1. CONTACT STRESS BETWEEN BODIES

2. Points to be covered: Introduction Hertz theory Firmness and hardness
Mechanical damage
Dead load and
Impact damage

3. Contact stresses between bodies
Hertz theory:
In 1896 Heinrich Hertz proposed a solution for contact stresses in two elastic isotropic bodies. Such as the case of two spheres of same material touching each other.

4. Assumptions: The materials of the contacting bodies is homogeneous.
The load applied are static.
Hooke’s low holds.
Contacting stresses vanish at the opposite ends of the body.
The radii of curvature of the contacting solid are very large when compared with the radius of the surface of contact.
The surface of the contacting bodies are sufficiently smooth so that tangential forces are eliminated.

5. Hertz theory gives the
contact area
Maximum compressive surface stresses
Combined deformation of the contacting bodies at the point of contact.
In fig show the general case where the two bodies, 1 and 2, with minimum and maximum radii of curvature R1 & R’1 for body 1 and R2 & R’2 for body 2 are pressed together with load F.

7. Maximum contact stress, Smax Where, a and b are the major and minor semi axes of the elliptic contact area Note: The maximum contact stress is 11/2 times the average pressure on the surface of contact.

8. The values of a and b in may be calculated from the following equation:
Where,
m and n are constants
R= radii of curvature
µ and E = Poisson’s ratio and modulus of elasticity of the contacting bodies,

9. The combined deformation of the two bodies along the axis of load at the point of contact is given by The values of k, m and n depend on the principle curvatures of the bodies at the point of contact

10. For the case of a spherical body on flat plate can be obtained by
R1= R’1= ∞ for the plane R2 =R’2 = d/2 for the spherical body D= diameter of the sphere The radius of the circular contact area, a a = 0.721(Fad)1/3 The maximum contact stress, Combined deformation at the point of contact,

11. For the case of two spherical bodies in contact can be obtained

12. Firmness and Hardness Firmness:
Firmness is an important textural attribute in fruits and vegetables in connection with readiness of the crop for harvest, quality evaluation during storage for fresh market as well as prior to processing, and its influence on the correlation between the quality of the raw material and that of the processed or manufactured product.

13. Hardness:
Hardness of grains is an important in evaluating their feeding value as well as their size reduction and milling characteristics. Hardness of several agronomic crops as well as some manufactured food products is also important to find out other physical and chemical properties during and after processing.

14. Mechanical damage
Damage is the failure of the product under either excessive deformation when it is forced through fixed clearance or excessive force when it is subjected to impact.
In seeds and grains, most of the damage occurs in handling as well as mechanical conveyors and other equipment.
The damage resulting from the impact forces

15. Causes of mechanical damage
external forces under static or dynamic condition or internal forces.
Internal forces can be result of physical changes such as in temperature and moisture content or chemical and biological changes.
Failure is usually occure through a rapture in the internal or external cellular structure of material.
The maximum shear theory assumes that failure begins when the max shear stress in the material becomes equal to one half of the max stress at the yield point in a simple tension test.

16. Impact load Impact load:
Impact is the force created by the collision are exerted and removed in very short period of time and that the collision produces stress waves which travel away from the region of contact.

17. THANK YOU