Direction Of Plastic Flow Research Articles

Numerical Simulation Study on Evolution Process of Carrying-Soil Effect of Rectangular Pipe Jacking

The carrying-soil effect is an important factor affecting the success or failure of rectangular pipe jacking construction. Because it is difficult to explore the dynamic evolution process of the carrying-soil effect in the field test, this paper relies on the pipe jacking project of a comprehensive pipe gallery in Suzhou City, and uses ABAQUS 2021 finite element software to simulate the jacking process of rectangular pipe jacking. Based on the theory of plastic mechanics of rock and soil and the related research and application status, the equivalent plastic strain index is introduced as the basis for judging the failure boundary of soil in the numerical simulation results, and the boundary between the carrying-soil area and the surrounding soil is determined, that is, the shear fracture surface. According to the principle of plastic potential energy, the development direction of the fracture surface is consistent with the direction of plastic flow, so as to predict the development direction of the boundary of the carrying-soil area. According to the change in the equivalent plastic strain cloud map with the jacking mileage, the evolution process of the carrying-soil effect is clarified, and the dynamic evolution law of the carrying-soil area is revealed, which is of great significance for predicting the disturbance of the surrounding soil during the construction of rectangular pipe jacking and accurately evaluating the environmental effect of the construction.

Non-coaxial plasticity of similar weakly cemented soft rock under directional shear stress path

The plastic flow behavior of soft rock exhibits non-coaxial features under complex stress paths, while traditional plasticity theories are ill-equipped to adequately represent this, which leads to the mechanism of soft rock failure still unclear. To investigate the evolution law of strain increments and non-coaxial characteristics of weakly cemented soft rock, the directional shear tests are conducted using the hollow cylinder apparatus (HCA). The results show that non-coaxiality does not occur when α is distinct from 0° or 90°. The oscillation of the non-coaxial angle is significantly more variable in soft rock experiencing combined tension–torsion (45° < α < 90°), as opposed to those under the influence of combined compression-torsion (0° < α < 45°). The non-coaxiality swiftly dissipates when the sample is approaching the failure state. The stress rate is decomposed into stress magnitude and direction to describe non-coaxial features of plastic strain. And a new method for non-coaxial stress rate is proposed which can express the plastic strain increment directions. The spherical interpolation coefficient method is utilized to describe the continuous change in non-coaxial plastic flow direction between tangential and normal directions of the yield surface. The non-coaxial parameter (Δ) is introduced to quantify the non-coaxial characteristics of soft rock and its validity is confirmed through test results. This method effectively captures the principal stress direction influence on non-coaxial behavior of soft rock and have significance for rock mechanics.

Characterization and modeling of biaxial plastic anisotropy in metallic sheets

The anisotropic behavior of cold-rolled sheet metals has been extensively studied, typically characterized by uniaxial loading tests in different directions to determine yield strengths and plastic flow (Lankford r-values). However, biaxial principal stress states often focus solely on yield loci in the RD/TD (rolling/transverse) directions, with limited studies on other loading directions. This study analyzes the relationship between the principal stress yield loci and the material principal anisotropic stress directions based on the Hill48 yield function. Biaxial tensile tests are conducted on DP590 high-strength steel using cruciform specimens cut in various directions different from the sheet RD/TD directions. The evolution of the anisotropic yield locus and plastic flow of DP590 under biaxial tensile directions beyond the traditional RD/TD anisotropic directions is revealed. Furthermore, a modified Hill48 model that considers any principal stress direction of loading is proposed, accurately describing the continuous evolution of equi-biaxial tension stress, near-plane strain stress, and plastic flow direction for different principal stress directions of loading. The issues of failing to predict plastic flow under biaxial loadings in the original Hill48 model, and the degraded representation of existing constitutive models when accounting for out-of-plane anisotropy are addressed by decoupling the relationship between anisotropic parameters and stress state. In addition, the proposed calibration strategy of anisotropic parameters, using experimental data from various principal stress directions of loading, effectively captures the anisotropic evolution caused by changes in principal stress directions. Comprehensive evaluation and verification of the plasticity model should consider yield locus for any principal stress directions of loading, and also the normal and shear planes.

Three-dimensional fractional plastic models for saturated sand using Caputo derivative and R-L derivative: A comparative study

The strength and dilatancy of sand are mainly influenced by the void ratio, confining pressure and stress path. In engineering, the stress-strain relationship of sand in three-dimensional stress state is complicated, where the state-dependent properties of sand are difficult to be described by traditional constitutive models. Thus, fractional plastic models based on different fractional derivatives were developed to capture such state-dependent behavior of sand. This paper attempts to make a comparative study of the fractional models based on two typical fractional derivatives, i.e., the R-L derivative and Caputo derivative. The results show that the different types of fractional derivatives are mainly reflected in the different order of differentiation and integration, which will have a significant impact on the calculation of plastic flow direction, stress-dilatancy ratio and fractional order parameter βin the constitutive model. By determining the constitutive parameters of the two models, the constitutive behaviors predicted by different models were compared with the corresponding test results of saturated sands under different initial mean pressures and different stress paths. The models can reasonably simulate the test results of saturated sands, where the dilatancy characteristic can be captured. Compared with R-L model, Caputo model can predict more volumetric strain in the dilatancy process, and has better prediction effect. Overall, the predicted effects of the two models are close, with a maximum difference of about 7 %.

Achieving Superior Strength–Ductility–Conductivity Combination in TiB2p/6201 Composites via Particle Rotation and Subgrain Refinement

The key factor in the material design of overhead power transmission lines is to obtain a desired balance among strength, ductility, and electrical conductivity. Herein, TiB2 particulate‐reinforced aluminum matrix composites are prepared to find a way out of the intrinsic dilemma behind this balance by tailoring the subgrain refinement. The interaction in the form of inhomogeneous deformation induced by the flexibility discrepancy between the rigid particles and soft matrix is studied. On the one hand, the hexagonal plate‐like TiB2 particles rotate with the inhomogeneous deformation, forcing the biggest exposed plane ((0001) basal plane) parallel to the plastic flow direction, which is beneficial for the dislocation multiplication and hindrance of dislocation slipping. On the other hand, inhomogeneous deformation generates plentiful geometry necessary dislocations and divides the microstructure into two types: in the particle‐rich region ultrafine grains are formed and in the particle‐free region significant subgrains refinement is observed. The subgrains with 3 wt% TiB2 are refined from ≈897 to ≈248 nm. Thanks to these microstructural benefits, the composites achieve the following strength–ductility–conductivity combination: ultimate tensile strength is 370 MPa, elongation after fracture is 11.2%, and electrical conductivity is 51.79% IACS. Besides, the elastic modulus reaches 75.43 GPa.

A three-dimensional elastoplastic constitutive model incorporating Lode angle dependence

A comprehensive three-dimensional elastoplastic constitutive model is presented to characterize the stress-strain behavior of cement stone under the true triaxial stress state. This constitutive model incorporates a three-dimensional yield function and a three-dimensional potential function. The three-dimensional yield function is designed to accurately represent the true triaxial stress state during hardening. The three-dimensional potential function is devised to depict the plastic flow direction under true triaxial stress state. The yield and potential functions include parameters that control the shape of the deviatoric and meridian planes, and these parameters vary with the plastic internal variable. Consequently, the yield function can accurately describe the stress state, and the potential function can precisely capture the variations in plastic flow direction. Additionally, a detailed procedure for determining the parameters of the yield function and potential function is proposed based on the full deformation process. The constitutive model is presented in the form of analytical solution. The comparison of experimental data with the constitutive model confirms its accuracy and validity. A sensitivity analysis of the deviatoric and meridian parameters in the potential function is performed, shedding light on their impact on the model behavior. Furthermore, the significance of incorporating Lode angle dependence into the potential function is discussed, emphasizing its essential role in accurately capturing strain in the direction of the intermediate principal stress.

High elongation heterostructure rare earth magnesium alloy based on rotating backward extrusion process

In this paper, Mg-9.5Gd-4Y–2Zn-0.5Zr cylindrical parts were prepared by the conventional backward extrusion (CBE) process and rotating backward extrusion (RBE) process. The effects of the two processes on the microstructure and mechanical properties of different orientation regions of rare earth magnesium alloy were analyzed and compared. The RBE process introduces a torsional shear quantity based on the CBE process. By changing the direction of plastic flow, has a positive effect on the elongation (EL) of the alloy. It was found that dynamic recrystallization (DRX) occurred in both CBE and RBE processes. With the transition of deformation, the strain continues to accumulate, and the DRX mechanism changes from discontinuous dynamic recrystallization (DDRX) to continuous dynamic recrystallization (CDRX). Compared with the CBE process, the grain refinement of the RBE process is more significant. After deformation, a more significant heterostructure is obtained in the RBE-45° region, and the average grain size reaches 24.7 μm. The ultimate tensile strength (UTS), yield strength (YS), and EL of the alloy in this region are 292.5 ± 7.7 MPa, 226.6 ± 7.4 MPa, and 21.5 ± 1.3 %, respectively. Although the strength is slightly lower than that of CBE alloy, better plasticity is obtained. The excellent strength-toughness synergy is attributed to the synergistic effect between heterogeneous regions of non-uniform microstructure. This study provides some theoretical guidance for the industrial production of large-size magnesium alloy cylindrical parts and subsequent applications.

A state-dependent non-orthogonal elastoplastic constitutive model for sand

The state-dependent deformation behavior of sand is reinterpreted from the perspective of strain increment magnitude and direction by analyzing the existing test data. A state-dependent non-orthogonal elastoplastic constitutive model for sand is established by incorporating the state variable into plastic strain increment magnitude and direction, respectively. For the magnitude of plastic strain increment, an S-type isotropic compression hardening rule applicable in large stress ranges is proposed, which is extended into a new hardening parameter for general stress states. Furthermore, the state variable is introduced into the newly proposed hardening parameter to consider the state dependence. On the other hand, the non-orthogonal plastic flow rule is employed to determine the plastic strain increment direction. To consider its state dependence, the relationship between the state variable and the parameter controlling the plastic flow direction is established. The comparison with the test results of four types of sand demonstrates that the proposed model can reasonably capture the state-dependent deformation behaviors of plastic strain increment magnitude and direction of sand.

Dynamic yielding and plastic flow behavior of Ti-6Al-4V under complex loading

The mechanical properties of metallic materials under complex loading at high strain rates are very important for material processing and engineering design. In this paper, a newly developed electromagnetic Hopkinson bar system is used to conduct dynamic experiments on Ti-6Al-4V titanium alloy under tension/compression-torsion loading conditions. The dynamic plastic behavior of the alloy, subject to complex stress states, was investigated at different loading rates under tension–torsion and compression-torsion conditions. A dynamic asymmetry yield criterion (DAYC) and loading surface (DALS) with different loading paths were proposed. The coupling effects of strain rate and stress state were considered in the yield and hardening functions. The results reveal non-uniformity in the initial yield surface and the expansion of loading surfaces at different stress states under high strain rates. Through comparison with experimental results, the reliability and accuracy of the proposed yield criterion and loading surface were validated. At last, a study on the direction of plastic flow was conducted, which demonstrated that the associated flow rule was basically satisfied.

Numerical Investigation of the Multiscale Characteristics of Elastoplasticity in Microheterogeneous Continuum Media Using a Simple Hollow Sphere Model

In this paper, we investigate the fundamental characteristics of plasticity in microheterogeneous continuum materials. Plasticity in such materials is a multiscale phenomenon with contrasting characteristics at different scales. A hollow sphere model, including a matrix embedding an oblate spheroidal pore, is considered as a sample representative elementary volume (REV) of a microheterogeneous material where, at the local level (microscale), a simple Drucker–Prager plasticity model is assumed for the matrix obeying the classical continuum theory of plasticity. The plasticity model is Lode angle independent with associated plastic flow and no hardening. We perform finite element numerical simulations on the REV to investigate the characteristics of the homogenized plasticity of the REV. It is seen that the homogenized plasticity shows complex characteristics such as Lode angle dependency, presence of cap, hardening, and nonassociativity. Well-established as these aspects are in the literature, they are often presumed in the plasticity models of heterogeneous materials in an ad hoc form. In contrast, we present here a systematic and lucid way to capture these aspects as emergent phenomena of heterogeneous microstructures. This has crucial implications in guiding the theoretical constitutive developments for elastoplastic materials toward adopting a multiscale approach that properly considers the effect of microstructure and naturally captures these aspects without the need for ad hoc assumptions. A fundamental assumption in the classical theory of plasticity is the plastic flow rule postulate, which states that the direction of plastic strain increment is governed only by the current state variables, independent of the loading increment direction. We show, through a stress probing exercise in 3D principal stress space, that the flow rule, assumed for the microscale plasticity, is not valid for the macroscopic plasticity. Indeed, the homogenized plastic flow direction in heterogeneous materials is governed by the current state variables and loading increment direction. Finally, we show that the plastic response is also a function of the stress path taken prior to loading. As such, nonclassical characteristics are observed for the plasticity of microheterogeneous materials. These nonclassical characteristics for the simple REV considered in this work (the hollow sphere model) align with some of the results observed in experiments or only reported for microdiscrete materials; herein, we show they are also valid for a broader range of materials endowed with microstructure, i.e., microcontinuous materials, and, as such, the fundamental assumptions in the classical theory of plasticity require revision before being applicable to the plastic behavior of heterogeneous materials.

A constitutive model for caprock siltstone subject to three-dimensional compression with emphasis on plastic potential and hardening law

Investigation of the strength, deformation and constitutive model of rocks under true three-dimensional stress is of much significance to scientifically and accurately predict the integrity of underground gas storage caprock. In general the intermediate principal stress and the minimum principal stress to which the caprock is subjected are not equal, and there is uncertainty in the in-situ stress test. In this study, the siltstone is taken from the caprock of the Hutubi gas storage in Xinjiang, with a buried depth of 3600 m. A series of true triaxial compression tests on siltstones were carried out using a true triaxial testing system for rocks, and the strength and deformation characteristics of siltstones under different intermediate principal stress conditions were studied. The elastoplastic constitutive model of rocks has been established: in the plastic part, the Mogi-Coulomb yield criterion has been modified so as to obtain the triple-mean-normal-stress yield function and triple-mean-normal-stress potential function suitable for rocks under the true three-dimensional stress state. The hardening law has been determined by fitting the relationship between the plastic deviatoric shear strain and the deviatoric stress in the true triaxial compression test. The constitutive model and the test data of siltstones have been verified by fitting. Finally, the influence of true triaxial stress on the permeability and breakthrough pressure of caprock siltstones has been discussed. The result indicates that with the increase of intermediate principal stress within a certain range, the peak strength of siltstones will also increase, and deformation in the direction of the intermediate principal stress will be restrained. Compared with the potential functions in other constitutive models, the triple-mean-normal-stress potential function proposed in this paper can accurately describe the plastic flow direction of siltstones under the true three-dimensional stress state. And the hardening law truly reflects the plastic deformation of siltstone specimens under different stress states during the loading process. The calculation result of the constitutive model is in good agreement with the test result. Under the true three-dimensional stress, the permeability of siltstones shows anisotropy. With the increase of the intermediate principal stress, the minimum value of siltstone permeability decreased by 8%, and the maximum value of breakthrough pressure increased by 4.3%.

An enhanced cutting plane algorithm of elastoplastic constitutive models for geomaterials

Integration of the nonlinear stress–strain relationship plays a critical role in the application of constitutive models to engineering practice. Aiming at the nonlinear integration problems commonly existing in elastoplastic constitutive models for geomaterials, we herein present a robust enhanced cutting plane algorithm (ECPA). This algorithm is based on the traditional cutting plane algorithm (CPA) with a new adaptive substepping technique. The accuracy of the CPA is first investigated via a series of numerical examples on a unified hardening/softening elastoplastic model with different nonlinearity degrees of yield functions and plastic potential functions. An intriguing observation is that the accuracy of CPA cannot be guaranteed as long as the plastic flow direction (i.e., ∂G/∂σ ) is not a constant during loading. To overcome this deficiency, a substepping technique for adaptively restricting substep increments solely related to the plastic flow direction was originally proposed and embedded into CPA. The robustness, including the accuracy and efficiency of the proposed ECPA, is evaluated by setting different increment steps and error tolerances. Finally, the ECPA is applied to the Modified Cam Clay (MCC) model, and the robustness of the ECPA is further assessed in element scale tests and a boundary value problem.

Constitutive model for soil-rock mixtures in the light of an updated skeleton void ratio concept

As a type of special geological body, soil-rock mixtures (SRMs) are widely found in nature and used in civil engineering. Many structures, such as rockfill dams, highways and tunnels, have used SRMs as building materials. Proper modeling of SRMs is of great importance to capture the complex behavior of this heterogeneous material. In this manuscript, a simple constitutive model incorporating the skeleton void ratio concept is proposed for SRMs with varying soil contents (sc). A prominent feature of the model is a unified description of the behavior of SRMs with varying sc such that only model parameters of pure rock and of pure soil are required. After calibration, the model shows a good capacity to predict the stress–strain response of SRMs under a wide range of sc, void ratios, and confining pressures. In particular, it captures well the non-associated behavior of rock-dominated SRMs with different sc. Furthermore, the sc-value is shown to modify the plastic flow direction of the material without influencing its yield surface.

Study on determining the plastic flow direction of soils with dilatancy

Study on determining the plastic flow direction of soils with dilatancy

A general plastic model for rockfill material developed by using Caputo fractional derivative

The gradient direction and fractional derivative direction of one function can be coaxial or non-coaxial, and this depends on the order value of fractional derivative. A fractional plasticity model was developed by using Caputo fractional derivative and a dilatancy equation pondering particle breakage for rockfill material in this study. In this fractional plasticity model, the gradient direction and fractional derivative direction of the plastic potential function derived from a dilatancy equation were deduced and further used as the plastic flow direction and loading direction respectively, and the order controls the non-associated feature between the plastic flow direction and loading direction. For validation, drained triaxial test results under different stress paths of five rockfill materials are simulated by the proposed fractional plasticity model. It can be found from comparisons between the drained triaxial compression test results of rockfill materials and corresponding model predictions that the proposed model can well capture the stress-strain characteristics of rockfill material, including strain hardening and volume change behaviors etc.

Surface crack analysis of the steering shaft gear after carburizing and quenching

The phenomenon of surface cracks in steering shaft gear after carburizing and quenching was analyzed by combining experimental research, theoretical analysis, and numerical simulation. The chemical composition, crack morphology, non-metallic inclusions, microstructure, microhardness, and forging process were analyzed and studied by means of directly reading spectrometer, metallographic microscope, scanning electron microscope, energy dispersive spectrometer, and micro hardness tester. The evolution process of surface crack morphology was numerically simulated and reproduced with the help of Deform 3D point tracking technology. The results show that linear surface cracks are formed on the surface of the round steel because of Alumina-type non-metallic inclusions, which destroy the continuity of the steel matrix during the rolling process. Surface cracks become arc-shaped due to the regular plastic flow direction of the material and propagate in the depth direction during the forging process. Crack provide a channel for the diffusion of C atoms during carburizing and quenching process, therefore carburized layer with gradient distribution is formed on both sides of the crack. The carburized layer reacts with oxygen during quenching and subsequent tempering, resulting in a certain degree of oxidation on both sides of the crack and the crack tail. Therefore, the surface cracks found in the steering shaft gear after carburizing and quenching are originated from the rolling cracks formed by non-metallic inclusions of steel. The rolling cracks have undergone further evolution in the subsequent forging and carburizing quenching process.

Constitutive Modelling of Temperature-Dependent Behaviour of Soft Rocks with Fractional-Order Flow Rule

This paper regards soft rock as a heavily overconsolidated clay and proposes a new fractional elastoplastic model to describe its temperature-dependent mechanical behaviour. Together with the critical state mechanics, the subloading surface concept is adopted to capture the irreversible plastic deformation developed inside the normal yield surface and provides a smooth transition between the elastic and plastic zones. In addition, the proposed model uses a fractional-order flow rule to account for the nonorthogonality between the plastic flow direction and the yield surface without introducing an extra plastic potential. The evolution law of the fractional-order is affected by the degree of overconsolidation and temperature. The proposed model is verified by the drained triaxial test data of Ohya rock under various confining pressures and temperatures with satisfactory performance. It can be found that an increase in the temperature will reduce the peak strength of soft rock and lead to a ductile failure pattern with a smaller tangent modulus.

Global transportation of plastics and microplastics: A critical review of pathways and influences

The rapid development of modern society has largely increased the usage of plastic. Concerns arise when vast amount of plastic waste has been generated and disposed. The accumulated evidences suggest that plastic waste in all the natural matrixes has become a global contaminant, principles such as geological and biogeochemical cycles for plastic pollution have been proposed. Before a full estimation of plastic mass flow, however, the pathways, directions and influences involved in plastic transportation are warranted to be addressed. We made this critical review based on the quantitative and narrative approaches in plastic and microplastic sources, sinks and transportation at global and historical scales. We also addressed the roles of anthropogenic influences in the global transportation of microplastic. The hydrological, meteorological, oceanic and even biological progresses naturally influence the plastic cycle and flow directions within the Earth's Four Spheres. Anthropogenic activities participated in all sections of plastic transportation, from sources to sinks. The contribution from anthropogenic activities remains unknown but several point sources including primary emissions and landfills have been confirmed. The primary outcomes point out that plastic pollution is highly complex issues in terms of natural and human-driven dynamics. We suggested that more efforts were needed in seeking the key sections in plastic transportation between environmental compartments at a global scale.

An anisotropic constitutive model for forming of aluminum tubes under both biaxial tension and pure shear stress states

In forming of complex thin-walled tubular parts, such as tube hydroforming with axial feeding, both biaxial tension and one axial tension & one axial compression (around the pure shear stress state) deformations are involved. The deformations under both biaxial tension and pure shear stress conditions cannot be accurately modeled and described with the symmetrical constitutive models based on the tensile properties. It is due to the fact that the anisotropic yielding and plastic flow behaviors of tubes are not well articulated over the entire range of stress states. To address this issue, an enhanced constitutive model was proposed based on the Yld2000–2d model (Barlat et al., 2003). The enhanced model improves the applicability of the Yld2000–2d by introducing an additional term, which can flexibly describe the change of the curvature of yield locus around the pure shear stress state. The yielding and plastic flow characteristics of the tubes under both biaxial tension and pure shear stress conditions can be well considered by the enhanced model and the model convexity can be strictly guaranteed. Moreover, the predictability of the proposed model for the deformation behaviors under these states was analyzed and compared with the quoted anisotropic constitutive models. The accuracy and efficiency were also verified and corroborated with the forming of AA6061-O tubes. It showed that the enhanced constitutive model can accurately predict the experimental yield loci and the plastic flow directions of the AA6061-O tube under both biaxial tension and pure shear stress deformations. The in-depth comparisons with the three benchmarked models and experiments were also conducted in terms of the predicted profile and wall thickness distribution of tube hydroforming, in such a way to further validate the enhanced model in terms of the efficiently and accurately modeling of the forming of complex tubes.

Model-based estimation of plastic debris accumulation in Banten Bay, Indonesia, using particle tracking - Flow model hydrodynamics approach

Coastal pollution caused by marine debris in Banten Bay is increasing and threatening the environmental and ecological sustainability of the bay's coastal area. This study aims to simulate the particle tracking of floating plastic debris within Banten Bay and to estimate the coastal debris accumulation for the period 2018 to 2028 based on numerical spatial modeling. To determine the dominant direction of plastic debris flow, we recorded floating plastic waste at four locations (Bojonegara port, Karangantu Estuary, Cibanten Estuary, and the Sunda Straits) by releasing wooden drifters. The numerical model was developed using a Particle Tracking module based on the Langevin equation. In comparison to data provided by the drifter survey, the particle tracking showed a similar distribution trace that tended to move westward during the northeast monsoon and eastward during the southwest monsoon. During the northeast monsoon, marine debris intake peaked, ranging from 2.25 kg to 5.75 kg. We estimated that over the ten years modeled plastic debris accumulation would increase by approximately 11%, to a maximum rate of 9.42 kg/day. Of particular concern, it is modeled that 41% of Banten Bay will be covered by plastic debris in 2028 if effective mitigations are not immediately applied. We recommend conducting a coastal cleanup operation every ten days so that coastal debris deposits can be well-controlled.