Plastic Shear Strain Research Articles

Coupling numerical model of hydraulic fracturing seepage in soft coal based on elastoplastic damage

In order to guide the field application of hydraulic fracturing of soft coal in coal mine, based on the elastic-plastic damage theory, the coupling numerical model of soft coal hydraulic fracturing seepage was studied. The porosity strain relationship equation, permeability strain relationship equation, the relationship between permeability and volume plastic tensile strain and volume plastic shear strain of coal and rock mass are derived, and the plastic correction equation and softening parameters are defined. The stress coupling equation and yield criterion are programmed and embedded into the finite difference software FLAC3D for numerical solution. The numerical simulation shows that the numerical calculation model of soft coal hydraulic fracturing conforms to the actual law, and the field fracturing radius investigation experiment is consistent with the numerical simulation results.

Direct Shear Experimental Study on the Mobilized Dilation Behavior of Granite in Alxa Candidate Area for High-Level Radioactive Waste Disposal

Dilation behavior is of great importance for reasonable modeling of the stability of the host rock of the repository for high-level radioactive waste disposal. It is a suitable method for carrying out direct shear experiments to analyze the dilation behavior of rock with well understood physical meanings. Based on a series of direct shear experiments on granite samples from the Alxa candidate area under different normal stresses, the shear stress‒shear strain and shear stress‒normal strain relations have been studied in detail. Five typical stages have been divided associated with the fracturing process and deformation behaviors of the granite samples during the experimental process, and the method to determine the typical stress thresholds has been proposed. It has also been found that the increasing normal stress may reduce the maximum dilation angle, and when the normal stress is relatively lower, the negative dilation angle may occur during the post-peak stage. According to the data collected from the direct shear tests, an empirical model of the mobilized dilation angle dependent on normal stress and plastic shear strain is proposed. This mobilized dilation angle has clear physical meanings and can be used in plastic constitutive models of the host rock of the repository, and this analysis can also be put forward to other types of geomechanical problems, including the deformation behaviors related to landslide, earthquake, and so on.

Effect of repeated rise and fall of water level on seepage-induced deformation and related stability analysis of Princeville levee

The Princeville levee, and flooding associated with Hurricanes Floyd and Matthew, is used as a case study in which the analyses are focused on the effect of repeated rise and fall of water levels (representing severe storm cycles) on the stability of the levee and the risk of failure. The analyses included strain-based and strength reduction approaches and are conducted using the finite element program Plaxis 2D. The limit equilibrium stability software “Slope/W” was also used for comparative study. The strain-based limit state approach considers the uncertainty of soil properties and is used to characterize the levee performance under repeated storm loading in terms of damage levels (or limit states). The strain-based analyses results show a progressive development of plastic shear strain zone within the levee as the number of storm cycles is increased. The accumulation of such shear strain leads to increasing the probability of exceeding a given performance limit state. As more flooding cycles are introduced, the shear strain values increase by a factor of 3.5 from cycle 1 to 6, and therefore reflect the increasing level of failure risk. In parallel, the deterministic stability factor of safety obtained from limit equilibrium method remains unchanged and slightly changes for strength reduction method with an increased number of rises and falls of the water level. The consideration of “rapid” drawdown conventionally used in limit equilibrium stability analyses (where no consideration for time is included), instead of more realistic rate based on drawdown hydrograph leads to conservative estimate of factor of safety. The analyses results demonstrate the increase in risk with repeated hydraulic loading.

Effective elastic-plastic response of particulate two-phase composite materials under multi-axial loading

In recent papers (Teng, 2014, 2018), an incremental elastic-plastic double-inclusion model was developed to determine the effective elastic-plastic response of two-phase composites of spherical or aligned spheroidal particles. For composites of purely elastic particles and elastic-plastic matrix of von Mises yield criterion with isotropic strain hardening, the double-inclusion model was formulated through the use of an isotropic matrix tangent stiffness tensor. The use of the isotropic tangent stiffness tensor, however, is only suitable for uniaxial loading or pure shear, but not for multi-axial loading. For in general the elastic-plastic tangent stiffness tensor of the matrix is inherently anisotropic, and during plastic deformation normal stress (strain) increment and shear strain (stress) increment are coupled, as a result of the anisotropy of the tangent stiffness tensor. In this paper, the original incremental elastic-plastic double-inclusion formulation presented in the previous papers (Teng, 2014, 2018) for composites of elastic spherical or aligned spheroidal particles and elastic-plastic matrix is modified by adding anisotropic corrections of stress increment defined in terms of the difference between the anisotropic and isotropic tangent stiffness tensors of the matrix. The resulting improved incremental double-inclusion model can be applied to multi-axial loading. Comparison of the model predictions to the results of the direct approach using representative volume elements containing many particles shows that the improved incremental elastic-plastic double-inclusion formulation is capable of predicting the effective elastic-plastic response of two-phase composites of spherical or aligned spheroidal particles under multi-axial loading.

Quantifying “transitional” soil behaviour

The last decade has seen an increasing amount of research on so called “transitional” soils that are characterised by incomplete convergence to unique normal compression lines and/or critical state lines in simple laboratory tests. This topic has often provoked reaction, perhaps because some have seen it as a challenge to critical state frameworks of soil behaviour. A particular issue is whether incomplete testing or other test defects might cause such an apparent behaviour. Confusion around the topic has not been helped by the wide range of degrees of convergence seen for different materials and differences seen between convergence in compression and shearing. This paper proposes a unifying means of plotting laboratory test data from such soils that will hopefully provide a rational framework for such discussions, since it makes explicit the degree of convergence towards unique volumetric states for different forms of loading. Data are examined for three “transitional” soils. The results show that bringing about convergence for these soils would require strains beyond those that may easily be applied and that the lack of convergence cannot solely be an artefact of test defects. Plastic volumetric strain was found to cause much faster convergence than plastic shear strain.

Microstructure Evolution of AA1070 Aluminum Alloy Processed by Micro/Meso-Scale Equal Channel Angular Pressing

The Micro/meso-forming of commercially pure aluminum, AA1070, processed at room temperature by equal channel angular pressing (ECAP) with a die channel angle of 90° through 4 deformation passes has been conducted. Microstructure features, such as grain size, misorientation angle distributions and the developed texture during the four deformation passes of micro/meso-ECAP have been investigated by Electron backscattering diffraction (EBSD) technique. Then, hardness measurements over the cross-section of the processed samples were correlated with the EBSD analysis. EBSD scans revealed that extended shear bands are formed and represent the microstructural feature induced during micro/meso-forming. Whereas, a non-uniform grain structure consisting of intensive low-angle grain boundaries was obtained in the first pass, a uniform ultrafine-grained structure of high-angle grain boundaries (in the range of 1–2 μm) was achieved at the fourth pass. Consequently, a significant improvement in the hardness value to 65.3%, with respect to the starting material, was achieved due to the enhancement of the fine grain structure. The texture analysis exhibited that the high plastic shear strain associated with micro/meso-scale ECAP was capable to develop a weak texture in the flow plane compared to the starting texture.

Macro-mechanical properties of saturated sandstone of Jushan Mine under post-peak cyclic loading: an experimental study

The mechanical properties of rocks are greatly affected by water action. Many underground structures can be failed by changes in the water environment. To reveal the mechanical properties of the rocks after saturation, a series of saturated sandstones are prepared to study the changes in the mechanical properties during post-peak cyclic loading and unloading. The results show that the strength characteristics of the sandstones decrease after saturation. There is an exponential function between the peak strength and the damage degree and between the crack damage stress and the damage degree. A new method for calculating the elastic modulus is proposed. The results of both calculation methods show that the elastic modulus of the saturated sandstones decreases. The relationship between the elastic modulus obtained by the two methods and the damage degree is quite different. After saturation, the dilatancy of the sandstones increases in the post-peak stage. The volumetric strain, the plastic shear strain, and the peak dilatancy angle all increase with increasing damage degree. Because of the filling by water molecules, the P-wave velocity increases. There is an exponential function relationship between the P-wave velocity and the damage degree. Because of the softening after saturation, more macroscopic failure cracks and fracture surfaces will be formed in the saturated sandstones. The research results of this paper can provide some guidance for excavation and engineering design in water-rich rock.

Mobilized Mohr-Coulomb and Hoek-Brown Strength Parameters during Failure of Granite in Alxa Area in China for High-Level Radioactive Waste Disposal

Strength parameters of the host rock is of paramount importance for modelling the behaviors of underground disposal repository of high-level radioactive waste (HLW). Mobilization of strength parameters should be studied for a better understanding and modelling on the mechanical behaviors of the surrounding rock, considering the effect of temperature induced by the nuclear waste. The granite samples cored from NRG01 borehole in Alxa candidate area in China for HLW disposal are treated by different temperatures (T = 20 °C, 100 °C and 200 °C), and then are used to carry out a series of uniaxial and tri-axial compression experiments under various confining pressures (σ3 = 0, 5, 10, 20, and 30 MPa) in this study. With the recorded axial stress—axial strain and axial stress—lateral strain curves, mobilization of both Mohr-Coulomb and Hoek-Brown strength parameters are analyzed with the increasing plastic shear strain. It has been found that NRG01 granite samples show generally similar cohesion weakening and friction strengthening behaviors, as well as the non-simultaneous mobilization of Hoek-Brown strength parameters (mb and s), under the effect of various treatment temperatures. Furthermore, the samples treated by higher temperatures show lower initial values of cohesion, but their initial friction angle and mb values are relatively higher. This should be mainly owing to the thermally induced cracks in the samples. This study should be helpful for a better modelling on the mechanical behaviors of NRG01 granite samples as the host rock of a possible HLW disposal repository.

The influence of non-linear stress-strain behavior of dense sand on seabed response to ice gouging

Subsea pipelines crossing the Arctic shallow waters are usually threatened by ice scour. A cost-effective solution to physically protect the pipeline against the ice gouging is to bury the pipeline in the seabed. Determining the minimum burial depth to minimize the construction cost and ensure pipeline integrity is a challenging design aspect. This requires proper modeling of the ice keel-soil interaction for an accurate assessment of the subgouge soil deformation and the keel reaction forces in a free field ice gouging analysis. In this study, the ice gouging process in dense sand was simulated by advanced large deformation analyses using Coupled Eulerian-Lagrangian (CEL) approach in ABAQUS/Explicit. A modified Mohr-Coulomb (MMC) model was coded into a simplified user subroutine to incorporate the effect of plastic shear strain accumulation, loading condition, density, and confining pressure on the shear strength parameters of dense sand. The MMC model captured the non-linear pre-peak hardening and post-peak softening of the dense sand that is not modeled by conventional Mohr-Coulomb (MC) model. The existing test results and numerical studies were used to verify the performance of the MMC model in ice gouging analysis. A comprehensive parametric study was conducted to investigate the effect of ice keel configuration and soil model parameters on keel reaction forces, subgouge soil deformations, and the soil berm formations. The proposed model resulted in a more accurate prediction of the seabed response to ice gouging and showed the significance of modeling the strain rate dependency of dense sand in ice gouging analysis. The proposed methodology was found to be a strong but simple framework that can be effectively used in daily engineering practice.

Torsional Fatigue Failure of Additively Manufactured Stainless Steel of Reduced Specimen Size

The torsional fatigue response of as-built direct metal laser sintered (DMLS) stainless steel (SS) GP1 of reduced specimen size and horizontal build orientation subjected to cyclic loading at a highly plastic shear strain has been investigated. The average shear modulus, G, was found to be 55.36 GPa, with shear stress history revealing cyclic hardening to stabilization and softening to fracture. Findings suggest that stainless steel GP1 of reduced specimen size experiences fatigue crack initiation at voids near the surface, resulting in a star-spline brittle fracture response, and premature torsional fatigue failure within the low cycle fatigue regime. A noninteraction deformation constitutive model through finite element simulations has been used to successfully simulate the deformation response of the gage section under torsional fatigue conditions.

Bearing capacity of embedded foundations using quasi-kinematic limit analysis

Bearing capacity of rectangular foundations, with varying aspect ratios (1 ≤ L/B ≤ 5) and embedded at shallow to medium depths (D/B ≤ 5), has been evaluated by using the three-dimensional cell-based smoothed finite elements quasi-kinematic limit analysis. The results have also been obtained for circular and strip foundations by performing exclusively the axisymmetric and plane strain analyses. The associated optimization problem has been solved by employing the semidefinite programming (SDP). Shape factors (sc, sq and sγ) and depth factors (dc, dq and dγ) are given as a function of soil internal friction angle (ϕ). The shape factors have been expressed as a function of L/B, on the other hand, the depth factors have been given as a function of D/B and L/B. A thorough comparison of the results has been made with the different solutions available in literature. The variations of (i) power dissipation function, (ii) maximum plastic shear strain rates, and (iii) the nodal velocities patterns, have also been examined to interpret the failure mechanism.

A simple model for size effects in constrained shear

Simple shear of a ductile layer constrained between two rigid solids is analyzed using a conventional one dimensional strain gradient plasticity formulation. The aim of the analyses is to gain insight into the scaling relations and size effects seen in the experiments of Mu et al.(2014, 2016, 2017). Our analysis presumes that the deviation from previous predictions based on conventional strain gradient plasticity theory is not due to a defect in the theory but is due to a change in boundary condition that takes place when a sufficiently large plastic shear strain gradient develops at the layer boundaries. Predictions based on this presumption are qualitatively, and in some aspects, quantitatively consistent with a range of the observations.

Modelling the effect of surface passivation within higher-order strain gradient plasticity: The case of wire torsion

The effect of surface passivation on the torsional behavior of thin metallic wires is studied within two frameworks of higher-order strain gradient plasticity, i.e. the simplified version of Gudmundson theory and the Polizzotto theory. The elastoplastic solution to the wire torsion problem is obtained. The flexibility of the higher-order theories is emphasized by solving the torsion problem for two boundary conditions, i.e. with and without surface passivation. The two types of models predict similar trends related to the size effect and the passivation effect in the wire torsion. By accounting for a free energy involving one energetic length scale, a formula relating the normalized torque to the wire radius is derived. The formula confirms a standardized increase in strain hardening with diminishing wire diameter. The distributions of plastic shear strain and its gradient along the radial coordinate for the unpassivated and passivated wires are given. It is found that the plastic flow would be strongly suppressed at the passivated wire surface. Numerical results also show that the energetic length scale plays an important role in modelling the elevation of strain hardening due to passivation.

Implementation of a large deformation finite element modelling technique for seismic slope stability analyses

Post-slide investigations show large displacement of failed soil mass in many earthquake-triggered landslides. An Eulerian-based finite-element modelling (FEM) of large deformation of soil, for pseudostatic and dynamic loadings, is presented in this study. The Eulerian FEM is compared with Lagrangian-based explicit and implicit finite-element (FE) modelling approaches. The dynamic FE modelling of two hypothetical slopes for eight earthquake acceleration–time histories show that the failure surfaces develop progressively, which cannot be modelled using the traditional limit equilibrium method (LEM). A large plastic shear strain concentration (i.e. shear band formation) occurs when the strain-softening behaviour of soil is considered. The similarities and differences between the results of dynamic and pseudostatic FE analyses based on estimated pseudostatic coefficient from acceleration–time records are presented. The duration of an earthquake influences the failure process and displacement of the failed soil mass. The displacement of the toe obtained from FEM is compared with Newmark's simplified approach. The developed Eulerian-based FE modelling technique has been used to simulate large-scale landslides in sensitive clays due to earthquake loading [1].

Elastoplastic modelling of mechanical behavior of rocks with fractional-order plastic flow

The progressive transition in volumetric deformation from compression to dilation has been widely observed in rock-like materials under compressive stresses. This paper attempts to develop a fractional plasticity model for rocks by incorporating such volumetric compression/dilation transition state. Firstly, a fractional-order plastic flow rule suitable for describing soft rocks is proposed without using plastic potential. A unified hardening/softening function is introduced with the equivalent plastic shear strain as hardening variable. The fractional constitutive model is then adapted for brittle rocks. Comparisons between the fractional plastic model and some existing associated/non-associated plastic models demonstrate that the present model is capable of capturing correctly the transition state of volume compaction and dilation. Validations against experimental results from conventional triaxial compression tests indicate that the model allows to predict the main mechanical behaviors of rocks under different confining pressures.

Use of an energy‐based/critical plane model to assess fatigue life under low‐cycle multiaxial cycles

AbstractFor engineering components subjected to multiaxial loading, fatigue life prediction is crucial for guaranteeing their structural security and economic feasibility. In this respect, energy‐based models, integrating the stress and strain components, are widely used because of their availability in fatigue prediction. Through employing the plastic strain energy concept and critical plane approach, a new energy‐based model is proposed in this paper to evaluate the low‐cycle fatigue life, in which the critical plane is defined as the maximum damage plane. In the proposed model, a newly defined NP factor κ* is used to quantify the nonproportional (NP) effect so that the damage parameter can be conveniently calculated. Moreover, a simple estimation method of weight coefficient is developed, which can reflect different contributions of shear and normal plastic strain energy on total fatigue damage. Experimental data of 10 kinds of materials are employed to assess the effectiveness of this model as well as three other energy‐based models.

A numerical large strain solution for circular tunnels excavated in strain-softening rock masses

This paper presents a large strain numerical solution of a circular tunnel for the ground reaction curve (GRC) in strain-softening rock masses. Both the stress equilibrium equation and deformation compatibility equation are considered in a current coordinate. A series of examples are employed to validate the proposed solutions, and the results show that: (1) the displacement, softening and residual radii of larger strain solution are smaller than that of small strain solution, and their difference significantly increases with a decrease in the Young’s modulus. (2) the increasing Poisson’s ration and critical shear plastic strain decrease the displacement, softening and residual radii.

Effect of Fault Roughness on Aftershock Distribution: Plastic Off‐Fault Material Properties

AbstractWe perform spontaneous earthquake rupture simulations on rough strike‐slip faults with off‐fault plastic material properties. We examine the off‐fault stress change and coseismic damage pattern resulting from dynamic fault slip. We use the stress output from each simulation to calculate the Coulomb failure function (CFF). We calculate the CFF values on the extensional and compressional side of the fault using parallel receiver fault orientations. We also calculate the CFF values on the extensional side of the fault using variable receiver fault orientations determined using the angle at which plastic shear strain is maximum. We calculate the probability density function for the CFF values across the fault as a function of distance. We observe a similar overall trend of the CFF values with distance for the extensional and compressional sides—our simulations show a broad range of values in the near‐fault region, while a narrow range of values occurs further from the fault. In the near‐fault region, we observe many more positive CFF change zones using variable receiver fault orientations than using parallel orientations. We calculate the areas and amplitudes of these positive CFF zones as a function of distance away from the fault. Our comparison of CFF amplitudes as a function of rupture area suggests that the spatial aftershock distribution surrounding a fault is controlled by both stress heterogeneity and the coseismic damage zone complexity. The calculations of rupture areas using our model are consistent with ruptured areas of observed aftershocks in California.

Large-deformation finite-element modelling of earthquake-induced landslides considering strain-softening behaviour of sensitive clay

Large-scale landslides in sensitive clays cannot be explained properly using the traditional limit equilibrium or Lagrangian-based finite-element (FE) methods. In the present study, dynamic FE analysis of sensitive clay slope failures triggered by an earthquake is performed using a large-deformation FE modelling technique. A model for post-peak degradation of undrained shear strength as a function of accumulated plastic shear strain (strain-softening) is implemented in FE analysis. The progressive development of “shear bands” (the zone of high plastic shear strains) that causes the failure of a number of soil blocks is simulated successfully. Failure of a slope could occur during an earthquake and also at the post-quake stage until the failed soil masses come to a new static equilibrium. Upslope retrogression and downslope runout of the failed soil blocks are examined for varying geometries and soil properties. The present FE simulations can explain some of the conditions required for different types of seismic slope failure (e.g., spread, flowslide or monolithic slides) to be triggered, as observed in the field.

Evolution of nano-laminated structure formed by the thermally-assisted plastic deformation in dry sliding wear

Abstract The evolution of nano-laminated structure generated in dry sliding wear of a high strength martensite steel was investigated by using Scanning Electronic Microscopy (SEM) and Transmission Electron Microscopy (TEM). Gradient microstructure along the depth was observed with the top layer consisting of nano-laminated structure. During the sliding wear-induced plastic deformation, grains were refined and lamellar structures were formed as a result of generation of dislocation cell blocks bounded by geometrically necessary boundaries (GNBs) and incidental dislocation boundaries (IDBs). With increasing plastic shear strain and strain gradient, there is a continuous reduction in the spacing and length in dislocation cell blocks, leading to nano-laminated structures. The ultrafine nano-laminated structure with laminate spacing of 20 nm was observed at the sliding time of 120 min. However, the grain refinement is not a merely mechanical deformation process. The formation of Fe3O4 and FeO gave direct evidence that the highest temperature due to frictional heat could reach up to 600 °C. The result suggested that the formation of nano-laminated structure was governed by thermally-assisted plastic deformation.