Journal of Failure Analysis and Prevention

, Volume 12, Issue 5, pp 445–484 | Cite as

Stress-Based Uniaxial Fatigue Analysis Using Methods Described in FKM-Guideline

Feature

Abstract

The process of prevention of failure from structural fatigue is a process that should take place during the early development and design phases of a structure. In the ground vehicle industry, for example, the durability specifications of a new product are directly interweaved with the desired performance characteristics, materials selection, manufacturing methods, and safety characteristics of the vehicle. In the field of fatigue and durability analysis of materials, three main techniques have emerged: nominal stress-based analysis, local strain-based analysis, and fracture mechanics analysis. Each of these methods has their own strengths and domain of applicability—for example, if an initial crack or flaw size is known to exist in a structure, a fracture mechanics approach can give a meaningful estimate of the number of cycles it takes to propagate the initial flaw to failure. The development of the local strain-based fatigue analysis approach has been used to great success in the automotive industry, particularly for the analysis of measured strain time histories gathered during proving ground testing or customer usage. However, the strain life approach is dependent on specific material properties data and the ability to measure (or calculate) a local strain history. Historically, the stress-based fatigue analysis approach was developed first—and is sometimes considered an “old” approach—but the stress-based fatigue analysis methods have been continued to be developed. The major strengths of this approach include the ability to give both quantitative and qualitative estimates of fatigue life with minimal estimates on stress levels and material properties, thus making the stress-based approach very relevant in the early design phase of structures where uncertainties regarding material selection, manufacturing processes, and final design specifications may cause numerous design iterations. This article explains the FKM-Guideline approach to stress-based uniaxial fatigue analysis. The Forschungskuratorium Maschinenbau (FKM) was developed in 1994 in Germany and has since continued to be updated. The guideline was developed for the use of the mechanical engineering community involved in the design of machine components, welded joints, and related areas. It is our desire to make the failure prevention and design community aware of these guidelines through a thorough explanation of the method and the application of the method to detailed examples.

Keywords

Structural fatigue Durability analysis Failure prevention Stress-based fatigue analysis Surface finish effect 

List of symbols

A

Fatigue parameter

ad

Constant in the size correction formula

aR

Roughness constant

aP

Peterson’s material constant

aN

Neuber’s material constant

aSS

Siebel and Stieler material parameter

aG

Material constant in the K t/K f ratio

aM

Material parameter in determining the mean stress sensitivity factor

B

Width of a plate

b

Slope (height-to-base ratio) of an SN curve in the HCF regime

bM

Material parameter in determining the mean stress sensitivity factor

bW

Width of a rectangular section

bnw

Net width of a plate

bG

Material constant in the K t/K f ratio

CR

Reliability correction factor

CD

Size correction factor

Cu,T

Temperature correction factor for ultimate strength

Cσ

Stress correction factor for normal stress

Cτ

Stress correction factor for shear stress

Cb,L

Load correction factor for bending

Ct,L

Load correction factor for torsion

CE,T

Temperature correction factor for the endurance limit

Cσ,E

Endurance limit factor for normal stress

CS

Surface treatment factor

Cσ,R

Roughness correction factor for normal stress

Cτ,R

Roughness correction factor for shear stress

COVS

Coefficient of variations

D

Diameter of a shaft

DPM

Critical damage value in the linear damage rule

d

Net diameter of a notched shaft

deff

Effective diameter of a cross section

deff,min

Minimum effective diameter of a cross section

G

Stress gradient along a local x-axis

\( \bar{G} \)

Relative stress gradient

\( \bar{G}_{\sigma } (r) \)

Relative normal stress gradient for plate or shaft based on notch radius

\( \bar{G}_{\sigma } (d) \)

Relative normal stress gradient for plate or shaft based on component net diameter or width at notch

\( \bar{G}_{\tau } (r) \)

Relative shear stress gradient for plate or shaft based on notch radius

\( \bar{G}_{\tau } (d) \)

Relative shear stress gradient for plate or shaft based on component net diameter or width at notch

HB

Brinell hardness

2hT

Height of a rectangular section

Kax,f

Fatigue notch factor for a shaft under axial loading

Kax,t

Elastic stress concentration factor for a shaft under axial loading

Kb,f

Fatigue notch factor for a shaft under bending

Kb,t

Elastic stress concentration factor for a shaft under bending

Kf

Fatigue notch factor or the fatigue strength reduction factor

Ki,f

Fatigue notch factor for a superimposed notch

Ks,f

Fatigue notch factor for a shaft under shear

Ks,t

Elastic stress concentration factor for a shaft under shear

Kt

Elastic stress concentration factor

Kt,f

Fatigue notch factor for a shaft under torsion

Kt,t

Elastic stress concentration factor for a shaft under torsion

Kx,f

Fatigue notch factor for a plate under normal stress in x-axis

Ky,f

Fatigue notch factor for a plate under normal stress in y-axis

\( K_{{\tau_{xy} , {\text{f}}}} \)

Fatigue notch factor for a plate under shear

Kx,t

Elastic stress concentration factor for a plate under normal stress in x-axis

Ky,t

Elastic stress concentration factor for a plate under normal stress in y-axis

\( K_{{\tau_{xy} , {\text{t}}}} \)

Elastic stress concentration factor for a plate under shear stress

k

Slope factor (negative base-to-height ratio) of an SN curve in the HCF regime

Mi

Initial yielding moment

Mo

Fully plastic yielding moment

Mσ

Mean stress sensitivity factor in normal stress

N

Number of cycles to a specific crack initiation length

2N

Number of reversals to a specific crack initiation length

NE

Endurance cycle limit

Nf,i

Number of cycles to failure at the specific stress event

nK

K t/K f ratio or the supporting factor

nK,σ(r)

K t/K f ratio for a shaft under normal stress based on the notch radius

nK,σ(d)

K t/K f ratio for a shaft under normal stress based on component net diameter or width at notch

nK,σ,x(r)

K t/K f ratio for a plate under normal stress in x-axis based on notch radius

nK,σ,y(r)

K t/K f ratio for a plate under normal stress in y-axis based on notch radius

nK,τ(r)

K t/K f ratio for a plate or shaft under shear stress based on notch radius

nK,τ(d)

K t/K f ratio for a shaft under shear stress based on component net diameter or width at notch

ni

Number of stress cycles

O

Surface area of the section of a component

q

Notch sensitivity factor

Rr

Reliability value

R

Stress ratio = ratio of minimum stress to maximum stress

RZ

Average roughness value of the surface based on German DIN system

r

Notch root radius

rmax

Larger of the superimposed notch radii

S

Nominal stress

SC

Nominal stress of a notched component

Sa

Stress amplitude

Sm

Mean stress

Smax

Maximum stress

Smin

Minimum stress

Sσ,a

Normal stress amplitude in a stress cycle

Sσ,m

Mean normal stress in a stress cycle

Sσ,max

Maximum normal stresses in a stress cycle

Sσ,min

Minimum normal stresses in a stress cycle

Sσ,ar

Equivalent fully reversed normal stress amplitude

Sσ,E

Endurance limit for normal stress at 106 cycles

Sτ,E

Endurance limit for shear stress at 106 cycles

SE

Endurance limit at 106 cycles

SN,E

Nominal endurance limit of a notched component

SS,E,Smooth

Nominal endurance limit of a smooth component at 106 cycles

SS,E,Notched

Nominal endurance limit of a notched component at 106 cycles

SS,σ,E

Endurance limit of a smooth, polish component under fully reversed normal stress

Sσ,FL

Fatigue limit in normal stress at 108 cycles

SS,τ,E

Endurance limit of a smooth, polish component under fully reversed shear stress

SS,τ,u

Ultimate strength of a notched, shell-shaped component for shear stress

\( S_{{{\text{S,}}\tau_{xy} , {\text{E}}}} \)

Endurance limit of a notched, shell-shaped component under fully reversed shear stress

Sτ,FL

Fatigue limit in shear at 108 cycles

SS,ax,E

Endurance limit of a notched, rod-shaped component under fully reversed axial loading

SS,ax,u

Ultimate strength of a notched, rod-shaped component in axial loading

SS,b,E

Endurance limit of a notched, rod-shaped component under fully reversed bending loading

SS,b,u

Ultimate strength of a notched, rod-shaped component in bending

SS,s,E

Endurance limit of a notched, rod-shaped component under fully reversed shear loading

SS,s,u

Ultimate strength of a notched, rod-shaped component in shear

SS,t,E

Endurance limit of a notched, rod-shaped component under fully reversed torsion loading

SS,t,u

Ultimate strength of a notched, rod-shaped component in torsion

SS,x,E

Endurance limit of a notched, shell-shaped component under fully reversed normal stress in x-axis

SS,x,u

Ultimate strength of a notched, shell-shaped component for normal stress in x-axis

SS,y,E

Endurance limit of a notched, shell-shaped component under fully reversed normal stress in y-axis

SS,y,u

Ultimate strength of a notched, shell-shaped component for normal stress in y-axis

St,u

Ultimate tensile strength with R97.5

St,u,min

Minimum ultimate tensile strength

St,u,std

Mean ultimate tensile strength of a standard material test specimen

St,y

Tensile yield strength with R97.5

St,y,max

Maximum tensile yield strength

\( S^{\prime}_{\text{f}} \)

Fatigue strength coefficient

\( {\text{S}^{\prime}}_{{\sigma , {\text{f}}}} \)

Fatigue strength coefficient in normal stress

T

Temperature in degrees Celsius

tc

Coating layer thickness in μm

V

Volume of the section of a component

σe

Fictitious or pseudo-stress

σe(x)

Pseudo-stress distribution along x

\( \sigma_{\text{E}}^{\text{e}} \)

Pseudo-endurance limit

\( {{\sigma}}_{ \max }^{\text{e}} \)

Maximum pseudo-stress at x = 0

\( \Upphi (z) \)

Standard normal density function

\( \varphi = 1/(4\sqrt {t/r} + 2) \)

Parameter to calculate relative stress gradient

γW

Mean stress fitting parameter in Walker’s mean stress formula

Notes

Acknowledgments

The following people should be recognized for their technical support in writing this report: Robert Burger, Peter Bauerle, and Richard Howell of Chrysler Group LLC.

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Copyright information

© ASM International 2012

Authors and Affiliations

  • Sean A. McKelvey
    • 1
  • Yung-Li Lee
    • 2
  • Mark E. Barkey
    • 3
  1. 1.Altair EngineeringAuburn HillsUSA
  2. 2.Chrysler Group LLCAuburn HillsUSA
  3. 3.University of AlabamaTuscaloosaUSA

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