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Instability of plastic flow and their role in texture transformations Authors: Marta Gajewska Grażyna Kulesza Honorata Kazimierczak Katarzyna Stan Jagoda.

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Prezentacja na temat: "Instability of plastic flow and their role in texture transformations Authors: Marta Gajewska Grażyna Kulesza Honorata Kazimierczak Katarzyna Stan Jagoda."— Zapis prezentacji:

1 Instability of plastic flow and their role in texture transformations Authors: Marta Gajewska Grażyna Kulesza Honorata Kazimierczak Katarzyna Stan Jagoda Poplewska Piotr Bobrowski Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

2 Content 1.Plasticity and yield criteria 2.Fundamental relations between flow stress and strain 3.Mechanical aspects of plastic instability 4.Plastic anisotropy vs. crystallographic texture and sheet metal forming 5.The analysis of some important (microstructural) features of plastic deformation that are important for large strains 6.Roling and formation of 2 types of rolling texture Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

3 Instability of plastic flow and their role in texture transformations 1.Plasticity and yield criteria (uniaxial and multiaxial plastic flow analysis) Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

4 Stress Measure of the average force per unit area of a surface within the body on which internal forces act (as a reaction to external forces applied). These internal forces are distributed continuously within the volume of the material and may result in deformation of the body's shape. 1D case – normal stress { F II A shear stress } Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

5 Stress Moment on each axis is equal to zero (stress tensor is symmetric ) 3D – Cauchy stress tensor six independent variables Principal axes – set of coordinates for which all the components of shear stress are zero isotropic partdeviatoric part Hydrostatic pressure σ ij – i-component of force acting on a unit area with normal x j Stress deviator Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

6 Strain σ1σ1 σ1σ1 1D – linear strain3D strain The state of strain at a any point of a continuum body is defined as the sum of the changes in distance between this point and every other neighboring point (linear strain) and the changes in the angle between any pair of directions radiating from this point (shear strain) Relative displacement tensor Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

7 1 2 0 B0B BtBt state of relative displacement increment dγ 21 dγ pure strain increment rigid body rotation += symmetric tensorasymmetric tensor Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Strain

8 Elasticity vs. plasticity Hooks law σ = E ε Describes property of a material that returns to its original shape after the applied forces that made it deform is removed Describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces J. Lubliner, 2008, Plasticity theory Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

9 Huber-Mises-Hencky criterion Yielding occurs when some function of the principal stresses σ 1, σ 2, σ 3 reaches a critical value 2σ f 2 Yield surface for this criterion encloses an infinitely long circular cylinder σ f - flow stress Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

10 Yield surface corresponding to this criterion encloses an infinitely long hexagonal cylinder Yielding occurs when the maximum shear stress reaches a critical value 0,5 σ f Tresca criterion σ max, σ min – largest and smallest principal stress Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

11 Yield surface: Tresca vs H-M-H (2D) H-M-H: Tresca: Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

12 Yield surface: Tresca vs H-M-H (3D) Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

13 σ0σ0 σ0σ0 σ0σ0 σ0σ0 σ 1 (tension) σ 2 (tension) σ 1 (compression) σ 2 (compression) von Mises Tresca σ 3 = σ1σ1 σ2σ2 σ1σ1 σ1σ1 σ2σ2 σ2σ2 σ1σ1 σ2σ2 σ1σ1 σ1σ1

14 Instability of plastic flow and their role in texture transformations 2.Fundamental relations between flow stress and strain (basic descriptions, definitions and constitutive laws used to describe plastic deformations) Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

15 Strengthening consists the increase of flow stress with the increase of permanent plastic deformation. Material with plastic stress in the annealed condition of σ y 0 after permanent deformation ε has increased plastic stress σ p = f(ε). Stress-strain curve obtained from unidirectional tensile, compression or torsion tests is usually described by a simple Ludwik formula: σ y, k 1 – constans, n – hardening, which for most metals takes values in the range If the initial yield strength for annealed material is relatively small in relation to size of strengthening, the above relationship can be reduced to a good approximation to the model given by Hollomon: k 2, n – constans Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Stress-strain relations

16 Previous dependencies well describe the strengthening behavior of a large part of metals in range of deformation 0.5, i.e. in the range of deformation typically obtained in a tensile test of plastic metal. In the greater degree of deformation with which we deal in most of the forming operation, the strengthening is strongly reduced and appears more or less apparent linear range of the strengthening curve. Then to analytical description we needs two or more pairs of parameters (k i n) An alternative approach to the analysis of a wide range of deformation is based on the experimentally observed fact that the flow stress of most metals, for very large degrees of deformation aims to achieve saturation. This condition is described characteristic of each metal value of stress σ s. Constitutive equation describing the strengthening may be based, in this case on the relationship given by Voce'a: α – a dimensionless constant characteristic of the strengthening behavior This equation was modified by Hocket and Sherby to the form: Given by Lloyd and Kenny constant value p for aluminum was 0.5 Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Stress-strain relations

17 Differentiating Voces equation we obtain a linear dependence of the strengthening Θ on a decreasing flow stress values given by Kocks-Mecking equation: Θ 0 determines the initial value of strengthening Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Stress-strain relations

18 Referring to Kocks-Mecking equation, in a tension test the sample is getting strained but it is also becoming thinner with elongation. The latter implies that stress, which is load per unit area, is increasing. Thereby, two things are occurring simultaneously: material is strain hardening and also supporting increasing stress, thanks to the reduction in area. Naturally, a situation will arise when the increase in stress, due to decrease in cross section area, will become equal to the increase in load carrying capacity due to strain hardening. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Considère criterion

19 Description of the plastic material with strengthening provides a description of the relationship between stress and strain including effect of the strengthening of these relationships. Depending on whether this effect is an isotropic or anisotropic, makes a distinction between isotropic or anisotropic strengthening. Isotropic strengthening of isotropic material is called plastic deformation in which the area of plastic flow grows symmetrically with a maintaining of the form. Yield condition for such material is written by making the condition of plasticity on the parameter of strengthening. < 0 – elastic or stiff material = 0 – plastic material Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Geometrical interpretation

20 Isotropic strengthening in uni-dimensional case is manifested by the fact that the plastic strain σ is independent on the way of load. This property transfer to the case of (consisted) complex stress. With the growth of plastic deformation the flow area F(σ ij,κ)=0 is increased symmetrically irrespective of the way of the load. Increase of the plasticity area depends only on the strengthening parameter κ. As a measure of this parameter is accepted substitute plastic deformation ε, or specific work of plastic deformation w. Geomtrical interpretation of izotropic strengthening of material: a) unidirectional strain, b) in general loading reloading offloading Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Geometrical interpretation

21 Plastic flow of crystalline materials takes place by the movement of dislocations along cystal planes under the influence of an applied stress. Work hardening is a consequence of the fact that the stress required for dislocation movement usually increases during plastic flow as the dislocations become increasingly hindered by microstructural obstacles. In order to increasing size these obstacles are solute atoms, dislocations, precipitates and grain boundaries. The most imporatant variation in obstacle density is usually due to the dislocations themselves. Their behaviour in crystals under stress is therefore of paramount importance for understanding and modelling work hardening. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Work hardening

22 Stage I: The dislocations are usually confined to their slip planes and do not interact with each other so that the work hardening rate is very low (most easily seen in single crystals oriented for single slip). In polycrystals, which begin to deform plastically, Stage I is negligible since the movement of the first few dislocations is restricted by the grain boundaries at which they often pile-up. Stage II: The dislocation interactions on different slip systems give rise to a rapid multiplication of the dislocations and thereby a high, and roughly constatnt, work hardening rate. Stage III: Subsequently, and up to strains of order unity, the flow curve becomes parabolic as the work hardening rate decreases progresively down to values almost an order of magnitude lower than Stage II. In this stage, the dislocation multiplication processes are cunterbalanced by local dislocation annihilations (dynamic recovery due to localized cross-slip, climb and/or annihilation of segment of oppisite sign). These recovery mechanisms and therefore the work hardening rates are strongly temperature dependent. Stage IV: At higher strains 1 typical of many rolling and extrusion processes, many grains break up into bands of different orientations, separated by transition zones and grain boundaries. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Work hardening stages

23 The particular microscopic laws are often complex so the relatively simple analysis given below in terms of the total dislocation density can be considered as an illustration of the principles. The microscopic work hardening rate (dτ c /dγ) can be written in terms of the varaition of the dislocation density as: According to the analysis of Kocks and Mecking the rate of creation of dislocations (dρ + ) during a small strain increment dγ is inversely proportional to the mean dislocation slip distance λ so that (dρ + / dγ) = (1 / bλ) and the mean slip distance λ = C 1 /ρ ½, where C 1 is the average number of obstacles that the dislocation meets before stopping. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Microscopic hardening laws

24 During Stage II hardening, where dislocation annihilation is small and can be neglected, the above model gives a constant hardening rate: During Stage III the hardening rate decreases continuously as some of the dislocations are annihilated by dynamic recovery at a rate written (dρ - /dγ). The exact mechanisms of annihilation (cross-slip, climb) are the subject of current research but one can write that the rate of annihilation is proportional to the current density ρ and a probability of elimination P(T), which is strongly temperature dependent: Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Microscopic hardening laws

25 Consequently, Stage III work hardening rate becomes linear in τ c : At large strains and low temperatures dislocation annihilation is insufficient to completely balance the rate of creation. This result in the low, but non-zero, work hardening rate of Stage IV; there is no general agreement on the basis physical causes of this stage. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Microscopic hardening laws

26 Instability of plastic flow and their role in texture transformations 3.Mechanical aspects of plastic instability (based on stress – strain curves) Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

27 Instability: necking in tension shear-band development identifies what happens when a state of uniform strain gives way to one in which straining is more or less localized. Instability Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

28 Strain-induced hardening Geometrical softening in an incipient neck Schematic presentation of instability in tensile test Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

29 To initiate instability (a neck in this case): a/R ratio for characterizing neck sharpness Grafical mean of finding the necking strain Rods in tension Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

30 Mild steel often shows both stable and unstable necks Rods in tension Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

31 Mild steel often show both stable and unstable necks Rods in tension Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

32 Rods in tension Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

33 Local neck in a strip tension specimen. (Normal strain along X 2 must be zero) Diffuse necking Plane strain in the localized neck Sheets in tension Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

34 The criteria for localized and diffuse necking in pure tension. Sheets in tension Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

35 Instability of plastic flow and their role in texture transformations 4.Plastic anisotropy vs. crystallographic texture and sheet metal forming Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

36 Crystalline structure Crystal - periodic arrangement of atoms in space. Different array of atoms on particular planes. Mechanical, physical and chemical properties vary with testing direction An example : graphite – good electircal conductivity in the direction parallel to the layers, and much worse in the perpendicular direction. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Graphite crystal structure skywalker.cochise.edu/wellerr/ mineral/graphite/graphiteL.htm

37 Polycrystalline materials – many crystallites of different size, shape and orientation. Polycrystalline materials In isotropic materials all orientations occur with the same probability – properties in all directions are the same materials/ / Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

38 Texture Texture is the main structural reason of anisotropy in polycrystalline materials - properties change with testing direction Anisotropic properties: Mechanical properties: plasticity, elasticity, hardness, strength, Physical properties: optical properties, thermal expansion and conductivity, electric conductivity, magnetization, chemical (corrosion resistance) Crystallites orientation in the material is not random, Preferred orientation is formed Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

39 For example during rolling some crystallographic plane arrange parallel to rolling plane and rolling direction. As a result elongated grains in the rolling direction are formed. Texture of: crystallization, deformation (rolling, extruding), recrystallization Rolling direction Plastic anisotropy Not only orientation but also the grains size and shape is important. Aluminium ingot – example of the texture formed during crystallization Texture evolution of an ultrafine grained (UFG) C- Mn steel and its evolution during warm deformation and annealing R. Song, D. Ponge, D. Raabe ucation/Solidification/Crystaline_Growth.html Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

40 Recrystallization can produce texture completely different than that of the deformed material. Globular shape of grains smaller anisotropy Deformation-related recrystallization processes M. R. Drury and J. L. Urai Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

41 Sheet metal exibits special anisotropy. It is characterised by occurance of significant differiences in plastic properties in 3 mutually perpendicular directions: 1) rolling direction, 2) direction normal to rolling direction lying in the sheet metal plane 3) direction normal to sheet metal plane These are the main anisotropy directions. Sheet metal forming Anisotropic properties can have a major effect on subsequent process stages, especially sheet metal forming processes such as deep drawing and stretch forming. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

42 Types of anisotropy in sheet metal Plastic properties change in the direction normal to plane of sheet metal and in the direction lying in the plane of sheet metal. Plastic properties in the plane of the sheet metal change with direction. This kind of anisotropy is important from the standpoint of sheet metal deep- drawing Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim Normal Planar

43 How we can determine anisotropy? ε h – real deformation of thickness ε b - real deformation of width b 0 – initial sample width b - sample width after deformation h 0 – initial sample thickness h – sample thickness after deformation L 0 – initial sample length L – sample length after deformation Sample deformation used to determine normal and planar anisotropy of sheet metal Plastic anisotropy coefficients (Langford) – ratio of real deformation width to real deformation thickness of sample from metal sheet subjected to uniaxial tensile. From description of dr inż. Łukasz Cieniek - Anizotropia i tekstura krystalograficzna. Starzenie po odkształceniu, AGH Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

44 Constant value of r coefficient but larger from 1 normal anisotropy If r = 1 sheet metal has isotropic properties In practice 3 types of samples are investigated, which form 3 axis with rolling direction: 45°, 90° and 0°. This values are utilized to determine planar anisotropy and mean normal anisotropy Significant change in r coefficient with the change of α angle planar anisotropy Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

45 Geometric interpretation Ellipses are elongated (if r>1)or shorted (if r<1) in relation to ellipse of isotropic material. Yield criterion – is a mathematical expression of the stress states that will cause yielding or plastic flow. Shape of the yield surface Biaxial uniform streching Biaxial uniform compression 45° material with planar anisotropy Retraction of the ellipse main axis from the 45 ° slope indicates a planar anisotropy. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

46 Why is that so important? Important from the point of view of shaping by cold plastic deformation (it is basic parameter of deep-drawing sheet metal ) Low value of planar anisotropy is favorable High value of normal anisotropy is favorable, in that case material has a greater thinning resistance material deforms better in drawing operations Anisotropy in the mechanical properties can cause 'earing' in beverage can bodies. The ears must be cut off, leading to wastage. Photo courtesy of VAW aluminium AG aluminium.matter.org.uk Sheet metal for deep-drawing Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

47 Instability of plastic flow and their role in texture transformations 5.The analysis of some important (microstructural) features of plastic deformation that are important for large strains Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

48 A microstructure no deformed Microstructure evolutution with strain Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

49 A microstructure at small strain Microstructure evolutution with strain DDW - dense dislocation wall Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

50 A microstructure at large strain Microstructure evolutution with strain Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

51 In cubic metals the two basic methods of deformation are slip and twinning and the most significant material parameter with respect to the choice of method is the value of the stacking fault energy (γ SFE ). In metals with a low value of γ SFE, the difficulty of cross-slip reduces the ability of the material to change its shape during plastic deformation by slip alone, and therefore deformation twinning may occur. Homogeneous deformation Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

52 – is a function of the material, determines the extent to which unit dislocations dissociate into partial dislocations. Copper, α-brass and austenitic stainless steel have a low γ SFE and climb and cross slip of dislocations are difficult in these metals (recrystallization is easier). Metals such aluminium and α-iron have a high γ SFE and climb is easy (recovery is easier). Stacking fault energy (γ SFE ) Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

53 Slip occurs in directions in which the atoms are most closely packed, since this requires the least amount of energy; Homogeneous deformation - slip Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

54 When mechanical deformation is created by twinning, the lattice structure changes; The atoms move only a fraction of an interatomic space and this leads to a rearrangement of the lattice structure. Homogeneous deformation - twinning Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

55 Homogeneous deformation - slip vs. twinning Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

56 deformation bands transitions bands shear bands Non-homogeneus deformation Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

57 deformation bands transitions bands shear bands Non-homogeneus deformation The resulting deformation bands deform on different slip systems and may develop widely divergent orientations. The narrow regions between the deformation bands, which may be either diffuse or sharp, are termed transition bands. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

58 deformation bands transitions bands shear bands Non-homogeneus deformation - are noncrystallographic in nature, may pass through several grains, and even extend through the specimen. They are a result of plastic instability, and can be thought of as the rolling equivalent of the necking which occurs in a tensile test. Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

59 deformation bands transitions bands shear bands Non-homogeneus deformation TEM microstructure showing an advanced stage of shear band formation against a background of the compact twin-matrix layer structure after 67% compression Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

60 Solute Hardening Precipitation Hardening Dispersoids Hardening Influence of alloying elements Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

61 Solid Solution Hardening Precipitation Hardening Dispersoids Hardening Influence of alloying elements Solute atoms make dislocation motion more difficult increase the strength of a material Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

62 Solute Hardening Precipitation Hardening Dispersoids Hardening Influence of alloying elements Precipitations make dislocation motion more difficult increase the strength of a material Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

63 Solute Hardening Precipitation Hardening Dispersoids Hardening Influence of alloying elements Vickers hardness measurements of alloys after cold rolling (z=60%) and annealing for 1h in different temperatures A dispersion of particles will exert a retarding force or pressure on a low angle or high angle grain boundary and this may have a profound effect on the processes of recovery, recrystallization and grain growth. L.Lityńska-Dobrzyńska; Rola cyrkonu i skandu w procesach tworzenia struktur metastabilnych w stopach Al.-Mg-Si-Cu, IMIM PAN, Kraków 2009 Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

64 Solute Hardening Precipitation Hardening Dispersoids Hardening Influence of alloying elements Interaction of particles with grain boundary A dispersion of particles will exert a retarding force or pressure on a low angle or high angle grain boundary and this may have a profound effect on the processes of recovery, recrystallization and grain growth. M.J. Jones, F.J. Humphreys; Interaction of recrystallization and precipitation: The effect of Al3Sc on the recrystallization behaviour of deformed aluminium, Acta Materialia 51 (2003) 2149–2159 Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

65 Instability of plastic flow and their role in texture transformations 6.Roling and formation of 2 types of rolling texture (the influence of the texture on sheet metal forming) Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

66 Rolling and deep drawing RD ND TD εRDεRD ε ND A B C D E rad cir ε cir ε rad A B C D E A. Rollet Typical textures Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

67 Rolling texture Cu rolled to 90% Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

68 Brass and copper textures archive.uky.edu 0%2,5 % 5% 10%20% 30% Brass Copper [111] PF, 90% reduction Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

69 Negative aspects sheet metal forming deep drawing: Cu cups RDRD Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

70 Positive aspects Transformer metal plates (Fe-Si): –good textures for high magnetic coercion and permittivity: – {001} – cubic, {110} - Goss permanent magnets (Alnico): – direction oriented along the magnet axis Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

71 References Deformation Geometry for Materials Scientists, C. N. Reid, International series on materials science and technology vol. 11, Oxford: New York: Pergamon Press, 1973, 2-30, Mechanika Plastycznego Płynięcia w zarysie, T. Bednarski, PWN, 1995 Odkształcenie i pękanie metali, J. Wyrzykowski, E. Pleszakow, J. Sieniawski, WNT, 1999 Obróbka plastyczna, S. Erbel, K. Kuczyński, Z. Marciniak, PWN, 1977 Strukturalne aspekty odkształcenia metali, K. Przybyłowicz Dislocations and plastic deformation, I. Kovac, L. Zsoldos Deformation processing, W. A. Backofen, Addison-Wesley Publishing Company, 1972 Plasticity theory, J. Lubliner, 2008 Anizotropia i tekstura krystalograficzna. Starzenie po odkształceniu, Ł. Cieniek, AGH Recrystallization nad related annealing phenomena, F.J. Humphreys, M. Hatherly, Pergamon, 2002 Pasma ścinania w metalach o sieci reguralnej ściennie centrowanej, H. Paul, IMIM PAN, 2009 Engineering Materials 1. An Introduction to Properties, Applications and Design, M.F.Ashby, D.R.H. Jones, Elsevier Butterworth-Heinemann, 2005 aluminium.matter.org.uk Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim


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