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Physical modelling and analytical evaluation of deformation zones in the extrusion of non-axisymmetric profiles Cover

Physical modelling and analytical evaluation of deformation zones in the extrusion of non-axisymmetric profiles

Open Access
|Dec 2025

Figures & Tables

Figure 1

Configuration of plastic zones during extrusion of (a) circular, (b) square, (c) triangle, and (d) rectangle cross-sections.

Figure 2

Test stand schematic diagram.

Figure 3

Tool set for extrusion testing of model material (1 – container base, 2 – support plate, 3 – die, 4 – container, 5 – billet, 6 – embosser, and 7 – punch).

Figure 4

Extrusion test dies: (a) Circular die opening and (b) triangular die opening.

Figure 5

Extrusion test dies: (a) Square-shaped die opening and (b) rectangular die opening.

Figure 6

Stress–strain relationship obtained experimentally in the upsetting test for Pb1.

Figure 7

Preparation of split ingots for testing using the visioplasticity method: (a) Split ingot, (b) half of ingot with grid applied, and (c) assembled ingot prepared for testing.

Figure 8

Grid deformation during extrusion of lead through flat dies with various orifice shapes (λ = 12).

Figure 9

Scheme of measuring the depth of the plastic zone L pz, the dead zone L dz, and the dead zone angle α dz.

Figure 10

Relationship between the plastic zone depth (L pz) and the cross-sectional shape of the extruded product.

Figure 11

Relationship between the height of the dead zone (L dz) and the cross-sectional shape of the extruded product.

Figure 12

Relationship between the dead zone angle (α dz) and the cross-sectional shape of the extruded product.

Figure 13

Relationship of maximum extrusion force (F max) to plastic zone depth (L pz), cross-sectional shape of the extruded product, and extrusion ratio (λ).

Figure 14

Relationship of maximum extrusion force (F max) to dead zone height (L dz), cross-sectional shape of the extruded product, and extrusion ratio (λ).

Figure 15

Relationship of maximum extrusion force (F max) to dead zone angle (α dz), cross-sectional shape of the extruded product, and extrusion ratio (λ).

Figure 16

Axial strains (ε z) and radial strains (ε r) as functions of ingot length for extruded cross-sections at λ = 12.

Figure 17

Velocity distribution in the die orifice region (λ = 12).

Figure 18

Division of the plastic zone volume into three components: V 1, V 2, and V 3.

Figure 19

Method for Selecting the Point that Defines the Boundary of the Plastic Zone.

Figure 20

Relationship between volume of plastic zone V pz, shape of an die orifice, and extrusion ratio λ.

Figure 21

Relationship between extrusion force (F max) obtained from experimental measurements and analytically evaluated deformation zone parameters (L pz, L dz, α dz, V pz) for non-axisymmetric profiles.

Figure 22

Plastic flow of material during the transition from a circular billet cross-section to product cross-sections: square, triangular (A-A), triangular (B-B), and rectangular (A-A).

Chemical composition of the material used in the study (Pb1) – weight%_

PbAgAsBiFeCuZnSbSn
99,980.00050.00050.01000.00060.00050.00050.00050.0005

Extrusion parameters_

Extrusion speed (mm/s)1
Extrusion ratio λ 3; 12; 60

Basic mechanical properties of the material used in the study (Pb1)_

Unit
Tensile strength R m MPa17
Yield strength R e MPa5
Elongation A %45
DOI: https://doi.org/10.2478/msp-2025-0040 | Journal eISSN: 2083-134X | Journal ISSN: 2083-1331
Language: English
Page range: 17 - 37
Submitted on: Jul 17, 2025
|
Accepted on: Nov 6, 2025
|
Published on: Dec 2, 2025
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Beata Pawłowska, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.