With High Ductility? How to Make Strong Metals Yan Beygelzimer

With High Ductility? How to Make Strong Metals Yan Beygelzimer
Donetsk Institute of Physics and Technology National Academy of Sciences of Ukraine The title of my talk is “”.

Outline 1. How do we try to do it? First way: fragmentation
Second way: consolidation 2. How do we try to explain and to predict it? Mechanics of the processing Structure, ductility, strength 3. Final Thoughts Here is the outline of my talk. First I will give some motivation for why the problem is important. Then I will justify the use of continuum mechanics. In the main part of the talk I will describe the model and present the implications.

How do we try to do it? Severe plastic deformation (SPD)
Twist Extrusion First way: Fragmentation Second way: Consolidation Here is the outline of my talk. First I will give some motivation for why the problem is important. Then I will justify the use of continuum mechanics. In the main part of the talk I will describe the model and present the implications.

Some of the SPD Techniques
Equal Channel Angular Extrusion High Pressure Torsion This slide shows the schemes. In HPT, a thin disk is twisted between two anvils under pressure. In ECAE, a bulk specimen is extruded through an angular channel. As a result, the bulk accumulates large equivalent strain 3d Forging Twist Extrusion (Y.Beygelzimer, 1999)

The idea of TE: Twist channel
The main idea is very simple. A prism bulk is extruded through a die with a twist channel. Everything is shown on the slide. (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.)

The idea of TE: Equivalent strain e1
Twist channel Equivalent strain e1 As a result, the bulk accumulates equivalent strain of about 1. The shape and the dimensions of the work piece don’t change. The shape and the dimensions of the work-piece do not change!

The idea of TE: Equivalent strain e2
Twist channel Extruding the same specimen again gives equivalent strain of about 2 and so on. This way repeated twist extrusion… Repeated twist extrusion leads to grain refinement

Twist Extrusion: Two in One
Fragmentation Consolidation Twist Extrusion Here is the outline of my talk. First I will give some motivation for why the problem is important. Then I will justify the use of continuum mechanics. In the main part of the talk I will describe the model and present the implications.

Grains refinement. UFG materials
Fragmentation Grains refinement. UFG materials Breaking of a brittle particles This cartoon illustrates the process of grain refining using SPD This is what SPD does.

Why should we care about grain refinement during severe plastic deformation?
This is one of few effective techniques for obtaining ultrafine-grained (UFG) materials First, I should convince (ubedit’) you that the problem is important. So why should we care about … The reason is that this is one of few ….

Grain refinement Coarse
This cartoon illustrates the process of grain refining using SPD This is what SPD does.

Grain refinement UFG

Ultrafine-Grained Materials
What are they? Metals with grain size ~ nm Why are they appealing? Significantly improved properties Qualitatively different properties not seen in conventional materials I want to define what UFG materials are. They are metals with grain size ~ nm. Due to their refined microstructure (by which I mean small grain size) they provide attractive properties that cannot be achieved in conventional materials with the same chemical composition.

High strength and ductility of UFG materials
! ! One of such attractive properties is a combination of high strength and high ductility (which is important in many applications) R.Z. Valiev, I.V. Alexandrov, Y.T. Zhu and T.C. Lowe, “Paradox of Strength and Ductility in Metals Processed by Severe Plastic Deformation,” J. Mater. Res. 17, 5-8 (2002).

Twist extrusion of the Ti
50 mm 50 mm This slide shows one of our experimental results on UFG Ti obtained by TE. Initial state After 3 passes

Twist extrusion of the Ti
This slide shows one of our experimental results on UFG Ti obtained by TE.

SPD of the Ti This slide shows one of our experimental results on UFG Ti obtained by TE.

Plates for traumatology are made of UFG Ti
This slide shows one of our experimental results on UFG Ti obtained by TE.

Twist extrusion of the Al-Mg-Sc-Zr alloy
Chemical composition: Al - 3 wt.%Mg - 0,3 wt.%Sc – 0,10 wt.%Zr Initial grain size dav=100 µm Twist extrusion: T= ºC 5 passes CW + 1 pass CCW Standard direct extrusion: T= ºC dav= µm dmin= 0.129µm dmax=1.032 mm dav=0.325 µm dmin= 0.077µm dmax=0.671 mm

SPD of the Cu * * * *N. Krasil’nikov, R.Valiev 440 15 420 18 426 393
ECAE, 16 passes, without BP 18 426 393 TE, 3 passes, with BP Uniform elongation, % Tensile strength MPa Yield stress, State 40 145 80 As received 14 360 320 ECAE, 2 passes 25 470 ECAE, 16 passes, * * * *N. Krasil’nikov, R.Valiev

ECAE of the Cu Wei Wei, Guang Chen, Jing Tao Wang, Guo Liang Chen
This slide shows one of our experimental results on UFG Ti obtained by TE. Wei Wei, Guang Chen, Jing Tao Wang, Guo Liang Chen Journal of Advanced Materials 2005 (in press)

Three present-day ways to increase strength and ductility of UFG materials
Cryogenic processing to produce a bimodal grain structure Formation of second-phase particles to modify the propagation of shear bands Developing aging and annealing treatments that can be applied to the UFG materials in the post-processed condition I want to define what UFG materials are. They are metals with grain size ~ nm. Due to their refined microstructure (by which I mean small grain size) they provide attractive properties that cannot be achieved in conventional materials with the same chemical composition.

Breaking of a brittle particles
This cartoon illustrates the process of grain refining using SPD This is what SPD does.

TE of secondary Al alloy
Al-88%; Si-9,5% … Initial state 1 pass σy=50МPа δ=1% σy=205МPа δ=14%

Twist Extrusion of phosphorous Cu (P 9%)
1 pass Initial state 11 420 Twist Extrusion 4 360 Direct Extrusion, µ=4.5 d , % YS, МPа Treatment YS,MPa Back pressure = 200 MPa, T= 623 K

Twist extrusion of the Al-Mg-Sc-ZR alloys
Chemical composition: Al – 3 wt.%Mg - 0,3 wt.%Sc – 0,15 wt.%Zr SEM, As-deformed structure, TE – 5 passes, Tdef= ºC Longitudinal section SEM, As-cast structure Cross-section 0.5µm 0.5µm

Consolidation I will discuss two questions about SPD techniques.
I believe that these questions are among the most important ones when working with SPD.

Consolidation of nanostructural Cu powder by Twist Extrusion
Back pressure = 200 MPa, T= 473 K Initial powder, D=250 µm 1 pass 2 passes Compression test after 2 passes: Yield stress = 450 MPa Breaking strain = 28% Tensile test after 2 passes: Yield stress = 200 MPa Breaking strain = 15%

Consolidation of nanostructural Cu powder by Twist Extrusion
State Density, % Diameter of the coherent-scattering region L, nm powder - 100 TE, 1 path 99.2 36 TE, 2 paths 99.6 55

Consolidation of amorphous Al86Ni6Co2Gd6 melt-spun ribbons by Twist Extrusion
Microhardness and the volume fraction of the amorphous phase in the compacted samples. X-ray diffraction patterns

Consolidation of the cutting of the secondary Al alloy by Twist Extrusion
d=12 mm Yield stress = МPа; = 20-24%

How do we try to explain and to predict it?
The questions Mechanics of the processing The Problem The Model Predictions I will discuss two questions about SPD techniques. I believe that these questions are among the most important ones when working with SPD.

The questions Parameters of the process?
Strength and Ductility of the materials? Structure of the materials? I will discuss two questions about SPD techniques. I believe that these questions are among the most important ones when working with SPD.

Mechanics of metal flow
I will discuss two questions about SPD techniques. I believe that these questions are among the most important ones when working with SPD.

Stream lines 4 5 6 1 2 3 7 8

Kinematically-admissible velocity field
1. Volume constancy condition 2. Boundary condition I will discuss two questions about SPD techniques. I believe that these questions are among the most important ones when working with SPD.

Kinematically-admissible velocity field
- form function I will discuss two questions about SPD techniques. I believe that these questions are among the most important ones when working with SPD. P- function which is varied

Finding function P on the experimental stream lines
Theoretical stream line

Metal Deformation under Twist Extrusion
We showed that most of the deformation achieved by Twist Extrusion is Simple Shear at the ends of the twist channel. We showed that most of the deformation achieved by Twist Extrusion is Simple Shear at the ends of the twist channel

Equivalent strain for TE pass
The average equivalent strain during one pass e=tan() Distribution of the strain Yield stress, Cu

The Problem with Theoretical Model
One of the main problems faced by any theoretical model is the need to capture the multi-level character of plastic deformation One of the main problems faced by any approach for describing grain refinement and fracture Is the need to capture the multi-level character

Metal Structure is Determined by the Image of the Loading Process
P1,T1,... P2,T2,... P3,T3,... P4,T4,... Grain refinement e2 e1

But … The Image of The Loading Process depends on this structure
The reason is that the structure defines the mechanical properties of the materials.

Macro-Micro Interdependency
Metal Structure Image of the Loading Process I call this macro-micro interdependency

The Problem We are trying to produce a given ultrafine homogeneous structure In reality, however, the specimen may respond with a number of bad things: highly inhomogeneous structure, deformation localization or fracture. The reason why this happens is precisely the “Interdependency”.

Our approach to capture the interdependency
Internal parameters Continuum model FEM A mechanics of solids approach is to use a continuum model with internal variables capturing the structure of the material. Based on such a model, we can compute the stress-strain state and the internal variables allow us to capture the interdependency. Internal parameters will allow us to account for the interdependency between the stress-strain state and the structure.

Internal parameters serve as special envoys representing the micro-level processes at the macro-level  S We propose the continuum model describes two main interrelated processes simultaneously happening in metals under severe plastic deformation, namely grain refinement and fracture. Для описания этих процессов в модель введены две внутренние переменные: площадь высокоугловых границ в единице объема материала и объем микронесплошностей в единице объема материала. Для построения модели the number of assumptions were used. This made the developed instrument much less precise than, for example, electronic or optical microscopes. On the other hand, however, this allowed us to make several general conclusions that may help to systematize the experiment.

Model of the material The constitutive equations of the model have the following form:

Constitutive equations of the Mises’s model
RVE The constitutive equations of the model have the following form:

Porous body with structurally inhomogeneous matrix
RVE Beygelzimer Y. et al., (1994) Engin. Fracture Mech., 48, N5 Beygelzimer Y. Proceedings of International Workshop on Modelling of Metal Powder Forming Processes, Grenoble, France, July 21-23, 1997 The constitutive equations of the model have the following form:

Plausible reasoning RVE
The constitutive equations of the model have the following form:

Loading surfaces    = 0   , (16)
This is the loading surface for this loading function for different theta. , (16)

Loading surfaces of the cutting of the secondary Al alloy
, MPa This is the loading surface for this loading function for different theta. P, MPa : %, %, %, 4- 3%. , (16)

Porous body with structurally inhomogeneous matrix at <<1
The constitutive equations of the model have the following form: , s (d) a

We propose the continuum model describes two main interrelated processes simultaneously happening in metals under severe plastic deformation, namely grain refinement and fracture. Для описания этих процессов в модель введены две внутренние переменные: площадь высокоугловых границ в единице объема материала и объем микронесплошностей в единице объема материала. Для построения модели the number of assumptions were used. This made the developed instrument much less precise than, for example, electronic or optical microscopes. On the other hand, however, this allowed us to make several general conclusions that may help to systematize the experiment. Beygelzimer Y., Shevelev A. On the Development of Fracture Models for Metal Forming// Russian Metallurgy (Metally), Vol., N5, p. 452–456, 2003

The model of grain refinement and viscous fracture
Beygelzimer Y. Grain refinement versus voids accumulation during severe plastic deformations of polycrystals: Mathematical simulation, Mechanics of Materials, V. 37, N7, p , 2005 We propose the continuum model describes two main interrelated processes simultaneously happening in metals under severe plastic deformation, namely grain refinement and fracture. Для описания этих процессов в модель введены две внутренние переменные: площадь высокоугловых границ в единице объема материала и объем микронесплошностей в единице объема материала. Для построения модели the number of assumptions were used. This made the developed instrument much less precise than, for example, electronic or optical microscopes. On the other hand, however, this allowed us to make several general conclusions that may help to systematize the experiment.

Main characters of the Model
Accumulative Zone – a “spring”, the part of crystals in which dislocation charges accumulate during plastic deformation; AZs emerge due to the inhomogeneity of shear along the sliding plane. Void – a bit of an emptiness Embryo – an embryo of high-angle boundary (a partial disclination) Scale 500 nm At the beginning I introduce three characters which will help me to explain physical assumptions of the model In russian literature it’s known as .

Pictures of Main Characters

The Birth of an Accumulative Zone
During plastic deformation of polycrystals there are regions where dislocations get plugged. Such regions cause bendings of the crystalline lattice. There are regions of polycrystals where dislocations get plugged during plastic deformation. Such regions cause bendings of the crystalline lattice.

The Birth of an Accumulative Zone
The model postulates that AZs emerge in two places: hurdles that exist in polycrystals before deformation high-angle boundaries that emerge during deformation. Rubber with a cut illustrates the emergence of a bending when a shift is plugged.

Relaxations of Accumulative Zones in coarse grained materials
There are different relaxation mechanisms for accumulative zones. When talking about large cold deformations, we will distinguish two main mechanisms: Emergence of high angle boundaries (leading to grain refinement) Emergence of voids (leading to fracture) There are various relaxation mechanisms. When talking about large deformations, we will distinguish two main mechanisms: emergence of disorientation boundaries and emergence of micropores. The first mechanism leads to grain refinement, while the second mechanism leads to fracture.

Relaxations of Accumulative Zones in coarse grained materials
There are various relaxation mechanisms. When talking about large deformations, we will distinguish two main mechanisms: emergence of disorientation boundaries and emergence of micropores. The first mechanism leads to grain refinement, while the second mechanism leads to fracture.

Boundary sliding boundary Prandtl model

Relaxations of Accumulative Zones in ultrafine grained materials
Sliding plane This happens when d is close to dc So grain refinement is essentially a transformation of bendings of a crystalline lattice into high-angle boundaries. This decreases elastic energy of a polycrystal. Grain refinement increases the area of high-angle boundaries and decreases fragment size. However, I believe that when the fragments become sufficiently small, they stop dividing. This is due to the fact that elastic stresses relax by fragment sliding along high-angle boundaries. This effect can be explained on a simple mechanical model shown here. Elastic beam represents a fragment. Fragment environment is represented by a slider pressed to the beam. There is friction with limiting value Tc between the slider and the beam. Movement of the slider bends the beam. When the bending reaches a critical curvature Kp, a plastic zone emerges. This leads to a decrease of elastic energy, and the bending transforms into a disorientation boundary. This boundary is an analog of a high-angle boundary. Since friction has its limiting value, it is easy to show that there must be some limiting beam length such that any beam with length less than this value can not be bent to curvature (кЁрвиче) Kp. Plastic zones can’t appear in such short beams, thus there can be no disorientation boundaries. Plastic zones can appear only when the following condition is satisfied: Однако, с нашей точки зрения, когда фрагменты становятся достаточно малыми, они перестают делиться. Это связано с тем, что упругие напряжения релаксируют путем проскальзывания фрагмента по высокоугловым границам. Этот эффект поясняет простая механическая модель, приведенная на слайде. Упругая балка соответствует фрагменту. Окружению фрагмента соответствует ползун, прижатый к балке. Между ползуном и балкой есть трение, предельное значение которого равняется Тс. Движение ползуна вызывает изгиб балки. Когда кривизна балки достигает критического значения Кр происходит образование пластической зоны. В результате упругая энергия уменьшается, а изгиб заменяется границей разориентации. Это аналог высокоугловой границы. Так как трение имеет предельное значение, то легко показать, что есть предельно малая длина балки, которую нельзя таким образом согнуть до кривизны Кр. В такой короткой балке уже не может возникнуть пластическая зона, т.е. не может появиться граница разориентации. d

So grain refinement is essentially a transformation of bendings of a crystalline lattice into high-angle boundaries. This decreases elastic energy of a polycrystal. Grain refinement increases the area of high-angle boundaries and decreases fragment size. However, I believe that when the fragments become sufficiently small, they stop dividing. This is due to the fact that elastic stresses relax by fragment sliding along high-angle boundaries. This effect can be explained on a simple mechanical model shown here. Elastic beam represents a fragment. Fragment environment is represented by a slider pressed to the beam. There is friction with limiting value Tc between the slider and the beam. Movement of the slider bends the beam. When the bending reaches a critical curvature Kp, a plastic zone emerges. This leads to a decrease of elastic energy, and the bending transforms into a disorientation boundary. This boundary is an analog of a high-angle boundary. Since friction has its limiting value, it is easy to show that there must be some limiting beam length such that any beam with length less than this value can not be bent to curvature (кЁрвиче) Kp. Plastic zones can’t appear in such short beams, thus there can be no disorientation boundaries. Plastic zones can appear only when the following condition is satisfied: Однако, с нашей точки зрения, когда фрагменты становятся достаточно малыми, они перестают делиться. Это связано с тем, что упругие напряжения релаксируют путем проскальзывания фрагмента по высокоугловым границам. Этот эффект поясняет простая механическая модель, приведенная на слайде. Упругая балка соответствует фрагменту. Окружению фрагмента соответствует ползун, прижатый к балке. Между ползуном и балкой есть трение, предельное значение которого равняется Тс. Движение ползуна вызывает изгиб балки. Когда кривизна балки достигает критического значения Кр происходит образование пластической зоны. В результате упругая энергия уменьшается, а изгиб заменяется границей разориентации. Это аналог высокоугловой границы. Так как трение имеет предельное значение, то легко показать, что есть предельно малая длина балки, которую нельзя таким образом согнуть до кривизны Кр. В такой короткой балке уже не может возникнуть пластическая зона, т.е. не может появиться граница разориентации.

G(,)=0 P(,;µ)=0 G(,)=0 P(,; S,; µ)=0 K(S,, ,;µ)=0
Equations of the Model Classical Plasticity Theory: G(,)=0 General P(,;µ)=0 Constitutive Proposed model with internal parameters capturing the structure: P(,; S,; µ)=0 G(,)=0 K(S,, ,;µ)=0 General Constitutive Kinetic This is a high-level picture of what is going on. In Classical Plasticity Theory, we have a system with two groups of equations: general equations which are material-independent, And constitutive equations describing the material. In the proposed model, there is also a group of kinetic equations describing the dependencies among internal parameters which describe the structure.

Loading function The constitutive equations of the model have the following form:

Kinetic equations Quasimonotonic loading Cyclic loading .
This is a system of kinetic equations which summarizes the birth, life, and death of characters. Cyclic loading

Prediction

metals become ideally plastic.
Prediction (i) As : Ideal Plasticity Land Metals don’t fracture and don’t harden under sufficiently high pressure when equivalent strain is very large, i.e., metals become ideally plastic. The reason is boundary sliding , (16)

for sufficiently large equivalent strain
Prediction (ii) Ductility grows for sufficiently large equivalent strain The reason is boundary sliding

с  The term responsible for the birth of voids
α* decrease for sufficiently large strain. Ductility grows for sufficiently large strain.

Prediction (iii) P Grain refinement intensity grows and fracture decreases with the increase of pressure in the center of deformation. , (16)

 The reason is p grows with pressure increase  p, MPa 0.1 420 840
1120  

Correspondence with experimental results: Influence of pressure on the microstructure of molybdenum at hydroextrusion: e=0.36 30m e=0.60 e=0.92 Pb Pb = 0,1 MPa Pb = 800 MPa

Correspondence with experimental results:
Effect of pressure on fragment size distribution Hydroextrusion of molybdenum (e=0.6). 40 20 f,% l, 100 µm , GPa

Use in Twist Extrusion Twist Extrusion based on hydro-mechanical extrusion Twist Extrusion based on mechanical extrusion with backpressure , (16)

Model-based prediction for Twist Extrusion
- Рb  0.1 MPa - Рb = MPa P P

Prediction (iv) To get intense grain refinement, one needs to choose deformation schemes with small value of ductility and to perform deformation under pressure. Grain refinement intensity is typically higher for simple shear than for uniaxial elongation , (16)

The reason is simple shear has smaller ductility (under the same pressure).
Ductility diagram, steel 08X18H10T (Experiment data V.Kolmogorov, et al., 1986)  c(0), tension under pressure c(0) is the metal ductility at p=0 c(0), torsion с(0) S

Ductility diagrams for various metals show that, as a rule, ductility с(0) of tension greater than that of torsion. (Experiment data V.Ogorodnikov and I.Sivak, 1999)

Prediction (v) Quasi-monotone deformations provide higher grain refinement intensity than cyclic deformations. 0.1 0.2 0.3 0.4 0.5 0.6 0.8 strain S, 1/mkm N, m-2 S, m-1   , (16)

Cyclic deformations provide higher ductility than quasi-monotone deformations
porosity  , (16)

In order to increase the intensity of grain refinement under cyclic deformation, one has to increase the amplitude of deformation. For example, in Twist Extrusion we combine clockwise and counter-clockwise dies. , (16)

clockwise clockwise A , (16)

counter-clockwise clockwise 2A , (16)

To avoid cyclic deformation we combine Twist Extrusion with Spread Extrusion
, (16)

Prediction (vi) Sufficiently high pressure in the center of deformation prevents strain localization P Layers of the voids

Prediction (vii) Grain size distribution
Self-similar stage 0,5 When there are fragments with size dc dc , (16)

Self-similarity of Experimentally Obtained Distributions
Cu, torsion (V.Panin et al., 1985) 93% 46% 0.28 =4.61 1.07 . Обработка экспериментальных распределений показывает, что они обладают таким свойством.

Prediction (iv) During the self-similar stage of grain refinement, the fragment boundary mesh in the cross-section of the specimen represents a fractal set with dimension , 1< <2.  . 1< <2 - fractal dimension. During the self-similar stage  is constant

  Hall-Petch . were During the self-similar stage  is constant

When sufficiently many indivisible fragments of size dc appear, the self-similarity of the boundary mesh gets violated. In this case   .

Simulation of the grain refinement processes by Cellular Model
Initial grain Plastic deformation D s М Deformation continues . Rotation moments appear Moment stresses relax through grain splitting Beygelzimer Y., et al., Philosophical Magazine A, 79, N10, (1999)

Limiting Grain size distribution (Cellular Model)
Cu 10µm Grain size, μm

Final Thoughts Model parameters are obtained through compression and torsion tests

What do we hope for? One can substitute the classical plasticity model by the above model in any FEM package to directly compute the stress-strained state of a metal and its interdependence with the structure Continuum model FEM Model parameters are obtained through compression and torsion tests

What do we hope for?

What do we have? The model is relatively new
The limits are not entirely explored A long way toward good parameter estimation … but there are grounds for hope I think that there are enough grounds for hope

With High Ductility? How to Make Strong Metals Yan Beygelzimer

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