A yield equation for rock

1986 ◽  
Vol 23 (1) ◽  
pp. 9-17 ◽  
Author(s):  
Paul Michelis ◽  
E. T. Brown
Keyword(s):  
Plastic Strain ◽  
Work Hardening ◽  
Triaxial Compression ◽  
Flow Rule ◽  
Work Softening ◽  
Strain Behaviour ◽  
Strain Invariant ◽  
Energy Dissipated ◽  
Extensive Experimental Data ◽  
Work Done

A yield equation for isotropic, homogeneous, geotechnical materials has been developed and applied to the work-softening and work-hardening behaviour of granular rocks. The development of this yield equation was based on a comparison of the work done and the energy dissipated within a sample undergoing yield in triaxial compression. The formulation takes into account friction and dilatancy and also an experimental observation leading to the derivation of a nonassociated flow rule. The analysis of extensive experimental data indicates that the flow rule is consistent for work-softening and -hardening behaviour, and validates the application of the incremental theory of plasticity to the irrecoverable strain behaviour of rocks in which the predominant mode of deformation is cataclastic. The yield equation, which is expressed in terms of readily indentifiable material parameters, predicts yield strength or strength at a given value of plastic strain invariant, and relates stress and strain increments at yield. Key words: rocks, yield, plastic strain, work softening, work hardening, energy, dilatancy, nonassociated flow.

A new strain-gradient theory for an isotropic plastically deformed polycrystalline solid body

2017 ◽  
Vol 23 (9) ◽  
pp. 1333-1344 ◽  
Author(s):  
AS Borokinni ◽  
AP Akinola ◽  
OP Layeni ◽  
OO Fadodun
Keyword(s):  
Plastic Strain ◽  
Solid Body ◽  
Strain Gradient ◽  
Plasticity Theory ◽  
Flow Rule ◽  
Gradient Plasticity ◽  
Polycrystalline Solid ◽  
Work Done ◽  
Strain Gradient Plasticity Theory ◽  
Internal Microstresses

This study considers strain-gradient plasticity theory in the context of small deformations for an isotropic solid body with a view to investigating the distortion effects associated with the divergence of plastic strain through the Burgers tensor. The principle of virtual power is employed and the constraint of irrotationality is imposed on the plastic component of the gradient of the displacement vector. It is obtained that the gradient, curl, and divergence of the plastic strain in the body are mutually related. This relation establishes the existence of work done through the divergence of plastic strain as distinct from the work done through the gradient of the plastic strain. Consequently, a polycrystalline solid body undergoing distortion associated with the divergence of plastic strain exhibits new internal microstresses; and the obtained model, consisting of the microforce balance, constitutive relations, and plastic flow rule, extends the known Gurtin–Anand model in a natural fashion. Furthermore, in the governing flow rule, it is revealed that the internal microstresses associated with the divergence of plastic strain act as opposing agents to the internal microstresses associated with the gradient of the plastic strain via the length scales Q, L, and the gradient of the divergence of the plastic strain. This work shows the distortion effects associated with the divergence of plastic strain which the Gurtin–Anand strain-gradient plasticity theory in literature does not apprehend.

Yielding and Flow of Sand in Triaxial Compression: Parts II and III

1967 ◽  
Vol 4 (4) ◽  
pp. 376-397 ◽  
Author(s):  
H B Poorooshasb ◽  
I Holubec ◽  
A N Sherbourne
Keyword(s):  
Plastic Strain ◽  
Experimental Evidence ◽  
Potential Function ◽  
Triaxial Compression ◽  
Strain Increment ◽  
Flow Rule ◽  
Plastic Strain Increment ◽  
Yield Loci

In Part I,* based on experimental evidence, the existence of a potential function to define the gradient of the plastic strain increment vector was proved. The study is continued in Part II by defining the term yielding, a discussion of the form of the yield loci and a presentation of the “flow rule.”

Gradient of Soil Constitutive Model

2010 ◽  
Vol 168-170 ◽  
pp. 1126-1129
Author(s):  
Wen Xu Ma ◽  
Ying Guang Fang
Keyword(s):  
Plastic Strain ◽  
Strain Gradient ◽  
Soil Analysis ◽  
Natural Material ◽  
Flow Rule ◽  
The Finite Element Method ◽  
Gradient Effect ◽  
Non Local ◽  
Associated Flow Rule ◽  
Plastic Strain Gradient

For the soil is a very complex natural material, significant strain gradient effect exist in soil analysis. Based on the "gradient" phenomenon, we add the plastic strain gradient hardening item into the traditional Cambridge yield surface. By using the consistency conditions and associated flow rule, we get the explicit expression of plastic strain gradient stiffness matrix. And the finite element method of plastic strain gradient is also shown in this article. Plastic strain gradient is actually a phenomenological non-local model containing microstructure information of the material. It may overcome the difficulties in simulating the gradient phenomenon by traditional mechanical model.

A New Nonlinear Stress-Strain Model for Soils at Various Strain Levels

2013 ◽  
Vol 631-632 ◽  
pp. 782-788
Author(s):  
Cheng Chen ◽  
Zheng Ming Zhou
Keyword(s):  
Compression Test ◽  
Triaxial Compression ◽  
Small Strain ◽  
Empirical Formulas ◽  
Stress Strain ◽  
Strain Behaviour ◽  
Proposed Model ◽  
Nonlinear Stress ◽  
London Clay ◽  
Strain Model

Soils have nonlinear stiffness and develops irrecoverable strains even at very small strain levels. Accurate modeling of stress-strain behaviour at various strain levels is very important for predicting the deformation of soils. Some existing stress-strain models are reviewed and evaluated firstly. And then a new simple non-linear stress-strain model is proposed. Four undetermined parameters involved in the proposed model can be obtained through maximum Young’s module, deformation module, and limit deviator stress and linearity index of soils that can be measured from experiment directly or calculated by empirical formulas indirectly. The effectiveness of the proposed stress-strain model is examined by predicting stress-strain curves measured in plane-strain compression test on Toyota sand and undrained triaxial compression test on London clay. The fitting results of the proposed model are in good agreement with experimental data, which verify the effectiveness of the model.

scholarly journals Studying Deformation Behaviors in Austenitic Stainless Steels within a Temperature Range of 143 K < T < 420 K

2021 ◽  
pp. 22-30
Author(s):  
S. A Barannikova ◽  
A. M Nikonova ◽  
S. V Kolosov
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Localization ◽  
Work Hardening ◽  
Deformation Localization ◽  
Linear Hardening ◽  
Jerky Flow ◽  
Temperature Range ◽  
Α Phase ◽  
Flow Stage

This work deals with studying staging and macroscopic strain localization in austenitic stainless steel 12Kh18N9T within a temperature range of 143 K < T < 420 K. The visualization and evolution of macroscopic localized plastic deformation bands at different stages of work hardening were carried out by the method of the double-exposure speckle photography (DESP), which allows registering displacement fields with a high accuracy by tracing changes on the surface of the material under study and then comparing the specklograms recorded during uniaxial tension. The shape of the tensile curves σ(ε) undergoes a significant change with a decreasing temperature due to the γ-α'-phase transformation induced by plastic deformation. The processing of the deformation curves of the steel samples made it possible to distinguish the following stages of strain hardening, i.e. the stage of linear hardening and jerky flow stage. A comparative analysis of the design diagrams (with the introduction of additional parameters of the Ludwigson equation) and experimental diagrams of tension of steel 12Kh18N9T for different temperatures is carried out. The analysis of local strains distributions showed that at the stage of linear work hardening, a mobile system of plastic strain localization centers is observed. The temperature dependence of the parameters of plastic deformation localization at the stages of linear work hardening has been established. Unlike the linear hardening, the jerky flow possesses the propagation of single plastic strain fronts that occur one after another through the sample due to the γ-α' phase transition and the Portevin-Le Chatelier effect. It was found that at the jerky flow stage, which is the final stage before the destruction of the sample, the centers of deformation localization do not merge, leading to the neck formation.

scholarly journals Energy Evolution Law of Marble Failure Process Under Different Confining Pressures Based on Particle Discrete Element Method

2021 ◽  
Vol 8 ◽  
Author(s):  
Yan-Shuang Yang ◽  
Wei Cheng ◽  
Zhan-Rong Zhang ◽  
Hao-Yuan Tian ◽  
Kai-Yue Li ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Energy Dissipation ◽  
Axial Strain ◽  
Triaxial Compression ◽  
Failure Process ◽  
Rock Failure ◽  
Biaxial Compression ◽  
Energy Evolution ◽  
Confining Pressures ◽  
Energy Dissipated

The energy dissipation usually occurs during rock failure, which can demonstrate the meso failure process of rock in a relatively accurate way. Based on the results of conventional triaxial compression experiments on the Jinping marble, a numerical biaxial compression model was established by PFC2D to observe the development of the micro-cracks and energy evolution during the test, and then the laws of crack propagation, energy dissipation and damage evolution were analyzed. The numerical simulation results indicate that both the crack number and the total energy dissipated during the loading process increase with confining pressures, which is basically consistent with the experiment results. Two damage variables were presented in terms of the density from other researchers’ results and energy dissipation from numerical simulation, respectively. The energy-based damage variable varies with axial strain in the shape of “S,” and approaches one more closely than that based on density at the final failure period. The research in the rock failure from the perspective of energy may further understand the mechanical behavior of rocks.

scholarly journals Stress-strain behaviour of Toyoura sand in undrained triaxial compression

2019 ◽  
Vol 92 ◽  
pp. 15010 ◽  
Author(s):  
Katarzyna Dołżyk-Szypcio
Keyword(s):  
Stress Ratio ◽  
Triaxial Compression ◽  
State Parameter ◽  
State Theory ◽  
Natural State ◽  
Strain Behaviour ◽  
Characteristic Points ◽  
Toyoura Sand ◽  
Undrained Conditions ◽  
Parameter Values

The stress-plastic dilatancy relationship for Toyoura sand sheared under undrained triaxial conditions was analysed by use of Frictional State Theory. Under undrained conditions, plastic strain increments are counterbalanced by elastic strain increments. The linear stress ratio-plastic dilatancy relationships at different stages of sand shear were obtained by assuming that Poisson's ratio is a function of shear strain. Contrary to a drained condition, natural state parameter values are not special for characteristic points of sand behaviour under undrained conditions.

scholarly journals A Consistent Relationship between the Stress and Plastic Strain Components and Its Application in Deep Drawing Process

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Yong Zhang ◽  
Qing Zhang ◽  
Xianrong Qin ◽  
Yuantao Sun
Keyword(s):  
Plastic Strain ◽  
Deep Drawing ◽  
Metal Forming ◽  
Yield Criterion ◽  
Flow Rule ◽  
Drawing Process ◽  
Deep Drawing Process ◽  
Dimensional Changes ◽  
Consistent Relationship ◽  
Strain Components

As von Mises yield criterion and associated flow rule (AFR) are widely applied in metal forming field, a semitotal deformation consistent relationship between the stress and plastic strain components and the rule of dimensional changes of metal forming processes in a plane-stress state are obtained on the basis of them in this paper. The deduced consistent relationship may be easily used in forming interval of the workpiece. And the rule of dimensional changes can be understood through three plastic strain incremental circles on which the critical points can be easily determined on the same basis. Analysis of stress and plastic strain evolution of aluminum warm deep drawing process is conducted, and the advantage of nonisothermal warm forming process is revealed, indicating that this method has the potential in practical large deformation applications.

Entropy Interpretation of the Elastic–Plastic Strain Invariant

2018 ◽  
Vol 59 (6) ◽  
pp. 1078-1084
Author(s):  
L. B. Zuev ◽  
A. G. Lunev ◽  
O. S. Staskevich
Keyword(s):  
Plastic Strain ◽  
Elastic Plastic ◽  
Strain Invariant
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