Mechanical Properties of Materials & Structures Flashcards
What is a structure?
What is a structure material?
Structure - an arrangement of one or more materials in a way that is designed to sustain loads
Structure Material - any material that may be used to construct a structure
What is a mechanical property?
The basic mechanical behaviour of a material, measured using simple, idealised tests and divorced from the material’s shape and size
In materials/structures, what do the following symbols mean:
- sigma?
- epsilon?
- eta?
sigma - stress
epsilon - strain
eta - coefficient of viscosity
What is deformation?
Change in shape or size of a structure, or any part of it
What does knowledge of mechanical properties allow for?
Prediction of what will happen to a body when it is loaded
Formula for stress?
stress = force / cross-sectional area
sigma = F/A
Relationship between stress and materials?
Stress is independent of the shape and size of a material.
If there are 2 bars made from the same material, and one has a cross-sectional area double that of the other, it will take twice as much force to break the wider one.
Therefore, the stress in the materials will be the same
stress 1 = F/A
stress 2 = 2F/2A
SI units of stress?
N m^-2 (same as pressure or Pascal)
Formula for strain?
Strain = change in length / original length
strain = epsilon
Relationship between strain and material?
Elongation is dependent on the length of the structure.
If there are 2 bars with the same cross-sectional area but one is 2x the length of the other, the strain in the longer bar will be 2x that of the shorter bar.
What are axial loads?
Tension or compression
Load applied along a geometric axis of a structure (not across i.e. bending or twisting)
What does a stress-strain curve illustrate?
Why else is it useful?
How a material deforms as it is loaded
It can also be used to compare different materials to see if one is relatively more or less stiff, tough, ductile and/or brittle
Although some materials may predominantly exhibit one of these characteristics, all materials will have all of these behaviours to a certain degree depending upon the magnitude of the load to which they are subjected
6 regions and points of particular interest in a stress-strain curve?
Proportional limit Elastic limit Yield point Strain hardening Ultimate strength Rupture point
What is the proportional limit (P)?
Between the origin and the proportional limit, P, the stress-strain curve is in a straight line.
i.e. the stress is directly proportional to the strain (thus if the stress is doubled so is the strain)
What is the elastic limit (E)?
The greatest stress which can be applied to a material without causing permanent deformation (elastic behaviour).
If this point is passed and the material is unloaded, it will not return to its original shape and size (plastic behaviour)
What is elastic behaviour?
How does this appear on a stress-strain curve?
When a material deforms instantaneously upon loading and returns to its original shape and size once it is unloaded (e.g. rubber)
In the elastic region, therefore, the curve follows back down the same path to the origin
What is plastic behaviour?
How does this appear on a stress-strain curve?
When a material deforms instantaneously upon loading, but retains its new shape and size when unloaded (e.g. putty).
The material may partially recover some of its original shape (elastic recovery), but not completely, and there will remain a residual strain
Past the elastic limit, E, the material will not follow back down the same path to the origin, and will not return to the origin
What is the yield point (Y)?
Once passed, the material will undergo considerable elongation (yielding) without a corresponding increase in stress.
This is indicated by the flatness of the region following the yield point. In this region, the material may exhibit perfectly plastic behaviour (no elastic recovery). The stress at the yield point is called the yield stress
What is strain hardening?
After undergoing the large strain that can occur during yielding, the material begins to strain/work harden. In this region, the material undergoes changes in its atomic and crystalline structure resulting in increased resistance to further deformation
What is ultimate strength (U)?
What happens after this point?
This occurs at the highest point of the stress-strain curve. It is the maximum stress the material can withstand before beginning to fail.
After this point, stretching occurs with an actual reduction in stress, resulting in NECKING/waisting in the material, whereby the cross-sectional area of the material is reduced
The stress the bar can withstand after the ultimate strength point is reduced, but not due to loss of material strength, purely due to reduction in cross-sectional area. The thinnest part of the ‘neck’ is used to calculate this.
What is rupture point (R)?
What is stress at this point called?
When the material breaks
Stress at this point is called rupture stress
What is a brittle material?
What is a ductile material?
Brittle - a material that can only sustain a limited strain before breaking e.g. glass
Ductile - a material which plastically deforms before breaking e.g. copper
What is Hooke’s Law?
Up to a certain level of stress, the strain produced is proportional to the applied stress
(this limit is the proportional limit, what it refers to is the linear region of the graph)
What is the stiffness of a material?
How is it measured?
How difficult it is to deform under loading
Measured by Young’s Modulus (modulus of elasticity)
What is Young’s Modulus?
What are the SI units?
Young’s Modulus = Stress / Strain
E = sigma / epsilon
(it is the mathematical equivalent of Hooke’s Law)
It is equal to the gradient of the stress-strain curve (only true until the proportional limit)
SI units = N m^-2 (Pascals)
What does it mean if a material has a small Young’s modulus?
A large Young’s Modulus?
Only a small amount of stress is required to produce a large amount of strain (i.e. it is flexible) e.g. rubber
A large amount of stress is required to produce only a small strain (i.e. it is stiff) e.g. diamond
What is rigidity?
Formula?
Relationship between rigidity and area?
An indication of a material’s ability to resist axial deformation. It is the product of Young’s Modulus and the bar’s cross-sectional area:
Rigidity = EA
E= Young's Modulus A= Area
As area increases, rigidity increases
What is stiffness?
Formula?
The force required to produce a unit deflection (i.e. the force required to elongate or shorten a bar by 1 metre)
k = F / change in length
k = stiffness F = force
Therefore, from the Young’s Modulus equation:
k = EA/length
Thus stiffness is equal to the rigidity per unit length
What is flexibility?
Formula?
What relationships can be deduced from these equations?
The deflection under a fit load
(therefore the inverse of stiffness)
f = change in length/F = length/EA = 1/k
An increase in the length of a bar will mean a reduction in stiffness, and an increase in flexibility.
Similarly, an increase in the cross-sectional area of a bar will mean an increase in its stiffness and reduction in its flexibility
How do rigidity, stiffness and flexibilty differ from Young’s Modulus?
Unlike Young’s Modulus, rigidity, stiffness and flexibility are not solely dependent upon the material, but also the material’s shape and size
What is viscous behaviour?
3 materials which exhibit viscous behaviour?
When a material does not deform instantaneously when a load is applied - the strain is prolonged
Once the load is removed, the material will not return to its original shape and size. This means that no energy is stored in the material, and all the energy required to deform it is dissipated as heat.
Water, air and blood plasma
What are the stresses in a viscous material dependent on?
The strain rate
Can the behaviour of a viscous material be represented by Hooke’s Law and Young’s Modulus?
No
Formula for coefficient of viscosity?
Coefficient of viscosity = stress/strain rate
eta = sigma/epsilon dot
How to work out the strain rate?
strain rate = change in strain / change in time
epsilon dot = delta epsilon / delta t
SI units of coefficient of viscosity?
Nm^-2 .s
Newton per metre squared second
Pascal per seconds
What is the approximate coefficient of viscosity of water at room temp?
Blood plasma?
Water = 0.1 Pa .s
Blood = 0.12 Pa .s
What is viscoelastic behaviour?
When a material demonstrates viscous behaviour in that it will not respond to loads instantaneously, and elastic behaviour in that it returns to its original shape and size once the load is removed
2 properties that viscoelastic materials will show?
Creep
Stress Relaxation
What is creep?
What are the 3 stages?
When a constant load is applied, after the initial deformation, the material will continue to slowly deform over a long period of time, until equilibrium or rupture. Usually the changes are too small to be of real concern, however soft materials and those exposed to high temperatures will creep more noticeably.
1st stage - the elastic strain, equal to the material’s stress-strain curve
2nd stage - constant creep rate, which is equal to the gradient of the creep curve
3rd stage - the material begins to neck and the deformation accelerates until fracture
What is stress relaxation?
If a material is kept under constant strain, the stress in it will gradually diminish over time. This is due to a change in the ordering of the atoms within the material
