1 fatigue - Fundamentals of machine design and drawing 考试用图标 PDF

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Fundamentals of machine design and drawing 考试用图标...

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From%the%Specimen%– To%the%Component • There&are&many&factors&affecting&fatigue&strength • Factors&related&to&the&component: – – – –

Size,&CS Notches,&Kf Surface&finishing,&CF Surface&treatments&(mechanical,&thermal&or&chemical,&coatings…)

• Factors&related&to&service&conditions: – – – –

Loading&mode,&CL Reliability, CR Temperature Environment&(moisture,&corrosives…)

• The&fatigue&limit&of&the&component&material&σCD-1 will&be&then:

s Dc -1 = s D -1 (Õ Ci ) • With&σD-1 fatigue&limit&of&the&material&(in&reverse&bending)

From%the%Specimen%– To%the%Component Scale%Effect%CS 1.00

CS

0.95

Bending&and&torsion&(CS)

0.90 0.85 0.80 0.75 0.70

Tension&Compression&(CL)

0.65 0.60 10

30

50

70

90

110 130 150 170 190

d [mm]

• Only&for&loading&modes&with&stress&gradient&(bending&and&torsion) • Not&to&be&considered&in&tension&and&compression&(with&CL =&0.7) Machine Design - Fatigue

45

From%the%Specimen%– To%the%Component Surface%Finishing%Effect%CF 0.8 1.6

0.9

3.2 6.3

0.8 10 0.7 40

0.6 0.5

160

0.4 200

Surface roughness, Ra (μm)

CF

1.0

400

Machine Design - Fatigue

600

800

1000

1200

1400

Rm (MPa) 46

From%the%Specimen%– To%the%Component Reliability%Effect%CR • Endurance&data&reported&in&the&literature&are&B50&values • Therefore,&they&correspond&to&50%&reliability&(=100%&- 50%& of&failure&probability) • If&a&greater&reliability&(=smaller&probability&of&failure)&is& required,&a&reduced&strength&is&expected Reliability 50% 90% 95% 99% 99.9% 99.990% 99.999% 99.9999% 99.99999% 99.999999% 99.9999999%

CR Factor 1.000 0.897 0.868 0.814 0.753 0.702 0.659 0.620 0.584 0.551 0.520

Stress%Concentration and%Notch%Sensitivity • Discontinuities,&similarly&to&what&happens&in&static&loading,&by& increasing&the&effective&stresses,&reduce&the&fatigue&strength&(or& the&fatigue&life)&of&a&material • This&reduction&is&taken&into&account&with&a&Fatigue0StressConcentration0Factor0Kf00:&that&is&defined&by&rating&the¬ched&and& unnotched&endurance&limits&obtained&by&testing

s N ,unnotched specimen Kf = s N , notched specimen

or, more precisely

s D-1,unnotched specimen Kf = s D-1,notched specimen

• The&effect&on&fatigue&is&less&than&the&theoretical&value: 1 £ K f £ Kt • A&Notch0Sensitivity0Factor0q is&defined&as&follows: K f -1 q= Kt -1

Machine Design - Fatigue

50

Stress%Concentration and%Notch%Sensitivity • The&Fatigue Stress&Concentration&Factor&can&be&calculated as:

K f = 1 + q(K t - 1)

1

Notch/sensitivity,/q

0.8

Reversed&bending& or& reversed&axial& loads

0.6 0.4 Steels Aluminum/alloy

0.2

0 0

0.5

1

1.5 2 2.5 Notch/radius,/r (mm)

3

3.5

4

• Notch&sensitivity&q depends&on&the&material • Therefore&Kf depends on&the&material&(q),&the¬ch&geometry& and&loading&mode&(Kt)

Stress%Concentration and%Notch%Sensitivity • The&Fatigue Stress&Concentration&Factor&can&be&calculated as:

– r notch&radius& – ρ average&grain&size

Grain+size, Ör (mm½)

K f = 1 + q(K t - 1) • For&steels the&Neuber&equation&can&be&used: 1 q= r 1+ r 0.5 • With:

0 0

1000

2000

Ultimate+Tensile+Strength,+Su (MPa)

Machine Design - Fatigue

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