scholarly journals Plastic flow of isotropic rigid body at uniform deformation

2021 ◽  
Vol 66 (2) ◽  
pp. 186-193
Author(s):  
O. M. Dyakonov
Keyword(s):  
Plastic Flow ◽  
Shape Change ◽  
Plane Deformation ◽  
Wire Drawing ◽  
The Body ◽  
Shear Stresses ◽  
Rigid Plastic ◽  
Rectangular Profile ◽  
Deformation Force ◽  
Material Points

The mathematical analysis of plastic flow processes under uniform plane, axisymmetric and volumetric deformation is carried out. The analysis is based on the external shape change of the body, which determines the movement of material points. It is shown that the plastic flow of an isotropic rigid-plastic body under plane deformation obeys the hyperbolic law, and for axisymmetric and volumetric deformations – the inverse square law. Spatial-geometric expressions of these laws made it possible to reveal and explain in a new way the physical essence of plastic shear. It is proved that the stressed state of a body under uniform tension-compression deformation is complex and cannot be defined as “linear”. The normal stress, which coincides with the direction of the resulting deformation force, is not the main one, since in the areas perpendicular to this direction, the shear stresses are not equal to zero. Examples of solving technological problems are given: extrusion of cylindrical billets and wire drawing, rolling of a wide strip of rectangular profile. It is shown that the problems of determining the stress-strain state of isotropic rigid-plastic bodies along the known trajectories of movement of material points are statically definable.

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 1. Kinematic and stress states of the billet

2021 ◽  
pp. 65-71
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Complete System ◽  
Shape Change ◽  
Plane Deformation ◽  
System Of Equations ◽  
Flow Rates ◽  
Die Forging ◽  
The Matrix ◽  
Stress States ◽  
Theory Of Plastic Flow

On the basis of the complete system of equations of the theory of plastic flow, the kinematic and stress states of the billet are determined when the channels are extruded under conditions of plane deformation of the misaligned position of the punch and the matrix. Keywords: die forging, extrusion, misaligned position, punch, matrix, plane deformation, plastic flow rates, stresses. [email protected]

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 2. Determination of the extrusion force, maximum pressure on the matrix wall and the heights of the walls, taking into account the elastic deformation jf the matrix

2021 ◽  
pp. 63-69
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Elastic Deformation ◽  
Shape Change ◽  
Plane Deformation ◽  
Maximum Pressure ◽  
Extrusion Force ◽  
System Of Equations ◽  
The Matrix ◽  
Theory Of Plastic Flow

On the basis of the system of equations of the theory of plastic flow, the forces, the maximum pressure on the wall of the matrix and the heights of the obtained walls when extruding channels are determined, taking into account the elastic deformation of the matrix. Keywords: die forging, extrusion, misalignment, punch, matrix, plane deformation, stresses. [email protected]

Blunting of a Plane Strain Crack Tip Into a Shape With Vertices

1977 ◽  
Vol 99 (4) ◽  
pp. 290-297 ◽  
Author(s):  
Robert M. McMeeking
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Crack Tip ◽  
The Body ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Crack Tips ◽  
Stress And Deformation ◽  
Material Points ◽  
Growth Of Voids

When monotonically increasing tensile opening loads are applied to a cracked, plane strain, elastic-plastic body, the crack tip will blunt until fracture occurs. At least within the rigid-plastic model for nonhardening material, the shape of the blunted tip is not unique. The blunted tip shape may have two or more sharp corners, or be smoothly curved. When the shape involves corners, the opening is predominantly accommodated by shearing of the material at the corners. This shearing transports material from the interior of the body onto the crack surface. In contrast, the smoothly blunted crack tip involves no such transfer of material points from the interior. However, the smoothly blunted crack, which was originally sharp, involves infinite strains on the crack tip surface. The crack with corners on the tip has large but finite strains on the crack tip surface. The stress and deformation field in front of a crack with two corners and with three corners on the tip, as calculated using the slip line method, is presented for the nonhardening, fully plastic, deeply cracked, double edge-notched thick panel. As in the case of the smoothly blunted crack tip, the elevated stress between the crack tips cannot be maintained very close to the crack tip, due to a lack of constraint. The stress distribution in the case of the crack tip with vertices on it differs from that of the smoothly blunted crack tip case. In particular, immediately in front of the crack tip with three corners, the stress is higher than that immediately in front of the smoothly blunted crack tip. An approximation for a power law hardening material indicates that the maximum stresses near the blunted crack tip is much the same for a crack with vertices on the tip as for a smoothly blunted crack tip. The details of the stress distribution, though, will depend on the mechanism by which the crack blunts. These results for stress and strain and some calculations of the growth of voids near the crack tips indicate the same fracture process could lead to different fracture toughnesses, depending on the type of mechanism by which the crack blunts.

scholarly journals Movement of a finite body in channel flow

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160164 ◽  
Author(s):  
Frank T. Smith ◽  
Edward R. Johnson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Flow Instability ◽  
Flow Direction ◽  
Finite Size ◽  
The Body ◽  
Thin Body ◽  
Shear Stresses ◽  
Unsteady Interaction ◽  
High Reynolds

A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at medium-to-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos ⁡ ( π / 7 ) , i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

scholarly journals An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

2009 ◽  
Author(s):  
Lin Sun ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Incompressible Flows ◽  
Simple Algorithm ◽  
Flow Region ◽  
Solid Material ◽  
The Body ◽  
Immersed Boundary ◽  
Material Points ◽  
Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

scholarly journals Rock Failure Analysis Based on a Coupled Elastoplastic-Logarithmic Damage Model

2017 ◽  
Vol 62 (4) ◽  
pp. 753-774
Author(s):  
M. Abdia ◽  
H. Molladavoodi ◽  
H. Salarirad
Keyword(s):  
Constitutive Model ◽  
Plastic Flow ◽  
Mechanical Response ◽  
Damage Model ◽  
Yield Function ◽  
Irreversible Thermodynamics ◽  
Stiffness Degradation ◽  
Shear Stresses ◽  
Rock Materials ◽  
Damage Process

Abstract The rock materials surrounding the underground excavations typically demonstrate nonlinear mechanical response and irreversible behavior in particular under high in-situ stress states. The dominant causes of irreversible behavior are plastic flow and damage process. The plastic flow is controlled by the presence of local shear stresses which cause the frictional sliding. During this process, the net number of bonds remains unchanged practically. The overall macroscopic consequence of plastic flow is that the elastic properties (e.g. the stiffness of the material) are insensitive to this type of irreversible change. The main cause of irreversible changes in quasi-brittle materials such as rock is the damage process occurring within the material. From a microscopic viewpoint, damage initiates with the nucleation and growth of microcracks. When the microcracks length reaches a critical value, the coalescence of them occurs and finally, the localized meso-cracks appear. The macroscopic and phenomenological consequence of damage process is stiffness degradation, dilatation and softening response. In this paper, a coupled elastoplastic-logarithmic damage model was used to simulate the irreversible deformations and stiffness degradation of rock materials under loading. In this model, damage evolution & plastic flow rules were formulated in the framework of irreversible thermodynamics principles. To take into account the stiffness degradation and softening on post-peak region, logarithmic damage variable was implemented. Also, a plastic model with Drucker-Prager yield function was used to model plastic strains. Then, an algorithm was proposed to calculate the numerical steps based on the proposed coupled plastic and damage constitutive model. The developed model has been programmed in VC++ environment. Then, it was used as a separate and new constitutive model in DEM code (UDEC). Finally, the experimental Oolitic limestone rock behavior was simulated based on the developed model. The irreversible strains, softening and stiffness degradation were reproduced in the numerical results. Furthermore, the confinement pressure dependency of rock behavior was simulated in according to experimental observations.

Pressure crack-figures on diamond faces I. The octahedral face

1955 ◽  
Vol 230 (1182) ◽  
pp. 287-293 ◽  
Keyword(s):  
Plastic Flow ◽  
Strong Evidence ◽  
Crack Formation ◽  
The Body ◽  
Multiple Cracks ◽  
Primary Crack ◽  
Typical Instance ◽  
Surface Distortions ◽  
Multiple Beam Interferometry ◽  
Ring Cracks

By pressure with a diamond ball, oriented hexagonal-shaped ring cracks (pressure marks) are produced on the octahedral face of a diamond. Typical ring cracks have a side length of the order of 1/25mm and appear at stresses of the order of 1·4 x 10 11 dyn cm -2 . The development of these figures is studied, using regularly increasing loads. After primary crack formation, further increase of loading leads to the appearance of concentric multiple cracks. The permanent surface distortions accompanying these percussion marks are studied with multiple-beam interferometry. It is established that the region within the hexagonal figure is effectively at the zero undisturbed level. At the perimeter there is a discontinuity, the surface rising in a typical instance by some 300 Å. There is then a gradual smooth fall off to zero level. It is considered that the interferograms offer strong evidence for the existence of plastic flow. The volume of displaced material surrounding a typical primary crack is some 10 -9 cm 3 . The mechanism of the hexagonal crack formation is discussed in terms of directions of easy cleavage, and accompanying cracking effects within the body of the crystal are discussed.

Rigid-Plastic Finite Element Simulation of Cold Forging and Sheet Metal Forming by Eulerian Meshing Method

2014 ◽  
Vol 970 ◽  
pp. 177-184 ◽  
Author(s):  
Wen Chiet Cheong ◽  
Heng Keong Kam ◽  
Chan Chin Wang ◽  
Ying Pio Lim
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Large Deformation ◽  
Sheet Metal ◽  
Metal Forming ◽  
The Body ◽  
Cold Forging ◽  
Rigid Plastic ◽  
Element Analysis ◽  
Linear Solution

A computational technique of rigid-plastic finite element method by using the Eulerian meshing method was developed to deal with large deformation problem in metal forming by replacing the conventional way of applying complicated remeshing schemes when using the Lagrange’s elements. During metal forming process, a workpiece normally undergoes large deformation and causes severe distortion of elements in finite element analysis. The distorted element may lead to instability in numerical calculation and divergence of non-linear solution in finite element analysis. With Eulerian elements, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. Four types of cold forging and sheet metal clinching were conducted to investigate the effectiveness of the presented method. The proposed method is found to be effective by comparing the results on dimension of the final product, material flow behaviour and punch load versus stroke obtained from simulation and experiment.

On the Plastic Flow of Coulomb Solids Beyond Original Failure

1959 ◽  
Vol 26 (4) ◽  
pp. 599-602
Author(s):  
A. W. Jenike ◽  
R. T. Shield
Keyword(s):  
Velocity Field ◽  
Stress Field ◽  
Plastic Flow ◽  
Yield Function ◽  
Two Dimensions ◽  
Rigid Plastic ◽  
Variable Yield ◽  
Angle Of Friction ◽  
Effective Angle

Abstract Principles developed for rigid-plastic solids exhibiting Coulomb’s properties are adapted to the analysis of flow beyond original failure. A variable yield function is proposed to account for the changes of cohesion during flow and equations are evolved for the stress field in two dimensions. It is shown that, while in the stress field an effective angle of friction larger than the actual angle of friction is mandatory for these materials, in the velocity field the materials can be assumed incompressible.

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