Slip-line Solutions Research Articles

An investigation of force and pressure analysis during the process of equal channel angular pressing to M1 copper using finite element and upper-bound methods

This article presents two methods to determine pressing forces to the M1 copper plate. The first approach employs the upper-bound method, and the second method combines numerical simulation with a central composite design. The upper-bound method uses physical analysis to determine the deformation zone and establish the division of the rigid block model. The findings were identical to the slip-line solution method. The results obtained from the three-dimensional simulation performed using Qform software combined with a central composite design have provided regression equations that help determine the force and punching pressure. The impact of each parameter on the pressing force is similar in both approaches, and the difference between the two methods is insignificant and falls within a dependable range.

Slip Line Solution for Active Earth Pressure of Retaining Walls with Relief Shelves Subjected to Base Rotation

Slip Line Solution for Active Earth Pressure of Retaining Walls with Relief Shelves Subjected to Base Rotation

Slip-Line Solution for the Active Earth Pressure of Narrow and Layered Backfills against Inverted T-Type Retaining Walls Rotating about the Base

In this research, we used a slip-line method for a typical failure mechanism simulated with adaptive finite-element software to investigate the active earth pressure of narrow and layered backfills against inverted T-type retaining walls rotating around the base mode. The slip-line field calculation models for the inverted T-type retaining wall with narrow and layered backfills were established considering the effect of the heel bottom plate and the inverted T-type retaining wall characteristics. Subsequently, the limit equilibrium and finite difference methods were used to solve the stress state of each point. The earth pressure acting on the stem and the second failure surface can be obtained by converting the boundary conditions. The proposed method was verified by comparing its results with those from finite-element limit analysis and existing theoretical solutions. Furthermore, several extensive parametric studies have investigated the effects of backfill width, heel length, and interface strength. The results show that increasing interface strength and decreasing backfill width help reduce the earth pressure against the stem and second failure surface. The change in the length of the heel bottom plate exhibited a dual effect.

Slip-Line Solution to Earth Pressure of Narrow Backfill against Retaining Walls on Yielding Foundations

When a retaining wall is adjacent to a natural slope, the overturning of the wall is usually caused by a yielding foundation. At the point of overturning, the narrow backfill behind the wall has reached the active limit state. However, in previous studies, the foundation conditions of the retaining wall were not fully considered when the earth pressure on the retaining wall with the narrow backfill was calculated. To comprehensively consider the stress state of the retaining wall, the finite-element limit analysis method was employed to study the failure mode of a retaining wall adjacent to a natural slope. The simulation results indicate that the sliding surface starts from the wall heel, with one side developing at the surface of the natural slope and the other developing in the ground in front of the wall. Based on this failure mechanism, a slip-line computational model for the retaining wall was established. When the slip-line solution was compared with the finite-element solution, the results were in good agreement. The plastic zone of the soil was determined by the slip-line field. In addition, the slip-line solution gave the active earth pressure of the narrow backfill, the passive earth pressure of the soil in front of the wall, and the foundation bearing capacity. Moreover, several extensive parametric studies were conducted. Thus, the shape of the narrow backfill, the rough soil–wall interface, and the low-strength backfill are all conducive to reducing active earth pressure on a retaining wall.

Characterization of material flow mechanism for chamfered tools utilizing coupled slip-line-slab method

Sintered carbide tools with their edge chamfered have superior resistance against brittle fracture of the main edge. Such advantage is mainly attributed to the formed built-up edge (BUE) anterior to the chamfer face. However, as the cutting process, certain materials including cracked BUE in that vicinity will inevitably flow aside along the chamfer face, which eventually causes severe notch wear and lateral burr formation. Given this deficiency, both theoretical and experimental works were carried out for the cutting process with chamfered tools in the current study. In the theoretical part, the material flow mechanism was analyzed and modeled by classifying the process into three typical modes concerning specific chip-tool contact patterns, for which three sets of modified slip-line solutions were developed accordingly. Furthermore, a unique solution to the three-dimensional (3-D) material flow status was achieved by combining slip-line theory with the slab method. On this basis, the effects of tool preparation factors, i.e. chamfer width, chamfer angle, tool-workpiece friction coefficient and rake angle, on the BUE extrusion were discussed in detail. The results indicate that with proper chamfered edge design, accumulative BUE will be flowing in an optimal condition. In this case, the lateral burrs were found effectively restrained as had been evidenced by conducting extensive orthogonal cutting experiments with chamfered tools. By comparing with released models and experimental measurements, the present model yields more accurate predictions of material flow states. These findings of present study can contribute to the optimal design of cutting tools with chamfered edge.

Plasticity-Based Estimation of Active Earth Pressure Exerted by Layered Cohesionless Backfill

Abstract A slip line solution is proposed to analyze the active earth pressure on cantilever retaining walls supporting a layered cohesionless backfill. The reduction in earth pressure in the prese...

Cutting temperature prediction in negative-rake-angle machining with chamfered insert based on a modified slip-line field model

Chamfered inserts have shown superior edge resistance and prolonged tool life in practical machining process. However, such kind of inserts find limited application in metal cutting due to the inadequate understanding of their sophisticated influences on cutting performance. Researches on material flow mechanism and heat generation issues in the vicinity of the chamfer may contribute to the comprehensive cognition of high-performance cutting with chamfered inserts. In this paper, a novel slip-line field model has been developed for negative-rake-angle machining with chamfered insert. The slip-line field geometry concerning dead metal zone (DMZ) formation is demonstrated utilizing the slip-line approach. Moreover, an iterative methodology is developed to determine local shear flow stresses, interface frictional factors and heat sources intensity. Then, analytical modeling of temperature fields in tool and workpiece is carried out by employing classical orthogonal cutting theory and semi-boundary heat transfer principles. Finally, two main approaches including two-dimensional (2-D) finite-element (FE) simulations and orthogonal cutting trials of AISI 304 stainless steel are adopted for verification. Simulated slip-line field geometry with respect to DMZ and involved angles are extracted to compare against the predictions from the proposed slip-line solution. The simulated and measured temperature fields are compared with the predicted results from the developed thermal model. In addition, a contrastive model from previous literature is also compared with the proposed model. Encouraging agreements have been detected between those comparisons, which indicate the reasonableness and reliability of the given analytical model. The result reveals that the presented model gives much better prediction of temperature distribution upon chamfer insert over the contrastive model, especially at the DMZ-tool interface.

Applications of anisotropic slipline theory with non-uniform lattice rotation

Anisotropic slipline theory, with non-uniform lattice rotation field, is used to discuss new slipline solutions for the plane strain problems of punch indentation and mode 1 stationary crack in a ductile single crystal with piecewise linear yield locus. The proposed solution allows for both linear dislocation arrays and sectors with bulk dislocation density. Such features provide considerable latitude in the number of allowable stress discontinuities, and their orientation, when compared to the solutions which assume uniform lattice rotation.

Influence of plastic anisotropy on the limit load of highly under-matched scarf joints with a crack subject to tension

A new semi-analytical plane strain upper bound limit load solution for highly under-matched scarf joints with a crack subject to tension is provided. It is assumed that plastic deformation is fully confined to the soft weld material. A numerical technique is only necessary to evaluate ordinary integrals. Distinguished features of the solution are that (i) plastic anisotropy of the weld material is taken into account and (ii) the asymptotic behavior of the chosen kinematically admissible velocity field in the vicinity of the bi-material interfaces coincides with that of the real velocity field. This ensures that the stress boundary condition is satisfied at these interfaces. Hill’s quadratic yield criterion is adopted. It is shown that the effect of plastic anisotropy on the limit load is significant. Therefore, this material property can affect the accuracy of predictions of conventional flaw assessment procedures. The accuracy of the solution at a certain set of parameters is verified by comparison with a numerical slip-line solution.

An accurate upper bound solution for plane strain extrusion through a wedge-shaped die.

An upper bound method for the process of plane strain extrusion through a wedge-shaped die is derived. A technique for constructing a kinematically admissible velocity field satisfying the exact asymptotic singular behavior of real velocity fields in the vicinity of maximum friction surfaces (the friction stress at sliding is equal to the shear yield stress on such surfaces) is described. Two specific upper bound solutions are found using the method derived. The solutions are compared to an accurate slip-line solution and it is shown that the accuracy of the new method is very high.

Ultimate bearing capacity of a pipeline on clayey soils: Slip-line field solution and FEM simulation

The ultimate bearing capacity of a cylindrical foundation (e.g. a submarine pipeline, circular mooring lines) on clayey soils is analyzed analytically and numerically by employing the slip-line field theory and the plane-strain finite element method respectively. A slip-line field solution is presented, taking into account of circular configuration of the pipe, the pipe embedment, and the pipe–soil interfacial cohesion. The derived bearing capacity factors for a smooth rigid pipe may limit to those for the conventional rectangle-shaped strip footing while the pipe embedment is approaching zero. A plane-strain finite element model is further proposed to simulate the quasi-static process of the pipeline penetrating into the clay soil, in which the contact-pair algorithm and adaptive meshing technique are employed, and the Drucker–Prager constitutive model is used for modeling the soil plasticity. Comparison indicates that the present numerical results match well with the derived slip-line solutions. According to the obtained vertical load–displacement curves, concurrently referring to the plastic strain field and the soil incremental-displacement vector field, the shear failure types and the corresponding collapse loads can be thereby determined for the pipeline foundations on clayey soils.

Slip-line solution to active earth pressure on retaining walls

The slip-line method is commonly used to solve the limit earth pressure on retaining walls, but to date there are still a number of problems that have not yet been solved. Based on limit equilibrium theory, the backfill is considered to be an ideal elastic-plastic material, which obeys the Mohr–Coulomb yield criterion, and is assumed to be an ideal continuous medium that is isotropic, homogeneous and incompressible (or non-expansive). Various factors of influence are considered in the calculation model. An elastic overburden is proposed as a replacement for traditional tension cracks. A new concept – stress singularity – and its stress boundary conditions are introduced, and a statically determinate and solvable mathematical model for the limit equilibrium problem is established without considering the stress–strain relationship of the soil. The slip-line stress field in the plastic zone of the backfill is solved by using the slip-line method, following which the active earth pressure on retaining walls and the soil reaction on the slip surface are derived. The geometric and mechanical similarity principle is first proposed by dimensionless analysis. The results show that the slip-line solution to active earth pressure is generally always greater than or equal to Coulomb's solution, and coincides with Rankine's solution or the classical Coulomb solution that satisfies the non-singularity conditions. Hencky's first and second theorems are not generally applicable.

Use of internal and external variables and extremum principle in limit equilibrium formulations with application to bearing capacity and slope stability problems

Limit equilibrium methods, satisfying both force and moment equilibrium can be formulated using assumptions on the internal variables or the external variables. Even though most stability methods are based on force and moment equilibrium, as well as the Mohr–Coulomb yield criterion, there are great differences between the results of the different formulations due to variations in the assumptions. The authors believe that the use of the interslice force function f(x), the thrust line or the base normal forces should provide an equivalent concept at the ultimate/failure state. In the present study, the authors have used the well-known bearing capacity solutions to determine f(x), the thrust line and the base normal forces for a “horizontal slope”. The equivalence between the different formulations under the ultimate condition is demonstrated. It is shown that it is not important which forces are used in the stability formulation, external boundary forces or internal forces, if only that the ultimate state is considered. It is also demonstrated in the present paper that the maximum extremum from the limit equilibrium analysis is equivalent to the slip line solution using a classical bearing capacity problem.

An analytical force model for orthogonal elliptical vibration cutting technique

The elliptical vibration cutting (EVC) technique has been found to be a promising technique for ultraprecision machining of various materials. In each overlapping EVC cycle, the thickness of cut (TOC) of work material, and the tool velocity get continuously varied. These two inherent phenomena, in fact, introduce transient characteristics into its cutting mechanics, which are considered to be different from the one applied for conventional cutting technique. Recently, a few theoretical models have been developed to understand the material removal mechanism with the EVC technique; however, in those studies, the transient phenomena were not considered. In the present research, an analytical force model for the orthogonal EVC process was developed in order to fully understand the EVC mechanism, and to more accurately predict the transient cutting force values. Three important factors: (i) transient TOC, (ii) transient shear angle, and (iii) transition characteristic of friction reversal were investigated and analyzed mainly based on geometric modeling and the Lee and Shaffer's slip-line solution. Mathematical evaluation shows that they may have significant influence on EVC process, and thus on its output performance. In order to validate the proposed force model, a series of low-frequency orthogonal EVC tests were conducted. The experimental transient cutting force values were compared with the predicted values calculated using the proposed model, and they are found to be in a good agreement with each other.

Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method

The interslice force function f(x) is a major assumption of the limit equilibrium method, which is important but has not been adequately considered in the past. In this paper, f(x) is taken as the control variable, and the upper and lower limits of the factor of safety for a general slope will be determined by a global optimization analysis. Based on this approach, f(x) will be determined and investigated. We demonstrate that f(x) cannot be arbitrarily assigned if a set of acceptable internal forces is required. The approach can be presented practically as a lower bound approach with the advantage that failure to converge is virtually eliminated, which is not possible with all other existing rigorous methods. The present attempts to answer several important questions in the basic theory of slope stability analysis, and provides a f(x) based on the lower bound approach statically admissible forces throughout the whole failure zone. Currently, different assumptions will give different factors of safety to the same problem, and this situation will be overcome by the use of the proposal. The proposal is also proven to give a result equal to the slip line solution for a simple footing on clay which is not possible for other classical slope stability methods, which has demonstrated that the applicability of the present for general difficult problems.

Undrained collapse of a shallow plane-strain trapdoor

The problem considered here is the plastic collapse of a strip trapdoor overlain by a relatively thin layer of homogeneous undrained clay (idealised as a rigid–plastic Tresca material). Although the simple ‘vertical slip' solution is intuitively appealing, and provides an upper bound that previous authors have found difficult to improve, it cannot be exact, because it implies an inadmissible stress field. This note describes the stress and velocity fields of a new slip-line solution that improves the upper bound slightly, but more importantly, satisfies all the boundary conditions of the problem (and is therefore a candidate for exactness). A comparison with closely bracketed bounds obtained using finite element limit analysis suggests that for cover ratios up to about 1·3, the new analytical solution is indeed the exact one.

Mechanics of continuous equal-channel angular extrusion

The paper discusses possible approaches for realization of continuous equal-channel angular extrusion (ECAE). A practical interest presents Conform ECAE (CECAE) converting an inlet channel into a friction press. Slip line solutions and plastic zones are analyzed for different cases of active and passive frictions. It is shown that CECAE provides lower extrusion pressure, higher effective strains and better approximation to simple shear deformation mode than ordinary ECAE. Specific distributions of plastic friction depending on a slip between material and roll are introduced for the beginning stage, steady CECAE and during slippage. The paper describes a few designs of CECAE. Optimization of the main characteristics is performed for the concept of CECAE with an additional coining roll.

Active Pressure for Circular cut with Berezantzev's and Prater's Theories, Numerical Modeling and Field Measurements

A simplified slip line solution of the axi-symmetric active earth pressure based on a general lateral stress coefficient for general c-φ soil system is developed in the present paper. The results from the simplified slip line analysis are compared with those by Prater and results from numerical modeling. It is found that Prater's method may give surprising results and the limitations of Prater's results are also discussed in this paper. The authors have also investigated the importance of the lateral stress coefficient and the lower bound of the coefficient which are not considered in the past.

A generalized slip line solution to the active earth pressure on circular retaining walls

The slip line method was extended to calculate the active earth pressure on circular retaining walls in general cases. The slope of the backfill, wall friction and wall inclination were taken into account in the calculation. Two solutions were proposed and a computer program was coded for each one. By parametric study, it is observed that, the slope of the backfill, wall friction and wall inclination influences the results greatly, especially for the wall inclination. The comparison with existing solutions was made and a good agreement was observed. The generalized slip line solution is found useful in determining the active earth pressure in general cases, and can be referred to for design purpose.

Nonlinear Failure Criterion and Passive Thrust on Retaining Walls

The effect of nonlinearity of the failure criterion on the passive thrust on smooth and rough vertical retaining walls is studied theoretically. Limit analysis upper bound estimates based on block-type failure mechanisms are constructed. An alternative, a priori linearization, approach is discussed. It is shown that for smooth walls both approaches, as well as the Rankine-type slip line solution, yield similar results. For rough walls, however, the ambiguity in the a priori linearization makes it difficult to compare the results. This deficiency is absent in the limit analysis nonlinear solutions.