3 year dental materials science

16.11.2007 Dental Materials - Graham Cross 1

3rd Year Dental Materials Science

Dr. Graham CrossSchool of Physics and CRANN

SFI Nanoscience Building, Rm 1.5

http://www.tcd.ie/Physics/People/Graham.Cross/

[email protected]


Oct. 26: Basic metallurgy and alloysNov. 2: Properties of materials, thermalsNov. 16: Mechanics of solids and fluids

Topics

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


• Stress and strain

• Elasticity and viscosity: Solids vs. fluids

• Rheology and Plasticity

• Viscoelasticity

Mechanical properties of materials


• 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 behaviourWhen 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.

Solids vs. liquids

How can we understand the reaction of materials to forces independently of the geometry of the tested object?


• Stress is the force per unit area applied to an object:

Stress

ForceArea

σ =• Units = N/m2 or Pascals (Pa)• Also: 1 bar = 101.3 kPa• 1 MPa = 106 Pa

Compressive Tensile Shear

• Different ways of applying stress, over a surface:


• Adhesion may be defined simply as a force interaction between two materials at an interface where they are in contact.• Failure occurs at a critical stress level

Adhesion

Mechanical Chemical

Interface must support a solely tensile load:


Area of contact and stress

Chemical Adhesion

• Rough surfaces mean small contact 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

• Adhesive strength depends on true contact area limited by roughness:


• 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:

Strain

dll

ε =

Different kinds of strain


Many properties can be determined from it:

• Elastic modulus• Tensile strength• Yield strength• Ductility• Resilience• Fracture toughness

Stress vs. strain curve

Stressσ

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.

A principle way to characterize mechanical properties of solid materials.


• Reversible stretching, compression, or deforming of a body

Elasticity

Strain εεlimit

εlimit = 0.02 Ceramics/Metals= 0.1 Polymer glasses> 5 Some elastomers!

Eσ ε=

• Different modulus are defined for different types of deformation:

• Young’s modulus• Shear modulus• Bulk modulus

• In the linear elastic range, the ratio of stress to strain is called a modulus

Stressσ


Elastic Modulus

BulkB=10 GPa

Young’sE=3 GPa

ShearG=1 GPa

Before

After

Polystyrene:


• Shear strain γ is a skew: it changes shape, not volume.• Very important when we consider flow.

Shear strain

dyh

γ ≡

d dy h dy dtdt dt hγ

= =

yvddt hγ

=

Shear strain rate:h


• What shear stress τ must be applied between the two plates to get vy?

Simple fluid flow

Force

yv dh dt

γτ ∝ =

vy velocityin y direction

x

NB: Fluid velocity at walls is zero with respect to wall(Fluid “sticks” to the walls)

y

Shear ForceArea

τ =

Stress is proportional to shear strain rate!

• Newton’s law of fluid flow:Shear stress τ is proportional to the flow velocity gradient normal to flow:

• Consider fluid between to large plates of area A:

h


Why shear is important for flow

Forcebetweenatoms

Distance of separation

Attractive

Repulsive

Bonding energy

• 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!

Difficult!

A liquid changes shape, not volume, freely


Solid vs. Liquid

Energy Positionsolid

Atoms deep in energy well

(Low Temperature)

vacancy


Solid vs. Liquid

Energy Positionsolid


(Low Temperature)

vacancy


Solid vs. LiquidEnergy Position

Energy Position

solid

liquid


Atoms can hop over energy barrier!

(Low Temperature)

(High Temperature)

vacancy


• Viscosity η describes the way momentum is transferred by a fluid during flow

ViscosityForce

ddtγτ ∝

ddtγτ η= 100Honey

1040 (?)Glass

0.015Mercury

0.0089Water

0.00018Air

Viscosity ηPa s

Fluid

η Units: Pa s(Poise)

• For simple fluids it is a constant of proportionality between shear stress and shear rate (Newton):


• 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.

Rheology


• 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 mouldingFollowed by large increase in viscosity during setting

Working time – time the material can be easily manipulatedSetting time – time at which viscosity goes very high

Time dependent material response


• Poor rheological properties- no well defined setting time

Viscosity and setting time of pastes

Viscosityη

Time tTime tTime t

• Ideal rheological properties- long working time- sudden setting time

• Good rheological properties- long working time- reasonable setting time


Shear rate dependent flow

Shear rate

ShearStress

τ

ShearStress

τ

Shear rate ddtγ

Newtonian linear fluid a) Dilatant

b) Pseudoplastic (shear thinning)

a

b

ddtγ

Fluids: Instead of a stress vs. strain curve, we plot a stress vs. strain rate curve

ddtγτ η=


• Ductile behaviour of a solidthat occurs above a special shear stress threshold called the “yield stress”: τyield

• This occurs for many metals and glassy polymers

• Ceramic materials tend to fracture, not yield

Plasticity: flow of solids

Shear Stressτ

Strain ε

τyield

Ductility

Like a liquid, plastic flow of solids involves shape change, not volume change


Shearing a solid: Plastic flowEnergy Position

Energy Position

solid

sheared solid

One line of atoms changes neighboursStress, not temperature, increases the energy level


• Response of materials with both elastic and viscous character:

time dependent• Eg. Elastomers

• Two important forms:• Creep• Stress relaxation

Viscoelasticity

• Visualized by combining mechanical components of• Springs (elastic): instant response to stress• Dash-pots (viscous): slow response


•Eg. Weight of a gold filling, effect on elastomer padding layer

• Important for dental amalgams:- Melting temperature is close

to room temperature- Teeth clenching- Creep may be precursor to

fracture at filling edge.

Creep

Stress

Strain

Time

σ

0

σ

• Time dependent dimensional change of materials under constant stress.


• 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.

Stress relaxation

Time t

Stressσ

Applied Dental Materials – 8th Edition 1998, John F. McCabe, Angus W. G. Walls, Blackwell, Oxford, UK.

For more examples, see:

When a viscoelastic material is under constant strain a gradual reduction in stress can occur

3 year dental materials science

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