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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.
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
So, Stress =
Change in Area
Hookes law Stress and Strain
Strain may be either elastic / plastic or a combination
Stress may be - Simple
Simple : Stress can be classified based on their directions.
1. Tensile stresses
2. Compressive stresses
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.
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
Cross sectional are ⊥
Perpendicular to the
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
The bracket will debond due to the shear stress produced which will be
due to the shear stress failure of the luting agent.
Shear 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.
Plastic stresses on the other hand cause deformation and may be high
enough to produce fracture. Example of the elastic shear deformation.
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.
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 is the stress at which plastic strain which produces slight
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.
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
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
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
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.
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 σ 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
is an engineering property of the material called Poisson’s ratio
-ex = -ey
for an ideal isotropic material of constant volume the ratio is 5.
Most engineering material have values of 3
These can be defined as the strain that occurs when the material is
stretched to its proportional limit.
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
Since E =
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 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.
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 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
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.
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.
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.
Diametral Compression Test is used. This test is used for materials that
exhibit elastic and not plastic deformation.
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
Tensile stress =
π x D x t
P – load
D – diameter
π – 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
σ – flexural strength.
l – distance between the supports.
b – width of the specimen.
d – depth or thickness of the specimen.
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
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
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.
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.
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.
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.
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
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.
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
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.
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
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.
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
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
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.
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:
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).
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
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
It is suitable for brittle materials so it is used for the measured of
hardness of tooth structures.
Similar to Brinnel test but instead of a steel ball a diamond in the shape
of a square based pyramid is used.
Impression – square instead of round
Uses - Dental casting gold alloys
- Tooth structure as it measures the hardness of brittle materials.
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
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
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 19µm.
Other less sophisticated tests like Scholl and Barcol are employed for
increasing the hardness of dental materials particularly rubbers and plastics.
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
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.
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
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
Areas of high stress concentrations are caused by one or more of the
1. Large surface or interior flaw such as porosity, grinding roughness and
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
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.
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.
Phillips’ Science of DENTAL MATERIALS / Kenneth J. Anusavie/
RESTORATIVE DENTAL MATERIALS / Robert G. Craig & John M.
Powers / 11 th Edition
Stress and Strain
Modulus of elasticity
Flexibility and Resilience
Other mechanical properties
Factors that cause fracture or failure
Criteria for selection of dental materials
Dr. N.Upendra Natha Reddy