Evolution of Strain Gradient Formulation in Capturing Localization Phenomena in Granular Materials

2021 ◽  
pp. 1-34
Author(s):  
Omar Al Hattamleh ◽  
Balasingam Muhunthan
Keyword(s):  
Flow Stress ◽  
Plastic Strain ◽  
Granular Materials ◽  
Strain Gradient ◽  
Confining Pressure ◽  
Plastic Strain Rate ◽  
Gradient Term ◽  
Compression Tests ◽  
Shearing Rate ◽  
Coulomb Type

Abstract This paper highlights the use of incorporating strain gradient into flow stress to study localization behavior in materials. Pioneered by Zbib and Aifantis in the late 1980s, the formulation enabled incorporation of length scales into continuum formulations naturally. The formulation has also evolved into being able to study the effects of microstructure and heterogeneity on localization in granular materials. A multi-slip Mohr-Coulomb type plasticity model with the flow stress in the constitutive equation modified with a higher order gradient term of the effective plastic strain is used for this purpose. The possibility of abrupt changes of mobilized friction caused by intense shearing rate often leads to particle breakage. Its effects on localization is accounted for by modifying the material properties such as mobilized friction using a scaling parameter averaged over a representative elementary area. The change of shearing rate in the integration points was monitored through quasi-statistically measure parameter called inertia number. The inertia number was set to be all the time to consider quasi static less than l.0E-3. The formulation was implemented into a finite element code and used to simulate plane strain compression tests on dry sand. The model highlights effects of confining pressure, anisotropic microstructure, the non-coaxial angle between the direction of principal stress and principal plastic strain rate directions on shear band characteristics.

scholarly journals Quantitative 3D imaging of partially saturated granular materials under uniaxial compression

2021 ◽  
Author(s):  
Marius Milatz ◽  
Nicole Hüsener ◽  
Edward Andò ◽  
Gioacchino Viggiani ◽  
Jürgen Grabe
Keyword(s):  
Granular Materials ◽  
Uniaxial Compression ◽  
Water Clusters ◽  
Local Strain ◽  
Confining Pressure ◽  
Mechanical Effect ◽  
Compression Tests ◽  
Initial Water ◽  
Interfacial Areas ◽  
Membrane Effects

AbstractGauging the mechanical effect of partial saturation in granular materials is experimentally challenging due to the very low suctions resulting from large pores. To this end, a uniaxial (zero radial stress) compression test may be preferable to a triaxial one where confining pressure and membrane effects may erase the contribution of this small suction; however, volume changes are challenging to measure. This work resolves this limitation by using X-ray imaging during in situ uniaxial compression tests on Hamburg Sand and glass beads at three different initial water contents, allowing a suction-dependent dilation to be brought to the light. The acquired tomography volumes also allow the development of air–water and solid–water interfacial areas, water clusters and local strain fields to be measured at the grain scale. These measurements are used to characterise pertinent micro-scale quantities during shearing and to relate them to the measured macroscopic response. The new and well-controlled data acquired during this experimental campaign are hopefully a useful contribution to the modelling efforts—to this end they are shared with the community.

scholarly journals An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems

2018 ◽  
Vol 45 (2) ◽  
pp. 177-188
Author(s):  
Adebowale Borokinni ◽  
Odunayo Fadodun ◽  
Adegbola Akinola
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Plane Strain ◽  
Strain Gradient ◽  
Dissipative Process ◽  
Strain Gradient Plasticity ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Gradient Plasticity ◽  
Plane Strain Problem

This article considers a plane strain gradient plasticity theory of the Gurtin?Anand model [M. Gurtin, L. Anand, A theory of strain gradient plasticity for isotropic, plastically irrotational materials Part I: Small deformations, J. Mech. Phys. Solids 53 (2005), 1624?1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin?Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.

An Elastoplastic Model for Granular Materials Exhibiting Particle Crushing

2007 ◽  
Vol 340-341 ◽  
pp. 1273-1278 ◽  
Author(s):  
De An Sun ◽  
Wen Xiong Huang ◽  
Dai Chao Sheng ◽  
Haruyuki Yamamoto
Keyword(s):  
Shear Strength ◽  
Granular Materials ◽  
Triaxial Compression ◽  
Model Performance ◽  
Confining Pressure ◽  
Model Parameters ◽  
Compression Tests ◽  
Particle Crushing ◽  
Wide Range ◽  
Triaxial Compression Tests

A practical elastoplastic constitutive model for granular materials is presented. And the model is suitable for description of the material behaviour for a wide range of stresses, including those sufficient to cause particle crushing. With a limited number of model parameters, the model can predict the confining-pressure dependent stress-strain relation and shear strength of granular materials in three-dimensional stresses, especially of variation of shear strength and dilatancy characteristics due to particle crushing under high confining pressure. The model parameters, which have clear physical meanings, can be determined from the results of isotropic compression test and conventional triaxial compression tests. The model performance is demonstrated for triaxial compression tests of a sand for a wide range of the confining-pressure from 0.2MPa to 8.0MPa.

scholarly journals Nonlinear Volumetric Deformation Behavior of Rock Salt Using the Concept of Mobilized Dilatancy Angle

2016 ◽  
Vol 10 (1) ◽  
pp. 524-531 ◽  
Author(s):  
Yan Chen ◽  
Linjian Ma ◽  
Pengxian Fan ◽  
Xupu Yang ◽  
Lu Dong
Keyword(s):  
Plastic Strain ◽  
Rock Salt ◽  
Axial Strain ◽  
Triaxial Compression ◽  
Equivalent Plastic Strain ◽  
Confining Pressure ◽  
Compression Tests ◽  
Confining Stress ◽  
Dilatancy Angle ◽  
Deformation Properties

Post-yield strength and deformation properties of rock salt are of great importance to the stability of rock surrounding deep underground storage caverns. Uniaxial and triaxial compression tests were performed to explore the volume change of Qianjiang rock salt under different confining stress states. The experimental results indicate that the dilatancy angle first increases rapidly then decreases gradually and drives to a constant with equivalent plastic strain. A higher confining stress results in a lower peak dilatancy angle. With the increase of confining pressure, the dilatancy angle decreases nonlinearly. Based on the volumetric-axial strain curves of rock salt, a mobilized dilatancy angle model taking into account the effects of confining pressure and the equivalent plastic strain was developed using nonlinear fitting. The new model was implemented in the software FLAC3D and verified effective to predict the volumetric dilatancy behavior of rock salt.

scholarly journals Hot Workability of 300M Steel Investigated by In Situ and Ex Situ Compression Tests

Metals ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 880 ◽  
Author(s):  
Rongchuang Chen ◽  
Haifeng Xiao ◽  
Min Wang ◽  
Jianjun Li
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Hot Working ◽  
Ex Situ ◽  
Lower Strain Rate ◽  
Hot Workability ◽  
Compression Tests ◽  
300M Steel ◽  
Lower Strain

In this work, hot compression experiments of 300M steel were performed at 900–1150 °C and 0.01–10 s−1. The relation of flow stress and microstructure evolution was analyzed. The intriguing finding was that at a lower strain rate (0.01 s−1), the flow stress curves were single-peaked, while at a higher strain rate (10 s−1), no peak occurred. Metallographic observation results revealed the phenomenon was because dynamic recrystallization was more complete at a lower strain rate. In situ compression tests were carried out to compare with the results by ex situ compression tests. Hot working maps representing the influences of strains, strain rates, and temperatures were established. It was found that the power dissipation coefficient was not only related to the recrystallized grain size but was also related to the volume fraction of recrystallized grains. The optimal hot working parameters were suggested. This work provides comprehensive understanding of the hot workability of 300M steel in thermal compression.

A Modified Peric Model for Al-Mg Alloy Sheet with Rate-Independent Initial Yield Stress at Warm Temperatures

2019 ◽  
Vol 287 ◽  
pp. 3-7
Author(s):  
Yong Zhang ◽  
Qing Zhang ◽  
Yuan Tao Sun ◽  
Xian Rong Qin
Keyword(s):  
Flow Stress ◽  
Plastic Strain ◽  
Strain Rate ◽  
Yield Stress ◽  
Constitutive Models ◽  
Mg Alloy ◽  
Initial Yield Stress ◽  
Initial Yield ◽  
Rate Dependent ◽  
Dependent Flow

The constitutive modeling of aluminum alloy under warm forming conditions generally considers the influence of temperature and strain rate. It has been shown by published flow stress curves of Al-Mg alloy that there is nearly no effect of strain rate on initial yield stress at various temperatures. However, most constitutive models ignored this phenomenon and may lead to inaccurate description. In order to capture the rate-independent initial yield stress, Peric model is modified via introducing plastic strain to multiply the strain rate, for eliminating the effect of strain rate when the plastic strain is zero. Other constitutive models including the Wagoner, modified Hockett–Sherby and Peric are also considered and compared. The results show that the modified Peric model could not only describe the temperature-and rate-dependent flow stress, but also capture the rate-independent initial yield stress, while the Wagoner, modified Hockett–Sherby and Peric model can only describe the temperature-and rate-dependent flow stress. Moreover, the modified Peric model could obtain proper static yield stress more naturally, and this property may have potential applications in rate-dependent simulations.

Model of Microstructure Development in Hot Deformed Magnesium Alloy AZ31 Type

2013 ◽  
Vol 197 ◽  
pp. 232-237 ◽  
Author(s):  
Dariusz Kuc ◽  
Eugeniusz Hadasik
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Rolling Process ◽  
Microstructure Development ◽  
Compression Tests ◽  
Magnesium Alloy Az31 ◽  
Hot Rolling Process ◽  
Alloy Type ◽  
Relaxation Curves

The paper presents a model of microstructure changes elaborated for magnesium alloy type AZ31. In previous papers, the function of flow stress was defined on the basis of uniaxial hot compression tests. On the basis of marked relaxation curves and quantitative tests of structure the softening indicators were defined together with elaboration of equations which describe the changes in the grain size. Marked coefficients of equations were introduced in the code of simulation program. Calculations were conducted for given temperature values from 450 ÷ 250°C and strain rate from 0.01 to 10 s-1, which correspond with rolling temperature range of this alloy. Prepared model will allow the proper choice of parameters in hot rolling process of this alloy to achieve the assumed microstructure.

Constitutive Modeling for Flow Stress Behavior of Nimonic 80A Superalloy During Hot Deformation Process

2016 ◽  
Vol 35 (3) ◽  
pp. 327-336 ◽  
Author(s):  
Sendong Gu ◽  
Liwen Zhang ◽  
Chi Zhang ◽  
Wenfei Shen
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
Hot Deformation ◽  
Critical Strain ◽  
Volume Fraction ◽  
Constitutive Models ◽  
Avrami Equation ◽  
Peak Strain ◽  
Compression Tests ◽  
Nimonic 80A

AbstractThe hot deformation characteristics of nickel-based alloy Nimonic 80A were investigated by isothermal compression tests conducted in the temperature range of 1,000–1,200°C and the strain rate range of 0.01—5 s–1on a Gleeble-1500 thermomechanical simulator. In order to establish the constitutive models for dynamic recrystallization (DRX) behavior and flow stress of Nimonic 80A, the material constantsα,nand DRX activation energyQin the constitutive models were calculated by the regression analysis of the experimental data. The dependences of initial stress, saturation stress, steady-state stress, dynamic recovery (DRV) parameter, peak strain, critical strain and DRX grain size on deformation parameters were obtained. Then, the Avrami equation including the critical strain for DRX and the peak strain as a function of strain was established to describe the DRX volume fraction. Finally, the constitutive model for flow stress of Nimonic 80A was developed in DRV region and DRX region, respectively. The flow stress values predicted by the constitutive model are in good agreement with the experimental ones, which indicates that the constitutive model can give an accurate estimate for the flow stress of Nimonic 80A under the deformation conditions.

An Experimental Study on the Effect of Prior Plastic Straining on Creep Behavior of 304 Stainless Steel

1993 ◽  
Vol 115 (2) ◽  
pp. 200-203 ◽  
Author(s):  
Z. Xia ◽  
F. Ellyin
Keyword(s):  
Stainless Steel ◽  
Plastic Strain ◽  
Strain Rate ◽  
Creep Behavior ◽  
Test Procedure ◽  
Constant Strain Rate ◽  
304 Stainless Steel ◽  
Creep Model ◽  
Plastic Strain Rate ◽  
Creep Tests

Constant strain-rate plastic straining followed by creep tests were conducted to investigate the effect of prior plastic straining on the subsequent creep behavior of 304 stainless steel at room temperature. The effects of plastic strain and plastic strain-rate were delineated by a specially designed test procedure, and it is found that both factors have a strong influence on the subsequent creep deformation. A creep model combining the two factors is then developed. The predictions of the model are in good agreement with the test results.

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