High-cycle Fatigue | Online Calculator

Fatigue Calculators







High-cycle Fatigue

In this calculation, a cyclic strength of the parts of defining dimension DL, with simple geometry (shafts, bushings, plates) and without welded joints is determined. The calculation is performed within 105 ÷ 107 loading cycles using any cycle asymmetry coefficient. When making this calculation, the shear component and tensile component of the load are taken into account.

The first part of the calculation determines the tensile fatigue strength σ-1part and shear fatigue strength τ-1part of the part (fatigue strengths of the parts under tension and shear). The fatigue reduction factor K is also calculated. In the absence of information on the material fatigue strength σ-1, it can be determined based on the tensile strength σm. The calculated value of the fatigue strength σ-1calc can be used in further calculations.

For the calculation, the relative stress gradient G, stress concentration factor αp and surface roughness Rz of the part should be specified.

After calculation of the fatigue characteristics of the part (σ-1part, τ-1part, K), you can calculate the number of part failure loading cycles N and safety factor n. For this purpose, it is necessary to specify the maximum and minimum tensile and shear stresses of the cycle (σmax, σmin, τmax, τmin). It is necessary to consider that nominal stresses are set without regard to concentrations in this case, calculated by the formulas of the form σ = P/A or σ = [Mx/Ix]*Y, etc. The stress setting obtained by finite element analysis with the simultaneous introduction of stress concentration factor αp = 1 will give an incorrect final result.

High-cycle fatigue
High-cycle fatigue calculation

INITIAL DATA

DL - Diameter or thickness of the part;


σm - Material ultimate tensile strength;


σ-1 - Material fatigue strength;


G - Stress gradient.
It can be found by formula dσ1 / σ1*dx. σ1 - stress in the assumed fracture zone;


Rz - Roughness of the part surface;


αp - Stress concentration factor;


σmax - Maximum tensile stress of the cycle;


σmin - Minimum tensile stress of the cycle;


τmax - Maximum shear stress of the cycle;


τmin - Minimum shear stress of the cycle.

RESULTS DATA

σ-1calc - Calculated fatigue strength of material. It can be applied if the values of fatigue strength for thr material are absent in standards;


σ-1part - Tensile fatigue strength of the part;


τ-1part - Shear fatigue strength of the part.


K - Fatigue strength reduction factor;


N - Number of cycles to failure;


n - Safety factor.

Part size (DL)

Tensile strength (σm)

Fatigue strength (σ-1)

Stress gradient (G)

Surface roughness (Rz)

Stress concentration factor (αp)

Circular cross-section

Polygonal cross-section

Anizotropic material

Fatigue strength (σ-1calc)

Tensile fatigue strength (σ-1part)

Shear fatigue strength (τ-1part)

Fatigue reduction factor (К)


Max. tensile stress (σmax)

Min. tensile stress (σmin)

Max. shear stress (τmax)

Min. shear stress (τmin)

Number of cycles to failure N

Safety factor n

BASIC FORMULAS

Fatigue strength σ-1calc:

σ-1calc = [(55/100) - (1/10000)*σm]*σm;

Fatigue reduction factor:

K = [(Kσ / K) + 1 / K - 1] * [1 / (Kυ*KA)];

Kυ = 1 - stress hardering coefficient.

Kσ / K = 2αp / (1 + Θσ)

Θ = (1 / 88.3)*(L/G);

L = π*DL for round cross-section; L = 2*DL for polygonal cross-section;

νσ = 0.211 - 0,000143*σm;

K = 1 - 0.22*lg(Rz)*[lg(σm / 20) - 1];

KA - anizotropic ratio;

Tensile fatigue strength:

σ-1part = σ-1 / K;

Shear fatigue strength:

τ-1part = 0.6*σ-1 / K;

Number of cycles to failure:

For σmin = -1*σmax and τmin = τmax:

[(σmax - σmin) / 2]m * N = σ-1partm * NG;

NG = 2*106 - base number of cycles to failure;

m = [5 + σm(MPa) / 80] / K.

INITIAL DATA

DL - Diameter or thickness of the part;


σm - Material ultimate tensile strength;


σ-1 - Material fatigue strength;


G - Stress gradient.
It can be found by formula dσ1 / σ1*dx. σ1 - stress in the assumed fracture zone;


Rz - Roughness of the part surface;


αp - Stress concentration factor;


σmax - Maximum tensile stress of the cycle;


σmin - Minimum tensile stress of the cycle;


τmax - Maximum shear stress of the cycle;


τmin - Minimum shear stress of the cycle.

RESULTS DATA

σ-1calc - Calculated fatigue strength of material. It can be applied if the values of fatigue strength for thr material are absent in standards;


σ-1part - Tensile fatigue strength of the part;


τ-1part - Shear fatigue strength of the part.


K - Fatigue strength reduction factor;


N - Number of cycles to failure;


n - Safety factor.

MATERIAL PROPERTIES

Steel

Tensile strength

MPa (psi)

Yield strength

MPa (psi)

Reduction in area

%

Fatigue strength

MPa (psi)

1015

424 (61.5*103)

324 (47*103)

69

217 (31.5*103)

1040

717 (104*103)

490 (71*103)

57

317 (46*103)

4130

758 (110*103)

655 (95*103)

63

304 (44*103)

5140

1000 (145*103)

862 (125*103)

58

380 (55*103)

6150

1434 (208*103)

1331 (193*103)

43

676 (98*103)

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