STRESS

What is solid deformation?

∙ Concept: internal resistance offered by a ‘unit area’ of a metal to an externally applied  load/force

o σ = F/A

∙ Types:

o normal (tensile and compression)

o shear (resistance force parallel to area)

o torsion (shear stress)

o bearing

o bending/flexure

∙ Inertia (I): resistance to bending geometry to area

∙ Bearing: a solid eventually deforming from its original shape  

o Example: a key is a sprocket and gear

∙ Stress results in  “strain”

o Visible deformations

o Physical and measurable

∙ Strain: ε = ẟ/L

How do you deform plastic?

∙ Deformation:

1. Elastic (reversible)

2. Plastic (permanent shape change)

∙ R. Hooke (1678)

o “ut tension” (as extension)

o “sic vis” (thus force)

∙ Dislocations: misregistry of the atoms

o When the atoms slip causing elongation

DESIGN PROPERTIES: Don't forget about the age old question of How does economic growth create employment?

∙ Linear elastic relationships:

o E= σ/ε  

A. Proportional limit We also discuss several other topics like What are the two types of compounds?

B. Elastic limit (not going back strain-wise)

C. Yield point (yield strength):

o Value of stress where significantly (noticeable) strain with little or no increase in  stress

What material property does an item require if it needs to withstand high pulling forces?

o Aluminum does not have a well-defined yield point

o 2% offset line for the not well-defined metals

***BE ABLE TO CALCULATE VALUES FOR EXAM***

I.) Strength

o Tensile strength (ultimate test or strength): represents highest value of stress on the stress- strain diagram

II.) Stiffness

o Property that enables a metal to withstand high stress without great strain o Resistance to any sort of deformation  

o Modulus of elasticity: measure of metals stiffness (the bigger the better) III.) Ductility (tensile load/forces)

o Property of a metal enabling it to undergo considerable “plastic deformation” under  a tensile load before actual rupture

o Characterized by percent elongation:

 (final length-gauge length/gauge length) *100

 Considered ductile if % elongation > 5%

 High % elongation indicates a highly ductile metal

o Poisson’s Ratio (µ)

 η= εx/εa ; x=cross-sectional area, a=elongation  If you want to learn more check out What is the selective permeability of the membrane?

 for metals typically between 0.25-0.35

IV.) Toughness (shock/impact loads)

o Ability of a metal to deform plastically and absorb ‘energy’ prior to fracture o Units are energy based ft-lb/in If you want to learn more check out What did ernest rutherford discover in 1899?

o Good toughness is a combination of strength and ductility

o Measured by total area taken under the stress-strain diagram

o Testing method: Charpy-Izod Test

o Temperature: variable that has a profound influence on a metal’s toughness V.) Hardness  

o The resistance of a metal to localized plastic (permanent) deformation (indentation) o Shows a metals resistance to wear and cracking in compression

o A materials hardness is an indicator of a metals strength  

o Hardness tests are non-destructive and most widely used

o Rockwell Hardness Test: tests wearibility, strength, ductility, and machine ability   Has a scale ranging from softest to hardest

 Measured on HRC (Hardness Rockwell scale)

STRENGTHENING MECHANISMS:

∙ Basic mechanisms for strengthening  If you want to learn more check out What is the means by which a sender transmits a message?

 1. Grain size reduction: 

o Grain boundaries act as barriers as dislocation motion

o Grain size greatly influences mechanical properties and can be regulated/controlled  by: Don't forget about the age old question of What is intentional discrimination?

 rate of solidification

 plastic deformation followed by some heat treatment method

 size reduction improves both a metals strength and toughness  2. Solid solution alloying: 

o Involves alloying of metals with “impurity atoms” (substitutional and interstitial) o Impurity atoms create “lattice strains”

 3. Strain hardening (cold working): 

o the degree of the plastic deformation is expressed as a % cold worked o Hardnessbrittleness ex. Stainless steel (if not worked correctly) o Cold working (strain hardening) BENEFITS:

 Surface finish

 Better dimensional accuracy and tolerancing

 Increase in strength and hardness  

∙ Heat Treating

1. Hardening

2. Softening “Annealing”

o Annealing: restores the pre-cold worked conditions/properties of a metal o Steps of Annealing 

1. Recovery:

 Results in the removal of residuals internal stresses  

 Requires an increase in temperature (just below recrystallization  

temperature)

Example: steel 1000-1300 F

  Thermal energy: removes atoms and gets lattice to gain normalcy  

2. Recrystallization (Post recovery)

 The formation of new set of grains (strain-free) equiaxed (same size  

generally) and low dislocation density

3. Grain growth  

 Two critical factors:  

o Temperature

o Time: more time the greater the grain size

o benefits ductility, malleability, bending

∙ example: hydraulic cylinders are cold worked DOM (drawn over mandrel)  MECHANICAL FAILURES

∙ A FAILURE IS NOT A FRACTURE!!!

∙ Types of failures: wear/erosion, corrosion, distortion

∙ Most common failures:

o Improper material selection

o Improper material process

o Inadequate component design

o Component misuse

∙ Fracture modes:

 o Brittle unstable  

 speed is very rapid with very little (if any) advancing plastic deformation  occurring suddenly catastrophically without any warning

  types:

I. transgranular: crack passes through grain boundaries

II. intergranular: crack follows the grain boundaries  

 o Ductile (what we want to happen)

 gives warnings with advancing elastic/plastic deformations occurring

  sequence: 

I. necking occurs

II. micro voids (internal voids)coalescence

III. fracture occurs  

results in a “cup and cone” feature  

∙ stress concentrations (raisers)

o not as strong predicted by theory

o voids and impurities (inclusions) microscopic flaws  

o avoid 90 degree angles in design

FATIGUE:

∙ the application of a force on a flaw that forms a crack that spreads under repeated stress  ∙ represents failure under cyclic stresses:

o axial (tension/compression)

o flexural (bending)

o torsional (twisting)

o thermal stresses  

∙ is the cause for approximately 90% of all mechanical element failures   ∙     Fatigue life: total number of stress cycles that will cause a fatigue failure at some specified stress amplitude

 ∙     Fatigue strength: maximum stress level that a metal can sustain without failing for some  specified number of cycles

∙    Example: a small area of material subjected to flexural stress

o Help offset crack initiation  

o (shot) “peening”: place compressive stresses at the surface so they’re will not be a  tear  

o Cracks will not grow within compressive environment

o OR a smooth polished finish (avoid surface scratches and sharp fillets)  ∙     Thermal fatigue: component subjected to high/low operating temperatures on a cyclical  basis

o σ thermal= ΔT*E*αL