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Mechanical Properties Chapter 4

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Professor Joe Greene

CSU, CHICO

MFGT 041

- Objectives
- Mechanical properties in solids (types of forces, elastic behavior and definitions)
- Mechanical properties of liquids_ viscous flow (viscous behavior and definitions)
- Viscoelastic materials (viscoelastic behavior and definitions, time dependent)
- Plastic stress-strain behavior (plastic behavior and definitions, interpretation and mechanical model of plastic behavior)
- Creep and Toughness
- Reinforcements and Fillers

- Polymers are Viscoelastic materials that exhibit
- liquid (viscous) or
- solid (elastic) properties
- Depending upon the time scale of the event;
- Short time (fast) event will act like a solid;
- Long time (slow) event will act like a liquid.

- Depending upon the temperature of the event
- Example, Silly Putty
- Roll into a ball and drop it to the ground and it BOUNCES like a solid
- Place it on a table and leave overnight and it will FLOW and flatten out into a puddle like a liquid.
- Heat up the silly putty and the drop it and it will STICK to the ground like a liquid.
- Chill silly putty to bellow room temperature and leave rolled up on a table and it will STAY rolled up at that cold temperature

- Example, Silly Putty

- Mechanical Properties
- Deal directly with behavior of materials under applied forces.
- Properties are described by applied stress and resulting strain, or applied strain and resulting stress.
- Example: 100 lb force applies to end of a rod results in a stress applied to the end of the rod causing it to stretch or elongate, which is measured as strain.

- Strength: ability of material to resist application of load without rupture.
- Ultimate strength- maximum force per cross section area.
- Yield strength- force at yield point per cross section area.
- Other strengths include rupture strength, proportional strength, etc.

- Stiffness: resistance of material to deform under load while in elastic state.
- Stiffness is usually measured by the Modulus of Elasticity (Stress/strain)
- Steel is stiff (tough to bend). Some beds are stiff, some are soft (compliant)

- Mechanical Properties
- Hardness: resistance of materials to surface indentation or abrasion.
- Example, steel is harder than wood because it is tougher to scratch.

- Elasticity: ability of material to deform without permanent set.
- Rubber band stretches several times and returns to original shape.

- Plasticity: ability of material to deform outside the elastic range and yet not rupture,
- Bubble gum is blown up and plastically deforms. When the air is removed it deflates but does not return to original shape.
- The gum has gone beyond its elastic limit when it stretches, set it remains plastic, below the breaking strength of the material.

- Energy capacity: ability of material to absorb energy.
- Resilience is used for capacity in the elastic range.
- Toughness refers to energy required to rupture material

- Hardness: resistance of materials to surface indentation or abrasion.

shear

- Principle factors are in three main areas
- manner in which the load is applied
- condition of material specimen at time of test
- surrounding conditions (environment) during testing

- Tests classification- load application
- kind of stress induced. Single load or Multiple loads
- rate at which stress is developed: static versus dynamic
- number of cycles of load application: single versus fatigue

- Primary types of loading

compression

tension

torsion

flexure

- Moisture
- 100F, 100% R.H.
- 1 Day, 7 Days, 14 Days

- Temperature
- Room Temperature: Most common
- Elevated Temperature: Rocket engines
- Low Temperature: Automotive impact

- Salt spray for corrosion
- Rocker Arms on cars subject to immersion in NaCl solution for 1 Day and 7 Days at Room Temperature and 140 F.

- Acid or Caustic environments
- Tensile tests on samples after immersion in acid/alkaline baths.

- Stress: Intensity of the internally distributed forces or component of forces that resist a change in the form of a body.
- Tension, Compression, Shear, Torsion, Flexure

- Stress calculated by force per unit area. Applied force divided by the cross sectional area of the specimen.
- Stress units
- Pascals = Pa = Newtons/m2
- Pounds per square inch = Psi Note: 1MPa = 1 x106 Pa = 145 psi

- Example
- Wire 12 in long is tied vertically. The wire has a diameter of 0.100 in and supports 100 lbs. What is the stress that is developed?
- Stress = F/A = F/r2 = 100/(3.1415927 * 0.052 )= 12,739 psi = 87.86 MPa

0.1 in

1 in

10in

- Example
- Tensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the stress that is developed? What is the Load?
- Stress = F/A = F/(width*thickness)= 100lbs/(1in*.1in )= 1,000 psi = 1000 psi/145psi = 6.897 Mpa
- Load = 100 lbs

- Block is 10 cm x 1 cm x 5 cm is mounted on its side in a test machine. The block is pulled with 100 N on both sides. What is the stress that is developed? What is the Load?
- Stress = F/A = F/(width*thickness)= 100N/(.01m * .10m )= 100,000 N/m2 = 100,000 Pa = 0.1 MPa= 0.1 MPa *145psi/MPa = 14.5 psi
- Load = 100 N

- Tensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the stress that is developed? What is the Load?

100 lbs

1 cm

5cm

10cm

- Strain: Physical change in the dimensions of a specimen that results from applying a load to the test specimen.
- Strain calculated by the ratio of the change in length and the original length. (Deformation)
- Strain units (Dimensionless)
- When units are given they usually are in/in or mm/mm. (Change in dimension divided by original length)

- % Elongation = strain x 100%

lF

l0

Linear

(Hookean)

Stress

Non-Linear

(non-Hookean)

Strain

- Stress-strain diagrams is a plot of stress with the corresponding strain produced.
- Stress is the y-axis
- Strain is the x-axis

- Stiffness is a measure of the materials ability to resist deformation under load as measured in stress.
- Stiffness is measures as the slope of the stress-strain curve
- Hookean solid: (like a spring) linear slope
- steel
- aluminum
- iron
- copper

- All solids (Hookean and viscoelastic)
- metals
- plastics
- composites
- ceramics

- Modulus of Elasticity (E) or Young’s Modulus is the ratio of stress to corresponding strain (within specified limits).
- A measure of stiffness
- Stainless SteelE= 28.5 million psi (196.5 GPa)
- Aluminum E= 10 million psi
- CopperE= 16 million psi
- MolybdenumE= 50 million psi
- NickelE= 30 million psi
- TitaniumE= 15.5 million psi
- TungstenE= 59 million psi
- Carbon fiberE= 40 million psi
- Glass E= 10.4 million psi
- CompositesE= 1 to 3 million psi
- PlasticsE= 0.2 to 0.7 million psi

- A measure of stiffness

Initial Modulus

Tangent Modulus

Secant Modulus

Stress

Strain

- Modulus: Slope of the stress-strain curve
- Initial Modulus: slope of the curve drawn at the origin.
- Tangent Modulus: slope of the curve drawn at the tangent of the curve at some point.
- Secant Modulus: Ratio of stress to strain at any point on curve in a stress-strain diagram. It is the slope of a line from the origin to any point on a stress-strain curve.

- Tensile tests yield a tensile strain, yield strength, and a yield stress
- Tensile modulus or Young’s modulus or modulus of elasticity
- Slope of stress/strain
- Yield stress
- point where plastic
deformation occurs

- Some materials do
not have a distinct yield point

so an offset method is used

Yield stress

1000 psi

Stress

Yield strength

Slope=modulus

0.002 in/in

Strain

- Stress is measured load / original cross-sectional area.
- True stress is load / actual area.
- True stress is impractical to use since area is changing.
- Engineering stress or stress is most common.
- Strain is elongation / original length.
- Modulus of elasticity is stress / strain in the linear region
- Note: the nominal stress (engineering) stress equals true stress, except where large plastic deformation occurs.
- Ductile materials can endure a large strain before rupture
- Brittle materials endure a small strain before rupture
- Toughness is the area under a stress strain curve

Stress

Strain

- Energy Capacity: ability of a material to absorb and store energy. Energy is work.
- Energy = (force) x (distance)
- Energy capacity is the area under the stress-strain curve.
- Hysteresis: energy that is lost after repeated loadings. The loading exceeds the elastic limit.

Stress

Strain

Elastic strain

Inelastic strain

- Creep
- Measures the effects of long-term application of loads that are below the elastic limit if the material being tested.
- Creep is the plastic deformation resulting from the application of a long-term load.
- Creep is affected by temperature

- Creep procedure
- Hold a specimen at a constant elevated temperature under a fixed applied stress and observe the strain produced.
- Test that extend beyond 10% of the life expectancy of the material in service are preferred.
- Mark the sample in two locations for a length dimension.
- Apply a load
- Measure the marks over a time period and record deformation.

Fixed

lF

l0

Tertiary Creep

Creep

(in/in)

Secondary Creep

Constant

Load

Primary Creep

Time (hours)

- Creep versus time

- Polymer Flow in Pressure Flow (Injection Molding)

FIGURE 2. (a) Simple shear flow. (b) Simple extensional flow. (c) Shear

flow in cavity filling.(d) Extensional flow in cavity filling.

Ref: C-MOLD Design Guide

- Viscosity is a measure of the material’s resistance to flow
- Water has low viscosity = easy to flow
- Syrup has higher viscosity = harder to flow

- Viscosity is a function of Shear Rate, Temp, and Pressure
- increase Shear Rate = Viscosity Decreases
- Increase Temperature = Viscosity Decreases

Ref: C-MOLD Design Guide

Non-Newtonian

Shear Thickening

Viscosity,

cps

or Pa-sec

Newtonian

Non-Newtonian

Shear Thinning

Shear Rate, sec -1

- Viscosity is a measure of the material’s resistance to flow.
- Newtonian Material. Viscosity is constant
- Non-Newtonian: Viscosity changes with shear rate, temperature, or pressure
- Polymers are non-Newtonian, usually shear thinning

Fig 4.4

- Viscosity is a measure of the material’s resistance to flow.
- Liquids: (paints, oils, thermoset resins, liquid organics) Measured with rotating spindle in a cup of fluid, e.g., Brookfield Viscometer
- Resistance to flow is measured by torque.
- The spindle is rotated at several speeds.
- The fluid is heated to several temperatures.

- Liquids: (paints, oils, thermoset resins, liquid organics) Measured with rotating spindle in a cup of fluid, e.g., Brookfield Viscometer

Cone, radius r

q

Plate

w

- Melts: (plastic pellets, solid particles)
- Resistance to flow is measured by torque in cone-and-plate, e.g., Rheometrics viscometer
- The plates are heated and the toque is measured
- Resistance to flow is measured by flow through tube
- Capillary rheometer
- Melt Indexer

- Melt Flow Index

- Melt index test measure the ease of flow for material
- Procedure (Figure 3.6)
- Heat cylinder to desired temperature (melt temp)
- Add plastic pellets to cylinder and pack with rod
- Add test weight or mass to end of rod (5kg)
- Wait for plastic extrudate to flow at constant rate
- Start stop watch (10 minute duration)
- Record amount of resin flowing on pan during time limit
- Repeat as necessary at different temperatures and weights

- Plastics exhibit viscoelastic behavior, to an applied stress
- Viscous liquid: Continuously deform while shear stress is applied
- Elastic solid: Deform while under stress and recover to original shape

Ref: C-MOLD Design Guide

- Plastics exhibit viscoelastic behavior, to an applied stress
- Viscous liquid: Simple dashpot
- Viscoelastic liquid: Spring and Dashpot in series (Maxwell model)
- Viscoelastic solid: Spring and Dashpot in Parallel (Voight model)
- Elastic solid: Simple Spring
- Figure 4-6

- Time Dependence of Viscoelastic properties
- Viscous liquid: Constant viscosity: Newtonian
- Viscoelastic liquid: Viscosity changes at different rates, e.g., higher shear rate reduces viscosity or Shear thinning plastics
- Viscoelastic solid: Solid part has a memory to applied stress and needs time for the stress to reach zero after an applied load.
- Elastic solid: Simple Spring: Hook’s Law on spring constant
- Figure 4-7