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A subroutine to evaluate creep-fatigue damages based on time-fraction and hysteresis energy methods

CompanyA subroutine to evaluate creep-fatigue damages based on time-fraction and hysteresis energy methods
CompanyA subroutine to evaluate creep-fatigue damages based on time-fraction and hysteresis energy methods

A subroutine to evaluate creep-fatigue damages based on time-fraction and hysteresis energy methods

/MC1-1032/13
/MC1-1032/13/MC1-1032/1/MC1-1032/2/MC1-1032/3/MC1-1032/4/MC1-1032/5/MC1-1032/6/MC1-1032/7/MC1-1032/8/MC1-1032/9/MC1-1032/10/MC1-1032/11/MC1-1032/12
Free

Introduction

A user-defined subroutine is developed and implemented in the finite element software, ABAQUS to predict the cyclic hardening, the stress relaxation during hold time and finally to demonstrate the damage evolution once the damage initiated. The final stage of the material behaviour (i.e. failure) is simulated numerically for the low cycle fatigue (LCF) tests where a hold time is introduced to demonstrate the effect of creep as well as fatigue. For the tests with continuous cyclic loading (without hold time) a hysteresis energy-based phenomenological model was implemented in a USDFLD subroutine. Further, this model in combination with the creep damage model based on the time-fraction law are employed simultaneously to replicate the experimental results in which the hold time was introduced. In the end, the FE results were compared with the experimental results and good agreement observed.

Definition of the parameters inside the code

STATEV(1)       STORES VALUE OF THE PREVIOUS CREEP INCREMENT

STATEV(2)       STORES VALUE OF TOTAL CREEP DAMAGE BASED  ON COCKS AND ASHBY MODEL

STATEV(3)       STORES VALUE OF TOTAL CREEP DAMAGE BASED ON RICE AND TRACEY MODEL

STATEV(4)       STORES VALUE OF THE STRESS

STATEV(5)       STORES VALUE OF PLASTIC STRAIN

STATEV(6)       STORES VALUE OF THE SUM OF ENERGY

STATEV(7)       STORES VALUE OF THE UPDATED STRESS

STATEV(8)       STORES VALUE OF THE UPDATED PLASTIC STRAIN

STATEV(9)       STORES VALUE OF THE TIME INCREMENT

STATEV(10)       STORES VALUE OF THE UPDATED SUM OF ENERGY

STATEV(11)       STORES VALUE OF THE STRESS

STATEV(12)       STORES VALUE OF DAMAGE INCREMENT PER CYCLE

STATEV(13)       STORES VALUE OF TOTAL FATIGUE DAMAGE

VMISES                    EQUIVALENT VON MISES STRESS

DEP              INCREMENT IN PRIMARY CREEP STRAIN

DEC             INCREMENT IN SECONDARY CREEP STRAIN

DTIME                    TIME INCREMENT

TIME(1)                    STEP TIME

TIME(2)                    TOTAL TIME

STARTTIME                TIME OF DAMAGE INITIATION

DMAX                    MAXIMUM DAMAGE

Creep-Fatigue Interaction

 In austenitic stainless steel, the damage mechanism of components in aircraft engines and power-generating plants which are subjected to the combined cyclic loading as well as creep can be associated to the interaction of different operating conditions such as temperature intervals, strain range levels, strain rates, frequency and environmental effects which may lead to both creep and/or fatigue failures. 

1

Hold Time Effect

Cyclic loading strain against time waveforms with various hold times 

2

 

Creep-Fatigue Damage Models

The overall damage could be decomposed as following;

3

D t,   D c,  D f   are the total, creep and fatigue damage respectively. In the tests without hold time, the above expression can be expressed as  D t= D f

The linear-damage-summation method can be described by the following equation.

 

The failure is believed to occur when D t  equals unity

4

 

In the developed user defined damage model sub-routine, the overall damage is assumed to follow the following expression.

5

Hysteresis Loops Decomposition

The inelastic strain energy density, in the tests where the hold time is introduced, can be decomposed into inelastic and elastic. A typical overlap of the inelastic hysteresis loops for the test conducted under TMF condition is illustrated here.

6

 

Experimental Loading Waveform

Loading waveform for dwell test (tests with hold time) at strain range of ∆ɛ=±0.8% at 650 °C

7

Parameters Required For FE Simulation

Creep rupture properties of the material under investigation 

8

 

Life-fraction damage model damage fractions as per damage summation rule for LCF tests

9

Damage normalization factor ,λ

10

FE vs. Experimental results 

 

Cree-Fatigue damages for LCF tests at 650°C with ∆ε=±1.0%

11

Evolution of plastic strain energy

12

Our Achievements:

  1. Simulation of the Creep-Fatigue damages
  2. Prediction of the evolution of plastic strain energy density
  3. Hysteresis loops decomposition
  4. Damage model based on time-fraction law for creep portion
  5. The implementation of the proposed subroutine in Abaqus