Stress, Strain and Moduli Flashcards
How many independent components of stress are required to describe the state of stress at a point?
6
Polymers have larger Young’s moduli than metals
FALSE
How many independent moduli are required to characterise an isotropic material?
2
Note that although 4 moduli (Young’s modulus, shear modulus, bulk modulus and Poissons ratio) are commonly reported once you know 2 of any these for an isotropic material you can calculate any of the others
The stiffnesses of Al and ordinary window glass are about the same
TRUE
How many independent elastic moduli are required to characterise a unidirectional continuous fibre composite?
5
Poisson’s ratio of a typical metal is
1/3
Shear stress causes changes in volume
FALSE
soda-lime-silica glass has a shear modulus of 29 GPa and a Poisson’s ratio of 0.22. The values of its shear modulus and bulk modulus respectively are:
29 GPa and 42 GPa
For a typical metal the Young’s modulus and the bulk modulus have approximately the same value.
TRUE
What are the typical values for the shear modulus of metals?
G ~ 25GPa - 80GPa
What are the typical values for the shear modulus of ceramics and glasses?
G ~ 30GPa - 125GPa
What are the typical values for the shear modulus of polymers?
G ~ 0.02 - 3GPa
What are the typical values for the shear modulus of Diamond?
G ~ 480 GPa
What are the typical values for the poissions ratio of metals?
v ~ 0.3 - 0.35 (often assumed 1/3)
What are the typical values for the poissions ratio of ceramics and glasses?
v ~ 0.15 - 0.3
What are the typical values for the poissions ratio of polymers?
v ~ 0.3 - 0,45
What are the typical values for the poissions ratio of rubber?
v ~ 0.5 (incompressible)
What are the typical values for the poissions ratio of cork?
v ~ 0
What are the typical values for the youngs modulus of metals?
E ~ 70GPa - 200GPa
What are the typical values for the youngs modulus of ceramics and glasses?
E ~ 70GPa - 400GPa
What are the typical values for the youngs modulus of polymers?
E ~ 0.5 - 8 GPa
What are the typical values for the youngs modulus of Diamond?
E ~ 1150GPa
What are the typical values for the bulk modulus of metals?
B ~ 70GPa - 170GPa
What are the typical values for the bulk modulus of ceramics and glass?
B ~ 42GPa - 320GPa
What are the typical values for the bulk modulus of Polymers?
B ~ 1 - 15GPa
What are the typical values for the bulk modulus of Diamond?
B ~ 440GPa
The number of independent stress components required to describe stress at a point is
6
Which of the following can be described as isotropic materials?
Plywood
Steel
Window glass
Wood
Steel, Window Glass, Wood
The number of independent moduli needed to relate stress and strain in an orthotropic material is
9
The number of independent moduli needed to relate stress and strain in an isotropic material is
2
Under plane strain conditions the following stresses have non-zero values σxx, σyy, σzz, and σxy,
TRUE
A metal object with E = 97 GPa, ν = 0.31 is subject to the following stresses σxx = -45 MPa, σyy = -9 MPa and σzz = 77 50 MPa calculate the strain εyy
- 0.000295 +/- 2%
What are isotropic materials?
isotropic materials have the same properties in all directions
Resolving forces acting on a small volume elements gives how many components of stress?
9
σxx σxy σxz
σ σyx σyy σyz
σzx σzy σzz
3 normal stresses (σxx, σyy and σzz)
3 shear stresses (σxy, σxz and σyz)
Plane stresses in isotropic materials
σxx, σyy and σxy are non-zero
σzz = σxz = σyz = 0
I.E εxx, εyy and εxy are non zero
εxz = εyz = 0
