Viscoplastic Stress Research Articles

A semi-conservative depth-averaged material point method for fast flow-like landslides and mudflows

We present a two-dimensional semi-conservative variant of the depth-averaged material point method (DAMPM) for modeling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier–Stokes equations with the inclusion of an appropriate bed friction model and material rheology, namely Voellmy and the depth-integrated Bingham viscoplastic stress model, respectively. After assessing the accuracy and performance of the proposed numerical method by means of several idealized benchmarks, we test its behavior in a realistic scenario.

A finite element study on the effects of thickness and material nonlinearity on the equilibrium path of axially loaded circular cylindrical shells

Research has been carried out in recent years dealing with Lighter than Air Structures (LTAS), in which the innermost volume is taken to be a vacuum. Variations of a thin membrane over a frame were considered in order for such structures to have buoyancy potential while being capable of sustaining atmospheric pressures. The need for extremely thin membranes became evident as a result of the weight constraint The potential for the development of a viscoplastic stress field and instability led to the study of a classical problem: the instability of circular cylindrical shells under compressive loading. Thus, in order to obtain information related to the nonlinear geometric and material effects that can eventually be used in the LTAS, this study focused on what increasingly smaller membrane thicknesses and changes in the modulus can have on the equilibrium path of circular cylindrical shells. Considering shell thicknesses from 1E−3 to 1E−6m and using the Johnson-Cook constitutive relationship, results show that (1) the equilibrium path is highly dependent on shell thickness, and (2) inelastic strains drive path deviations and distinct post-collapse shapes. Furthermore, a reduction in the yield stress can result in plasticity before collapse, effectively changing the path of equilibrium and the post-collapse shape. Solutions were found using SIMULIA® Abaqus finite element (FE) software. At the present time these membrane thicknesses and material properties are not available. It is felt that, with the advancement of material science, they will become available in the immediate future.

Lithology-controlled stress variations of Longmaxi shale – Example of an appraisal wellbore in the Changning area

The Longmaxi shale is an extensive, prolific unconventional play in southwestern China. Its development in the Changning area is affected by ineffective hydraulic fracturing (HF) stimulation, fault reactivation and casing damage. It is suspected that the stress contrast within and between the shale reservoirs and the formations above and below matters to hydraulic fracture propagation and reservoir stimulation. To this end, the Longmaxi shale in the Changning area deserves a dedicated quantification of the in situ stress state and its variations. In this study, we re-visit the available data from one of the play’s first appraisal wellbores (X01) for an integrated geomechanics study, focusing on profiling the stress across the Longmaxi and its adjacent formations. Combining geophysical logs and other stress indicators, we re-interpret its stress profile in the context of lithological variations. The resulting stress variations are modeled primarily through a viscoplastic stress relaxation framework, compared with the results via the frictional equilibrium and an elastic theory (the Extended Eaton model). We offer some discussions on the differences and similarities of these stress profiling methods, and examine their applicability to Longmaxi shale in the Changning area. Our objective is to connect the lithology-controlled stress variations to the first-order complexities (HF ineffectiveness and fault reactivation) that have been observed in the area to date.

Double-diffusive natural convection of Casson fluids in an enclosure

This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra, yield number, Y, buoyancy ratio number, Nr, and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined.The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%.

Norton-Hoff model for deformation of growing solid shell of thin slab casting in funnel-shape mold

A funnel-type mold is commonly used to provide necessary clearance for the submerged entry nozzle in the thin slab casting (TSC). The partially solidified shell is subjected to the mechanical deformations, which can lead to the defects formation and, as a results, to a breakout. Traditionally, the results of the flow simulation, performed by the finite volume method (FVM), are fed to the external package for the finite element analysis of stress and strain. A coupled model was assembled using “creeping solid” approach by blending the Norton-Hoff viscoplastic stress for the solidifying shell with the Newtonian viscous stress of the liquid melt. The FVM was used to combine both liquid and solid stress models within a single solver. The iterative procedure based on the improved both side diffusion method was introduced to treat the nonlinear relation between the viscoplastic stress and the strain rate. The modeled shell thickness was verified by previously published breakout measurements and the simulation results. Temperature distribution, obtained during the TSC simulation, dominantly corresponds to the viscoplastic range. Developed numerical approach is robust and has direct industrial application.

Anisotropic microstructure and thixo-compression deformation behavior of extruded 7075 aluminum alloy in semi-solid state

In order to examine the micro-mechanism behind the thixotropic behavior of semi-solid alloys, microstructural effects on the compression deformation of semi-solid 7075 aluminum alloy prepared by recrystallization and partial melting (RAP) method were investigated. The fibrous and deformed microstructure of as-extruded 7075 aluminum alloy can transform into elongated and globular grains via reheating to semi-solid states, and exhibiting dominated {100}<001> recrystallization texture and preferred crystal growth in extrusion direction. The anisotropic microstructure of semi-solid alloys depends on the remelting temperatures to a great degree. Correspondingly, the initial peak stress of compression stress-strain curves also demonstrated as anisotropic behavior. It was analyzed that the crystallographic texture caused orientation dependent Young's modulus and a corresponding elastic response, and the disagglometation of the saturated solid skeleton led to an increase of viscoplastic stress, which relates to the amount of bonds between solid grains.

Modeling the motion of fuel particles in a fluidized bed

A semiempirical model for the mixing of fuel particles in a fluidized bed is presented and validated against experimental data from the literature regarding lateral fuel mixing. The model of fuel particle mixing categorizes the fluidized bed into three mixing zones: a rising bubble wake solid zone, an emulsion zone with sinking bulk solids, and a splash zone located above the dense bed. In the emulsion zone, the axial motion of the fuel particle is described by a force balance, applying a viscoplastic stress model, i.e., with a dominant yield stress and only a minor contribution of the shear stress, using an empirical expression from the literature. In the lateral direction, the model is divided into so-called ‘recirculation cells’, which are crucial for the lateral mixing.Comparisons of the modeled and measured lateral dispersion coefficients of different fuel types measured in three different large-scale fluidized bed units under both hot and cold conditions (covering a broad range of coefficients: 10−4–10−1 m2/s) reveal satisfactory agreement. The validated model was used to investigate how the lateral mixing of fuel particles depends on the excess gas velocity, the bed height, and the lateral distribution of bubbles over the bed cross-section (which is typically uneven in industrial FB furnaces), as well as the size and density of the fuel particles.

A case study of vertical hydraulic fracture growth, stress variations with depth and shear stimulation in the Niobrara Shale and Codell Sand, Denver-Julesburg Basin, Colorado

We have carried out a geomechanical study of three wells, one each in the Niobrara A, Niobrara C, and Codell Sandstone to investigate how the state of stress and stress variations with depth affect vertical hydraulic fracture growth and shear stimulation of preexisting fractures. We determine that the higher magnitudes of measured least principal stress values in the Niobrara A and C shales are the result of viscoplastic stress relaxation. Using a density log and a vertical transverse isotropy velocity model developed to accurately locate the microseismic events, we theoretically calculated a continuous profile of the magnitude of the least principal stress with depth. This stress profile explains the apparent vertical hydraulic fracture growth as inferred from the well-constrained depths of the associated microseismic events. Finally, we determine that because of the upward propagation of hydraulic fractures from the Niobrara C to the Niobrara A, the latter formation experienced considerably more shear stimulation, which may contribute to the greater production of oil and gas from that formation.

Finite Difference Modeling of the Interstand Evolutions of Profile and Residual Stress during Hot Strip Rolling

Elastic recovery and viscoplastic stress relaxation occur in the interstand of hot rolling, impacting the evolutions of strip profile and residual stress, which are major concerns for obtaining high-quality flat products. A better understanding of the evolutionary mechanisms would help develop shape control strategies. Therefore, a quasi-3D steady-state elasto-viscoplastic rolling model is developed based on the finite difference method. Predictions of spread, profile, and residual stress are validated through comparisons with a two-stand finite element model. The new model is also complemented with a roll stack model and with a viscoplastic constitutive model calibrated by hot compression tests to simulate a seven-stand hot rolling industrial experiment with low carbon steel. Comparisons between the predicted and measured profiles show a satisfactory accuracy. The simulation costs approximately a minute of CPU time, enabling the new model to run massive parametric campaigns for process optimization. It is found that during the interstand elastic recovery, the transverse compressive stress releases and the strip velocity tends to be uniform, revealing residual stress after a significant change of stress pattern. The stress relaxation mainly occurs at the edge near the roll bite and therefore increases the edge drop of the profile; it also decreases the center crown by changing the distribution of the rolling pressure in the roll bite.

Particle-scale numerical modeling of thermo-mechanical phenomena for additive manufacturing using the material point method

A fundamental numerical model at the powder particle scale based on the material point method (MPM) is developed for selective laser sintering (SLS). In order to describe the thermo-mechanical phenomena, a laser heat source model with a Gaussian energy distribution and the Perzyna viscoplastic model with a return mapping algorithm are employed. The principal process conditions, such as the laser power and radius, and the scanning speed are systematically varied. Based on the obtained temperature distribution generated by laser irradiation under these conditions, elastic–viscoplastic stresses were calculated to evaluate the deformation of powder particle pairs under the driving force of surface tension via a simple two-dimensional test case. The developed MPM model can capture minute changes of the deformation behavior and the temperature distribution history during melting and consolidation at the particle scale. Melting and consolidation of particle pairs during SLS are basic nature in determining the final product quality. The model can help to evaluate variations in the fusion of microscopic areas, melted by a laser, resulting from variations in the process conditions.

Predicting Lithology-Controlled Stress Variations in the Woodford Shale from Well Log Data via Viscoplastic Relaxation

Summary We report here a study of lithology-controlled stress variations observed in the Woodford shale (WDFD) in north-central Oklahoma. In a previous study, we showed that the magnitude of the minimum horizontal stress Shmin systematically varied with the abundance of clay plus kerogen in three distinct WDFD lithofacies. In this study, we demonstrate that it is possible to quantitatively estimate the observed stress variations using elastic properties determined from well logs as proxies for laboratory-inferred parameters via a relatively simple viscoplastic constitutive relationship. The modeled variations of Shmin along the two horizontal wells that encounter the three lithofacies along their respective well trajectory are in good agreement with measured values obtained from multistage hydraulic fracturing (HF). We believe that the application of the workflow described here in the context of viscoplastic stress relaxation can facilitate the understanding of layer-to-layer stress variations with lithology and thus contribute to improved HF effectiveness.

Integration of viscoplastic effects in a one-dimensional constitutive model for ground response analysis

During an earthquake, strain-rate effects affect both the stiffness and damping behaviour of soils, yet existing constitutive models for ground response analysis are typically formulated within a rate-independent framework. In this paper, a one-dimensional (1D) viscoplastic stress–strain model is presented to introduce strain rate effects in ground response analysis. Its constitutive equations are based on a model that uses a cubic spline fit of the modulus reduction curve and a coordinate transformation technique to match any input modulus reduction and damping curve. A viscous stress component is added to model the effect of strain rate on the mechanical behaviour of soils using a single input parameter. The model is able to reproduce the linear increase in shear strength with the logarithm of shear strain rate and allows the introduction of viscous effects in 1D ground response analysis with control over damping and modulus reduction behaviour. The model is implemented in a software for ground response analysis and used to predict the results of a centrifuge test modeling 1D wave propagation. The results show that the model accurately predicts the amplification and attenuation of shear waves, in a context where strain rates impact the response of the model significantly.

On modelling viscoplastic behavior of the solidifying shell in the funnel-type continuous casting mold

As it is known from literature, the metals tend to follow a viscoplastic law at high temperatures. Thereby, based on the authors’ previous developments to simulate the behavior of the equiaxed crystals packed bed, a viscoplastic stress model is applied to the thin slab casting process. The model is reduced to the single phase mixture formulation for faster and robust simulations. In this idea, the solidifying shell represents a ‘creeping solid’ and the Norton-Hoff type stress model is formulated with the model parameters obtained experimentally. A coupling procedure is established to converge the non-linear terms. The influence of the stress model parameters is investigated. Next the model is applied for the simulation of the thin slab casting to improve a previously developed technique: a viscoplastic rheology is applied to calculate the motion of the solidifying melt instead of imposing the velocities of the mush. The simulation results show that the most deformations happen at the funnel part of the mold, causing highest strain rates and the significant drop of the viscoplastic ‘apparent viscosity’ according to the Norton-Hoff law. The solid shell velocities are mostly uniform at the straight parts of the strand but a slight acceleration of the shell is observed along the funnel surface. Strong compression / expansion zones are detected at the funnel part, which could lead to defects formation. The solid shell thickness was successfully predicted as well and compared to the previous work by the authors.

Plasticity in vitreous silica induced by cyclic tension considering rate-dependence: Role of the network topology

In this paper, we investigate the visco-plastic stress response of vitreous silica under tension using molecular dynamics simulations. Firstly, we show significant rate-dependence by alternately subjecting vitreous silica to loading and relaxation. Using this strategy, we eliminate viscous effects, a quasi-static hysteresis is obtained and remaining plastic deformations are observed. We investigate the medium-range order at various deformation states on the quasi-static hysteresis. We demonstrate that, although, the short-range order does not noticeably differ at various deformation states on the quasi-static hysteresis, the medium-range order, evaluated through the ring statistics, shows significant changes. Based on the observation of similar trends regarding the ring statistics, three groups, i.e. small-, medium- and large-sized rings, are classified and their changes are linked to the plastic behavior. Furthermore, in order to link the medium range order to rate-dependence, changes in the ring statistics, caused through mechanical relaxation, are investigated and discussed.

Microseismic evidence for horizontal hydraulic fractures in the Marcellus Shale, southeastern West Virginia

An integrated analysis of multistage hydraulic fracture stimulation done in three horizontal wells in the Marcellus Shale in southeastern West Virginia revealed that nearly half (14 out of 31) of the examined stages initiated horizontal hydraulic fractures. The study was performed in an area characterized by a transitional strike-slip/reverse faulting stress state where the maximum horizontal principal stress (SHmax) is oriented N55°E. The stages that produced horizontal hydraulic fractures were all within the organic-rich Lower Marcellus Shale. Two lines of evidence indicate horizontal hydraulic fracture propagation. The measured least principal stress of those stages was of similar magnitude to the vertical stress (SV), indicating that the vertical stress and microseismic events are limited to a narrow horizontal layer and do not propagate vertically out of the Lower Marcellus Shale. Both lines of argument indicate that the vertical stress is the least principal stress, perhaps due to viscoplastic stress relaxation in the clay- and kerogen-rich Lower Marcellus Shale. In the 17 stages where perforations were placed in the stiffer Onondaga and Cherry Valley formations, the measured least principal stresses were less than the magnitude of SV, indicating that Shmin was the least principal stress. The microseismic data indicate vertical hydraulic fracture propagation, principally upward outside the Marcellus Shale. Significant gas was produced from the two wells with horizontal fractures in the organic-rich Lower Marcellus Shale, perhaps because twice as much proppant was used as in stages characterized by vertical fracture propagation.

Analytical approach of asymmetrical thermomechanical rolling by slab method

In this paper, based on the slab method and focusing on the rate-dependent flow condition, asymmetrical thermomechanical rolling (ATMR) is investigated to establish a new model for calculation of the rolling force. Unlike the former models where the rate-dependent condition of the yield shear stress has not been considered, in this study, a visco-plastic flow stress formulation of material is used for applying the rate and temperature sensitivity parameters and kinetic of work hardening and softening of the material. Comparison of the present analytical model with experimental data and other models reveals the precision of calculation. An asymmetrical rolling index (ARI) is introduced to evaluate the effects of rolling parameters on asymmetrical conditions of the rolling process. Using the response surface methodology (RSM), the interaction effects and contribution of rolling parameters are studied. Investigations indicate that the speed rate plays a role as an intensifier of the parameters’ effect on the ARI. Furthermore, the occurrence of high value of speed rate with a low percent of thickness reduction leads to the restricted rise of the ARI levels. The verification of the statistical models indicates an acceptable competency of results.

Three-Dimensional Problems of Thermoviscoplasticity: Focus on Ukrainian Research (Review)

Methods and results of studying the three-dimensional viscoplastic stress–strain state of engineering structures under thermomechanical loading are presented. The following classes of thermoviscoelastic problems are considered: axisymmetric problems, nonaxisymmetric problems for bodies of revolution, three-dimensional problems for arbitrarily shaped bodies, three-dimensional problems for isotropic and anisotropic bodies of revolution

Viscoplastic Deformation of the Bakken and Adjacent Formations and Its Relation to Hydraulic Fracture Growth

We report laboratory studies of the time-dependent deformation of core samples from four different formations in the Williston Basin—the Lodgepole Formation, the Middle and Lower Bakken Formations, and Three Forks Formation. The laboratory tests reveal varying amounts of viscoplastic deformation in response to applied differential stress. The time-dependent deformation is generally greater in rocks with higher clay and organic content and can be described by a power-law function. Because the magnitude of the creep strain is linearly proportional to the applied differential stress, we can utilize viscoelastic theory and geophysical logs to estimate the degree to which tectonic stress is affected by viscoplastic stress relaxation. We suggest that viscoplastic stress relaxation results in the Upper and Lower Bakken Formations acting as frac barriers during hydraulic fracture stimulation in the Middle Bakken, but the Lodgepole and the Three Forks Formations are not frac barriers.

Development and Validation of a Uniaxial Nonlinear Viscoelastic Viscoplastic Stress Model for a Fuel Cell Membrane

Proton exchange membranes (PEMs) in operating fuel cells are subjected to varying thermal and hygral loads while under mechanical constraint imposed within the compressed stack. Swelling during hygrothermal cycles can result in residual in-plane tensile stresses in the membrane and lead to mechanical degradation or failure through thinning or pinhole development. Numerical models can predict the stresses resulting from applied loads based on material characteristics, thus aiding in the development of more durable membrane materials. In this work, a nonlinear viscoelastic stress model based on the Schapery constitutive formulation is used with a viscoplastic term to describe the response of a novel membrane material comprised of a blend of perfluorocyclobutane (PFCB) ionomer and poly(vinylidene fluoride) (PVDF). Uniaxial creep and recovery experiments characterize the time-dependent linear viscoelastic compliance and the fitting parameters for the nonlinear viscoelastic viscoplastic model. The stress model is implemented in a commercial finite element code, abaqus®, to predict the response of a membrane subjected to mechanical loads. The stress model is validated by comparing model predictions to the experimental responses of membranes subjected to multiple-step creep, stress relaxation, and force ramp loads in uniaxial tension.

Fatigue crack initiation, slip localization and twin boundaries in a nickel-based superalloy

The study of fatigue in metals, and fatigue initiation specifically, lends itself to analysis via an emerging set of characterization and modeling tools that describe polycrystals on the meso- or microstructural length scale. These include three-dimensional characterization techniques, elastic anisotropic and visco-plastic stress models, new approaches to the statistical description of stress and strain distributions, synthetic microstructure modeling, and improved tools for manipulating the large datasets generated. A specific example of analysis in both 2D and 3D of fatigue cracks in a nickel-based superalloy is given where all the cracks are effectively coincident with coherent twin boundaries. A spectral method is used to analyze the stress state based on a fully anisotropic elastic calculation. The results indicate that, although a high resolved shear stress is associated with the locations of the observed cracks, the length of the trace of the twin boundary is more strongly correlated with crack formation.