1. Lab #1 due TODAY!!!!!  HW#5 due Wednesday, 2/11
Lecture 9 – Deformation and Damage
Lab #1 due TODAY!!!!! 
HW#5 due Wednesday, 2/11
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

2. Lecture 9 – Deformation and Damage
Contact Stresses (handout from Mohsenin book)
Hertz Problem of Contact Stresses
Importance:
“In ag products the Hertz method can be used to determine the contact forces and displacements of individual units”
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

3. Lecture 9 – Deformation and Damage
Assumptions:
Material is homogeneous
Loads applied are static
Hooke’s law holds
Contacting stresses vanish at the opposite ends
Radii of curvature of contacting solid are very large compared to radius of contact surface
Contact surface is smooth
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

4. Lecture 9 – Deformation and Damage
Maximum contact stress occurs at the center of the surface of contact
a and b are the major and minor semiaxes of the elliptic contact area
For ag. Products, consider bottom 2 figures in Figure 6.1
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

5. In the case of 2 contact spheres, pg 354:
Lecture 9 – Deformation and Damage
In the case of 2 contact spheres, pg 354:
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

6. Lecture 9 – Deformation and Damage
To determine the elastic modulus, E…
for steel flat plate:
for steel spherical indentor:
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

7. Lecture 9 – Deformation and Damage
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

8. Lecture 9 – Deformation and Damage
Stacked particles (grain, seeds, dirt clods)
Figure 5.1
Dropped particles
Grain bin and handling damage
Figure 5.3 – Table 5.13: example of product testing.
Broken or damage material: determined using sieves.
Bruised fruit: determined by visual inspection, spectral reflectance, Magness-Taylor pressure tester.
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

9. BAE2022/BAE4400 Physical Properties of Biological Materials
HW#5 (continued)
Problem 3:
One half of a soybean seed is shaped into a beam with a square cross section of 1.15 mm by 1.15 mm. The sample beam is supported at two points 0.5 mm apart and a load is applied halfway between the support points. If the ultimate tensile strength is 5.23 MPa, what would be the force F (newtons) required to cause the sample to fail?
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

10. BAE2022/BAE4400 Physical Properties of Biological Materials
HW#5 Assignment
Problem 4:
A block of bologna has a bottom surface of 3 cm x 4 cm. The block is held securely in a meat slicing machine. The blade that moves across the top surface of the salami applies a uniform lateral force of 16 N. The shear modulus, G, of the bologna is 1.7 kPa. Estimate the how far the top surface of the salami will move compared to the bottom surface.
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

11. BAE2022/BAE4400 Physical Properties of Biological Materials
HW#5 Assignment
Problem 5:
An hydrostatic bulk compression test on a sample of oranges indicates an average bulk modulus of 325 psi. Testing of specimens from the same group of oranges shows a compression modulus E of 412 psi. Some of the whole oranges are subjected to a parallel plate test. The average orange diameter is inches and the axial deformation for the whole oranges was inches for a force of 4.25 lbs. Estimate the modulus of elasticity for the whole oranges using the Hertz formula for contact stresses.
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials

12. BAE2022/BAE4400 Physical Properties of Biological Materials
HW#5 Assignment
Problem 6:
A 8 lb. crate of apples is placed on top of an open box of strawberries (single layer). A previous test of a similar box of strawberries indicated a compression modulus of 312 psi. The average diameter of a strawberry is inches. The axial deformation at 8 lb is inches. Estimate the modulus of elasticity for the strawberries using the Hertz formula. (Bulk modulus = 218 psi)
1/26/07
BAE2022/BAE4400 Physical Properties of Biological Materials