Föreläsning 3 - stiffness

Question 1

What does density depend on?

Answer 1

• Atomic weight of the atoms.
• Number of atoms/ volume

In composites it depends on volume fraction and density of the constituents.

Density of polymer foams, tree etc. is low due to the voids.

Question 2

How can we view atomic bonds and stiffness?

Answer 2

We can compare it to linear springs.

S = stiffness of the atomic bond
n = number of bonds/ area
E- modulus = S*n

Elastic behaviour = the material is beahving as a spring, springing back at unloading

Deep binding energy curve:
- High E-modulus
- High melting temp.

(see good pic in slides)

Question 3

Can we change the types of atomic bonds in materials with processes?

Answer 3

No!

The types of atomic bonds influence things such as E-modulus, melting temp and thermal expansion. We can not change it with processes,

Question 4

Describe how a tensile test affects both brittle and ductile materials

Answer 4

Brittle:
- Elastic behaviour up to fracture stress
- Fracture stress = fracture
- Ceramics, glass for example

Ductile:
- Elastic behaviour up to yield stress
- Yield stress = stress when the material starts to deform plastically
- Fracture stress = highest stress
- We get elastic behaviour at unloading, even after plasticity
- Metals, polymers

(good pics in slides)

Question 5

What decides the stiffness of polymers?

Answer 5

• Properties of components
• Volume fraction
• Orientation
• Shape

(see pic in slides)

Question 6

Describe the relationship between stress and strain. What can strain be a result of?

Answer 6

• Strain is a geometrical property.

Strain can be a result of:
- Mechanlical loads: stress = E * strain
- Temperature: strain = coefficient of thermal expansion * change in temperature
- Electrical and magentical fields
- Moisture

Question 7

Name the elastic constraints

Answer 7

There are a minimum of two elastic constraints (isotropic material)
- E- modulus
- Poissons number

There are more elastic constraints for e.g. composites, wood (non-isotropic)

(see good pic in slides)

Question 8

Name some different load cases

Answer 8

Tie, column, beam, shaft, shell.

We have to determine the type of load case for materials selection.

Question 9

What is a performace index?

Answer 9

• A numerical value M that indicates how effective the material is in a specific load case and in a specific shape.
• To determine a performance index, we must know what should be optimized (price, weight…) and load case.
• We use function, objective and free variables from the translation.
• Performance index is used to rank materials

(examples is slides)

Question 10

What is a material index?

Answer 10

Combination of material properties in the equation for performance.

Sometimes a single property, sometimes a combination.

Question 11

How do plots for performance index work?

Answer 11

• With density on x-axis, a performance index with a exponent of m is represented by a line with slope 1/m
• All materials on the line have the same performance index = equally good
• Better up to the left

Question 12

How do we rank materials?

Answer 12

1. Choose performance index
2. Make plot
3. Choose slope of line
4. Find material with best performance index

Question 13

What performance index should we use if deformation is deciding?

Answer 13

Stiffness