Week 1 Introduction to Materials Science PDF

Materials and Structures 24TTA002 Dr Yi Liu Senior Lecturer in Polymers and Composites Office: S2.048 Email: [email protected] Tel: 01509 223156  Overview -Module Specification on Learn...

Materials and Structures 24TTA002 Dr Yi Liu Senior Lecturer in Polymers and Composites Office: S2.048 Email: [email protected] Tel: 01509 223156  Overview -Module Specification on Learn For example: -Combination of Lectures and Tutorials and Labs -Staff Contact: Dr Yi Liu, Dr Andrew Watson -Timetable and Email Notifications Timetable The lectures will be on every Thursday from 10 to 12 in the room T003. Please pay attention to your timetables. You can contact me during my office time. Office: S2.048 Email: [email protected] Lab session will be on Tuesday or Wednesday from week 5. Please check you timetable, and don’t miss your session There is a Learn test worth 20% of the module toward the end of Semester 1 (details to follow). The rest of the assessment is split between a lab report and an exam, both in Semester 2. The exam will cover material from the whole course (both materials and structures).  Syllabus The course is broadly in two parts: materials (semester 1) and structures (semester 2). In the materials part: Overview of materials: metals, plastics, elastomers, ceramics, and glass. Fundamentals of structure. Characteristic properties of the different material types. Introduction to: chemical and physical aspects of materials; the Periodic Table and chemistry associated with materials. Atomic structure and bonding. Simple crystals and unit cells. Elastic and plastic behaviour, theoretical strength, defect theory, and an introduction to dislocations. Mechanical testing: tensile, impact, hardness, fatigue and creep. Mechanical properties of composites. Materials properties requirements and the relationship to material's specifications. Evaluating materials selection for a given application, particularly using Ashby plots. Materials processing and applications. Material tetrahedron Materials tetrahedron Processing-Structure-Properties-Performance Principle  - Overview of materials science and engineering. Topic 1 - Classification of materials: metals, ceramics, polymers, and Introduction to composites. Materials Science - Materials selection in aerospace and automotive applications. - Atomic Structure and Bonding Topic 2 - Polymers Structure of - Metals Materials - Ceramics and glasses - Composites Topic 3 - Stress-strain behaviour, Young's modulus, yield strength, and Mechanical toughness. Properties of - Comparison of mechanical properties across different Materials materials. Topic 4 - Overview of processing techniques: casting, forging, Processing and extrusion, injection moulding. Manufacturing - Materials Selection for Aerospace and Automotive Techniques Applications  Topic 1 Introduction to Materials Science Reading list: Materials Science and Engineering, William D. Callister (Chapter 1- Introduction; Chapter 2-Atomic Structure and Interatomic Bonding) Introduction to Materials Science aluminium oxide  Introduction to Materials Science The structure of the atom and electronegativity Bohr’s model of an atom Protons and neutrons form the nucleus The nuclear force holds together the nucleus: it is stronger than the repulsion (Coulomb force) between protons Electrons orbit around the nucleus Atoms have diameters in the range of 10-10 meters, nuclei have diameters in the range 10-15 m Atoms are electrically neutral, number of protons = number of electrons The number of neutrons may vary (isotopes)  Introduction to Materials Science Do you know that… If a hydrogen atom would be as big as The O2 (Millennium Dome), the nucleus would be the size of a pea.  Introduction to Materials Science Periodic table  Introduction to Materials Science https://twitter.com/FHSchools/status/925339152077545472/photo/3  Introduction to Materials Science Atoms Atomic number 13 This denotes the number of Al electrons, and will help us think about bonding Atomic mass 26.982 Will come in handy when thinking about density later!  Introduction to Materials Science Moles The concept of mole and molecular weight Atoms can rarely be found as individual entities Most of the times they will be interacting with other atoms Understanding why and how this happens can help us understanding the properties of materials When 2 (or more) atoms react to form a new species, this will be called a MOLECULE* When dealing with molecules, we have to describe the relative amounts of atoms needed to form them  Introduction to Materials Science Mole and molecular weight The concept of mole and molecular weight The 14th Conférence Générale des Poids et Mesures established the definition of the mole in 1971: The mole is the amount of a substance of a system which contains as many elementary entities as there are atoms in 12 gram of carbon-12; its symbol is "mol." The number of these entities is known as “Avogadro’s number” and it is N= 6.022x1023 entities So, 1 mole of Hydrogen weighs ~ 1 g 1 mole of Carbon weighs ~ 12 g 1 mole of Oxygen weighs ~ 16g And they all contain the same number of atoms!  Introduction to Materials Science Calculation Molecular weight of ethylene C2H4  Introduction to Materials Science Covalent bond the two atoms will share electrons forming a COVALENT BOND For polymers, this is the main type of bond that we will deal with  Introduction to Materials Science Covalent bond  Introduction to Materials Science Electronegativity Electronegativity  Introduction to Materials Science Number of bonds Between any two atoms max 6 bonds* can be formed, but for the atoms that we consider max 3 bonds can be formed The first bond formed is called sigma (or single), the second and third are called pi (or double/triple) * The formation of 4,5 or even 6 (very rare!) bonds between two atoms is only found for transition metals (columns 3 to 12) or for very unusual situations  Introduction to Materials Science Bonds Increasing the number of bonds between two atoms will bring them closer Moreover, the rotation around a single bond is allowed, while double and triple cannot: rigid molecules!  Introduction to Materials Science Benzene and the aromatic ring The aromatic group was described for the first time by Kekule’ in 1865, suggesting a structure with alternating single and double bonds Further studies suggested that all 6 carbon atoms are equivalent and at the same distance from each other: the ‘pi’ electrons are Do you know that… The term 'aromatic' delocalised derived from the fact that many of the compounds have a sweet scent  Introduction to Materials Science Classes of Materials Image credit: DoITPoMS  Introduction to Materials Science Intermolecular interactions (‘weak bonds’) The polarity of bonds in molecules is responsible also for the type of interactions that will exists between them. The three main ones are: 1) Hydrogen bonding When Hydrogen is covalently bonded to O, F, N the bond will have a strong polarity Opposite charged dipoles will attract each other, the interaction between them ~ 10 times weaker than a covalent bond: HYDROGEN BONDING Do you know that… hydrogen bonding in water is responsible for the density of liquid water at 4°C being higher than solid water (ice)  Introduction to Materials Science Intermolecular interactions http://io9.com/the-very-first-image-of-a-hydrogen-bond-1426759827  Introduction to Materials Science Intermolecular interactions 2) Dipole-dipole forces All bonds between atoms of different electronegativity will have a certain polarity and the resulting dipoles will tend to attract/repel each other, but the forces involved will be weaker than the Hydrogen bonding Dipole-dipole interactions occur when partial charge form within a molecule because of the uneven distribution of electrons.  Introduction to Materials Science Intermolecular interactions 3) London (dispersion) forces (a.k.a. Van der Waals forces) The electron cloud moving around the atoms of a molecule creates instant dipoles, that in turn induce dipoles into neighbouring atoms/molecules: these dipoles will attract each other These forces are temporary and very weak  Introduction to Materials Science Other bonds: - Ionic Bonds : Found predominantly in ceramics (e.g., alumina (Al₂O₃), sodium chloride), some polymers with ionic groups (e.g., ionomers), and salts. - Covalent Bonds: Predominant in polymers, ceramics, and semiconductors (e.g., silicon, diamond, graphene, glass). - Metallic Bonds: Found in metals and metal alloys (e.g., steel, aluminum, titanium). - Pi-Pi Stacking: Found in aromatic compounds (e.g., graphene, polycyclic aromatic hydrocarbons)  Introduction to Materials Science Group Discussion: 15 minutes Automotive Uses of Metals Aeronautical  Introduction to Materials Science Group Discussion: Automotive Uses of Polymers Aeronautical  Introduction to Materials Science Group Discussion: Automotive Uses of Ceramics and Glasses Aeronautical  Introduction to Materials Science Group Discussion: Automotive Uses of Composites /Hybrids Aeronautical  Introduction to Materials Science How to select materials using Ashby plots and performance indexes Materials selection Design criteria: -Cost -Weight -Strength -Stiffness -Aesthetics -Durability -Manufacturability -The “Feel” By Billy Wu at Imperial :https://www.youtube.com/watch?v=9RQkvcsRzbo Introduction to Materials Science Introduction to Materials Science  Introduction to Materials Science The course in one slide... The atomic, microscopic structure of the materials profoundly aspects the macroscopic properties of the material, and of the component. You need to understand these connections to be a good engineer.  Introduction to Materials Science Characteristic properties of metals Characteristic properties of ceramics Hard Hard Shiny Not ductile Good conductors of electricity Resistant to wear, corrosion, weather Good conductors of heat High melting point Strong Not good conductors of heat Stiff Electrically insulating Ductile / formable Not strong in tension, but strong in Able to bear loads compression Resistant to shock Brittle Low impact strength and low shock resistance Materials and Structures 24TTA002 Dr Yi Liu Senior Lecturer in Polymers and Composites Office: S2.048 Email: [email protected] Tel: 01509 223156  - Overview of materials science and engineering. Topic 1 - Classification of materials: metals, ceramics, polymers, and Introduction to composites. Materials Science - Materials selection in aerospace and automotive applications. - Atomic Structure and Bonding Topic 2 - Polymers Structure of - Metals Materials - Ceramics and glasses - Composites Topic 3 - Stress-strain behaviour, Young's modulus, yield strength, and Mechanical toughness. Properties of - Comparison of mechanical properties across different Materials materials. Topic 4 - Overview of processing techniques: casting, forging, Processing and extrusion, injection moulding. Manufacturing - Materials Selection for Aerospace and Automotive Techniques Applications  Topic 2 Structure of Materials  Topic 2 Polymers  Learning outcomes After this set of lectures, you will be able to: - Describe a typical polymer molecule in terms of its chain structure and, in addition, how the molecule may be generated from repeat units. - Draw repeat units for common polymers. - Describe addition and condensation polymerization mechanisms. - Calculate number-average molecular weights and degree of polymerization for a specified polymer.  Polymer Science What is a polymer?  Polymer Science Plastic identification code - Plastic Container Code System PLA (Polylactic acid)  Polymer Science PE - Polyethylene PP - Polypropylene PS - Polystyrene PLA - Polylactic acid What in common?  Polymer Science “Polymer” What does it mean?  Polymer Science “Polymer” Poly (greek: polus) - mer (greek: meros) Many Part Parts Monomer  Polymer Science “Polymer” Poly (greek: polus) - mer (greek: meros) Many Part IUPAC (International Union of Pure and Applied Chemistry) Polymer: “A molecule of high relative molecular mass, the structure of which essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass.” IUPAC Polymer Education: http://iupac.org/polyedu/index.html Monomers IUPAC Purple Book (free download)  Polymer Science Ethylene is a gas at ambient temperature and pressure. It can reach with an initiator or catalyst (R): Active site Polymer chain Polyethylene  Polymer Science Vinyl chloride monomer Chlorine Poly(vinyl chloride) (PVC)  Polymer Science Tetrafluoroethylene monomer 4 Fluorine atoms Polytetrafluoroethylene (PTFE) Water repellent fabrics Trade name Teflon (fluorocarbon family) 14  Polymer Science Methyl group Phenyl group Aromatic ring  Polymer Science How are polymers classified?  Polymer Science Classifications Several common ways to classify polymers: Polymerization Source type Structure There are also some other ways to classify: for examples according to Performance (Specialty, Engineering, Bulk)  Polymer Science Classifications Common ways to classify polymers: Linear Thermoplastic Structure Chemical Thermoset Crosslinked Branched Elastomer Physical Thermoplastic  Structures of Materials Polymers are everywhere Think about polymers you met in our daily life. List them out, we will have a discuss during tutorial session. Natural Synthetic  Polymer Science Origins We can classify them according to their origins… Natural Synthetic/ semi-synthetic Cellulose PE PET SILK RUBBER PS  Polymer Science Polymerisation: Process of converting a monomer or a mixture of monomers into a polymer. The reactions by which polymerisation occur are grouped into two general classifications, according to the reaction mechanism: - Addition - Condensation  Polymer Science Addition polymerisation (sometimes called chain reaction polymerisation) is a process by which monomer units are attached one at a time in chainlike fashion to form a linear macromolecule. The composition of the resultant product molecule is an exact multiple of that of the original reactant monomer. 1) Initiation step: an active centre is formed by a reaction between an initiator (or catalyst) species and the monomer unit.  Polymer Science 2) Propagation: linear growth of the polymer chain by the sequential addition of monomer units to this active growing chain molecule. Chain growth is relatively rapid; the period required to grow a molecule consisting of 1000 repeat units is on the order of 10-2 to 10-3 s.  Polymer Science 3) Termination: the growth of each polymer chain is completed. - The active ends of two propagating chains may link together to form one molecule. - Two growing molecules react to form two “dead chains”.  Polymer Science Condensation polymerization (or step reaction polymerisation) is the formation of polymers by stepwise intermolecular chemical reactions that may involve more than one monomer species. This stepwise process is successively repeated, producing a linear molecule. Reaction times for condensation polymerisation are generally longer than for addition polymerisation.  Polymer Science The polyester poly(ethylene terephthalate) (PET) Nylon Fishing lines  Polymer Science Once the polymerisation is completed, do all polymer chains have the same length?  Polymer Science During polymerisation, not all chains will grow to the same length; this results in a distribution of chain length or molecular weights. Polymer Chains  Polymer Science Number-average molecular weight Mi is the mean molecular weight of size range i xi is the fraction of the total number of chains within the corresponding size range.  Polymer Science 𝑀𝑛 = (0.05×7500)+ xi Mi (0.18×12500)+ (0.21×17500)+ 0.05 7500 (0.27×22500)+ (0.19×27500)+ 0.18 12500 (0.08×32500)+ 0.21 17500 (0.02×37500)= 20950 0.27 22500 0.19 27500 0.08 32500 𝑀𝑛 = 20950 0.02 37500  Polymer Science Degree of polymerisation (DP) the average number of repeating units in one chain m is the molecular weight of the repeat unit.  Polymer Science Example: Polyethylene Atom Atomic weight (g/mol) C 12.01 H 1.01 ഥ 𝑛= 4000 g/mol 𝑀 m = 2(12.01 g/mol) + 4(1.01 g/mol) = 28.06 g/mol DP = 143 ഥ 𝑛= 35000 g/mol 𝑀 m = 2(12.01 g/mol) + 4(1.01 g/mol) = 28.06 g/mol DP = 1247  Polymer Science Determine the average molecular weight and the degree of polymerisation. 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑒𝑟 𝑜𝑓 𝑝𝑜𝑙𝑦𝑚𝑒𝑟 𝑐ℎ𝑎𝑖𝑛𝑠 = 4000 + 8000 + 7000 + 2000 = 21000 4000 8000 𝑥1 = = 0.190 𝑥2 = = 0.381 21000 21000 7000 2000 𝑥3 = = 0.333 𝑥4 = = 0.095 21000 21000  Polymer Science 𝑀1 = 2500 g/mol 𝑀2 = 7500 g/mol 𝑀3 = 12500 𝑔/𝑚𝑜𝑙 𝑀4 = 17500 g/mol 𝑥1 𝑀1 = 475.0 g/mol 𝑥2 𝑀2 = 2857.5 g/mol 𝑥3 𝑀3 = 4166.7 𝑔/𝑚𝑜𝑙 𝑥4 𝑀4 = 1662.5 g/mol ഥ 𝑛= (475.0+2857.5+4166.7+1662.5) g/mol = 9161.7 g/mol 𝑀 DP = 326.5  Polymer Science Classification based on the chemical structure: Homopolymer A-A-A-A-A-A-A-A-A One type of repeating unit. Alternating copolymer Two types of repeating units, arranged A-B-A-B-A-B-A-B-A alternately along the polymer chain. Block copolymer The repeating units are in groups or blocks A-A-A-A-A-B-B-B-B of the same type.  Polymer Science Graft copolymer Branched copolymer in which the chemical structure of the braches is different from that of the main chain. B B B A-A-A-A-A-A-A-A-A-A-A-A-A-A-A-A B B B -B-B-B-B  Polymer Science Linear polymers are those in which the repeat units are joined together end to end in single chains. Polyethylene, poly(vinyl chloride), polystyrene, poly(methyl methacrylate), nylon, fluorocarbons. Branched polymers have side-branch chains are connected to the main ones. Low density polyethylene (LDPE) Crosslinked polymers have adjacent linear chains joined one to another at various positions by covalent bonds. Elastomers (crosslinking), rubber (vulcanisation)  Polymer Science Network polymers have multifunctional monomers forming three or more active covalent bonds make three dimensional networks. Epoxies, polyurethanes, and phenol-formaldehyde resins  Polymer Science Macromolecular structures single chains (linear or branched) strongly entangled coils with weak inter-molecular interaction forces between chains single chain - Van der Waals - hydrogen bonds low stiffness due to weak interaction (strong intra-molecular interactions - covalent bonds - are not loaded !! )  Polymer Science Thermoplastic/thermoset Thermoplastics soften/melt when heated, they can be shaped and then cooled down to a solid object (no chemical change during heating/cooling), then re-melted and re-shaped if needed. water Polymer Science  Polymer Science Some examples of TP/TS: Which is the main difference you can notice in term of structure? TP TS Bakelite (Polyoxybenzylmethylenglycolanhydride) Epoxy resin Polystyrene Nylon 6  Polymer Science Examples of Thermosets Vulcanised rubber Polyurethane Polyformaldehyde (Bakelite) Cyanoacrylate Often quite complex formulations – fillers, stabilisers, process aids, pigments How are the polymer chains arranged?  Polymer Science What is crystallisation Crystallisation of polymers is a process associated with partial alignment of their molecular chains. These chains fold together and form ordered regions called lamellae, which compose larger spheroidal structures named spherulites. Polymers can crystallize upon cooling from the melt, mechanical stretching or solvent evaporation. Crystallization affects optical, mechanical, thermal and chemical properties of the polymer. The degree of crystallinity is estimated by different analytical methods and it typically ranges between 10 and 80%, thus crystallized polymers are often called "semi-crystalline".  Polymer Science Polymers can be amorphous and partially crystalline (semicrystalline). Amorphous polymer Semicrystalline polymer Crystalline regions Semicrystalline polymers have crystalline regions dispersed within the remaining amorphous material. The molecular chains are packed to produce an ordered atomic array. 46  Polymer Science (Semi)-Crystalline and Amorphous Thermoplastics* ▪ Crystallisation is usually energetically favourable unless chains are too irregular or bulky ▪ Crystallisation in polymers is never complete ▪ (Semi)-crystalline polymers (e.g.PE) are usually translucent/opaque and tough * Thermosets are fully amorphous  Polymer Science The degree of crystallinity is: ρs is the density of the sample (mass/volume) ρa is the density of the amorphous polymer ρc is the density of the crystalline polymer  Polymer Science Example: Calculate the degree of crystallinity of Polyethylene (PE) 𝑚𝑎𝑠𝑠 𝜌𝑠 = = 0.925 𝑔/𝑐𝑚3 𝑣𝑜𝑙𝑢𝑚𝑒 Amorphous region Crystalline region 𝜌𝑎 = 0.870 𝑔/𝑐𝑚3 𝜌𝑐 = 0.998 𝑔/𝑐𝑚3 𝜌𝑐 > 𝜌𝑎 Why? The polymer chains are more closely packed together for the crystalline structure than for the amorphous one. 49  Polymer Science 𝜌𝑠 = 0.925 𝑔/𝑐𝑚3 𝜌𝑎 = 0.870 𝑔/𝑐𝑚3 𝜌𝑐 = 0.998 𝑔/𝑐𝑚3 0.998(0.925 − 0.870) % 𝑐𝑟𝑦𝑠𝑡𝑎𝑙𝑙𝑖𝑛𝑖𝑡𝑦 = × 100 = 46.4% 0.925(0.998 − 0.870)  Polymer Science Low-density polyethylene 𝜌 = 0.910 − 0.940 𝑔/𝑐𝑚3 High-density polyethylene 𝜌 = 0.940 − 0.970 𝑔/𝑐𝑚3 Difference in crystallinity degree?  Polymer Science Low-density polyethylene High-density polyethylene 𝜌 = 0.910 − 0.925 𝑔/𝑐𝑚3 𝜌 = 0.940 − 0.970 𝑔/𝑐𝑚3 Crystallinity: 50-65% Crystallinity: 70-95% The degree of crystallinity has profound effects on the mechanical, thermal and optical properties of polymers.  Polymer Science What is crystallization A video showing what happens when you cool down a mass of molten PEO (polyethyleneoxide) It is observed with a polarised light microscope https://www.youtube.com/watch?v=a4VtJieJ-ug Other examples  Polymer Science The crystallization process  Polymer Science Step 1. Nucleation Do you want to know more about nucleation and crystallisation? http://media.wiley.com/product_data/excerpt/82/04714452/0471445282.pdf  Polymer Science Step 2. Chain folding Polymer chains are too long to crystallise in extended fashion: they fold  Polymer Science Step 3. Formation of lamellae  Polymer Science Step 4. Spherulites Polymer crystallites begin at a nucleation point, then grow outwards – the lamellae tend to twist as they grow, and we end up with a “spherulitic structure” Spherulites are often big enough to scatter light, which is why crystalline polymers are translucent (or opaque) rather than transparent Start of a Spherulite  Polymer Science Spherulite Structure Visible under cross-polarised light as Maltese crosses with dark/light circles  Structures of Materials SUMMARY - Most polymeric materials are composed of very large molecular chains with side groups of various atoms (O, Cl, etc.) or organic groups. - Synthesis of high-molecular-weight polymers is attained by polymerization, of which there are two types: addition and condensation. - Chain length may be specified by degree of polymerization - the number of repeat units per average molecule. - Four different polymer molecular chain structures are possible: linear, branched, crosslinked, and network. - When the molecular chains are aligned and packed in an ordered atomic arrangement, the condition of crystallinity is said to exist. Materials and Structures 24TTA002 Dr Yi Liu Senior Lecturer in Polymers and Composites Office: S2.048 Email: [email protected] Tel: 01509 223156 Topic 2 Metals  Metals What are Metals? Metals are a class of materials characterized by their high electrical and thermal conductivity, malleability, and ductility. Common metals: Iron (Fe), Copper (Cu), Aluminium (Al), Gold (Au), etc.  Metals Key Properties: High electrical conductivity: metals conduct electricity due to the presence of free electrons. Thermal conductivity: metals are good conductors of heat. Malleability and ductility: metals can be shaped into thin sheets (malleability) or stretched into wires (ductility). Lustre: Most metals have a shiny appearance. Density and strength: Metals typically have high density and strength, making them ideal for structural applications.  Metals Types of Metals: Metals are basically two main groups: ferrous metals and non-ferrous metals. Ferrous metals are the ones that have iron in them, while non-ferrous metals don’t have any iron. It’s as simple as that!  Metals Crystal Structure A lattice is a periodic array of points in space. A crystal has atoms associated with these points. Most metals crystallise as one of: BCC (body-centred cubic) FCC (face-centred cubic) HCP (hexagonal close packed) Many can adopt a range of dierent structures depending on external conditions like temperature and pressure (polymorphism, allotropy).  Metals Unit cell Here is a 2D simple square lattice.  Metals Unit cell The unit cell is the smallest group of atoms which has the same symmetry as the crystal structure (here square). Three possibilities are shown in red. The crystal lattice can be built up by periodically repeating the unit cell in all directions.  Metals Conventional and primitive unit cells We usually use a conventional unit cell to describe the symmetry of the crystal, probably one of the left two in this case. The primitive unit cell is the smallest possible unit cell and contains only one atom.  Metals Face-centred cubic lattice FCC lattice has an atom at each corner of the cube, and one at the centre of each face. There are atoms in each conventional unit cell. Example FCC metals: Al, Ca, Ni, Cu, Sr, Ag, Pt, Au, Pb [crystal structures of each element non-examinable]  Metals Body-centred cubic lattice BCC lattice has an atom at each corner of the cube, and one at the centre of the cube. There are Atoms in each conventional unit cell. Example BCC metals: Li, Na, K, V, Cr, Mn, Fe, Mo, W [crystal structures of each element non-examinable] Dr  Metals Hexagonal close-packed lattice HCP lattice conventionally has a hexagonal unit cell. There are 12 atoms at the corners, two on the centres of the top and bottom faces, and three in a triangle. There are atoms in each conventional unit cell. Example HCP metals: Mg, Ti, Co, Zn, Zr [crystal structures of each element non- examinable]  Metals Density How do we measure density?  Metals Density measurement The reduction in mass in the fluid of known density tells us the volume The density can then be calculated using where m1 is the mass of the object, m2 is the mass when weighed in the fluid and is the density of the fluid.  Metals Density and crystal structure  Metals Density and crystal structure  Metals Density and crystal structure  Metals Density and crystal structure  Metals Density change on phase transition Mechanical Properties of Metals 20  Learning outcomes After this set of lectures, you will be able to: - Define engineering stress and engineering strain. - Given an engineering stress-strain diagram, determine the modulus of elasticity, the tensile strength and estimate the percentage elongation. - For a specimen being loaded in tension, given the applied load, the instantaneous cross-sectional dimensions, be able to compute true stress.  Mechanical properties of metals The mechanical behaviour of metals can be investigated by applying an external force or load. The load can be applied in tension, compression or shear. Tension or tensile tests A specimen is deformed, usually to fracture, with a gradually increasing tensile load that is applied uniaxially along the long axis of a specimen.  Mechanical properties of metals The output of a tensile test is recorded as load or force versus elongation. Mechanical properties of metals  Mechanical properties of metals The load-deformation characteristics depend on the specimen size. To minimize these geometrical factors: - load is converted in stress - elongation is converted in strain. F Stress A0 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑙𝑜𝑎𝑑 𝜎= 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝐹 𝑁 𝜎= 𝜎 = 2 = 𝑃𝑎 𝐴0 𝑚  Mechanical properties of metals Strain 𝐹𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ − 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝐸𝑙𝑜𝑛𝑔𝑎𝑡𝑖𝑜𝑛 𝜀= = 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝑙 − 𝑙0 𝜀= 𝜀 𝑖𝑠 𝑢𝑛𝑖𝑡𝑙𝑒𝑠𝑠 𝑙0 Mechanical properties of metals  Mechanical properties of metals For most metals that are stressed in tension and at relatively low levels, stress and strain are proportional to each other through the relationship: Hooke’s law 𝜎 = 𝐸𝜀 E is the elastic modulus or Young’s modulus 𝜎 𝐸= [𝐸] = 𝑃𝑎 𝜀 The Young’s modulus is a measure of the stiffness or rigidity of a material. Mechanical properties of metals 29  Mechanical properties of metals Deformation in which stress and strain are proportional is called elastic deformation. A plot of stress (ordinate) versus strain (abscissa) results in a linear relationship. Elastic deformation is non-permanent. When the applied load is released, the piece returns to its original shape. 30  Mechanical properties of metals Exercise A piece of copper originally 305 mm long is pulled in tension with a stress of 276 MPa. If the deformation is entirely elastic, what will be the resultant elongation? The elastic modulus of copper is 110 GPa. 31  Mechanical properties of metals Solution 𝜎 𝜎 = 𝐸𝜀 𝜀= 𝐸 276 𝑀𝑃𝑎 276 × 106 𝑃𝑎 𝜀= = 9 = 0.0025 110 𝐺𝑃𝑎 110 × 10 𝑃𝑎 𝑙 − 𝑙0 𝜀= 𝑙 − 𝑙0 = 𝜀 𝑙0 𝑙0 𝑙 − 𝑙0 = 0.0025 × 305 𝑚𝑚 = 𝜀 𝑙0 = 0.77 𝑚𝑚 𝐸𝑙𝑜𝑛𝑔𝑎𝑡𝑖𝑜𝑛 = 0.77 𝑚𝑚 32  Mechanical properties of metals Exercise A specimen of copper having a rectangular cross section 15.219.1 mm2 is pulled in tension with 44500 N, producing only elastic deformation. Calculate the resulting strain. 33  Mechanical properties of metals Solution 𝐹 44500 N 44500 𝑁 6 𝜎= = = = 153.28 × 10 Pa 𝐴0 15.219.1 mm2 290.32 × 106 𝑚2 The elastic modulus of copper is 110 GPa. 𝜎 153.28 × 106 Pa 𝜀= = 9 = 0.0014 𝐸 110 × 10 𝑃𝑎 34  Mechanical properties of metals Exercise Consider a cylindrical nickel wire 2.0 mm in diameter and 3104 mm long. Calculate its elongation when a load of 300 N is applied. Assume that the deformation is totally elastic. The elastic modulus of nickel is 207 GPa. 35  Mechanical properties of metals Solution 𝐴0 = 𝜋 𝑟 2 𝐴0 = 3.14 𝑚𝑚2 𝐹 300 N 6 Pa 𝜎= = = 95.5 × 10 𝐴0 3.14 mm2 𝜎 95.5 × 106 Pa 𝜀= = 9 = 0.00046 𝐸 207 × 10 𝑃𝑎 𝑙 − 𝑙0 = 𝜀 𝑙0 𝑙 − 𝑙0 = 0.00046 × 3 × 104 𝑚𝑚 = 𝜀 𝑙0 = 1.38 𝑚𝑚 𝐸𝑙𝑜𝑛𝑔𝑎𝑡𝑖𝑜𝑛 = 1.38 𝑚𝑚 36  Mechanical properties of metals For most metallic materials, elastic deformation persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain. Plastic deformation occurs. Plastic deformation is permanent and nonrecoverable. 37  Mechanical properties of metals A structure or component that has plastically deformed experiences a permanent change in shape. It may not be capable of functioning as intended. Plastic deformation Elastic deformation 38  Mechanical properties of metals Brittle: A metal that experiences Ductile: A metal that experiences very little or no plastic plastic deformation upon deformation upon fracture. fracture.  Mechanical properties of metals The tensile strength TS is the stress at the maximum on the engineering stress-strain curve. It is the maximum stress that can be sustained by a structure in tension. 40  Mechanical properties of metals Necking: a small constriction or neck begins to form. The deformation is confined at this neck. 41  Mechanical properties of metals The cross-sectional area is decreasing rapidly within the neck region, where deformation is occurring. Can we still use the previous definition of stress? 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑙𝑜𝑎𝑑 𝐹 𝜎= 𝜎= 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝐴0 42  Mechanical properties of metals Engineering or nominal stress 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑙𝑜𝑎𝑑 𝐹 𝜎= 𝜎= 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝐴0 True stress 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑙𝑜𝑎𝑑 𝜎𝑇 = 𝐼𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑑𝑢𝑟𝑖𝑛𝑔 𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝐹 𝜎𝑇 = 𝐴𝑖 43 Mechanical properties of metals 44  Mechanical properties of metals Exercise 45  Mechanical properties of metals Solution 570 MPa 46  Mechanical properties of metals Solution 200 𝑀𝑃𝑎 E= = 200 𝐺𝑃𝑎 The correct answer is D 0.001 47  Mechanical properties of metals Exercise A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile tested to fracture and found to have an engineering breaking stress of 460 MPa. If its cross-sectional diameter at fracture is 10.7 mm, determine the true breaking stress. 48  Mechanical properties of metals Solution Calculate the load applied to the sample. 𝐴0 = 𝜋 𝑟 2 𝐴0 = 128.7 𝑚𝑚2 𝐹 = 𝜎𝐴0 = 460 𝑀𝑃𝑎 × 128.61 𝑚𝑚2 = 59202 𝑁 𝐴𝑖 = 89.9 𝑚𝑚2 𝐹 59202 𝑁 𝜎𝑇 = = 2 = 658.5 𝑀𝑃𝑎 𝐴𝑖 89.9 𝑚𝑚 49  Mechanical properties of metals Toughness is the resistance of a material to the propagation of a crack. 50  Mechanical properties of metals Simple fracture is the separation of a body into two or more pieces in response to an imposed stress. Any fracture process involves two steps - crack formation and propagation – in response to an imposed stress. Brittle fracture takes place without any appreciable deformation and by rapid crack propagation. The direction of crack motion is very nearly perpendicular to the direction of the applied tensile stress. 51 ”Materials Science and Engineering” by W. D. Callister  Mechanical properties of metals Ductile fracture takes place with a plastic deformation. 52  Mechanical properties of metals (a) Highly ductile fracture in which the specimen necks down to a point. (b) Moderately ductile fracture after some necking. 53  Mechanical properties of metals Fracture toughness is a material property that is a measure of a material’s resistance to brittle fracture when a crack is present. Material property: Its value is independent of the way it is measured. 54  Mechanical properties of metals Cracks propagate when the applied stress exceeds a critical value. This critical value is the fracture toughness, K1c. 55 ” Materials engineering, science, processing and design” by M. Ashby, et al., Elsevier (2007).  Mechanical properties of metals A sample containing a sharp crack is loaded. The crack suddenly propagates when the tensile stress σ* is reached. 56  Mechanical properties of metals Example: A specimen at 25 °C with a crack of 1 cm width K1c = 6 MPa m1/2 Will the sample fail under a stress of 10 MPa? 𝐾 = 𝜎(𝜋𝑐)1/2 = 10 MPa (3.14 × 0.5 𝑐𝑚)1/2 = 1.25 MPa m1/2 K < Kc no failure 57  Mechanical properties of metals Here we consider toughness as impact resistance: The ability of the material to withstand the application of a sudden load without failure. We can measure the energy necessary to cause fracture at high rates of force application. 58  Mechanical properties of metals Charpy impact tester V-notch The specimen is in the shape of a bar of square cross section, into which a V-notch has been machined. 59  Mechanical properties of metals Charpy impact tester The load is applied as an impact blow from a weighted pendulum hammer released from a fixed height. The specimen is positioned at the base as shown. Upon release, a knife edge mounted on the pendulum strikes and fractures the specimen at the notch. 60 Mechanical properties of metals 61  Mechanical properties of metals SUMMARY - Engineering stress is defined as the instantaneous load divided by the original specimen cross-sectional area. - Engineering strain is expressed as the change in length divided by the original length. - True stress is defined as the instantaneous applied load divided by the instantaneous cross-sectional area. - The slope of the linear elastic region of the stress-strain curve is the modulus of elasticity, per Hooke’s law. - Tensile strength is taken as the stress level at the maximum point on the engineering stress-strain curve. 62  Topic 2 Ceramics and Composites  Ceramics A ceramic is a nonmetallic, inorganic solid, such as oxides, nitrides, and carbides “mixed” bonding—a combination of covalent, ionic, and sometimes metallic. General properties ✓Brittle ✓High compressive strength ✓Poor electrical /thermal conduction ✓Chemical insensitivity  Ceramics Classification of Ceramics  Ceramics Ceramics applications Ceramic filters for screening debris from molten metals during casting gas turbine engine components cutting tool  Ceramics Atomic Bonding in Ceramics Bonding: -- Can be ionic and/or covalent in character. -- % ionic character increases with difference in electronegativity of atoms. Degree of ionic character may be large or small:  Ceramics Ceramic Crystal Structures Oxide structures – oxygen anions larger than metal cations – close packed oxygen in a lattice (usually FCC) – cations fit into interstitial sites among oxygen ions  Ceramics Factors that Determine Crystal Structure 1. Relative sizes of ions – Formation of stable structures: --maximize the # of oppositely charged ion neighbors. - - - - - - + + + Adapted from Fig. 12.1, Callister & Rethwisch 8e. - - - - - - unstable stable stable 2. Maintenance of Charge Neutrality : F- CaF 2 : Ca 2+ + --Net charge in ceramic cation anions should be zero. --Reflected in chemical F- formula: A m Xp m, p values to achieve charge neutrality  Ceramics Coordination # and Ionic Radii (FYI) Coordination # increases with To form a stable structure, how many anions can surround around a cation? r cation Coord ZnS r anion # (zinc blende) Adapted from Fig. 12.4, < 0.155 2 linear Callister & Rethwisch 8e. 0.155 - 0.225 3 triangular NaCl (sodium 0.225 - 0.414 4 tetrahedral chloride) Adapted from Fig. 12.2, Callister & Rethwisch 8e. 0.414 - 0.732 6 octahedral CsCl (cesium chloride) 0.732 - 1.0 8 cubic Adapted from Fig. 12.3, Callister & Rethwisch 8e.  Ceramics Rock Salt Structure Same concepts can be applied to ionic solids in general. Example: NaCl (rock salt) structure rNa = 0.102 nm rCl = 0.181 nm rNa/rCl = 0.564  cations (Na+) prefer octahedral sites Adapted from Fig. 12.2, Callister & Rethwisch 8e.  Ceramics Glass Structure Basic Unit: Glass is noncrystalline (amorphous) 4- Fused silica is SiO2 to which no Si0 4 tetrahedron impurities have been added Si 4+ Other common glasses contain O2- impurity ions such as Na+, Ca2+, Al3+, and B3+ Na + Quartz is crystalline Si 4+ SiO2: O2- (soda glass) Adapted from Fig. 12.11, Callister & Rethwisch 8e.  Mechanical properties of Ceramics Ceramic materials are more brittle than metals. Why is this so? Consider mechanism of deformation – In crystalline, by dislocation motion – In highly ionic solids, dislocation motion is difficult few slip systems resistance to motion of ions of like charge (e.g., anions) past one another  Mechanical properties of Ceramics Flexural Tests – Measurement of Elastic Modulus Room T behavior is usually elastic, with brittle failure. 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials. cross section F L/2 L/2 d R b  = midpoint rect. circ. deflection  Mechanical properties of Ceramics Flexural Tests – Measurement of Elastic Modulus Determine elastic modulus according to: F F L3 x E= (rect. cross section) F  4bd 3 slope =  F L3 E= (circ. cross section)   12R 4 linear-elastic behavior  Mechanical properties of Ceramics Flexural Tests – Measurement of Elastic Modulus 3-point bend test to measure room-T flexural strength. cross section F L/2 L/2 d R b  = midpoint rect. circ. deflection location of max tension  Mechanical properties of Ceramics Flexural Tests – Measurement of Elastic Modulus Flexural strength: Typical values: Material fs (MPa) E(GPa) 3Ff L fs = (rect. cross section) Si nitride 250-1000 304 2 2bd Si carbide 100-820 345 Al oxide 275-700 393 Ff L fs = (circ. cross section) glass (soda-lime) 69 69 3 R  Composites What are the classes and types of composites? What are the advantages of using composite materials? How do we predict the stiffness and strength of the various types of composites?  Composites Composite Combination of two or more individual materials Mud + Straw = Brick Stone + Cement = Concrete Design goal: obtain a more desirable combination of properties (principle of combined action) – e.g., low density and high strength  Composites Composite Huge driving force for composites with lightweight yet strong and stiff structures  Composites Phase types: -- Matrix - is continuous -- Dispersed - is discontinuous and surrounded by matrix Matrix (primary phase) Continuous and but not always Present in the greater quantity Ceramic, metallic or polymeric matrix Reinforcement / reinforcing phase (2nd phase) Enhances mechanical properties of matrix  Composites Examples of composites: (a) particulate, random; (b) discontinuous fibres, unidirectional; (c) discontinuous fibres, random; (d) continuous fibres, unidirectional.  Composites Terminology/Classification Matrix phase: -- Purposes are to: woven - transfer stress to dispersed phase fibers - protect dispersed phase from environment -- Types: MMC, CMC, PMC metal ceramic polymer 0.5 mm cross Dispersed phase: section -- Purpose: view MMC: increase y, TS, creep resist. CMC: increase KIc 0.5 mm PMC: increase E, y, TS, creep resist. -- Types: particle, fiber, structural  Composites Classification: Particle-Reinforced (i) Particle-reinforced Fiber-reinforced Structural Examples: - Spheroidite matrix: particles: steel ferrite () cementite (ductile) (Fe C) 3 (brittle) 60 m - WC/Co matrix: particles: cemented cobalt WC (ductile, (brittle, carbide tough) : hard) 600 m particles: carbon - Automobile matrix: black tire rubber rubber (stiff) (compliant) 0.75 m  Composites Classification: Particle-Reinforced (iii) Particle-reinforced Fiber-reinforced Structural Elastic modulus, Ec, of composites: -- two “rule of mixture” extremes: upper limit: Ec = Vm Em + Vp Ep E(GPa) Data: 350 lower limit: Cu matrix 30 0 w/tungsten 250 1 Vm Vp = + particles 20 0 Ec Em Ep 150 0 20 40 60 80 10 0 vol% tungsten (Cu) (W) Application to other properties: -- Electrical conductivity, e: Replace E’s in equations with e’s. -- Thermal conductivity, k: Replace E’s in equations with k’s.  Composites Classification: Fiber-Reinforced Particle-reinforced Fiber-reinforced Structural Fibers very strong in tension – Provide significant strength improvement to the composite – Ex: fiber-glass - continuous glass filaments in a polymer matrix Glass fibers – strength and stiffness Polymer matrix – holds fibers in place – protects fiber surfaces – transfers load to fibers  Composites Classification: Fiber-Reinforced Particle-reinforced Fiber-reinforced Structural Critical fiber length for effective stiffening & strengthening: fiber ultimate tensile strength fiber diameter fd fiber length  shear strength of 2 c fiber-matrix interface Ex: For fiber glass, common fiber length > 15 mm needed For longer fibers, stress transference from matrix is more efficient Short, thick fibers: Long, thin fibers: fd d fiber length  fiber length  f Low fiber efficiency 2 c High fiber efficiency 2 c  Composites Classification: Structural Particle-reinforced Fiber-reinforced Structural Laminates Stacked and bonded fiber-reinforced sheets Stacking sequence: e.g., 0º/90º Benefit: balanced in-plane stiffness Sandwich panels Honeycomb core between two facing sheets Benefits: low density, large bending stiffness face sheet adhesive layer honeycomb 26 Materials property charts 27 Materials and Structures 24TTA002 Dr Yi Liu Senior Lecturer in Polymers and Composites Office: S2.048 Email: [email protected] Tel: 01509 223156 Mechanical properties of polymers 2  Learning outcomes After this set of lectures, you will be able to: - Make schematic plots of characteristic stress-strain behaviours observed for polymeric materials. - Describe/sketch the various stages in the elastic and plastic deformations of a polymer. - List four characteristics or structural components of a polymer that affect both its melting and glass transition temperatures. - Cite the differences in behaviour and molecular structure for thermoplastic and thermosetting polymers. 3  Mechanical Properties The deformation and fracture of a polymer can be determined by tensile, compression or impact tests. In a typical tensile experiment, the sample is elongated until it breaks. 4 Book “Introduction to physical polymer science” by L.H. Sperling, John Wiley & Sons (2006).  Deformation MechanicalofProperties polymers When a material is loaded, the atoms within the material are displaced and the material responds with a deformation. This deformation determines the mechanical behaviour of the material. Reversible deformations: the deformation disappears after unloading Elastic deformations Irreversible deformations: the deformation remains after unloading Plastic deformations 5  Deformation MechanicalofProperties polymers The mechanical stress is defined as the force applied divided by the area the force is acting on. If the force is perpendicular If the force is parallel to the to the area. area. 6  Deformation MechanicalofProperties polymers All deformations, also called strains, can be composed from changes in lengths and angles of the component. Normal strain Shear strain 7  Deformation MechanicalofProperties polymers Polymers are termed viscoelastic as they display both viscous and elastic types of behaviour. Combination of:  Ideal elastic solid Hooke’s law σ: tensile stress 𝜎 𝐸= 𝑙−𝑙0 𝜀 ε: tensile strain = 𝑙0 E: Young’s modulus  Ideal liquid 𝐹 𝜏= shear stress 𝐴 𝑑𝛾 ∆𝑥 Newton’s law 𝜏 = 𝜂 𝛾= shear strain 𝑑𝑡 𝐿 η: dynamic viscosity 8  Deformation MechanicalofProperties polymers A distinctive feature of the mechanical behaviour of polymers is the way in which their response to an applied stress or strain depends upon the rate or time period of loading and temperature. Low temperatures Elastic behaviour High rates of strain Hooke’s law 𝜎 = 𝐸𝜀 High temperatures Viscous behaviour (liquid) Low rates of strain 𝑑𝛾 Newton’s law 𝜏 = 𝜂 𝑑𝑡 9  Deformation MechanicalofProperties polymers Virtually all solid polymers - amorphous polymers below the glass transition temperature, or crystalline polymers below the melting temperature - undergo a permanent shape change when subjected to a stress of sufficient magnitude. The onset of irreversible deformations (the transition from elastic to plastic behaviour) is termed yielding. Yielding is of tremendous technological importance, defining upper limits of service stress in load-bearing applications or the conditions required for shaping parts during manufacturing. 10  Mechanical Properties Brittle polymer: it fractures while deforming elastically. Ductile material: Initial elastic deformation, followed by yielding and a plastic deformation. Elastic material: Large recoverable strains produced at low stress. 11  Deformation MechanicalofProperties polymers (a) Low extensibility followed by brittle fracture (b) Localised yielding followed by fracture (c) Necking and cold drawing Yield Yield Yield (d) Homogeneous deformation with indistinct yield (e) Rubber-like behaviour 12  Deformation MechanicalofProperties polymers Yielding When a tensile stress is applied to a polymer, a neck or deformation band can occur, with the plastic deformation concentrated either entirely or primarily in a small region of the specimen. Yield involves an irreversible deformation and takes place by a shearing mechanism in which molecules slide past one another. 13  Deformation MechanicalofProperties polymers There are multiple ways by which the structure may react to an applied force. Molecular response may be by (a) stretching (b) bending covalent bonds in the chain (c) by rotation about bonds in the chain backbone; (d,e) by displacement of neighbouring chain segments. 14  Deformation MechanicalofProperties polymers Nominal or engineering stress (𝜎𝑛 ): the load (F) at any time during the deformation divided by the initial cross-sectional area (A0). 0 l True stress (𝜎): the load at any time during the deformation divided by the actual cross-sectional area at any time. 15  Deformation MechanicalofProperties polymers Formation of nano-patterned photonic surfaces via polymer cold-drawing Fabrication process of metallic micro/nano-patterns on flexible substrates through mechanical stretching. J. Mater. Chem. C 6, 4649, 2018 16  Deformation MechanicalofProperties polymers Self-powered ultrasensitive and highly stretchable temperature-strain sensing composite yarns Fabricate a new class of trimodal, stretchable transducers. The fabricated transducer can sense strain (first mode), and temperature (second mode) and can power itself thermoelectrically (third mode). Mater. Horiz., 2021, 8, 2513-2519 (image from SI) 17  Deformation MechanicalofProperties polymers Cold-drawing of a composite structure Fragmentation process that takes place during cold-drawing of a fibre consisting of a brittle core embedded in a ductile cladding. It is a controllable and sequential fragmentation of the core to produce uniformly sized rods. Nature, 534, 529, 2016 18  Deformation MechanicalofProperties polymers Nature, 534, 529, 2016 19  Linear Fracture Mechanics Mechanical Properties Polymers do not always fail mechanically by yielding (becoming ductile). They can fail by brittle fracture. 20  Mechanical Properties Brittle plastic The specimen fails at its maximum load, at comparatively low strains. 21 http://www.materials.unsw.edu.au/tutorials/online-tutorials/2-properties  Linear Fracture Mechanics Mechanical Properties The process of brittle fracture involves two stages: crack initiation and crack propagation. The principal two theories used to describe brittle fracture are: - assume that fracture takes place through the presence of pre-existing cracks or flaws in the polymer; - are concerned with what happens near the crack Griffith fracture theory when a load is applied; Irwin model - define a fracture-toughness parameter; - apply strictly only for materials that are perfectly elastic for small strains; - describe linear fracture mechanics. 22  Linear Fracture Mechanics Mechanical Properties Griffith fracture theory As a crack propagates from a pre-existing flaw, it produces a new surface area. It is assumed that the energy needed to produce this area comes from elastically stored energy which is concentrated near the flaw. The growth of the crack is associated with: - The amount of work being done on the system by external forces - A change in the elastically stored energy. 𝑙 The difference between these quantities (external work and elastic energy) is the energy available for the formation of the new surface. 𝑙𝑜𝑎𝑑 23  Linear Fracture Mechanics Mechanical Properties Now we compute the energy available for crack growth. 24  Linear Fracture Mechanics Mechanical Properties Griffith fracture theory For an infinite and thin plate with an elliptic through crack, the energy balance is: ∆𝑈𝑡𝑜𝑡 = ∆𝑈𝑠 − ∆𝑈𝑒 𝑙 ∆𝑈𝑠 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 ∆𝑈𝑒 = elastic energy change 𝑙𝑜𝑎𝑑 The crack will propagate if the total energy of the system decreases. Book “Fracture Kinetics of Crack Growth” 25  Linear Fracture Mechanics Mechanical Properties ∆𝑈𝑠 = 2𝛾𝑙 𝛾 is the free energy per unit area of surface 𝜋𝜎 2 𝑙 2 𝐸 is the Young’s modulus of a thin sheet in ∆𝑈𝑒 = plane stress 4𝐸 𝜋𝜎 2 𝑙 2 ∆𝑈𝑡𝑜𝑡 = ∆𝑈𝑠 − ∆𝑈𝑒 = 2𝛾𝑙 − 4𝐸 The critical stress that initiates the crack propagation is defined by 𝑑∆𝑈𝑡𝑜𝑡 =0 𝑑𝑙 26  Linear Fracture Mechanics Mechanical Properties ∆𝑈𝑠 = 2𝛾𝑙 𝑑∆𝑈𝑡𝑜𝑡 =0 𝑑𝑙 For small values of l, the linear term (increase in surface energy) is dominant. 𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑙 For large values of l, the decrease in elastic energy becomes dominant. ∆𝑈𝑡𝑜𝑡 𝜋𝜎 2 𝑙 2 ∆𝑈𝑒 = − 4𝐸 Up to the critical point, the crack will grow only if the stress is increased. Beyond that point, crack growth is spontaneous. 27  Linear Fracture Mechanics Mechanical Properties 𝑑∆𝑈𝑡𝑜𝑡 𝑑 𝜋𝜎 2 𝑙 2 = 2𝛾𝑙 − =0 𝑑𝑙 𝑑𝑙 4𝐸 𝜋𝜎 2 𝑙 4𝛾𝐸 𝜎𝑏 = Breaking stress 2𝛾 − =0 𝜋𝑙 2𝐸 The stress at which the fracture occurs varies inversely with the critical crack size. The crack growth in a linear elastic body is controlled by the elastic modulus and the surface energy. 28  Linear Fracture Mechanics Mechanical Properties Irwin model For an infinite sheet with a central crack, the stress field around the crack in a linear elastic material can be defined by the stress intensity factor KI: 𝜋𝑙 𝐾𝐼 = 𝜎 2 𝑙 The subscript I indicates loading normal to the crack. 𝑙𝑜𝑎𝑑 29  Linear Fracture Mechanics Mechanical Properties Irwin model The fracture stress is reached when 𝐾𝐼 reaches a critical value 𝐾𝐼𝑐 , which is the critical stress- intensity factor and is a measure of the fracture toughness. 2 𝜎𝑏 = 𝐾𝐼𝑐 𝜋𝑙 𝑙 The fracture toughness is a measure of the resistance of a material to brittle fracture when 𝑙𝑜𝑎𝑑 it contains a crack. It is a material property. 30  Linear Fracture Mechanics Mechanical Properties 4𝛾𝐸 Griffith fracture theory 𝜎𝑏 = 𝜋𝑙 2 Irwin model 𝜎𝑏 = 𝐾𝐼𝑐 𝜋𝑙 2 2 𝐾𝐼𝑐 𝐾𝐼𝑐 𝛾= 𝐺𝑐 = 2𝐸 𝐸 𝐺𝑐 is the critical strain-energy-release rate It takes account of all the energy required to produce new crack area. It includes the energy required to produce any accompanying plastic deformation of the material surrounding the crack. 31  Linear Fracture Mechanics Mechanical Properties One typical geometry used in studying the fracture of brittle polymers is three-point bending test. 32  Exercises: Brittle failure 33  Linear Fracture Mechanics Mechanical Properties Exercise A long strip of polymer 1 cm wide and 1 mm thick, which contains no cracks, is subjected to a tensile force of 100 N along its length. This produces a strain of 0.3%. Another strip of the same polymer is identical except that it has a crack of length 1 mm perpendicular to its long axis at its centre. If the value of 𝛾 for the polymer is 1500 J m-2, estimate the tensile load necessary to break the second strip. 1 mm 1 mm 1 cm 1 cm 1 mm  Linear Fracture Mechanics Mechanical Properties Solution 𝛾 = 1500 𝐽𝑚−2 4𝛾𝐸 𝜎𝑏 = 𝑙 = 1 𝑚𝑚 𝜋𝑙 E is the Young’s modulus 100 𝑁 𝜎 10 × 106 𝑃𝑎 9 𝜎 = −5 2 = 10 𝑀𝑃𝑎 𝐸= = −3 = 3.33 × 10 𝑃𝑎 10 𝑚 𝜀 3 × 10 4 × 1500 𝐽𝑚−2 × 3.33 × 109 𝑃𝑎 6 𝑃𝑎 𝜎𝑏 = = 79.4 × 10 𝜋 × 10−3 𝑚 𝑙𝑜𝑎𝑑𝑏𝑟𝑒𝑎𝑘 = 79.4 × 106 𝑃𝑎 × 10−5 𝑚2 = 794 𝑁 If the tensile load applied exceeds 794 N, the crack will propagate. 35  Mechanical Properties Yield strength: the stress at this maximum. Tensile strength: the stress at which the fracture occurs. Elastic (Young’s) modulus: the slope of this linear region (the change in stress divided by the corresponding change in strain). Elongation at break (fracture strain): the elongation at the moment of rupture by the initial length. 36  Mechanical Properties The mechanical properties of polymers are highly sensitive to the rate of deformation, temperature and environmental conditions. 37 Book “Introduction to physical polymer science” by L.H. Sperling, John Wiley & Sons (2006).  Mechanical Properties Glass transition temperature (Tg) The temperature at which the polymer experiences the transition from rubbery into glassy states. The temperature below which the polymer chains are in a “frozen” state. Tg is usually applicable to amorphous and semicrystalline polymers. 38 Book “Introduction to physical polymer science” by L.H. Sperling, John Wiley & Sons (2006).  Mechanical Properties (melting > 130ºC) (melting > 150ºC) (melting > 250ºC) (melting > 200ºC) PP PLA PET PS Rubbery Rubbery Rubbery 100 °C Water boils 95°C 75°C Rubbery 60°C 37 °C Body temp. 22 °C Room temp. 0 °C Glassy Glassy Glassy ≈ 0°C Glassy Water freezes  Mechanical Properties Adding hot water around 90 degree C PP PLA PET PS Plastic cup  Mechanical Properties Which ones do you think can hold the hot water properly?  Mechanical Properties Amorphous polymers 1 - Glassy region - Young’s modulus is constant - Polymer is stiff and (typically) brittle 42  Mechanical Properties Amorphous polymers 2 - Glass transition region - Young’s modulus drops - At Tg, the polymer assumes a rubbery behaviour Glass-Transition Temperature 43  Mechanical Properties Amorphous polymers 3 - Rubbery plateau region - Young’s modulus is almost constant - Polymer behaves like a rubber Glass-Transition Temperature 44  Mechanical Properties Amorphous polymers 4 - Rubbery flow region - Polymer exhibits both rubber elasticity and flow properties Glass-Transition Temperature 45  Mechanical Properties Amorphous polymers 5 - Liquid flow region - Polymer flows readily Glass-Transition Temperature 46  Mechanical Properties Crosslinked polymers Glass-Transition Temperature 47  Mechanical Properties Semicrystalline polymers Glass-Transition Temperature Melting Temperature 48  Mechanical Properties Tm is the melting temperature: the transformation of the solid polymer to a viscous liquid occurs. The main transition exhibited by the crystalline part of the polymer is a melting from an ordered crystal to a liquid, disordered state. 49  Mechanical Properties Reduced chain flexibility Bulky side groups and polar groups Tg increases Polystyrene (PS) Polyethylene (PE) Tg= -110 °C Tg= 100 °C Poly(vinyl chloride) (PVC) Tg= 87 °C 50  Mechanical Properties Molecular Structure and Transition Temperatures Tg Tm Repeating unit Stiff bonds correspond to higher Stiff bonds correspond to higher Tg Tm Molecular Weight/ Lower MW will move easier, so Effects not dramatic Distribution Tg is reduced Branches Branches increase the free Branches reduce the crystallinity volume decreasing the Tg and so the Tm Side groups Bulky, inflexible groups hinder Bulky group hinder movements movement increasing Tg increasing Tm Tacticity Tacticity influence chain packing Only regular polymer (iso-syndio) and so Tg (high packing, less free will have a Tm volume) Copolymerisation Intermediate between the two Effect depends on the type of homopolymers copolymer (1 or 2 Tm) Crosslinking Crosslinks reduce the free Crosslinks reduce mobility volume, increasing Tg increasing Tm Intermolecular Strong cohesive forces between Strong cohesive forces between forces chains increase Tg chains increase Tm