Deformable body Mechanics Unit 1: Mechanical properties of materials and structures (class) Flashcards
What is a structure?
an arrangement of one or more materials in a way that is designed to sustain loads
What is a material?
a type of matter used to construct structures
Are mechanical properties independent of material or structure?
structure
Which symbol represents stress?
sigma σ
Which symbol represents strain?
epsilon ε
Which symbol represents the coefficient of velocity?
eta η
What is deformation?
change in shape or size of a structure or any part of it
How do we calculate stress?
force (N) / area (m2)
What units do we use for stress?
pascal = N/m2
How can stress tell us the strength of a material?
it is the same regardless of size or shape of material
a bar with twice the cross-sectional area will require twice to break it but the stress within them will be the same
What is strain and how do we calculate it?
a measure of deformation
change in length/ original length
What are axial loads?
a load applied a geometric axis of a structure producing pure tension or compression
What do stress-strain curves show?
how a material deforms as it is loaded
What is the proportional limit in a stress-strain curve?
the point at which the straight line finishes and stress stops being directly proportional to strain
What is the elastic limit in a stress-strain curve?
the greatest stress that may be applied to a material without causing any permanent deformation
describe a material that exhibits elastic behaviour
it instantly deforms under a load and returns immediately to its original size and shape eg rubber
describe a material that exhibits plastic behaviour
it deforms instantly under a load and retains this new shape/size when the load is removed eg putty
In structures which region of the stress-strain curve must the material remain within?
elastic region as a material that is plastic is of no use because it will deform greatly under a small increase in load
What happens beyond the yield point?
the material will undergo considerable elongation without an increase in stress ie. just maintaining the load will cause continual deformation
What type of behaviour is in the region following the yield point?
plastic
What happens after the ultimate strength of the material is reached?
stretching occurs with a reduction in stress
results in a reduced cross-sectional area called necking
What do we call
a) a material that can sustain only limited strain before breaking?
b) a material that deforms plastically before breaking?
a) brittle
b) ductile
What is Hooke’s law?
up to the proportional limit, the strain is proportional to the applied stress
What is Young’e modulus a measure of and how do you calculate it?
the stiffness of a material
stress/strain
What symbol represents young’s modulus?
E
What is rigidity?
the ability to resist axial deformation
How do we calculate rigidity?
young’s modulus x cross-sectional area
What are the units of rigidity?
N
What is stiffness?
the force required to produce a unit deflection
How do we calculate stiffness? give 2 ways
applied force / change in length
young’s modulus x cross sectional area / original length
What is flexibility?
the deflection under a unit load
How do we calculate flexibility and what units do we use?
1/stiffness
m/ N
Is strength determined by Young’s modulus?
no
Describe viscous behaviour
material does not deform instantly when a load is applied. The strain is prolonged. once the load is removed the material will not return to its original size and shape.
this means that no energy is stored in the material and all the energy is required to deform is dissipated as heat.
Give 3 examples of materials that exhibit viscous behaviour
water
blood plasma
air
What are stresses arising in viscous materials dependent on?
strain rate
What is the coefficient of viscosity equal to?
η = stress/ strain rate
How do we represent strain rate?
epsilon dot
What is the strain rate?
change in strain / change in time
what are the units for the coefficient of viscosity?
Nm-2.s / Pa.s
Describe viscoelastic behaviour
viscous in that it responds to the rate of loading and elastic in that it returns to its original size and shape after the load is removed
Give 2 examples of materials that show viscoelastic behaviour
articular cartilage
cortical bone
What is creep?
developing strain over time when a constant load is applied
Name some examples of creep
soft metals eg lead
wood
concrete (noticeable after years)
What is stress relaxation?
in a material under constant strain the stress diminishes over time
what is strain hardening?
material undergoes changes in its atomic and crystalline structure resulting in an increased resistance to further deformation
Give the regions of the strain stress curve in order
elastic
plastic
strain hardening
necking
what is young’s modulus equal to on the stress-strain curve?
gradient upto the proportional limit ie. the elastic region
In a stress-strain curve what is the highest stress on the diagram?
ultimate stress
