MATSE 259 Exam 1 With Complete Solutions
Hooke's Law
σ = Eε
σ: engineering stress
ε: engineering strain
E: modulus of elasticity
Elastic Elongation and Strain
v = -εx/εz = -εy/εz
applied tensile stress, elastic elongation and accompanying strain
Tensile Strength
(MPa or psi)
-Stress at max of stress-strain curve
-Max stress that can be sustained by a structure in tension
Toughness
-Ability of material to absorb energy up to a fracture
-Area under stress-strain curve up to point of fracture
Ductility
degree of plastic deformation that is sustained at fracture
Ductile Material
experiences significant plastic defamation upon fracture
Brittle Material
experiences very little or no plastic deformation upon fracture
Percent Elongation
%EL = (lf-l0)/l0 * 100
(l0 is L nought)
l0: original gauge length
lf: fracture length
Percent Reduction in Area
%RA = (A0-Af)/A0 * 100
A0: original cross-sectional area
Af: cross-sectional area at fracture
True Stress
σ(subT) = F/Ai
, True Strain
ε(subT) = ln(li/l0)
Strain Hardening (concept)
Region from onset of plastic deformation up to necking
Strain Hardening (equation)
ε(subT) = K*ε(subT)^n
K: strength coefficient (stress when ε(subT)=1)
n: strain hardening component
Primary Interatomic Bonds
ionic
covalent
metallic
-all bonds involve valence electrons
-depend on electron structures of constituent atoms
-tendency of atoms to assume stable electron structures
Unit Cell
-basic unit or block of crystal structure
-chosen to represent symmetry
-all atom positions in the crystal may be generated by translations
Coordination Number
each atom has same number of nearest neighbor or touching atoms
Atomic Packing Factor
APF = (volume of atoms in unit cell)/(total unit cell volume)
FCC: 74%
BCC: 68%
HCP: 74%
Face Centered Cubic (FCC)
-each corner, center of all faces
-4 total atoms
Body Centered Cubic (BCC)
-each corner, one in center
-total of 2 atoms
APF for FCC
APF = 0.74
Hooke's Law
σ = Eε
σ: engineering stress
ε: engineering strain
E: modulus of elasticity
Elastic Elongation and Strain
v = -εx/εz = -εy/εz
applied tensile stress, elastic elongation and accompanying strain
Tensile Strength
(MPa or psi)
-Stress at max of stress-strain curve
-Max stress that can be sustained by a structure in tension
Toughness
-Ability of material to absorb energy up to a fracture
-Area under stress-strain curve up to point of fracture
Ductility
degree of plastic deformation that is sustained at fracture
Ductile Material
experiences significant plastic defamation upon fracture
Brittle Material
experiences very little or no plastic deformation upon fracture
Percent Elongation
%EL = (lf-l0)/l0 * 100
(l0 is L nought)
l0: original gauge length
lf: fracture length
Percent Reduction in Area
%RA = (A0-Af)/A0 * 100
A0: original cross-sectional area
Af: cross-sectional area at fracture
True Stress
σ(subT) = F/Ai
, True Strain
ε(subT) = ln(li/l0)
Strain Hardening (concept)
Region from onset of plastic deformation up to necking
Strain Hardening (equation)
ε(subT) = K*ε(subT)^n
K: strength coefficient (stress when ε(subT)=1)
n: strain hardening component
Primary Interatomic Bonds
ionic
covalent
metallic
-all bonds involve valence electrons
-depend on electron structures of constituent atoms
-tendency of atoms to assume stable electron structures
Unit Cell
-basic unit or block of crystal structure
-chosen to represent symmetry
-all atom positions in the crystal may be generated by translations
Coordination Number
each atom has same number of nearest neighbor or touching atoms
Atomic Packing Factor
APF = (volume of atoms in unit cell)/(total unit cell volume)
FCC: 74%
BCC: 68%
HCP: 74%
Face Centered Cubic (FCC)
-each corner, center of all faces
-4 total atoms
Body Centered Cubic (BCC)
-each corner, one in center
-total of 2 atoms
APF for FCC
APF = 0.74
