Jan 08, 2016
Mechanical PropertiesChapter 4
Professor Joe Greene
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
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
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)
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
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
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.
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
– 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
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
• 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%
• Stress-strain diagrams is a plot of stress with the corresponding strain produced.
• Stress is the y-axis
• Strain is the x-axis
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
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
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.
Testing Procedure• Tensile tests yield a tensile strain, yield strength, and a yield
• Tensile modulus or Young’s modulus or modulus of elasticity– Slope of stress/strain
– Yield stress
– point where plastic
– Some materials do
not have a distinct yield point
so an offset method is used
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
• 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.
Strain Elastic strain Inelastic strain
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.
• Creep versus time
Primary CreepSecondary Creep
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)
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
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
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.
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
Cone, radius r
Viscosity Testing• Melt Flow Index
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
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
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
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