1. A new severe plastic deformation technique: Twist Extrusion
Yan Beygelzimer
Donetsk Institute of Physics and Technology
Ukrainian National Academy of Sciences

2. Ultrafine-grained materials
What do I mean?
Metals with grain size ~ nm
Why are they appealing?
Dramatically improved and/or different properties not seen in conventional materials, for example, increased strength and toughness.
Where can they be applied?
Medical and electronic applications
I am very thankful to professor Li for inviting me to give a talk here.
The focus of my talk will be on a new technique for obtaining ultrafine-grained materials, but first
I want to explain what I mean by such materials.
By UFG materials I mean metals with ….
Due to their refined microstructure (small grain size) they provide attractive properties that cannot be achieved
in conventional materials with the same chemical composition.
Among such attractive properties are ….
What are the applications?
It is an interesting and broad question, but totally outside the scope of this talk.
I personally think that the most promising are medical and electronic applications.

3. Ultrafine-grained materials
How does one obtain UFG materials?
Roughly speaking, there are two major directions:
Consolidation of powder materials
Refining of coarse-grained materials
We will be concerned with the second direction
What are the methods for obtaining UFG materials?
We are going to talk about the second direction here.

4. UFG materials obtained via refining
The standard way:
Severe Plastic Deformations (SPD) of coarse-grained materials
Now the term “SPD” covers any large plastic deformation obtained using simple shear
The main method of refiining coarse-grained materials is using severe plastic deformations.
Now the term “SPD” covers any large deformation obtained using simple shear.

5. Refining of materials via SPD
This cartoon illustrates the process of grain refining using SPD

6. Refining of materials via SPD

7. Standard SPD Techniques
High Pressure Torsion
Equal Channel Angular Pressing

8. High Pressure Torsion

9. Equal Channel Angular Pressing
dgdgdg

10. Main properties of SPD techniques
High Pressure Torsion
gives high quality UFG materials
specimen size: thickness ~10m, diameter ~ 5mm, limited industrial use
Equal Channel Angular Pressing
lower quality materials, but still good enough
specimen size: length ~100mm, diameter
~20mm
Gives the highest quality ufg materials
Specimens are small
Therefore the technique has limited industrial use
Specimen size is big enough

11. This talk: We propose a new SPD technique – Twist Extrusion (TE)
We show that it extends the potential of severe plastic deformations for obtaining bulk UFG materials. This is due to certain properties of the strain-stressed state of the material in the twist matrix, as well as some technological potentialities of direct extrusion.

12. Outline Main idea of TE Technological schemes TE mechanics
Relationships between TE and other SPD processes
TE equipment
Preliminary experimental results
Conclusion
P.S.
Finally I am going to talk about a new SPD scheme that we propose. We called it Twist Extrusion
This is the plan for the rest of the talk.
First, I am going to explain the main idea of TE
Then I will talk about different technological schemes and the theory of the process.
After that, I will discuss the relationships between TE and other SPD techniques
Then I will briefly describe the equipment that we used and preliminary experimental results that we obtained.
Finally, I will conclude and briefly talk about the research currently done in my lab.

13. The main idea of TE: Twist channel
The main idea is to extrude a prism bulk through a die with a twist channel.
The angle between the twist line and the direction of extrusion change along the vertical axis of the die;
furthermore, it is equal to zero on its starting and ending points.
The above properties of the channel geometry guarantee that the extrusion does not change the form
of the work-piece, which allows us to accumulate severe plastic deformations by iteratively extruding
the bulk through the die.

14. The main idea of TE: Equivalent strain e1
Twist channel
Equivalent strain e1
The shape and the dimensions of the work-piece do not change!

15. The main idea of TE:
Equivalent strain e2
Twist channel

16. The main idea of TE: and so on…
Refining is a result of large plastic deformations

17. Twist extrusion work-piece
Cross-section of a work-piece can be arbitrary (which is hard to achieve in ECAP)
By extruding on a mandrel, it is possible to obtain products with inner channels (which is impossible in ECAP).
These are the immediate technological advantages of TE

18. Technological schemes for Twist Extrusion
Technological implementation of TE is possible with the use of known metal forming processes.
Moreover, technological implementation of TE is easy, because it can be done using well-known metal
forming processes

19. Twist Extrusion based on Hydro-extrusion
Allows one to achieve:
high plasticity
small contact friction
high-speed deformation
(with the strain rate ~104 с-1)
Main disadvantage:
The necessity to condense the workpiece.
This is one possible technological scheme based on hydro-extrusion

20. Twist Extrusion based on hydro-mechanical extrusion
Advantage: does not have the problems of hydro-extrusion-based scheme.
Metal plasticity is also high (due to the pressure of surrounding liquid)
However, the value of the maximum deformation during one pass is limited by the fact that the workpiece can be deformed outside the matrix.
Another possibility is a scheme based on hydro-mechanical extrusion
…limited by the fact that the workpiece can become unstablle. In other words, it can be deformed outside the matrix.

21. Twist Extrusion based on direct extrusion with a thick lubrication layer
Metal plasticity is high.
The value of the maximum deformation during one pass of pressing is not limited by the unstability of the workpiece.
Friction loss is higher than in other schemes.
A different scheme can be based on the direct extrusion with a thick lubrication layer

22. Semicontinuous hydrostatic Twist Extrusion-Drawing
Allows one to obtain long-length products (e.g. wire)
Metal plasticity is lower than in previous schemes due to stretching strains of drawing.

23. Twist Extrusion based on Linear Continuous Extrusion
Allows one to obtain long-length products
Metal plasticity is high
Deformation per pass is limited to a condition of friction

24. Mechanics of TE
In order to investigate the mechanics of TE we performed experiments using modeling clay specimens.
Based on the experiments we suggested a kinematically admissible velocity field, which was then used for investigating the mechanics of TE using the variational principle.

25. The experiment using modeling clay
We extruded a clay specimen (with color markers) through a dismountable matrix.
The figure shows a half of the matrix with a template cut from the original specimen

26. The experiment using modeling clay (cont.)
The experiment showed that the markers were smeared, which signifies that the material cross-flows inside the cross-section.
Figure: cross-sections of the specimen with (a) initial and (b) smeared markers.

27. Kinematically admissible velocity field
V=V1 + V2
V1 - is the component of KF related to motions of the cross-section as a whole;
V2 - is the component of KF related to the cross-flow within the cross-section.
V V2 x y z  z 
Therefore, we represent the kinematically adimissible velocity field as a sum of two components:
one capturing the motion of the cross-section as a whole, the second one related to the cross-flow within the cross-section  y x

28. Kinematically admissible velocity field (cont.)
- function defining the form of the cross-section,
=0 on the boundary,
>0 inside the cross-section,
<0 outside the cross-section on the boundary,
These are the expression for the two components
|P|=|V2| on the boundary,
P is a parameter defined by the variational principle

29. Computational results Velocity fieldb
a=15 mm, b=25 mm
m=60; =90; m=0,15 a

30. Computational results Equivalent strain
a=15 mm, b=25 mm
m=60; =90; m=0,15
The size of the equivalent deformation during one pass can be estimated using the formula
e=tan(),
where  is the maximal value of the twist angle.

31. Relationship between TE and other SPD processes
TE includes elements ECAP, HPT and Forging. In the extreme it is basically reduced to these processes. For example, when b/a is large, then TE is similar to HPT. In the case when the extrusion axis is far from the specimen boundary, then TE corresponds to ECAP.
The ratio of b to a

32. Our Installation for Twist Extrusion
We have the following two installations:
TE based on hydro-extrusion and hydro-mechanical extrusion;
TE based on direct extrusion with thick lubrication layer.

33. Twist extrusion based on hydro-extrusion and hydro-mechanical extrusion

34. Installation for Twist Extrusion based on Hydro-Extrusion and Hydro-Mechanical Extrusion

35. Twist extrusion based on direct extrusion with thick lubrication layer

36. Experimental results
Preliminary experiments on copper and titanium showed the following:
Metal flow is twisted.
The hardening of metals is high.
Grain refining is intense.

37. Experimental results for copper
Figure: a specimen in a twist die

38. Experimental results for copper (cont.)
The specimen after the TE based on the direct extrusion with a thick lubrication layer
Dimensions: 25x15x80mm, Extrusion speed: V0.002 m/s, The pressure during the third pass: P=600 MPa The hardness after the first three passes: (Hm)max=1150 MPa

39. Experimental results for copper (cont.)
Figure: the specimen after high-speed Twist hydro-extrusion.
Dimensions: 13x13x500mm, Pressure: P=1100 Mpa, Shot rate: V100 m/s.
Interesting! Unlike in slow extrusion, the specimen came out twisted. This is due to the kinetics of plastic deformations.

40. The structural evolution of titanium at room-temperature TE
Initial grain size is d50 m.
After three TE passes (=6), we already have d1m. a b c d
Cross -
50 m
Shear strain: a-=0, b-=2, c,d-=6

41. Condition of the specimen
Mechanical properties of titanium after TE (three passes, shear strain 6)
Condition of the specimen
в MPa
0.2 MPa
, %
initial state
470
400 30
TE (c)
882
800 15
TE (c)+TT
900
733 37
TE (l)
541
486 12
TE (l)+TT
523
465
TE (c)+TT+CR,
834
804
TE (l)+TT+CR
773
743 32
Cross-section (c)
This table illustrates the mechanical properties of titanium after the first three passes of TE
The first line shows the initial properties of the specimen. Notice that the tensile strength is low,
And the plasticity is high.
The second line shows the properties of the cross-section cut of the specimen after the three passes.
Notice that tensile strength increased, but the plasticity went down.
However, if you combine TE with annealing, the strength does not degrade too much,
but the plasticity dramatically goes up.
Next line shows the properties of the longitudinal cut of the specimen.
The properties are rather bad.
Adding annealing does not significantly improve the situation.
However, when you combine TE with annealing and cold rolling, both cuts have good properties.
Longitudinal (l)
*TT denotes annealing for 1 hour at 300C.
CR-cold rolling with 50% reduction

42. Anisotropy of the mechanical properties of TE products
We believe that the anisotropy is caused by a severe shift along the planes orthogonal to the extrusion axis. When the pressure is not sufficient, the shift results in the occurrence of several layers of micro-pores along these planes.
The properties in a longitudinal direction can be improved both by increasing the counter-pressure and by combining TE with other metal forming processes.
Pc- counter pressure
I will explain what, as I believe, causes such anisotropy of the mechanical properties.
… higher than the initial….
These are our preliminary investigations, the reason may be much more complicated. 
Small Pc,
Big Pc,

43. Conclusion
Even a single pass of Twist Extrusion provides sufficiently large severe plastic deformations of prism samples.
The size of the equivalent deformation during one pass can be estimated using the formula e=tan(), where  is the maximal value of the twist angle.
The dimensions of the specimen do not change after TE, which allows to repeat TE iteratively, accumulating deformations.

44. Conclusion Several TE passes already suffice to obtain UFG materials
TE expands the potential of other SPD techniques in controlling the structure of materials and the specifications of end products.
To eliminate the anisotropy of properties we recommend to combine TE with ECAP and traditional metal forming processes (rolling, drawing).

45. P.S.
We investigated the evolution of metal structure under plastic deformation, in particular TE. This is a multi-level problem, whose main difficulty is due to the fact that the processes on different levels are interdependent.
And finally I want to make one point. We ….
This cartoon illustrates the point

46. P.S. The cartoon speaks for itself.
This is the ruler of the macro-world and
this is the ruler of the micro-world, but it is not clear who is governing whom,
They are interdependent.

47. P.S. (cont.)
Classical models of mechanical plasticity do not allow to formulate and solve such problems.
Such models are built on constitutive relationships for the Representative Volume Element (RVE). Here RVE is considered to be a point without dimensions, while the most interesting and exciting processes happen inside RVE

48. P.S. (cont.)
The situation is the same as the one that Alice experienced in the beginning of her adventures in the Wonderland. Through a tiny door, she saw a rat hole and a beautiful garden beyond it. But she couldn’t enter the garden, because the hole was too narrow.

50. Our goal
It happened so that Alice shrank, which made it possible for her to enter the Wonderland.
We are trying to do the same.
We developed a cellular model of polycrystals and proposed two new notions for representing microprocesses on the macrolevel:
thick yield surface and the cloud of internal stress.

51. Our approach Our approach is based on the following ideas:
First of all, this is the self-consistent field approach.
Secondly we use a cellular automata technique,
and we suggest to ….

52. Structure of RVE 1
Representative volume element (RVE) is the smallest possible volume that can represent the properties and the behavior of the whole body

53. Structure of RVE 2 Each RVE is split into 27 (333) smaller elements.
In general, other spatial structures and other numbers of components are possible.

54. Structure of RVE 3
Each smaller cube is also split into 27 smaller elements that repeat their structure.

55. Structure of RVE 4

56. Structure of RVE 5
Plastic deformation of a complex unit is carried out by the joint strain and rotation of its constituent units.
Inelastic deformation of a simple unit is performed via the dislocational glide.

57. Hierarchy of levels 1
level n+1
level n

58. Hierarchy of levels 2

59. Thick yield surface (TYS) and the Cloud of internal stresses (CIS) of polycrystalline materials
TYS and CIS recursively split
into smaller elements. Every split
occurs by splitting the higher-level
elements into lower-level elements.
The structure can be treated as a fractal in case of scaling.

60. Cellular Model Simulation
We modeled the loading of a poly-crystal along the radius path.
Every time we entered the thick yield surface so that the residual strength was guaranteed to be at least .2
The following slides show the evolution of the cloud during consecutive loadings.

61. Cloud of internal stresses (calculated using Cellular model)

62. Cloud of internal stresses (calculated using Cellular model)

63. Cloud of internal stresses (calculated using Cellular model)

64. Cloud of internal stresses (calculated using Cellular model)

65. Remarks Pink points denote the centers of clouds in previous loadings.
It can be assumed that these points lie on a classical loading surface.
The following slides illustrate the evolution of the cloud at sign-alternating loadings. This corresponds to the Bauschinger effect.

66. Cloud of internal stresses (calculated using Cellular model)
Loading

67. Cloud of internal stresses (calculated using Cellular model)
Continuing to load in the same direction

68. Cloud of internal stresses (calculated using Cellular model)
Unloading

69. Cloud of internal stresses (calculated using Cellular model)
Continuing to unload

70. Cloud of internal stresses (calculated using Cellular model)
Continuing to unload

71. Cloud of internal stresses (calculated using Cellular model)
Finishing to unload

72. Cloud of internal stresses (calculated using Cellular model)
Just a new geometrical object allowing one to estimate internal stresses according to the change of its size, shape, fractal dimension, etc.

73. Acknowledgments We are grateful to Professor Li for the invitation.
We acknowledge the travel support of CRDF grant TGP654.
We also thank Vladimir Stolyarov and Hamit Salimgareev for mechanical testing of titanium specimens.