Quiz 8 Chap 6

Deformation when loaded, return to original shape when loading removed. what is this

elastic

deformation when loaded, some permanent shape change occurs

Plastic

WHat does this mean: crack growth when loaded - separation into two pieces

Failure - Chapter 8

Viscoelastic

deformation under load, but deformation is time dependent in addition to load dependent, return to original shape over time

Elastic vs Plastic Deformation

• Elastic is temporary and reversible

• Plastic is permanent and irreversible

Simple tension cable

• Force applied perpendicular to and away from area of interest

• By convention, tensile stress is positive

Simple compression

• force applied perpendicular to and toward area of interest

• compressive stress is negative

Shear

force applied parallel to area of interest

Shear is the mechanism for

plastic deformation

Tensile, ε_z, vs Lateral strain, ε_x

Tensile strain refers to the stretching along the direction of the force, while lateral strain refers to the simultaneous thinning (or thickening) of the material's cross-section.

• Lateral strain is negative while tensile strain is positive

Force vs elongation graph

Depends on specimen size - not useful for comparison

Elastic deformation

nonpermanent and reversible deformation

explain (linear-elastic)

• force on an elastic object is directly proportional to the change in length of the object

• slope = stiffness (constant)

Explain the green (nonlinear-elastic)

• Still elastic, but Force is not proportional to change in length of the object

• stiffness is changing (slope not constant)

Modulus of Elasticity, E AKA Young’s Modulus

measures stiffness

• higher E = stiffer material

Elastic Modulus depends on

interatomic bonding forces

• strongly bonded = larger E

• weakly bonded = smaller E

Elastic modulus is proportional to

the slope of the the interatomic force-interatomic separation curve (dF/dr)_r0

Poisson’s ratio

ratio of lateral strain to tensile stain

• negative because material gets thinner when stretched

Axial strain def

stain along the loading direction

lateral/transverse strain def

strain perpendicular to the axial direction

Resilience

• ability of a material to absorb energy during elastic deformation (defined by yield point)

• energy recovered when load released

• resilience specified by modulus of resilience, U_r

Modulus of Resilience, U_r approx by

Area under stress-strain curve to yielding

Plastic deformation

permanent and irreversible deformation

explain

• graph starts linear - elastic region

• graph starts to curve - plastic deformation begins

• the slanted line at the end is the elastic deformation returning back to its original state.

• Ends with the permanent deformation

Transition from elastic to plastic deformation is

gradual (lnear line starts to curve more and more)

Yield Strength, σ_y

stress at which noticeable plastic deformation has occurred

plastic strain, ε_p

portion of strain that is permanent (non-recoverable)

standard plastic strain value when a material doesn’t have a clear yield point (noticable plastic deformation)

ε_p = 0.002

Metals/Alloys in Yield strength graph

• wide range

• easy to measure

Ceramics/graphite/semiconductors in Yield strength graph

• hard to measure

• since in tension, fracture occurs before yielding (brittle)

Polymers in Yield strength graph

• Much lower range

• softer, more deformable

Composites/fibers in Yield strength graph

• hard to measure

• failure happens differently (matrix cracking, fiber break), fracture usually occurs before yield

Yield strength is mainly meaningful for ___ and not meaningful for ____

• ductile materials (metals)

• brittle materials (ceramics/composites)

Poisson’s ratio can be used to calculate the transverse deformation in the

elastic region

Tensile Strength (TS)

max stress on engineering stress-strain curve

For metals, the maximum on the stress-strain curve (TS) appears at

the onset of noticeable necking

Neck/necking def

• localized increase in stress

• leads to fracture at the neck

After necking begins:

• area decreases rapidly in one spot

• load capacity drops, engineering stress decreases

Explain

1. Load - material goes elastic, then plastic to point D

2. Unload - path is linear (elastic slope), and only elastic strain is recovered. The remaining strain is plastic

3. Reapply load - Follows same linear line back up, no new plastic deformation until reaching higher stress

explain

strain increases to a larger value → after unloading it drops partially, but not to 0.

• the remaining strain is the permanent plastic strain, ε_p

ductility def

amount of plastic deformation at failure

2 types of ductility

• % elongation

• % reduction in area

explain

• Little Plastic deformation → short curve → small % elongation

• Significant plastic deformation → long curve → large % elongation

Toughness def

amount of energy absorbed before fracture

approximation of toughness

approximate by area under stress strain curve with units energy per unit volume

what materials are associated with +small toughness

ceramics

large toughness are common in what kindve materials

metals

what material is associated w/ very small toughness

reinforced polymers

brittle fracture is associated with

small toughness

ductile fracture means

large toughness

Engineering stress vs true stress

• engineering stress uses original area A₀

• True stress uses current area A_i

Engineering strain vs true strain

• Engineering strain uses total change relative to original length

• true strain accumulates incremental strain using a log expression

True vs engineering line on stress-strain

• Before necking - curves are close

• after necking - engineering curve drops, true curve increases