3rd Year Dental Materials Science Dr. Graham Cross School of Physics and CRANN SFI Nanoscience Building, Rm 1.5 http://www.tcd.ie/Physics/People/Graham.Cross/
[email protected]
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Dental Materials - Graham Cross
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Topics Oct. 26: Basic metallurgy and alloys Nov. 2: Properties of materials, thermals Nov. 16: Mechanics of solids and fluids Textbooks – Further Reading Applied Dental Materials – 8 th Edition 1998, John F. McCabe, Angus W. G. Walls, Blackwell, Oxford, UK. • Restorative Dental Materials – 10th Edition 1997 Editor Robert G. Craig, Mosby – Year Book, Inc, St. Louis, USA • Notes on Dental Materials – 6th Edition 1992 Editor E.C. Combe, Churchill Livingstone, Edinburgh, UK • Phillip’s Science of Dental Materials – 10th Edition 1996, Editor Kenneth J. Arusavice, W.B. Saunders Company Philadelphia, USA • Dental Materials, Properties and Manipulation – 6th Edition 1996 Editors Robert G. Craig, William J. O’Brien, John M. Power, Mosby – Year Book, Inc, St. Louis, USA 16.11.2007
Dental Materials - Graham Cross
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Mechanical properties of materials
• Stress and strain • Elasticity and viscosity: Solids vs. fluids • Rheology and Plasticity • Viscoelasticity 16.11.2007
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Solids vs. liquids • We all understand generally what the difference between solid and a liquid is, but in practice this difference can be blurred.. • A very general distinction is this: • Elastic behaviour When you apply and then remove a force, fast or slow, the object returns to its original shape! • Inelastic behaviour (flow) When you apply and remove a force, the shape of the object is permanently changed. How can we understand the reaction of materials to forces independently of the geometry of the tested object? 16.11.2007
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Stress • Stress is the force per unit area applied to an object:
Force σ= Area
• Units = N/m2 or Pascals (Pa) • Also: 1 bar = 101.3 kPa • 1 MPa = 106 Pa
• Different ways of applying stress, over a surface: Compressive
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Tensile
Dental Materials - Graham Cross
Shear
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Adhesion • Adhesion may be defined simply as a force interaction between two materials at an interface where they are in . • Failure occurs at a critical stress level Interface must a solely tensile load:
Mechanical 16.11.2007
Chemical Dental Materials - Graham Cross
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Area of and stress • Adhesive strength depends on true area limited by roughness:
Chemical Adhesion • Rough surfaces mean small area, so a small force makes a large stress at local points on surface, causing failure • Polishing a surface to make it smooth increases area and reduces stress 16.11.2007
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Strain • Strain ε is a measure of the change in dimension of an object that occurs by the application of stress. • It is defined as a relative displacement:
dl ε= l Different kinds of strain
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Stress vs. strain curve A principle way to characterize mechanical properties of solid materials.
Many properties can be determined from it: • Elastic modulus • Tensile strength • Yield strength • Ductility • Resilience • Fracture toughness
Stress σ
Strain ε • This is an intrinsic signature of a material • Why would a force vs. displacement curve not be?
See: Applied Dental Materials – 8th Edition 1998, John F. McCabe, Angus W. G. Walls, Chapter 2.
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Elasticity • Reversible stretching, compression, or deforming of a body
Stress σ
• In the linear elastic range, the ratio of stress to strain is called a modulus
σ = Eε
εlimit
εlimit = 0.02 Ceramics/Metals = 0.1 Polymer glasses > 5 Some elastomers! 16.11.2007
Strain ε
• Different modulus are defined for different types of deformation: • Young’s modulus • Shear modulus • Bulk modulus
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Elastic Modulus
Before
After
Polystyrene:
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Bulk B=10 GPa
Young’s E=3 GPa
Dental Materials - Graham Cross
Shear G=1 GPa 11
Shear strain • Shear strain γ is a skew: it changes shape, not volume. • Very important when we consider flow.
dy γ≡ h Shear strain rate: h
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d γ dy h dy dt = = dt dt h dγ vy = dt h
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Simple fluid flow • Consider fluid between to large plates of area A: • What shear stress τ must be applied between the two plates to get vy? Shear Force τ=
x h y
Force
Area
vy
• Newton’s law of fluid flow: Shear stress τ is proportional to the flow velocity gradient normal to flow: v dγ
τ∝
y
h
=
dt
Stress is proportional to shear strain rate! 16.11.2007
velocity in y direction
NB: Fluid velocity at walls is zero with respect to wall (Fluid “sticks” to the walls)
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Why shear is important for flow Force between atoms
Bonding energy Repulsive Distance of separation
Difficult!
Attractive
• Compressive/tensile stress: - Changing the distance of separation of atoms is difficult (volume change) • Shear stress: - Changing neighbours between atoms is much easier (shape change) Easy! 16.11.2007
A liquid changes shape, not volume, freely
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Solid vs. Liquid Energy
solid
Position
(Low Temperature)
Atoms deep in energy well
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Dental Materials - Graham Cross
vacancy
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Solid vs. Liquid Energy
solid
Position
(Low Temperature)
Atoms deep in energy well
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vacancy
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Solid vs. Liquid Energy
solid
Position
(Low Temperature)
Atoms deep in energy well
vacancy
Energy
liquid
Position
(High Temperature)
Atoms can hop over energy barrier! 16.11.2007
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Viscosity • Viscosity η describes the way momentum is transferred by a fluid during flow • For simple fluids it is a constant of proportionality between shear stress and shear rate (Newton):
dγ τ∝ dt dγ τ =η dt 16.11.2007
η Units: Pa s (Poise)
Force
Fluid
Viscosity η Pa s
Air
0.00018
Water
0.0089
Mercury
0.015
Honey
100
Glass
1040 (?)
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Rheology • Study of the flow of all materials, including solids and complex liquids such as polymer melts, colloids, suspensions, slurries, pastes, etc. • Consider a complex fluid, a polymer melt: What happens when you shear this material? • Molecules both flow and they change their shape… they “relax” • Gives rise to both shear rate (dγ/dt) and time dependent behaviour.
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Time dependent material response • Due to mechanical reasons such as relaxation time of constitutive particles in transient (ie. non-steady) flows • Or due to chemical reasons such as setting times • Usually viscosity will be used to measure this: Initial low viscosity for dispensing and moulding Followed by large increase in viscosity during setting Working time – time the material can be easily manipulated Setting time – time at which viscosity goes very high 16.11.2007
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Viscosity and setting time of pastes Viscosity η
Time t
• Poor rheological properties - no well defined setting time
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Time t
• Ideal rheological properties - long working time - sudden setting time Dental Materials - Graham Cross
Time t • Good rheological properties - long working time - reasonable setting time 21
Shear rate dependent flow Fluids: Instead of a stress vs. strain curve, we plot a stress vs. strain rate curve a) Dilatant
Newtonian linear fluid
τ =η
dγ dt
b) Pseudoplastic (shear thinning)
Shear Stress τ
Shear Stress τ
b
a
Shear rate 16.11.2007
dγ dt Dental Materials - Graham Cross
Shear rate
dγ dt 22
Plasticity: flow of solids • Ductile behaviour of a solid that occurs above a special shear stress threshold called the “yield stress”: τyield • This occurs for many metals and glassy polymers
Shear Stress τ τyield
• Ceramic materials tend to fracture, not yield
Strain ε
Ductility
Like a liquid, plastic flow of solids involves shape change, not volume change 16.11.2007
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Shearing a solid: Plastic flow Energy
solid
Position
sheared solid Energy
Stress, not temperature, increases the energy level 16.11.2007
Position
One line of atoms changes neighbours Dental Materials - Graham Cross
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Viscoelasticity • Response of materials with both elastic and viscous character: time dependent • Eg. Elastomers • Two important forms: • Creep • Stress relaxation • Visualized by combining mechanical components of • Springs (elastic): instant response to stress • Dash-pots (viscous): slow response 16.11.2007
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Creep • Time dependent dimensional change of materials under constant stress.
•Eg. Weight of a gold filling, effect on elastomer padding layer
σ 0
• Important for dental amalgams: - Melting temperature is close to room temperature - Teeth clenching - Creep may be precursor to fracture at filling edge. 16.11.2007
Stress
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Strain σ
Time 26
Stress relaxation When a viscoelastic material is under constant strain a gradual reduction in stress can occur
Stress σ
• Eg. Dental waxes, resins, and gels • Manipulate into shape, then stress drops over time • This can, in turn, lead to dimensional changes on other surrounding loaded structures. For more examples, see: Applied Dental Materials – 8th Edition 1998, John F. McCabe, Angus W. G. Walls, Blackwell, Oxford, UK.
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Time t 27