1. ELASTIC PROPERTIES OF MATERIALS

2. Elastic Properties of Foods
Many food systems are solids or display partial solid behavior
Knowledge of solid behavior important to understanding solids, semi-solids, and visco-elastic foods
To understand food texture, we need to understand how foods respond when we apply forces to them

3. Elastic Properties and Texture
Food texture is evaluated by application of forces to the food
The perceived texture of a food is a combination of its mechanical properties and structure
Measurement of elastic properties well defined; measurement of “texture” more tenuous

4. Solid Foods Solid behavior is characterized by elastic properties
Examples of elastic solid foods:
egg shells
macaroni noodles
hard candies

6. Strength of Materials
The study of the elastic properties of materials usually falls under “strength of materials: how do bridges, concrete, steel bolts respond to small deformations
Food texture concerned with weakness of materials- how forces cause large deformations in the food that it breaks or disintegrates

8. Stress/Strain Relations
Solids described by the strain produced by an applied stress
Stress: force per unit area that causes a strain
Strain: some fractional change in the dimensions of a material due to stress.
The type of strain produced depends on the way in which the stress is applied

9. Normal vs Shear Stress
Normal Stress: acts perpendicular to a surface area
Area A
Force

10. Shear Stress: acts parallel to the area
Force

11. Stress and Strain If a force acts on an eraser, it will stretch
If the cross-section of the eraser is twice as large it will take twice the force to stretch it the same amount. The stress is defined as the force per area

12. Usually expressed as a fraction of change per length of material
The strain is a measure of how much the material deforms when subject to a stress
Usually expressed as a fraction of change per length of material l
Area A F ∆l F

13. Hooke’s law
Stress = Constant X Strain

14. Area A
Force F
Force F
Force 2 F
Force 2 F
Area 2A

15. The stress is opposed by intermolecular forces within the material
The stress is opposed by intermolecular forces within the material. The more the material, the greater the internal force resisting the stress.

16. Types of Stress Three types of stress are possible
Tension stress
Compression stress
Shear stress
Other stresses (twisting, bending) are derived from these

17. Tension Stress
Tension stress is the force per unit area that produces a small elongation of a material (l) l
Area A F ∆l F F

19. Compressive Stress
Compression stress is the force per unit area that produces a reduction in length
Area A ∆l F F F l

21. Shear Stress
Shear stress acts tangent to a surface and moves the surface out of line with layers underneath F

23. Hydrostatic Pressure
Hydrostatic pressure is a variation of compression in which the stress acts inward in all directions

24. ELASTIC MODULI
The rheological properties of solids are described by elastic moduli which relate the amount of deformation caused by a given stress
Assumptions:
elements are elastic: complete recovery occurs when stress is removed
small strains are applied (1-3%)
material is continuous, homogeneous

25. There are 4 elastic moduli for solids, all of which are variations of Hooke’s law
Stress = Constant X Strain

26. Young’s Modulus:

27. Shear Modulus:

28. Bulk Modulus:

29. Poisson’s Ratio
Usually, when you stretch a sample in one direction, it contracts in the other direction
Defined by Poisson’s ratio µ

31. The elastic moduli and Poisson’s ratio are sufficient information to describe the elastic properties of a material

32. Superposition Principle
In the simple case, stress is linearly proportional to the strain produced
The resulting displacements of more than one stress is the sum of the displacements

33. Example: Volume Compression
For a block in a tank of water, we could consider linear compression along each direction

34. Force in any one direction is countered by a force due to squeezing of the other sides
Thus:

35. For a small displacements

36. Bending
An objects resistance to bending depends on both material properties and its shape (not just cross sectional area)
Bending is a combination of compression and tension

37. The forces form a couple that tend to rotate the bar

38. The upper half of the bar is compressed; the lower half is under tension
Upper and lower surfaces are distorted the most and experience the greatest compression and tension forces

39. The beam bends with radius R. The torque is given by:

41. Buckling
Failure often occurs due to large torques rather than simple linear compression or tension
Large diameter-thin wall tructures tend to fail by buckling
If the center of gravity of a hollow cylinder is off-center, the weight will exert a force about a point

43. Twisting
If a cylinder is fixed at one end, and coupled forces are applied at the other, a torque is produced that twists the object.

44. The problem is similar to bending but we consider a polar moment of inertia
The torque T is related to the deformation a

45. Large Deformations
As more and more force is applied over an area, the strain increases
After a certain point, Hooke’s law may no longer apply

46. A typical stress-strain curve

47. Linear Region: Hooke’s law obeyed
Stress proportional to strain
Linear limit reached at point A

48. A to B: material still elastic and returns to orignal state when force removed
Stress not proportional to strain
Point B: elastic limit

49. B to C: further stress causes rapid increase in strain
If force removed object does not return to original dimensions
Point C: ultimate tension strength. Even smaller force will cause deformation

50. D: fracture point
Curve from B-D: plastic deformation
Area under curve up to D is work required to break the material

51. B-D is “plastic deformation”
Brittle materials: C and D are close together
Ductile materials: C and D are far apart
Area under curve up to point D is energy needed to break the material

52. Brittle

53. Ductile

54. Malleability: a material's ability to deform under compressive stress; this is often characterized by the material's ability to form a thin sheet by hammering or rolling.
Ductility: mechanical property used to describe the extent to which materials can be deformed plastically without fracture

55. Ductile fracture
Completely ductile fracture

56. Ductile materials deform quite a bit (through plastic deformation) before they break
Brittle materials deform very little before they break

57. Brittle material
Stress
Ductile material
Strain

58. Ductile Brittle

59. There are two principal stages of the fracture process:
Fracture is a process of breaking a solid into pieces as a result of stress.
There are two principal stages of the fracture process:
Crack formation
Crack propagation

60. Ductile fracture
Ductile materials undergo plastic deformation and absorb significant energy before fracture.
A crack, formed as a result of the ductile fracture, propagates slowly and when the stress is increased.

61. Permanent deformation at the tip of the advancing crack that leaves distinct patterns in SEM images.
Fractures are perpendicular to the principal tensile stress, although other components of stress can be factors.
The fracture surface is dull and fibrous.There has to be a lot of energy available to extend the crack.

62. Brittle Fracture
Very low plastic deformation and low energy absorption prior to breaking.
A crack, formed as a result of the brittle fracture, propagates fast and without increase of the stress applied to the material.
The brittle crack is perpendicular to the stress direction.

63. There is no gross, permanent deformation of the material.
Characteristic crack advance markings frequently point to where the fracture originated.The path the crack follows depends on the material's structure. In metals, transgranular and intergranular cleavage are important. Cleavage shows up clearly in the SEM.