CHAPTER 4 Mechanical Properties of Biomaterials 4 1

CHAPTER 4 Mechanical Properties of Biomaterials 4. 1 Introduction Molecular mechanisms behind the mechanical properties Nature of chemical bonds and subunit structures Mechanical properties 1. tensile/compressive properties 2. shear/torsion properties 3. bending properties 4. viscoelastic properties 5. hardness

4. 2 Mechanical Testing Methods, Results, and Calculations Forces: tensile, compressive, shear, torsion 4. 2. 1 Tensile and shear properties (1) Calculation for tension and shear tests 1) tension testing dog-bone geometry load and specimen elongation [stress (s) & strain (e) relationship]

4. 2. 1 Tensile and shear properties (1) Calculation for tension and shear tests 1) tension testing engineering stress & engineering strain s and e relationship [Hooke’s law] geometry of specimen (shapes) 2) compression testing s < 0, e<0 3) shear testing shear stress (t) and shear strain (g) 4) torsion forces torsion stress (t) and torsion strain (g) torque force (T)

(2) Stress-strain curve and elastic deformation stress-strain curve s=Exe modulus of elasticity or Young’s modulus [stiffness of materials] t=Gxg shear modulus [slope of the stress-strain curve in the elastic region] Elastic elongation & contraction (transverse strain) Poisson’s ratio (n) isotropic material n = 0. 25 relationship between the shear and elastic moduli E = 2 G (1+n)

(3) Molecular causes of elastic deformation resistance (interatomic bonding force) E & (d. F/dr)ro high E (very stiff materials) force separation curve ceramics > metals > polymers (4) Stress-strain curves and plastic deformation permanent deformation (metals and polymers) linear and non-linear regions elastic and plastic deformation Yield strength (sy) Yield point strain (eyp) 0. 2% strain offset

Elastic deformation Yield strength Plastic deformation Ultimate tensile strength [tensile strength] Necking Plastic deformation with decreased stress Fracture Yield strength key design parameter

Ductility: ability of a material to deform plastically before breaking Low ductility --- brittle % elongation vs. % area reduction Semicrystalline polymers Yield point -- neck -- polymer chain orientation -- resistance -- growth of the necked region -- stress increase to deform the polymer -- fracture

Engineering stress and strain --- True stress and strain (5) Molecular causes of plastic deformation ceramics metals polymers Elastomers (rubbers)

(6) Causes of plastic deformation - metals and crystalline ceramics – Slip: Force vs. slip plane 1) single crystal material in tension shear forces --- dislocation glide resolved shear stress (tr) tr > tcrss [slip] 2) polycrystalline materials more complex multigrain structure macroscopic deformation

(7) Causes of plastic deformation - amorphous polymers and ceramics (glasses) – deformation via viscous flow Newton’s law [rate of deformation & applied stress] t=hxg amorphous materials as cooled liquid shear force ---- continuous deformation with time

(8) Causes of plastic deformation - polymers (general) testing temperature 증가, strain rate 감소 ----- E 감소, tensile strength 감소, ductility 증가 1) temperature ductility vs brittleness 2) strain rate necking phenomenon (9) Causes of plastic deformation - semi-crystalline polymers and elastomers – 1) semicrystalline polymers tensile force chain orientation change in spherulite shape (necking phenomenon)

Synthesis and processing parameters ---- deformation behavior 영향 Chain mobility 감소 ---- strength 증가, ductility 감소 a) polymer crystallinity b) mol. wt. c) X-linking 2) Elastomers Amorphous with coiled chains w/ free bond rotations --- X-linking (prevention of plastic deformation) T>Tg tensile strength chain alignment

4. 2. 2. Bending Properties Ceramics: inherent brittleness of the materials Bending test compressive force tensile force Modulus of rupture Stress-strain curves with little plastic deformation

4. 2. 3. Time-Dependent Properties (1) Creep plastic deformation under constant load over time at specified temp. strain vs. time curve a) primary creep: repositioning of aspects of the material with loading b) secondary creep: equilibrium & minimum creep rate c) tertiary creep: rapid elongation to material failure parameters for creep: e (steady state creep rate), tr (time to rupture) stress and temp 증가: e 증가, tr 감소

Creep curve for polymers negative strain w/ compressive loading even at low temp & stress (2) Molecular causes of creep – Metals sliding of grain boundaries or vacancy migration a) stress-induced vacancy diffusion grain elongation along the line of applied stress (Nabarro-Herring creep) cf) Coble creep b) dislocation climb diffusion of an entire row of vacancies

(3) Molecular causes of creep – Ceramics more resistant to creep deformation to maintain electroneutrality, difference in diffusivities, fewer point defects grain boundary sliding (4) Molecular causes of creep – Polymers movement of chains in the amorphous regions via viscous flow % crystallinity and Tg crystallinity 증가 --- creep 감소 T<Tg: no time-dependent deformation (no rotation or slide) only elastic deformation up to the fracture T>Tg: time-dependent deformation (polymer chain movement) viscous flow (creep and stress relaxation) (5) Stress relaxation and its causes creep: stress --- strain 증가 stress relaxation: decrease in stress over time under constant strain --- stress 감소 chain movement in the amorphous regions % crystallinity and T>Tg (viscous flow)

(6) Mathematical models of viscoelastic behavior T>Tm: viscous liquid T<Tg: elastic solid Tg<T<Tm: viscoelastic property a) applied step load b) elastic d) viscous ----- c) viscoelastic creep and stress relaxation Silly Putty bouncing vs. stretching rate of strain

Model to explore viscoelastic responses a) elastic component Hooke’s Law (spring) b) viscous compoent Newton’s Law (dashpot) (7) Viscoelastic behavior – Maxwell model spring and dashpot in series (직렬) e = e 1 + e 2 & s = s 1 = s 2 a) creep: strain increase linearly with time (not valid) b) stress relaxation: exponential decrease in stress over time (valid)

(8) Viscoelastic behavior – Voigt model (Kelvin model) spring and dashpot in parallel (병렬) e = e 1 = e 2 & s = s 1 + s 2 a) creep: exponential response in strain over time (valid) b) stress relaxation: Hooke’s law, no viscous portion (invalid) Maxwell for stress relaxation and Voigt for creep Combination to predict creep and stress relaxation behavior Spring-dashpot system: general behavior of a polymer

4. 2. 4 Influence of Porosity and Degradation on Mechanical Properties pores: elastic modulus (-), strength of biomaterials (-) a) cross section area (-) b) stress concentrators by pores [stress increase to localized area] biodegradable materials for implants – mechanical properties poly(glycolic acid): chemical structure and presence of pores designing of biodegradable implants or tissue engineering scaffolds

4. 3 Fracture and Failure 4. 3. 1. Ductile and brittle fracture 1) Ductile failure [metals, polymers] plastic deformation cone-shaped appearance slow crack propagation stable crack ductile fracture (warning) higher strain energy 2) Brittle facture [ceramics, polymers] little plastic deformation (no warning) Charpy & Izod impact tests ductile-to-brittle transition temperature T<Tdbtt: brittle fracture

4. 3. 2 Polymer crazing: fracture of amorphous thermoplastic polymers near scratches or flaws perpendicular to the axis of tensile stress fibrils + voids ---- degradation of fibrils and expansion of voids [crack formation in the crazed area] 4. 3. 3. Stress concentrators amplification of applied stress at the tip of the flaw elliptical crack --- increase in stress at the edges of the crack (local increase) stress concentrators or stress raisers [notches, sharp corners, pores] Maximum stress at the crack tip (sm) brittle > ductile materials ceramics higher fracture strengths in compression > tension lower localized stress amplification

4. 4 Fatigue & Fatigue Testing 4. 4. 1. Fatigue repeated loading --- fracture at stresses less than the tensile or yield strength fatigue fracture: brittle with no plastic deformation repeated stress --- # of dislocations --- imperfections in crystals --- flaws ---- cracks cf) strain hardening a) crack initiation b) crack propagation c) final failure Nf = N i + N p 4. 4. 2. Fatigue testing rotating-bending apparatus & uniaxial tension-compression machine stress (S) & # of cycles (N) to failure S = (smax –smin)/2

Fatigue limit or endurance limit no fatigue failure below a certain level of stress ex) titanium Fatigue strength: stress level causing the failure Fatigue life: # of cycles for the fracture kinetics of crack propagation 4. 4. 3. Factors that affect fatigue life a) regional stress concentrator b) amplitude of the applied stress c) impurity in the surface region d) other stress raisers e) biodegradable materials f) environment of the implant corrosive fatigue

4. 5 Methods to Improve Mechanical Properties dislocation glide or slip --- plastic deformation slip reduction 1) inclusions of additives a) metal alloys (impurity – cancel the lattice strain) b) polymers (fillers – entanglement and X-linking) 2) processing a) polycrystalline materials grain boundaries ---- dislocation movement smaller grain – more grain boundaries – stronger b) cooling rate metal: rapid cooling --- small grains --- grain boundaries 증가 polymer: rapid cooling --- low % crystallinity --- low overall strength thermal history of materials

4. 6 Techniques: Introduction to Mechanical Analysis dynamic mechanical analysis (DMA) mechanical properties during oscillatory loading 4. 6. 1 Mechanical testing (1) Basic principles uniaxial loading at a controlled amplitude and rate sample shape tensile testing smaller X-section reproducible region of breakage (2) Instruments stress and strain curve a) grip/actuator; b) load cell; c) extensometer; d) processor (3) Information provided stress vs strain stress/strain vs time modulus, yield & tensile strength, fatigue life, etc.