mechanical properties

Question 1

engineering/normal stress

Answer 1

force/area =F/A = sigma

Question 2

engineering/normal strain

Answer 2

change in length/ original length =l-lo/lo= epsilon

Question 3

young’s modulus

Answer 3

E= stress/strain

Question 4

hookes law

Answer 4

stress=E*strain

Question 5

typical E for metals

Answer 5

~70Gpa-200GPa

Question 6

typical E for ceramics and glass

Answer 6

~70Gpa -400GPa

Question 7

typical E for polymers

Answer 7

~0.5-8Gpa

Question 8

typical E for diamonds

Answer 8

~1150GPa

Question 9

Poisson’s ratio

Answer 9

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

Question 10

typical v for metals

Answer 10

~0.3-0.35 (1/3 assumed)

Question 11

typical v for ceramics and glass

Answer 11

0.15-0.3

Question 12

typical v for rubber

Answer 12

~0.5 in compressible

Question 13

typical v for cork

Answer 13

0

Question 14

Shear stress

Answer 14

F/A = tau

Question 15

shear strain

Answer 15

gamma = radians of movement

Question 16

shear modulus

Answer 16

G= tau/gamma

Shear stress/shear strain

Question 17

volume-metric strain

Answer 17

change in vol/ og vol

Question 18

bulk modulus

Answer 18

pressure/ vol strain

B= - P/(deltaV/V)

Question 19

3 normal stresses

Answer 19

sigma 11 , sigma 22, sigma 33

Question 20

3 shear stresses

Answer 20

sigma 12, sigma 13, sigmas 23

Question 21

equal stresses

Answer 21

sigma 21=12
31=13
23-32

Question 22

moduli

Answer 22

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

Question 23

isotropic materials - mechanical properties

Answer 23

uniform in all directions eg glass

only need 2 moduli to relate stress to strain

Question 24

equi fro stress 11

Answer 24

stress11= 1/E [strain11-v(strain22+strain33) ]

same for other numbers

Question 25

equi for shear stress 12

Answer 25

stress12 = strain 12/ G same for other numbers

Question 26

equis relating G B E and V

Answer 26

G=E/(2(1+v)) B=E/(3(1-2v))

Question 27

equi for true stress

Answer 27

true stress =ln(1+strain) only until necking happens true stress = (1+strain)stress

Question 28

power law hardening

Answer 28

true stress = K true strain^n

Question 29

uniform true strain

Answer 29

epsilon u= n

Question 30

ultimate tensile strength

Answer 30

stress u = stress t /exp(strain t) = (Kn^n)/exp(n)

Question 31

tensor form uniaxial stress

Answer 31

stress 0 0 0 0 0 0 0 0

Question 32

tensor form hydrostatic pressure

Answer 32

-p 0 0 0 -p 0 0 0 -p

Question 33

tensor form biaxial stress

Answer 33

stress 1 0 0 0 stress2 0 0 0 0

Question 34

tensor form pure shear

Answer 34

0 stress12 0 stress12 0 0 0 0 0

Question 35

tensor form plane stress

Answer 35

stress11 stress12 0 stress12 stress22 0 0 0 0

Question 36

conventions for stress analysis

Answer 36

normal stress tension is +ve | shear stress clockwise is +ve

Question 37

assumptions for stress analysis

Answer 37

``` stresses are -in equilibrium -static materials are -isotropic -linear elastic deflections are small ```

Question 38

angled plane - forces and area

Answer 38

normal force =Fcos a shear force = Fsin a Area = A/cos a

Question 39

angled normal stress

Answer 39

stress n =Fcos a/(A/cos a) = stress*cos a^2

Question 40

angled shear stress

Answer 40

stress s = Fsin a /(A/cosa)= stress* sin a* cos a

Question 41

von mises yield criterion

Answer 41

maximum sistortion energy (stress1-stress2)^2 +(stress3-stress1)^2 +(stress2-stress3)^2 =2stressys^2 stress1^2 + stress3^2 -stress1stress3 =stressys^2

Question 42

tresca yield criterion

Answer 42

stressys= stress1 - stress3 max shear stress stressxymax = (stress1-stress3)/2