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.

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.

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.

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.

Deformations in Idealized 2D Extrusion Welding

2013 ◽  
Vol 554-557 ◽  
pp. 2507-2522 ◽  
Author(s):  
Henry Valberg ◽  
Dirk Nolte ◽  
Sepinood Torabzadeh Khorasani
Keyword(s):  
Strain Distribution ◽  
Dead Zone ◽  
Effective Strain ◽  
Metal Flow ◽  
Extrusion Process ◽  
Experimental Information ◽  
Grid Pattern ◽  
Seam Weld ◽  
Extrusion Welding ◽  
Material Points

Metal flow inside the container and in the metal behind a butt-ended die bridge in idealized aluminum extrusion welding has been investigated by FEA and experiment with respect to the deformation of the material flowing around the bridge and into the layers close the extrusion seam weld. Along the mid-axis of the extrusion process the effective strain subjected to the extrusion material can be determined in three different ways. One way is to determine the strains from grid pattern experiments that reveal the real deformations. When it comes to FEA there are two options; the strains can be determined from the initial and final positions of a number of material points distributed along the mid-axis of the material, where after traditional theoretical strain-equations can be used to calculate the effective strain distribution along the axis. Another possibility is to use the post-processor of the software to calculate the strain distribution. In this work the effective strain distribution along the mid-axis of the billet inside the container volume were determined by all these three methods. The effective strain in the thin layer of the squeeze zone ahead of the dead zone in front of the die bridge determined from the experiments was found to be much larger than the strains elsewhere along this axis. The same was the case when effective strain was determined by FEA from the computed position of the points, but this strain value was predicted approximately 10% lower than the corresponding value from the experiments in the layer with the heaviest strains. However, when this effective strain distribution was calculated by the post-processor of the software the high-strain layer in the squeeze zone was not revealed at all, instead the effective strains were predicted rather even over the whole length of the mid-axis. Corresponding effective strain distributions were determined along the mid-axis of the extrusion material in the weld chamber also, and after outflow of this material into the extrusion seam weld of the resulting profile where no experimental information is available. When this effective strain distribution was computed by FEA, based on initial and final position of points, very different strain values were obtained as compared to when same strains were collected directly from the post-processor. It is believed that the first results, i.e., the effective strains computed from the points are quite accurate, while those values calculated by the post-processor are less reliable.

Finite Element Analyses of Extrusion with a Two Stage Die and Manufacturing of Gradient Micro-Structures

2012 ◽  
Vol 528 ◽  
pp. 23-31 ◽  
Author(s):  
Yeong-Maw Hwang ◽  
Sergei Alexandrov ◽  
Yeau Ren Jeng ◽  
Tze Hui Huang ◽  
Oleg Borisovich Naimark
Keyword(s):  
Finite Element ◽  
Aluminum Alloy ◽  
Strain Rate ◽  
Cross Sections ◽  
Effective Strain ◽  
Hot Extrusion ◽  
Extrusion Process ◽  
Element Analysis ◽  
Strain And Strain Rate ◽  
Micro Structures

This paper aims to manufacture aluminum alloy metals with gradient micro-structures using hot extrusion process. The extrusion die is designed to have a straight channel part combined with a conical part. Materials pushed through this specially-designed die generate a non-uniform velocity distribution at cross sections inside the die and result in different strain and strain rate distributions. Accordingly, a gradient microstructure product can be obtained. At first, temperature, effective strain, and effective strain rate distributions at the die exit are discussed for different inclination angles in the conical die using the finite element analysis. Then, hot extrusion experiments are conducted to obtain aluminum alloy products with gradient micro-structures. The effects of the inclination angle on the grain size distribution at cross sections of the products are also discussed.

A New Formulation of Generalized Velocity Field for Axisymmetric Forward Extrusion Through Arbitrarily Curved Dies

1987 ◽  
Vol 109 (2) ◽  
pp. 161-168 ◽  
Author(s):  
D. Y. Yang ◽  
C. H. Han
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Effective Strain ◽  
Extrusion Pressure ◽  
Grid Pattern ◽  
Forward Extrusion ◽  
Area Reduction ◽  
Theoretical Predictions ◽  
Die Profile ◽  
New Formulation

A new analytic method is proposd for estimating the extrusion pressure, the final effective strain of the extruded billet, and the grid distortion patterns in axisymmetric forward extrusion through arbitrarily curved dies. A generalized kinematically admissible velocity field is derived to formulate an upper-bound solution. The corresponding upper-bound extrusion pressure is then obtained by optimizing the process parameters. The effects of area reduction, frictional condition, die length, and the die profile are discussed in relation to the extrusion pressure, the distorted grid pattern, and distribution of the final effective strain on the cross-section of the extruded billet. In the computation a biquadratic polynomial is chosen for the die profile. The work-hardening effect is incorporated in the formulation. Experiments are carried out for AISI 4140 steel billets at room temperature. The theoretical predictions both in the extrusion load and deformed configuration are in excellent agreement with the experimental results and the results computed by the finite element method.

Metal Cutting as a Property Test

1967 ◽  
Vol 89 (3) ◽  
pp. 489-493 ◽  
Author(s):  
F. Lira ◽  
E. G. Thomsen
Keyword(s):  
Strain Rate ◽  
Metal Cutting ◽  
Effective Strain ◽  
Strain Rates ◽  
Rate Analysis ◽  
Cutting Test ◽  
Strain And Strain Rate ◽  
Conventional Tests ◽  
Strain Data ◽  
Cutting Speeds

It is suggested that a metal-cutting test can be utilized as a high-strain-rate property test at strains larger than those normally achievable in conventional tests. The strain and strain-rate analysis is performed on the chip root of a composite specimen whose interface records the necessary information in terms of deformed grid lines which become streamlines. In the stress analysis, it is necessary to assume that the shear stress calculated from transducer forces is constant throughout a thin shear zone observed at the higher cutting speeds. The results can be converted into effective-stress and effective-strain data and should permit the establishment of stress, strain rate, strain, and temperature relationships for materials at the larger strains and at the higher strain rates.

The effects of strain and strain rate on residual microstructures in copper

1986 ◽  
Vol 44 ◽  
pp. 420-421
Author(s):  
M. F. Stevens ◽  
P. S. Follansbee
Keyword(s):  
Strain Rate ◽  
Applied Stress ◽  
Threshold Stress ◽  
Rate Sensitivity ◽  
Viscous Drag ◽  
Strain Rates ◽  
Strain And Strain Rate ◽  
Threshold Strength ◽  
Mechanism Transition ◽  
Intrinsic Strength

The strain rate sensitivity of a variety of materials is known to increase rapidly at strain rates exceeding ∼103 sec-1. This transition has most often in the past been attributed to a transition from thermally activated guide to viscous drag control. An important condition for imposition of dislocation drag effects is that the applied stress, σ, must be on the order of or greater than the threshold stress, which is the flow stress at OK. From Fig. 1, it can be seen for OFE Cu that the ratio of the applied stress to threshold stress remains constant even at strain rates as high as 104 sec-1 suggesting that there is not a mechanism transition but that the intrinsic strength is increasing, since the threshold strength is a mechanical measure of intrinsic strength. These measurements were made at constant strain levels of 0.2, wnich is not a guarantee of constant microstructure. The increase in threshold stress at higher strain rates is a strong indication that the microstructural evolution is a function of strain rate and that the dependence becomes stronger at high strain rates.

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