Professional Engineering Review Session Materials Properties (5.D.)

1. Professional Engineering Review SessionMaterials Properties (5.D.) Steve Hall, Ph.D., P.E. shall5@lsu.eduLouisiana State University AgCenter

2. Current NCEES Topics Primary coverage:Exam % V. D. Materials Properties; Bulk Solids 4% Overlaps with: I. D. 1. Mass and energy balances ~2% I. D. 2. Applied psychrometric processes ~2% V. C. Mass transfer between phases 4%

3. References PE Review Manual; FE Review Manual Ma, Davis, Obaldo, Barbosa, 1998. Engineering Properties of Foods and Other Biological Materials, ASAE. Mohsenin,1986. Physical Properties of Materials Rao, Rizvi, Datta, 2005. Engineering Properties of Foods. Merva, 1995. Physical Principles of the Plant Biosystem. Reynolds and Richards, 1996. Unit Operations and Processes in Environmental Engineering.

4. Standards D241.4: Density, specific gravity and mass-moisture relationships of grain for storage D243.e: Thermal properties of grain and grain products D245.5: Moisture relationships of plant-based ag products EP545: Loads exerted by free-flowing grain on shallow storage structures (S&E) Hellevang, AE-84, Temporary grain storage, http://www.ag.ndsu.edu/publications/landing-pages/crops/temporary-grain-storage-ae-84

5. Specific Topics Rheology Density, specific gravity Moisture content in ag and food products Thermal properties of grain and grain products Loads on structures from grain/flowing products Bonus: Psychrometrics (moisture 5D; ID Psychrometrics)

6. Rheology: The study of deformation and flow of matter (especially interesting in agricultural and biological materials)

7. Stress/Strain at the atomic level

9. Stress/Strain • Stress s = Fnormal to area/A • Shear Stress t = Fparallel to area/A • Strain e=dL/Lo [m/m; or %] • Young’s modulus E: s = Ee or E = s/e • For bar, d = PL/AE or FL/AE Tension compression

10. Stress-strain

11. Stress/strain for steel and rubbera) linearity (E constant?) b) average E typically lower in biomaterials

12. Hair

13. Hysteresis cycles of a rubber

14. Stress vs. Conventional StrainConventional: F/AoriginalTrue Stress: F/Aactual

15. Reminder: Stress/Strain • Stress s = Fnormal to area/A • Shear Stress t = Fparallel to area/A • Strain e=dL/Lo [m/m; or %] • Young’s modulus E: s = Ee or E = s/e • For bar, d = PL/AE or FL/AE Tension compression

16. Sample problem • A steel bar with known dimensions is subjected to an axial compressive load. The modulus of elasticity and Poisson’s ration are known. What is the final thickness of the bar? • A) 19.004mm • B) 19.996mm • C) 20.00mm • D) 20.004mm

18. Sample problem, food materials emphasis • A block of cheese with known dimensions is stacked and thus subjected to an axial compressive load. The modulus of elasticity and Poisson’s ration are known. What is the final thickness of the sample?

20. Stress-Strain Models

21. Creep behavior of cheddar cheese

22. Sample problem, materials emphasis • A block of cheese with known dimensions is stacked and thus subjected to an axial compressive load. After being stacked for 2 hours, what is the final thickness of the sample?

23. Solution • From the graph, strain after 2 hours (120 min) is approx 0.09. (be careful with extrapolation, but could use eqn for longer times). • Original dimensions: 100 x 100 x 100mm • Strain .09mm/mm so 100-100(.09) = 91mm tall • Poisson’s ratio 0.3 so expansion (in width) .03mm • 103x103x91mm tall

24. Stress relaxation of potato tissue

25. Stress/Strain (estimate E)A (chord/secant); B secant; C tangent apparent modulus

27. A: Shearing of a Newtonian Fluid B: Shear Stress Versus Shear Rate for Newtonian, Pseudoplastic (Shear Thinning), and Dilantant (Shear Thickening), Plastic, and Casson-Type Plastic Fluids Rheological Behavior of Fluids

28. Shear modulus and viscosity

29. Viscosity: m is resistance to flow F/A = t = mdu/dy Kinematic viscosity is viscosity over density: u = m/r Newtonian type Fluids

30. Values of Viscosity for Food Products and Agricultural Materials Which are Newtonian

31. µ =Viscosity (Pa s) µф=A Constant (Pa s) Ea=Activation Energy (Kcal g-Mole) R=Gas Constant (kcal/g-mole ºK) T=Absolute Temperature (ºK) Definition: Viscosity of Fluid Decreases with Temperature (Change is typically 2% per Degree Celsius) Arrhenius Relationship:

32. A: Apparent Viscosity as a function of time B: Shear Stress as a function of shear rate Behavior of Time-Dependent Fluids

33. Moisture impacts rheology

34. Break stretch (but don’t strain too much!)

35. Bulk Density • Bulk density is a property of particulate materials like sand or grain. It is defined the mass of many particles of the material divided by the volume they occupy. • Bulk Density = M/V [kg/m3] • The volume includes the space between particles as well as the space inside the pores of individual particles.

36. D241.4: food properties:bulk density, moisture

37. D241.4: grain properties

38. D243.3: thermal properties of grain

39. EP545: Loads exerted by free-flowing grain on shallow storage structures

40. EP545 • Total equivalent grain height: taken as the “average” grain height if the top grain surface is not horizontal (may not be, angle of repose) • Design approach, shallow grain holding structures: • Determine material properties (bulk density, angle of repose, coefficient of friction) • Use properties to calculate total equivalent grain height • Calculate static pressures (static vertical pressure at any point, static lateral pressure, and vertical pressure on floor) • Calculate resultant wall forces (resultant lateral force, resultant shear force) • Ex., Lateral force per unit length PH = LH2/2 where • L is the lateral pressure (function of depth z) and H is the equivalent grain height • Lateral pressure L(z) = kV(z) • Where L(z) = lateral pressure at grain depth z, psf (pounds per square foot) • k = ratio of lateral to vertical pressure, dimensionless and assumed to be 0.5 • V(z) = vertical pressure at equivalent grain depth z, psf • V(z) = Wg where W is the bulk density (lb/ft3), g is acceleration to due gravity

41. Hellevang • Overview of temporary grain storage (free reference http://www.ag.ndsu.edu/publications/landing-pages/crops/temporary-grain-storage-ae-84) • The pressure grain exerts per foot of depth is called the equivalent fluid density • Table 1. Approximate equivalent fluid density of some peaked grains. Crop Equivalent Fluid Densitylb/cu. ft Barley 20 Corn (shelled) 23Oats 14 Grain Sorghum 22 Soybeans 21 Sunflower (non-oil) 9 Sunflower (oil) 12 Durum wheat 26HRS wheat 24

42. Particle size distribution • Different for different materials! • Good reference: Chapter 35, CE manual, soil properties and testing • Sieve sizes and corresponding opening sizes (ASTM) • Typical particle size distribution (for soil): • Remember statistics for particle size distribution • Research on particle size distributions of nanoparticles • Normal distribution • Mean (“average”) particle size • Measure of dispersion of particle size (standard deviation, for example)

43. Particle size distribution

44. Sample questions • A building with an 8-foot high wall is storing grain. Grain was placed into the storage building and leveled until it is within 6 inches of the top of the wall. The grain density is 60 pounds per bushel. The lateral force per unit length at the base of the wall is most nearly • (a) 638, (b) 672, (c) 717, (d) 1360

45. Solution: use Hellevang Answer is B

46. Sample questions • If corn is treated as a non-cohesive granular material (shelled), the equivalent fluid density (pounds per cubic foot) is most nearly: • (a) 22 • (b) 28 • (c) 35 • (d) 56

47. Solution • Look up in Hellevang table! • Hellevang’s table for shelled corn: 23 #/sqft • Answer is A • Do not be deterred by the fact that the values are not exactly the same! PE questions are constructed to accommodate minor differences in tabulated values!

48. Break! • Stretch, drink of water, short break…

49. Water in Biological Materials Steve Hall, Ph.D., P.E.Louisiana State University AgCenter

50. Moisture impacts rheology