孔洞形状对层状岩石力学特性影响的FDEM数值模拟研究

为揭示孔洞形状对层状岩石力学性质和破坏模式的影响,采用有限元-离散元耦合数值模拟方法(FDEM)开展系列数值模拟研究。首先,阐述FDEM模拟层状岩石的基本原理,然后,开展不同层理倾角完整试样的单轴压缩模拟,并与试验结果进行对比验证。最后,对含有圆形、椭圆形、三角形、矩形和方形孔洞的层状岩石试样(β为0°、30°、45°、60°和90°)进行单轴压缩模拟研究。研究结果表明:对于不同孔洞形状的试样,抗压强度和试样破坏程度随层理倾角的增大呈V字型变化趋势,且均在层理倾角为0°时抗压强度取得最大值,在90°时破坏程度最为严重;孔洞的存在严重削弱了试样的力学性能,且削弱幅度与孔洞形状密切相关,其中方形和圆形孔洞对抗压强度的削弱能力最弱。将含不同形状孔洞试样的破坏模式随层理倾角的变化主要分为穿层理面拉剪混合破坏(β=0°)、沿层理面与穿层理面混合拉剪破坏(β=30°)、沿层理面剪切破坏(β=45°和60°)和沿层理面拉剪劈裂破坏(β=90°)。

In-situ Micro-CT analysis of deformation behavior in sandwich-structured meta-stable beta Ti−35Nb alloy

Beta Ti−35Nb sandwich-structured composites with various reinforcing layers were designed and produced using additive manufacturing(AM)to achieve a balance between light weight and high strength.The impact of reinforcing layers on the compressive deformation behavior of porous composites was investigated through micro-computed tomography(Micro-CT)and finite element method(FEM)analyses.The results indicate that the addition of reinforcement layers to sandwich structures can significantly enhance the compressive yield strength and energy absorption capacity of porous metal structures;Micro-CT in-situ observation shows that the strain of the porous structure without the reinforcing layer is concentrated in the middle region,while the strain of the porous structure with the reinforcing layer is uniformly distributed;FEM analysis reveals that the reinforcing layers can alter stress distribution and reduce stress concentration,thereby promoting uniform deformation of the porous structure.The addition of reinforcing layer increases the compressive yield strength of sandwich-structured composite materials by 124%under the condition of limited reduction of porosity,and the yield strength increases from 4.6 to 10.3 MPa.

玻璃球宏细观冲击特性的SHPB试验和耦合数值模拟研究

为研究玻璃球的宏细观冲击特性,该文开展了不同相对密实度玻璃球的一维霍普金森杆(SHPB)冲击试验和离散元-有限差分法耦合数值模拟研究。结果表明:一维冲击荷载下玻璃球经历初始弹性、屈服、颗粒间互锁硬化和颗粒破碎硬化四个阶段。基于耦合数值模拟发现,颗粒平均配位数随着冲击荷载时程不断增加,但增加的速率逐渐下降,其原因是配位数变化取决于孔隙压缩和以旋转为主的颗粒重排,随着试样压缩变形的发展,孔隙压缩和颗粒重排需要克服更大的颗粒间互锁效应,因此逐渐变缓。而试样孔隙率在弹性阶段基本不变,在屈服阶段和互锁硬化阶段近似线性下降,其原因是孔隙率变化受控于颗粒整体移动,弹性阶段颗粒整体移动尚未发展,屈服之后颗粒整体移动产生的孔隙压缩随荷载时程呈线性发展。冲击荷载下,颗粒位移以整体移动为主,相对位移为辅,因此,颗粒位移对试样的初始密实度不敏感。颗粒旋转需要克服周围颗粒的互锁效应,互锁效应取决于试样级配和颗粒粒径,对密实度较敏感。

基于FDEM数值模拟的软岩隧洞大变形预测

软岩隧洞收敛变形量预测对隧洞施工方法、设备选型和支护设计具有重要意义。采用有限元-离散元耦合数值模拟方法(FDEM)对软岩隧洞掘进过程开展了模拟研究,并调研了地应力量值对隧洞收敛变形量的影响。结果表明:隧洞大变形机理为开挖卸荷引起径向应力降低、切向应力升高,升高的切向应力造成围岩发生共轭剪切破坏,并持续向深处完整围岩扩展,深部破裂块体对浅部碎裂岩块的接触挤压产生宏观空隙,造成体积增大,发生具有碎胀效应的挤压大变形;随着围岩强度应力比的降低,围岩收敛变形量呈指数函数增大,相关系数高达0.996,为软岩隧洞收敛变形量预测提供了经验公式。

FLOW STRESS MODELING FOR AERONAUTICAL ALUMINUM ALLOY 7050-T7451 IN HIGH-SPEED CUTTING

The high temperature split Hopkinson pressure bar （SHPB） compression experiment is conducted to obtain the data relationship among strain, strain rate and flow stress from room temperature to 550 C for aeronautical aluminum alloy 7050-T7451. Combined high-speed orthogonal cutting experiments with the cutting process simulations, the data relationship of high temperature, high strain rate and large strain in high-speed cutting is modified. The Johnson-Cook empirical model considering the effects of strain hardening, strain rate hardening and thermal softening is selected to describe the data relationship in high-speed cutting, and the material constants of flow stress constitutive model for aluminum alloy 7050-T7451 are determined. Finally, the constitutive model of aluminum alloy 7050-T7451 is established through experiment and simulation verification in high-speed cutting. The model is proved to be reasonable by matching the measured values of the cutting force with the estimated results from FEM simulations.

Flexible-die forming process with solid granule medium on sheet metal

Certain non-metallic granules （NMG） were selected as the research object. It was proposed to conduct the volume compression experiments as well as those on the NMG physical properties at high stress levels. Then, not only the volume compression ratio curve but also the extended Drucker-Prager linear model were obtained. In addition, through the friction strength tests, parameters of the Mohr-Coulomb model were gained, which proved in basic agreement with those of the extended Drucker-Prager linear model. Additionally, curves of the friction coefficients between the NMG and the sheet metal trader different pressures were also obtained. Based on the material performance experiments, numerical analysis in respect of flexible-die forming process with solid granule medium （SGM） was conducted. The die and device for experiments of solid granule medium forming （SGMF） on sheet metal were designed and manufactured. Typical parabolic parts were successfully trial-produced. The tests and simulation results show that the sheet formability is significantly improved for the extraordinary friction performance during interaction between the SGM and the sheet metal surface. The process control and die structure are simple, and the shaped work-pieces enjoy many advantages, such as satisfactory surface quality and favorable die fitability, which offers a brand-new method and means for processing and preparation of sheet metals.

Identification of processing window for extrusion of large thick-walled Inconel 625 alloy pipes using response surface methodology

Identifying suitable processing window is necessary but difficult for achieving favorable microstructure and performance in extrusion of large thick-walled pipe with difficult-to-deform Inconel 625 alloy. In this work, a method was established for identifying the extrusion process window considering temperature control using response surface methodology. Firstly, the response surface models, which correlate temperature rise and peak temperature to key extrusion parameters, have been developed by orthogonal regression based on finite element calculated data. Secondly, the coupled effects of the key extrusion parameters on the temperature rise and peak temperature have been disclosed based on the regression models. Lastly, suitable extrusion processing windows, which are described by contour map of peak temperature in the space of extrusion speed and initial billet temperature, have been established for different extrusion ratios. Using the identified process window, a suitable combination of the key extrusion parameters can be determined conveniently and quickly.

Friction coefficient in rubber forming process of Ti-15-3 alloy

The forming limit diagram of Ti-15-3 alloy sheet was constituted at room temperature. The effects of different punch and rubber hardness on the limit principal strain distributions were investigated experimentally. Finite element analysis models of the samples with dimensions of 180 mm×180 mm were established to analyze the friction coefficients of different interfaces. Effects of various friction coefficients on the strain distributions were studied in detail. Finally, the friction coefficients in the cold forming were determined by contrasting the strain results between the experimental data and the simulated ones.

Analysis of deformation characteristic in multi-way loading forming process of aluminum alloy cross valve based on finite element model

The deformation characteristic in the forming process of aluminum alloy 7075 cross valve under multi-way loading was investigated by numerical simulation method. The results indicate that there exist 4 deformation patterns in the multi-way loading forming process of cross valve, such as forward extrusion, backward extrusion, forward-lateral extrusion and backward-lateral extrusion; one or several patterns occur at different forming stages depending on loading path. In general, the main deformation pattern is forward extrusion or backward extrusion at the initial stage; the main deformation pattern is backward extrusion at the intermediate stage, and the backward extrusion and forward-lateral extrusion occur at the final stage. In order to improve the cavity fill and reduce the forming defects, the lateral extrusion deformation should be increased at the initial and intermediate stages, and the forward extrusion deformation at the final forging stage should be reduced or avoided.

Effect of geometrical parameters on forming quality of high-strength TA18 titanium alloy tube in numerical control bending

The forming quality of high-strength TA18 titanium alloy tube during numerical control bending in changing bending angle β, relative bending radius R/D and tube sizes such as diameter D and wall thickness t was clarified by finite element simulation. The results show that the distribution of wall thickness change ratio Δt and cross section deformation ratio ΔD are very similar under different β; the Δt and ΔD decrease with the increase of R/D, and to obtain the qualified bent tube, the R/D must be greater than 2.0; the wall thinning ratio Δto slightly increases with larger D and t, while the wall thickening ratio Δti and ΔD increase with the larger D and smaller t; the Δto and ΔD firstly decrease and then increase, while the Δti increases, for the same D/t with the increase of D and t.

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.

Analysis of the Elastic-Plastic Dynamic Finite Element on a Jointed Rock Mass

Aim To study the elastic plastic dynamical constitutive relations about a jointed rock mass under explosion load and its computer simulation. Methods\ Stress history is taken into account and stresses will follow changes in time during a period of explosion load. According to the principle of static force balance, the corresponding nodal concentrated force is calculated and the nodal displacement is counted. The elastic plastic dynamic finite element equations are thus obtained. Results\ A finite element method is given for a jointed rock mass under explosion load. Conclusion\ The problem of large plastic deformation for jointed rock mass on blasting was efficiently resolved through dynamic finite element analysis and the range of damages by blasting simulated, and this pushes forward the problem to engineering practice.

Contrast between 2D inversion and 3D inversion based on 2D high-density resistivity data

The 2D data processing adopted by the high-density resistivity method regards the geological structures as two degrees, which makes the results of the 2D data inversion only an approximate interpretation;the accuracy and effect can not meet the precise requirement of the inversion. Two typical models of the geological bodies were designed, and forward calculation was carried out using finite element method. The forward-modeled profiles were obtained. 1% Gaussian random error was added in the forward models and then 2D and 3D inversions using a high-density resistivity method were undertaken to realistically simulate field data and analyze the sensitivity of the 2D and 3D inversion algorithms to noise. Contrast between the 2D and 3D inversion results of least squares inversion shows that two inversion results of high-density resistivity method all can basically reflect the spatial position of an anomalous body. However, the 3D inversion can more effectively eliminate the influence of interference from Gaussian random error and better reflect the distribution of resistivity in the anomalous bodies. Overall, the 3D inversion was better than 2D inversion in terms of embodying anomalous body positions, morphology and resistivity properties.

Combined method for fast 3-D finite element modeling of nondestructive testing signal

A combined method for the fast 3-D finite element modeling of defect responses in nondestructive testing of electromagnetics is presented. The method consists of three numerical techniques: zoom-in technique, difference field technique and iterative solution technique. Utilizing the zoom-in technique, the computational zone focuses on a relatively small domain around the defect. Employing the difference field technique, the axisymmetrical field solution corresponding to the case with no defect can be used to simplify the mesh generation and obtain the modeling results quickly. Using the iterative solution technique, the matrix equation system in the 3-D finite element modeling of nondestructive probe signals can easily be solved. The sample calculation shows that the presented method is highly effective and can consequently save significant computer resources.

Numerical simulation of LWD resistivity response of carbonate formation using self-adaptive hp-FEM

Most of the carbonate formation are highly heterogeneous with cavities of different sizes, which makes the prediction of cavity-filled reservoir in carbonate rocks difficult. Large cavities in carbonate formations pose serious threat to drilling operations. Logging-whiledrilling （LWD） is currently used to accurately identify and evaluate cavities in reservoirs during drilling. In this study, we use the self-adaptive hp-FEM algorithm simulate and calculate the LWD resistivity responses of fracture-cavity reservoir cavities. Compared with the traditional h-FEM method, the self-adaptive hp-FEM algorithm has the characteristics of the self-adaptive mesh refinement and the calculations exponentially converge to highly accurate solutions. Using numerical simulations, we investigated the effect of the cavity size, distance between cavity and borehole, and transmitted frequency on the LWD resistivity response. Based on the results, a method for recognizing cavities is proposed. This research can provide the theoretical basis for the accurate identification and quantitative evaluation of various carbonate reservoirs with cavities encountered in practice.

Nonlinear dynamical response of high-voltage transmission lines based on cable dropping

In order to study the dynamic response of high-voltage transmission lines under mechanical failure, a finite element model of a domestic 500-kV high-voltage transmission line system is established. The initial equilibrium condition of the coupling system model is verified by nonlinear static analysis. The transient dynamic analysis method is proposed to analyze the variation law of dynamic response under cable or insulator rupture, and the dynamic response of structural elements next to the broken span is calculated. The results show that upper crossarm cable rupture has no effect on cable tension at adjacent suspension points, but it has a significant influence on tension in the insulator and the tower component of the upper crossarm next to the broken span. The peak tension in the conductor of the upper crossarm at the suspension point exceeds the design value under insulator rupture. Insulator rupture has no effect on the tower component of the upper crossarm, but it has a significant influence on insulator tension of the upper crossarm. Insulator rupture should be taken into account in the design of overhead transmission lines. The research results can provide a theoretical basis for the design of transmission lines.

Finite element analysis of pressure on 2024 aluminum alloy created during restricting expansion-deformation heat-treatment

Metals heat-treated under high pressure can exhibit different properties. The heat-induced pressure on 2024 aluminum alloy during restricting expansion-deformation heat-treatment was calculated by using the ABAQUS finite element software, and the effects of the mould material properties, such as coefficient of thermal expansion （CTE）, elastic modulus and yield strength, on the pressure were discussed. The simulated results show that the relatively uniform heat-induced pressure, approximately 503 MPa at 500 ℃, appears on 2024 alloy when 42CrMo steel is as the mould material. The heat-induced pressure increases with decreasing the CTE and the increases of elastic modulus and yield strength of the mould material. The influences of the CTE and elastic modulus on the heat-induced pressure are more notable.

MULTI-MATERIAL NUMERICAL SIMULATION OF MOVING SHOCK INTERACTING WITH CONSECUTIVE BUBBLES

Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.

倾斜底板非对称底鼓灾变机理及灾变模式研究

深部高应力倾斜底板岩层易发生非对称底鼓灾害。采用有限元-离散元耦合数值方法(FDEM)研究倾斜底板非对称底鼓灾变机制、灾变模式,以及岩层倾角对底鼓模式的影响。结果表明:(1)应力驱动型底鼓灾变机制为碎胀性的渐进挤压大变形,环形切向集中应力是造成上述灾变的应力驱动源;(2)当倾角为15°~30°时,非对称底鼓特征明显;当倾角为45°~75°时,非对称特征减弱;当倾角为0或90°时,底板呈对称底鼓特性。

Finite element analysis of stress distribution and burst failure of SiC_f/Ti-6Al-4V composite ring

A three-dimensional cyclic symmetry finite element model of titanium-matrix composites（TMCs） ring was developed to investigate the stress distribution and burst failure. The effects of fiber volume fractions, reinforced areas, thermal residual stresses and two different temperatures on stress distribution were studied. The burst speed was obtained through analyzing the hoop tensile stresses under a series of rotating speeds. The results indicate that at the two different temperatures, the influences of fiber volume fractions and reinforced areas on stress level and distribution are different. Some proposals are provided for the structure design of the TMCs ring. With regard to thermal residual stresses, a larger reinforced area is an advisable choice for design of the ring at higher temperature.