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CHAPTER 1 La estructura de los metales


Outline • Crystalline structure of metals and Slip Systems – BCC – FCC – HCP

• • • • •

Plastic deformation of single crystalline structure Imperfections of single crystalline structure (Grains) Grain size and grain boundary Plastic deformation of polycrystalline metals Recovery, recrystallization and grain growth 2



Introducción • Porque cada específicas?.





• Cómo medimos y evaluamos sus propiedades? • Porqué algunos metales son suaves y otros duros? • Porqué algunos metales son frágiles, mientras otros son dúctiles y se les puede dar forma fácilmente sin fracturarse? • Porqúe algunos metales pueden soportar temperaturas elevadas, mientras otros no pueden? 4

Structura Cristalina de los Metales Crystalline Structure

Un solo cristal


Celda unitaria

Cada ladrillo

Estructure cristalina

Arreglo o configuracion ordenada de ladrillos.


Estructura Cristalina: Modelo de las esferas duras • Cada esfera representa a un átomo. • La manera en que estos átomos se encuentran arreglados determina el comportamiento y propiedaes del material. • La razón por la cual los metales forman diferentes estructuras cristalinas es para minimizar la energía requerida para ajustarse a un patrón regular. 6

Structura Cristalina CĂşbica centrada en el cuerpo - bcc

Figure 1.2 La estructura cĂşbica centrada en el interior (bcc): (a) modelo de esferas duras; (b) celda unitaria; y (c) un monocristal con muchas celdas unitarias. Fuente:7 W. G. Moffatt, et al., The Structure and Properties of Materials, Vol. 1, John Wiley &

Sistemas de deslizamiento de la estructura cristalina BCC • En la estructura cúbica centrada en el cuerpo (BCC): – 48 posibles sistemas de deslizamiento – Cuando se aplica un esfuerzo cortante en el material, la probabilidad es grande para que se origine deslizamiento en el material. – Los metales con una structura cristalina BCC generalmente tienen una buena resistencia y una moderada ductilidad. – Algunos de los metales con esta estructura son, molybdenum,and tungsten 8

Structura Cristalina CĂşbica Centrada en las caras - fcc

Figure 1.3 La estructura cristalina cĂşbica centrada en las caras (fcc): (a) el modelo de esferas duras; (b) celda unitaria; y (c) monocristal con muchas celdas unitarias. Fuente: W. G. Moffatt, et al., The Structure and Properties of Materials, Vol. 1, John Wiley & Sons, 1976. 9

Sistemas de deslizamiento de la estructura cristalina FCC • En la estructura cúbica centrada en las caras (FCC): – Existen 12 sistemas de deslizamiento. – La probabilidad para el deslizamiento es moderada. – Los metales con una structura cristalina FCC generalmente tienen una buena resistencia y una moderada ductilidad. – Eg.Aluminio, Cobre, oro y plata. 10

Estructura Cristalina Hexagonal Compacta (hcp)

Figure 1.4 La estructura cristalina hexagonal compacta (hcp): (a) celda unitaria; y (b) monocristal con muchas celdas. Fuente: W. G. Moffatt, et al., The Structure and Properties of Materials, Vol. 1, John Wiley & Sons, 1976. 11

Sistemas de deslizamiento de la estructura cristalina HCP • La estructura cristalina hexagonal compacta (hcp), posee: – 3 systemas de deslizamiento – Baja probabilidad de deslizamiento. – Sin embargo, una mayor cantidad de sistemas de deslizamiento se activan a elevada temperatura. – Los metales con estructura HCP generalmernte son frágiles a temperatura ambiente. – Por ejemplo, el berilio,magneso, y el zinc 12

Two Plastic Deformation Mechanisms for Single Crystals • Slipping Figure 1.5 Permanent deformation (also called plastic deformation) of a single crystal subjected to a shear stress: (a) structure before deformation; and (b) permanent deformation by slip. The size of the b/a ratio influences the magnitude of the shear stress required to cause slip.

• Twinning Figure 1.6 (a) Permanent deformation of a single crystal under a tensile load. Note that the slip planes tend to align themselves in the direction of the pulling force. This behavior can be simulated using a deck of cards with a rubber band around them. (b) Twinning in a single crystal in tension.


Slipping • Slipping of 1 atom plane over an adjacent place. • Require certain amount of shear stress to undergo plastic (permanent) deformation. • Shear stress proportional to b/a • • b/a different for different direction within the crystal , called anisotropic (e. g.woven cloth) 14

Twinning • Portion of the crystal forms a mirror image of itself across the plane of twinning. • Usually occur in hcp and bcc metals by plastic deformation;occur in fcc by annealing. 15

Slip Lines and Slip Bands Figure 1.7 Schematic illustration of slip lines and slip bands in a single crystal (grain) subjected to a shear stress. A slip band consists of a number of slip planes. The crystal at the center of the upper illustration is an individual grain surrounded by other grains.

Slip System • Combination of a slip plane & its direction of slip • Slip system >= 5, Ductile 16

Recopilación de los sistemas de deslizamiento BCC



Sistema de deslizamiento



3 (more at high temperature)

Probabilidad de deslizamiento




Ductilidad (>5)








Esfuerzo cortante









Cr Alpha Iron (<912ºC or >1394ºC)

Cu, Al Gamma Iron (912ºC ~ 1394ºC)


(Alotropía o polimorfismo)


Imperfection Category for Single Crystals • Point defect, such as vacancy, interstitial atom, impurity • Line defect, called dislocation • Planar imperfection, such as grain boundaries • Volume or bulk imperfections, such as voids/inclusions 18

Point Defect • Vacancy (missing atom) • Interstitial atom (extra atom in the lattice) – Self-interstitial atom

• Impurity atom (foreign atom) – Substitutional impurity atom – Interstitial impurity atom


Point Defects in a Single Crystal Lattice Extra atom

Foreign atom

Missing atom

Extra atom

Figure 1.9 Schematic illustration of types of defects in a single-crystal lattice: self-interstitial, vacancy, interstitial, and substitutional.


Line Defection: Dislocation • Line defect in the orderly arrangement of metal’s atomic structure • Most significant defects • Require less shear stress to allow slip than a plane in a perfect lattice • 2 type dislocations ~ Edge Dislocation ~ Screw Dislocation 21

Edge and Screw Dislocation Figure 1.8 Types of dislocations in a single crystal: (a) edge dislocation; and (b) screw dislocation. Source: (a) After Guy and Hren, Elements of Physical Metallurgy, 1974. (b) L. Van Vlack, Materials for Engineering, 4th ed., 1980.


Movement of an Edge Dislocation

Figure 1.10 Movement of an edge dislocation across the crystal lattice under a shear stress. Dislocations help explain why the actual strength of metals in much lower than that predicted by theory.

Requires lower shear stress to cause slip than a plane in a perfect lattice: 1. Earthworm moves forward through a hump that starts at the tail and moves toward the head; 2. Moving a large carpet by forming a hump at one end and moving it to the other end. The force required to move a carpet is much less than that required to slide23 the carpet along the floor.

Imperfection In Metal Structure (General) • Actual strength of metal is 1 to 2 orders of magnitude lower than theoretical calculation strength lever • This is due to defect & imperfection in the crystal structure • Structure Sensitive: Mechanical & electrical properties of metal, such as yield, fracture strength & electrical conductivity, adversely affected by those defect • Structure Insensitive: Physical & chemical properties, such as melting point, specific heat, coefficient of thermal expansion & elastic constants are not sensitive to those 24 defect

Strain (Work) Hardening • Dislocation can become entangled & interfere with each other (Example: moving two humps at different angles across a carpet with

the two humps interfering with each other’s movement, making it more difficult to move the carpet)

• Impeded by barriers, such as grain boundaries & impurities inclusions in the materials • Entanglement and impediment increase the shear stress required for slip • The effect of an increase in shear stress increases the strength of metal at ambient temperature – Strengthening wire by reducing its cross-section by drawing it through a die – Producing the head on a bolt by forging it – Producing sheet metal for automobile bodies and aircraft fuselages by rolling


Solidification of Polycrystalline Structure Figure 1.11 Schematic illustration of the stages during solidification of molten metal; each small square represents a unit cell. (a) Nucleation of crystals at random sites in the molten metal; note that the crystallographic orientation of each site is different. (b) and (c) Growth of crystals as solidification continues. (d) Solidified metal, showing individual grains and grain boundaries; note the different angles at which neighboring grains meet each other. Source: W. Rosenhain.


Grain Boundary

Grain or Crystalline Structure


Grain Sizes T A B L E 1 . 1 2 3 A S T M N o . G r a i n s / m m G r a i n s / m m – 3 1 0 . 7 – 2 2 2 – 1 4 5 . 6 0 8 1 6 1 1 6 4 5 2 3 2 1 2 8 3 6 4 3 6 0 4 1 2 8 1 , 0 2 0 5 2 5 6 2 , 9 0 0 6 5 1 2 8 , 2 0 0 7 1 , 0 2 4 2 3 , 0 0 0 8 2 , 0 4 8 6 5 , 0 0 0 9 4 , 0 9 6 1 8 5 , 0 0 0 1 0 8 , 2 0 0 5 2 0 , 0 0 0 1 1 1 6 , 4 0 0 1 , 5 0 0 , 0 0 0 1 2 3 2 , 8 0 0 4 , 2 0 0 , 0 0 0

N =2

n −1

• N: Number of grains • n: Grain size Large Grains (Low strength, hardness, and ductility): zinc on the surface of galvanized sheet steels Small Grains: car bodies, Appliances, and Kitchen utensils


Plastic Deformation of Polycrystalline Metal • Each grain takes places by the mechanisms for single crystals • Grain boundary remains intact & mass continuity is maintained • The greater the deformation, the stronger the metal become ~ Because of GB entanglement of dislocation

• The smaller the grain sizes, the higher the strength for metals ~ Because they have a large grain-boundary surface area per unit volume of metal 28

Plastic deformation of Polycrystalline Metal (Anisotropy) • Anisotropy (As a result of plastic deformation, the grain have elongated in 1 direction & contracted in the other. Its properties in vertical direction are different from horizontal direction.) – Preferred orientation – Mechanical fibering

• Anisotropy influences mechanical & physical properties (increase in strength and decrease in ductility) 29

Preferred Orientation

â&#x20AC;˘ Also called crystallographic anisotropy â&#x20AC;˘ Slip planes tend to align themselves with the direction of deformation 30

Anisotropy (Texture) (b)

Figure 1.13 (a) Schematic illustration of a crack in sheet metal that has been subjected to bulging (caused by, for example, pushing a steel ball against the sheet). Note the orientation of the crack with respect to the rolling direction of the sheet; this sheet is anisotropic. (b) Aluminum sheet with a crack (vertical dark line at the center) developed in a bulge test; the rolling direction of the sheet was vertical. Source: J.S. Kallend, Illinois Institute of Technology.


Mechanical Fibering • Result from the alignment of impurities, inclusions & voids in the metal during deformation – Impurities weaken the grain boundaries. Metal will be weaken and less ductile when tested in the vertical direction. – E.g. Plywood


Summary of Plastic Deformation â&#x20AC;˘ Plastic deformation causes increase in strength, decrease in ductility & causes anisotropic behavior â&#x20AC;˘ Plastic deformation can be reversed and properties of the metal can be brought back to their original level, by heating the piece in a specific temperature range for a period of time (annealing) 33

Recovery, Recrystallization and Grain Growth Figure 1.14 Schematic illustration of the effects of recovery, recrystallization, and grain growth on mechanical properties and on the shape and size of grains. Note the formation of small new grains during recrystallization. Source: G. Sachs.

New equiaxed and strain-free grains

i) Recovery ii) Recrystallization iii) Grain growth


Recovery • Below recrystallization temperature of the metal • Stresses in the highly deform region relieved • Subgrain boundaries begin to form (polygonization) • No change in mechanical properties (strength and hardness) • Small increase in ductility


Recrystallization • Recrystallization temperature defines as a temperature at which complete recrystallization occurs within 1 hour – Temperature range,0.3Tm & 0.5Tm (Tm=Melting point)

• Decrease density of dislocation • Decrease strength (Lead, tin, cadmium and zinc recrystallize at room temperature. Thus when these metals are cold worked, they do not work-harden.)

• Increase ductility 36

Effect on Recrystallization by Prior Cold Working – At constant amount of deformation by prior cold work, recrystallization time decreases with increasing temperature in Fig 3.17a – At constant temperature, the more the prior cold worked, the less time it takes to recrystallize (The amount of cold work increase, the # of dislocations & energy stored in dislocation also increase. This energy supplied the work require for recystallization.) in Fig.3.17b – The higher the amount of deformation, the lower the grain size become after recrystallization Fig. 3.18 – To restore isotropy from anisotropy, require higher temperature than recrystallization temperature


Fig. 3.17a Constant Deformation

Fig. 3.17b Constant Temperature

Elongation (%) Fig. 3.18 Recrystallization Grain Size

Fig. 3.19 Orange peel


Grain growth • To raise temperature higher than recrystallization, grain begin to grow and size may exceed original size (Fig. 1.14) • Do affects mechanical properties (Fig. 1.14) • Large grains, produce rough surface, when stretched or compressed to form a part (Fig. 3.19) 39

Homologous Temperature Ranges for Various Processes TABLE 1.2 Process Cold working Warm working Hot working

T/Tm < 0.3 0.3 to 0.5 > 0.6


Assignment â&#x20AC;˘ Read Chapter 3.1-3.9


PPT sobre estructura cristalina de metales