Plane Strain Tests Research Articles

Challenge for methane hydrate production by geotechnical engineering

Methane hydrate (referred to as MH hereafter) has come to be seen as a future energy source and as such research and development is being conducted in order to prepare for production of it. The MH reservoirs are located in the deep sea bed at over 1000m in sea depth. In Japan, the reservoirs are found in the Nankai Trough on the Pacific Ocean side of main island. MH mostly exists in the void space of the sand layers in the turbidite. In order to produce MH from the MH bearing layers, it is important to first make clear and understand the mechanical properties of the host sands of MH bearing sands in order to understand the MH bearing layer. A series of mechanical tests were performed on MH bearing sediments with various host sands by using temperature controlled high stress triaxial shear testing apparatus. A high pressure and low temperature plane strain testing apparatus was also developed for visualizing the deformation of methane hydrate bearing sand due to methane hydrate production. Using this testing apparatus, plane strain compression and methane hydrate dissociation by depressurization tests were performed with the measurement of localized deformation. On the basis of the experimental results, an elastoplastic constitutive model for methane hydrate-bearing sand was developed. The bonding effect due to the cementation by methane hydrate was introduced into the model. The simulation was performed on triaxial behaviour of methane-hydrate bearing sand under various pressure and temperature condition.

Development of a Global Indicator to Assess Mechanical Tests

Full-field measurement methods have emerged in the last years and these methods are characterized by directly providing displacement and strain fields for all points over the specimen surface. Thus, the design of heterogeneous tests can be performed for material parameter identification purposes since the inhomogeneous strain fields can be measured. However, (i) no defined criterion yet exists for designing new heterogeneous tests, (ii) it is rather difficult to compare and rate different tests and (iii) a quantitative way to define the best test for material behavior characterization of sheet metals has yet to be proposed. Due to this, the goal of this work is the development of a global indicator able to assess mechanical tests. The proposed indicator quantifies the strain state range, the deformation heterogeneity and the strain level achieved in the test, based on a continuous evaluation of the strain field up to rupture. This global indicator was applied to rank some classical tests, such as uniaxial tensile, simple shear, plane strain and biaxial tensile tests. These tests were carried out numerically by reproducing the virtual behavior of DC04 mild steel. A constitutive model composed by the non-quadratic Yld2004-18p yield criterion combined with a mixed isotropic-kinematic hardening law and a macroscopic rupture criterion was used. The performance of the tests was compared with the indicator and a ranking was established. The results obtained show that biaxial tension is the test providing more information for the mechanical behavior characterization of the material. It was also verified that plane strain test presents a better performance than simple shear and uniaxial tensile tests.

A J2–J3 approach in plastic and damage description of ductile materials

This paper illustrates a methodology to improve the description of the plastic behavior and the fracture prediction for ductile materials under complex loading conditions. To this purpose, a plasticity model and a damage estimation model are proposed. The former, differently from the classic J2 plasticity theory, takes into account the effect of the third deviatoric invariant on the plastic flow. The latter assumes that damage accumulation is governed by both stress triaxiality and deviatoric parameters, and takes advantage of the new plasticity formulation. The two models rely on the same theoretical foundation, where a specific function is invoked to describe the subsequent yield surfaces and the damage accumulation up to fracture. Both have been implemented into a commercial finite element code via user subroutines. Three steel alloys have been tested under very different stress states: tensile tests on smooth and round notched bars, plane strain tests, torsion tests, and combined tension–torsion tests on hollow and solid cylindrical bars have been executed. For the last ones, several tension—torsion-loading ratios have been applied. These kinds of tests allow to explore a wide domain of the governing parameters for both models. The experimental results from tensile and torsion tests are used to calibrate the proposed plasticity model and the damage model; combined tests are used for validation purposes. The experimental–numerical comparison of global quantities made by using a standard plasticity approach confirms the need for a more accurate plastic description in the large strain range. The proposed plasticity model is able to provide a very good match until fracture for all tests available. Moreover, the damage model has the potential to take into account the experimental evidence, predicting the fracture initiation accurately. In particular, its validation by using tension–torsion tests shows to be really significant.

Determination of soil properties for plane strain condition from the triaxial tests results

SummarySignificant difference in stress–strain behavior of dense cohesionless soil has been observed between plane strain and triaxial test conditions. At present, majority of geotechnical laboratories have no plane strain testing facility. Therefore, geotechnical professionals are more dependent on the conventional triaxial test for soil properties, whereas many geotechnical structures prevail close to plane strain condition. A method has been proposed to determine soil properties for plane strain condition from the conventional triaxial tests. This method can especially be used to determine the internal friction angle and stress–strain relationship for plane strain condition from triaxial tests results. Copyright © 2015 John Wiley & Sons, Ltd.

The Application of Improved Duncan-Chang Model in Unloading Soil

On the basis of the representative samples of silty clay found in Wuhan, China, the lateral unloading of soil’s stress path produced by excavating foundation pit engineering, was simulated by triaxial experiment. A series of consolidated- drained true triaxial test and normal triaxial test were conducted. According to the results of tests, the parameter of the Duncan-Chang Model was determined. A modulus formula was used for the foundation soil in the lateral unloading stress path tests to replace the modulus formula of Duncan-Chang Model based on the σ3 =const . Moreover, the Duncan- Chang hyperbola nonlinear elastic constitutive model was used to simulate the plane strain test. A method to improve the ability of Duncan-Chang model in order to take into account the effects of the intermediate principal stress on the strength and deformation was presented as well as all the model parameters were also determined. The adaptability of the model for unloading the stress path was verified by comparing the theoretical stress-strain relationship and empirical stress-strain relationship.

Dilatancy and Friction Angles Based on In Situ Soil Conditions

AbstractDilatancy influences almost all aspects of the behavior of granular material, ranging from shear strength to stress-strain behavior. However, there is no practical method for estimating the dilatancy angle based on in situ soil properties, although the variables that influence dilatant behavior are well-known. This paper attempts to link the dilatancy angle to preshear mean effective stress and relative density for cohesionless soils. Accordingly, it may be possible to estimate the dilatancy angle by using variables that can be measured or calculated during the soil exploration phase of a design project. For this purpose, an experimental study is conducted on Silivri sand and the obtained results are used to quantify the relationship between dilatancy angle and preshear soil properties. An equation for the dilatancy angle is proposed that requires only two unit-independent soil constants, which can be obtained by conducting triaxial or plane strain tests. Moreover, the proposed dilatancy equation ...

Prediction of plane strain undrained diffuse instability and strain localization with non-coaxial plasticity

In this paper, undrained diffuse instability and strain localization of frictional materials under plane strain conditions were studied. Based on a 3D non-associated Mohr–Coulomb hardening model, the theoretical criteria for diffuse instability and strain localization were proposed by the second-order work theorem and the vanishing of the determinant of the acoustic tensor. The criteria were used to predict the instability characteristics of soil specimen in isotropically and anisotropically consolidated plane strain tests. The studies showed that, when the soil specimen was loaded under strain-controlled loading mode, the soil becomes potentially unstable slightly before the shear stress reaches its peak value. The initiation of diffuse instability accompanies with the peak of shear stress, and strain softening occurs with further loading. Strain localization was predicted by the vanishing of the determinant of the acoustic tensor, and it is shown to occur after the diffuse instability. The non-coaxial plasticity flow rule was adopted to improve the prediction the onset of strain localization, while the inclusion of non-coaxial plasticity flow rule shows no influence on diffuse instability. Both diffuse instability and strain localization occur at the hardening stage of the soil and result in the reduction of the deviatoric shear stress.

Anisotropy and tension–compression asymmetry modeling of the room temperature plastic response of Ti–6Al–4V

The mechanical behavior of the alloy Ti–6Al–4V is characterized using uniaxial tension, uniaxial compression, simple shear and plane strain tests in three orthogonal material directions. The experimental results reveal tension/compression asymmetry, anisotropic yielding and anisotropic strain-hardening. These features are incorporated into an elasto-plastic constitutive law based on the macroscopic orthotropic yield criterion “CPB06” adapted to hexagonal metals. A new identification method for the yield criterion parameters is proposed by inverse modeling of the axial strain field of compression specimens in the three orthogonal directions of the material. The sensitivity of different sets of material parameters to the identification method is also analyzed and the capacity of the model to accurately predict the forces and displacement field is discussed. A validation of the best set of identified CPB06 material parameters is performed by comparing the load–displacement curves in different loading directions for tensile tests on notched round bars with different levels of stress triaxiality and for compression tests on elliptical cross-section specimens, both tests involving multiaxial strain fields and large deformations.

On the elasto-viscoplastic behavior of the Ti5553 alloy

The elastoviscoplastic behavior of the Ti5553 alloy is characterized and compared to the classical Ti-6Al-4V alloy. The true stress-strain curves are determined based on tensile tests performed under different strain rates at room temperature and at 150°C, from which the elastic constants and the parameters of a Norton-Hoff viscoplastic model are identified. The strength of the Ti5553 alloy is 20-40% higher than the strength of the Ti-6Al-4V alloy. The Ti5553 alloy constitutes thus a promising candidate for advanced structural applications. In view of modeling structural applications of forming operations, the elastic and plastic initial anisotropy of the two alloys is investigated by combining compression on cylinders with elliptical sections, uniaxial tensile tests in different material directions, plane strain and shear tests. The initial anisotropy of the different alloys is very weak which justifies the modeling of the mechanical behavior with an isotropic yield surface. The identified elastoviscoplastic model is validated by comparing experimental results with FE predictions both on cylindrical notched specimens subjected to tensile tests and on flat specimens subjected to plane strain conditions.

Uniaxial near plane strain tensile tests applied to the determination of the FLC0 formabillity parameter

b An alternative procedure for the determination of the FLC 0 value, the limit strain value corresponding to the plane strain mode of the Forming Limit Curves (FLC), a critical parameter in the sheet formability analysis, is suggested and compared with conventional Nakazima simulation tests. The procedure was tested using two different materials: interstitial-free quality steel (IF) and a spheroidized SAE 1050 steel. The intrinsic tensile test, in a near plane strain state, was performed using a small number of samples, with dimensions suggested by the literature. The results were checked against Nakazima test results using the same materials. The plane strain test was reliable in determining consistent FLC 0 values and should be preferred since it is not affected by the geometric aspects and by friction, which do affect the Nakazima test. The reliability of the FLC 0 values obtained by near plane strain was also corroborated through comparison with literature data.

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UNDRAINED SHEAR STRENGTH OF K0CONSOLIDATED SOFT CLAYS UNDER TRIAXIAL AND PLANE STRAIN CONDITIONS

Theoretical formulas for predicting the undrained shear strength of K0consolidated soft clays under the stress path related to triaxial and plane strain tests are presented within the framework of critical state soil mechanics. An inclined elliptical yield surface is adopted to take account of the initial anisotropic stress state. The undrained strength is determined by combining the undrained stress path in the volumetric stress–strain space and the initial yield surface in the deviator-mean stress space. The derived mathematical expressions are functions of the critical state frictional angle, the plastic volumetric strain ratio and the overconsolidation ratio, which can be simplified into the solutions for isotropically consolidated clays under triaxial tests or under plane strain tests. The results calculated by using the theoretical formulas obtained in this paper are in good agreement with the available collected test results. It indicates that these new formulas are applicable to triaxial and plane strain tests on normally and lightly to moderately overconsolidated soft clays.

Microstructure and Mechanical Properties of Al-Li Alloy 2397-T87 Rolled Plate

The microstructure, tensile property and fracture toughness of Al-Li alloy 2397-T87 rolled plate were investigated by optical microscopy, scanning electron microscopy, transmission electron microscopy, X-ray diffraction, tensile and plane-strain fracture toughness tests. The results show that a pronounced texture variation through the plate thickness was found. Near the surface, Goss texture dominated. While in the center of the plate, typical β fiber texture and a scattering of cube texture were observed. And the subsurface layer exhibited a very weak texture. From the center to the subsurface, the fraction of β fiber texture and cube texture decreased. In contrast, the fraction of shear type texture reaching the maximum in subsurface layer increased. The tensile properties in different layers along the thickness direction were inhomogeneous. The strengths near the surface were lower than those in the center. And the through-thickness strength properties variation in the rolling direction was more remarkable than that in the long transverse direction. In the same thickness layer, the fracture toughness and the strengths were anisotropic. The strengths in the rolling direction were higher than those in the long transverse direction and the short transverse direction, and the strengths in the short transverse direction were the lowest. The fracture toughness in L-T orientation was the highest, followed by that in T-L orientation, and the fracture toughness in S-L orientation was the lowest.

Impact of anisotropy and viscosity to model the mechanical behavior of Ti–6Al–4V alloy

This paper compares the predictions of an isotropic thermo-elasto-viscoplastic approach and of an anisotropic thermo-elastoplastic one with experimental results representative of the mechanical behavior of Ti–6Al–4V at moderate temperatures and low strain rates. The first model is the well known Norton–Hoff viscoplastic constitutive law with isotropic von Mises yield locus identified by using monotonic tension tests performed at strain rates from 10−3s−1 to 10−1s−1 and at temperatures up to 400°C. The second model is a thermo-elasto-plastic one defined by the orthotropic yield criterion CPB06. It takes into account the anisotropy and the strength differential (SD) effect in tension–compression of Ti–6Al–4V at RT, 150°C and 400°C. The identification of the SD effect is done by using tension and compression tests and the anisotropy behavior is identified by using shear, plane strain, tension and compression tests performed in three orthogonal material directions. The accuracy of the load and displacement predictions of the two macroscopic constitutive models are compared to experimental results obtained from tests performed on specimens with multiaxial loadings and large strain at several temperatures.

The Critical State Constitutive Model and Strain Localization for Hostun Sand

Aiming at the limitation of traditional constitutive theories which can not explain the decrease of inclination angle of shear bands correctly when confining pressure increases, a state-dependent critical state model is employed to analyze strain localization of Hostun sands. Firstly, the critical state formulation and model parameters are calibrated through available drained triaxial test results of Hostun sand. Then an analysis of strain localization is performed on the drained plane strain tests. The results show that the state-dependent critical state model is capable of simulating the effect of initial effective confining pressure on inclination angle of shear bands.

Interaction between catenary riser and soft seabed: Large-scale indoor tests

Nowadays, steel catenary riser (SCR) has become the most favorable method for oil and gas transportation in deep water. Accurate analysis of riser fatigue is heavily dependent on the interaction between riser and the seabed soil, which is a research focus in recent years. This paper aims to simulate the 3D interaction between SCR and typical clay seabed through large-scale indoor tests in 1g condition. The dynamic pipe•soil interaction is modeled through applying cyclic motion at one end of the pipe. The trench formation, pipeline behavior and the excess pore water pressure beneath the pipe invert are all analyzed in detail.The apparently dynamic embedding process and the ladled shape trench at touchdown zone (TDZ) were observed, which can be attributed to soil softening. The suction at the pipe/soil interface was captured and the accumulation of excess pore pressure was visualized. The results based on this study indicate that: the excess pore water pressures at different positions along the pipe axis vary with different trends, which may be attributed to their corresponding pipe trajectories. Therefore the accurate loading history simulation is very important for conventional 2D plane strain tests. It is found that, after 200 cycles, the maximum dynamic embedment factor fdyn along the axis of the model riser was up to 1.6, the pipe embedment depth increased by up to 60% and the average bending moment increased by up to 31.0%.

A modification to dense sand dynamic simulation capability of Pastor–Zienkiewicz–Chan model

A modification to the nonlinear Pastor–Zienkiewicz–Chan (PZC) constitutive model without any change in the number of model parameters is introduced in order to simulate stiffness degradation of dense sands at dynamic loading. The PZC model is based on generalized plasticity and was verified by good prediction of liquefaction and undrained behavior of saturated sand. The PZC is a robust model that can predict drained dynamic behavior of sands, especially stiffness increase in loose sand at reloading of dynamic loading. Yet, this model does not show stiffness degradation of dense sand at reloading. The modification is made through modifying the stress memory factor, HDM, which is multiplied by the plastic modulus, HL. This modification does not influence reloading behavior of loose sand. The modified PZC model is verified via results of drained cyclic tests. Two cyclic triaxial tests on loose and dense specimens, along with two cyclic plane strain tests on dense sand are utilized for validation. The model simulation shows that the modified PZC model is able to predict the stiffness degradation of dense sand at reloading well.

Plane Strain Testing with Passive Restraint

A plane strain condition for testing rock is developed through passive restraint in the form of a thick- walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young's modulus and Poisson's ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana lime- stone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young's modulus and Poisson's ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.

Development of high-pressure low-temperature plane strain testing apparatus for methane hydrate-bearing sand

A high-pressure low-temperature plane strain testing apparatus was developed for visualizing the deformation of methane hydrate-bearing sand due to methane hydrate production. Using this testing apparatus, plane strain compression tests were performed on pure Toyoura sand and methane hydrate-bearing sand with localized deformation measurements. From the results, it was observed that the methane hydrate-free specimens, despite their relatively high density, showed changes in compressive volume. Marked increases in the initial stiffness and strength of the methane hydrate-bearing sand were observed (methane hydrate saturation of SMH=60%). Moreover, the volumetric strain changed from compressive to dilative. For the specimens with methane hydrate, a dilative behavior above SMH=0% was observed. An image analysis showed that the shear bands of the methane hydrate-bearing sand were thinner and steeper than those of the host sand. In addition, the dilative volumetric strain in the shear band increased markedly when methane hydrate existed in the pore spaces.

Solutions of the second elastic–plastic fracture mechanics parameter in test specimens under biaxial loading

Extensive finite elements analyses have been conducted to obtain solutions of the A-term, which is the second parameter in a three-term elastic–plastic asymptotic expansion, for test specimens under biaxial loading. Three mode I plane-strain test specimens, i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analyzed include shallow to deep cracks, and the biaxial loading ratios analyzed are 0.5 and 1.0. Solutions of A-term were obtained for materials following the Ramberg–Osgood power law with hardening exponent of n = 3, 4, 5, 7 and 10. Remote tension loading was applied which covers from small-scale to large-scale yielding. Based on the finite element results, effects of biaxial loading on crack tip constraint were discussed. Empirical equations to predict the A-term under small-scale yielding to fully-plastic condition were developed using estimation methods developed earlier. Based on the relationships between A and other commonly-used second fracture parameter Q and A2, the present solutions can be used to calculate parameters Q and A2 as well. The results presented in the paper are suitable to determine the second elastic–plastic fracture parameters for test specimens for a wide range of crack geometries, material strain hardening behaviors under biaxial loading conditions.