Analysis of the energy and damage evolution rule for sandstone based on the particle flow method

We use the particle flow code PFC3D to simulate the triaxial compression of sandstone under various radial stresses and loading strain rates to determine the triaxial stress-strain curves, crack propagation path, and contact forces to investigate the failure process of sandstone. We analyze the energy and damage evolution during triaxial compression. The results indicate that the tension and shear-induced cracks increase with the increase of radial stress under the same loading strain rate. Both normal and tangential contact forces exhibit strong anisotropy and increase with radial stress and strain rate. The normal contact force has an approximately symmetrical distribution with respect to the horizontal plane, whereas the tangential contact force has an approximately symmetrical distribution with respect to the axis. For the characteristics of the energy evolution, the boundary energy density, strain energy density, and dissipated energy density all increase linearly with the radial stress, and the boundary energy density increases at the fastest rate, followed by the strain energy density and dissipated energy density. In the post-peak stage the primary energy consumption is the dissipated energy. After that, in the remaining stage the strain energy decreases gradually. By analyzing the evolution of the damage variables in the prepeak area we observed that the damage variable followed an exponential relationship with the axial strain. When the loading strain rate is constant, the damage variable corresponding to the same strain value decreases with increase of radial stress. The results indicate that the increase in radial stress delays the damage acceleration. In contrast, the effect of the loading strain rate on the damage variable is small. The findings reveal the internal structural evolution of rocks during deformation and failure.

     

Strong force networks in granular mixtures

Using the results of 3D discrete element method simulations we study the force transmission through binary mixtures of sand and silt sized spheres under one-dimensional compression. Three types of contact are categorized depending on the size of the two spheres in contact. The contributions of each contact type to the deviator stress are dependent on the proportion of silt sized spheres. We demonstrate that the magnitude of the deviator stress is solely due to the normal and tangential forces at contacts transmitting normal forces greater than a characteristic normal force, which is generally slightly greater than the average normal force. The maximum packing efficiency was obtained with the mixture of 30 % silt sized spheres and this mixture corresponds to a transition point when there are enough silt sized particles to start to separate the sand sized particles from each other and establish contacts between silt sized spheres that contribute to the deviator stress.     

Statistical properties of a 2D granular material subjected to cyclic shear

This work focuses on the evolution of structure and stress for an experimental system of 2D photoelastic particles that is subjected to multiple cycles of pure shear. Throughout this process, we determine the contact network and the contact forces using particle tracking and photoelastic techniques. These data yield the fabric and stress tensors and the distributions of contact forces in the normal and tangential directions. We then find that there is, to a reasonable approximation, a functional relation between the system pressure, P, and the mean contact number, Z. This relationship applies to the shear stress τ, except for the strains in the immediate vicinity of the contact network reversal. By contrast, quantities such as P, τ and Z are strongly hysteretic functions of the strain, ε. We find that the distributions of normal and tangential forces, when expressed in terms of the appropriate means, are essentially independent of strain. We close by analyzing a subset of shear data in terms of strong and weak force networks.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

树盘干缩异向性引起应变的测算及分析

研究探讨了干燥过程中树盘受抑制干缩应变、自由干缩应变、弹性应变、黏弹性蠕变应变以及机械吸附蠕变的图像解析测算法;运用该方法测算了白桦树盘常规缓慢干燥(含水率分布均匀)过程中干缩异向性引起的弦向各应变,分析了干燥过程中不同含水率阶段的应力状态及应力与各应变的关系。结果表明:应变的图像解析测算法可满足精度要求;树盘干燥至fiber saturation point(FSP)以下,弦向首先受拉伸应力作用,随着干燥的进行,拉伸应力转变为压缩应力;应力方向与各应变对应关系不同,与黏弹性蠕变应变无明显对应关系,与机械吸附蠕变基本对应。     

Effect of alternating stress on the creep of frozen soils

Cyclic creep behaviour of a frozen saturated sand and frozen clay was studied by superimposing alternating stresses over a mean static compressive stress on the samples. Cyclic loading increased the creep rate of these materials considerably, which could be due to the increase in unfrozen water content generated by the transient thermal energy produced by mechanical cycling. The strain increment per cycle was found to increase with increasing strain in the frozen sand; whereas it decreased in the frozen clay, showing a tendency for hardening. The difference could be due to the fact that the mean stress on the sample was larger than a threshold stress in the former and smaller in the latter material.     

Discrete element modelling and simulation of sand mould manufacture for the lost foam process

This paper presents a numerical model of mould manufacture for the lost foam casting process. The process of mould filling with sand and sand compaction by vibration are modelled using spherical (in 3D) or cylindrical (in 2D) discrete elements. The motion of discrete elements is described by means of equations of rigid body dynamics. Rigid particles interact among one another with contact forces, both in normal and tangential directions. Numerical simulation predicts defects of the mould due to insufficient sand compaction around the pattern. Combining the discrete element model of sand with the finite element model of the pattern allows us to detect possible distortion of the pattern during mould filling and compaction. Results of numerical simulation are validated by comparison with experimental data. Copyright © 2004 John Wiley & Sons, Ltd.     

Suitable rolling resistance model for quasi-static shear tests of non-spherical particles via discrete element method

Rolling resistance is a main consideration in quasi-static shear test simulations of particles via the discrete element method. However, not all rolling resistance models can satisfy the required objectivity and rate independence. A suitable model for spherical particles has been selected from five models in our previous works. In the current study, this model is combined with four normal and tangential contact models to confirm its applicability. After confirmation, the model is generalized to simulate direct shear tests on non-spherical particles. The stress–strain and dilatancy curves are rate-independent, and the relative rolling velocity between particles is objective. Furthermore, objectivity and rate independence for arbitrarily shaped particles are unchanged when normal stresses, volume fractions, or normal and tangential contact models are changed. Simulation results are also consistent with other experiment findings. For comparison, results are calculated for two other rolling resistance models; the shear curve at a single speed is consistent with the experiment, which has three stages: elastoplastic increasing, yielding, and keeping. However, the stress–strain curves at different shear rates do not coincide, which means that the models conflict with the rate independence of quasi-static granular systems. The virtues and defects of the five rolling resistance models are discussed from the perspectives of objectivity and rate independence. These two properties provide criteria for determining the appropriateness of a model, which has been rarely discussed in former studies.     

Analysis of the sealing performance and creep behavior of the inner casing of a 1000 MW supercritical steam turbine under bolt relaxation

The creep behavior and sealing performance of the inner casing of a 1000 MW supercritical steam turbine were investigated during 200,000 h of steady operation at high temperatures. The influence of the stress relaxation of bolts on creep behavior and sealing performance was specifically demonstrated. A constitutive creep model based on continuum damage mechanics and a multiaxial creep strain formula was used to describe the stress–strain behavior and calculate the multiaxial strain. Due to significant bolt relaxation in the high-temperature region, stress in the steam inlet region decreased dramatically; likewise, multiaxial creep strain decreased markedly in this region. Contact pressure significantly decreased during the first 10,000 h, especially in the regions between bolts 1 and 9, and the largest decrease in contact pressure exceeded 340 MPa. This reduced sealing performance at high temperatures. Further comparison of the contact pressure and the opening displacement at the contact surface was carried out with and without bolt relaxation. The massive difference of 153 MPa between these two cases in the primary creep phase demonstrated that bolt relaxation significantly influences sealing performance.     

Fatigue behavior of ferritic–pearlitic–bainitic steel in loading with positive mean stress

The effect of positive mean stress on the fatigue behavior of ferritic–pearlitic–bainitic steel has been studied. Specimens, produced from a massive forging, were cycled with two constant stress amplitudes and various positive mean stresses. Plastic strain amplitude and cyclic creep rate were measured during cyclic loading and the effect of the mean stress on saturated plastic strain amplitude and mean strain at half-life was established. Plastic strain amplitude is weakly dependent but creep strain increases with the mean stress exponentially. Fatigue life decreases with the mean stress for both stress amplitudes. The contributions of cyclic plastic strain and cyclic creep to the fatigue damage were evaluated and discussed in relation with the Manson-Coffin curve.     

Meniscus and viscous forces during separation of hydrophilic and hydrophobic surfaces with liquid-mediated contacts

Adhesion due to the formation of meniscus bridges has been of interest since the early 20th century. Extensive studies have been carried out analytically and numerically. Adhesive or repulsive forces contributed by meniscus and adhesive viscous forces can be significant and become one of the main reliability issues when the contacting surfaces are smooth and/or when the normal load is small, as is common for micro/nanodevices. Previous numerical studies mainly focus on static meniscus analysis for hydrophilic surfaces. More recently, analysis of meniscus and viscous forces during separation of both hydrophilic and hydrophobic surfaces with symmetric and asymmetric contact angles have been carried out. These studies are useful to understand the relative roles of meniscus and viscous forces during the separation process. In this paper, a comprehensive review of analytical and numerical modeling of the meniscus and viscous forces are presented. The analyses for both forces during normal and tangential separation of hydrophilic and hydrophobic smooth or rough surfaces with symmetric and asymmetric contact angles, and viscous forces during tangential separation are presented. The analyses provide a fundamental understanding of the physics of the separation process and insight into the relationships between meniscus and viscous forces. Implications of these analyses in macro/micro/nanotechnologies are discussed.     

POST-BUCKLING ANALYSIS WITH FRICTIONAL CONTACTS COMBINING COMPLEMENTARITY RELATIONS AND AN ARC-LENGTH METHOD

A linear complementarity problem formulation combined with an arc-length method is presented for post-buckling analysis of geometrically non-linear structures with frictional contact constraints. The arc-length method with updated normal plane constraint is used to trace the equilibrium paths of the structures after limit points. Under the proportional loading assumption, the unknown load scale parameter used in the arc-length method is expressed in terms of contact forces, and eliminated to formulate as a linear complementarity problem. The unknown contact variables such as contact status and contact forces can be directly solved in this formulation without any ad hoc technique. Complicated non-linear buckling behaviours, such as snap-buckling, can be efficiently solved by the developed method, as shown by several buckling and post-buckling problems with frictional contact constraints.     

Dynamic buckling of elastic–plastic square tubes under axial impact—II: structural response

Dynamic elastic–plastic buckling of thin-walled square tubes is studied from the viewpoint of elastic–plastic stress wave propagation, which originates from an axial impact loading. The influence of the impact velocity and the striking mass on the development of the buckling shape is discussed when considering the transient deformation process. It is shown that the maximum load, which results from a high velocity impact load and occurs at t=0, is a function of the impact velocity and is related to the speed of the elastic–plastic stress waves propagating along the tube. The predictions for the initiation of buckling based on a numerical simulation of the axial impact of strain rate insensitive square tubes using the FE code ABAQUS show good agreement with the results from experiments on aluminium alloy tubes impacted at various initial velocities. A comparison between the buckling initiation in square tubes and geometrically equivalent circular tubes reveals differences in the response, which are attributed to the stress wave propagation phenomena and to the structural differences between the two structures.     

Creep Behavior of High‐Nb TiAl Alloy at 800–900 °C by Directional Solidification

Cold crucible directional solidification Ti44Al6Nb1.0Cr alloy is crept at 800–900 °C. Experimental results show that creep lifetime significantly decreases with the increasing creep temperature. When creeping at 900 °C under 130 MPa, the T_Q twinning is activated in lamellar structures. The T_Q twinning shows a strong dependency on temperature during creep under low creep‐stress and it can overcome α₂ lamellae and transfer into adjacent γ lamellae. The hardening by mechanical twinning and the softening by α₂ lamellar dissolution take place at different zones in lamellar structures and the strain incompatibility between hardening zone and softening zone promotes the microcracks to form in lamellar structures. The deformation characteristic of hard and soft lamellae is studied. Moreover, recrystallization γ phase formed in lamellar structures near colony boundary during creep at 900 °C accelerates the creep failure.

     

Discrete element simulation of dynamic behaviour of partially saturated sand

The discrete element method (DEM) together with the finite element method (FEM) in LS-DYNA was employed to investigate the dynamic behaviour of sand under impact loading. In this approach, the partially saturated sand was modelled in DEM with capillary forces being taken into account through an implicit capillary contact model, while other solids were simulated using FEM. A slump test was first performed with dry sand to calibrate the contact parameters in DEM. Low velocity impact tests were then conducted to investigate the effect of water saturation on the shape and height of sand piles after impact, and to validate the simulations. It was found in the experiments that an increasing water saturation (in the range between 10 and 30 %) affected the height of sand pile for a given drop height due to an increasing cohesion between particles. The simulations captured the experimental ejecta patterns and sand pile height. Finally, a low confinement split Hopkinson pressure bar test from earlier literature was modelled; the DEM–FEM simulations could reproduce the trends of experimentally observed stress–strain curves of partially saturated sand under high strain rate loading, indicating that it was feasible to model dynamic behaviour of dry and wet sand with low saturation (<20 %) in LS-DYNA; however, a number of questions remain open about the effect of grain shape, grain crushing and viscosity.     

Nanoindentation creep deformation behaviour of high nitrogen nickel-free austenitic stainless steel

Nanoindentation tests of the high nitrogen nickel-free austenitic stainless steel (HNS) were performed with peak load in a wide range of 100–600?mN to investigate the nanoindentation creep deformation behaviours. The results of the nanoindentation creep tests have demonstrated that the load plateaus, creep strain rate and creep stress of the cold-rolled HNS are larger and its creep stress exponent is smaller than the solution-treated HNS. The analysis reveals that the obvious creep deformation behaviour in the cold-rolled HNS arises from the rapidly relaxed dislocation structures in the initial transition regime, while the small creep deformation behaviour of the solution-treatedHNS is mainly attributed to that the stable dislocation structures for the intensive interactions between dislocations.     

DEM investigation on the evolution of microstructure in granular soils under shearing

The mechanical behaviors of granular soils at different initial densities and confining pressures in the drained and undrained triaxial tests are investigated micromechanically by three-dimensional discrete element method (DEM). The evolutions of the microstructure in the numerical specimen, including coordination number, contact force and anisotropies of contact normal and contact force, are monitored during the shearing. The typical shear behaviors of granular soils (e.g. strain softening, phase transformation, static liquefaction and critical state behavior) are successfully captured in the DEM simulation. It is found that the anisotropies of contact normal, normal and tangential contact forces comprise the shear resistance and show different evolution features during shearing. After large strain shearing, the microstructure of the soil will finally reach a critical state, although the evolution path depends on the soil density and loading mode. Similar to the macroscopic void ratio $e$ and deviatoric stress $q$ , the coordination number and anisotropies of contact normal and contact force at the critical state also depend on the mean normal effective stress $P^{\prime }$ at the critical state.     

Investigation of the fabric evolution and the stress-transmission behaviour of sands based on X-ray μCT images

This paper presents the use of X-ray micro-tomography (X-ray $\mu$CT) and image processing and analysis techniques to investigate the stress transmission and buckling of inter-particle contacts within a granular material. A triaxial testing of a miniature Leighton Buzzard sand (LBS) sample was carried out with full-field in-situ X-ray $\mu$CT scanning. High-spatial-resolution CT images of the sample were acquired at several loading stages of the test. Image processing and analysis techniques were used to quantify the inter-particle contact evolution (contact gain, contact loss and contact movement), fabric, contact duration and buckling of stress-transmission contacts based on the CT images. The results indicated that contact gain and loss, and contact movement played two competing roles in determining the overall fabric evolution of the sample. Contacts with a longer duration were more likely to orient in the major principal stress direction and form a stress-transmission contact network. A gradual decrease in the buckling rate of the stress-transmission contacts was observed outside of the shear band, and a relatively stable buckling rate was observed within the shear band during the shear. The results suggested that jamming occurred outside of the shear band and that unjamming occurred within the shear band.     

FEM simulation of viscous properties for granular materials considering the loading rate effect

The deformation and strength characteristics of sandy soils as a kind of granular materials are very complex. The experimental results show that when the strain rate suddenly changes in monotonic loading (ML) case, the stress–strain curve of sandy soils changes sharply and then gradually converges into the original inferred one that would be obtained by continuous ML at constant strain rate after having exhibited clear yielding. Similar behaviors are also observed when ML is restarted at a constant strain rate following a creep loading or stress relaxation stage. An elasto-viscoplastic constitutive model for granular materials is developed, which consists of three components. One of the most important features of the model is that it can take into account the effects of loading rate due to viscous properties on the stress–strain behavior. The stress ratio-axial strain–time relations from four drained plain strain compression (PSC) tests on the saturated Toyoura sand are successfully simulated by the finite element method (FEM) code incorporating the proposed constitutive model. It is shown that the FEM code can simulate the viscous behaviors of sand accurately under arbitrary loading history.