Materials M1

3 Lecture focus Reproduced from “Materials and Man’s Needs”, National Academy of Sciences, Washington D.C., 1974.

6 Solid Materials Material Bonding • As two atoms come close together they experience attractive forces between the (negative) electron clouds and the (positive) nuclei. • The two atoms also experience the repulsive force between the two nuclei as well as the repulsive force between the two electron clouds. • At a separation (r o ) the sum of both the attractive forces and the repulsive forces equals zero. • Significant other parameter - Temperature

9 Solid Material - Bonding Types of interatomic and intermolecular bonds Primary (strongest bonds) • Ionic • Covalent • Metallic Secondary (Weaker) • Van der Waals • Hydrogen ( Callister Pg. 34) M1 Lab B

12 Primary Bonds Metallic Bonding • Ions in a ‘sea ‘ of electrons • Metallic bonding involves the attraction between ion cores and valence electrons • Common in metals and their alloys • The free valence electrons act as a “glue” to hold the ion cores together. • Bonding may be weak with low melting point (e.g., Hg) or strong with high melting point (e.g., W). • Presence of mobile electrons means good heat and electrical conductivity, and in terms of mechanical properties enables the feature of ductility in many metallic materials . M1 Lab B

15 Structure and order Crystalline and amorphous Crystalline materials – atoms pack in regular periodic 3D arrays. Typical of • Metals • Many ceramics • Some polymers Amorphous (Non – Crystalline) materials – atomic arrangement is purely random. Typical of • Many polymers • Glasses • Complex structures • Rapidly solidified solids

18 Crystal Structures and Crystallography Crystals and Grains in Metallic Materials • The adjacent figure shows a section through an ingot of cast aluminium. • This has been obtained after the aluminium has been extracted from its ore, refined at high temperature in the molten condition and then allowed to solidify. • In everyday life metallic materials generally appear as shiny, machined or perhaps painted or coated surfaces. • However, deeper analysis shows that the bulk solid material consists of crystals, or grains. • How and where the crystals form on solidification has a major bearing on the properties of these materials, and thus their applications. • The crystal and grain structures need to be understood so that they can be modified to develop the useful engineering materials we have today and for the future.

21 Crystal Structures and Crystallography (Ashby GL1-13) Metallic Crystal Structures • Simple Cubic (SC) • Body Centred Cubic (BCC) Reasons for metals’ dense packing: • Typically, only one element is present, so all atomic radii are the same. • Metallic bonding is not directional. • Nearest neighbor distances tend to be small in order to lower bond energy. • Electron cloud shields cores from each other • Have the simplest crystal structures. Coordination Number (CN) = Number of nearest neighbours Atomic Packing Factor (APF) = Volume of atoms in unit cell Volume of unit cell Examples: • Iron • Chromium • Manganese • Molybdenum Lab A

22 Crystal Structures and Crystallography (Ashby GL1-13) Metallic Crystal Structures c a A sites B sites A sites Examples: • Nickel • Gold • Copper • Aluminium Examples: • Titanium, • Magnesium • Zinc • Zirconium • Face Centred Cubic (FCC) • Hexagonal Close Packed (HCP) Lab A

23 Densities of Material Classes (Callister) ρ metals > ρ ceramics > ρ polymers Why? Data from Callister ρ (g/cm ) 3 Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers 1 2 20 30 Based on data from Callister (Pg. 8) *GFRE, CFRE, & AFRE are Glass, Carbon, & Aramid Fiber-Reinforced Epoxy composites (values based on 60% volume fraction of aligned fibers in an epoxy matrix). 10 3 4 5 0.3 0.4 0.5 Magnesium Aluminum Steels Titanium Cu,Ni Tin, Zinc Silver, Mo Tantalum Gold, W Platinum G raphite Silicon Glass -soda Concrete Si nitride Diamond Al oxide Zirconia HDPE, PS PP, LDPE PC PTFE PET PVC Silicone Wood AFRE * CFRE * GFRE* Glass fibers Carbon fibers A ramid fibers Metals have... • close -packing (metallic bonding) • often large atomic masses Ceramics have... • less dense packing • often lighter elements Polymers have... • low packing density (often amorphous) • lighter elements (C,H,O) Composites have... • intermediate values In general ρ : Density

24 Crystal Structures and Crystallography (Ashby GL1-13) Miller Indices A pseudo-quantitative method of describing crystallographic orientations, i.e., atomic locations in terms of coordination, planes and directions. Reciprocals of the (three) axial intercepts for a plane, cleared of fractions and common multiples. All parallel planes have same Miller indices. Principle 1. Read off intercepts of plane with axes in terms of a , b , c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no commas i.e., (hkl) M1

25 Crystallographic Directions 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a , b , and c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [ uvw ] e.g. 1, 0, ½ => 2, 0, 1 => [201] -1, 1, 1 Families of directions represented by < uvw > z x Principle where the overbar represents a negative index [111] => y

26 Crystallographic Planes z x y a b c 4. Miller Indices (110) a b c z x y a b c 4. Miller Indices (100) 1. Intercepts 1 1  2. Reciprocals 1/1 1/1 1/  1 1 0 3. Reduction 1 1 0 1. Intercepts 1/2   2. Reciprocals 1/½ 1/  1/  2 0 0 3. Reduction 1 0 0 a b c M1

27 Crystallographic Planes (cont.) 4. Miller Indices (634) example 1. Intercepts 1/2 1 3/4 a b c 2. Reciprocals 1/½ 1/1 1/¾ 2 1 4/3 3. Reduction 6 3 4 (001) (010), Family of Planes represented by { hkl } (100), (010), (001), E.g. {100} = (100), z x y a b c · · · M1

28 Imperfections and Defects in Crystals Crystal Defects Phase Boundary Grain Boundary Vacancy Interstitial Solute Dislocations Substitutional Solute

29 Imperfections and Defects in Crystals Edge Dislocation The edge of an extra portion of a plane of atoms, or a half‐plane, terminates within the crystal It is a linear defect, that centers on the line defined along the end of the extra half‐plane of atoms (the dislocation line) Screw Dislocation Formed by a shear stress that is applied to produce the distortion shown in the Figure The atomic distortion is also linear and along the dislocation line Dislocations

30 Imperfections and Defects in Crystals A transmission electron microscopy (TEM) image of a titanium alloy in which the dark lines are dislocations. (Callister Pg. 105) Dislocations

31 Learning Outcome Check 2 ❑ What are Millers Indices used to represent? ❑ What is the difference between FCC, BCC and HCP crystal structures? ❑ Name three types of crystalline defects ❑ What are the two main types of dislocation

32 Strengthening Mechanisms in Metallic Materials (Ashby Pg. 128-163) Elastic and Plastic Deformation Fundamental Mechanical Properties • Strength Usually considered as the tensile strength, which is defined as the maximum force required to fracture per unit cross sectional area in tension. In most cases however, the yield strength, the force at which the material begins to permanently deform, is the limiting factor. • Ductility This is considered to be the capacity to undergo deformation (generally under tension) without rupture. This is distinct from malleability. • Toughness This is the ability to withstand bending or deflection, or absorb energy, without fracture. Effectively, it is the resistance to fracture, and described by the area under the stress-strain curve for a material. • Hardness This is ability to resist plastic deformation, indentation or abrasion. This property is very important in an engineering application where resistance to wear is a requirement. M1

33 Mechanical Properties in relation to Structure How to define or determine these properties?... By testing… Primary Tests Tensile Test • One of the most valuable and commonly used of the mechanical tests for materials. • Data on strength, toughness and ductility • Expensive, relatively slow (loading rate) and destructive • Load capacity: a great range available • Loading method: mechanically or hydraulically Hardness Test • Surface indentation with a known load • Quick, low cost, semi destructive Impact Test • Strike standard specimen with calibrated pendulum load • Quick, intermediate cost, destructive Strengthening Mechanisms in Metallic Materials ( Callister Pg.226 ) Lab B

34 Strengthening Mechanisms in Metallic Materials extensometer specimen T S Adapted from Fig. 6.3, Callister & Rethwisch 8e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials , Vol. III, Mechanical Behavior , p. 2, John Wiley and Sons, New York, 1965.) Tensile Testing Nominal Stress (MPa) Strain Fracture Ultimate Tensile Strength (UTS) Yield Strength Necking Elastic deformation Lab B

35 Strengthening Mechanisms in Metallic Materials Elastic Deformation A result of an extension of the interatomic bonds, retractable after the load is removed (reversible) It occurs when a material is loaded within its elastic limit and stress and strain are proportional s e Hooke's Law : s = E e σ : Stress [MPa] E: Young’s modulus or modulus of elasticity [ GPa] e: Strain (no units) F: Force [N] A: Cross-sectional area [m 2 ] L: Length [cm] where s and e are defined as: Initial rod Rod pulled L L D L s s s = F e = D L L A M1 Lab B

36 Strengthening Mechanisms in Metallic Materials Plastic Deformation A result of interatomic bonds being broken and atoms moving to different positions relative to each other (irreversible or permanent deformation). This occurs when the material is loaded beyond its elastic limit. Plastic (permanent) deformation after load is removed Plastic strain Simple Tensile Test curve Stress (MPa) Strain Elastic (reversible) deformation ‘Non - linear’ plastic deformation Atoms remain in same position relative to each other Slip has now occurred Yield point: plastic deformation starts M1

37 Strengthening Mechanisms in Metallic Materials Slip Systems and Dislocation Theory • In crystalline solids, the plastic deformation process is also known as SLIP , as planes of atoms tend to slide over each other into new stable positions • Slip occurs on close packed planes and in close packed directions within the crystal – so that the atoms can follow the shortest path to their new positions under the most favourable energetic conditions • The combination of slip plane and slip direction is known as a slip system . Slip plane - plane on which easiest slippage occurs - highest planar densities (and large interplanar spacing) Slip direction - directions of movement - highest linear densities 12 x {111}(110) systems in a FCC unit cell (Callister Pg. 185)

38 • In practice, plastic deformation occurs by incremental movement of discrete slip events, i.e. the motion of large numbers of dislocations. • Dislocation motion is analogous to the mode of locomotion employed by a caterpillar. • The permanent deformation by dislocation movement in crystals is approximately 1000 times less than that expected by theoretical calculation in a perfect crystal structure and where all atoms on the slip plane move simultaneously. Strengthening Mechanisms in Metallic Materials Dislocation Motion and Plastic Deformation (Callister Pg. 201)

39 Strengthening Mechanisms in Metallic Materials Dislocation Movement and Interaction • Any process or treatment that will restrict or prevent the movement of dislocations within the crystals or grains will result in strengthening (and hardening). • Strength is increased by making dislocation motion difficult. • Strength of metals may be increased by: • Decreasing grain size • Solid solution strengthening • Precipitate hardening • Cold working or work hardening

40 Learning Outcome Check 3 ❑ What is the difference between strength and toughness? ❑ What properties can we determine from the tensile test? ❑ Name two methods to determine toughness of a material. ❑ What is the overall principle behind strengthening metals?

41 Strengthening Mechanisms in Metallic Materials Pure Metals Copper (Electrical) Aluminium (Electrical/Decorative) Refractories (Mo, W) – High temperature Nickel (Electrical, Electronic) • Pure metals for load bearing applications are of little use. Alloying • In order to improve mechanical properties (and many other properties) various mechanisms or treatments are employed, and alloying with other elements is performed. • Alloying is either to neutralise the effect of undesirable trace elements, or to modify and improve desired properties for specific applications.

42 Strengthening Mechanisms in Metallic Materials Alloys can be produced with mixtures of : – Metals/Metals e.g., Cu-Zn (Brass) – Metals/Non‐metals e.g., Fe‐C (Steel) – Metals/Gas e.g., FeCrNiN (a Stainless Steel) Intersolubility of elements varies from ~0% to 100% – Al‐Sn immiscible in both liquid and solid state – Cd‐Bi soluble in liquid state only – Cu‐Zn limited solubility of Zn in Cu in solid state – Cu‐Ni mutual soluble in liquid and solid state Alloying A metal alloy is a mixture or series of metallic solid solutions or phases, composed of two or more elements

43 Strengthening Mechanisms in Metallic Materials Strengthening by Reducing Grain Size • Most commercial metals are made up of polycrystalline grains, of random crystallographic orientations, with a common grain boundary • When these metals are subjected to loading, the dislocation motion must take place across the common boundary, from grain A to grain B • The grain boundary acts as a barrier for dislocation, because: ➢ the two grains are randomly orientated, a dislocation passing into B needs to change its direction of motion, which becomes more difficult as the misorientation increases ➢ the atomic disorder within a grain boundary region will result in a discontinuity of slip planes from one grain to another Metals having small grains – relatively strong and tough at low temperatures Metals having large grains – good creep resistance at relatively high temperatures A fine‐grained material is harder and stronger due to a greater total grain boundary area to imposed dislocation motion Check out the Hall-Petch Equation σ y = σ 0 +K d -1/2 σ y : Yield Strength [MPa] d: Grain size [mm] σ 0, k: Constants M1

44 Strengthening Mechanisms in Metallic Materials Cold Work - Strain Hardening or Work Hardening It is the phenomenon whereby a ductile metal becomes harder and stronger as it is plastically deformed. During plastic deformation there is multiple dislocation movement and addition, which eventually leads to interaction and entanglement of these defects. Entanglement restricts their movements. • In single crystals: dislocation movements ‐> plastic deformation/slip • In polycrystalline metals: dislocation movements occur preferentially in grains with slip systems that is most favourably located relative to the load direction. • Rotation occurs to bring the grains into more favourable position, so as to keep the grain boundaries in contact • Most grains will eventually have a plane in the direction of deformation. • A considerable amount of distortion will have occurred, and the materials will have gone straining or work hardening. How a metal becomes harder and stronger as it is plastically deformed, or work hardened. However, this effect can be ‘removed’ by heat treatment

45 Learning Outcome Check 4 ❑ How does grain size reduction result in strengthening of metals? ❑ How does work hardening result in strengthening of metals? ❑ What is an alloy?

46 Strengthening Mechanisms in Metallic Materials Formation of alloys A useful alloy is only formed when the elements in question are mutually soluble in the liquid state . Upon cooling, the following conditions may occur: • Insoluble in the solid state ‐ they separate out as particles of the two pure metals. • Complete or partial solubility in the solid state ‐ in the former case a single solid solution forms , whilst in the latter a mixture of two different solid structures results. • An intermetallic compound, or an intermediate phase forms in the solid state.

47 Strengthening Mechanisms in Metallic Materials Constitution of Alloys • The resulting constitution of alloys: – Single phase solid solution – Multiphase alloy – Multiphase alloy with precipitates – Highly strained metastable states • For load bearing alloys, the required properties are a combination of strength and toughness. • These properties are controlled to a large extent by adjusting the structure of the alloy to control the behaviour of dislocations. • On a microstructural level this is done by affecting the atomic lattice configurations of the alloy.

48 Strengthening Mechanisms in Metallic Materials Solid Solutions • A solid solution forms when metals dissolve in all ratios one into the other. • A solid state phase in which the primary element has incorporated atoms of the secondary element(s) into the primary lattice. • Sites for the secondary element atoms can be: Normal primary element sites: substitutional solid solution (SSS) Between primary element sites: interstitial solid solution (ISS) • Both SSS and ISS atoms create strain field within crystal lattice, which act to resist dislocation movement M2

49 Strengthening Mechanisms in Metallic Materials Substitutional solid solution Interstitial solid solution M2

50 Strengthening Mechanisms in Metallic Materials Several factors are known that control ranges of substitutional solid solubility in alloy systems. – Crystal‐structure factor ‐ as indicated above complete solid solubility of two elements is never attained unless the elements have the same type of crystal lattice structure. – Relative size factor ‐ the size factor is favourable for solid solution formation when the difference in atomic size is less than about 15%. – Chemical‐affinity factor ‐ the greater the chemical affinity of two elements, the more restricted is their solid solubility. Generally, the further apart the elements are in the periodic table, the greater is their chemical affinity. Substitutional Solid Solution

51 Strengthening Mechanisms in Metallic Materials Interstitial Solid Solutions • An interstitial solid solution (b) is formed when atoms of small atomic size fit into the spaces of the lattice structure of the larger atom elements. • The best known and most important to engineers is the interstitial solution of carbon in iron, which results in steel. The more carbon atoms present the stronger the alloy, due to the distortion, which occurs interfering with the movement of dislocations on the slip planes of the alloy. Substitutional Interstitial

52 Strengthening Mechanisms in Metallic Materials Solid Solution Strengthening Alloys are stronger than pure metals because: • Impurity atoms imposing lattice strains on the surrounding host atoms • Lattice strain field interactions between dislocations and the impurity atoms result • Dislocation movement is restricted and therefore strength is increased a. Compressive strains imposed on host atoms b. Larger impurity atoms, leading to partial cancellation of impurity‐dislocation lattice strain, but a roughening of the slip plane thus causing internal friction and impeding the dislocation movement Callister Pg.196 Next…. How to determine the optimum alloy compositions and treatments …..Phase Equilibrium Diagrams!

53 Learning Outcome Check 5 ❑ What is a solid solution? ❑ Distinguish between; a substitutional solid solution, and; an interstitial solid solution. ❑ Give three factors that would control substitutional solid solubility? ❑ How does alloying result in strengthening of metals? ❑ Give a very common engineering example of an interstitial solid solution?