Ch 4 - Mechanical Properties of Biomaterials Flashcards
Dynamic mechanical analysis (DMA)
• “Dog-bone” geometry: tensile stress at middle of sample → more reproducible fracture
• Instrumentation
1 . Grips/activator (holds sample, moves grip)
2. Load cell (records instantaneous load)
3. Extensometer (records instantaneous length)
4. Computer (converts signals to σ-ε curve)
- Tensile, compressive, creep and stress relaxation tests
General σ-ε curves (∀ material)
I. Ceramic: linear, steep slope (\elastic deformation, stronger bonds)
II. Metal (linear, then inverted parabola) = better for loads b/c ductile and more \plastic deformation
III. Semi-crystalline polymer (linear, then upward curl)
IV. Elastomer (logarithmic, then upward curl)
Engineering stress
σ = F⊥ / A_o
where A_o = init. CSA
* Meas. in Pa
** Engr. assumes neglig. change in size during testing
Engineering strain
ε = (L_i − L_o) / L_o
- Dimensionless
- Engr. assumes neglig. change in size during testing
Shear testing
Produces forces // to top and bottom faces of sample
Shear stress
τ = F_(||) / A_o
* F_|| = shear force, can cause sample defor. of angle θ
Shear strain
γ=tan(θ)
Torsion forces
Twists cylindrical specimen to cause deformation of angle φ
Hooke’s law
σ = Eε
where E = \elastic modulus
Elastic modulus
“E” = linear slope of stress-strain curve
- Meas. in MPa
- Stronger interatomic bonds = ↓ defor. = ↑ E (∴ more energy to separate)
Elastic deformation
Linear stress/strain relationship
Shear modulus (modulus of rigidity)
“G” = slope of τ-γ curve in elastic region
s.t. τ = Gγ
Transverse strain
ε_t = Δd /d_o
* Subsequential contraction ⊥ to axial tension
Poisson’s ratio
ν = −ε_t / ε_a
* Dimensionless, must be [+]!
Elastic & Rigid Moduli
E = 2G (1 + ν)
direction dependence
[polymers]
• along axis: 1 ° covalent bonds, mech prop’s similar to metals/ceramics
• else: 2 ° forces dominate, reduces mech prop’s
Plastic deformation
• Permanent, sample never completely returns to original shape
• Non-linear portion of stress/strain curve
* Does not follow Hooke’s law
Yield strength
“σ_y” = stress end of elastic region (start plastic defor.)
- Draw 0.2% offset line (0.002) on x-axis, // to elastic portion
- Key design param. b/c end of elasticity
Yield point strain
“ε_yp” = strain at end of elastic region
* Draw 0.2% offset line (0.002) on x-axis, // to elastic portion
Ultimate Tensile Strength (UTS)
[crystalline e.g. metals/ceramics]
“σ_UTS” = necking of specimen
∴ no longer uniform strain across entire specimen, only defor. at necking area
Fracturing strength
“σ_f” = stress at fracture
* after onset of necking, ↓ stress to cause further plastic defor.
∴ σ_frac < σ_UTS
Ductility
Ability of material to deform plastically before breaking
Brittleness
- Mat’ls w/ low ductility
* Fracture w/ little plastic deformation e.g. ceramics
% ELongation
% EL = (L_f − L_o) / L_o ∗100
where “o” = initial, “f” = fracture
% Area Reduction
% AR = (A_o − A_f) / A_o ∗100
where “o” = initial, “f” = fracture
Plastic defor.: polymers
• Chains become oriented w/ direction of load
• Resist defor. along axes b/c 1 ° interxns ∴ specimen elongation along ENTIRE gauge length (not just necked area, like metals)
• Before frac, signif ↑ σ neces. (b/c overcoming 1 ° bonds within aligned chains) → upward curl
* Complex b/c ∀ grain randomly oriented
** Depends on testing envir e.g. ↑ Temp, ↓ strain rate ∴ E ↓, strength ↓, ductility ↑
Elasticity
- Stretch bonds, return to normal length after load removed
* Char. only of \elastomers
Elastomers
• Allow large recoverable strains at low stress levels
• Subset of polymers e.g. rubber
• Amorphous in unstressed state: coiled chains w/ nearly free bond rotations about backbone
* b/c the chains are crosslinked, chains cannot slide past each other ∴ no plastic defor.
** Above T_g, tensile force allows uncoiling of chains/alignment along axis (but NOT sliding) → increased entropy ∴ favors original state (like springs)
** would NOT strengthen an elastomer, b/c want to maintain elasticity
Resolved shear stress
[metals/crys. ceramics]
τ_r = σ cos(ϕ) cos(λ)
where ϕ = Normal ⊥ to slip plane and λ = angle of slip dir. (both w.r.t vertical)
Critical Resolved Shear Stress (CRSS)
[metals/crys. ceramics]
“τ_crss” = amount of shear stress in slip plane to initiate slip
* Factor in determining σ_y of material
** Slip occurs if τ_crss achieved in LEAST favorably aligned grain
Processing polymers: Heating
• Grain growth favored at high T
∴ faster cooling → more, smaller grains • More, small grains LESS likely to be aligned
→ Reduce likelihood of slip ∴ STRONGER, σ_y ↑
Processing polymers: Additives
- Smaller atom can sit in compressive region around edge defect and cancel lattice strain
- Driving force ↓ ∴ slip ↓
strain rate
Faster, higher strain = less time to rearrange chains along axis of loading (in neck region) ∴ ↓ defor.
Plastic deformation:
Semi-crystalline Polymers/Elastomers (molecular level)
- Semi…polymers = spherulites → plastic defor. = interxns b/w lamellae & amorph. regions
1 . Tie chains extend, lamellae slide past each other
2. Lamellae reorient s.t. chain folds align along axis of loading
3. Blocks of crystalline phases separate (break 2 ° bonds)
4. Blocks and tie molec’s extend, oriented along axis of applied tensile force (1 ° covalent bonds still intact, until fracture) - High force necessary to overcome tie molec/covalent bonds
** Any changes that inhibit chain motion (need higher energy to overcome): ↑ σ_y, ↓ ductility
1 ° v. 2 ° bonds
1 ° = crosslinking (when broken → fracture)
2 ° = % X-talinity
* also ↑ MW
=> ↓ chain sliding, ↑ σ_y, ↓ ductility
Ductile fracture
“cone shape” = plastic deformation prior to breaking
• Crack propagation is slow and stable
• Preferred mode of failure (b/c warning signs from shape change)
Brittle fracture
- Little/no plastic deformation (less slip)
* Flat fracture surface (little warning)
Charpy and Izod impact tests
Measures impact energy and determines D2B transition temp. (when mat’l fractures brittle-y)
Polymer crazing
Network of fine cracks on surface (⊥ to tensile stress), but CAN support some load
Stress raisers
• Small flaws which ↑ localized stress → crazes
• e.g. notches, sharp corners and pores
* More signif. for brittle mat’l b/c plastic defor. ↓ localized stress
Creep
• Plastic deformation of sample under constant (tensile) load (ε) over time
• 1 °, 2 ° (\SS creep rate), 3 °
• Key param: \SS creep rate and \time to rupture “t_r”
* must be greater than T_g to have viscous effects
** if ↑ Temp OR ↑ σ → then rate ε ↑ , t_r ↓
Primary creep
↑ ε w.r.t time, while creep rate (slope) ↓
* due to repositioning of defects e.g. dislocations
Secondary creep
• Linear relationship b/w creep & ε (typ. longest period)
* SS creep rate (dε/dt = 0)
Tertiary creep
- Gross defects inside mat’l
* e.g. GB separ, cracks/voids → rapid elongation to mat’l failure
Molecular causes of creep: Metals
- GB sliding
- Migration of vacancies (esp. at high Temp) → \stress-induced vacancy diffusion
- \dislocation climb
Stress-induced vacancy diffusion
- Extra vacancies due to loading (⊥ to axis of loading)
- Vacancies migrate // to axis of loading
- Atoms move in opp. direction
Nabarro-Herring creep
Atomic diffusion opp. of \stress-induced vacancy diffusion → elongation of grain along axis of applied stress
Coble creep
Vacancies migrate along GB (than through bulk of grain)
Dislocation climb
Dislocation moves 1 atomic spacing by diffusion of entire row of vacancies to extra partial plane of edge dislocation
Molecular causes of creep: Ceramics
• GB sliding = main microstructural rearrangement
* More resistant to creep b/c electroneutrality
Molecular causes of creep: Polymers
• Chain sliding in amorphous regions via viscous flow
• % X-talinity and temp (w.r.t T_g)
→ ↑ % X-tal → creep ↓ b/c less amorphous
→ Below T_g, NO CREEP b/c chains cannot rotate/slide
Stress relaxation
[polymers]
↓ stress over time under constant strain
* Similar to creep, depends on % X-talinity and temp (above T_g)
Fatigue fracture
• Failure due to repeated loading/dislocations, at stresses signif. less than σ_UTS tensile/yield strengths
• Brittle, little plastic deformation (even in ductile materials)
* Fatigue → ↑ # dislocations → \crack initiation (high σ) → \crack propagation (↑ in size ∀ successive loading cycle) → failure (rapid)
Fatigue life
• N_f = N_i + N_p
where N_i = # cycles at crack initiation & N_p = # cycles at propagation to critical size for failure
• ↑ σ or \stress raisers → # cycles to failure ↓ (faster)
* Biodegradable mat’ls = more flaws and pores
Corrosion fatigue
Failure due to cyclic stress + chem attack
How to improve mechanical properties
Reduce mvmt of dislocations/slip OR chain sliding
*Polycrystalline mat’l gen’lly stronger b/c GB discourage dislocation mvmt (smaller grains = more GB/vol = stronger)
Methods to improve mech prop’s: Additives
- [metals] \alloys: reduce lattice strain
* [polymers] \fillers: strength ↑ by acting as crosslinks
Methods to improve mech prop’s: Processing
• Polycrystalline, quick cooling → more GB/vol (smaller GB) ∴ stronger (higher yield strength) b/c less likely for grains to align (less suscep. to shear stress)
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