Mechanical Flashcards
Deform
change shape
Fail
break
Mechanical Properties
Stiffness
Strength
Toughness
Materials can gradually degrade and fail over time as a result of
Wear
Creep
Fatigue
The Tensile Test
- Take sample of material
- Pull ends to stretch it
- Measure force F
- Measure stretch L-Lₒ
-know diagram
Tensile Test practicalities
- any size, but parallel sides
- cross section same throughout
- can make ends of specimen bigger so its easy to grip in testing machine
Stress/Strain curve
- to see how sample stretches for given applied force
- x-axis: stress
- y-axis: strain
-X on curve indicates point which sample breaks
Stress formula
σ = Force/Area
N/m² or Pa
Strain formula
ε = (L-Lₒ)/Lₒ
No units
Cross sectional area
For rectangular A = width x thickness
For circular, A = πr²
Types of stress
Tensile stress (pulling)
Compression (pushing)
Shear
Pressure
Compression and Tensile stress
Pushing is still known as tensile stress, but has negative value
Shear
A type of stress that causes sliding
Shear stress formula
τ = Force/Area
Shear Strain formula
γ = L/Lₒ = Tanθ
Pressure
created by having same force acting in all directions eg. hydrostatic pressure underwater
Pressure formula
P = F/A, same as tension but written as positive when compressive
Strain due to pressure
A change in volume, called dilatation
Dilatation formula
△=-(V-Vₒ)/Vₒ
Any type of stress
can be expressed as a mixture of these three:
tension, shear, pressure
Stress/Strain curve: First Stage
- Elastic Deformation
- When line is straight at start
- material behaves like spring
- remove stress, strain goes back to zero
- stress ∝ strain
Stiffness
- Slope of stress/strain curve in elastic region
- called Young’s Modulus (or elastic modulus), E
- if line is straight E=stress/strain at any point in line ie E = σ/ε
-we measure E when applied stress is tensile, most materials have same E value in compression as in tension
Yield Strength and Plastic Deformation
Above certain stress, σᵧ, line becomes flatter and curved,
σᵧ
This point where line stops being straight is called yield stress or yield strength of the material
Deformation can be
Temporary (elasticity)
Permanent (plasticity)
Bending
Creates tension on one surface, compression on the other, no stress or strain in middle
Common types of bending
- Cantilever Bending
- Three-point bending
- Four-point bending
diagrams in lecture 2 slides
Testing for bending
We test for deflection (d) of the loading point as a function of the applied force F
Bending Equations
will be given on exam, know what the letters stand for
Other Types of Stiffness
-If material loaded in shear or with a pressure, different elastic modulii can be calculated: Shear Modulus (G) Bulk Modulus (k)
Poisson’s Ratio
v = εₜ / ε
- ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force
- There will be some strain in two directions perpendicular to loading direction.
- If vol of piece stays constant, transverse strain εₜ will be half longitudinal strain ε
Tensile and compressive deformation
Tensile deformation is considered positive and compressive deformation is considered negative.
True Stress and True Strain
- During test specimen gets thinner, so cross section area decreases
- But Stress = F/A so stress bigger than we thought
Nominal Stress/Engineering Stress
F/Aₒ
Aₒ = area of original, unstretched piece
-We plot nominal stress on stress strain curves usually
True Stress
The correct value, F/A
Nominal Strain
(L-Lₒ)/Lₒ
True strain will be smaller
Elastic Energy
- If you load up material in elastic region to some stress σ, area under line is measure of energy used in doing it.
- Energy per unit volume of material in sample
- This energy is stored in material, will be released if you unload it
Hysteresis
- Non-linear Elasticity
- When stress/strain line curved in elastic region, sometimes loading and unloading lines are different
- E is into constant
- Some energy is lost (given by area between lines)
buckling
what happens when you have a long, thing, structure loaded in compression
stiffness
- How much material deforms under load when deforming elastically
- quantified by property called Young’s Modulus
Above yield strength
- Stress/strain non-linear relationship
- Two things can be happening:
a. plastic deformation
b. damage
Plastic Deformation
The permanent distortion that occurs when a material is subjected to tensile, compressive, bending, or torsion stresses that exceed its yield strength and cause it to elongate, compress, buckle, bend, or twist
-diagram in lecture slides 3
Finding plastic strain
Distance between Origin and new point on x-axis on stress/strain graph
Damage
If, when you come down to zero after loading and unloading, there is no plastic strain
- material becomes less stiff
- due to internal damage
Damage form
Usually takes form of cracks
Ultimate Tensile Strength (UTS)
The stress at the maximum point and the strain where it finally breaks ε(subscript f)
Ductility
The breaking strain
Energy under whole stress/strain curve
energy per unit volume needed to make it fail (sometimes called toughness)
Elastic Recoil
- Black triangle in stress/strain curve (see lecture slide 3 diagram)
- You get some energy back in elastic recoil
Brittle Materials
- In brittle materials, failure may occur before any change in slope of line
- Yield Strength and Ultimate Tensile Strength the same
Compression - young’s modulus and yield strength
- Young’s modulus normally same as in tension
- Yield strength usually higher when damage happens
Shear - yield strength
-Yield strength half of what it is in tension
τᵧ = σᵧ/2
Importance of strength
- can’t use material above its strength, it will break or become permanently deformed or damaged
- σᵧ is maximum allowable stress
- Designers usually apply safety factor, allowing material to be used only up to fraction of its measured strength
Factor of Safety
Factor of safety = ultimate stress/actual stress
When we want yield strength to be low
- In manufacturing operations like forging, wire-drawing, sheet rolling
- If σᵧ low and ε(subscript f) high, can deform material into new shape using little energy and avoiding failure
applications of strength
- sets upper limit to stress we can use material
- sets lower limit to stress at which we can plastically deform it
How does glass berak?
- breaks without yielding
- no plastic deformation, no damage before failure - happens without warning
Yield strength of glass
-much higher than stress it normally fails at
Brittle Fracture
the sudden, very rapid cracking of equipment under stress where the material exhibited little or no evidence of ductility or plastic degradation before the fracture occurs.
Materials that experience brittle fracture
- Ceramics
- Many Polymers
- Metals under certain circumstances
- rubber
tough vs brittle materials
- tough materials fail after absorbing lot of energy, strain a lot before failing
- brittle materials fail with little energy absorption at low strains, fail by cracking
Definition of Toughness 1
- Area under stress/strain curve
- energy per unit volume needed for failure
- j/m^3
- brittle materials have low values bc no yield point , UTS low even tho E may be high
Definition of Toughness 2
- energy absorbed in fast fracture using specimen containing a notch
- Material notched to create flaw, struck with swinging heavy pendulum
- fracture energy is measured by how high pendulum rises after impact
Definition of toughness 3 - used in Mechanical Engineering
-The fracture toughness
Fracture Toughness Test
like a normal tensile test except specimen already contains a crack
