Mechanical Properties Chapter 4

1. Mechanical PropertiesChapter 4 Professor Joe Greene CSU, CHICO MFGT 041

2. 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

3. 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

4. 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)

5. 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

6. Mechanical Test Considerations 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

7. 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.

8. 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

9. Stress 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 100 lbs 1 cm 5cm 10cm

10. 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% lF l0

11. Stress-Strain Diagrams 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

12. 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

13. 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

14. Modulus Types 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.

15. 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 Yield stress 1000 psi Stress Yield strength Slope=modulus 0.002 in/in Strain

16. 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

17. Energy Capacity 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

18. 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.

19. Creep Results Fixed lF l0 Tertiary Creep Creep (in/in) Secondary Creep Constant Load Primary Creep Time (hours) • Creep versus time

20. Mechanical Properties in Liquids (Viscous Flow) • 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

21. Viscous Flow • 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

22. Newtonian and Non-Newtonian Flow 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

23. 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.

24. Viscosity Measurements 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

25. Viscosity Testing • Melt Flow Index

26. 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

27. Viscoelastic models • 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

28. 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

29. 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