Dental materials a complexity that involves the mathematics of Engineering, the science of materials, and arts of dentistry (without one the others are useless) each of these is depended on the other only together can they be effective so let us explore the mathematical complexities of dental materials
Mechanical properties D.M
Out of the four common material property categories namely physical, chemical mechanical and biological. We shall discuss mechanical properties
Definition: mechanical properties are subset of physical properties that are based on the laws of mechanics that is the physical science that deals with energy and forces and their effects on the bodies. They are the measured response, both
Elastic reversible on force removal
And plastic irreversible or non elastic
Of material under an applied force are distribution of forces.
Mechanical properties are expressed most often in units of stress and stain.
They can represent measurement of
1) Elastic or reversible deformation (i.e. proportional unit resilience and modulus of elasticity)
2) Plastic are irreversible deformation (Percent elongation and hardness)
3) A combination of elastic and plastic deformation such as toughness and yield strength
To discuss these properties one must first understand the concepts of tress and strain
Depending on the forces three simple types of tresses are classified
a) Compressive stress
b) Tensile stress
c) Shear stress
d) Flexural (bending) stress
Compressive stress: if a body is placed under a load the tends to compress are
shorten it, the internal resistance to such a load is called a” compressive stress” a compressive stress is associated with the strain here forces are directed to each other in a straight line
Tensile stress: a tensile stress is caused by a load that tends to stretch or elongate a body. A tensile stree is always accompanied by a shear strain, Here forces act paralled to each
d) Flexural Bending stress
is produced by bending forces and may generate all three types of stress in a structure. It can occur in fixed partial dentures or cantilever structures
As shown in above figure. Tensile stress develops on the tissue side of the FPD. And compressive stress develops on the occlusal side.
For a cantilevered FPD the maximum tensile stress develops with the occlusal surface if you can visualize the unit bending downward toward the tissue the upper surface becomes more convex or stretched and the opposite surface becomes compressed
Mechanical properties based on elastic deformation
There are several important mechanical properties measuring reversible deformation and includes
1) Elastic modulus ( young’s modulus or modulus of elasticity or hook’s law )
2) Dynamic young’s modulus
3) Flexibility
4) Resilience
5) Poisson’s ratio
! ) elastic modulus ( young’s modulus or modulus of elasticity
Definition : if any stress value equal to or less than the proportional limit
Is divided by its corresponding strain value, a constant of proportionality will result. This constant of proportionality is known as the modulus of elasticity or young’s modulus it is represented by the letter E
E = Stress
----------- giga Newton’s / sq m or giga pascules
Strain ( 1 giga Newton / m2 6N / m2 = 10. 3 MN / M2
Elastic modulus describes the relative stiffness or rigidity of a material
This phenomenon can play a role in burnishing of margins of crown
Elastic modulus of various materials
Materials Elastic modulus (G N/m2)
1)Enamel 84.1
2) Destin 18.3
3) Feld spathic porcelain 69.0
4) Composite resin 16.6
5)Acrylic denture resin 2.65
6) Cobalt – chromium partial 218.0
denture alloy
7) Gold (type-4) alloy 99.3
Enamel has higher elastic modulus (3-4 times) then dentin and is stiffer or more brittle, while dentin is more flexible and tougher, ceramic have higher modulus then polymers and composites.
2) Dynamic Young’s modulus
Elastic modulus can be measured by a dynamic method, since the velocity at which sound travels through a solid can be readily measured by ultrasonic longitudinal and transverse wave transclucers and appropriate receivers. The velocity of the sound wave and the density of the material can be used to calculate the ‘elastic modulus’ and
‘Poisson ratio’ values. This method of determining ‘dynamic elastic moduli’ is less
complicated than conventional tensile or compressive tests.
If instead of uniatial tensile or compressive stress a shear stress was induced
The resulting shear strain could be used to define a shear modulus for the material. The
Shear modulus (G) \, can be calculated from the elastic modulus (I) and poisons ratio
(V), using equation
E E
G= ----------- = ------------ = 0.38 E
2 (1+V) 2 (1+0.3)
A value of 0.3 for Poisson’s ratio is typical. Thus, the shear modulus is usually about 38% of the elastic modulus.
4) Flexibility :
The maximum flexibility is defined as the strain occurring when the material is stressed to its proportional unit. A larger strain or deformation with slight stresses is called flexibility and is an important consideration in orthodontic appliances.
5) Resilience:
Resilience can be defined as the amount of energy absorbed with in a unit volume of a structure, when it is stressed to its proportional limit. It is popularly associated with springiness .for example when an acrobat falls on a trapeze net the energy fall is absorbed by he resilience of the net and when this energy is released the acrobat is again into the air.
The above is a stress-strain that illustrates the concepts of resilience and toughness. The area bounded by the elastic region is a measure of resilience and the total area under the stress-strain curve is a measure of toughness.
The restorative material should exhibit a moderately high elastic modulus and relatively low resilience thus limiting the elastic strain.
6) Poisson’s Ratio:
When a tensile stress or compressive stress is applied to a cylinder or rod, there is simultaneous axial and lateral strain, within the elastic range, the ratio of the lateral to the axial strain is called POISSONS RATIO
Lateral strain
POISSONS= ----------------------
Axial strain
For ideal isotropic material it is 0.5
For most engineering materials it is 0.3
2) MECHANICAL PROPERTIES BASED ON PLASTIC DEFORMATION
(Irreversible deformation)
Now, we come to properties that are determined from stresses at the end of elastic region of stress-strain, plot viz
1) Proportional limit
2) Elastic limit
3) Yield strength (proof stress)
4) Permanent (plastic) deformation.
*) Strength:
Strength is the stress necessary to cause either fracture or plastic deformation.
The strength of a material can be described by one or more of the following properties,
1)Proportional limit
2) elastic limit
3) Yield strength
4) Permanent deformation
1) Proportional limit:
Defn: The greatest stress that may be produced in a material such that the stress is directly proportional to strain.
For E.g.: A wire is loaded in tension in a small increments until the wire ruptures without removal of the load each time, and plotted stress on vertical co-ordinate and the corresponding strain is plotted on the horizontal co-ordinate a curve as shown below
The point ‘P’ is the proportional limit and up to point ‘B’the is proportional to strain and beyond ‘P’ the strain is no longer elastic and stress is no longer proportional to strain.
2) Elastic limit:
The elastic limit is defined as the maximum stress that a material will withstand without permanent deformation,(for all practical purposes, therefore). The elastic limit and the proportional limit represent the same stress within the structure and the terms are often interchangeable in referring to the stress involved. However they differ in that one describes the elastic behavior of the material where as the other deals with stress to strain in the structure.
3) Yield Strength it is the stress at which the material begins to function in a plastic manner, this yield strength is defined as the stress at which a material exhibits a limiting deviation from proportionality of stress to strain. It is used when proportional limit cannot be accurately determined.
It is described in terms of percent offset.
Elastic limit, proportional limit and yield strength though defined differently have close values but yield strength is always greater than the other two (proportional limit, elastic limit).
4) Permanent (plastic) deformation
If a material is deformed by a stress beyond its proportional limit before fracture and the force removed. The strain does not become 0 due to plastic or permanent deformation, thus it refers to the stress which a material get permanently deformated i.e it remains bent, stretched or deformed
It is the stress at which the material begins to function in a plastic manner. Thus yield strength is defined as the stress at which a material exhibits a limiting deviation from proportionality of stress to strain. It is used when proportional limit cannot be accurately determined.
It is described in terms of percent offset.
Elastic limit, proportional limit and yield strength though defined differently have close values but yield strength is always greater then the other two.
(i.e. proportional ;limit , elastic limit)
3) Permanent (plastic) Deformation:
If a material is deformed by a stress beyond its proportional limit before fracture and the force removed the strain doesn’t become zero due to plastic or permanent deformation. Thus it refers to the stress beyond which a material get permanently deformated i.e. it remains bent stretched or deformated .
Now, Let’s have a look at different types of strength
It is the material stress required to fracture a structure.
1) Diametral Tensile Strength:
Tensile strength is generally determined by
Now let’s have a look at different types of strength,
It is the maximal stress required to fracture a structure
1) Diametral Tensile Strength:
Tensile strength is generally determined by subjecting a rod, wire or dumbbell shaped specimen to tensile load, since such test is quit difficult to perform for brittle materials because of alignment and gripping problems, another test has become popular for brittle materials because of alignment and gripping problems, another test has become popular for determining this property for brittle dental material is refered to as” Diametral compression test”
Compressive load is placed against the side of a short cylindrical (specimens). The vertical compressive forces produces a tensile stress and fracture occurs along this vertical plane, Have tensile stress is directly proportional to compressive load
_2P_ P= Load
Tensile Stress = Dt D= Diameter
T= Thickness
This test simple to conduct and provides excellent reproducibility of result.
Flexure Strength ( Transverse strength or Modulus of rupture)
This property is essential a strength test of a beam supported at each end, under static load. It is a collective measurement of all types of stress.
When the load is applied, the specimen bends, the principal stress is applied, the specimen bends, the principal stress on the upper surface are compressive, where as those on the lower surface are tensile.
The mathematical formula for computing the flexure strength is
= 3Pl = flexural strength
2 bd2 = Distance between support
= Width of the specimen
=Depth or thickness specimen
= Maximum load at the point of fracture
it is preferred for brittle materials
Fatigue strength:
Stress values well below the ultimate tensile strength can produce premature fracture of a dental prosthesis or material because microscopic flows grow slowly over many cycles of stress. This phenomenon is called fatigue failure
Fatigue strength is the endurance limit i.e. maximum stress cycles that can be maintained without failure
It can be determined by subjecting a material to a cyclic stress of a maximum known value and determining the number of cycles that are required to produce failure.
Static fatigue is a phenomena attributed to the interaction of a constant tensile stress with structural flow over time. It is a phenomenon exhibited by certain ceramic materials in wet environment; certain ceramics also demonstrate dynamic fatigue failure.
1) Impact strength:
Impact strength may be defined as the energy required to fracture a material under an impact force
A charpy type impact tester and Izod impact tester are used to test.
A material with a low elastic modulus and a high tensile strength is more resistant to impact forces.
A low elastic modulus and a low tensile strength suggest low impact resistance
Other mechanical properties: Toughness is defined as the amount of elastic and plastic deformation energy required tp fracture a material and is a measure of resistance to fracture, Toughness is stress stain cure upto fracture and depends on strength and ductility
Fracture toughness:
Fracture toughness is a mechanical property that describes the resistance of brittle materials to the catastrophic propagation of flows under times the square root of crack length i.e Mpa. M½ or tnN.M 3/2
Brittleness:
Brittleness is the relative inability of a material to sustain plastic deformation before fracture of a material occurs. It is considered as the opposite of toughness for example Amalgams, ceramics and composites are brittle at oral temperature; They fracture without plastic strain. Hence, brittle materials fracture at or near their proportional limit however, a brittle material is not necessarily weak, for example Glass is drum in to a fibers or Glass infiltrated alumina core ceramics.
3) Ductility and Malleability:
Ductility represents the ability of a material to sustain a large permanent deformation under a tensile load before it fractures. For example a metal that may be readily drawn into a wire is said to be ductile
Malleability: The ability of a material to sustain considerable permanent deformation without rupture
Under Compression:
As in the most ductile and malleable metal which silver is second, platinum B 3rd rank in ductility and copper ranks 3rd in malleability
Ductility is measured by 3 common methods
a) Percent elongation after fracture:
The simplest and most commonly used method is to compare the increase in length of a wire or rod after fracture in tension to its length before fracture. Two marks are placed on the wire as the gauge length (for dental, materials, the standard gauge length is usually 51mm) the wire or rod is then pulled a part under a tensile load, the fractured ends are fitted together, and the gauge length is again measured, the ratio of the increase in length after fracture to the original gauge length is called the present elongation and represents ductility
b) The reduction in area of tensile test specimens:
The necking or cone-shaped constriction that occurs at the fractured end of a ductile wire after rupture under 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 referred to as the reduction in area
c) 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, with the grater the number, the greeter the number, the greater is the ductility of the material.
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 most other disciplines, the concept of hardness is” resistance to indentation”
Numerous properties like strength proportional limit and ductility interact to produce hardness
Hardness tests, are included in ADA specifications for dental materials, there are various scales and tests mostly based on the ability of the material surface to resist penetration by a point under a specified load, these test include Burcol, Brinells Rock well, share, Vickers and Knoop
1) Brinell bard ness test:
- One of the oldest test used to
determining the hardness of metals
- A hardness steel ball is pressed under a specified load into the polished surface of a material the load is divided by the area of the projected surface of the indentation and the quotient is referred to ad Brinell hardness number or BHN
- Brinell hardness test has been extensively used for determining the hardness of metals and metallic materials used in dentistry.
- BHN is related to the proportional limit and the ultimate tensile strength of dental gold alloys
Rockwell hardness test:
It is some what similar to the
Brinell test in that a steel ball or conical diamond point is used. Instead of measuring the diameter of the impression the depth of penetration is measured directly by a dial gauge on the instrument. Different indenting points for different materials are used and designated as RHN
These two BHN and RHN are unsuitable for brittle materials
Vickers Hardness test:
- Is the same principle of hardness
- Testing that is used in the Brinell test
- Instead of a steel ball, a square based
- Pyramid is used. Although the pression
- Is square instead of round the load is divided by the projected area of indentation and
designated as VHN
- The Vickers test is employed in the ADA specification for dental casting gold alloys,
also it is suitable for brittle materials, Hence used for measure tooth hardness
4) Knoop Hardness test:
This employs a diamond tipped tool cut in geometric configuration. The impression is rhombic in outline and the length of the largest diagonal is measured the projected area is divided into the load to give the KHN
The hardness value is virtually independent of the ductivity of the tested material thus hardness of tooth enamel can be compared with that of gold, porcelain, load can be varied from 1g to 1kg so that both hand and soft materials can be tested
The knoop and Vickers tests are classified as micro hardness test while Brinell and Rock well are macro hardness test. Knoop and Vickers can measure hardness in thin object too
Other less sophisticated tests are SHORE and BARCOL to measure hardness of materials like rubber and plastics, types of dental materials; these utilize portable indenters and are used in industry for quality control the principle of these tests is alos based on resistance to indentation
Stress concentration factors of material
Stress concentration factors refer to the microscopic flows or micro and macro structural defects on the surface or within the internal structure, these factors are more accentuated in brittle material and are responsible for unexpected fractures at stress much below ultimate strength. The stress higher when the flow is perpendicular to direction of tensile stress and flows on the surface accumulated higher stresses
Areas of high stress concentration are caused by following factors
1) Surface flows i.e. voids are inclusions
2) Interior flows i.e. voids or inclusions
3) A sharp internal angle at the pulpal axial angle of a tooth preparation for an amalgam or composite restoration
4) A large difference in elastic modulus or thermal expansion coefficient across a bonded interface
5) Hertzian load i.e. applied at a point on a brittle material
There are several waysto minimize these stress concentrations, thus reduce the risk of clinical fracture
1) The surface can be polished to reduce the depth of the flow
2) Internal line angles of tooth preparation should be wel rounded to minimize the risk of cosp fracture
3) The materials must be closely matched in their coefficient of expansion or contraction
4) The cusp tip of an opposing crown or tooth should be well rounded distribute stress over a larger area for brittle materials
Mechanical properties of tooth structure and mastication forces
The mechanical properties of enamel and dentin varies one type of tooth to another, within individual teeth than between teeth and position of tooth.
That is cuspal enamel is stronger than enamel on other surfaces of tooth stronger under longitudinal compression than lateral compression
On the other hand, Dentin is considerably stronger in tension (50MPa) than enamel (10MPa), compressive strength of enamel and dentin are comparable the proportional limit and modulus of elasticity of enamel are higher than dentin
Mastication forces :
Mastication or bitting forces varies mankedly varies from one area of the mouth to another and from one individual to another.
For the molar
Bibe force range from: 400 to 890N (90 to 200 pounds)
Premolar area : 222 to 445N (50 to 100 pounds)
Cuspid region : 133 to 334N (30 to 75 pounds)
Incisor region : 89 to 111N (20 to 55 pounds)
Generally higher metals than and greater in beyond adults than in children
Conclusion:
As we have seen there are various properties governing the performance of the material. Different properties make to particular material more suitable for a given situation for example Higher strength in posterior restoration Better electivity is required in cast restorations.
Thus, a through knowledge and in-depth understanding of these mechanical properties will help us to select and deliver the most suitable material for every situation.
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