S-N Curve for Torsional Shear PDF

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S-N Curve Description: Fatigue properties of materials are described using the fatigue limit or the S-N curve. The S-N curve describes the relation between cyclic stress amplitude and number of cycles to failure. On the horizontal axis the number of cycles to failure is given on logarithmic scale. On the vertical axis the stress amplitude of the cycle is given. S-N curves are derived from fatigue tests. Tests are performed by applying a cyclic stress with constant amplitude on specimens until failure of the specimen. In some cases, the test is stopped after a very large number of cycles (N>10^6). The results are then interpreted as infinite life. The purpose of this S-N curve is to identify the life of material how long it can stand with its position and how times it takes to fail. We also can identify the failure point at which material can break down.

S-N diagram of three wires:

S-N Curve for Torsional Shear 800

700

Fatgue Strength(MPa)

600

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0 0

2000000

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No. of Cycles(N) Sfw for D1(MPa)

Sfw for D2(MPa)

Sfw for D3(MPa)

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Wire1 Diameter: Sfw(dia1) 800

Fatgue Strength sfw(MPa)

700 600 500 400 300 200 100 0 0

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10000000

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No. of Cycles(N)

Wire2 Diameter: Sfw(dia2) 700

Fatgue Strength sfw(MPa)

600 500 400 300 200 100 0

0

2000000

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No. of Cycles(N)

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Wire3 Diameter: Sfw(dia3) 700

Fatgue Strength Sfw(MPa)

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No. of Cycles(N)

Equations and Calculations: For finding fatigue strength of different diameter of (chrome vanadium) wire, for this first, I find S ut, Sut = Adb For this A and b value I used table 14.4 (A232) For different three diameter I find three values of Sut, Diameter (4.033mm) wire Sut = 1559.59 MPa Diameter (7.033mm) wire Sut = 1438.537 MPa Diameter (10.033mm) wire Sut = 1366.163 MPa And, for Sms = 0.6*Sut Diameter (4.033mm) wire Sms = 935.754 MPa Diameter (7.033mm) wire Sms = 863.122 MPa Diameter (10.033mm) wire Sms = 819.697 MPa And for Fatigue strength of (Chrome v) wire, For life cycle 103 Sfw = 0.46*Sut For life cycle 104 Sfw = 0.44*Sut 3

For life cycle 105 Sfw = 0.42*Sut For life cycle 106 Sfw = 0.40*Sut For life cycle 107 Sfw = 0.38*Sut

Comments: 1. From this I concluded that by increasing the diameter of wire, fatigue strength also increases. Fatigue strength depends on diameter of wire. 2. As we noticed form the diagram that at same number of cycles with different diameter have different fatigue strength value and with greater diameter have largest value than smaller diameter wires.

3. And as in this diagram it is a numerically solution (S- N diagram) but in actual there is a larger number of cycles are applied to achieve their S–N diagram.

Reference: 1. https://www.fatec-engineering.com/2018/02/20/description-of-a-s-n-curve/

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Paper Work Calculations:

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