Extension of the ANSYS@ creep and damage simulation

I

FORSCHUNGSZENTRUM ROSSENDORF ~WISSENSCHAFTLICH-TECHNISCHEBERICHTE

FZR-296Juli 2000

M!CEWED.Nov3MnB

OSTIEberhard Altstadt and Thomas Moessner

Extension of the ANSYS@ creep

and damage simulation capabilities

I

I

WM4854070

-———–—_______

I

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in electronic image products. Images are

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Extension of the ANSYS@ creep and damage simulation capabilities

Abstract

The user programmable features (WI?) of the ftite element code ANSYS@ are used to generatea customized ANSYS-executable including a more general creep behaviour of materials and adamage module, The numerical approach for the creep behaviour is not restricted to a singlecreep law (e.g. strain hardening model) with parameters evaluated from a limited stress andtemperature range. Instead of this strain rate - strain relations can be read from external creepdata files for different temperature and stress levels.

The damage module accumulates a darnage measure based on the creep strain increment andplastic strain increment of the load step and the current fracture strains for creep and plasticity(depending on temperature and stress level). If the damage measure of an element exceeds acritical value this element is deactivated.

Examples are given for illustration and verification of the new program modules.

Extension of the ANSYS@ creep and damage simulation capabilities Page 3

Contents

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2. Input of the creep data of the materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. Calculation of the creep strain increment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1 Linear interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2 Non-linear interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. Damage module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .>

4.1 Damage model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2 Calling the darnage procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3 Plotting the damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. Additional files created . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1 Log-File of cr&p data base input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2 Log-File of the damage calls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3 Damage backup file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1 Tensile bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2 Disk with centre hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.1 Material behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.2 Purecreep atconstant temperature . . . . . . . . . . . . . . . . . . . . . . .6.2.3 Creep and plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendixl: Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix 2: CRPGEN command reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page 4

Page 6

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Page 8Page 8

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Nomenclature

Latin

c1 ... C4coefficients of the time hardening creep equationdl ... dbD

AD

K

qPar

R,

st

At

TUPFWI ... WgX,y

Greek

&

t

&crfrac

Ecreqv

AE;V

&p]frac

~ p]eqv

AE&

vc1

CJeqv

CJH

coefficients of the strain hardening creep equationdamage parameter

damage incrementKelvintemperature exponent for non-linear interpolationPascalstress exponent for non-linear interpolation; radius

triaxiality function

secondtime

time incrementtemperatureuser programmable featuresweighting factors for interpolation of the creep strain incrementcoordinates

strain

strain rate

creep fracture strain

effective (equivalent) creep strain

effective creep strain increment

plastic fracture strain

effective (equivalent) plastic strain

effective plastic strain increment

Poisson’s number

mechanical stress

von-Mises equivalent stress

hydrostatic stress


Indices

creqvfiatHLmaxminplPrefsTtan

creepequivalentfracturehigh, hydrostatic, holelowmaximumminimumplasticprimaryreferencesecondarytertiarytangential

.


L Introduction

The creep behaviour of materials is usually described by analytical formulas (creep laws) witha number of free coefficients, e.g.:

,=d,o[&~.Ed3.exP[-*] (1)

The coefficients (cl... c1in eq. 1) are used to adapt the creep laws to creep test results performedat constant load and temperature. However, in practice it is often diftlcult to achieve a satisfyingadjustment for a wide range of temperatures and stresses with only one set of coefficients.Instead it appears that the coefficients itself are dependent on the temperature or on the stresslevel. Therefore a supplementary tool is developed which allows to describe the creepbehaviour of a material for different stress and temperature levels independently. This isespecially useful if strong stress andlor temperature gradients arq present and if both primaryand secondary creep are to be considered in the analysis. Additionally it is possible to calculatethe creep damage and deactivate elements whose accumulated damage is greater or equal toone.

The user programmable features (UPF) available on the ANSYS@ distribution media were usedto develop the tools. The Compac@ Visual Fortran Compiler (Rev. 6.1) was used for

progr amming and for generating the customized ANSYS-executable on a Windows/NT@platform.

2. Input of the creep data of the materials

The creep behaviour of a material can be described by the

d“ = f(&cr;o;T)

strain hardening representation

(2)

The time hardening representation or the work hardening representation can in general betransformed into eq (2). The relation eq (2) is transferred into the ANSYS database by meansof a number of discrete pairs of the form

I

.&(1) ~ (1). .. .. .

.

& (n) E(n) r=umst;u=const

(3)

Several of such sets for different temperature and stress levels can be combined. The completecreep data base then is as follows:


1 T1I I. . . TK

----.---------------------i--J------------------------------u K.MK%l__ ““” :Jy: j-’j__ ‘K1 ____”::_______J _______

E: ““”frac

&l;M1 1 ““” [ &g ““” EEm————-—————------———-———---4-–~–––--—-———————————------———-—-

Nl,, o“. N I .. .Ml

I N .. .K;l N K;MK

I .

& K;MK;l; E K;MK;l

I . . . 1.1 . . .. . .

1 “.1. . .

. . . . . .

(&l:l;N;&l;l;N)o-"(&l;Ml;N;gl;MIN)i"""i(&K;l;N;&K;l;N)““” (EK-N;EK;MK;N

(4)

The first index refers to the temperature, the second index to the stress and the third to thestrain. K is the number of temperature levels, Mk the number of stress levels within the k-th

temperature level and Nk;m the number of strain rate-strain pairs for the m-th stress level

within the k-th temperature level.

The UPF routine userOl /1/ is used to realise the creep data input into ANSYS. The data mustbe provided by the user as a set of ASCII files (for each temperature-stress level one file). Thes~cture of a creep data file is demonstrated in the following example:

8. 73150E+02 ! ! Temperature K3.00000E+05 ! ! stress kpa

3.50000E-01 ! ! Creep fracture strain

1.00000E+02 ! ! n~er of strain Sets in this file

O. OOOOOE+OO 6.0000 OE-05 ! ! setl : epsl depsl4. 97257E-04 7. 55093E-05 ! ! set2: eps2 deps21. 16640E-03 8. 85600E-05 ! ! Set3: eps3 deps31. 92061E-03 9. 72162E-05 ! ! set4: eps4 deps42.73599E-03 1.03866E-04 ! ! set5: eps5 deps5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6. 16071E-01 4. 83579E-03 !! set98: eps98 deps986.56547E-01 5.16142E-03 !! set99: eps99 deps996.99738E-01 5.50632E-03 !! setlOO: eps100 deps100

Table 1: creep data fde example

Thecreepdatafiles mustbenamedaccording tothepattermba sename.c??where ??standsfor the sequent fde number (01 .... nflles). To read the creep data files use the following ANSYScommands/3,4/:


! ! set co~nd n- associated with UPF Userol

/uCmd, usrl, 1! ! specify the names and the number of the creep data files

usrl,filename ,nfiles,log_key, intp_key! ! instruct ANSYS to use the user defined creep law

/prep7&,creep,mat

tbdata,l,l I((t! 100

Table 2:ANSYS inputexample for using theuserdefmed creep database

Iflog_key=l, acontrol output file ejobnam>.crlg is written. Ifthe argument intp_key=l, thenon-linear interpolation scheme is activated (section 3).

For the generation of the creep data files the supporting program CRPGEN is available(command reference in Annex 2).

3. Calculation of the creep strain increment

To realize the calculation of the creep strain increment according to the non-standard creep law,the UPF usercr.f was modified and linked to the customized ANSYS executable /1/. In this

routine the scalar creep strain increment A& Cr = &CroAt is determined from the creep data

(input see section 2) by multi-linear interpolation

AEcr = [W106L;L.+ W20iuL;H + W~”&L;H;L+‘4”& L;H;H

.

+W5 “&H;~. + W6 “‘H;L;H + ‘7 “‘H;H;L + ‘8 “‘H;H;H ],At(5)

3.1 Linear interpolation

Assuming that the strain rate depends linearly on stress and temperature between two databasepoints, the weighting factors in eq. (5) are:

Extension of the ANSYS” creep and damage simulation capabilities Page 9

(TH-T)&..-CJ)+ L;LE)E)

‘1 = (TH - TJ(CJL;H - ~~L)”(&~~H - ‘LAL)

(TH-T)* (OL,H-O)O(C-EL,LL)

‘2 = (TH- TL)o(o L.H- CJL,L)*(&UL;H - &UL;L),

(TH-T)O (O- OUL)*(EUH,H-E)

‘3= (TH- TL). (oL,H- CJL,L)O(&LH.H - &LH;L),,

(T’H-T)O(G - OuL)*(E-tuH,L)’

‘4 = (TH- TL)o(o L.H- ~L;L)o(&L;H;H - &UH;L)

(T- TL)S(CJH,H ‘O)”(&H;L;H –&)

‘5= (TH - TL)o(o H;H - OH,L)O(&HLH - &H.LL),, ,,

(T- TL)o(o H,H- o)o(&- &H,L,L)

‘6= (TH- TL)”(~H;H- ~H;L)”(&HLH- ‘HLL),, ,,

(T- TL). ((J- CJH,L)O(EH;H;H- E)

‘7 = (TH- TL)”(CJH;H- oH;L). (& H;H;H - &H;H;LJ

(6)

(T- TL). (o - OH.L)O(E- &H;H;L),

‘8= (’IH - TL)o (CJH;H - OH;L)O(&H.H.H - &HHL),, >,

(1

8

zWi=l

i=l

The quantities without index E, o, T are the actual values of the current element integration

point. The indexed quantities are the values from the creep data base eq. (3). They form thesmallest intervals which the actual quantities are enclosed in. The meaning of the indices is Llow bound (largest data base value which is smaller than the actual integration point value) andH: high bound (smallest data base value which is greater than the actual integration pointvalue). The first index refers to the temperature, the second index to the stress and the third tothe strain.

TL<TSTH

{~L,L>aH.L}~ ~ ~ {~L.H3~H,H},

}< &< {8L.L.~9ELH.H?&I-I.L.H>&H;H;H}{& L.L.L>&~H;L9&H;L;L> &H;H;L - , , , , , ,>,

(7)

All stresses and strains in eq. (4-6) are equivalent values. The components of the creep strain

tensor increment, A E~, arecalculated according to the Prandtl-Reuss flow rule /2,6/.


The creep data base eq. (3) has to be provided in such a way that the actual temperature and theequivalent stress of the elements do not exceed the maximum values of the creep data base. Ifthe actual temperature or stress values are smaller than the smallest values of eq. (4), the creepstrain increment is zero for this step.

3.2 Non-1inear interpolation

If the temperature steps and/or the stress steps in the creep database are not sufficiently small,the creep strain increment might be overestimated, since the strain rate in general depends over-proportionally on the stress and on the temperature respectively. That’s why a non-linearcalculation of the weighting coefficients is useful.

Assuming that the strain rate depends exponentially on the stress, i.e.

&= A.or

the according interpolation between two points is:

(+0’ 0’–0;&= “El+ “&*

0;–0: 0;–0;

the exponent r can be estimated from

ln(t2)-ln(&,)

‘= ln(o,)-k(~l)

(8)

(9)

(lo)

Similarly, if it is assumed that the strain rate dependency on the temperature can be describedby

~ = K. ~-W (11)

the appropriate interpolation between two points is

~-qfT2 _ ~-q/T ~-q/T _ ~-q/T1

~=~–q/T2 _ ~–q/T1 “El+ ~–q/T2 _ ~–qlT1 *E2

The parameter q can be estimated from

ln(E2)- ln(&~)q= 1 1

(12)

(13)

Of course, the parameter q can change with the stress level and the accumulated creep strain as


the parameter r maybe dependent on temperature and strain.Applying the above equations to the calculation of the weighting coefficients, one obtains:

(e-%fh _ @T).((& - orL)o(&L.H -E)WI = (e-d% _ @/T’).(~:H - ~:L)o(&~~H - ‘LLL)

> ,

(e-%% - ~-qL/T).((j:H - (JrL)o(&- &L;LL)W2“ (e-d% _ ~-qL/TL)@:H - 6;~)”(&L;fiH- ‘I&L)

(e-qH/TH ‘_~-%/T). ((yr L-@ L) O(&LHH-&);;

W3 = (e-qdT~ - e-qH’TL). (6}H - 6~L)” (&~H;H - ‘~HL)>

(e-%f’b _~-qH/T), (~rL-~:L)o(&-&LHL)W4 =

;;(e-%l% _ ~-qH/TI- ). (O fiH -0 ~L)” (&GH;H - E L;H;L)

w _ (e-qLtT ‘rH ‘ ~H- e-qL’TL)o(o H.H -6 )s(&H;~H - ‘)

5- (e-q. /T.-e ‘qL/TL ) .(~ :.H - ~ :;L) o(E H;~H - ‘H;UL)

(e-qdT _ ~-qdTL ‘ rH)-(CJH,H -GrH)>(E-~H,L;L)

W6 =(e-qdT~

–e ‘q’/T’ ). (CJ ~.H -6 ~,L)” (&H;UH - E H;UL)

(e-qH/T ‘_e-qIf/TL. ).(~rH- ~~L). (&H HH-&)

W7 =;;

(e-%r/Tri –e ‘qH/T’) ● ((J~.H- ~ f.L) “(EH;H;H - E H;H;L),

(e-%/T _e-qH/TL ).(~rH- ~:.L)o(&-&HHL);;

‘8 = (e-qrdT. - e-qH’TL ) -(~ ~.H -6 ~. L)” (E H;H;H - & H;H;L)

with the parameters

ln(~ H;~L) - ln(i ~~L) .qL =

11 3 qH =@ H;H;L) - ln(iL;H;L)

11

(14)

‘L =

—_ —

TL TH

h(i L:H:&)- ln(&L:L:L)

—_ —

TL TH

h(& H;H;L)- ln(&H;UL)‘H =

ln(~ H;H ) - ln(o H;L)

(15)

It should be noted that in the above equations the index of q, always corresponds to the second

index of &,00(stress level) and the index of r. always corresponds to the fiist index of& ..O

(temperature level).


4. Damage module

4.1 Damage model

The material damage due to significant creep strains is modelled by a damage measure whichis incrementally accumulated at the end of a load step or substep. This damage includes also theprompt plastic deformation of the structure. The damage increment is:

[

At;v h:,AD=

c:.@,T) 1‘(T) ““+ &:ac(16)

with &~& being the creep fracture strain of the uniaxial creep tes~ at constant stress and

temperature and &~C the plastic fracture strain (true strain) of the tensile test. Rv is a function

which considers the damage behaviour in dependence on the triaxiality of the stress tensor /8/:

[12

2RV==. (1+ Y)+3. (1-2V). ~

eqv

(17)

where o ~ is the hydrostatic stress and ~ ~v is the von-Mises equivalent stress. Alternatively,

the triaxiality function can be set to 1.The damage increment is calculated for each element by averaging its nodal equivalent creepand plastic strains. The accumulated darnage is

Idstep

D= ~ADi (18)j=l

If the element darnage reaches the value of D=l, the element is killed by setting its death flagto 1 (refer to the ,,element birth and death” section of /3/).

4.2 Calling the damage procedure

The creep damage module is realized in the subroutine dmg_Ol and a number of supportingroutines. The invocation of this module is initialized by the user routine USER02. Once thisinitialization has been done the creep darnage routine is automatically called after each substepor after each loadstep, depending on the settings with the outres command. This is realized bythe UPFS USOLBEG, USSFIN, and USOLFIN respectively. If all substeps are written to theresult file (outres,all,all), the damage routine is called after each substep. Otherwise thedamage routine is called after each loadstep (default). If the analysis is a restart analysis, thepreviously accumulated darnage values are resumed from the binary file ejobnam>.dsav.

Notes:● It is not necessary to invoke the usrcal command, the initialization for USOLBEG,

USSFIN, ULDFIN, USOLFIN and USEROU is done automatically.


● It is not recommended to issue outres specifications other than outres,allfieq, sinceelement- and DOF-solutions need to be stored on the result file for creep damageevaluation

‘o activate the damage accumulation and the element killing, use the following commands:

! ! set coxumand name associated with UPFS (begin level)/ucxnd, usr2, 2/ucmd, usr3, 3

! ! calculate creep darnage/solu. . . .

! ! set the output f recpency (optinal )outres, all, freq

! ! initialize the damage procedure! ! the calling frequency depends on the oulxes settings

usr2, dmgcrit! ! set fracture strains

usr3, epfr_key, epbrO, cltem, clsig

. . . .Solv. . . .

Table 3: ANSYS input example for the use of the creep darnage module

The argument dmgcrit of the usr2-command is used to select a damage criterion (dmgcrit=2:

triaxiality according to eq. 17; dmgcrit=l: R, = 1, dmgcrit=O: no damage calculation).

The usr3-command provides an additional possibility to calculate the creep fracture strain orthe plastic fracture strain according to:

epfi_ key= O E& = epbrO+ cltem. T + clsig” o(19)

epfi_ key= 1 &AC = epbrO + cltem. T

If the usr3-command is not entered (or entered with all arguments zero), the current creepfracture strain is calculated from the creep data base values (see creep file example, table 1) bymulti-linear interpolation:


(TH-T)@LH-@~: (TH-T)@-QOE~:E:JT,o)=

(TH- TL)o(o L;H- ‘L;L ) + (TH-TL). ((JLH-~L;L)(20)

(T- TL)O(OH;H-O) CE~L+(T- TL)O(O-a H;H)OE::

+ (TH - TL)@H;H - OH;L) (TH- TL)@H;H - %;,)

For the meaning of the indices see sections 2 and 3. The plastic fracture strain &&Cis calculated

from the last strain-stress point of the MISO-table or of the MKIN table (interpolation betweenthe temperatures). Refer to the tb, tbpt, tbtemp commands /3,4/.

The usr2- and usr3-commands can also be used with an ANSYS standard creep law (c6<1OO),

however, in this case the creep fracture strain must be entered via usr3 since it is otherwise notavailable.

After the SOIVcommand the scalar ANSYS parameter ,,dmgmax” is available which representsthe maximum creep damage of all elements at the current loadstep.

Note”-If an element is killed, the stress distribution may promptly and significantly change. So it isrecommended to observe the process of element killing after each load step using the standardANSYS commands (esel, *get). If one or more elements are killed during the load step, the timeincrement for the next step should be sufficiently small.

4.3 Plotting the damage

The darnage D is calculated for each element whenever the cr_dmg-routine is invoked (section4.2). To make this quantity available for the postprocessing it is written it to the NMISC-records of the elements (refer to /5/ for the description of the standard non-summablemiscellaneous element output - NMISC). The UPF USEROU was employed to realize theadditional nmisc-output. The damage value is automatically stored on the first place after thelast standard-NMISC output. The graphical output during the postprocessing can easily berealized with the commands etable, pletab, esol /4/. The output frequency to the result fdedepends on the settings of the outres command /4/. Table 4 shows an ANSYS input example.

! ! post-processing/postlset ,.. .etable, crdmg, nmisc, 26 ! ! 26 if element is plane42

pletab, crdmg, avg

Table 4: ANSYS input example for plotting of the creep darnage

Note: The creep damage calculated with the stresses and strains of the n-th result set is storedin the (n+ 1)-st result set of the result file. This unintended shift is due to the fact that theUSEROU routine is called he~ore USSFIN (damage calculation after a substep) and ULDFIN


(damage calculation after a loadstep). This cannot be influenced by the UPF programmer.However, in the additional file ejobnam>.dmg (see section 5) the assignment between theelement results and the calculated damage is correct. The command-macro ,,pldrng.mat” can beused as a work around for this problem.

5. Additional files created

5.1 Log-File of creep data base input

To verify the input of the creep data files the log-file ejobnam>.crlg can be created @mmrzdefaults to ,,file”). Thk ASCII file contains the base name of creep data files, the number oftemperature levels, the number of stress levels per temperature, the number of strain rate - strainpairs for each level and the first twenty of such pairs. The file is written, if the third argumentof the ucri-command is set to 1: (for example: usrl, testcrp, 5, 1)

5.2 Log-File of the damage calls

This ASCII file is named ejobnam>.dmg and contains information on current load step,substep, time, number of elements and number of nodes. Moreover, for each element theaverage temperature, stresses, creep strains, plastic strains and accumulated damage isrecorded. The log-information is appended each time the dreg-routine is called. The file isnewly created in the fiist loadstep, if the analysis is not a restart.

5.3 Damage backup file

This binary file is named ejobnamxdsav and contains the accumulated damage. This file isnecessary if a restart analysis is performed. In the case of a restart the creep data base must beinput in the same way as in the first analysis, since the creep data base is not stored in thedb-file (cf. usrl-command). Additionally, the previously accumulated darnage must be inputfrom the dsav-file. This is automatically initialized if a restart analysis is performed.

6 Examples

6.1 Tensile bar

For verification of the creep module a simple model which consists of only one element wasused (Fig. Al). The creep data base is generated according to equation (1) with the coefficients:

dl = 6.9372E -23 S-l dz = 3.367

d~= -0.459 dd = 22392 K

o ,,f = 1Pa

(21)

For this ,,hypothetical” material a reference solution can be obtained using the ANSYS standard


creep equation. So the purpose of this example is● to show that user creep module works correctly● to demonstrate the influence of the interpolation method (cf. section 3)

The load for the model in Fig. Al is a constant stress of o = zoo” ma and the temperature is

lOOOK.The creep data base is generated for the following temperature and stress levels:

TL= 973.15K au = 150MPa CJLH= 250MPa(22)

TH = 1073.15K o= = 150MPa Om = 250MPa

The creep curves are calculated for a time range of 10 s with an integration step width of0.025s. Figure A2 shows the results for linear interpolation (cf. eq. 6) and Fig. A3 for non-linear interpolation (cf. eq. 14). With linear interpolation the creep strain is too high (what isclear in view of eqs. 1 and 21), whereas the results with non-linear interpolation meet exactlythe reference solution.

6.2 Disk with centre hole

The model is shown in Fig. A4. The disk is loaded at its free end by a tensile stress inx-direction. Fig. A5 shows the tangential stress of the well known elastic solution exhibiting a

stress maximum of 0 ~ ma = 30 ~ at the 90° position.

6.2.1 Material behaviour

The material of the disk is assumed to be the French reactor pressure vessel steel 16MND5.The creep behaviour of this material at high temperatures was investigated within a extensiveexperimental program fi.mded by the European Commission/9/. Based on the experimental datathe ANSYS creep database is generated.

The creep curves are subdivided into three sections (cf. Fig. A6):I primary creep range (t e tP)II secondary creep range (tP c t c tJ111 tertiary creep range (t~ c t c ~ )

The creep curves were generated at different temperature and stress levels according to thefollowing equations:

C,,(T)I &= CIP(T) .~ C2P(TJ .t’3pfT) ~ =

.~ c2P(TJ .tc3p(T)+l

1+ C3P

II &= CJT)mc2 S(T) .tc’s(T) & = &p +% (m . ~ cM(T) . [tcdT)+l —

1+ c3~t~s(T)+l] (23)

III i = C1~(T)”CJ’2T(T) . tc3T(T) E = &s +C,,(T)

1+ C3T.~ C2T(T) .[tc3T(T)+1 _ t~(T)+l ]


For the primary creep stage an equivalent strain hardening representation is:

i = DIP (T). (y ‘zP(T) ,~ dsp(T) with

D,, = [C,,, (1+ c,,)’”* d,, = c“ d,, = ~;:1+ C3P 3P

(24)

The coefficients of the primary creep stage were taken from the work of IKONEN /9/ whosummarized a couple of creep test performed in a temperature range of 600-1300”C. Accordingto the experimental data in /9/ it was assumed that the transition between primary and secondary

creep takes place at a creep strain of & = &p = 0.1, and the transition between secondary and

tertiary creep at a creep strain of & = &~ = 0.2. The fracture strain is about e ~W = &~ = 0.8.The times for the creep stages can be calculated by (cf eq. 23):

[ 1-(1+ C3P)i&p 1+:3,tp=Clp● 0’2’

To get a smooth transitionmust il.dilll the relations:

[ 1-o+ C3J” (Es- &p)+ ~c3,+~ 1+~”t~=Clsou‘2s P

r1.—

I(1+cYI-)”(&T- Es) ~ ,C3T+1 I’+C’TtT =

(25)

[ c,@c2T ‘ ‘s j

between the stages of the creep curve the coefficients Cl~ and Cl~

c,, =Clp.$3P-C3S)

C*T =Cls ,t~S-c3TJ

c 2P = C2S = C2T

(26)

Table 5 shows the parameters for the creep curves. The coeftlcients DIP, 4P and c$p areparameters fitted to the experiments by IKONEN /9/, the other coefficients follow from thesefitted parameters by using the above equations. The coefilcients are related to the stress unitMPa and the time unit sec.


T[K] 873.15 973.15 1073.15 1173.15 1273.15 1373.15 1473.15 1573.15

D,, 3.890E-142.394E-121.412E-115.672E-112.54OE-101.890E-091.571E-082.954E-07

d2P 3.418 3.411 3.316 3.366 3.367 3.340 3.346 3.620

d3P -0.201 -0.218 -0.454 -0.455 -0.459 -0.470 -0.476 -0.436

C,p 6.621E-12 2.778E-10 3.069E-08 8.072E-08 2.354E-07 1.028E-06 4.553E-06 2.542E-05

C2P 2.846 2.800 2.281 2.313 2.308 2.272 2.267 2.521

C3P -0.167 -0.179 -0.312 -0.313 -0.315 -0.320 -0.322 -0.304

c,~ eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4)

~2s 2.846 2.800 2.281 2.313 2.308 2.272 2.267 2.521

C3S 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

c IT eq. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4) eqs. (3,4)

C2T 2.846 2.800 2.281 2.313 2.308 2.272 2.267 2.521

C3T 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Ep 0“1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

Es 0“2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

ET 0“8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

Table 5: Parameters of the creep curves for the steel 16MND5

Figure A7 shows the creep strain and the creep strain rate at T=1373 K and o = 10 MPa as an

example.

In some load cases creep and prompt plasticity occur simultaneously. Therefore, thetemperature dependent o – & curves are shown in Figure AS. A multi-linear isotropichardening is assumed and the flow rule of von-Mises is used.

6.2.2 Pure creep at constant tem~erature

At fiist the development of stresses and damage is studied assuming pure creep (no promptplastic deformation) at a constant temperature of 1370 K. The creep deformation leads to arelatively quick release of the stress concentration near the hole. Figures A9 and AlO show thetangential stress and the accumulated damage after 1000 s. Figures All and A12 show thesame quantities after 9900s. The elements which were killed in the meantime are not shown. Itis remarkable that in spite of reduced cross section area the maximum stress is still lower thanit was in the beginning of the calculation. This is a consequence of the stress relocation. Thedevelopment of the darnage and the stress over the time for some locations on the y-axis isshown in the Figures A13 and A14. In Fig. A14 the effects of stress relocation and of the

element killing can be clearly seen. Figure A15 shows the creep strains of the two points (O;rJand (O;1.5rJ over the time. The element at (O;1.5rJ fails at a slightly lower total creep strainwhich is a consequence of the higher triaxiality factor at this location.


6.2.3 Creev and vlasticitv

In this load case creep and plasticity are combined. As before the temperature is constant (1370

K) and the stress load is o ~ = 10MPa. The Figures A16 and A17 show the tangential stress

and the accumulated damage after 1000s. Figures A18 and A19 show the same quantities after4800s. The development of the damage and the stress over the time for some locations on they-axis is shown in the Figures A20 and A21. Figure A22 shows the equivalent creep strain andthe equivalent plastic strain of the two points (O;r~) and (O;1.5r~) over the time.

The stress near the hole exhibits a slightly different behaviour compared to the pure creep case(ref. Fig. A21, red curve). It starts with a lower value since a prompt plastic deformation occursand the maximum stress is limited to the initial yield stress. After that the stress is increasingdue to the plastic hardening of the material. After some 800s a stress relocation starts to developas a consequence of the increasing creep deformation.

The progress of damage looks also somewhat different than in the pure creep case (ref. Fig.A20). The damage value at t = O s is not zero but up to 0.29. This is the result of the promptplastic deformation. The contribution of the plastic strain to the damage leads to a shorter timeat which the first element fails (4300s vs. 8400s in the pure creep case, Fig. A13). The failureof the fust element causes a prompt increase of the damage in the neighboring elements sincethe stress relocation leads to another prompt plastic strain increment. This effect can also beseen in the strain curves (Fig. A22). Contrary, in the pure creep case the killing of the fustelement only causes a steeper gradient in the damage curves of the neighboring elements (Fig.A13).

Comparing the damage (Fig. A20) with the plastic strains and creep strains (Fig. A22) it can bestated that the relative contribution of the plastic strain to the damage is larger than that of thecreep strain. This is due to the fact that in the case of the 16MND5 steel the plastic fracturestrain is smaller than the creep fracture strain (see also eq. 16).

References

/1/

/21/3//4//5/161

[7//8/

/9/

ANSYS Programmer’s Manual. ANSYS, Inc., 1998ANSYS User’s Manual - Theory (Rev. 5.5). ANSYS, Inc., 1998ANSYS User’s Manual - Analysis guide (Rev. 5.5). ANSYS, Inc., 1998ANSYS User’s Manual - Command reference (Rev. 5.5). ANSYS, Inc., 1998ANSYS User’s Manual - Elements manual (Rev. 5.5). ANSYS, Inc., 1998Becker, A.A.: Background to Material Non-Linear Benchmarks. NAFEMS-reportRO049 (International Association for the Engineering Analysis Community)Azodi, D., P. Eisert, U. Jendrich, W.M. Kuntze: GRS-Report GRS-A-2264Lemaitre, J.: A Course on Darnage Mechanics. ISBN 3-540-60980-6, 2nd editionSpringer-Verlag Berlin, Heidelberg, New York, 1996Ikonen, K., 1999, “Creep Model Fitting Derived ffom REVISA Creep, Tensile andRelaxation Measurements”, Technical Report MOSES-4/99, VTT-Energy, Espoo,Finland.


Appendix 1: Figures

Extension of the ANSYS@ creep and darnage simulation capabilities Page 21

“E.,;;

.

l--“/...,.,.;.=,.,,,.,..-G: :~--:, ., ,- . . .. . .. .. ,. .=.., ., ..,. !

., .-,’ “.1

200 M??a

}

Fig. Al: Model of the tensile bar

(x 1O**–2>2.4

2.04 -EPT_LIN

/

1 .68- .-/ ‘

.5 1.32/ ‘ E PY_RE E’

a.

/

+ .96/ ‘ / ~

m.

0. / / ‘

al .6-

2e. 24

-.12-

–.48 EPZ_REF

-.84 .EPZ_LIN

-1.20 2 4 6 8 10 ~2

1 3 5 7 9 11 13

time (s)

SIG=200MPA, T=1OOOK, DELTA SIG=1OO, DELTA T=1OO

Fig. A2: Tensile bar, creep curves (axial strain and lateral strain)vs. time, linear interpolation and reference solution.

i---

c. 1O**-2>1.26~

EPY_NLI

I EPY F.E!S

1 .07-

.88-

.: .69 / y

:i= .50-

A

61

. / ‘

. .310. / “0. 12-

-.06 - ‘L

-.25--

w .

-.44 -

EPZ_REF

---% EPZ_NLI

\ ~-.63

0 2 4 6 a 10 121 3 5 7 9 11 13

time (s)

SIG=200MPA, T=1OOOK, DELTA_SIGCdOO ,DELTA_T=100

Fig. A3: Tensile bar, creep curves (axial strain and lateral strain)vs. time, non-linear interpolation and reference solution

_——-—


,.,-,..:,:“ .-..

zx -l—

------ ..”. . .

lug. A4: Model of the rectangular disk with a centre hole; uniform stress at x=a

(red); symmetry conditions at x=O and y=O (blue)

1-

,,: ,,’

., . . . . ,., l--

ANSYS 5.6MAY 22 200009:58:14NODAL SOLUTIONSTEP=lSUB =1TIME= .1OOE-O4SY lAVG jRSYS=lDMX =.010673SMN =–.103E+O8SMNB=– .109E+O8SMX =.308E+08SMXB=.322E+08PRE S-.1 OOE+O8

-.103E+O8-.573E+07-.117E+07.339E+07.796E+07.125E+08.171E+08.216E-I-08.262E+08.308E+08

Fig. A5: Tangential stress (elastic solution)


7 I

tp

II III

Fig. A6: Scheme of a creep curve with primary, secondary and tertiary creepstage

Fig. A7: Creep curves (creep strain and creep strain rate over the time) for

16MND5 at T = 13731Qo = 10MPa.


MISO Table For Material 1

(xII-2$*61

ANSYS .5.6

MAY 25 2000

18:32:49

Table Data

800.

720-I m?

Ill 1~1 l“

320 !C5P I I I I 1 I 1 I I

O;+.L, , ,j.5121

.25 .75 1.252.5 ““

1.75 2.25

EPS

T1 =300

T2 =475

T3 =675

T4 =775

T5 =875

T6 =975

T7 =1075

T8 =1275

T9 =1375

TIO =1475

Fig. AS: Stress-strain-curves of 16MND5 for the temperature range from 300K to 1475 K(true stress and strain) based on/9/.


,;_x

IWJSYS 5.6MAY 23 200011:36:19NODAL SOLUTIONSTEP=llSUB =137TIME=1OOOSY (AVG )RSYS=lPowe rGraphicsEFACET=lAVRES=MatDMX =.026037SMN - .102E+O8SMX =.198E+08

–.102E+O8= _.690E+07m _-35~~+fJ7m .2~802~m -3~2E+07~ .647E+07u .981E-I-07Q -~32j3+~*u .165E+08m J98E+O$3

~lg. AY: DISK WIUI hole (Material 16MND5). Pure creep at T==1373 K and

O.= loMPa.Tangential stress after lOOOs.

ANSYS 5.6MAY 23 200011:37:17AVG ELEMENT SOLUTIONSTEP=I1SUB =137TIME=1OOOCRDMG {AvGjDMX =.026037SPIN =.004353SMX =.167568

Fig. AlO: Disk with hole (Material 16MND5). pure creep at T=1373 K and

CTO= loh@a. Darnage tier 1000s.


ANSYS 5.6MAY 23 200012:16:59NODAL SOLUTIONSTEP= 103BUB =439TIME=9900SY (AVG )RSYS=lPc.werGraphicsEFACET=IAVRES=MatDMX =.107927SMN =-.126E+O8SMX =.182E+08

–.126E+08-.915E+07-.572E+07-.230E+07.112E+07.455E+07.797E+07.114E+08.148E+08.182E+08

Fig. All: Disk with hole (Material 16MND5). Pure creep at T=1373 K and

O.= lohlll?a. Tangential stress after 9900s,

ANSYS 5.6MAY 23 200012:17:46AVG ELEMENT SOLUTIONSTEP=103SUB =439TIME=9900CRDMG (AVG)DMX =.107927SMN =.022717SMX =.962179

Fig. A12: Disk with hole (Material 16MND5). Pure creep at T=1373 K and

O.= 10MPa. Damageafter9900s.


l-dC-76E<la

1.00

.90

. so

.70

.60

.50

.40

.30

.20

.10

0

l)NG-DMG- 3

/ y

/ i

/

/ /

/ ‘ ,/ DMG-3

/ ‘ / ‘/ /

/

/ / ‘ m“IG-4

/ / -

0f> 30*

4.8 6.4 8,8 2.4

9.64 5.6 7.2 8.8 10.4

*3)


G ~ = Iowa. Darnage over time at four points: DMG-1 at (x=O; y=r~), DMG-2

at (O; 1.5 r~), DMG-3 at (O; 2.5 r~), DMG-4 at (O; b).

[> 10**6)4CI

36

32

2s

24

20

16

12

8

4

0

1\

- — *_ —~ ~ *——~ - ~ —————————7 . —

o 1.6 3.2 4.8 6.4 8.8 2.4 4

9.65.6 7.2 8.8 1

5-tan–3

S–tan- 4

S–tan–2

S-tan- 1

0.4


o ~ = lo~a. Tangential stress over time at four points (see Figure A13)


1.00

90

80

.70

zH .60<IXt-fn

.50

,40

30

.20

10

0

// A

/ ~// ‘

--- / ‘/ ///-/ ‘“ /

0 1.6 3.2 4.8 6.4 8 9.6.8 2.4 4 5.6 7.2 8.8 1

TIME ( s)

EPPL-2EPPL-I

EPCR-2EECE.–1

{X? O**3)

0.4

.- —--- .Fig. A15: Disk with hole (Material 16MND5). Pure creep at T=1373 K and

O.= 10~a. Equivalent creep strain over time at points 1 and 2 (see Figure

A13)


gx—

ANSYS 5.6JUL 6 200012:52:44NODAL SOLUTIONSTEP=llSUB =3.34TIME=1OOOSY (AvG )RSYS=lPowerGraphicsEFACET=lAVRE S=MatDMX =.027558SMN =-.103E+O8SMX =.200E+08

-.103E+O8= -_~95E+07m _-359~+f37m -221048❑ -3~5~+07

.651E+07n .988J5+07m -132E+08n .16&3+08= .200E+08

—. . . - —. . . . . . .- —l!ig. A16: Disk with hole (Material 16MND5) .Creep andplasticity at T=1373K

andoO=lOMPa .Tangentialstress after 1000s.

ANSYS 5.6cfuL 6 200012:53:19AVG ELEMENT SOLUTIONSTEP=llSUB =134TIME=1OOODMG (AVG)DMX =.027558SMN =.004256SMX =.656388

.004256

.076715

.149174

.221633

.294092

.366551

.439011

.51147

.583929

.656388

—. .—Fig. A17: Disk with hole (Material 16MND5). Creep and plasticity at T=1373 K

and 00= 10MPa. Damageafter1000s.


ANSYS 5.6JUL 6 200013:05:52NODAL SOLUTIONSTEP=53SUB =145TIME=4800SY (AvGlRSYS=lPowerGraphicsEFACET=lAVRES=MatDMX =.063181SMN =-. 108Z+O8SMX =.184E+08

–.108E+O8-.752E+07-.428E+07-.104E+O7.220E+07.544E+07.868E+07

u .119E+08m -152~+~*- -184~+~8

Fig. A18: Disk with hole (Material 16W5) .CreepandpIasticiN at T=1373K

and 00 = loMl?a. Tangentials t.resstitir 4800s. -

ANSYS 5.6JUL 6 200013:06:37AVG ELEMENT SOLUTIONSTEP=53SUB =145TIME=4800DMGDMXSMNSMX

(3ivG

=.063181=.013981=1.005.013981.124105.234229.344353.454477.564601.674725.7’84849.8949731.005

i)

-9—A4nn., . . . . . . . . . -... —— ---rig. AIY:~lsK wlmnole[~ate~ti 16MND5). Creep andplastici~ atT=1373K

andoO= lo~a.DamageWrMOOs.


1,00

.90

.80

.70

40

.30

.20

.10

0 *2}

\m.. -.m - . . . . . . . . . . . ..-. — —-. —J!qg. AAJ: DISK wm hole [Material 16MNlJ5). Creep and plasticity at T=1373 K

and 00= loMl?a. Darnage over time at fonr points: DMG-1 at (x=O; y=r~),

DMG-2 at (O; 1.5 r~), DMG-3 at (O; 2.5 r~), DMG-4 at (O; b).

CXIO* *E?)2524

21

\ \

18 S–tan–2f d ~ —

15 ~ - 5-tan–3~

12S–tan–4

.9

6-

3:-tan- 1

0 (X IO**2}o 8 16

424 32

1240

2048

28 36 44 52

Fig. AZl: Disk with hole (Material 16MND5). Creep and plasticity at T=1373 K

ando O= lohlll?a. Tangential stress over time at four points (see Figure A13)


rxl

5.00

4.50

4 <00

3.50

3.00

2.50

2.00

1.50

!.00

,50

0**–1)

E PCR–2

2)I I I t 1 Io v I I I I (*IO**

o 8 16 24 32 40 I 484 12 20 28 36 44 52

TIME < S)

. .. —-— --- . . . . . . . m.fi-mr7

Fig. A22: Disk with hole (Material 16MND3). Creep arm plastlcny at 1=15 ls A

and o ~ = 10MPa. Equivalent creep strain and equivalent plastic strain overtime

at points 1 and 2 (see Figure A13)


Appendix 2: CRPGEN command reference

CRPGEN for Win NT/9x (Rev 1.4) - Command Reference Page 34

CRPGEN for WIN NT / 9x (Revision 1.4)Command Reference

clear

Delete all preceding settings of the crda~ time, epmax, sigma, temp commands.

crdat,stloc,cl ,c2,c3,c4,c5,c6

Set the creep parameters (cl-c~,cT-clO)and select creep law (cb). M’ZOC refers to the frostcreep parameter to be input (e.g. crdat,4,cl,c2,c3 reads the constants CA,c~ and Cb).If c~= Ouse strain hardening model according to:

[1E=cl”oc’” Ec3”exp -9T

If Cb= 1 use time hardening model according to:

[1C4E=cpc’ .tc3. exp –~

If Cb= 2 use time hardening model according to:

H~=cl”cJc2” [tc3+cT .tc8+cg. tc’O]. exp –q T

(c, is unused)

(cS is unused)

(c, is unused)L ‘J

cnvsig,si~ac,[sigofl

Convert a creep function to another stress unit system (e.g. from Pa to MPa). This commandcan be used to change existing creep data files to use them in different engineering unitsystems. The stress level in a creep data fde is changed according to:

0 new = sigfac” 0 ~1~+ sigoff. Thecommand should only be used in connection with read

and write.Example:

read,file1.cO1cnvsig,1.0e+06wnte,file2.cOl

epmax,epnzax

Define the maximum strain up to which the creep curve&(&) is to be generated. Command

is required for c~ = O (see crdat).


exit

Terminate the program. The data base is not automatically saved. Use the write command. I

plot,plkey

Plot creep curves. If plkey = O, plot &(t) and ~ (t) , if plkey = 1 plot ~(&).

prdat

Print creep parameters to standard output.

read$kameRead a creep data file. jlzame is the ASCII file containing a creep curve

& = &(&) ~=const;T=const

rsolve

Continue the solution after the change of creep parameters. This command can be used togenerate creep curves which are governed by different creep equations (e.g. primary,secondary and tertiary creep stage). A solve command must have been entered before the f~strsolve command. An additional time or epmax command is also required, where theendtime or epmax argument must be greater than that of the previous solve or rsolve process.

Stress and temperature must not be changed after the solve command.Examplesigma,100temp,800crdat,l,1.Oe-l6,2.2,-0.14,9860,0,1time,3000steps,200solvecrdat,1,3.0e-15,2.2,0.01,9860,0,1time,5600steps,150rsolvewnte,crpdat.cO1

sigma,sigma

Define the stress level for the creep curve.


solve

Start generation of creep data. Command requires creep parameters to be input (see crdat,time, epmax, steps).

steps,nstep

Define the number of time/ strain steps; nstep pairs [&; i ] are to be generated.

temp,temp

Define the temperature level for the creep curve to be generated.

time,endtirne

Set maximum time for creep data generation to endtime. This command is required for CG= 1(see crdat-command) and for plotting time-dependent creep curves (see plot,O)

write$ame

Write generated creep data to the ASCII file j%ame.


General Shell Commands (Macro-Lanwage)

delvar

Clear all defiied variables. See also: Definition of variables, *stat

*do,dovar,dostart,dostop[,dostep]

Execute a do-loop within a command fide (see /inp). The command is not possible fromstandard input. The loop variables dostart,dostop, dostep can be numbers, variables orexpressions (dostart e= dostop; dostep > O). The loop must be closed by *enddo in the samecommand file where it was opened. The loop body must not refer to another command file.Up to 10 do-loops can recursively be opened at the same time.

echo,key

Switch on/off command echo to standard output

leof

Terminate the input stream from the current input file and redirect it to the prior unit.

help

Open help file (Acrobat Reader required).

*if,exprI ,op,expr2,thencommand-block

[*elseif,exprl,op,expr2,then][command-block]

. ..0

[*else][command-block]

*endif

Branching within a command file (not possible from standard input). exprl and expr2 arenumerical values, variables or expressions; op={eq, ne, lt, gt, le, ge }. The syntax is similar tothe FORTRAN prog amming language, but *endif and then are required. Recursive if-statements are possible.


/input$zanze

Directs input stream to file frame. Recursive switches are possible.If files with extention ,,.mat” (macros) are existing in the current working directory, thesemacros files can be input by simply typing the basename of the macro file (e.g. type ,,macOl”to input the command file ,,macOl .mac”).

/out&me

Switch program printouts from standard output to file frame. If fname is not input, switchback to standard output.

*stat

Printall defiied variables. See also: Deftition of variables, delvar

Definition of variables

Variables can be defined byvar=valuewhere value can be a number, a name of a variable, a numerical expression or a characterstring. The name of the variable var must begin with a letter and can consist of 8 characters.Expressions can be assembled from numbers and numerical variables. Valid operators are:

left (opening) brackec ( right (closing) brackek

ph.Is (addition): + minus (subtraction): -

multiplication: * division: 1

power operation **

)

The defined variables are global ones. The character equivalents of variable values can beused in command strings by: strl %varname%str2 (%varmune% is replaced by its charactervalue). For example the following commands are equivalent

Varl=’xyz’read,file%varl YO read,fllexyz

vnum=23siglab, 1,s%vnum%b siglab,l ,s23b

Floating point variables are truncated to integer. If for example a=3.25E+Ol, then the resultof %a% is ,,32”.

Documents

Extension of the ANSYS@ creep and damage simulation