Flow Characteristics Through Conical Converging Dies

1966 ◽  
Vol 88 (4) ◽  
pp. 410-419 ◽  
Author(s):  
B. Avitzur
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Effective Strain ◽  
Flow Characteristics ◽  
Published Data ◽  
Grid Pattern ◽  
Effective Strain Rate ◽  
Strain And Strain Rate ◽  
Distorted Grid ◽  
Flow Through

A velocity field is considered to describe flow through conical dies. The expected distorted grid pattern is studied. Strain and strain rate fields are analyzed. Effective strain and effective strain rate distributions and their averages are defined. Application to processes like drawing extrusion and hydrostatic extrusion is discussed. Analysis is compared with experimental published data.

Analysis of Plastic Flow Through Inclined Planes in Plane Strain

1967 ◽  
Vol 89 (2) ◽  
pp. 361-375 ◽  
Author(s):  
B. Avitzur ◽  
J. Fueyo ◽  
J. Thompson
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Dead Zone ◽  
Effective Strain ◽  
Grid Pattern ◽  
Independent Variables ◽  
Strain And Strain Rate ◽  
Distorted Grid ◽  
Flow Through ◽  
Inclined Planes

A wide strip of thickness t0 is pulled or extruded through inclined planes converging with semiangle α and exit gap tf. While passing through the die, the thickness of the strip changes from t0 to tf, its length increases, but no change occurs in its width. A kinematically admissible velocity field is assumed to describe the flow. The expected distorted grid pattern is studied. Strain and strain rate fields are analyzed. Effective strain and effective strain rate distributions and their averages are defined. The same velocity field is utilized to obtain an upper-bound solution for the drawing and extrusion forces. Maximum reductions possible are predicted and the optimal included angle between the planes, required to minimize the forces, is evaluated. Formation and prevention of a dead zone are indicated. The analytical results are compared with other solutions and with published experimental data, where the independent variables are: Thicknesses t0 and tf, semiangle of the die α, friction (m), and flow stress of the material.

Comparison of Two Complete Solutions in an Axisymmetric Extrusion With Experiment

1969 ◽  
Vol 91 (3) ◽  
pp. 543-548 ◽  
Author(s):  
A. H. Shabaik ◽  
E. G. Thomsen
Keyword(s):  
Strain Rate ◽  
Effective Strain ◽  
Cone Angle ◽  
Low Friction ◽  
First Approximation ◽  
Strain And Strain Rate ◽  
Conical Die ◽  
Stream Lines ◽  
Half Cone ◽  
Half Cone Angle

An upper-bound and a potential solution to a forward extrusion problem were compared with experimental results obtained by the visioplasticity method. The process consisted of extruding a 2-in-dia billet of preforged lead through a conical die having a half-cone angle of 45 deg under the condition of relatively low friction. The comparison was made for steady state stream lines, velocities, strain rate components, effective strain and strain rate, grid distortion, and stress distribution. It was found that the curves were generally of similar shape and that some differences existed in magnitude only. It is suggested that the theoretical solutions can be used to advantage to a first approximation in predicting all important variables.

Creep Analysis of Orthotropic Rotating Cylinder

1980 ◽  
Vol 102 (4) ◽  
pp. 371-377 ◽  
Author(s):  
N. S. Bhatnagar ◽  
V. K. Arya ◽  
K. K. Debnath
Keyword(s):  
Strain Rate ◽  
Effective Stress ◽  
Anisotropic Material ◽  
Isotropic Material ◽  
Effective Strain ◽  
Angular Speed ◽  
Stress And Strain ◽  
Tangential Strain ◽  
Effective Strain Rate ◽  
Stress And Strain Rate

The stress and strain-rate distributions in the wall of a hollow thick-walled circular cylinder, rotating about its own axis with a constant angular speed, have been obtained using Norton’s law for the steady-state creep. The cylinder is assumed to be made of a homogeneous and orthotropic material. The numerical computations, for a number of steels and steel alloys commonly used to manufacture the cylinder, have been carried out for three cases of anisotropy. The effect of anistropy and of exponent n in creep law has been studied. It is observed that the stress and strain-rate distributions are significantly affected by the anisotropy of material and the value of exponent n. It is also noticed that the values of the effective stress for an anisotropic material for which the ratios of axial to tangential strain rate and of radial to tangential strain rate are equal to 1.2, are lower than the corresponding values for an isotropic material for which these ratios are 1.0. And, because of a power law between effective strain rate and effective stress, much lower values of the effective strain rate for the foregoing anisotropic material than those for the isotropic material will be obtained. Thus the use of the aforementioned anisotropic material may be beneficial for the manufacture of the cylinders because (i) it will result in a longer life for the cylinders (because of the lowest strain rate), or (ii) it will allow the cylinder to sustain larger forces without a risk of failure under creep.

A Theory on the Mechanics of Axisymmetric Extrusion through Conical Dies

1968 ◽  
Vol 10 (5) ◽  
pp. 367-380 ◽  
Author(s):  
E. R. Lambert ◽  
Shiro Kobayashi
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Effective Strain ◽  
Cone Angle ◽  
Basic Flow ◽  
Deformation Characteristics ◽  
Flow Lines ◽  
Admissible Velocity ◽  
Stress Components ◽  
Good Agreement

For axisymmetric extrusion through conical dies, an admissible velocity field without discontinuities was obtained by superposition of basic flow patterns. Based on this velocity field, the upper bound to the average forming pressure and the detailed mechanics were calculated for the extrusion of a rod with a semi-cone angle of 45° and a reduction of 75 per cent in area. Three different friction conditions along the die were considered and their influence on the deformation characteristics was discussed. Flow lines, velocity components, grid distortion, strain-rate components, effective strain rate, effective strain, and stress components were plotted. A comparison of the present results with those obtained experimentally (visioplasticity) shows good agreement.

The Study of Distorted Grid Patterns for Flow-Through Conical Converging Dies by the Multi-triangular Velocity Field

1984 ◽  
Vol 106 (2) ◽  
pp. 150-160 ◽  
Author(s):  
J. Pan ◽  
W. Pachla ◽  
S. Rosenberry ◽  
B. Avitzur
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Cone Angle ◽  
Wire Drawing ◽  
Perfectly Plastic ◽  
Distorted Grid ◽  
Upper Bound Technique ◽  
Independent Process ◽  
Flow Through ◽  
Reduction In Area

A variety of velocity fields may be used to analyze the intermediate and final distorted grids for the so-called “flow-through” metal forming processes such as wire drawing, rolling, extrusion, etc. In this paper the triangular velocity field describes the flow of homogeneous, perfectly plastic Mises’ material through a conical converging die. The traditional triangular velocity field was treated and the solution extended. The shape of the distorted grids was uniquely determined by the minimization of the power (drawing or extrusion stresses) required to cause its distortion for a given set of independent process parameters, i.e., process geometry-reduction in area and semi-cone angle, and friction. Actual power (forming stress requirements) was estimated by the upper-bound technique. For the unitriangular velocity field, the power was minimized with respect to the shape of the workpiece (the shape of the triangle). For the multitriangular velocity field, the power was minimized with respect to the shape and the number of triangles. Further, the number of triangles was treated as a real number. Thus, the accurate lower upper-bound was found and the reasonable solution in predicting real distortion grid patterns was then obtained. The analysis determines the severity of the distortion as a function of process geometry and friction.

scholarly journals Size- and speed-dependent mechanical behavior in living mammalian cytoplasm

2017 ◽  
Vol 114 (36) ◽  
pp. 9529-9534 ◽  
Author(s):  
Jiliang Hu ◽  
Somaye Jafari ◽  
Yulong Han ◽  
Alan J. Grodzinsky ◽  
Shengqiang Cai ◽  
...  
Keyword(s):  
Strain Rate ◽  
Optical Tweezers ◽  
Effective Strain ◽  
State Diagram ◽  
Elastic Solid ◽  
Incompressible Material ◽  
Cell Physiology ◽  
Mechanical Resistance ◽  
Scaling Analysis ◽  
Effective Strain Rate

Active transport in the cytoplasm plays critical roles in living cell physiology. However, the mechanical resistance that intracellular compartments experience, which is governed by the cytoplasmic material property, remains elusive, especially its dependence on size and speed. Here we use optical tweezers to drag a bead in the cytoplasm and directly probe the mechanical resistance with varying size a and speed V. We introduce a method, combining the direct measurement and a simple scaling analysis, to reveal different origins of the size- and speed-dependent resistance in living mammalian cytoplasm. We show that the cytoplasm exhibits size-independent viscoelasticity as long as the effective strain rate V/a is maintained in a relatively low range (0.1 s−1 < V/a < 2 s−1) and exhibits size-dependent poroelasticity at a high effective strain rate regime (5 s−1 < V/a < 80 s−1). Moreover, the cytoplasmic modulus is found to be positively correlated with only V/a in the viscoelastic regime but also increases with the bead size at a constant V/a in the poroelastic regime. Based on our measurements, we obtain a full-scale state diagram of the living mammalian cytoplasm, which shows that the cytoplasm changes from a viscous fluid to an elastic solid, as well as from compressible material to incompressible material, with increases in the values of two dimensionless parameters, respectively. This state diagram is useful to understand the underlying mechanical nature of the cytoplasm in a variety of cellular processes over a broad range of speed and size scales.

scholarly journals Structure and Flow in the Margin of the Barnes Ice Cap, Baffin Island, N.W.T., Canada

1973 ◽  
Vol 12 (66) ◽  
pp. 423-438 ◽  
Author(s):  
Roger Leb. Hooke
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Effective Strain ◽  
The Other ◽  
Baffin Island ◽  
Glacier Surface ◽  
Effective Strain Rate ◽  
Ice Cap ◽  
Single Maximum ◽  
Flow Law

The structure and flow field in the margin of the Barnes Ice Cap was determined through observations on the ice-cap surface, in four bore holes, and in a 125 m ice tunnel. A band of fine bubbly white ice with a single maximum fabric appears at the glacier surface about 160 m from the margin. This band is overlain by coarse blue ice with a four-maximum fabric, and underlain by alternating bands of fine ice with a single-maximum fabric and moderately coarse ice with a two or three-maximum fabric. The effective strain rate was determined from the bore-hole and tunnel deformation data, and possible variations in the other three parameters in Glen’s flow law, , were studied. It appears that τ xy is independent of depth near the surface, and that relative to the coarse blue ice, A is 40 to 50% lower in the white ice and possibly 10% lower in the fine blue ice. Dips of foliation planes decrease rapidly with increasing depth and distance from the margin. This foliation is assumed to have developed near and parallel to the bed some distance from the margin. An analysis based on this assumption predicts the observed change in dip, but suggests that it did not develop under the present flow field. The ice cap was probably thicker a few tens of years ago, and the observed foliation pattern may be a relict from that time.

scholarly journals Structure and Flow in the Margin of the Barnes Ice Cap, Baffin Island, N.W.T., Canada

1973 ◽  
Vol 12 (66) ◽  
pp. 423-438 ◽  
Author(s):  
Roger Leb. Hooke
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Effective Strain ◽  
The Other ◽  
Baffin Island ◽  
Glacier Surface ◽  
Effective Strain Rate ◽  
Ice Cap ◽  
Single Maximum ◽  
Flow Law

The structure and flow field in the margin of the Barnes Ice Cap was determined through observations on the ice-cap surface, in four bore holes, and in a 125 m ice tunnel. A band of fine bubbly white ice with a single maximum fabric appears at the glacier surface about 160 m from the margin. This band is overlain by coarse blue ice with a four-maximum fabric, and underlain by alternating bands of fine ice with a single-maximum fabric and moderately coarse ice with a two or three-maximum fabric.The effective strain rate was determined from the bore-hole and tunnel deformation data, and possible variations in the other three parameters in Glen’s flow law, , were studied. It appears that τxy is independent of depth near the surface, and that relative to the coarse blue ice, A is 40 to 50% lower in the white ice and possibly 10% lower in the fine blue ice.Dips of foliation planes decrease rapidly with increasing depth and distance from the margin. This foliation is assumed to have developed near and parallel to the bed some distance from the margin. An analysis based on this assumption predicts the observed change in dip, but suggests that it did not develop under the present flow field. The ice cap was probably thicker a few tens of years ago, and the observed foliation pattern may be a relict from that time.

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