DEM analysis of the size effects on the behavior of crushable granular materials

Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.     

Cohesive zone simulation of grain size and misorientation effects on hydrogen embrittlement in nickel

The size and misorientation effects on hydrogen embrittlement of a four grain nickel aggregate are studied with the help of hydrogen informed cohesive zone model. The grain misorientation angle is parameterized by fixing the lower grains while rotating the upper grains about the out-of-plane axis. Brittle failure of the grain aggregate is observed and nominal strength obtained. In the crack-free situation, the grain misorientation exerts an obvious weakening effect on the nominal strength, which is most pronounced at misorientation angles around 20°. Such trend applies to the pre-cracked situation but is much less pronounced. Both misorientation and pre-crack lead to size effect. The nominal strength shows a decreasing trend with the grain size, indicating that grain refinement tends to improve the load bearing capacity, which coincides with the observation in practice. Further, it is shown that the size effect diagram without hydrogen can be divided into three regimes. The conclusions apply to the case with hydrogen, except that the trend of the size effect curve can be affected by large grain sizes due to the longer absolute distance of hydrogen diffusion. These results provide guidelines for grain boundary engineering and for nanomechanical tests aiming at calibrating the intergranular decohesion parameters.     

晶粒尺寸对304奥氏体不锈钢组织演变和性能的影响

研究了初始织构相近而晶粒尺寸不同的304奥氏体不锈钢在后续10%压缩变形和热处理过程中微观组织、力学和耐蚀性的变化。结果表明,具有相似织构而晶粒尺寸不同的样品变形热处理后其织构不同,粗晶在变形中织构的变化更大;织构相近时抗拉强度对晶粒尺寸的依赖较大;织构不同时,织构对硬度和抗拉强度的影响大于晶粒尺寸和微应变的影响;变形热处理后普通大角度晶界和晶内微应变的增大降低了试样的耐腐蚀性能;初始晶粒尺寸较小的试样在变形热处理后出现四种密排面平行于外表面的织构,其耐点蚀的性能更优。     

Micromechanical modeling of intrinsic and specimen size effects in microforming

Size effect is a crucial phenomenon in the microforming processes of metallic alloys involving only limited amount of grains. At this scale intrinsic size effect arises due to the size of the grains and the specimen/statistical size effect occurs due to the number of grains where the properties of individual grains become decisive on the mechanical behavior of the material. This paper deals with the micromechanical modeling of the size dependent plastic response of polycrystalline metallic materials at micron scale through a strain gradient crystal plasticity framework. The model is implemented into a Finite Element software as a coupled implicit user element subroutine where the plastic slip and displacement fields are taken as global variables. Uniaxial tensile tests are conducted for microstructures having different number of grains with random orientations in plane strain setting. The influence of the grain size and number on both local and macroscopic behavior of the material is investigated. The attention is focussed on the effect of the grain boundary conditions, deformation rate and the grain size on the mechanical behavior of micron sized specimens. The model is intrinsically capable of capturing both experimentally observed phenomena thanks to the incorporated internal length scale and the crystallographic orientation definition of each grain.     

A two-site mean field model of discontinuous dynamic recrystallization

The paper describes a new model of discontinuous dynamic recrystallization (DDRX) which can operate in constant or variable thermomechanical conditions. The model considers the elementary physical phenomena at the grain scale such as strain hardening, recovery, grain boundary migration, and nucleation. The microstructure is represented through a set of representative grains defined by their size and dislocation density. It is linked to a constitutive law giving access to the polycrystal flow stress. Interaction between representative grains and the surrounding material is idealized using a two-site approach whereby two homogeneous equivalent media with different dislocation densities are considered. Topological information is incorporated into the model by prescribing the relative weight of these two equivalent media as a function of their volume fractions. This procedure allows accounting for the well-known necklace structures. The model is applied to the prediction of DDRX in 304 L stainless steel, with parameters identified using an inverse methodology based on a genetic algorithm. Results show good agreement with experimental data at different temperatures and strain rates, predicting recrystallization kinetics, recrystallized grain size and stress-strain curve. Parameters identified with one initial grain size lead to accurate results for another initial grain size without introducing any additional parameter.     

Prediction of grain growth of coarse-grained austenite in Nb–V–Ti microalloyed steel

Abstract

Grain growth of coarse-grained austenite in Nb–V–Ti microalloyed steel during equalisation was predicted by extending the previous investigation. The prediction worked with initial austenite grain size distribution instead of average grain size. An improved model taking into account the holding time was used in the prediction. The result showed that only part of initial austenite grains grow at each equalisation temperatures, but the grain size of growing grains is expanded to a wider range with increasing equalisation temperature, which indicates that grain size distribution should be considered when grain growth of coarse-grained austenite is evaluated. The predicted austenite grain size distribution is close fit to the measured one and further work is expected to improve the quality of model prediction.     

Grain growth modelling: 3D and 2D correlation

One of the significant challenges in the modelling of grain growth is the link between 3D models and their 2D simplifications.

In the present study a 3D model of grain growth has been investigated which takes into account change in volume of individual grains randomly sampled from a population of a given initial size distribution. For different kinetics of growth, changes in the size of grain sections are studied. The fictitious effect of the generation of new grains in a 2D approximation of 3D growth (due to the growing grains hitting the observation plane) has been studied in detail. The influence of different types of initial grain size distributions on the grain growth has been investigated.     

Density of grain boundaries and plasticity size effects: A discrete dislocation dynamics study

Discrete dislocation dynamics simulations are carried out to systematically investigate the microstructural and geometrical size dependence of films under tension that have a varying number of grains through their thickness. By varying film thickness, grain size and aspect ratio, more insight is gained into the competition between grain boundary hardening and film thickness effects. This provides a seamless link between previous dislocation plasticity studies and qualitative agreement with experimental data. In the simulations, plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. Grain boundaries are treated as impenetrable to dislocation motion. The numerical results show that the grain size dependence of yield in thin films as well as in bulk polycrystals is controlled by the density of grain boundaries.     

Climbing motion of grains in vibrating tubes with different geometries

By inserting a vibrating tube into a static grain layer, the grains can climb along the tube, which presents a new way to convey grains continuously. In this study, both tubes with different sizes and cross-section shapes are used to probe the effect of geometry on climbing motion of grains. Under same vibration strength, grains in small diameter tube can climb directly into an equilibrium height. The grains in large diameter tube can’t climb directly. However, if enough grains are initially filled in the tube to a certain height, the grains can climb much higher. The grain climbing is more sensitive to the tube size rather than shape of tube cross-section. With same tube diameter, the climbing motion becomes difficult with increase of grain diameter. Consistent with the experimental results, a model based on force analysis is presented.     

Phase field simulation of abnormal grain growth mediated by initial particle size distribution

The uniform initial particle size distribution was considered to be an important condition for the preparation of dense ceramics. With the rapid development of templated grain growth method, it is necessary to add large template particles into small matrix to promote the epitaxial growth of grains. However, abnormal grain growth will inevitably occur in this process. In this work, a phase field method was employed to study the growth behavior of the large grains into the small matrix. The effect of initial particle size distribution on the grain growth kinetics was investigated. Our simulations revealed that the growth rate of large grains slowed down as the initial grain size distribution widened. Regulating the initial grain size distribution will be an effective way to control abnormal growth of grain. It was found that the growth rate of a large grain was proportional to the number of surrounding grains. These results have implications for the design of the functional ceramics with a target grain microstructure.     

Microstructure and strength of pure Cu with large grains processed by equal channel angular pressing

The pure Cu rods with an initial grain size of 410 μm were treated by using equal channel angular pressing (ECAP). The deformed microstructure and mechanical properties of ECAPed Cu samples were investigated. Special attention was paid on the refinement of grain size and local micromechanics of ECAPed Cu samples. The original coarse grains were refined to 320 μm after 4 passes. The final grains were composed of dislocation cells with a size of 500 nm–3 μm after 5–8 passes. The yield strength reached a saturation value of 368 MPa after 5 passes. The maps of microhardness distribution illustrated the inhomogeneity of local mechanical properties. The dislocation subdivision was the main deformation mode to refine the grain size, while twin fragmentation was restrained by dislocation slips for the reason of large initial grain size. Furthermore, the strengthening of ECAPed Cu was discussed.     

Polycrystal models for the analysis of intergranular crack growth in metallic materials

In polycrystal materials the intergranular decohesion is one important damage phenomena that leads to microcrack initiation. The paper presents a mesoscale model, which is focused on the brittle intergranular damage process in metallic polycrystals. The model reproduces the crack initiation and propagation along cohesive grain boundaries between brittle grains. An advanced Voronoi algorithm is applied to generate polycrystal material structures based on arbitrary distribution functions of grain size. Therewith, the authors are more flexible to represent realistic grain size distributions. The polycrystal model is applied to analyze the crack initiation and propagation in statically loaded samples of aluminium on the mesoscale without the necessity of initial damage definition.     

初始晶粒尺寸对高温交叉轧制镁合金板材组织和力学性能的影响

目的 揭示晶粒尺寸对多道次高温交叉轧制AZ31镁合金板材组织和力学性能的影响规律及机制.方法 通过对不同初始晶粒尺寸的镁合金板材进行高温交叉轧制变形及热处理,获得不同状态的镁合金板材,采用金相显微分析、X射线衍射(XRD)分析及室温拉伸实验等手段研究镁合金板材的晶粒组织(形态、尺寸、取向)及力学性能.结果 经过多道次交...     

热工艺对激光选区熔化Hastelloy X合金组织及拉伸性能的影响

采用激光选区熔化技术制备Hastelloy X试样,研究热等静压和固溶处理对Hastelloy X试样显微组织及拉伸性能的影响。结果表明:沉积态组织中可观察到熔池形貌、柱状晶及晶内的胞晶结构,无析出物,其拉伸性能表现出高强度低塑性特点,高温拉伸断口沿激光扫描熔化道断裂。经热等静压后,组织演变为等轴晶,晶界及晶内存在较多的析出物,裂纹愈合,试样拉伸强度降低,塑性提升,尤其是高温屈服强度降低了约48%,高温伸长率提升了约59%。经热等静压+固溶处理后,晶粒尺寸及形貌与热等静压态相比近乎无差异,但晶内析出物明显减少,该状态下的综合拉伸性能最优。     

Developing Ultrafine Grain Sizes Using Severe Plastic Deformation

Severe plastic deformation may be used as a processing tool to achieve a refinement in grain size in metallic alloys to the submicrometer or nanometer range. This paper describes recent developments using the procedure of equal‐channel angular pressing (ECAP) in which samples are pressed through a die containing a channel bent into an L‐shaped configuration. The shearing associated with passage through the die introduces bands of subgrains which evolve, with additional pressings, into arrays of grains separated by boundaries having high angles of misorientation. The process of ECAP is a useful tool for both increasing the strength and toughness of an alloy at ambient temperatures and achieving a potential for superplastic forming of the alloy at rapid strain rates at elevated temperatures.     

Influence of size effect on the springback of sheet metal foils in micro-bending

To analyze the unloading springback of sheet metal foils after micro-bending process, a constitutive model is proposed based on the surface layer model by which the sheet foil is divided into surface layer and inner portions. For the inner portion, each grain is envisaged as a composite, comprised of grain interior and grain boundary work-hardened layer. The classical composite model is then used to calculate its flow stress. For the surface layer portion, a model without grain boundary strengthening is constructed to represent the flow stress in this zone. The developed method is verified through the comparison of the calculated strain–stress curves with the tensile test results of four kinds of pure copper sheet foils with different thicknesses ranging from 0.1 mm to 0.6 mm. To investigate the effect of thickness and grain size on the springback of pure copper sheet foils, three-point bending tests are carried out. A finite element (FE) model for predicting the springback in micro-bending process is further developed, which takes into account the deformation behavior and orientation of each grain. The influences of grain size and thickness on the springback of sheet foils are investigated. The research results show that the decrease of sheet foil thickness or the increase of grain size results in a big springback. The scatter of springback angle is mainly attributed to the elastic anisotropy of surface grains and increases with the reduction of grains along the thickness direction. A good agreement between the experimental results and the analytical calculations shows that the developed FE model can predict the springback of sheet metal foils well in micro-bending process.     

制备工艺对n型Bi_2Te_3基材料热电性能和抗压强度的影响

以商用区熔(ZM)n型Bi2Te3基材料为原料,采用简单研磨结合放电等离子烧结技术(ZM+SPS)和熔体旋甩(MS)结合放电等离子烧结技术(MS+SPS)制备了n型Bi2Te3基块体热电材料.对三种不同工艺制备出样品的微结构、热电性能和力学性能进行了研究.FESEM微结构表征结果表明:区熔样品的晶粒粗大,有较强的取向性;经SPS烧结后,晶粒细化,取向性大为降低;而区熔样品经MS+SPS后,晶粒得到进一步细化,且没有明显的取向性.对三组样品进行的热电性能和抗压强度测试,结果表明:区熔原料最大ZT值为0.72(430K),抗压强度仅为40MPa;经SPS后,样品的最大ZT值为0.68(440K),抗压强度为110MPa,相比区熔样品提高了175%;MS+SPS样品的最大ZT值为0.96(320K),其室温ZT值相比区熔样品提高了64%,抗压强度相比区熔样品提高了400%,达到200MPa.     

Breakage of an artificial crushable material under loading

The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.     

Grain refinement and mechanical behavior of a magnesium alloy processed by ECAP

Equal-channel angular pressing (ECAP) is an effective tool for refining the grain structure of magnesium alloys and improving the ductility at moderate temperatures. However, grain refinement in these alloys differs from other metals because new grains are formed along the boundaries of the initial structure and these newly formed grains slowly spread to consume the interiors of the larger grains in subsequent passes. A model is presented for grain refinement in magnesium alloys processed by ECAP based on the principles of dynamic recrystallization where new fine grains are formed along the initial boundaries and along twin boundaries. This model provides an explanation for a wide range of experimental data and introduces the concept of grain size engineering for achieving selected material properties in magnesium alloys.     

A CDM-based failure model for predicting strength of notched composite laminates

This paper investigates the ultimate tensile failure strength of laminated composites containing a central circular hole. Based on continuum damage mechanics, a Principal Damage Model is developed by combining the generalized standard material model with the Principal Damage concept of composite materials. Three in-plane failure modes: fiber breakage, matrix cracking, and fiber/matrix interface debonding are included in the present model. After obtaining material constants and damage relations from standard tensile tests, the material constitutive relations with damage model are implemented into commercial finite element code, abaqus. By comparing the predicted results with the experimental data, the proposed model has proven to be capable of predicting failure strength and load–deflection relations of notched laminated composites. The effects of hole size and specimen width are discussed in detail. In addition, the advantage of the present model is demonstrated through comparison with other existing models.