Fatigue Analysis of a Simple Shaft under Combined

Bending and Torsion

Material baseado em exemplo da HBM-nCODE e Ansys

PRESENTATION TOPICS

• Introduction

• SAE notched shaft Specimen

• Geometry and FEM model

• Boundary Conditions

• Linear Static Analysis Results

• Overview: Fatigue Life Estimation

• Conclusion

• References and Used Software

Introduction

Courtesy nCode

Introduction

Aloha Airlines Flight 243 (1988)

Introduction

• Fatigue life is estimated based on crack

initiation method.

• A notched shaft under combined bending and

torsion loads is analised.

• Two loading are combined , each load with its

own loading history.

• Linear stresses used for the calculation is

obtained from bending and torsion loading

independently.

• Standard SAE notched shaft [1] is modeled.

• This kind of specimen was used [1] to produce experimental

results for multiaxial fatigue ,and later, these results were

compared to 5 different theories to estimate life to multiaxial

fatigue (not the scope of this example).

SAE notched shaft specimen

Geometry

Finite Element Model: Mesh

Boundary Condition: Fixed Support

Boundary Condition: Force

Boundary Condition: Moment

• Two static analysis were performed

– Bending due to unitary force

– Torsion with a moment of 1000 N.mm

– Following slides present stress distribution and

dispacements

Linear Static Structural Analysis

Results: Applied load is unitary force

Von Mises Equivalent

Stress

Maximum

Principal Stress

Displacements

Results: Applied load is a Moment

Von Mises Equivalent

Stress

Maximum

Principal Stress

Displacements

Overview: Fatigue Life Estimation

• Crack Initiation(E-N) is the selected method

1. Stresses and strains calculated froma linear static analysis

2. Material Properties: E-N Curve and Cyclic Stress-Strain Curve

3. Variable Amplitude Loading: cycles counting performed through

Rainflow counting method

4. Neuber Correction to consider local plastic strain

5. Mean Stress Correction performed using either Morrow or Smith-

Water-Thompson Methodologies

6. Damage Accumulation and Fatigue Life Calculation peformed using

Palmgreen-Miner rule.

Select Method for Life Estimation: Crack Initiation

• Note:

• Ansys Design Life is not limited to crack initiation.

• One may perform:

– S-N analysis

– da/dN (Crack Propagation based of LEFM)

– Vibration Fatigue (frequency domain fatigue life

estimation)

– Among other capabilities

Select Method for Life Estimation: Crack Initiation

Material Properties

Análise de

Fadiga

Material Properties: Carbon Steel SAE1045_390_QT

Curva E-N

Curva Tensão Deformação Cíclica

Propriedades extraídas do banco de dados do Ansys Design Life

nCode Material Propoerties Library Available

Geometry for Life Estimation using FEM

Geometry for Life Estimation using FEM

Loading

Análise de

Fadiga

LOADING : FORCE

Loading History: Force x Time

LOADING: MOMENT

Loading History: Moment x Time

Fatigue calculation in Ansys Design Life

Fatigue calculation in Ansys Design Life

“Gliphs”

Ambiente de cálculo

Results

Análise de

Fadiga

Results

Results: Life

Results: Damage

Results: Spreadsheet format

New Calculation Cycle (optimization)

Análise de

Fadiga

• One may change and try different values without running

linear static analysis again:

– Material

– Mean Stress Correction

– Loading Value, Scale and Offset

– Certainty of Survival

– Other parameters ...

New Calculation Cycle (optimization)

• A typical example of Fatigue Life Estimation was presented

• Finite Element Method (Ansys WB) and Ansys Design Life

were used to perform the analysis

• Selected Method for Fatigue Life Estimation: E-N

• Remember: Good Estimation is expected if you have good

imput data ( material properties, geometry and loading)

• We expect to demonstrate the easy of useness and flexibility

of these calculation tools.

Conclusion

• [1] Bannantine, J.A. Comer, J.J., Handcrock, J.L.

Fundamentals of Metal Fatigue Analysis Prentice-Hall

1990

• [2] nCode - DesignLife Worked Examples:

3 AN-NC-DL-WE 14.50.083 © 2012 HBM UK Ltd.

References

1. Ansys Mechanical 14.5

2. Design Life - GlyphWorks V8.0 ISR3 Release Build 125

Used Software

THANK YOU !!

OBRIGADO!!