Chapter 4

%EL or % Elongation

%Elongation = (length at fracture - original length) / original length; measure of DUCTILITY

What does a fatigue limit imply?

A material will not fracture under a certain load, regardless of the number of cycles experienced, thus Its S vs N graph is a monotonic descend which approaches an asymptotic constant S with increasing N; below a certain stress level, fatigue failure will not occur

What does a fatigue strength/stress imply?

A material will not have a clear fatigue limit, but instead the curve continues downward with decreasing values of applied stress, so there is no stress level under which fatigue failure will not occur

What does a spring model?

A spring models Hooke's law to explain the elastic component of the response of creep and stress relaxation

Toughness

CALUCLATED BY AREA UNDER STRESS VS STRAIN CURVE; how much energy a material can absorb before it breaks; integral of sigma*depsilon from 0 to epsilonf

Young's Modulus or modulus of elasticity

E=sigma/epsilon or E=stress/strain (MPa)

S vs N plots

S = stress amplitude or difference between maximum and minimum applied stress divided by 2 (S=(sigma max - sigma min)/2); N = number of cycles to failure

shear stress

Tao; parallel force/area of applied force

Maxwell Model

The Maxwell model proposes a spring and dashpot in series; when a stress (sigma) is applied, the resulting strain (epsilon) in the system is the addition of the strain in each of the components --> the stresses are equal. This model has minimal predictive value for creep conditions; it is appropriate for stress relaxation predictions

Voigt Model

The Voigt model proposes a spring and dashpot in parallel --> the strains (epsilon) are equal between the elements but the stresses (sigma) are additive; This model is appropriate for creep experiments; it is not appropriate for stress relaxation conditions

why is it difficult for ceramic materials to deform plastically?

The number of possible slip planes in ceramics is limited by requirements of electroneutrality: so ceramic materials are generally brittle

Elastic deformation

The sample returns to its original shape after release of the load: sigma=E*epsilon ; linear region

Fatigue limit or endurance limit

The stress amplitude value at which the S-N graph goes from monotonic decay to horrizontal

What does a dashpot model?

The viscous portion of the creep and stress relaxation response is modeled by a dashpot

What materials typically do/do not have a yield strength?

ceramics and polymers typically do not possess a yield strength, while metals do

relative tensile strengths

ceramics can have medium-high tensile strengths, metal tensile strengths are generally higher than polymer tensile strengths

Relative elongation to failures for materials

ceramics: 0% elongation; metals and polymers can have moderate to high elongation to failures

stress relaxation test

constant strain is maintained --> d(epsilon)/dt=0

Why are polycrystalline materials usually stronger than their equivalent single-crystal materials?

constraints imposed by neighboring grains do not allow for enough slipping of each grain; thus polycrystalline materials generally have higher yield strengths: i.e. the presence of grain boundaries hinders overall slip in the material

yield strength

draw a line parallel to the elastic portion at a .002 offset and where this line connects with the curve is the yield point (stress at stain = .002) BEGINNING OF PLASTIC DEFORMATION

elastic deformation

elastic materials allow large recoverable strains at low stress --> amorphous region can be stretched out and returned to normal once force is no longer applied ; E=sigma/epsilon=stress/strain ELASTIC DEFORMATION IS NOT PERMANENT

what is an elastomer?

elastomers are amorphous materials in their unstressed state, composed of coiled chains with nearly free bond rotations around the backbone; the chains are crosslinked at given points to prevent chains from slipping past each other (preventing plastic deformation)

fracture stress/strain

end of stress vs strain curve (subscript f)

creep test

exert a constant load on the specimen while maintaining the system at a fixed temperature --> resulting strain is recorded as a function of time: d(sigma)/dt=0

viscoelastic

exhibiting both viscous and elastic properties: between Tg and Tm, polymeric materials are viscoelastic; a viscoelastic material is a material for which the relationship between stress and strain depends on time; real materials exhibit a viscoelastic response

fatigue fracture

failure at stresses significantly less than the tensile or yield strength due to repeated loading (the material has been subjected to many cycles of altering stress or strain); characterized as brittle

Do all metals experience fatigue fracture?

for some metals, including certain titanium alloys, below a certain stress level fatigue failure will not occur, regardless of the number of cycles the sample experiences --> instead we see just monotonic decay for S vs N graphs and we look at the fatigue strength at Ni cycles

engineering stress

from measured load (sigma); engineering stress = perpendicular applied force/cross sectional area; units are pascals

engineering strain

from measured specimen elongation (epsilon); engineering strain = ( sample length after desired tensile test time - original sample length) / (original sample length); basically dL/L0; dimensionless

ultimate tensile strength/stress (UTS)

highest point on stress vs strain curve; stress subscript UTS; highest stress material can undergo

Describe fatigue testing

in fatigue testing, specimens are exposed to cycles of stress at relatively high stress values (usually 2/3 of the static tensile strength), and the number of cycles to failure are observed; other specimens are subjected to lower levels of stress and the corresponding number of cycles is recorded for each set of samples --> allows generation of stress (S) vs number of cycles to failure (N) plots

How does a biomaterial's flaws contribute to fatigue fracture?

increased stress resulting from flaws in a biomaterial can act to nucleate cracks, which eventually results in fatigue fracture; the maximum stress generally occurs at the surface of a component, thus impurities in the surface region can also reduce fatigue life

describe the general cause of plastic deformation for semi-crystalline polymers

interactions between the lamellar and amorphous regions in response to a tensile force: overall significant chain orientation in semicrystalline polymers (as seen in necking phenomenon); any changes that inhibit chain motion within these polymers increase the observed strength and decrease the ductility (increase polymer MW, crystallinity, or crosslinking the polymer)

fatigue strength

many alloys containing metals such as aluminum do not demonstrate a clear fatigue limit, but the curve continues downward with decreasing values of applied stress --> characterized by fatigue strength which is the stress level that will cause failure after a given number of cycles

brittle materials

materials with low ductility: material will fracture with very little plastic deformation/no plastic deformation (most ceramics; lower area under stress vs strain curve = more brittle

Molecular causes of plastic deformation: metals

metals undergo plastic deformation due to dislocation glide along a plane called the slip plane : crystalline and lamellar region slide past each other --> breaking of secondary bonds

necking

occurs between the ultimate tensile strength and fracture

plastic deformation

permanent deformation from which the sample cannot return to its original shape following loading. occurs between the yield point and the ultimate tensile strength; stress @ strain = .0002 (.2%offset) for yield strength. PLASTIC DEFORMATION IS PERMANENT and really only for metals**

Creep

plastic deformation of a sample under constant load over time; for ceramics its only of concern at temperatures over .4Tm; for polymers it can occur at or around RT

How does fatigue fracture work?

repeated stress increases the number of dislocations and creates more and more imperfections in the crystal structure

shear strain

shear force causes deformation: gamma; tan(theta)

what causes elastic deformation?

slight changes in atomic spacing and stretching of bonds causes elastic deformation: the stiffness of a material directly reflects the amount of energy required to move atoms in a material from their equilibrium positions (ceramics are stiffer than metals) --> the stiffness of polymers is typically directionally dependent

Hooke's law

stress and strain are proportional to each other at all values; sigma=E*epsilon

ductility

the ability of a material to deform plastically before breaking; can be qualified by area under stress vs strain curve: greater area=more ductile; CALCULATED AS %EL (% elongation) --> whichever material has the greatest failure strain (i.e. extends furthest to right on stress vs strain curve)

Fatigue life (Nf)

the number of cycles required to cause fatigue fracture at a specified stress; Nf=Ni + Np ; Ni is the number of cycles required for crack initiation and Np is the number of cycles needed for propagation to the critical size for failure

what's unique about elastomers?

they allow large elastic deformation at low stresses due to their distinctive chain structure