simulation is carried out for triaxial test and plane strain test. Through comparing the experimental results and the discrete element numerical simulation results, the feasibility and rationality of the designed measurement methods and the discrete element numerical simulation are verified. The measuring methods developed in this paper can be further applied to the tests of other fine particles.

Comparative study of shear strength characteristics of dry cohesionless sands from triaxial, plane-strain and direct shear tests

ABSTRACT Knowledge of strength properties and deformational behaviour of soils under different loading conditions is necessary in the analysis of most of the geotechnical engineering problems. This paper presents a comparative study of shear strength characteristics of sands as obtained from triaxial, plane-strain and direct shear test results. The experimental results on shear strength characteristics of dry sands obtained from triaxial, plane-strain and direct shear tests, were analyzed in order to investigate the effect of soil relative density or soil porosity on the angle of shearing resistance, dilatancy factor, particles interlocking, and volumetric strain and axial strain at failure. Furthermore, the results were used to develop correlations connecting between the angle of shearing resistance of triaxial condition test and the direct shear test, and between the angle of shearing resistance of plane-strain and triaxial compression conditions. The correlations developed take into account the interaction between soil relative density, dilatancy factor and particles interlocking. Good agreement has been obtained between the predicted results values using the proposed methods and the results of the present experimental investigation and those available in the literature

A Stress-Dilatancy Relationship for Rockfill Incorporating Particle Breakage and Intermediate Principal-Stress Ratio

Rockfill material is widely used for construction of high rockfill dam, which undergoes significant particle breakage and three-dimensional stress path induced by the water pressure, earthquake, etc. The dilatancy equation, defined as the function of the dilatancy dg and the stress ratio η, is regarded as the foundation of elastoplastic constitutive model. Therefore, a dilatancy equation considering the influence of particle breakage and intermediate principal stress ratio b was proposed in this paper. A series of test data from rockfill materials including conventional triaxial test, constant-b test and plane strain test were used to verified the applicability of the equation. It was found that the proposed dilatancy equation considering two important factors (i.e., particle breakage and b-value) agree well with the rearranged test data of the rockfill material in terms of dg-η. While the other dilatancy equations showed significant poorer predictions when ignoring one or two of the factors. That is, the proposed dilatancy equation can well describe the dilatancy behavior of rockfill material when considering the combined influences of the particle breakage and b-value.

Cyclic behavior of soils and numerical analyses in cold regions and seismic zones

The solutions of boundary value problems involving strain-softening material property contain serious difficulties from both modeling of strain-localization and a viewpoint of numerical procedure. Mesh size-dependent hardening modulus is considered to alleviate the mesh size-dependency of the solution. The elasto-plastic soil model with kinematic hardening model considering the cumulative deformation by cyclic loading is developed. In finite element analyses, the dynamic relaxation method combined with the generalized return-mapping algorithm is applied to the static drained and un-drained tri-axial tests and plane strain tests. The cyclic behavior of retaining wall problems by freeze and thaw in cold regions is also analyzed. Finally the dynamic progressive failure analysis of rockfill dam is carried out.

Influence of Local Inhomogeneity of Thermomechanical Treatment Conditions on Microstructure Evolution in Aluminum Alloys

The influence of local inhomogeneity of the stress–strain condition on structure and texture evolution during thermomechanical treatment of aluminum alloys is studied in this work. For this purpose, laboratory rolling and plane strain tests that simulated roughing mill thermomechanical modes were performed. For all processes, the local inhomogeneity of structure evolution was estimated. For this purpose, x-ray texture analysis, EBSD and optical microscopy were used. Additionally, the calculations which allow to evaluate local inhomogeneity of stress–strain conditions for the each process were performed. The experimental results were compared with mathematical simulation output. They indicated structure and texture evolution inhomogeneities, especially during the plane strain and industrial rolling processes. In the plane strain test, typical local deformation zones occurred with different resulting grain size and texture effects than those observed in both rolling processes. This difference was mainly associated with different stress states, strain intensity and strain rate distribution throughout the deformation zone. This study demonstrated that the inhomogeneity of these parameters has a strong impact on structure and texture evolution in the first stage of thermomechanical treatment. In the center layer, laboratory rolling could adequately generate the structure and texture effects observed during rolling of ingots in a commercial mill. Plane strain tests can generate useful results only in the case of adequate choice of sample geometry.

Calibration of anisotropic yield function by introducing plane strain test instead of equi-biaxial tensile test

Abstract The equi-biaxial tensile test is often required for parameter identification of anisotropic yield function and it demands the special testing technique or device. Instead of the equi-biaxial tensile test, the plane strain test carried out with the traditional uniaxial testing machine is suggested to provide the experimental data for calibration of anisotropic yield function. This simplified method by using plane strain test was adopted to identify the parameters of Yld2000-2d yield function for 5xxx aluminum alloy and AlMgSi alloy sheets. The predicted results of yield stresses, anisotropic coefficients and yield loci by the proposed method were very similar with the experimental data and those by the equi-biaxial tensile test. It is validated that the plane strain test is effective to provide experimental data instead of equi-biaxial tensile test for calibration of Yld2000-2d yield function.

Creep behavior of gold thin films investigated by bulge testing at room and elevated temperature

The creep behavior of 200-nm thick gold films was investigated by plane-strain bulge testing between 23 and 100 °C. The polycrystalline gold films were produced by thermal evaporation and their columnar microstructure was stabilized by a preliminary heat treatment at 120 °C. The creep tests were performed at constant stress values between 80 and 300 MPa over 12 h, using a custom-built bulge tester. The stress exponent calculated from the creep data decreased from 4.3 to 2.8 between 23 and 100 °C, suggesting a possible transition in deformation mechanisms. The stress exponent and activation energy measured around room temperature point toward the climb of dislocations at grain boundaries being the rate-limiting deformation mechanism. Above 75 °C, scanning electron microscope inspections of tested membranes suggest an increased contribution of diffusion and of grain-boundary mediated deformation, as evidenced by the formation of grooves along grain boundaries. This is presumably the reason for the decrease of the apparent stress exponent and sudden increase of the apparent activation energy.

A plane strain testing apparatus characterized by flexible loading and noncontact deformation measurement and its application to the study of shear band failure of sand

A new type of plane strain apparatus is developed to study the mechanical properties and shear band failure of soil, which possesses the advantages of flexible loading for lateral confining pressure and noncontact measurement and high measurement accuracy for surface deformation. In addition, the whole deformation procedure of the specimen can be recorded with images, which can be used to describe the development of strain localization and the shear band. It can be seen that the deformation process has three obvious stages, that is, the hardening stage, the softening stage, and the residual stage. The measured inclination angles of shear bands decrease as confining pressure or the mean size increases. In addition, it can be observed that the sand presents continuing growth of the unrecoverable plastic deformation inside the shear band and exhibits almost elastic deformation outside. From the detection results for local points in the specimen, the stress–strain relationships are different for different parts, and the sand sample behaves like an uneven structure instead of an even element, which means that the usual method of measuring the stress–strain relationship of the soil sample is only a macroscopic approximation.

Development of a novel plane strain test apparatus for frozen soils

In this paper, a novel apparatus enable of high controlling accuracy of temperature was developed for plane strain test of frozen soils. A cryostat was used to control test temperature. To improve temperature distribution uniformity of frozen soil specimens, two guiding plates were installed into the cryostat to force cooling air distribute uniformly surround specimen. According to test results, the temperature difference between different monitored points and average temperature can be controlled at ±0.2 °C. By taking Chinese standard sand as study object, compression tests under different axial strain rates were conducted. The images on the surface with strain restrained were captured during loading process, and strain localization evolution was analyzed with PIV technique. It was indicated that, with decrease of strain rate, shear band inclination and width do not change notably, while the strain field distributes more uniformly and concentration of which was decreased.