FEMFAT4.7 疲劳强度评估核心方法与影响因子

摘要：

本文为 FEMFAT 4.7 疲劳强度评估核心理论手册，系统阐述基于 Miner 线性累积损伤准则的疲劳寿命计算方法。手册以局部构件 S‑N 曲线为核心，通过应力梯度、平均应力、表面粗糙度、表面强化、温度、统计、工艺参数等多因子修正，结合临界切面法处理多轴应力状态。采用 Neuber 准则考虑局部塑性与平均应力重分布，提供 Haigh 图、雨流计数与损伤等效数据压缩功能，覆盖钢、铸铁、铝镁合金等材料。完整给出 S‑N 曲线三参数（疲劳极限、斜率、循环极限）计算流程，为有限元节点疲劳强度精准评估提供完整理论与算法支撑。

Contents

MAGNA POWERTRAIN

CONTENTS 1

NOTATION AND ABBREVIATIONS 2

1       INTRODUCTION 4

2       THEORETICAL BASIS   6

2.1         LOCALPLASTIFICATION 8

2.2          THE STRESS MECHANICS SERIES INFLUENCE  9

2.3          OPERATIONAL STRENGTH OF COMPONENTS 10

3       THE SYSTEM OF S/N CURVES 11

3.1          INFLUENCE OFTHE STRESS GRADIENT 12

3.2          THEHAIGH DIAGRAM 17

3.3          THE CRITICAL CUTTNG PLANE METHOD 19

3.4          THE MEAN STRESS INFLUENCE ON THE LOCALCOMPONENT S/NCURV 22

3.4.1      The mean stress influence on the endurance stress limit  22

3.4.2      Mean stress influence on the slope of theS/N curve    25

3.5          THE TECHNOLOGICALINFLUENCE OF STANDARDS 31

3.5.1      The surface roughness influence factor  31

3.5.2      The influence factors ofsurface treatments  34

3.5.3      Influence of tempering condition    41

3.6          OTHER INFLUENCE FACTORS 42

3.6.1      The technological parameter influence     42

3.6.2      The thermal influence factor  46

3.6.3      The statistical influence factor    48

3.7          THE SUPERPOSTTION OFINFLUENCE FACTORS 49

3.7.1      The endurance stress limit of the local componentS/N curve   49

3.7.2      The slope of the local componentS/N curve    50

3.7.3      The endurance cycle limit of the local componentS/N curve   50

4       BIBLIOGRAPH 51

Notation and abbreviations

IFK2               Slope exponent of the incipient fracture S/N curve

IFK3               Material group-dependent exponent

f1,af                  Combined factor for surface roughness and degree of forging influencing the

endurance stress limit

f2,af                     Combined   factor   for   the   technological   treatment   of   surfaces   influencing   the

endurance   stress   limit

ftot,af                  Overall factor influencing the endurance stress limit

fGS,af                General surface factor influencing the endurance stress limit

fTI,af                 Temperature-dependent factor influencing the endurance stress limit

fTP,af                Technological parameter influencing the endurance stress limit

fm,af                  Mean stress factor influencing the endurance stress limit

fm,sf                  Mean stress factor influencing the slope

fm,cf                 Mean stress factor influencing the endurance cycle limit

fGR,af                Stress gradient factor influencing the endurance stress limit

fGR,sf                 Stress gradient factor influencing the slope

fGR,cf                Stress gradient factor influencing the endurance cycle limit

fsT,af                Statistical factor influencing the endurance stress limit

fDF,af                Factor of the degree of forging(can be defined by user)influencing the endurance

stress limit

fsR,af                Surface roughness factor influencing the endurance stress limit

fsP,af                Shot peening factor influencing the endurance stress limit

fRO,af                Rolling factor influencing the endurance stress limit

fCH,af                Carburizing factor influencing the endurance stress limit

fNI,af                 Nitriding factor influencing the endurance stress limit

fcN, af                Carbonitriding factor influencing the endurance stress limit

fH,af                 Induction hardening factor influencing the endurance stress limit

fFH,af                Flame hardening factor influencing the endurance stress limit

Kc                   Slope of the local component S/N curve KM                  Slope of the material S/N curve

Ncf,M               Endurance cycle limit of the material S/N curve

Ncf,C                Endurance cycle limit of the local component S/N curve

OUTS                 Ultimate tensile stress

Oy                  0.002 strain offset yield strength of the material

σ           Local stress

Oaf,C               Endurance stress limit of the local component S/N curve

OA,tsc                Material alternating stress limit for tension/compression

OA,b                Material alternating stress limit for bending

T                     Local shear stress

TF                     Shear yield point

TA,to                 Alternating  stress limit(shear  stress)under torsion

Xmax                 Absolute stress gradient

X'                  Relative stress gradient

a                                     Amplitude*   m                         Mean stress*  u                                   Upper stress*

1                            Lower stress*

e                                 Equivalent stress*

af                          S/N curve endurance stress limit* sf                          Slope of the S/N curve*

cf                    S/N curve endurance cycle limit*

*                     Recurring indices

1   Introduction

Estimates of fatigue life are made using FEMFAT by means of the influence factors method for the technical incipient fracture criterion.S/N curves are calculated at the FEM nodes from the material  strength data.These  S/N  curves  are influenced by the local component properties,the prevalent stress conditions and,in particular,the stress gradient.The program is based on our own experience  and  methods,and  the  methods  described  in  the  former  TGL19340  and  the  FKM Guideline [FKM94]for determining influence factors.By comparing the external stresses and the operational strength of the component,the lifetime of the component can be estimated on the basis of the linear hypothesis of damage accumulation after Miner [MINER 45]).

The  FEMFAT BASIC  program  uses  the  load  spectrum  as  the  external  stress,similar  to  the concept  of  nominal   stress.The   treatment  of  the   various   stress  relationships(Ri,Oai)in  the individual load spectrum stages is performed in  FEMFAT by determining the local component SN curve corresponding to the respective stress relationship(Ri,Oai)

Fig. 1.1           Schematic representation of a component S/N curve

A local component S/N curve,such as that shown  in Fig.1.1,is described in a log-log plot by the following three parameters:

● the endurance stress limit σaf,C;

·the endurance cycle limit Nef,c and;

·the   slope   kc.

The main purpose of the influence factors method is to determine these three parameters in terms of the unique "Iocal conditions".The method therefore emphasizes placing the parameters into the correct functional relationship to each other,see Equations 1.1,1.2 and 1.3.

Table 1.1 shows the influence factors that can be taken into consideration in FEMFAT. Their influence on the local component S/N curve is explained in the following sections in order to provide the user with an overview of the most important theoretical fundamentals of the basic module.More detailed information can be taken from the appropriate cited literature.

2  Theoretical basis

The Miner linear damage accumulation hypothesis [MINE45]forms the basis for almost all known methods of estimating fatigue life in operational situations (Equation 2.1).

                                  (2.1)

The damage contribution of a stress cycle of a random stress with the stress amplitude  Sai and mean stress S mi is given as the reciprocal of the number of cycles that can be measured(Di=1/N;) under the same stress and operating conditions as for an S/N test Ni=N(Sai,S mi).The individual damage contributions are totalized in the course of the fatigue life estimate.When a damage total D=1 is reached,component failure occurs.

The stress amplitude Sa and the mean stress S m can,for example,be defined as the nominal or local stress.Accordingly,these concepts are known as the nominal stress concept or principal of local  strains. In  FEMFAT, these are the local elastic  stresses,and can be determined from the external stress by means of a structural elastic FEM an alysis of each component.

The structural elastic FEM ana lysis can be carried out using a unit load.Because of the linear relationship,the external stress,given as load spectra(stepped load spectra,synthetic load spectra) or a rain-flow matrix,can be directly transformed into the local elastic stresses of an FEM node. This makes the relatively time-consuming notch base stress simulation unnecessary.Any local plastification occurring,and the resulting series influence caused by stress mechanics processes, must therefore be dealt with separately.

The following modifications to the original Miner rule(OM)can be used in FEMFAT in order to deal with the damaging effects of stress cycles below the endurance stress limit of the component S/N curve:

·The elementary Miner rule(EM).Using the elementary Miner rule,the creep strength domain SN  curve with slope k is extended until the stress amplitude oa=0.

·The modified Miner rule(MM).Below the endurance  stress  limit oE,the modified Miner rule proposed by Haibach [HAIB 83]employs a fictitious extension to the creep strength domain with a slope 2k-1.

2.1 Local plastification

Whenever the local stress exceeds the material's yield stress,local plastification occurs,which is considered by  FEMFAT in ana logy to the  principal  of  local  strains.The  first  stress-curve  is adopted as the history for all stress cycles.The displacement of the closed hystereses loops caused by the local plastification is then taken into consideration. Fig.2.1.1   schematically  shows  this procedure.Transformation of the local elastic stress to the elastic-plastic stress is given by the Neuber rule [NEUB 61].

Fig.2.1.1         Schematic representation of the mean stress redistribution

2.2 The stress mechanics series influence

Load spectra describe the size and frequency of the stress cycles expected during the design working life of a component.A load spectrum does not contain any information on the sequence of occurrence of individual stress cycles. FEMFAT therefore attempts to limit the effects of the stress mechanics series influence by assuming so-called "favorable"and "unfavorable"series. Matrix elements with mean compressive stresses and mean tensile stresses are differentiated(Fig.2.2.1).

Fig.2.2.1        Schematic representation of the stress mechanics series influence

It  can be  easily  seen  in  Fig.2.1.1  that  the  "favorable"or  "unfavorable"effect  of the  stress mechanics  series  influence  for  a  mean tensile  stress  is  the reciprocal  of that  for  a  mean compressive stress.

2.3 Operational strength of components

Use of the elastic local stress for damage assess ment requires that the component operational strength be according locally formulated.

Therefore,the corresponding local component S/N curve for the FEM node under consideration is determined in FEMFAT for each element of the load matrix,characterized by load amplitude and the mean load,from the material operational strength taking existing influences on the component into consideration (see Fig.2.3.1).

Fig.2.3. 1        Determination of the local component S/N curve

Because determination of the local component S/N curve plays a central role in the basic module, this procedure will be  described  in  detail  in  a  separate  section  entitled  "The  system  of  S/N curves".

3   The system of S/N curves

The theories and methods upon which FEMFATis based are:

·The  basic  method  of  the  concept  of  nominal  stress  (load  spectra,Haigh  diagram,linear hypothesis of damage accumulation after Miner and its modifications).

·The procedures for determining the influence factors and for taking into account their effects on  the  fatigue  behavior  of  a  component,an alogous  to  TGL19340,the  FKM  Guideline [FKM 94]and the synthetic system of S/N curves [HUCK 83].

● The method for determining the critical cutting plane [FEM 2][EICH95].

Just as is the component S/N curve in the nominal stress concept,the local component S/N curves of the FEM nodes are a  central element of  FEMFAT. The  estimates  for  these  S/N  curves therefore have a critical influence on the fatigue life an alysis. Fig.3.1   schematically  shows the influences to which a component S/N curve may be subject.

Fig.3.1            Influences on a component S/N curve

The critical component operational strength influence parameters are shape,material properties, mechanical and thermal loading affecting the component,environmental conditions and the initial conditions corresponding to the component production influences.The quality of the fatigue life an alysis  depends  heavily  on  how  precisely  the  influence  parameters  can  be  recorded  and estimated,either by employing the concept or by the methods implemented in the program.

One of the principal tasks of FEMFAT is to describe these parameters using tried and tested methods and to incorporate them into the estimate of the local component  S/N curves.In the following Sections 3.1 to 3.6 the effects of the individual influencing factors are explained.The superposition of all influencing factors is the topic of Section  3.7.

3.1 Influence of the stress gradient

The aim of calculating support factors for the finite element evaluation is to automatically record the notch influence occurring in components with regard to damage effectiveness.This allows a component strength assess ment,based on reference material data for unnotched specimens [EICH 89].

A  concept  developed  earlier  by   Siebel  and  collaborators  [SIEB  48][SIEB49]combined  the influences of the  stress  concentration  factor,the  stress type,the  size  of the  component,and the effect of notch geometry on the notch factor by formulating the universally applicable hypothesis of the micro support effect,which occurs in the endurance stress limit range.It is assumed here that the existence of a stress gradient,whether caused by a stress concentration at a notch and/or by bending and torsion,causes the elements below the material surface to support the elements at  the surface enduring higher stresses.This explains why,for example,s mooth bending specimens always display a higher endurance stress limit than s mooth,axially stressed specimens.

This support effect is determined in  FEMFAT by means of the relative stress gradient x.   The equivalent Mises stresses ov of the respective nodes in the FEM structure are calculated for this purpose  and  then  the  mean  formed.Calculation  of the  stress  gradient  is  performed  using Equation 3.1.1 for each element between neighboring nodes.

(3.1.1)

The  result  is  the  maximum   stress  gradient  Xmax(regardless  of  direction)at  each  node.The corresponding relative stress gradient x'is then derived using Equation 3.1.2.

(3.1.2)

The following methods of recording the  "support effect"or the support factor are implemented in

FEMFAT:

·Stieler's  method,see  TGL19340.

● The IABG method [HUCK83].

● The FEMFAT method.

According to Stieler,the support factor is a function of the relative stress gradient and the material yield stress.

(3.1.3)

The support factor for three material groups is given in [HÜCK 83];it has been calculated on the basis of a statistical set of about 600 S/N curves with different notch forms.See equations 3.1.4, 3.1.5 and 3.1.6.

A  model  (Equation  3.1.7)was  proposed  in  [EICH  89],which  well  described  the  ratio  of the cyclic compressive-tensile strength to the cyclic flexural fatigue strength;it was used to calculate the support factor n or fGR,af.

(3.1.7)

Here,σA,b represents the material alternating stress limit for bending and σA,tsc the material alternating stress limit for tension/compression.The material parameter v takes into consideration the non-proportional increase in the support effect with regard to the stress gradient x.It can be seen  that,in  the   case  of  a   s mooth  specimen  under   flexural  load  with   a  diameter  d=b,the parameter fGR,af exactly represents the ratio of the cyclic flexural fatigue strength to the cyclic tensile/compressive strength.The cyclic tensile/compressive strength σA,tsc is multiplied by the

factor fGR,af to determine the endurance stress limit of the local component S/N curve. The material parameters v are summarized in Table 3.1.1.

The influence of the relative stress gradient on the slope kc,GR of the local component S/N curve is determined using Equations 3.1.8 and 3.1.9,and on the endurance cycle limit Nef,C,GR using Equations  3.1.10  and  3.1.12,in  a  similar  manner  to  the  synthetic  system  of  S/N  curves  after [HUCK 83].

(3.1.8)

(3.1.9)

fGR,sf                Stress gradient influence factor affecting the slope of the local component S/N

curve

kc,GR               Slope of the local component S/N curve as a result of the gradient influence

kM                   Slope of the material S/N curve at R=-1

IFK2               Slope exponent of the incipient fracture S/N curve

IFK3               Material group-dependent exponent

The   following   values   for  IFK2  and  IFK3  were   assumed  in FEMFAT afte  r [HUCK 83]  and [ZHAN 05],see Table 3.1.2.

Table 3.1.2 Material parameters

For cast steel:

Ncf,C,GR=Nc,MfGR,cf                                                                                (3.1.10)

Nef,C,GR           Endurance cycle limit of local component S/N curve as result of gradient influence

Ncf,M               Endurance cycle limit of the material S/N curve at R=-1

fGR,cf                Gradient   influence   factor   affecting   the   endurance   cycle   limit   of   the   local

component S/N curve

(3.1.11)

For other materials:

Ncf,C,GR=Ncf,MfGR,f                                                                                (3.1.12)

                                       (3.1.13)

The influence of the stress gradient on the local component S/N curve is described with the aid of these equations.It can be recognized that slope exponent kc of the local component S/N curve influences the endurance cycle limit.

The  following  diagrams  show  the  effect  of the  relative  stress  gradient  on  the  local  component  S/N curve  for  various  materials.

Fig.3.1.1  Influence of gradient on the endurance stress limit of the local component S/N curve

Fig.3.1.2 Influence of gradient on the slope of the local component S/N curve

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