LIMIT OF FATIGUE STRESS-ENDURANCE LIMIT STUDY

LIMIT DEFINED FOR FLUCTUATING STRESSES : ENDURANCE LIMIT

Limit of Fluctuating stresses

All components subjected to fluctuating stresses contains a Max. Stress Amplitude value for which it completes infinite cycles(10⁶) of revolutions. This max. value of Stress Amplitude with a definite magnitude gave us concept of ENDURANCE LIMIT(E.L)

“{E.L}-APPROXIMATE ESTIMATION”- NECESSITY OF THIS BIG STEP:

Laboratory method of determining Endurance Limit of materials ,although being precise ,was also time consuming and long termed process. Also, a single S N CURVE to plot required many no. of tests on the material . So, finding endurance limit {E.L} for each and every material became difficult.

To solve this issue, approximate estimation of E.L ( Endurance Limit) taken in design.

This always come in use when experimental data of E.L are not given.

STUDY OF ENDURANCE LIMIT {E.L} AND APPLICATION OF THIS ANALOGY IN DESIGN :

Two Separate notations for Endurance strength used in this analysis :

S_e‘= Endurance strength of a rotating beam specimen that subjected to reversed bending stress (N/mm²)

S_e= Endurance strength of a mechanical component that subjected to reversed bending stress (N/mm²)

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APPROXIMATE RELATIONSHIP BETWEEN S_e‘ and S_ut ( FOR VARIOUS MATERIALS)

FOR STEELS	Se‘=0.5 Sut
CAST IRON AND CAST STEELS	Se‘=0.4 Sut
WROUGHT ALUMINUM ALLOYS	Se‘=0.4 Sut
CAST ALUMINUM ALLOYS	Se‘=0.3 Sut

This difference in E.L values S_e‘ and S_e came due to a no of factors. These factors came due to working conditions specifications. For rotating beam specimen , there are standard specifications and working conditions which are fixed.

But , on the other hand, the actual component face different specifications and working conditions.

So, various factors came in study in order to compensate this effect. These factors are , therefore, called “derating” factors.

Derating factors : These factors have the duty to degrade or reduce the E..L of the standard rotating beam specimen until it matches with the test component’s E.L value.

DERATING FACTORS : IMPORTANT FACTORS TO BE STUDIED

1) SURFACE FINISH FACTOR ( K_a) :

Surface of rotating beam specimen polished to mirror finish. Final polishing done in axial direction to avoid circumferential scratches. The actual component is not so finished in surface terms . Here , stress concentration arises due to surface finish variations. Therefore, E.L values seems reduced here. The surface finish factor (K_a) now comes in action to compensate this reduction effect.

K_a values depends on the parameter of Ultimate tensile strength (S_ut).

Therefore, as ultimate tensile strength increases, the K_a values decreases .

For finding K_a, refer to the chart given in DESIGN OF MACHINE ELEMENTS, V B BHANDARI .

2) SIZE FACTOR ( K_b ) :

The rotating beam specimen taken with fixed diameter (7.5 mm). It has been observed that larger machine parts induces larger flaw or fault chances in a component. This leads to stress concentration , and ultimately reduced E.L values.

Therefore , K_b values came in as to compensate the reduction between standard and practical values.

d ≤  7.5 mm	Kb = 1.0
7.5 mm < d ≤  50 mm	Kb = 0.85
d > 50 mm	Kb = 0.75

3) RELIABILITY FACTOR ( K_C) :

The greater the likelihood of survival of a part, greater will be the reliability of a material.

The standard deviation of E.L tests is 8 % of the mean values.

The reliability factor ( K_c) used to achieve this reduction due to stress concentration effects on the material.

RELIABILITY R (%)	KC
50	1.000
90	0.897
95	0.868
99	0.814
99.9	0.753
99.99	0.702
99.999	0.659

4) MODIFYING FACTOR TO ACCOUNT FOR STRESS CONCENTRATION (K_d):

The reduction in E.L values are due to stress concentration. The stress conc. factor for cyclic loadigng found out to be usualkly lesser than the theoretical stress conc. factor.

So, a modifying factor is taken to account for this reduction . It is denoted by K_d.

K_d= 1/ K_f