1 -- annotated -- Introduction, atomic structure and bonding, material classes

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Mechanical Behavior of Engineering Materials or: why things break and how to stop them… Hayden Taylor hkt@berkeley.edu
Week 1: Course introduction, classes of materials, and atomic and crystal structures
How can engineered objects fail ? Excessive deformation Elastic Plastic Fracture Fast fracture Fatigue Wear Corrosion Others? Images courtesy Grace O’Connell
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Etcheverry Hall north elevator, about an hour ago
V&A Café, about 55 minutes ago
Some high-profile failures, and how they were addressed Beauvais Cathedral, 1284 Hyatt Skywalk, 1981 Champlain Towers, 2021 Tacoma Narrows, 1940 Golden Gate Bridge, 1987 anniversary Titan Submersible, 2023 Blue Origin rocket, 2022 Severn Bridge, 1967
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Ways of thinking about failure, lifetime, and risk in engineering Learning iteratively through failure vs codifying learning over time What probability of failure is acceptable? Risk ~ likelihood × severity Likelihood of failure can change with time Fatigue, creep, corrosion – all time- or cycle-dependent processes Planned obsolescence
Structure of the class Build from bottom up
Materials engineering: the beauty of nature, activated by human ingenuity https://www.azom.com/article.aspx?ArticleID=13961
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Classes of materials and their general attributes Materials property databases that the library subscribes to: https://guides.lib.berkeley.edu/c.php?g=4436&p=15752 But: always base real designs on manufacturer data and/or direct testing of the material itself, rather than generic values: they vary greatly between producer and even batch Adapted from Table 27.1, Jones and Ashby ed. 2 vol. 2 Class E Young’s modulus 𝝈𝝈 𝒚𝒚 Yield stress 𝑲𝑲 𝑰𝑰𝑰𝑰 Fracture toughness Thermal properties Other attributes ( advantages / disadvantages ) Metals Stiff E ~ 100 GPa Low in pure metals: 𝝈𝝈 𝒚𝒚 ~ 1 MPa alloy for strength and hardness Tough 𝐾𝐾 𝐼𝐼𝐼𝐼 > 50 MPa m 0 . 5 High melting point: 𝑇𝑇 𝑚𝑚 1000 . Good thermal shock resistance. Ductile: formable ( 𝜖𝜖 𝑓𝑓 ~20% ). Often require coatings for corrosion resistance. Ceramics Stiff E ~ 200 GPa Very high yield & hardness ( 𝝈𝝈 𝒚𝒚 > 3 GPa) Very low toughness 𝐾𝐾 𝐼𝐼𝐼𝐼 2 MPa m 0 . 5 High melting point: 𝑇𝑇 𝑚𝑚 2000 . Poor thermal shock resistance. Moderate density. Corrosion resistant. Low formability powder methods. Polymers Low stiffness E ~ 2 GPa Low yield strengths ( 𝝈𝝈 𝒚𝒚 ~2 100 MPa) Toughness often low 𝐾𝐾 𝐼𝐼𝐼𝐼 1 MPa m 0 . 5 Low glass transition temperature: 𝑇𝑇 𝑔𝑔 ~ 100 creep Ductile and formable. Corrosion resistant. Low density. Composites Stiff E > 50 GPa Strong ( 𝝈𝝈 𝒚𝒚 200 MPa) Tough 𝐾𝐾 𝐼𝐼𝐼𝐼 > 20 MPa m 0 . 5 Risk of creep due to polymer matrices Fatigue resistant. Corrosion resistant. Low density. Poor formability (after initial production). High cost.
Material selection evolution: bridges Ironbridge, Shropshire, UK, 1781 (cast iron) Clifton Suspension Bridge, UK, 1864 (wrought iron) https://commons.wikimedia.org/w/index.php?curid=25693468 Brooklyn Bridge, 1883 (steel cables)
Material selection evolution: aircraft 1903 Wright biplane Low-density wood Steel wire Silk 1935 Douglas DC3 Early aluminum alloys 2010 Boeing 787 Dreamliner 1 50 wt% composites 20 wt% aluminum 15 wt% titanium 20% lower fuel consumption per passenger mile* 1 http://www.boeing.com/commercial/787family/programfacts.html * Compared with similar-sized aircraft 1 1968 Boeing 747 Mostly aluminum alloys (2000, 7000 series) Some titanium alloys CFRP Steel
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There may be multiple valid material choices for a particular function Example: Coca-Cola packaging 1. http://retroguyswonderland.blogspot.com/2011/04/evolution-of-coke-bottle.html 2. freevectors.net 3. fabulesslyfrugal.com 4. http://www.thecoca-colacompany.com/ourcompany/historybottling.html Long evolution of glass bottles 1 c. 1960 Aluminum can 2 c. 1977 PET bottle 3 c. 2007 Aluminum bottle 1
Discussion: requirements for materials used in two objects Screwdriver Folding chair
Course logistics Course staff Instructor: Hayden Taylor, hkt@berkeley.edu , 6181 Etcheverry Hall GSIs: Abrar Khan, Jennings Ye Lectures: Fridays 2-5pm; recorded; breaks at 3 and 4pm Discussions Four sections: please attend your scheduled section; if you need to change, respond to survey from the GSIs Homeworks: 10 HWs; equal weight; questions will be a mix of those graded by completion and by correctness. Midterms: Online; 48 hours each; open book. Final exam: Dec 14; cumulative; closed-book; in-person. Sign up (HW1) for in-person lab demos which will take place in October.
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Types of atomic bond: primary Ionic Covalent Metallic
Types of atomic bond: secondary
Model for interatomic potentials and forces Consider example of the ionic solid NaCl Attractive force Repulsive force
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Simple model for interatomic bond: compression and tension springs
Ionic bonding
Generalizing the interatomic bond model Potential energy Interatomic force
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Summary of bond types Category Melting points Bond type Typical attractive exponent, m Typical repulsive exponent, n Directional? Bond energy Comments Primary Ionic 1 8 to12 No Large Ceramics Covalent 1 8 to12 Yes Variable (diamond large, Bi small) Semiconductors, ceramics, polymer chains Metallic 1 8 to 12 No Variable (W large, Hg small) Electrostatic attraction between nuclei and surrounding e Secondary Van der Waals 6 12 Yes Smallest Intermolecular; between polymer chains. Lennard Jones potential Hydrogen 6 12 Yes Smallest
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Atomic packing Dense random packing (DRP) Model atoms as spheres with diameter D equal to equilibrium spacing Close-packed plane All atoms are at equilibrium spacing from nearest neighbors in all directions
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Hexagonal close-packed (HCP) Close-packed planes can be stacked in two possible sequences: ABA – this one is called close-packed hexagonal (CPH) ABC is also possible
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Face-centered cubic (FCC) structure Observe that FCC is the same structure as that given by ABC stacking of close-packed layers
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Photo illustrating an example of an FCC plane (green atoms) within an ABC- stacked hexagonal close-packed structure
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Body-centered cubic (BCC) structure Task: calculate packing fraction of BCC
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Summary: atomic structures Type of structure Number of atoms per unit cell Side length of unit cell Atomic packing fraction (APF) Examples (how do we know all this?) Dense random packing (DRP) ~64% Glasses, liquids Close-packed hexagonal (CPH) Ti, Zn, Cd, Zr Face-centered cubic (FCC) 𝛾𝛾 -Iron, Cu, Al, Au, Ni, Pt, Ag Body-centered cubic (BCC) 𝛼𝛼 -Iron, Cr, W Atoms modeled as spheres with diameter D equal to equilibrium spacing
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Two other examples of crystal structures
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Polymorphism: different crystal structures for the same material Carbon: diamond vs graphite There are other allotropes as well: buckyballs, nanotubes… World’s largest diamond World’s largest pencil
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Miller indices for atomic planes Report the plane as:
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Families of planes
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