lect7 - Biology 427 Lecture 7. Strength and toughness of...

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Unformatted text preview: Biology 427 Lecture 7. Strength and toughness of biological materials Recap stress, strain, stiffness and strength of biomaterials: measures of material properties Strength revisited and the limits to the size of terrestrial vertebrates Energy relations in biological materials: toughness and resilience Plastic deformations: an introduction to time-dependent material properties. stress (!) : the distribution of force over an area strain ("): a dimensionless measure of length change stiffness (E): the change in stress required for a change in strain (the slope of a stress-strain curve): a material property bone 200 Material Youngs Modulus (Mpa) ! Locust cuticle 0.2 hair (MPa) Rubber 7 Human cartilage 24 resilin Human tendon 600 Cheap plastic 1,400 0 0.2 0.4 0.6 Plywood 14,000 " Human bone 21,000 Glass 70,000 Brass 120,000 Iron 210,000 Diamond 1,200,000 stress (!) : the distribution of force over an area strain ("): a dimensionless measure of length change stiffness (E): the change in stress required for a change in strain (the slope of a stress-strain curve) a material property strength (!max): the stress at failure 60 Baluchitherium: about 30 Tons Could the foot bones support its weight? !max = 100 MPa = Fmax/Area ! (MPa)40 20 Tendon Fmax =108*Area = 151 104 N m = 151 103Kg = 151 T 0.06 diameter = 14 cm = 151 10-4 m2 0.02 0.04 0.05 " stress (!) : the distribution of force over an area strain ("): a dimensionless measure of length change stiffness (E): the change in stress required for a change in strain (the slope of a stress-strain curve) strength (!max): the stress at failure 60 material strength (MPa) arterial wall 2 human cartilage 3 cement 4 cheap aluminum 70 glass 100 human tendon 100 human bone 110 human hair 200 spider silk 350 1000 0.06 titanium steel wire 3000 Energy Basics for Materials W = ! F dx W = vol 60 ! AL F dx 60 s (MPa) Force 40 20 Tendon 40 20 ! (MPa) 40 20 0.02 0.04 e 0.05 0.02 0.04 x 0.05 0.06 0.02 " 0.04 0.05 0.06 The energy imparted is the mechanical strain energy The energy imparted is the mechanical strain energy that can be returned or be so great as to break the material U = ! ! d" W = vol F ! A dx L U = ! ! d" ! (MPa) 40 20 ! (MPa) For Hookean materials !=E" 60 60 40 20 0.02 0.04 0.05 0.06 U = ! E " d" = E "2/2 U = ! ! d!/E = !2/2E toughness: the energy per unit volume required to break a material T = ! ! d" 0.02 " 0.04 0.05 0.06 " T = !2max /2E (if Hookean) 103 collagen U = 100 MJ/m3 10 nylon keratin silk chitin 1 steel 0.1 cast iron The energy imparted is the mechanical strain energy that can be returned or be so great as to break the material U = ! ! d" 0.01 60 not all of the energy imparted is returned Strength (MPa) bone 102 fir oak shell concrete ! (MPa) 0.001 40 20 energy returned energy imparted = Resilience (R) stony coral 101 3 10 104 E (MPa) 105 106 0.02 " 0.04 0.05 0.06 The story of the pregnant (gravid) locust locusts are migratory light weight important in flight fertilized eggs in dehydrated state live in very arid climates trick: bury the eggs ~ 8 cm beneath surface E = 105 MPa The energy imparted is the mechanical strain energy that can be returned or be so great as to break the material or be lost as a permanent deformation (plastic deformation) 2 cm U = ! E " de = E "2/2 = 1011 9/2 ~ 5 1011 J/m3 = 5 108 J/kg with 1 g of abdomen -> 5 105 J ~8cm M = 0.005 kg PE = Mg h h = 107m = 104km Any examples in humans? 60 ! (MPa) 40 20 0.02 " 0.04 0.05 0.06 ...
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