Biomaterials - Lecture notes 1-10 PDF

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Biomaterials Mechanical Loading -

Important mechanical properties of a material are strength, hardness, ductility, and stiffness Mechanical loading has three principle loading scenarios: o tension o compression o shear  torsion is a variant of shear loading wherein, a structure is rotated about the longitudinal axis

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Three-point bending is where the upper surface is in compression, main body of the material is in shear, and the lower surface is in tension o The stress required to fracture a material using three-point bending is the flexural strength and is an important parameter for brittle materials o Examples of a three-point bending scenario in dentistry is a dental bridge which is a beam in flexure

Stress -

Force acting per unit cross sectional area upon the material Stress can lead to strain which is the fractional change in dimension caused by the force o Poisson’s Ratio is the ratio of the lateral and axial strains o Axial strain is usually larger than lateral strain and therefore, the ratio is usually in the range of 0.15-0.45 o Poisson’s ratio of 0.5 means there is no change in volume

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True stress takes into account the final area of the material and true strain takes into account the incremental changes in length Stress and strain have a linear relationship as long as elastic limit is not exceeded Youngs Modulus – the modulus of elasticity is the ratio of stress over strain o Indicates stiffness of a material Shear stress is the stress which is applied parallel or tangential to a face of the material o Shear stress measured as force/original area in shear o Shear strain measured as the width of the shear over the length of original material or simply the tangent of the angle change from the shear stress o Shear modulus is the ratio of shear stress over shear strain o Relationship between shear modulus and elastic modulus: E = 2G(1+v) where v is Poisson’s ratio, G is shear modulus

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Bulk Modulus is the behaviour of materials under compressive stresses o The bulk strain is the change on volume o 1/E = 1/3G+1/9B

Elastic Behaviour -

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Elastic limit – point where elastic deformation ceases and either failure of plastic deformation of the material will occur Abides Hooke’s Law where stress and strain increase proportionally o For ductile materials the elastic limit is also known as the yield stress Elastic deformation occurs – atomic bonds are stretched but not broken Up till the elastic limit any displacement of the material is reversible

Proof stress enables uniform positioning/estimation of the yield point for all materials – usually 0.2% because exact limit is difficult to accurately place Resilience is the capacity for a material to absorb energy when is undergoes elastic deformation and the energy can be recovered upon unloading – area under curve till the elastic limit Engineering stress-strain curve accounts for multiaxial loading and is responsible for the decrease in load just before failure

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True stress strain curve does not account for multiaxial loading so use a corrected true stress strain curve

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Stiff materials like enamel and alumina have a large Young’s modulus whereas, ductile materials like rubber have a low Young’s Modulus

Plastic Deformation -

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Strength is the amount of stress necessary to cause a certain fracture or certain amount of plastic deformation o Peak stress on the stress strain curve is also known as the ultimate tensile strength Plastic deformation occurs after the elastic limit has been exceeded and the deformation is irreversible o Atomic bonds break and reform between new neighbouring atoms which results in the movement of molecules or large number of atoms o Occurs by slip motion in crystalline solids and involves dislocation motion o Occurs via viscous flow in amorphous solids (plastics and liquids) Toughness is the energy the material absorbs till its fracture o Measured as the area underneath the stress strain curve o Some elastic energy will be recovered upon unloading but not all o A material is tough if it is both strong and ductile o Fracture toughness is a materials ability to resist fracture when a crack is present

Crystalline Structures -

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Unique arrangement of atoms in a crystal – very regular and local positions of atoms with respect to each other are repeated at an atomic scale Plastic deformation in a crystalline structure occurs via dislocations Edge dislocation – lattice distortion due an extra half a plane of atoms creates a line defect along an edge called the dislocation line Screw dislocation – formed by applied shear stress and is a one atom shift in a superior layer Mixed dislocation – combination of edge and screw dislocations and is most common – a screw dislocation will result in an edge dislocation (additional half a plane of atoms) further along the material The slip plane is the crystallographic plane along which the deformation occurs Dislocations can interact to create tensile and compressive forces o Compressive will repel other compressive forces o Tensile forces will repel other tensile forces o Tensile and compressive forces will attract o These stresses cause hindrance to dislocation and result in an increased required stress to cause deformation Dislocation pileups are sites of high strain energy because the local distortion of the crystal lattice become irregular and results in strain energy build up within the material o It is harder to plastically deform the material Work hardening is increasing the dislocation density of a material and thereby, increasing the stress required for deformation o Increased number of dislocation attractions and repulsions o Increased strain energy builds up in the material o Increased resistance to dislocation motion

Hardness -

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Measure of a materials resistance to localised plastic deformation o Is not an intrinsic property because depends on the geometry and dimensions of the material Hardness can be calculated a variety of ways, but the overall concept is the indenter penetration procedure o Initial point of contact – infinite contact because the contact area is theoretically infinitely small and therefore, there is an infinite stress and plastic deformation occurs

As the indenter penetrates the material the contact area increases so the stress applied decreases but is still greater than the yield stress and therefore, plastic deformation still occurs o When the indenter stops penetrating the material the contact area is large enough so that the stress is equal to the yield stress/elastic limit so no more plastic deformation can occur, and the indenter stops Indenter types o Knoop – flat square pyramid good for small thin materials o Brinell – spherical indenter and the hardness value from this test can also determine tensile strength is multiplied by 3.45 o Vickers – is a thicker square pyramid and the tensile strength can be calculated from the hardness value by dividing the hardness value by 3 o Rockwell – a conical indenter Elastic and plastic deformation occur around the contact area and plastic deformation will spread further than the immediate contact area Indentation generates complex stress strain patters including compression, shear, and tension so hardness cannot be directly related to strength measured in other ways Hardness of elastomeric materials can also be measured but there is no plastic deformation o Related to the elastic modulus o Measure stress required to impress a ball to a certain depth o Contact area of the material with the ball must be known o Hardness = load/contact area The depth or size of the resulting indentation is measured and related to the hardness value of the material Hardness is measure in pascals Soft materials will not be able to indent harder materials (cause plastic deformation) Materials which have a high elastic modulus are also hard and vice versa o

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Fractures -

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Local separation of an object or material into two or more pieces under the action of stress o Atomic bonds are broken o Crack formation and propagation Fractures in brittle materials happen rapidly and without warning and happen after some plastic deformation in ductile materials Tensile forces lead to unstable crack propagation in brittle materials, but compressive forces lead to stable crack propagation The fracture strength is also the ultimate tensile strength as it is the maximum stress the material can handle before fracture under immediate loading o Brittle materials will fail near the elastic limit o Ductile materials will undergo plastic deformation before failing Griffith’s Experiment o Increased volume of a material will result in a decreased strength o Due to the larger number of flaws and the probability of these flaws being larger in size o Griffith’s Criterion – critical stress required for a crack of a specified length to grow spontaneously Strength is determined by the biggest flaw under tension Brittle materials show a range of strength values because of the variability in flaw sizes Cracks will propagate spontaneously because the elastic energy stored in the material due to the applied stress exceeds the energy required to create new surfaces The critical stress is the stress at which a crack will spontaneously propagate and depends on the crack length

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Stress concentration sites are spots which have a small area and therefore, less stress is required to reach the critical stress at which a crack will grow – defects such as cracks, air bubbles or a sudden change in shape can cause this o To avoid fracture of dental restoration it is important to round angles during these treatments to reduce stress concentrations

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The critical stress intensity factor/fracture toughness is a method used to quantify a materials resistance to crack propagation (Kc) o Is an intrinsic property of a material o If the critical stress intensity is breached, then spontaneous crack propagation and failure of the material will occur (maximum stress intensity factor) o Measured by: single notch edge bend, compact tension, indentation The stress intensity factor is used to predict the stress intensity near the tip of a crack o Is a function of applied stress, crack length and geometry of the material o If the stress intensity factor is greater than the fracture toughness, then the crack will spontaneously propagate

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There are three modes of fracture: o Mode 1 – tensile – is the most common o Mode 2 – shear o Mode 3 torsion A fracture can be described by energy or stress o How much energy is required per unit area to create two new surfaces as the crack propagates – strain energy release rate o Stress state at the crack tip – the stress intensity factor

Fatigue -

Form of failure that occurs to structures subject to dynamic and fluctuating stresses o Undergoes cyclic loading – stress amplitude, stress range, mean stress o Estimated to cause 90% of metallic failures

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Mastication is a form of fatigue but isn’t perfectly cyclical but is a random loading pattern – 1000-1400 cycles per day, stresses range between 6-800 N

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The S-N curve o Fatigue limit – largest value of fluctuating stress not will no cause failure for an infinite number of cycles o Fatigue strength - stress which will result in failure for a specified number of cycles o Fatigue life – number of cycles to cause failure at a specified stress level

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Stages of fatigue failure o Crack initiation – cyclic loading can produce microscopic surface discontinuities resulting from dislocation slips that may also act as stress concentration sites. The concentrated stress exceeds the yield strength of the material resulting in plastic deformation and the

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initial microcracks propagate and the material strength decreases. The crack initiation occurs at stresses much lower than the critical stress intensity factor. o Propagation – the crack advances incrementally with each stress cycle perpendicular to the applied stress. The crack does not spontaneously propagate at this stage. o Final failure – the crack propagates until it reaches a critical dimension where upon spontaneous crack propagation occurs and the material fails and has reached its fatigue life There are a number of factors which affect the fatigue life of a material: o Mean stress of the cyclic loading o Design factors – stress concentration sites, polishing etc o Corrosion Stress corrosion fatigue is the combined action of stress and a corrosive environment which leads to crack formation – crack would not have developed due to applied stress or environment alone o Crack initiation is easier at corrosion pits as they act as stress concentration sites – failure can occur at lower than the yield stress o Stress can increase the driving force for corrosion reactions o Decreases the fatigue life Stress corrosion fatigue is influenced by whether the surface is rough or smooth o Rough surfaces have hills and valleys with different surface energies and therefore, some areas which have a high surface energy are more prone to corrosion because liquids can more easily wet the surface and the pores and notches act as stress concentration sites o Polishing results in a harder surface due to dislocation stresses and therefore, reduces the influence of stress corrosion fatigue and increases the stress at which the material will fail under cyclic loading Stress corrosion cracking occurs by moisture rupturing covalent bonds specifically Si-O-Si bonds o Stresses at crack tip help to induce this corrosion further and the crack propagation occurs at a stress intensity factor which is lower than the fracture toughness – subcritical crack propagation o Influenced by water, pH, and temperature o Results in strength degradation as the crack grows less stress is required to cause failure

Gypsum -

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Used to create models of dentition and investment impressions for casting metals Widely available natural material – calcium sulphate dihydrate Gypsum is heated to get gypsum plaster and is turned into calcium sulphate hemihydrate o Calcination – prolonged heating of substance at temperature below melting point o Wet calcination – decomposition of dihydrate in the presence of liquid because the temperature can be high enough and causes recrystallisation of the hemihydrate, so they are more regular and less porous –  Autoclave in super-heated steam pressure and then drying and grinding  Boiling in solution of calcium chloride then drying and grinding o Differences in heating methods and crystal structure provide the differences in performance Types of gypsum o 1. Impression plaster o 2. Plaster for low grade casts and imbedding casts in articulator mountings o 3. Stone for diagnostic casts and working casts for restorations made from denture base resins o 4. Die stone low expansion – working casts for fixed restorations

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5. Die stone high expansion – working casts for metallic removable restorations

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Bulk density (apparent density) is the mass of a sample divided by the volume it occupies and measures a specified degree of compaction o Plaster materials have a low bulk density because they are manufactured via calcination (open fire dry heating) which generates irregular particles. Imperfect, irregularly shaped crystals tend to adhere to each other with enclosed voids.

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Dihydrate and hemihydrate have different solubilities 2.1g/L for dihydrate and 8.8g/L for hemihydrate o Setting of calcium sulphate hemihydrate is just rehydration and forms calcium sulphate dihydrate and precipitates o Dihydrate precipitates in the form of needle like structures from crystal nuclei centres and interact with other needle spherulites and mechanical interaction occurs o The mechanical interaction imparts strength and setting expansion – there is also surface tension between the crystals which adds to the strength

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There are three stages of dimensional change during setting  Contraction as water is absorbed to form the dihydrate  Minima at “loss of gloss” when excess water is no longer present  Expansion as dihydrate crystals grow and make contact pushing the nuclei centres apart  At the end instead of 7% volumetric contraction there is about 0.05%-0.4% setting expansion – due to pushing apart between crystal nuclei and voids between needle spherulites  Expansion depends on the type of gypsum – type 4 die stones have the least expansion due to regular particles and less required water for setting  70% of expansion occurs within the first hour of setting

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Stages in setting o Fluid – crystal nucleation and is flowable under vibration o Plastic - needle spherulites grow from crystals and will not flow but can be moulded o Friable – solid but with low strength o Carvable – solid and reached maximum strength

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Gypsum setting reaction is the opposite of manufacture and therefore, is exothermic. More crystal nuclei the higher the temperature generated by the reaction o The induction period is where the supersaturated dihydrate will deposit nucleation centres to form nuclei for crystal growth

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Hygroscopic expansion occurs when the setting gypsum is placed in water and can achieve greater expansion than under normal setting o There is uninhibited crystal growth – unlimited water source o Decrease in strength because there is a loss of attraction between crystals, there is a loss of surface tension o Crystals grow bigger and the overall gypsum model is larger o Useful for making oversize models

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The theoretical water powder ratio for the hemihydrate to dihydrate reaction is 18.61:100 but there are other considerations to take into account o Enough water to fill the voids between the gypsum molecules o Additional water needed for dilatancy because the viscosity increases upon mixing  Additional volume needed for irregular particles to rotate and move freely during mixing as irregular particles will have a high viscosity

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Need enough water to form a slurry that is of a usable viscosity Therefore, the water powder ratio is more or less high than the theoretical volume Water powder ratio is higher in plaster materials and lower in die stones because the die stones have more regularly shaped particles

Increasing the water powder ratio, the space between the crystals are larger and the crystals themselves grow larger and the mechanical interaction is lower, and the overall strength of the material is lower. The setting time is also increased as the nucleation centres are further apart/less concentrated and therefore, it takes more time for them to come into contact. There are a number of ways to decrease the setting time: o Impurities act as nuclei for dihydrate nucleation like left over gypsum o Potassium sulphate o Sodium sulphate and sodium chloride – initially effective o Borax is an inhibitor increases setting time o Fineness – smaller particles have a greater surface area and faster the mix sets – increased concentration of nucleation centres o Manipulation – increased spatulation causes more nucleation centres to form and conversion of hemihydrate to dihydrate is shorter and faster setting time o Temperatures between 20 and 37 degrees increases the rate of reaction and shortens setting time. At temperatures between 37 and 100 degrees the rate of reaction decreases and setting time increases. At temperatures above 100 degrees the solubility of hemihydrate and dihydrate ...