mechanical properties Flashcards
engineering/normal stress
force/area =F/A = sigma
engineering/normal strain
change in length/ original length =l-lo/lo= epsilon
young’s modulus
E= stress/strain
hookes law
stress=E*strain
typical E for metals
~70Gpa-200GPa
typical E for ceramics and glass
~70Gpa -400GPa
typical E for polymers
~0.5-8Gpa
typical E for diamonds
~1150GPa
Poisson’s ratio
measure of contraction perpendicular to applied stress
as component gets longer it gets thinner
Ratio=fractional lateral contraction/fractional longitudinal extension
v= - transverse change/ longitudinal change
typical v for metals
~0.3-0.35 (1/3 assumed)
typical v for ceramics and glass
0.15-0.3
typical v for rubber
~0.5 in compressible
typical v for cork
0
Shear stress
F/A = tau
shear strain
gamma = radians of movement
shear modulus
G= tau/gamma
Shear stress/shear strain
volume-metric strain
change in vol/ og vol
bulk modulus
pressure/ vol strain
B= - P/(deltaV/V)
3 normal stresses
sigma 11 , sigma 22, sigma 33
3 shear stresses
sigma 12, sigma 13, sigmas 23
equal stresses
sigma 21=12
31=13
23-32
moduli
6 indie components of stress at a point
6 indie components of strain at a point
6x6=36 moduli to related stress to strain
but with symmetry there is 21 moduli to relate stress to strain
isotropic materials - mechanical properties
uniform in all directions eg glass
only need 2 moduli to relate stress to strain
equi fro stress 11
stress11= 1/E [strain11-v(strain22+strain33) ]
same for other numbers
equi for shear stress 12
stress12 = strain 12/ G
same for other numbers
equis relating G B E and V
G=E/(2(1+v))
B=E/(3(1-2v))
equi for true stress
true stress =ln(1+strain) only until necking happens
true stress = (1+strain)stress
power law hardening
true stress = K true strain^n
uniform true strain
epsilon u= n
ultimate tensile strength
stress u = stress t /exp(strain t) = (Kn^n)/exp(n)
tensor form uniaxial stress
stress 0 0
0 0 0
0 0 0
tensor form hydrostatic pressure
-p 0 0
0 -p 0
0 0 -p
tensor form biaxial stress
stress 1 0 0
0 stress2 0
0 0 0
tensor form pure shear
0 stress12 0
stress12 0 0
0 0 0
tensor form plane stress
stress11 stress12 0
stress12 stress22 0
0 0 0
conventions for stress analysis
normal stress tension is +ve
shear stress clockwise is +ve
assumptions for stress analysis
stresses are -in equilibrium -static materials are -isotropic -linear elastic deflections are small
angled plane - forces and area
normal force =Fcos a
shear force = Fsin a
Area = A/cos a
angled normal stress
stress n =Fcos a/(A/cos a) = stress*cos a^2
angled shear stress
stress s = Fsin a /(A/cosa)= stress* sin a* cos a
von mises yield criterion
maximum sistortion energy
(stress1-stress2)^2 +(stress3-stress1)^2 +(stress2-stress3)^2 =2stressys^2
stress1^2 + stress3^2 -stress1stress3 =stressys^2
tresca yield criterion
stressys= stress1 - stress3
max shear stress
stressxymax = (stress1-stress3)/2
