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# Mechanical properties

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• 1. 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 force Stress = 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 F So, Stress = Area Change in Area Strain = Unit area Hookes law Stress and Strain Strain may be either elastic / plastic or a combination 1
• 2. 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 &#x22A5; Perpendicular to the force direction 2
• 3. 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. Force 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&#xB0; permanent deformation. 3
• 4. 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&#x2019;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. 4
• 5. 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&#x2019;s modulus of elasticity and it is calculated as follows: E - Elastic modulus F - Applied force / load A - Cross sectional area &#x2206;l1 - Increase in length L0 - Original length By definition Stress = F/A Strain = l1/l0 Stress F/A Fl0 &#x2234; = = 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 5 250 200 150 100 50 0 PL PL E D
• 6. 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 &#x3C3; 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&#x2019;s ratio (v). -ex = -ey v = 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. 6
• 7. 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 P Since E = em P em = 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. 7
• 8. 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. 8
• 9. 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. 9
• 10. 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. 2P Tensile stress = &#x3C0; x D x t P &#x2013; load D &#x2013; diameter t- thickness &#x3C0; &#x2013; 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 &#x3C3; = 2bd2 &#x3C3; &#x2013; flexural strength. l &#x2013; distance between the supports. b &#x2013; width of the specimen. 10
• 11. d &#x2013; depth or thickness of the specimen. p &#x2013; 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. 11
• 12. 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 &#x2013; 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. 12
• 13. 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 &#x2013; 40 GPA 50-100MPa Amalgam &#x2013; 21GPA 460 MPa Composite Resin - 17 GPA / 30-9 MPa Polymethhymethacrylate &#x2013; 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 13
• 14. 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 &#xBD; 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&#xB0;C. They sustain little or no plastic strain before they fracture. If a brittle material fractures at or near its proportional limit. 14
• 15. 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 &#x2013; Third in ductility, Copper &#x2013; 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. 15
• 16. 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 &#x201C;gauge length&#x201D;. 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&#xB0;. 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 16
• 17. 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. 17
• 18. 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&#x2019;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&#x2019;s test Similar to Brinnel test but instead of a steel ball a diamond in the shape of a square based pyramid is used. 18
• 19. Impression &#x2013; 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 &amp; V tests used loads less than 9.8N. The indentations are small and are limited to a depth of less than 19&#xB5;m. Other less sophisticated tests like Scholl and Barcol are employed for increasing the hardness of dental materials particularly rubbers and plastics. 19
• 20. 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. 20
• 21. 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. 21
• 22. 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. 22
• 23. 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&#x2019; Science of DENTAL MATERIALS / Kenneth J. Anusavie/ Elaventh Edition RESTORATIVE DENTAL MATERIALS / Robert G. Craig &amp; John M. Powers / 11 th Edition 23
• 24. CONTENTS &#xF076; Introduction &#xF076; Stress and Strain &#xF076; Elastic limit &#xF076; Proportional limit &#xF076; Modulus of elasticity &#xF076; Flexibility and Resilience &#xF076; Strength &#xF076; Other mechanical properties &#xF076; Factors that cause fracture or failure &#xF076; Criteria for selection of dental materials &#xF076; References 24
• 25. Mechanical Properties Seminar by Dr. N.Upendra Natha Reddy Postgraduate Student 2004-2007 25
• 26. 26