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**MECHANICAL PROPERTIES**

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**Stress strain relations**

Restorative materials must withstand forces either during fabrication or mastication.

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Mechanical properties are importan in understanding and predicting the behavior of a material under load.

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**Force is gained through one body pulling or pushing on another one.**

The result of an applied force on a body is the change in the position of rest or motion of the body.

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**If the body to which the force is applied remains at rest, the force causes deformation of the body.**

The unit of force is the Newton N.

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The biting force on an adult teeth increases from the incisors to the molar region. Biting force on the first and second molars is varying from 400 to 800 Newton.

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**Anatomical form of the tooth. Location of the tooth. **

The force of occlusion and response of the underlying tissues depends on: Anatomical form of the tooth. Location of the tooth. Age of the patient. Malocculsion. Placement of restorative appliance.

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Stress When a force acts on a body tending to deform it, an internal resistance is developed to this external force application. The internal reaction is equal in intensity and opposite in direction to the external applied force and called STRESS.

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Both the applied force and internal resistance (stress) are distributed over a given area of the body and are designed as force per unit area. Stress = So stress = N/m2, MN/m2 or MPa,.

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Types of stresses 1- Tension: tension results when a body is subjected to two sets of forces away from each other in the same straight line.

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2-Compression: Compression results when a body is subjected to two sets of forces in the same straight line and directed toward each other. The result is shortening of the body.

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**3-Shear: Shear is the result of two sets of forces directed parallel to each other.**

The result is sliding of the molecules over each other.

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4- Torsion: Torsion results when a body is subjected to two sets of circular forces in opposite directions producing twisting of the body. 5- Bending. (3 points bending test)

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**Fig 2: The different types of stresses and their corresponding deformation**

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Strain Strain (E) is defined as the change in length per unit length of a body when subjected to stress. Strain has no unit or measurements but is represented as a pure number, obtained from the following equation:

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Strain (E) = If a sample of original length 2 mm is pulled to 2.02 mm, the deformation will be 0.02 mm. Strain is equal 2.02 – 2 mm / 2 mm = 0.01 or 1%.

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**Fig 3-a: the three basic types of stresses**

Fig 3-b: Complex stresses as produced by 3-point loading of a beam

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**Stress – strain relations:**

The stress-strain relationship of a dental material is studied by measuring the load and deformation and then calculating the corresponding stress and strain. The relationship between stress and strain is used to study the mechanical properties of dental materials.

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The stress is plotted vertically and the strain is plotted horizontally. As the stress is increased the strain is increased. In the initial portion or stage of the curve from 0 to A the stress is proportional to the strain (linear relation).

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**Specification for Dental Materials**

Any test specimen ready for testing should be prepared according to standardized dimensions approved by international specifications. The conditions of testing should be also standardized.

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**International Specifications for Dental Materials**

For dentistry we have the following specifications: American Dental Association (ADA). American Society for Testing and Materials (ASTM). International Standard and Organization (ISO).

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**Universal testing machine**

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Cylindrical specimen Compression Tension

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Stress-strain curve pl

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**Proportional limit and elastic limit**

The proportional limit is defined as the maximum stress that a material will sustain without the deviation of Proportionality of stress to strain.

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**Below the proportional limit no permanent deformation occurs in a structure.**

The region or area of the stress-strain curve below the proportional limit is called the Elastic region.

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**The region beyond the proportional limit is called the plastic region.**

The elastic limit is defined as the maximum stress that a material will sustain without permanent deformation.

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**Stress- strain curve for a material subjected to a tensile stress**

Proportional limit and elastic limit

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Yield strength The yield strength or yield stress (YS) is the stress at which the material begins to function in a plastic manner. At this stress a limited permanent deformation has occurred in the material.

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The yield strength is defined as the stress at which a material exhibits a specified limiting deviation of proportionality of stress to strain.

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**Fig 5: Offset yield strength**

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**The amount of permanent strain is arbitrarily selected for the material to be examined.**

It is indicated as 0.1, 0.2 or 0.5% permanent strain and is referred as the percent offset.

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Ultimate strength The ultimate tensile strength is the maximum stress that a material can withstand before failure in tension. The ultimate stress is determined by dividing the maximum load in tension or comparison by the original cross-sectional area of the test specimen.

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**Ultimate compressive strength**

Load at fracture 500 kg U.C.S = = D= 1cm h = 2 cm 500 X r2 500 3.14 X (0.5)2

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In restorative dentistry, the yield strength is more important than ultimate strength because it indicates when a material starts to permanently deform.

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Fracture strength The stress at which a material fracture is called fracture strength. The fracture strength is not necessarily the ultimate stress at which the material will fracture.

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**The ultimate tensile strength**

(Strain) F.S N/mm2 1000 800 Fig (4a) The ultimate tensile strength Fig (4b) Fracture strength

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**Elastic modulus (modulus of elasticity or Young's modulus)**

The elastic modulus represents the stiffness of a material within the elastic range. It can be determined from a stress-strain curve by calculating the ratio between the stress and strain on the slope of the linear region from the following equation:

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Elastic modulus E = Elastic modulus is determined in kg/cm2 or Mpa or GPa. To transfer from kg/cm2 to MPa we multiply by

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The stronger the forces of attraction between atoms and molecules the greater the value of elastic modulus and more the material will be rigid. The elastic modulus represents the slope of the elastic portion of the stress-strain curve.

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**Fig 7: Rigidity of material vs. elastic deformation at a load.**

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Elongation The deformation that results form the application of tensile stress is elongation. Elongation is important because it gives an idea about the workability of the alloy.

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% of Elongation = X 100 An alloy with high percent of elongation can be bent or adjusted without danger of fracture.

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Fig 8: Total strains

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Flexibility The term flexibility describes the amount of strain up to the elastic limit. So that flexibility is the total amount of elastic strain in a material.

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Fig 9: Total strain

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**Ductility and Malleability**

Ductility is the ability of a material to withstand a permanent deformation under tensile stress without rupture.

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**A metal which may be drawn into a wire is said to be ductile**

A metal which may be drawn into a wire is said to be ductile. Ductility is dependent upon plasticity and tensile strength. The ability of a material to withstand permanent deformation under compression, as in hammering or rolling in sheets, is called malleability.

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**How to describe strain ? Elastic strain = flexibility.**

Plastic strain = ductility or malleability.

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**Low elastic limit and low ductility**

Fig (10a) Low elastic limit and low ductility Fig (10b) High elastic limit and high ductility

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**Fig 11:Open margins of a casting**

Burnishing

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Resilience Resilience is the resistance of a material to permanent deformation. It indicates the amount of energy required to deform a material to its proportional limits. Resilience is measured as the triangular area under the elastic portion of stress-strain curve. The surface area of the triangle is 1/2 bh.

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**Fig 12(a): Stress-strain curves showing the area representing the resilience of a material**

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The units are m MN/m3 that represents the energy per unit volume of the material. (Transferred in joules). This property is important for orthodontic wire and denture liners.

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Toughness Toughness is defined as the amount of energy required to stress a material to the point of fracture. Toughness is the resistance of a material to fracture.

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**The area under the elastic and plastic portion of the curve represents the toughness of a material.**

It is difficult to calculate and the units of toughness are the same as resilience m MN/m3.

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**Fig 12b: Stress-strain curves showing the area**

Fig 12b: Stress-strain curves showing the area indicating the toughness.

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**Properties and Stress-Strain Curves**

The shape of a stress-strain curve and the magnitude of stress and strain allows the classification of materials as regard to their properties e.g. rigid, strong, stiff, weak and brittle.

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**Fig 13: Stress-strain curves for materials with various combinations of properties**

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**How to predict the properties of a material under testing from the stress-strain curve?**

The magnitude of the curve. The inclination of the curve in the elastic range. The amount of plastic deformation.

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**High magnitude = strong**

The magnitude to the curve. MN/m2 MN/m2 1000 200 High magnitude = strong Low magnitude = weak

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**The inclination of the curve in the elastic range.**

1000 MN/m2 0.1 MN/m2 800 4 Stiff and rigid Flexible Elastic modulus = E.M = E.M =

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**The amount of plastic deformation.**

MN/m2 MN/m2 Brittle = no or small amount of plastic deformation Ductile = large amount of plastic deformation

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