## Presentation on theme: "CHAPTER 7 Fatigue Failure Resulting from Variable Loading"— Presentation transcript:

6/25/2007 CHAPTER 7 Fatigue Failure Resulting from Variable Loading Dr. A. Aziz Bazoune King Fahd University of Petroleum & Minerals Mechanical Engineering Department Dr. Abdelaziz Bazoune

Lecture 23

7-10 Stress Concentration Factor and Notch Sensitivity
In fatigue: Stress concentration should always be taken into account.

Some materials are not fully sensitive to notches and a reduced value of Kt is used and the maximum stress is calculated as follows: (7-29) Kf is the fatigue stress concentration factor, for simple loading: (Ex 7.7) or

Notch sensitivity q index is defined by
(7-30) To find use Fig for steel and Al alloys , for reversed bending or reversed axial load. For reversed torsion use Fig For cast iron use to be conservative. For , then and the material has no sensitivity at notch at all. For , then and the material has full notch sensitivity.

In analysis or design work
Find first from the geometry of the part Specify the material Find Solve for from the following Equation (7-31) Figure 7-20 has its basis the Neuber equation, which is given by (7-32) Where is defined as the Neuber constant and is a material constant.

Equating Eqs. (7-31) and (7-32) gives the notch sensitivity equation
(7-33) For steel, with in kpsi, the Neuber equation can be approximated by a third polynomial fit of data as (7-34) Where is defined as the Neuber constant and is a material constant.

Table 7-8 Heywood’s Parameter for steels
A distinction in the configuration of the notch is accounted for in the modified Neuber equation (after Heywood), where the fatigue stress-concentration factor is given as (7-35) Table 7-8 Heywood’s Parameter for steels where Table 7-8 gives values of for steels for transverse holes, shoulders and grooves. Feature (a)1/2 (in)1/2 Sut in kpsi (a)1/2 (mm)1/2 Sut in MPa Transverse hole 5/Sut 174/Sut Shoulder 4/Sut 139/Sut Groove 3/Sut 104/Sut

Example 7-3 (Textbook) A steel has a minimum strength of 520 MPa and a machined Surface. Estimate ka . SOLUTION From Table 7-4, a=4.51 and b=-0.265 From Eq.(7-18) therefore

Remark From this chart , it is seen that the surface factor Ka for machined or cold drawn is always less than 0.8.

Example 7-4 (Textbook) SOLUTION From Eq. (7-19) From Table (7-5)

Example 7-5 (Textbook) SOLUTION From Eq. (7-26)
Interpolating from Table (7-6) gives From Eq. (7-8)

Example 7-6 (Textbook) SOLUTION See next page Figure 7-20
Equations (7-32) and (7-34) Equations (7-35) SOLUTION From Figure A-15-9 From Figure (7-20), for Sut = 690 MPa and r =3 mm From Eq. (7-31) See next page

From Eq. (7-34) with Sut = 690 Mpa=100kpsi, and Substitute into Eq. (7-32) with r =3 mm From Table 7-8 From Eq. (7-35) With 2.5% lower than a) and b)