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Biomaterials > Ch 4 - Mechanical Properties of Biomaterials > Flashcards

Ch 4 - Mechanical Properties of Biomaterials Flashcards

1
Q

Dynamic mechanical analysis (DMA)

A

• “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
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2
Q

General σ-ε curves (∀ material)

A

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)

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3
Q

Engineering stress

A

σ = F⊥ / A_o
where A_o = init. CSA
* Meas. in Pa
** Engr. assumes neglig. change in size during testing

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4
Q

Engineering strain

A

ε = (L_i − L_o) / L_o

  • Dimensionless
    • Engr. assumes neglig. change in size during testing
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5
Q

Shear testing

A

Produces forces // to top and bottom faces of sample

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6
Q

Shear stress

A

τ = F_(||) / A_o

* F_|| = shear force, can cause sample defor. of angle θ

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7
Q

Shear strain

A

γ=tan⁡(θ)

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8
Q

Torsion forces

A

Twists cylindrical specimen to cause deformation of angle φ

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9
Q

Hooke’s law

A

σ = Eε

where E = \elastic modulus

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10
Q

Elastic modulus

A

“E” = linear slope of stress-strain curve

  • Meas. in MPa
    • Stronger interatomic bonds = ↓ defor. = ↑ E (∴ more energy to separate)
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11
Q

Elastic deformation

A

Linear stress/strain relationship

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12
Q

Shear modulus (modulus of rigidity)

A

“G” = slope of τ-γ curve in elastic region

s.t. τ = Gγ

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13
Q

Transverse strain

A

ε_t = Δd /d_o

* Subsequential contraction ⊥ to axial tension

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14
Q

Poisson’s ratio

A

ν = −ε_t / ε_a

* Dimensionless, must be [+]!

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15
Q

Elastic & Rigid Moduli

A

E = 2G (1 + ν)

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16
Q

direction dependence

A

[polymers]
• along axis: 1 ° covalent bonds, mech prop’s similar to metals/ceramics
• else: 2 ° forces dominate, reduces mech prop’s

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17
Q

Plastic deformation

A

• Permanent, sample never completely returns to original shape
• Non-linear portion of stress/strain curve
* Does not follow Hooke’s law

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18
Q

Yield strength

A

“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
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19
Q

Yield point strain

A

“ε_yp” = strain at end of elastic region

* Draw 0.2% offset line (0.002) on x-axis, // to elastic portion

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20
Q

Ultimate Tensile Strength (UTS)

A

[crystalline e.g. metals/ceramics]
“σ_UTS” = necking of specimen
∴ no longer uniform strain across entire specimen, only defor. at necking area

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21
Q

Fracturing strength

A

“σ_f” = stress at fracture
* after onset of necking, ↓ stress to cause further plastic defor.
∴ σ_frac < σ_UTS

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22
Q

Ductility

A

Ability of material to deform plastically before breaking

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23
Q

Brittleness

A
  • Mat’ls w/ low ductility

* Fracture w/ little plastic deformation e.g. ceramics

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24
Q

% ELongation

A

% EL = (L_f − L_o) / L_o ∗100

where “o” = initial, “f” = fracture

25
% Area Reduction
% AR = (A_o − A_f) / A_o ∗100 | where "o" = initial, "f" = fracture
26
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 ↑
27
Elasticity
* Stretch bonds, return to normal length after load removed | * Char. only of \elastomers
28
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
29
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)
30
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
31
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 ↑
32
Processing polymers: Additives
* Smaller atom can sit in compressive region around edge defect and cancel lattice strain * Driving force ↓ ∴ slip ↓
33
strain rate
Faster, higher strain = less time to rearrange chains along axis of loading (in neck region) ∴ ↓ defor.
34
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
35
1 ° v. 2 ° bonds
1 ° = crosslinking (when broken → fracture) 2 ° = % X-talinity * also ↑ MW => ↓ chain sliding, ↑ σ_y, ↓ ductility
36
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)
37
Brittle fracture
* Little/no plastic deformation (less slip) | * Flat fracture surface (little warning)
38
Charpy and Izod impact tests
Measures impact energy and determines D2B transition temp. (when mat'l fractures brittle-y)
39
Polymer crazing
Network of fine cracks on surface (⊥ to tensile stress), but CAN support some load
40
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
41
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 ↓
42
Primary creep
↑ ε w.r.t time, while creep rate (slope) ↓ | * due to repositioning of defects e.g. dislocations
43
Secondary creep
• Linear relationship b/w creep & ε (typ. longest period) * SS creep rate (dε/dt = 0)
44
Tertiary creep
* Gross defects inside mat'l | * e.g. GB separ, cracks/voids → rapid elongation to mat'l failure
45
Molecular causes of creep: Metals
* GB sliding * Migration of vacancies (esp. at high Temp) → \stress-induced vacancy diffusion * \dislocation climb
46
Stress-induced vacancy diffusion
* Extra vacancies due to loading (⊥ to axis of loading) * Vacancies migrate // to axis of loading * Atoms move in opp. direction
47
Nabarro-Herring creep
Atomic diffusion opp. of \stress-induced vacancy diffusion → elongation of grain along axis of applied stress
48
Coble creep
Vacancies migrate along GB (than through bulk of grain)
49
Dislocation climb
Dislocation moves 1 atomic spacing by diffusion of entire row of vacancies to extra partial plane of edge dislocation
50
Molecular causes of creep: Ceramics
• GB sliding = main microstructural rearrangement | * More resistant to creep b/c electroneutrality
51
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
52
Stress relaxation
[polymers] ↓ stress over time under constant strain * Similar to creep, depends on % X-talinity and temp (above T_g)
53
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)
54
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
55
Corrosion fatigue
Failure due to cyclic stress + chem attack
56
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)
57
Methods to improve mech prop's: Additives
* [metals] \alloys: reduce lattice strain | * [polymers] \fillers: strength ↑ by acting as crosslinks
58
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) •

Biomaterials (6 decks)

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