MECHANICAL PROPERTIES

Introduction:

MECHANICAL PROPERTIES : are defined by the laws of mechanism that

is the science that deals with energy and forces and their effect on bodies.

Mechanical properties are the measured responses both elastic and

plastic, of materials under an applied force or distribution of forces.

Stress and Strain

When an external force acts on a solid body a reaction force results that

is equal in magnitude but opposite in direction to the external force.

The external force is called LOAD.

Internal forceStress =

Area on which it acts

Wherever stress is present strain is also seen in most of the cases.

Strain can be defined as the change in length per unit length

FSo, Stress =

Area

Change in AreaStrain =

Unit area

Hookes law Stress and Strain

Strain may be either elastic / plastic or a combination

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Stress may be - Simple

- Complex

Simple : Stress can be classified based on their directions.

1. Tensile stresses

2. Compressive stresses

3. Shear

Tensile stress is caused by a load that tends to stretch or elongate a

body. There are very few pure tensile stresses situations seen commonly. More

commonly seen are complex stresses, which will be discussed later. In fixed

bridges and crown prosthodontics a candy called jujubes is used because of its

adhesive nature to see how much tensile force is needed to dislodge a crown

when a patient opens his/her mouth.

Compressive stress

When a body is placed under a load that tends to compress / shorten it

the internal resistance to such a load is called compressive stresses.

With both tensile and compressive stresses the forces are applied at right angles

to the area which they act on

To calculate either tensile stress or compressive stress

Force=

Cross sectional are Perpendicular to the force direction

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Shear stress

This stress resists a twisting motion or the sliding of one body over

another is called shear stress

Example: If a force is applied on the enamel of a tooth by a sharp edged

instrument parallel to the interface between the enamel and an orthodontic

bracket.

The bracket will debond due to the shear stress produced which will be

due to the shear stress failure of the luting agent.

ForceShear stress =

Area parallel to direction of force

Shear stress failure is reduced in the oral cavity by the presence of

chamfers and bevels.

Complex stresses or Flexural stresses

In any body it is very difficult to produce a stress of one type.

Example: When a force is applied on a three unit bridges.

Example : When pressure is applied at point A, tensile stress develops on the

tissue side of the bridge compressive stress develops on the occlusal side.

Whereas in a cantelever bridge the opposite occurs.

Elastic and Plastic Stresses

Elastic stresses occur in ductile and malleable materials like gold. These

do not under 9° permanent deformation.

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Plastic stresses on the other hand cause deformation and may be high

enough to produce fracture. Example of the elastic shear deformation.

Elastic limit

When a tensile stress is applied on a wire and is increased in small

increments and then released after each addition of stress.

A stress value will be found after which the wire does not return to its

original length after it is unloaded. This value is called elastic limit.

So elastic limit can be defined as the greatest stress to which a material

can be subjected such that it will return to its original dimensions when the

forces are released.

Proportional limit

If the same wire is loaded till it ruptures without removal of the load

each time and if each stress and strain is plotted on a graph, the point where the

straight line graph curves is called the proportional limit. That is the point till

which stress is directly proportional to strain according to (Hooke’s law).

Yield strength

Yield strength is the stress at which plastic strain which produces slight

permanent deformation.

This should be within tolerable limits for different materials. Although

the term elastic limit, proportional limit and yield strength are defined

differently they have nearly same magnitudes and can be used interchangeably

for all practical purposes.

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These values are important in the evaluation of dental materials since

they represent the stress at which permanent deformation begins.

If they are exceeded by masticatory stresses the restoration / appliance

may no longer fit as originally designed.

Modulus of elasticity

The term elastic modulus describes the relative rigidity or stiffness of

the material.

If any stress equal to or less than the proportional limit is divided by its

strain a constant of proportionality will result. This is called Young’s modulus

of elasticity and it is calculated as follows:

E - Elastic modulus

F - Applied force / load

A - Cross sectional area

l1 - Increase in length

L0 - Original length

By definition

Stress = F/A

Strain = l1/l0

Stress F/A Fl0

= =Strain l1/l0 Al1 = E

If a stress strain graph is plotted for enamel and dentin with a simulated

compressive test, the following graph is obtained

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250

200

150

100

50

0

PLPL

ED

Which shows that elastic modulus of enamel is 3 times greater than dentin.

Dentin is capable of sustaining high load before it fractures so it is more

flexible and tougher than enamel.

Elastic modulus can be measured by a dynamic as well as static method.

Based on the velocity and density of the material the modulus and Poissons

ratio can be determined.

Poissons Ratio

When a tensile force is applied to an object it becomes longer and

thinner. Compressive force makes it shorter and thicker.

If an axial tensile stress z in the z direction of a mutually

perpendicular xyz coordinate system produce an elastic tensile strain and

accompanying elastic contractions in the x and y directions; then

The ratio of ex or ey

ez ez

is an engineering property of the material called Poisson’s ratio

(v).

-ex = -eyv =

ez ez

for an ideal isotropic material of constant volume the ratio is 5.

Most engineering material have values of 3

Flexibility

These can be defined as the strain that occurs when the material is

stretched to its proportional limit.

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The relation between maximum flexibility, proportional limit and

modulus of elasticity may be expressed mathematically as follows.

E = Modulus of elasticity

P= proportional limit

Em = maximum flexibility

PSince E =

em

Pem =

e

Resilience

As the inter atomic spacing increases internal energy increases. As long

as the stress is not greater than the proportional limit this energy is called as

resilience.

Resilience can be defined as the amount of energy absorbed by a

material when it is stressed to its proportional limit.

To compare the resilience of 2 materials we must plot stress strain

graphs and observe the area of elasticity in these graphs.

The material with larger elastic area has more resilience. When a dental

restoration is deformed during mastication, the chewing force acts on the tooth

structure, the restoration or both.

The magnitude of deformation is determined by the induced stresses. In

most dental restoration large stains are precluded due to the proprioceptive

response of the periodontal ligament.

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The pain stimulus causes the strain to decrease and the induced stress to

be reduced thus the damage to the teeth is prevented.

Example: A proximal inlay might cause excessive movement of the adjacent

tooth if large proximal strains develop during compressive loading.

So, materials should exhibit a high elastic modulus and low resilience

thereby inviting the elastic strain that is produced.

Strength

Strength is the stress that is necessary to cause fracture or a specified

amount of plastic deformation.

Mostly when strength is discussed we talk about the amount of stress it

requires to fracture.

But these 2 should be early differentiated. Strength can be defined by:

1. Proportional limit.

2. Elastic limit.

3. Yield strength.

4. Ultimate tensile strength, flexural strength, shear strength and

compressive strength.

Proportional limit the is stress above which stress is no longer directly

proportional to strain.

Elastic limit: The maximum stress after which plastic deformation starts.

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Yield strength: The strength required to produce a given amount of plastic

strain. And tensile strength, compressive strength etc. each of which are the

maximum stress to produce fracture.

Yield strength

It is often a property that represents the stress value at which a small

amount of plastic strain has occurred.

A value of either 1% or 2% is selected and is called percent offset.

So yield strength is the strength required to produce the particular offset

strain that has been chosen.

If yield strength values of 2 materials have to be seen then the percent

offset value has to be same.

Although the term strength implies that the material has fractured it has

just undergone permanent plastic deformation.

In a strain graph. A line drawn from the offset till it meets the stress

strain curve is called yield strength.

For brittle materials such as composites and ceramic the stress strain plot

is a straight line so there is no plastic region so yield strength cant be measured

at either 1% or 2% offset.

Diametral Tensile Strength

Tensile strength is determined usually by subjecting a load, wire etc. to

loading or a un axial tension test. But for brittle metals.

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Diametral Compression Test is used. This test is used for materials that

exhibit elastic and not plastic deformation.

Method

A compressive load is placed by a flat plate against the side of a short

cylindrical specimen or disk, the vertical force produces a tensile stress that is

perpendicular to the vertical plane that passes through the centre of the disk.

Fracture occurs along the vertical plane.

Here the tensile stress is directly proportional to the compressive load

applied.

2PTensile stress =

x D x tP – load

D – diameter

t- thickness

– 22/7 = 3.14

Flexure Strength or Transverse strength or Modulus of rupture is

essentially a strength test of a bar supported at each end (or a thin disk reported

along a lower support circle under a static load for the bar supported at 3 pt

flexure, the formula is

3pl =

2bd2

– flexural strength.

l – distance between the supports.

b – width of the specimen.

d – depth or thickness of the specimen.

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p – maximum load at the point of fracture.

Between these two zones we see the presence of the neutral axis where

there is no change.

This test is usually done for little mat is such as ceramics to simulate

stresses seen in dental prosthesis such as cantelevered bridges and multiple unit

bridges.

Fatigue strength

Most of the prosthetic and restorative fractures develop progressively

over many stress cycles after initiation of a crack from a critical flaw and then

by propagation of that crack until a sudden unexpected fracture occur.

Sometimes stress values much below the ultimate tensile strength can

produce premature fracture of a dental prosthesis because microscopic flaws

grow slowly over many cycles of stress. The phenomenon is called fatigue

failure.

Normal mastication can induce thousands of stress cycles per day within

a dental restoration for glasses and certain glass containing ceramics the

induced tensile stress and the presence of an aqueous amount causes an

extension of the microscopic flows by chemical attack and further reduce the

number of cycles to cause dynamics fatigue failure.

How to determine

The material is subjected to a cyclic stress of maximum known value,

the number of cycles that are required to produce failure are determined.

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If a graph is drawn of failure stress versus number of cycles to failure it

enables a calculation of a maximum service stress level or an endurance limit

that is the maximum stress that can be maintained without failure over an

infinite number of cycles.

If the surface is rough endurance limit is low. A rough brittle material

would fail in fewer cycles of stress. Fatigue may be of 2 types.

1. Static

2. dynamic

Static

Ceramic orthodontic brackets and activated wires within the brackets

represent a clinical system that can exhibit static fatigue failure.

The delayed fracture of molar ceramic crowns that are subjected to

periodic cyclic forces may be caused by dynamic fatigue failure.

Impact

The term impact is used to describe the reaction of a stationery object to

a collision with a moving object.

Impact strength – may be defined as the energy required to fractures a

material under an impact force.

A charpy type impact tester is usually used to measure impact strength.

A pendulum is released that swings down to fracture the centre of a specimen

that is supported at both ends. The energy lost by the pendulum during the

fracture of the specimen can be determined by the comparison of the length of

the swing after the impact with that of its free swing when no impact occurs.

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The dimensions shape and design of the specimen to be tested should be

identical for uniform results.

Another impact device called the IZOD IMPACT TESTER, the

specimen is clamped vertically at one end. The blow is delivered at a certain

distance above the clamped end instead of at the center of the specimen

supported at both ends and described for the charpy impact test.

With appropriate values for velocities and masses involved, a blow by

first to jaw can be considered an impact situation.

A material with low elastic modulus and high tensile strength is more

resistance to impact forces.

But if both the values are low imp resistance is also low.

Example : Dentalporcelain – 40 GPA 50-100MPa

Amalgam – 21GPA 460 MPa

Composite Resin - 17 GPA / 30-9 MPa

Polymethhymethacrylate – 3.5 GPA 460 MPA

Permanent plastic deformation

If a material is deformed by a stress to a point above the proportional

limit before fracture. The removal of the applied force will reduce the stress to

zero but strain does not decrease to zero because of plastic deformation. Thus if

the object does not return to its original dimension when the force is removed.

It remains plastically deformed.

Some other mechanical properties

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Toughness

It is defined as the amount of elastic and plastic deformation energy

required to fracture a material and it is the measure of the resistance to fracture.

Toughness can be measured as the total area under the stress strain curve

from zero stress to fracture stress. Toughness depends on strength and ductility.

The higher these 2 values are the greater the toughness.

Thus we can conclude that a tough metal may be strong, but a strong

metal may not be tough.

Fracture toughness

This is a property that describes the resistance of brittle metals to

catastrophic propagation of flaws.

It is given in units of stress times the square root of crack length.

i.e. MPa x m ½

or

MN m-3/2

Brittleness

Brittleness is the relative inability of a material to sustain plastic

deformation before fracture of a material occurs.

Example : amalgam ceramics and composites are brittle at oral temperature 5-

55°C. They sustain little or no plastic strain before they fracture.

If a brittle material fractures at or near its proportional limit.

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But a brittle material may not necessarily be weak. Example : a cobalt

chromium partial denture alloy has 1.5 % elongation but UTS of 870 MPa.

The UTS of a glass infiltrated alumina core ceramic is high 450 MPa but

it has 0% elongation. If it is drawn into a fibre with very smooth surfaces and

insignificant internal flaws its / tensile strength may be as high as 2800 MPa

and it will have 0% elongation.

Thus D materials with little or no elongation have little or no

burnishability as they have no plastic deformation potential.

Ductility and Malleability

Ductility is the ability of materials to sustain a large permanent

deformation without fracture.

Malleability is the ability of a material to sustain stress and not rupture

under compression as in hammering or rolling into a sheet is termed

malleability.

Gold is the most malleable and ductile metal and second is silver.

Platinum – Third in ductility,

Copper – Third in malleability.

Measurement of ductility

There are three common methods for measurement of ductility:

1. Percentage elongation after fracture.

2. Reduction in area in the fractured region ends.

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3. Cold bend test.

The simplest and most commonly used test is to compare the increase in

length of a wire or rod after fracture in tension to its length before fracture 2

marks are placed on the wire / rod a specified distance apart and this distance is

said to be “gauge length”. The standard GL for dental materials is 51mm.

The wire / rod is then pulled apart under a tensile load the fractured ends

are fitted together and length is measured. The ratio of the original length to

increased in length after fracture expressed in percent is called percentage

elongation.

Another method utilises the necking or cone shaped constriction occurs

at the fractured end of a ductile wire after rupture under a tensile load. The

percentage of decrease in cross sectional area of the fractured end in

comparison to the original area of the wire or rod is called reduction in area.

A third method is known as the cold bend test. The material is clamped

in a vise and bent around a mandrel of specified radius. The number of bends to

fracture is counted the greater the number the greater the ductility.

The first bend is made from vertical to horizontal all subsequent bends

are made through angles of 180°.

Structural and stress relaxation

After a substance has been permanently deformed there are trapped

internal stresses. This situation is unstable. The atoms that are displaced are not

in equilibrium positions. Through a solid-state diffusion process driven by

thermal energy they slowly move back to their equilibrium positions. The result

is a change in the shape or contour of the solid as a gross manifestation of the

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re arrangements in atomic or molecular positions. The material warps or

distorts this is called stress relaxation.

The rate of relaxation increases with an increase in temperature.

This phenomenon man result in an inaccurate fit of dental appliance.

Example: There may be many materials that may undergo relaxation at high

temperatures if they are cooled before usage.

Hardness

The term hardness is difficult to define. In mineralogy the relative

hardness of a substance is based on its ability to resist scratching. In metallurgy

and in most other disciplines the concept of hardness that is most generally,

accepted is its resistance to indentation.

The indentation produced on the surface of a material from an applied

force of a sharp point or an abrasive particle results from the interaction of

numerous properties. The properties that are related to the hardness of a

material are strength proportional limit and ductility.

The surface hardness tests used commonly in dentistry:

1. Barcol

2. Brinnel

3. Rockwell

4. Scholl

5. Vickers.

6. Knoop.

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The Brinnel Test

- One of the oldest test used.

- A hardened steel ball is pressed under a specified load into the

polished surface of a metal. The load is divided by the area of the

projected surface of the indentation and the quotient’s referred to

as the B.hardness no (abbreviation BHN).

Rockwell

It is somewhat similar to Brinnel, a steel ball or conical diamond pt is

used. The depth of the indentation is measured by a dial gauge on the

instrument. A number of indenting points with different sizes are available for

testing a variety of different materials.

The R.H.N. is designated according to the particular indenter and load

employed. Both these tests are not for brittle metal.

Same as the Brinnel test but a diamond in the shape of a square based

pyramid.

The lengths of the diagonals of the indentation are measured and

collaged. The Vickers test is employed in the A.D.A. specification for dental

casting alloys.

It is suitable for brittle materials so it is used for the measured of

hardness of tooth structures.

Vicker’s test

Similar to Brinnel test but instead of a steel ball a diamond in the shape

of a square based pyramid is used.

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Impression – square instead of round

Uses - Dental casting gold alloys

- Tooth structure as it measures the hardness of brittle materials.

Knoop

In this test a diamond indenting tool is used that is cut in geometric

configuration. The impression is rhombic in outline and the length of the

largest diagonal is measure.

The projected area is divided by load to give the knoop hardness no

when the indentation is made and the indentation is removed the shape of the

knoop indenter is causes elastic recovery of the projected impression to occur

along the short diagonal. The stresses are therefore distributed in a matter that

only the dimension of the minor axis are subject to change by relaxation.

So the hardness value is virtually independent of the ductility of the

material tested.

The load to be used may be varied over a wide range from 1gm to more

than one kg so that values for both hard and soft materials can be obtained by

this test.

Knoop and Vickers test are called microhardness tests. The Brinnel and

Rockwell are macrohardness test.

K & V tests used loads less than 9.8N. The indentations are small and

are limited to a depth of less than 19m.

Other less sophisticated tests like Scholl and Barcol are employed for

increasing the hardness of dental materials particularly rubbers and plastics.

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These tests used compact partable indenters of the type generally used in

industry for quality control.

The hardness no is based on the depth of penetration of the indent

patient into the materials.

Abrasion and Abrasion Resistance

Abrasion is a complex mechanism in the oral environment that involves

an interaction between numerous factors.

Usually hardness has often been used as an index of the ability of a

material to resist abrasion or wear that the reliability of hardness as a predictor

of abrasion resistance is limited.

Although it may be used to compare materials that are similar i.e. one

brand of cast metal with another brand of the same type of casting alloys it

cannot be used to evaluate different classes of materials eg. Synthetic resin

with metal.

The hardness of a material is only one of the factors that affect the wear

of the contacting enamel.

Other factors are:

1. Biting force.

2. Frequency of chewing.

3. Abrasiveness of the diet.

4. Composition of liquids.

5. Temperature changes.

6. Roughness of each surface.

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7. Physical properties.

8. Surface irregularities.

The excessive wear of tooth enamel by an opposing restoration is more

likely to occur. If the opposing restoration is rough therefore restorations

should be polished to mechanisms this type of abrasion.

Stress concentration factors

Unexpected fractures sometimes occur in high quality materials also.

The cause of this is the presence of small microscopic flaws on the

surface or within the external structure. These flaws are especially critical in

brittle materials.

There are 2 important aspects of these flaws.

1. Stress intensity increases with the length of the flaw especially when it

is oriented perpendicular to the direction of tensile stresses.

2. Flaws on the surface are associated with higher stresses than are flaws of

the same size in interior regions.

3. So surface finishing is very critical in material like ceramics, amalgams

and composites.

Areas of high stress concentrations are caused by one or more of the

following factors.

1. Large surface or interior flaw such as porosity, grinding roughness and

machining damage.

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2. Sharp changes in shape of the sharp internal angle at the pulpal axial line

angle of a tooth preparation for an amalgam restoration.

3. The interface region of a bonded structure in which the elastic moduli of

2 components are quite different.

4. The interface region of a bonded structure in which the thermal

expansion or thermal contraction coefficient of the two components are

different.

5. A load applied at a point to the surface of a brittle material.

Ways to minimize the stress concentration

1. Surfaces should be polished to reduce depth of flaws.

2. Notches should be avoided.

3. Internal line angles should be rounded to minimize the cusp fracture.

4. The elastic moduli of the materials must be closely matched.

5. The coefficient of expansion and contraction should be matched.

6. The cusp tip of an opposing crown or tooth should be rounded so that

occlusal contact areas in brittle material are larged.

Factors for selecting dental materials

The strength properties and values that have been got by various tests

represent the average stress value below which 50% of test specimens have

fractured and above which only 50% have survived.

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From an ultra conservative point of view the lowest strength values

should be used to compare materials and also to design a prosthesis to resist

fracture at a high level of confidence.

The magnitudes of mastication forces cannot be known to the extent that

the dentist can predict the stresses. To conclude, the true test for any material is

the test of time.

References:

Phillips’ Science of DENTAL MATERIALS / Kenneth J. Anusavie/

Elaventh Edition

RESTORATIVE DENTAL MATERIALS / Robert G. Craig & John M.

Powers / 11 th Edition

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CONTENTS

Introduction

Stress and Strain

Elastic limit

Proportional limit

Modulus of elasticity

Flexibility and Resilience

Strength

Other mechanical properties

Factors that cause fracture or failure

Criteria for selection of dental materials

References

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Mechanical Properties

Seminar byDr. N.Upendra Natha Reddy

Postgraduate Student2004-2007

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