Materials Science Quiz on Elastic Properties

True Stress and Strain

• Engineering stress and strain are not always "real" materials behaviour.
• True stress (σT) = F/Ai , where F is the force and Ai is the instantaneous cross-sectional area
• True strain (εT) = ln(A0/Ai) = ln(1+εE), where A0 is the original cross-sectional area, Ai is the instantaneous cross-sectional area, and εE is the engineering strain
• For elastic deformation, true stress is roughly equal to engineering stress, and true strain is equal to engineering strain
• For plastic deformation, true stress is approximately equal to engineering stress, and true strain is equal to engineering strain

The Range of E

• Different materials exhibit vastly different Young's moduli (E).
• Diamond has a very high E, indicating it is very stiff.
• Graphite has a lower E than diamond.
• Graphene has a very high E, comparable to diamond.
• Ice has a lower E compared to MgO.
• Lead has the lowest E among metals, meaning it's the least stiff.

Poisson's Ratio (v)

• Poisson's ratio (ν) is an elastic constant describing the proportionality between normal strain in one axis and the resulting normal strain in an orthogonal direction.
• Primarily, it relates extension to contraction.
• For incompressible materials, ν = 0.5.
• For most metals, ν is between 0.25 and 0.45
• For ceramics and glass, ν is between 0.1 and 0.3
• Natural cork has a Poisson's ratio near 0: meaning it is very easy to compress

Generalized Hooke's Law

• The total strain in one direction is equal to the sum of the strains generated by the various stresses in that direction.
• Equations for strains ε11, ε22, ε33 are presented relating stresses and strains

Compliance and Stiffness Constants

• Equations that define compliance (S) and stiffness (C) constants are provided
• α, β, and γ are the direction cosines of [hkl] direction

Polymers

• Thermoplastics can melt and re-melt
• Thermosets cannot melt after solidifying
• Differences lie in cross-linking

Thermoplastic Behavior

• Glassy, amorphous, partially crystalline, and leathery states of polymers
• Glass transition temperature (Tg)

Edge/Screw Dislocations

• Edge, screw displacements are mechanisms for the movement of edge dislocations.
• Images are provided of edge dislocation motion and screw dislocation motion

The Burgers Vector (b) and Burgers Circuit

• Right-hand/finish-start (RH/FS) convention for defining the Burgers vector
• Definition of b for edge and screw dislocations

Climb of Edge Dislocations

• Dislocation glide and climb are conservative and nonconservative motions, respectively
• Climb requires addition or removal of atoms/vacancies
• Climb is only important at elevated temperatures

Cross Slip in a Face-Centered Cubic Metal

• Sequence of events in cross slip are shown and described

Dislocation Core and Lattice Frictional Stress

• Frictional stress is low when a is large

Slip Systems in FCC and BCC

• Slip systems and directions in FCC and BCC are indicated, graphically

Slip Systems in Crystalline Materials

• Summarizes the number of possible slip systems in various materials, including FCC, BCC, and HCP structures

The Width of Dislocation Core

• Width of dislocation core affects Peierls-Nabarro stress and atomic displacements required for motion
• Temperature affects dislocation width

Why Ceramics are Brittle?

• Dislocation cores in ceramics are very small, leading to extremely high frictional stresses exceeding fracture strength, making dislocation motion difficult
• This causes stress concentration at crack tips, leading to brittle fracture

Dislocation Glide vs. Twinning

• Dislocation glide and twinning are competitive mechanisms for plastic deformation.
• FCC metals tend to exhibit slip over twinning at higher temperatures and strain rates
• BCC metals can exhibit twinning more readily due to yield strength dependence on temperature

Dislocation Multiplication - Frank-Read Source

• Explanation and diagrams of the Frank-Read source mechanism for dislocation multiplication

Plastic Flow in Single Crystals

• Schmid factor and Taylor factor are explained and pictured

Stress-Strain Behavior of FCC and BCC Metals

• Stages I,II,III of the stress-strain curves depending on temperature and strain rate
• Cross slip occurs readily in materials with high SFE

Temperature and Strain Rate Dependence of CRSS

• Temperature and strain rate dependence of critical resolved shear stress (CRSS) at various temperature regions, both thermally dependent (τ*) and athermal (τa) components

Creep Activation Energies vs. Self-Diffusion Activation Energies

• Correlation between high-temperature creep activation energies and self-diffusion activation energies
• Diffusional flow is associated with creep deformation

Nabarro-Herring Creep

• Description of the Nabarro-Herring (NH) creep mechanism
• NH creep is diffusion-controlled, important at high temperatures but less significant in metals than ceramics

Coble Creep

• Coble creep is a grain-boundary diffusion-controlled process
• High temperature creep is more sensitive to grain size than Nabarro-Herring creep

Creep Mechanisms Involving Dislocation and Diffusional Flow

• Description and equations for solute drag creep and climb-glide creep

Independent Creep Processes

• NH and Coble creep mechanisms operate independently (parallel or series)
• Coble creep dominates in fine-grained materials while NH creep is prevalent in larger grains

Diffusional Flow and Dislocation Creep

• Description of different creep mechanisms and their dominance based on stress and temperature

Summary

• Summary of creep, hardening mechanisms and controlling factors

Basic Principles of Reinforcement

• Overview of stress for the phases are the same
• Equations for stress in composite materials, and phase volume

Lamellar Arrangements of Two Phases

• Lamellar arrangements in composites utilizing phases, and forces applied to the phases

Tensile Test of a Fiber Composite

• Description of the force effect in a fiber composite

Stress-Strain Curves of Composites

• Discussion of stress-strain curves and stages in composites (Stages 1,2,3)

Composite Tensile Strength vs. Secondary Tensile Strength

• Relations between composite tensile strength to secondary tensile strength in composites

Case Studies - Superalloys

• Overview of superalloys, their importance, and composition, typically in Ni-based materials.

Strain-Rate Sensitivity

• Strain-rate sensitivity is important in materials behaviour
• High values of m (strain-rate sensitivity) indicates resistance to neck development in tension -Strain rate sensitivities increase with temperature

Crystalline, Polycrystalline, and Amorphous Structures

• Illustrations of the three basic crystal structures
• Crystal structures vary widely and this impacts their behaviour

Hardness vs. Strength

• Overview of the relationship between hardness and strength in materials

Oliver-Pharr Method

• Description of the Oliver-Pharr method for measuring the reduced elastic modulus

Multiaxial Loading Conditions

• Multiaxial loading and its implications for material response

Tresca Yield Criterion

• Overview of the Tresca yield criterion for biaxial loading conditions

The von Mises Yield Criterion

• Overview of the von Mises yield criterion for multiaxial stress states, and comparison to Tresca

(Note that some documents listed concepts not included in the notes if they are not discussed or relevant to the topics covered in the other sections.)

Test your knowledge on the properties and characteristics of different materials in this quiz focused on elasticity, stiffness, and dislocations. Discover how polymers, metals, and composites compare in terms of elastic modulus and Poisson's ratio. Challenge yourself with matching materials to their respective properties and understanding dislocation motion.