Slip-line Field Method Research Articles

Deformation Characteristics of Asymmetric Gradient Extrusion in Preparing Ultra-Fine-Grained Bulk Materials

In this paper, a novel method for the preparation of ultra-fine-grained bulk materials called asymmetric gradient extrusion (AGE) is proposed. In AGE, the cross-section of the extrusion channel is a rectangle, and two inclined planes are staggered along the extrusion direction. To realize repetitive extrusion, the thickness of the workpiece is limited to be equal to the width of the channel outlet. In order to study the mechanism of ultra-fine grain formation in AGE, the deformation characteristics of AGE were investigated. First, the slip line field method was used to theoretically analyze the deformation characteristics and grain splitting in AGE. Then, the plastic deformation behavior of bulk samples in AGE and traditional extrusion was investigated and compared with the finite element method. In addition, the deformation characteristic and microstructure variation of pure copper bulk samples in AGE were experimentally investigated. The results showed that the deformation characteristics of workpieces were highly related to the two inclined planes within the die channel. Two independent deformation zones can be formed with increasing distance between the two inclined planes. The shear effects in each deformation zone lead to grain splitting during extrusion. Compared with traditional extrusion, the advantage of AGE is its amazing ability to form high and uniform strain during extrusion, which leads to the formation of small and uniform grains in the workpiece. After six passes of AGE, an average grain size of 0.6 μm can be achieved. The enhancement and accumulation of dislocations within grains was the dominating mechanism of grain fragmentation. AGE shows impressive potential in the preparation of ultra-fine-grained bulk materials.

Estimation of Necessary Force for Isothermal Forging of Disc Piece of Aluminum Alloy 7075 by Slip Line Field Method

Estimation of Necessary Force for Isothermal Forging of Disc Piece of Aluminum Alloy 7075 by Slip Line Field Method

Coulomb, Tresca and Coulomb-Tresca friction models used in analytical analysis for rolling process of external spline

The plastic deformation during external spline rolling process (ESRP) is concentrated in the superficial area of workpiece. The numerical simulation for full 3D spline rolling process is time-consuming, and experimental measure during the rolling process is also difficult, and there is no clear physical meaning between results and parameters. The analytical models for ESRP have been modeled by slip-line field method (SLFM) with Coulomb friction model (CFM), Tresca friction model (TFM) and Coulomb-Tresca friction model (CTFM), respectively. The SLFM models can represent the influence of geometrical and frictional parameters on the ESRP. The slip line fields of ESRP under different friction models all contain 3 slip-line sub-regions for workpiece only with circular dedendum and all contain 5 slip-line sub-regions for workpiece with involute flank. Compared with experimental and numerical results, the error of SLFM (slip-line field method) result such as undeformed zone of the workpiece is less than 10 % between SLFM results and the experimental and FEM results. The error between SLFM and FEM for normal stress on contact surface is less than 10 %. The geometrical parameter and friction condition have an important influence on the applicability of CTFM. CTFM only works in the rolling process with small pressure angle (such as 14.5° for gear) and friction condition (0.7<m<0.8) between lubrication and dry friction; and for other cases, the CTFM degenerates into a TFM. The developed SLFM model in this study can provide a basis for studying deformation mechanism, rapidly determining reasonable parameter range, and simplifying finite element model of spline or gear rolling process. The results in this study also provided reference for selection of friction model in finite element analyses of complex profile rolling.

Solution of the problem of sheet bending by the slip line field method

One of the limitations imposed on this process of bending is the possibility of cracking on the surface of the sheet during bending. To predict this type of metal destruction, information is needed on the plastic properties of the material and the stress state in the deformation zone during the bending process. The solution of the problem of sheet bending under conditions of a flat-strained state by graphical construction of the slip line field using a rigid cylindrical mandrel has been analyzed. The material model is a perfectly plastic body. The stresses in the deformation zone and accumulated strains have been determined. The bending process is characterized as unidirectional and monotonous. It has been determined that the mean stress on the outer surface of the sheet during bending equals to 1, and it does not depend on the sheet thickness and the radius of the rigid cylindrical mandrel. Verification of the accuracy of the graphical solution is made. The resulting solution can be used as the basis for an experimental method for testing the plastic properties of metals.

Accurate Numerical Simulation Study on Bearing Capacity and Sliding Surface of Slope Foundation

The bearing capacity of slope foundation is an important condition for the stability of mountain transmission line. At present, the methods for studying the bearing capacity of slope foundation are mainly as follows, such as the Limit Analysis Method, Slip-Line Field Method and Numerical Simulation Method. In this paper, the numerical simulation method with high accuracy is used to study the bearing capacity changes of slope foundation under different slope ratios, slope border margin and foundation conditions with the help of the finite difference software FLAC3D. Based on the correlations obtained from above, the reasons and laws for the changes of the ultimate foundation bearing capacity can be found, which can provide some guidance for related engineering design.

表面微細テクスチャによる切削工具・切りくず間の付着拘束緩和が加工力低減に及ぼす影響

Cutting force can be reduced by using surface micro-textured tools even under dry conditions. In the previous research, it was found that the surface textures for reduction in cutting force must have concave portions intermittently at the contact region far away from the cutting edge. This result supposes that textures bring about a reduction in adhesive force acting at the interface and reduce cutting force. In order to investigate an effect of surface textures on reduction in adhesive force, dry friction tests with the loading and unloading process were carried out. The results indicated that the surface textures can reduce the adhesive force. Moreover, a cutting model established by the slip-line field method was proposed in order to consider the effect of adhesive force on the deformation field state including shear angle, chip curl radius and tool-chip contact length which strongly affects cutting force. The change in the deformation field state following the reduction in the adhesive force corresponds to the experimental results with the textured tools. From the results, it was suggested that the mechanisms of reduction in cutting force attached under dry conditions can be well described by considering the existence of adhesive restriction between tool and chip.

Experimental Research of Micro-Textured Tool for Reduction in Cutting Force

An effect of micro-textured tool on a reduction in cutting force has reported in recent years. Some researchers have discussed that the microstructures contribute to the reduction in friction force at tool-chip interface by acting as cutting fluid reservoirs. In this study, on the other hand, a reduction in cutting force achieved by using the textured tools was confirmed even under dry condition. The results of orthogonal cutting tests employing AISI 1045 steel with non-textured and textured tools indicated that the cutting force and calculated friction coefficient at the tool-chip interface definitely reduce at relatively high cutting speed. For this friction reduction effect, effective texture patterns and optimal area ratio of concave portion to total surface were empirically suggested. Moreover, from results of the tests using tools with sectionally textured surface, it was revealed that the texture only around the position in which the chip flow separates from the tool rake face is effective to reduce the cutting force. Close observation of both tool edges and formed chips under various cutting tests indicated that changes in geometry and dimensions of dead metal formed around the cutting edge is essential for the reduction in cutting force. Finally, a mechanical cutting model having an agreement with the experimental results was discussed by employing the slip-line field method.

Approximate Solution to the Sokolovskiĭ Concave Slope at Limiting Equilibrium

AbstractThe growth of precision autoguidance systems on construction equipment suggests that nonplanar slopes and landforms now can be constructed readily. Slopes with concave cross sections not only appear more like natural slopes, but can also have superior stability and erosion resistance. Thus, it is desirable to have the description of concave slopes that provide mechanical stability for a given set of soil properties. In this paper, an approximate solution that defines the geometry of critical concave slopes (factor of safety ≈1) in a frictional medium is developed, based on the slip-line field method. The approximate solution is compared with previous numerical results and validated via limit-equilibrium method and FEM analyses. The proposed solution is simple in form, and, when implemented with precision construction equipment, will allow the construction of embankments and reclaimed mine lands that appear more like those in nature and yet are more resistant to erosion.

Chatter Stability Model of Micro-Milling With Process Damping

This paper presents the prediction of cutting forces and chatter stability of micro-milling operations from the material's constitutive flow stress and structural dynamics of the micro-end mill. The cutting force coefficients are identified either using previously presented slip-line field or finite element methods by considering the effects of chip size, cutting edge radius, rake angle and cutting speed. The process damping caused by the plowing of round edge is modeled by finite element method. The frequency response function of the fragile micro-mill is measured through specially devised piezo actuator mechanism. Dynamic model of micro-milling with the velocity dependent process damping mechanism is presented, and the chatter stability is predicted in frequency domain. The proposed models have been experimentally verified in micro-milling of AISI 1045 steel.

Analytical Approach for Optimization of Chamfered Cutting Tool Preparation Considering Built-Up Edge Extrusion Behavior

A built-up edge (BUE) that is formed adjacent to a chamfered cutting edge is extruded along the cutting edge, if the appropriate chamfer geometry is selected. If a sharper BUE is stably extruded with high fluidity, notch wear at the depth-of-cut line and adhesion of the work material can be prevented. In this study, an analytical cutting model considering the BUE extrusion with a chamfered tool is proposed in order to optimize the chamfer preparation, i.e., chamfer angle and coefficient of friction between the chamfer face and the BUE, for the advantages of BUE extrusion. In this analysis, an empirical cutting model employing the slip-line field method and a BUE extrusion model using the slab method are coupled by static mechanics equilibrium. By coupling the two models, the shape of the BUE is uniquely determined. The calculated and experimental results in terms of actual rake angle and cutting force are roughly in agreement. The analytical results indicate that sharpness and the fluidity in the BUE extrusion can be simultaneously attained by preparing the tool with chamfer angle in which the material stagnation proceeds until the actual rake angle is equal to the rake angle of the tool.

Slip-line field modeling of orthogonal machining pressure sensitive materials

The slip-line field methods are widely used in solving cutting problem; however, most of which were focused on the pressure-independent materials. In this work, a new slip-line field model for orthogonal cutting of pressure sensitive materials is developed. Analytical characterization for orthogonal cutting process is obtained, which can give the explicit expressions for the shear angle, cutting force, and chip thickness in terms of the tool geometry, the friction coefficients on the tool flat, and the internal friction angle of the materials. To investigate the effect of the material and cutting parameters on cutting process, the finite element simulation is performed as well. The comparisons between the shear angle and cutting force predicted by the theoretical model with those obtained from finite element model simulation are made. The good agreement of the predicted results with the numerical results clearly reveals that the proposed slip-line field model can satisfactorily characterize the orthogonal cutting behavior of the pressure sensitive materials. Further analysis has demonstrated that the pressure sensitivity of materials has a significant influence on cutting process.

FLASH DESIGN OF DIE SHAPES FOR REDRAWING RECTANGULAR CUPS

This paper presents a die design technique for redrawing rectangular cups by the slip line field method. A slip line field is constructed around a redrawn cup of a product shape, and pre-drawn cups of arbitral shapes are also constructed in the field. The distributions of circumferential strain, streamline lengths and velocity in redrawing are calculated. Then die shoulder angles along the die fringe are determined so as to fill the condition that the material at a certain height on the wall of the pre-drawn cup must reach and pass through the inner fringe at the same time during the redrawing process. Because the calculation time for the analysis needs only a few seconds, it is possible to select the most proper process in which the strain distribution is relatively uniform among the pre-drawn shapes. The simulated result obtained using LS-DYNA shows the uniformity of the wall thickness of the redrawn product.

The New Technology of Floating Polishing of Large Die Surfaces

During the transferring process of the large die surfaces, there are extensive needs of die surface polishing. Since almost large die surfaces are free-form surfaces, currently, these are almost manually implemented. In order to overcome this barrier, this paper focuses on a new technology of floating polishing, including a) the design of polisher body which has five degrees of freedom and realize the floating polishing while keep the polishing head being indifference equilibrium within the working range, b) normal force of polishing head on die surface analyses and experimental verification by using the slip line field method, and c) establishments of the interference boundaries between dies surface features and polishing head. The research achievements will be used for the development of a portable, state-of-the-art polishing machine and the optimization of the associated polishing process parameters in near future.

Application of the slip-line field method to the analysis of die cavity filling

The article concerns the selected problems of closed-die forging. It is focused on the analysis of use the slip-line field method in flash design process. The new slip-line field elemental technique (SLFET) has been presented in this paper, too.The theoretical analysis is compared with the forging simulations made in the finite element method (FEM). As a tools were used the closed-dies with a flat parallel flash land. It assured extrusion process (parts with the boss) in plane strain conditions.Application of the slip-line field method permits to compute a load and efficient filling of die cavity (maximal height of the boss). An ideal plastic model of material has been utilized on the analysis. This work presents influences among flash land geometrical parameters on degree of die cavity filling and load. The poly-optimization of flash land parameters has been presented in here, too. Based on obtained conclusions, authors have worked out a computer program, which implements a new SLFET method.

Application of the slip-line field method to the analysis of die cavity filling

The article concerns the selected problems of closed-die forging. It is focused on the analysis of use the slip-line field method in flash design process. The new slip-line field elemental technique (SLFET) has been presented in this paper, too. The theoretical analysis is compared with the forging simulations made in the finite element method (FEM). As a tools were used the closed-dies with a flat parallel flash land. It assured extrusion process (parts with the boss) in plane strain conditions. Application of the slip-line field method permits to compute a load and efficient filling of die cavity (maximal height of the boss). An ideal plastic model of material has been utilized on the analysis. This work presents influences among flash land geometrical parameters on degree of die cavity filling and load. The poly-optimization of flash land parameters has been presented in here, too. Based on obtained conclusions, authors have worked out a computer program, which implements a new SLFET method.

Application of the slip-line field method to the analysis of die cavity filling

Application of the slip-line field method to the analysis of die cavity filling

Experimental validation of incipient failure of yield stress materials under gravitational loading

Recent theoretical work has investigated incipient failure of a cylinder of yield stress material under gravitational loading [Chamberlain et al., Int. J. Mech. Sci. 43, 793–815 (2001); 44, 1779–1800 (2002)]. This theoretical work, using the slip-line field method of plasticity, suggests that the height of incipient failure increases as the radius increases. In contrast, a simple heuristic model, the “uniform stress model,” predicts that the height of incipient failure is independent of the radius. We present detailed quantitative comparison of the slip-line and uniform stress models with experimental measurements, verifying the predictions of the slip-line model.

Development of the optimal blank calculation system in deep-drawing by the slip line field method and CAD

Development of the optimal blank calculation system in deep-drawing by the slip line field method and CAD

Cold compaction of an array of cylindrical fibres

The biaxial compaction of a square array of circular cylinders is studied using slip-line field, upper bound and finite element methods. Densification is assumed to occur by plastic deformation at the contacts. It is found that contact–contact interaction has a softening effect on the local indentation pressure at each contact. The yield surfaces resulting from hydrostatic and closed-die compaction are constructed at various stages of densification: the size and shape of the yield surface depend upon the loading history and upon the relative density of the compact. The finite element predictions suggest the formation of a vertex at the loading point for the entire densification process in the case of isostatic compaction. On the other hand, a vertex at the loading point is formed only for a relative density D⩽0.85 in the case of closed-die compaction.

Analysis of the stress concentration factor for a shallow notch by the slip-line field method

The relationships correlating the local stress and strain at the tip of a notch, the nominal stress expressed by the so called Neuber's rule and Moski and Glinka's equivalent energy density method are studied for a shallow notch,using the slip-line field method proposed in plastic mechanics, and an elastic-plastic solution for the area close to the notch. An elastic-perfect plastic material model is also used. It is found that for lower stress amplitude Moski and Glinka's method is with a good accuracy; however, the relative deviations of the actual stress concentration factors calculated by these two methods to the theoretical stress concentration factor are not small, even up to 20% for higher stress amplitude as the size of the plastic zone around the notch approaches the value of the radius of the notch curvature. While the geometric mean of the two expressions mentioned above can be considered as a reasonable expression to correlate the local stress-strain and the nominal stress, and thus the corresponding actual equivalent stress concentration factor can be evaluated, of which the relative deviations to the theoretical stress concentration factor is shown to be <5%, if the size of plastic zone close to the notch is not greater than the value of the radius of curvature of the notch.