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Computational strength verification with explicit recording of non-linear material deformation behavior
For components made of steel, cast steel and wrought aluminum alloys
ISBN 978-3-8163-0729-7
1st edition 2019
232 pages

This guideline is based on the final report of the AiF project No. 17612 Computational strength verification of mechanical engineering components with explicit recording of non-linear material deformation behavior [9], which has been significantly expanded for this guideline.

This FKM Guideline nonlinear was designed for
- small and medium-sized enterprises (SMEs)
- as well as larger companies
with fields of application in general mechanical engineering or related subject areas.

The FKM Guideline non-linear is divided into
- the static strength verification, Chapter 1
- the fatigue strength verification, Chapter 2
whose areas of application can be found in the individual chapters.
In comparison to the "Calculated strength verification for machine components",
- the statically permissible limit load can be significantly increased in some cases by the static strength verification presented here.
- a mechanism-oriented estimation of the technical crack life can be made by taking elastic-plastic material behavior into account in the fatigue strength verification.
The fatigue strength verification of this guideline can also be used if the verification of the static strength was carried out according to the "Calculated strength verification for machine components".

Contents

1 Static strength verification

1.1 General

1.2 Scope

1.3 Evaluation concept

1.3.1 Stress parameters

1.3.2 Failure criterion and failure limit curve

1.3.2.1 Failure criterion

1.3.2.2 Failure limit curve

1.3.2.3 Conservative estimation of the failure limit curve

121.4 Calculations

4.1 Necessary input data

1.4.2 Creating a finite element model

1.4.3 Description of the material behavior

1.4.4 Technological size input

1.4.5 FE analyses

1.4.6 Evaluation principle

1.4.6.1 Evaluation of the design condition

1.4.6.2 Failure assessment

1.5 Safety factors

1.5.1 General

1.5.2 Basic safety factors

1.5.3 Partial safety factor for cast components

1.5.4 Partial safety factor for non-ductile cast components

1.5.5 Total safety factor for the material

1.5.6 Safety factor for the load

1.6 Verification

1.7 Example: Strength assessment for bearing bracket

2. Fatigue strength verification

2.1 General

2.2 Scope

2.3 Preparation of the operating load sequence

2.3.1 Definition of the verification point

2.3.2 Statistical verification

2.3.2.1 Verification with standard deviation sL

2.3.2.2 Verification with standard deviation LSDs

2.3.2.3 Verification with lumped value for unknown scatter

2.3.3 Transfer factor c

2.3.4 Load sequence L for fatigue verification

2.4 Damage parameters PRAM and PRAJ

2.5 Comments on verification with PRAM

2.5.1 The local concept

2.5.2 Tensile strength for the material in the component

2.5.2.1 Experimental determination of the tensile strength

2.5.2.2 Estimation from standard or semi-finished product values

2.5.3 The cyclic stress-strain curve

2.5.3.1 Experimental determination

2.5.3.2 Computational estimation

2.5.4 Description of the material memory .

2.5.5 The damage parameter Woehler curve for the material

2.5.5.1 Experimental estimation

2.5.5.2 Computational estimation

2.5.6 The damage parameter Woehler curve for the component

2.5.6.1 Consideration of non-local influences on the component fatigue strength

2.5.6.2 Influence of roughness

2.5.6.3 Validation of the component S-N curve

2.5.7 Notch approximation method

2.5.8 The operating load sequence

2.5.8.1 The HCM algorithm

2.5.8.2 Classification

2.5.9 The damage parameter PRAM .

2.5.10 Verifications

2.5.10.1 Fatigue strength verification

2.5.10.2 Damage accumulation calculation

2.5.10.3 Fatigue strength verification

2.6 Verification with PRAM

2.6.1 Necessary input data

2.6.2 Preparation of the load sequence

2.6.3 Preparation of the cyclic stress-strain curve

2.6.4 Computational estimation of the material S-N curve

2.6.5 Estimation of the component S-N curve

2.6.5.1 Non-local input variables

2.6.5.2 Input of the roughness

.2.6.5.3 Validation of the component S-N curve

2.6.5.4 The component S-N curve for verification

2.6.6 The notch approximation method according to Neuber .

2.6.7 Application of the hysteresis counting method Rainflow HCM

2.6.8 Application of the damage accumulation calculation

2.6.8.1 Calculation of the damage effect of each vibration cycle

2.6.9 Nachweis der Bauteillebensdauer

2.6.9.1 Dauerfestigkeitsnachweis

2.6.9.2 Berechnung der Bauteillebensdauer

2.6.9.3 Betriebsfestigkeitsnachweis

2.7 Berechnungsbeispiele PRAM

2.7.1 Akademisches Beispiel

2.7.1.1 Aufbereitung der Lastfolge

2.7.1.2 Aufbereitung der zykl. Stress-strain curve

2.7.1.3 Preparation of the material S-N curve

2.7.1.4 Preparation of the component S-N curve

2.7.1.5 The notch approximation method according to Neuber

2.7.1.6 Application of the hysteresis counting method Rainflow HCM

2.7.1.7 Application of the damage accumulation calculation

2.7.2 Shaft with V-notch

2.7.2.1 Preparation of the load sequence

2.7.2.2 Preparation of the cyclic stress-strain curve

2.7.2.3 Preparation of the material S-N curve

2.7.2.4 Preparation of the component S-N curve

2.7.2.5 The notch approximation method according to Neuber

2.7.2.6 Application of the hysteresis counting method Rainflow HCM

2.7.2.7 Application of the damage accumulation calculation

2.8 Comments on verification with PRAJ

2.8.1 The local concept

2.8.2 Tensile strength for the material in the component

2.8.2.1 Experimental determination of the tensile strength

2.8.2.2 Estimation from standard or semi-finished product values

2.8.3 The cyclic stress-strain curve

2.8.3.1 Experimental determination

2.8.3.2 Computational estimation

2.8.4 Description of the material memory .

2.8.5 The damage parameter Woehler curve for the material

2.8.5.1 Experimental estimation

2.8.5.2 Computational estimation

2.8.6 The damage parameter S-N curve for the component

2.8.6.1 Consideration of non-local influences on the component fatigue strength

2.8.6.2 Influence of roughness

2.8.6.3 Validation of the component S-N curve

2.8.7 Notch approximation method

2.8.8 The service load sequence

2.8.8.1 The HCM algorithm

2.8.8.2 Classification

2.8.9 The damage parameter PRAJ

2.8.9.1 Calculation of the crack opening stress σopen

2.8.9.2 Calculation of the fixed crack-opening strain εopen,ein

2.8.9.3 Calculation of the crack-opening strain εopen with history

2.8.9.4 Adjustment of the fatigue strength PRAJ,D .

2.8.10 Verifications

2.8.10.1 Fatigue strength verification

2.8.10.2 Damage accumulation calculation

2.9 Verification with PRAJ

2.9.1 Necessary input data

2.9.2 Preparation of the load sequence

2.9.3 Preparation of the cyclic stress-strain curve

2.9.4 Computational estimation of the material S-N curve

2.9.5 Estimation of the component Wöhler curve

2.9.5.1 Non-local input variables

2.9.5.2 Input of the roughness

2.9.5.3 Validation of the component Wöhler curve

2.9.5.4 The component Wöhler curve for verification

2.9.6 The notch approximation method according to Seeger / Beste .

2.9.7 Application of the hysteresis counting method Rainflow HCM

2.9.8 Application of the damage accumulation calculation

2.9.8.1 Calculation of the damage effect of each fatigue cycle

2.9.8.2 Calculation of the component service life

2.9.8.3 Fatigue strength verification

2.9.8.4 Fatigue strength verification

2.10 Calculation examples PRAJ

2.10.1 Academic example

2.10.1.1 Preparation of the load sequence

2.10.1.2 Preparation of the cyclic stress-strain curve

2.10.1.3 Preparation of the material S-N curve

2.10.1.4 Preparation of the component S-N curve

2.10.1.5 The notch approximation method according to Seeger/Beste

2.10.1.6 Application of the hysteresis counting method Rainflow HCM

2.10.1.7 Application of the damage accumulation calculation

2.10.2 Shaft with V-notch

2.10.2.1 Preparation of the load sequence

2.10.2.2 Preparation of the cyclic stress-strain curve

2.10.2.3 Preparation of the material S-N curve

2.10.2.4 Preparation of the component S-N curve

2.10.2.5 The notch approximation method according to Seeger/Beste

2.10.2.6 Application of the hysteresis counting method Rainflow HCM

2.10.2.7 Application of the damage accumulation calculation .

3 Appendix - Fatigue strength

3.1 Implementation recommendation for FE models

3.1.1 Determination of the ultimate load shape number Kp

3.1.2 Determination of the highly stressed surface area with the extended method SPIEL

3.2 Examples for validation of the HCM algorithm .

3.2.1 Example 1 with memory 1 and inner loops

3.2.1.1 1. run

3.2.1.2 2. run

3.2.2 Example 2 with memory 1, 2 and 3 .

3.2.2.1 1st run

3.2.2.2 2nd run

3.3 Matlab function for maximum likelihood estimation

3.4 Matrices for calculation examples PRAM

3.4.1 Academic example

3.4.2 Wave with V-notch

3.5 Matrices for calculation examples PRAJ

3.5.1 Academic example