Materials Flashcards
What are forces that produce extension known as
Tensile forces
What are forces that compress an object known as
Compressive forces
What does a helical spring undergo when tensile forces are exerted
Tensile deformation
What does a helical spring undergo when compressive forces are exerted
Compressive deformation
Describe a force extension graph
Straight line from the origin to elastic limit of the spring - in this linear region, spring undergoes elastic deformation - it will return to its original length when the force is removed
Beyond this point - it will go plastic deformation - permanent structural changes occur and the spring won’t go back to its original length when the spring is removed
What is Hooke’s Law
Extension of the print is direct proportional to the force applied as long as the elastic limit of the spring is not exceeded
Hookes Law
F = kx
K = force constant (Nm^-1)
What is a force constant
Measure of stiffness of a spring
Larger force constant means it’s more difficult to extnemt
Where can Hookes Law also be applied to
Wires under tension
Concrete columns under compression
What happens to work done when a material has gone though plastic deformation and when it hasn’t
Some of the work done has gone to moving the atoms into new positions - is not recoverable
When it hasn’t - work done can be fully recovered
Work done by a force in extending the spring equation
Change in work done = force x change in extension
What is the area under a force extension graph
Work done
What is work done on a spring transferred into and is it recoverable
EPE
Yes because if the elastic behaviour of the spring
Equation for EPE
E = 1/2kx^2
For a spring obeying Hooke’s Law substitute into 1/2Fx (Area under graph)
What is the hysteresis loop
The loop formed by loading and unloading curves for objects that don’t obey Hooke’s Law
When is more work done - stretching a rubber band or decreasing it
Stretching a rubber band
What is the area inside the hysteresis loop
Thermal energy released when a material is loaded then unloaded
What is tensile strsss
Force applied per unit cross sectional area of the wire
Tensile stress formula
T.S = Force / cross sectional area
(Sigma is sign for T.S)
Tensile strain formula
Fractional change in the original length of the wire
Tensile strain formula
Extension / original length
T.S is represented with epsilon
What is a ductile material
A material that can easily be drawn into a wire or hammered into thin sheets
Describe a stress strain graph for a metal wire
Stress is directly to strain from origin to the limit of proportionality - obeys Hooke’s law in this region
Small curve to E - represents the Elastic
limit - some materials obey Hooke’s law to this limit - elastic deformation occurs beyond this limit
Curves up to Y1 - upper yield point
Curves down to Y1 - Lower yield point
Yield point is where the material extends rapidly - yield points may be absent in some materials - typical for mild steel
Y2 to UTS - Ultimate Tensile Strength - maximum stress a material can go under before breaking
What do strong materials have
High UTS
What is Young’s Modulus
Ratio of stress to strain for material within the limit of proportionality
Youngs Modulus Formula
YM = Tensile Stress / Tensile Strain
Nm^-2 or Pa
Fl/Ax
Determine Youngs Modulus
Measure diameter of a wire with a micrometer
Calculate cross sectional area with this measurement
Repeat and average measurements from several places along the wire for more accurate reading
Tensile force acting on wire can be calculated with F=mg (m is hanging Mass)
After applying each additional mass - extension calculated is (extended length - original length) - repeat these for 6 different masses
Plot a stress and strain graph after calculating them for each load
Youngs Modulus can be calculated up from the linear section of the graph
Stress Strain graph for brittle materials
Elastic behaviour up to its breaking point with plastic deformation (just straight lines both ways)
What are polymeric materials
Materials with long molecular chains
Stress strain graph for polymers
Dependent on material
Some show elastic behaviour and others show plastic behaviour
What is force directly proportionally to and when
Extension
For a spring obeying Hooke’s Law
What is the gradient of a force-extension grant
The force constant
Where does Hooke’s Law apply to besides springs
Wires under tension and concrete columns under compression
Any object that can be elastically squashed or extended
Loading curve (force-extension graphs) for a metal wire
Follows Hooke’s Law until the elastic limit of the wire
Unloading graph will be identical for forces less than the elastic limit
Beyond the elastic limit it is parallel to the loading graph but not identical to it - wire is permanently extended after the force is removed - longer than it was at the start
Loading curves (force-extension graph) for a rubber band
Do not obey Hooke’s Law - will return to its original length once Hooke’s Law is removed
Loafing and unloading curves are different - a loop is formed between them
Thermal energy released is area inside the hysteresis loop
Loading curves (force-extension graph) for polythene
Do not obeys Hooke’s Law - suffer plastic deformation under a relatively little force
What is the breaking strength of a material
The stress value at the point of fracture
