11 Pages

Materials Science & Engineering
Course Code
Scott Ramsay

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Deformation  and  Strengthening  Mechanisms     Dislocations     -­‐slip:  process  which  plastic  deformation  is  produced  by  dislocation  motion     -­‐slip  plane:  crystallographic  pane  along  which  dislocation  line  traverses     -­‐dislocation  motion  is  analogous  to  motion  of  a  caterpillar     -­‐dislocation  density:  number  of  dislocations  that  intersect  a  unit  area  of  a  random   section  or  total  dislocation  length  per  unit  volume       Characteristics  of  Dislocations     -­‐when  metals  are  plastically  deformed,  approximately  5%  of  deformation  energy  is   retained  internally,  remainder  dissipated  as  heat     -­‐major  portion  of  this  stored  energy  is  strain  energy  associated  with  dislocations     -­‐there  are  regions  in  which  compressive,  tensile  and  shear  lattice  strains  are   imposed  on  neighboring  atoms  (ex.  Atoms  immediately  above  and  adjacent  to   dislocation  line  are  squeezed  together)     -­‐atoms  may  be  thought  of  as  experiencing  a  compressive  strain  relative  to  atoms   positioned  in  perfect  crystal  and  far  removed  from  dislocation     -­‐shear  strains  also  exist  in  vicinity  of  edge  dislocation     -­‐for  a  screw  dislocation,  lattice  strains  are  pure  shear  only     -­‐lattice  distortions  may  be  considered  to  be  strain  fields  that  radiate  from   dislocation  line     -­‐strains  extend  to  surrounding  atoms  and  magnitude  decreases  with  radial  distance   from  the  dislocation     -­‐strain  fields  surrounding  dislocations  in  close  proximity  may  interact  in  such  a  way   that  forces  are  imposed  on  each  dislocation  by  combined  interactions  of  all   neighboring  dislocations     -­‐Example:  consider  two  edge  dislocations  that  have  the  same  sign  and  identical  slip   plane.  Compressive  and  tensile  strain  fields  for  both  lie  on  same  side  of  slip  plane;   strain  field  interaction  is  such  that  there  exists  between  these  two  isolated   dislocations  a  mutual  repulsive  force  that  tends  to  move  them  apart     -­‐two  dislocations  of  opposite  sign  and  having  same  slip  plane  will  be  attracted  to   one  another       Slip  Systems     -­‐slip  plane:  preferred  plane  which  dislocation  motion  occurs     -­‐plane  with  greatest  planar  density     -­‐slip  direction:  direction  of  movement   -­‐direction  with  highest  linear  density     -­‐combination  of  slip  plane  and  direction  is  called  slip  system     -­‐depends  on  crystal  structure  of  metal  and  is  such  that  atomic  distortion  that   accompanies  motion  of  dislocation  is  minimum           Possible  slip  systems  for  BCC  and  HCP  crystal  structures:       Burgers  vector  for  FCC,  BCC,  HCP:     𝑎 𝑏 𝐹𝐶𝐶 =   < 1102>   𝑎 𝑏 𝐵𝐶𝐶 =   < 1112>   𝑎 𝑏 𝐻𝐶𝑃 =   < 1120 >   3   Slip  in  Single  Crystals     -­‐resolved  shear  stresses:  shear  components  exist   at  all  but  parallel  or  perpendicular  alignments  to   stress  direction   -­‐magnitudes  depend  not  only  on  applied  stress  but   also  orientation  of  both  slip  plane  and  direction   within  plane     -­‐let  ϕ  be  the  angle  between  normal  to  slip  plane   and  λ  the  angle  between  slip  and  stress  directions   𝜏▯= 𝜎cos𝜙cos𝜆   -­‐slip  begins  on  most  favourably  oriented  slip   system  when  resolved  shear  stress  reaches  critical   resolved  shear  stress  (CRSS)   -­‐represents  minimum  shear  stress  required  to   initiate  slip     -­‐determines  when  yielding  occurs     -­‐magnitude  of  applied  stress  required  for  yielding:     𝜏 𝜎 ▯ ▯▯▯▯   (cos𝜙cos𝜆  ) ▯▯▯ -­‐minimum  stress  required  to  introduce  yielding   occurs  when  a  single  crystal  is  oriented  such  that   ϕ  =  λ  =  45  degrees     -­‐under  these  conditions: y   CRSS       Plastic  Deformation  for  Polycrystalline  Metals     -­‐due  to  random  crystallographic  orientations  of  numerous  grains,  direction  of  slip   varies  from  one  grain  to  another     -­‐gross  plastic  deformation  of  a  polycrystalline  specimen  corresponds  to  comparable   distortion  of  individual  grains  by  means  of  slip     -­‐polycrystalline  metals  are  stronger  than  their  single  crystal  equivalents   -­‐greater  stresses  required  to  initiate  slip     -­‐even  though  a  single  grain  may  be  favourably  oriented  with  applied  stress,  cannot   deform  until  adjacent  and  less  favourable  oriented  grains  are  capable  of  slip  also       Deformation  by  Twinning     -­‐plastic  deformation  in  some  metallic  materials  can  occur  by  formation  of   mechanical  twins     -­‐displacement  magnitude  within  twin  region  is  proportional  to  distance  from  twin   plane     -­‐twinning  occurs  on  a  definite  crystallographic  plane  and  in  specific  direction   dependent  on  crystal  structure     -­‐for  slip:  crystallographic  orientation  above  and  below  the  slip  plane  is  same  both   before  and  after  deformation     -­‐occurs  in  distinct  atomic  spacing  multiples     -­‐for  twinning:  reorientation  across  twin  plane     -­‐atomic  displacement  less  than  interatomic  separation     -­‐mechanical  twinning  occurs  in  metals  that  have  BCC  and  HCP  crystal  structures  at   low  temperatures     -­‐twinning  may  place  new  slip  systems  in  orientations  that  are  favourable  relative  to   stress  axis  so  that  the  slip  process  can  now  take  place         Grain  Size  Reduction     -­‐slip  or  dislocation  motion  takes  place  across  common  grain  boundary     -­‐since  two  grains  are  of  different  orientations,  dislocation  passing  from  grain  A  to   grain  B  will  have  to  change  direction  of  motion     -­‐atomic  disorder  within  a  grain  boundary  will  result  in  a  discontinuity  of  slip  planes   from  one  grain  to  another     -­‐for  high  angle  grain  boundaries,  dislocations  tend  to  back  up  at  grain  boundaries     -­‐these  back  ups  introduce  stress  concentrators  ahead  of  their  slip  planes  and   generate  new  dislocations  in  adjacent  grains     -­‐fine  grained  material  is  harder  and  stronger  than  one  that  is  coarse  grained     -­‐yield  strength  varies  with  grain  size  according  to  Hall  Petch  equation:     ▯▯/▯ 𝜎 ▯ 𝜎 +  𝑘 ▯ ▯   where:     d  –  average  grain  diameter  and  σ andy   are y  h  constants  for  particular  material       -­‐grain  size  may  be  regulated  by  rate  of  solidification  from  liquid  phase  and  by  plastic   deformation  followed  by  an  appropriate  heat  treatment     -­‐grain  size  reduction  improves  not  only  strength  but  also  toughness  of  many  alloys     -­‐small  angle  grain  boundaries  are  not  effective  in  interfering  with  slip  process   -­‐twin  boundaries  will  effectively  block  slip  and  increase  strength  of  material       Solid  Solution  Strengthening     -­‐another  technique  is  alloying  with  impurity  atoms  that  go  into  either  substitutional   or  interstitial  solid  solution     -­‐high  purity  metals  are  almost  always  softer  and  weaker  than  alloys  composed  of   same  base  metal   -­‐increasing  the  concentration  of  impurity  results  in  an  attendant  increase  in  tensile   and  yield  strengths     -­‐alloys  are  stronger  than  pure  metals  because  impurity  atoms  that  go  into  solid   solution  ordinarily  impose  lattice  strains  on  the  surrounding  host  atoms     -­‐lattice  field  interactions  between  dislocations  and  impurity  atoms  result  in   restricted  dislocation  motion     -­‐example:  impurity  atom  that  is  smaller  than  host  atom  for  which  it  substitutes   exerts  tensile  strains  on  surrounding  crystal  lattice     -­‐conversely  a  larger  substitutional  atom  imposes  compressive  strains  in  vicinity     -­‐solute  atoms  tend  to  diffuse  to  and  segregate  around  dislocations  in  a  away  to   reduce  overall  strain  energy     -­‐smaller  impurity  atom  is  located  where  tensile  strain  will  partially  nullify  some  of   dislocation’s  compressive  strain     -­‐resistance  to  slip  is  greater  when  impurity  atoms  are  present  because  overall   lattice  strain  must  increase  if  a  dislocation  is  torn  away  from  them     -­‐same  lattice  strain  interactions  will  exist  between  impurity  atoms  and  dislocations   that  are  in  motion  during  plastic  deformation     -­‐greater  applied  stress  is  necessary  to  first  initiate  and  continue  plastic  deformation   for  solid  solution  alloys       Strain  Hardening     -­‐ductile  metal  becomes  harder  and  stronger  as  it  is  plastically  deformed     -­‐temperature  at  which  deformation  takes  place  is  cold  relative  to  absolute  melting   temperature  of  metal  (cold  working)     -­‐most  metals  strain  harden  at  room  temperature     -­‐sometimes  convenient  to  express  degree  of  plastic  deformation  as  percent  cold   work:     𝐴 ▯ 𝐴 ▯ %𝐶𝑊 =  ×  100   𝐴 ▯ where:     A 0  is  the  original  area dand  A  is  the  area  after  deformation       -­‐ductility  experiences  reduction  with  increasing  %CW   -­‐strain  hardening  phenomenon  is  explained  on  basis  of  dislocation-­‐dislocation   strain  field  interactions     -­‐dislocation  density  in  a  metal  increases  with  deformation  or  cold  work,  due  to   dislocation  multiplication  of  formation  of  new  dislocations     -­‐average  distance  of  separation  between  dislocations  decreases     -­‐on  average,  dislocation-­‐dislocation  strain  interactions  are  repulsive     -­‐net  result  is  that  motion  of  dislocation  is  hindered  by  presence  of  other  dislocations     -­‐as  dislocation  density  increases,  resistance  to  dislocation  motion  by  other   dislocations  becomes  more  pronounced     -­‐therefore,  imposed  stress  necessary  to  deform  metal  increases  with  increasing  CW       Crystalline  Ceramics     -­‐hard  and  brittle  materials  due  to  difficulty  of  slip     -­‐for  crystalline  ceramic  materials  for  which  bonding  is  predominantly  ionic,  there   are  very  few  slip  systems  along  which  dislocations  may  move     -­‐consequence  of  electrically  charged  nature  of  ions     -­‐ions  of  like  charge  are  brought  into  close  proximity  to  one  another  because  of   electrostatic  repulsion     -­‐ceramics  where  bonding  is  highly  covalent,  slip  is  also  difficult  and  materials  are   brittle  because  covalent  bonds  are  strong,  limited  number  of  slip  systems  and   dislocation  structures  are  complex       Noncrystalline  Ceramics     -­‐does  not  occur  by  dislocation  motion  because  there  is  no  regular  atomic  structure     -­‐metals  deform  by  viscous  low,  same  manner  in  which  liquids  deform     -­‐rate  of  deformation  is  proportional  to  applied  stress
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