BE501 Biomaterials: Materials Science

Elastic Properties: mechanical testing

• All (man-made & biological) materials deform when subjected to a load
• Relationship between applied load and resultant deformation defines mechanical properties

• Stress = load (force) per unit area = F/A = s (N/m², Pa or MPa)
• Strain = deformation per unit length Dl/l_o = e (change in length relative to original length, in %)
• Young's Modulus = slope of stress-strain curve, E = s/e (N/m²)
• describes how springy a material is and how much elastic energy it can store
• materials with high Young's modulus are stiff and hard to stretch or bend
• graph of stress vs strain (MTS or Instron machine) shows how the material deforms:

Typical stress-strain curve

• Initial elastic deformation in the linear region
• removal of the applied load will result in a return to the original size and shape
• at yield point, the material enters the non-elastic, or plastic, region
• structural changes within the material begin to occur
• results in permanent deformation
• energy lost in the process and is not recovered when load is removed
• finally reaches ultimate stress, when it elongates rapidly and fractures

Terms

• Stress = Force/Cross-sectional Area (MPa)
• Strain = Change in Length/Original length (%, microstrain)
• Energy Absorbed = Area under the Load-Deformation Curve (J)
• Stiffness = Slope of Load-Deformation Curve (N/m)
• (Young's) Modulus of Elasticity = Slope of Stress-Strain Curve (MPa)
• Strain Rate = Rate at which Specimen is Deformed (m/s)
• Viscoelasticity = Strain Rate Dependent Properties of Biological Tissues
• Strength = Ultimate load of specimen OR Ultimate stress of material
• Toughness = Energy required to break specimen or material

Types of loading

• Compression
• Tension
• Shear
• Combinations (most common in biomechanics)
• bending
• stress occurs on concave surface
• tensile stress on convex surface
• e.g. load on femoral head causes compressive stress on medial and tensile stress on lateral shaft of femur.
• torsion
• e.g. at heel strike, foot pronation is associated with medial tibial rotation

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Friction

                                           F = m R

                                         therefore m = F/R

where F is the shear force required to make one surface slide on another & R the normal force pressing the surfaces together

                                        LOW m = "slippery"                        HIGH m = "rough"
 

Contact Surfaces	Coefficient of Friction (m )
Rubber tyre/dry road	1.0
Metal/metal	1.0
Glass/glass	1.0
Perspex/perspex	0.8
Perspex/steel	0.3
Wood/wood	0.25
Ice/ice	0.05
Synovial joints (Wright 1986)	0.02
Articular cartilage with saline	0.01
Articular cartilage with synovial fluid	0.004
Articular cartilage/articular cartilage	0.02 - 0.001

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Factors affecting frictional resistance

• relative sliding velocity (shear rate)
• apparent bearing area
• coefficient of viscosity
• applied load
• effective radius of curvature
• lubricant thickness
• elastic modulus of cartilage
• pressure/viscosity coefficient for lubricant

• defines the relationship between the mass of a fluid and its volume

Viscosity

• measure of friction between adjacent layers of fluid as the fluid flows
• When a liquid is viscous there is a lack of slippiness between adjacent layers of fluid due to "friction" between molecules of adjacent layers.

All surfaces, no matter how smooth they appear, are irregular (wavy, high spots, asperities)

e.g. two sheets of coarse sandpaper in contact

This explains why, normally, frictional resistance is independent of apparent contact area:

                                             F = m R

Therefore, frictional force is directly proportional to the applied load and independent of the apparent contact area

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Wear

• all artificial surfaces moving relative to each other will eventually "wear out"
• processes involved are physically, and chemically very complex
• abrasion
• adhesion
• fatigue
• erosion
• corrosion

Adhesive Wear occurs when local irregularities (asperities) on opposite surfaces, "weld" together

Anatomy of a Normal Joint

• Bone
• Articular cartilage
• Synovial fluid
• Ligament (capsule)
• Blood supply via capsule (periarticular arterial plexuses)
• Innervated in general by the nerves of supply to the muscles that act on them

Degenerative changes (osteoarthrosis, OA)

• cartilage thinning (joint space narrowing)
• increased wear
• marbled bone on articular surface
• marginal osteophytes
• thickened capsule

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Synovial Fluid Composition

• dialysate of blood plasma filtered through semipermeable walls of blood vessels
• clear and almost colourless (slightly yellowish)
• 1/3 of the protein concentration of blood plasma
• low glucose content
• hyaluronic acid (mucopolysaccharide) produced by synovial cells
• controls fluid content (retains water)
• controls protein content - binds with a specific protein to form a mucoprotein
• affects viscosity of fluid
• small but variable cellular component (most synovial cells and connective tissue cells removed by phagocytosis)
• volume only 0.2 - 0.5 mL, even in large joints such as the knee: increases with exercise

Properties

• Thixotropic effects
• viscosity is proportional to fluid film thickness / velocity of movement (shear rate between articular surfaces)
• viscosity inversely proportional to velocity gradient
• viscosity decreases as the shear rate increases (ie. as the speed of relative motion between the surfaces, increases)
• faster the sliding, the more slippery is the lubrication (like. pouring tomato sauce from a bottle)
• Viscoelastic effects
• acts like a gel when subjected to sudden compressive forces
• resists 'squeezing out' from between the articulating surfaces
• fluid deforms more easily during slower rates of deformation
• Temperature effects
• viscosity is inversely proportional to temperature
• need for warm-up before physical exertion
• Surface Properties
• Rheology (deformation of surfaces & flow): e.g. flow of synovial fluid within a joint
• Tribology (lubrication, friction & wear): e.g. synovial joint lubrication

• lubrication to reduce frictional resistance
• provide nutrition to articular cartilage
• protect the joint structures when subjected to large compressive forces
• provide a liquid environment within a narrow pH range
• remove various products of metabolism

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Chris Kirtley