Chapter 7 Fatigue Failure Resulting from Variable Loading Dr. A. Aziz Bazoune King Fahd University of Petroleum & Minerals Mechanical Engineering Department

Chapter Outline 7-1 Introduction to Fatigue in Metals     306 7-2 Approach to Fatigue Failure in Analysis and Design    312 7-3 Fatigue-Life Methods    313 7-4 The Stress-Life Method    313 7-5 The Strain-Life Method    316 7-6 The Linear-Elastic Fracture Mechanics Method    319 7-7 The Endurance Limit    323 7-8 Fatigue Strength    325 7-9 Endurance Limit Modifying Factors    328 7-10 Stress Concentration and Notch Sensitivity    335 7-11 Characterizing Fluctuating Stresses    344 7-12 Fatigue Failure Criteria for Fluctuating Stress    346 7-13 Torsional Fatigue Strength under Fluctuating Stresses    360 7-14 Combinations of Loading Modes    361 7-15 Varying, Fluctuating Stresses; Cumulative Fatigue Damage    364 7-16 Surface Fatigue Strength    370 7-17 Stochastic Analysis    373

LECTURE-22 7-9 Endurance Limit Modifying Factors 7-10 Stress Concentration and Notch Sensitivity

7-9 Endurance Limit Modifying Factors The rotating-beam specimen used in the laboratory to determine endurance limits is prepared very carefully and tested under closely controlled conditions. It is unrealistic to expect the endurance limit of a mechanical or structural member to match the values obtained in the laboratory. Some differences include Material: composition, basis of failure, variability Manufacturing: method, heat treatment, fretting corrosion, surface condition, stress concentration Environment: corrosion, temperature, stress state, relaxation times Design: size, shape, life, stress state, stress concentration, speed, fretting, galling

Marin’s Equation    Marin identified factors that quantified the effects of surface condition size loading temperature miscellaneous items Marin’s Equations is therefore written as: (7-17)

Marin’s Equation rotary-beam test specimen endurance limit (7-17) Endurance limit at the critical location of a machine part in geometry and condition of use rotary-beam test specimen endurance limit

(7-18) where is the minimum tensile strength and and are to be found in Table 7-4. Notice that and are different from those given by Eqs. (7-13) and (7-14) respectively. Table 7-4 Parameters for Marin surface modification factor, Eq. (7-18)

The size factor for bending and torsion may be given by: (7-19) For axial loading there is no size effect, so (7-20)

Non-Rotating Parts If a round bar in bending is not rotating or when a non-circular cross-section is used what is kb ? Assume that fatigue damage occurs in material that is stressed above 95% of its maximum stress. Equate the portion of a non-round part stressed with the similarly stressed area of a rotating beam specimen and obtain the effective diameter where. (7-23) as the effective size of a round corresponding to a non-rotating solid or hollow round. Table 7-5 provides areas of common structural shapes undergoing non-rotating bending.

Table 7-5 Areas of common non-rotating structural shapes Use de Eq. (7-23) for round and Eq.(7-24) for rectangular cross-sections

General form of load factor (7-25) Average kpsi MPa Bending 1 Axial 1.23 1.43 -0.078 0.85 Torsion 0.328 0.258 0.125 0.59 Values given in Textbook

(7-26) where

(7-27) Table 7-6 Effect of operating temperature on the tensile strength of steel.

If Reliability is not mentioned Otherwise Use Table 7-7 Table 7-7 Reliability factor Ka corresponding to 8% standard deviation of the endurance limit. If Reliability is not mentioned Otherwise Use Table 7-7

Residual stresses Directional characteristics (e.g. rolling, drawing) Corrosion Plating Metal spraying Frequency of cycling Fretting corrosion

7-10 Stress Concentration Factor and Notch Sensitivity In Chapter 4, it was pointed out that: The existence of irregularities or discontinuities, such as holes, grooves or notches, in a part increases the theoretical stresses significantly in the immediate vicinity of discontinuity. (4-48)

7-10 Stress Concentration Factor and Notch Sensitivity    

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

7-10 Stress Concentration Factor and Notch Sensitivity 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 (7-39) q for steel and Al alloys are given in Fig. 7-20 for reversed bending or reversed axial load for reversed torsion use Fig. 7.21. For cast iron use q = 0.20 to be conservative.

Figure 7-20 and Figure 7-21: Notch sensitivity curves.

References Design Theory http://deseng.ryerson.ca/DesignScience/ http://www-3.ibm.com/ibm/easy/eou_ext.nsf/Publish/6   Resources http://www.machinedesign.com/ASP/enggMechanical.asp?catId=373 http://www.engineersedge.com/ http://www.bearings.machinedesign.com/guiEdits/Content/BDE_6_4/bdemech_a02.aspx http://icrank.com/cgi-bin/pageman/pageout.cgi?path=/index_html.html Manufacturing http://www.efunda.com/processes/processes_home/process.cfm http://www.me.gatech.edu/jonathan.colton/me4210/mfgvideos.html