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Mechanical PropertiesChapter 4

Professor Joe Greene

CSU, CHICO

MFGT 041

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Chapter 4 Objectives• 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

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Viscoelastic Materials• 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

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Fundamentals of Mechanical Properties• 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)

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Fundamentals of Mechanical Properties• 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

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Mechanical Test Considerations• 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

tension compressionshear

torsion

flexure

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Standardized Testing Conditions• 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.

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Stress• 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

A

F

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Stress• 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

10cm 5cm

10in1 in

0.1 in

1 cm

100 lbs

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Strain• 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%

0l

l l0

lF

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Stress-Strain Diagrams

• Stress-strain diagrams is a plot of stress with the corresponding strain produced.

• Stress is the y-axis

• Strain is the x-axis

Stress

Strain

Linear(Hookean)

Non-Linear(non-Hookean)

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Stiffness• 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

kxF

E

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Modulus• Modulus of Elasticity (E) or Young’s Modulus is the ratio of stress to corresponding strain

(within specified limits).– A measure of stiffness

• Stainless Steel E= 28.5 million psi (196.5 GPa)• Aluminum E= 10 million psi• Copper E= 16 million psi• Molybdenum E= 50 million psi• Nickel E= 30 million psi• Titanium E= 15.5 million psi• Tungsten E= 59 million psi• Carbon fiber E= 40 million psi• Glass E= 10.4 million psi• Composites E= 1 to 3 million psi• Plastics E= 0.2 to 0.7 million psi

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Modulus Types• 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.

Stress

Strain

Initial Modulus

Tangent Modulus

Secant Modulus

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Testing Procedure• 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

Stress

Strain

0.002 in/in

1000 psi

Yield stress

Yield strength

Slop

e=m

odul

us

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Expected Results• 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

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Energy Capacity

• 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

Stress

Strain Elastic strain Inelastic strain

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Creep Testing• 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.

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Creep Results

• Creep versus time

Creep(in/in)

Time (hours)

Primary CreepSecondary Creep

Tertiary Creep

l0lF

Constant Load

Fixed

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Mechanical Properties in Liquids (Viscous Flow)

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

• Polymer Flow in Pressure Flow (Injection Molding)

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Viscous Flow

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

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Newtonian and Non-Newtonian Flow• 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

Shear Rate, sec -1

Viscosity, cpsor Pa-sec

Newtonian

Non-NewtonianShear Thinning

Non-NewtonianShear Thickening

Fig 4.4

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Viscosity Measurements• 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.

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Viscosity Measurements– 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

Plate

Cone, radius r

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Viscosity Testing• Melt Flow Index

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Melt 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

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Viscoelastic models

Ref: C-MOLD Design Guide

• 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

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Viscoelastic models• 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

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Viscoelastic models• 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