research on the controlling parameters of creep-thermal

Hindawi Publishing CorporationAdvances in Mechanical EngineeringVolume 2013 Article ID 406129 8 pageshttpdxdoiorg1011552013406129

Research ArticleResearch on the Controlling Parameters ofCreep-Thermal Fatigue Crack

Ming Yan Xiang-jun Zhu and Shi-jie Wang

School of Mechanical Engineering Shenyang University of Technology Shenyang 110870 China

Correspondence should be addressed to Ming Yan yanming7802163com

Received 2 August 2012 Revised 15 December 2012 Accepted 8 January 2013

Academic Editor Shandong Tu

Copyright copy 2013 Ming Yan et alThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The opening process of creep-thermal fatigue crack (CTFC) is studied by finite element method considering the bilinear kinematichardening and creep characteristic of the materialThe crack is closed under the compressive thermal stress during the heating andinsulating processes The appearance of tensile stress during the late cooling process which is normal to the crack face makes thecrack gradually open At this time the temperature of material around the crack has become lower than the creep temperaturetherefore the creep fracture mechanism parameter Clowast is not applicable The CTFC is quite shallow and comparatively the plasticzone is rather large thus the method of stress intensity factor is restricted A modified J-integral method is put forward accordingto the stress analysis of CTFC which has been proved to be path independent and validThemethod is used for not only the CTFCbut also any unloading crack or the crack in the residual compressive plastic strain field Experimental results show that themodifiedJ-integral can be used as the controlling parameter of the CTFC propagation

1 Introduction

For damage-tolerant design and remaining life prediction ofhigh-temperature components it is important to investigatecreep-fatigue crack growth behavior [1 2] A large numberof studies on creep-fatigue crack growth have been reportedin recent years Most of them are on the crack under creepthermomechanical fatigue (TMF) conditions which refer toa thermal cycling loading with an additional mechanicalloading

Typical creep thermomechanical fatigue model workswith one side fixed and the other side under cycling externalload the temperature cycles with the external loadThe TMFcrack opens under tensile load and the crack opening dis-placement increases continuously with the combinationeffect of tensile holding load and temperature thus the TMFcrack propagation can be thought of as the combination insome way of crack propagation caused by TMF and creepThe crack propagation caused by TMF can be characterizedby using stress intensity factor or 119869-integral as a controllingparameter and crack propagation caused by creep can becharacterized by using creep fracture mechanism parameter119862lowast as a controlling parameter [3ndash5]

In addition there are cooling duct in nuclear power plantsolar panel of aircrafts in low earth orbit pulsed high powerlaser driver hot work die roller of the hot mill cylinder ofhigh power diesel engine brake disk of high-speed trains andother components working under creep-thermal fatigue con-dition which refers to a pure thermal cycling Comparativelythe study on the controlling parameters of CTFC is paid lessattention [6ndash8]

Creep-thermal fatigue model is fixed on both sides andthere is no external load During heating process compres-sive elastic strain generates in the specimen during insulatingprocess compressive creep strain generates in the specimenand the cracks keep closed in both heating and insulatingprocesses However how could creep-thermal fatigue crackgrow Actually the inelastic strain generating during theheating and insulating processes could not recover freelyTherefore the tensile stress which is normal to the crack facesand generated in the late cooling process makes the crackopen and grow Thus it can be seen that there is really quite adifference between the mechanism of creep-thermal fatiguecrack and that of the thermomechanical fatigue crack thecontrol parameter of the creep thermomechanical fatiguecannot be used directly on the creep-thermal fatigue crack

at PENNSYLVANIA STATE UNIV on May 9 2016adesagepubcomDownloaded from

2 Advances in Mechanical Engineering

Table 1 Chemical composition (quality fraction) () of ZL111

Major elements ImpuritySi Cu Mn Mg Ti Fe Zn Sn Pb80 sim 100 13 sim 18 01 sim 035 04 sim 06 01 sim 035 lt04 lt01 lt001 lt005

Considering the bi-linear kinematic hardening and creepcharacteristic of the material the CTFC is analyzed by thefinite element method and its controlling parameters arestudied accordingly

2 Modeling and Material Properties

21 Modeling Assumption For convenience the actual com-ponent can be simplified to a rectangular plate (30mm times

10mm) fixed at both ends as shown in Figure 1(a) Assumethat the plate is in the plane stress state The temperature ofthe left side changes according to the curve shown in Figure 2and the temperature of the right side is always 30∘C A cracklies in the center of the left side and is enlarged in Figure 1(b)119877119860 and1198771198601015840 represent the crack faces (07mm)119877 is the cracktip

Generally in the finite element model the adjacentelements share one node to make the elements connect witheach other into a whole In the finite element model withcracks simulated crack elements have a fully coincidednode position on crack faces as is shown in Figure 1(b) theelements on both the up and down sides of the line AR Tosimulate the extrusion of the two crack faces during the heat-ing and insulating processes contact elements are used Tomeasure the singularity of the crack tip the elements aroundit should be quadratic with the midside nodes placed at thequarter points Such elements are called singular elements(Figure 1(c)) The mesh size at the crack tip is 003mm

22 Mechanical Properties of Material ZALSi9Cu2Mg (ZL111)is a kind of cast aluminumalloy and its chemical compositionis shown in Table 1 It is often used to cast the large dieselengine cylinder heads of naval vessels that are subject tothermal fatigue and creep damage in service

ZALSi9Cu2Mg (ZL111) has superior mechanical proper-ties under the room temperature and high temperature It isthematerial with bi-linear kinematic hardening [9] as shownin Figure 3 where OABC is the actual tensile curve and 119860is the yield point After yielding the relationship of stressand strain is nonlinear According to the bi-linear kinematichardening rule curve ABC can be replaced by straight lineAC and CDEF represents the unloading process

The creep equation of ZL111 is [10]

120576c= 119862112059011986221199051198623119890minus1198624119879

(1)

where 120576c is the creep rate (1119904)119862

119894(119894 = 1 2 3 4) are constants

From experiments 1198621= 05852 times 10

minus5 1198622= 2564 119862

3=

minus0764 and 1198624= 5196060 Other mechanical parameters

can be obtained by interpolation according to Table 2 119879represents the temperature (∘C)

119884

119883119874

(a)

119860(119860998400)119877

(b)

119874

119872

119873

119869

119870

119868 119875 119871

(c)

Figure 1 Finite element model

0 10 20 30 40 50 60 70 80 90 100Time (min)

230

210

190

170

150

130

110

90

70

50

30

Tem

pera

ture

(∘C)

Figure 2 Temperature curve


Advances in Mechanical Engineering 3

Table 2 Mechanical parameters of ZL111

Temperature (∘C) Linear expansionCoefficient (10minus6 sdot ∘Cminus1)

Elastic modulus(MPa) Poissonrsquos ratio Yield limit (MPa) Tangent modulus

(MPa)20 186 71500 031 180 10840100 189 69800 031 168 8670150 200 68000 031 155 6720200 215 65000 032 141 4740220 220 63000 032 136 2040

119860

119861

119862

119863

119864

119865

119874

120590

1205901

1205902

1205760 1205761 120576 1205762

Figure 3 The bilinear kinematic hardening model

3 Stress Analysis of CTFC

The commercial finite element package ANSYS and thesequential coupling analysis method are employed to com-pute the thermal stress First the initial conditions andboundary conditions for a thermal analysis are set to themodel to obtain the temperature field of the model at everydiscrete time Then put the nodal temperature as thecoupled-field loads and the structure boundary conditions tothe model for a stress analysis The stress and strain fields atevery discrete time can be obtained The temperature field isjust the thermal load for the stress analysis rather than theobjective of the paper and so it is out of discussion

Figure 4 shows the stress curve of the crack tip (119877 point)in one cycle it is obvious that the Mises equivalent stress isdominated by the 119884 component Its 119884 components of strainare shown in Figure 5

In the heating process (0ndash10min) the thermal strainincreases with the temperature and the model cannot expand

0 10 20 30 40 50 60 70 80 90 100

0

100

200

300

400

Stre

ss (M

Pa)

X stress componentY stress component

XY shear stress componentMises equivalent stress

Time (min)

minus200

minus100

Figure 4 Stress components of the crack tip

freely due to the restrictions at both ends so compressiveelastic strain and stress are produced the plastic compressivestrain appears when the stress reaches the compressive yieldpoint of the material In the insulating process (10ndash90min)compressive creep strain appears in the common role of com-pressive stress and time simultaneously the elastic compres-sive strain and compressive stress decrease and the thermalstrain and the plastic strain keep constant In the cooling pro-cess (90ndash100min) the thermal strain and compressive elasticstrain gradually disappear and the model trends to its initialshape Because the model is fixed at both ends and the com-pressive plastic and creep strain cannot get back freely thetensile stress which is normal to the crack faces is produced

If the tensile stress reaches the reverse yield point thematerial will yield reversely The crack opens gradually withthe increase of tensile stress

The pressure on points 119860 and 119877 is shown in Figure 6In the heating process (0ndash10min) the pressure on the crackfaces increases for the temperature of point 119860 is higher thanthat of point 119877 so the pressure on point 119860 is higher In theinsulating process (10ndash90min) the pressure on the crackfaces decreases slowly owing to stress relaxation the creeprate of point119860 is larger so its pressure decreasesmore sharplyIn the cooling process (90ndash100min) the pressure declinesrapidly the pressure on points 119860 and 119877 becomes zero at



0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

Time (min)

Y co

mpo

nent

s str

ain

Elastic strainPlastic strain

Creep strainThermal strain

times10minus3

minus4

minus2

Figure 5 Strain components in the 119884 direction of the crack tip

0 20 40 60 80 1000

20

40

60

80

100

120

140

160

180

Time (min)

Pres

sure

(MPa

)

119877 point119860 point

Figure 6 The pressure on points 119860 and 119877

95min which proves that the two crack faces separate at thistime Figure 7 shows the displacements in the 119884 direction ofpoints 119860 and 1198601015840 as well as their relative ones

Figure 8 is the deformation of the crack region at 100min(the deformation is magnified to 10 times) The red areaaround the crack tip is the tensile plastic zone outside whichis a green area Some compressive plastic strain produced inthe heating process remains here in various extents so it iscalled compressive plastic zone

One point is picked up in each of the tensile plastic zoneand compressive plastic zone randomly marked as 119879 and 119862Figure 9 gives the strain components in the 119884 direction ofpoints 119879 and 119862 Figure 10 gives their 119884 components of stress

0 20 40 60 80 100

0

2

4

6

8

Disp

lace

men

t (m

m)

Relative displacement

Time (min)

times10minus3

minus4

minus2

119860 point119860998400 point

Figure 7 The displacements in the 119884 direction of points 119860 and 1198601015840as well as their relative one

MNMX

Figure 8 The deformation of the crack region at 100min

From the figures stress and the elastic strain of the two pointsget to zero at the moment of the crack opening which is justas the crack tip

According to the above analysis it can be deduced thatthe compressive plastic strains produced in heating andcompressive creep strain produced in insulating cannot comeback freely during cooling which will make the CTFC openIt can be also concluded that the more the compressiveinelastic strain is during heating and insulating the larger thetensile stress the tensile strain and the opening displacementof CTFC will be at the end of cooling



0

1

2

3

4

0 20 40 60 80 100

Time (min)

times10minus3

minus3

minus1

minus2

Elastic strain of 119862 pointPlastic strain of 119862 point


Stra

in co

mpo

nent

s in119884

dire

ctio

n

Figure 9 Strain components in the 119884 direction of points 119879 and 119862

4 Controlling Parameters of CTFC

The CTFC opens gradually in the late cooling process Atthis time the temperature of the material around the crackhas become lower than the creep temperature Therefore thecreep fracturemechanismparameter119862lowast ismeaningless to theCTFC Suppose the stress intensity factor or 119869-integral will bethe controlling parameter of the CTFC in the following

41 Stress Intensity Factor Method The stress intensity factorof a crack for a linear elastic fracture mechanics analysis maybe computed according to a fit of the nodal displacementsin the vicinity of the crack [11 12] In the small-scale yieldingcondition the factor can be modified according to [13]

Generally the small-scale yielding condition for a cracklength 119886 is [13]

119903119901

119886le 01 (2)

where 119903119901is the size of plastic zone here it is themean distance

from the boundary of the tensile plastic zone to the cracktip The CTFC is always quite shallow [6] comparatively theplastic zone is rather largeThe small-scale yielding conditioncan be satisfied only when the singularity of the crack issmall

42 Proposition of aModified 119869-IntegralMethod The classicaldefinition of 119869-integral is given by

119869 = int120574

119908119889119910 minus int120574

T120597u120597119909119889119904 (3)

where 120574 represents any path surrounding the crack tip 119904 is thedistance along the path T is the stress tensor vector u is thedisplacement tensor vector 119908 is the strain energy density inthe monotonic loading process

0

50

100

150

200

250

300

Stre

ss co

mpo

nent

s in

di

rect

ion

(MPa

)

minus200

minus150

minus100

minus50

0 20 40 60 80 100

Time (min)

119884


Figure 10 Stress components in the 119884 direction of points 119879 and 119862

From the previous stress analysis of the CTFC thethermal stress near the crack does not loadmonotonously in atemperature cycle which does not meet the path-independ-ent conditionMoreover affected by the residual compressiveplastic strain field at the end of cooling the integral might benegative Thus the 119869-integral method must be improved toapplicable to be the CTFC

T120597u120597119909= (120590119909119899119909+ 120590119909119910119899119910)120597119906119909

120597119909+ (120590119910119899119910+ 120590119909119910119899119909)120597119906119910

120597119909 (4)

where 119899 is the unit outer normal vector to path 120574 It isobvious that the later term of the 119869-integral is naturally pathindependent and immune to the compressive plastic strainfield

According to the plastic deformation theory the strainenergy density is represented by

119908 = 119908119909119909+ 119908119909119910+ 119908119910119910

119908119894119895= int

120576

0

120590119894119895(119905) sdot 120576119894119895(119905) 119889119905

(5)

where120590119894119895 120576119894119895(119894 119895 = 119909 119910) are respectively the stress and strain

components Here only the improvement of 119908119910119910

similar tothat of 119908

119909119909and 119908

119909119910is discussed in detail

From the stress analysis of the CTFC the 119884 componentsof stress and elastic strain around the crack can be zero almostat the same timewhen the crack opensMoreover the coolingperiod can be regarded as amonotonic loading processThusonly the strain energy in this period should be computed

119908yy = int1199052

1199051

120590119910119910(119905) sdot 120576119910119910(119905) 119889119905 (6)

where 1199051stands for the moment of the opening and 119905

2is the

terminal time of cooling In order to eliminate the effect of



the residual compressive plastic strain field 120576119910119910(119905) is obtained

as

120576119910119910(119905) = 120576

119890

119910119910(119905) + 120576

119901

119910y (119905) minus 1205761199010

119910119910 (7)

where 120576119890yy(119905) 120576119901

yy(119905) are separately the elastic and plastic com-ponents of strain at the end of cooling 1205761199010

119910119910is the compressive

plastic strain produced in the heating processThe improvement of 119869-integral is put forward according

to the analysis of CTFC according to its definition Theintegral computed in this way is path independent Thus itcould be the controlling parameter of CTFC

In the linear elasticity small-scale yielding conditionsand plane stress conditions 119869-integral is related to stressintensity factor by the following relationship

119869 =1198702

Ι

119864 (8)

where 119864 is the elastic modulus Therefore the stress intensityfactor119870

Ιcan validate the modified 119869-integral cursorily

5 Examples

Take a group of concentric circles whose center is crack tipand radius is 119903 as the integral paths Figure 11 shows therelation between themodified 119869-integral and 119903119903

119901 Clearly the

modified 119869-integral is path independent as long as the integralpath is within the compressive plastic zone

The stress intensity factor and the modified 119869-integral arecalculated under different conditions The results are showninTables 3 4 and 5 In (8) the elasticmodulus119864 is 71175MPa

It is obvious that the stress intensity factor and the 119869-integral increases when the insulating time prolongs themaximum temperature increases and the crack grows Fromcalculating the stress intensity factor can be used as thecontrolling parameter of the CTFC only with a low heatingtemperature a short period of holding time and a deep crack

6 CTFC Propagation Test

The creep-thermal fatigue test machine is composed ofclamping mechanism infrared radiation heating devicehydropneumatic cooling system and control system Theoperational principle of the creep-thermal fatigue testmachine is shown in Figure 12 the specimens can be turnedupside down by the driving shaft which makes it easy andquick to heat and cool the specimensThe detailed size of thespecimen with cracks is shown in Figure 13The first secondand third specimens are used in the creep-thermal fatiguetest the temperature of the specimen cycles is from 30∘C to210∘C and the thermal cycle insulating time is 5 minutes at210∘C every time All the specimens undergo 1000 thermalcycles The length of the crack is detected for each 100 cyclesand the results are shown in Figure 14

The secant method [14] is used to measure the crackgrowth rate that is to calculate the gradient between two

0 1 2

1

04

05

0402

06

06

07

08

08

09

12 14 16 18119903119903119901

119869(J

mmminus2)

Figure 11 The relationship of 119869-integral and 119903119903119901

++

1 2 3 4 5 6 7 8

Figure 12 Operational principle diagram of the creep-thermalfatigue test machine 1 driving shaft 2 stock of the specimen 3unloading bolt 4 tightening bolt 5 infrared radiation heatingdevice 6 specimen 7 hydropneumatic cooling system and 8 armof the test machine

adjacent data points on the 119886-119873 curve to get the crack growthrate as

119889119886

119889119873asympΔ119886

Δ119873=119886119894+1minus 119886119894

119873119894+1minus 119873119894

(9)

where 119889119886119889119873 is the crack propagation under one thermalcycle Δ119886 is the crack propagation under Δ119873 thermal cycles119886119894and 119873

119894are the crack length and number of cycles of load

corresponding to the 119894th data pointAccording to the Paris formula

119889119886

119889119873= 119862119869119899

(10)

where 119862 and 119899 are constants related to material propertyenvironmental media and the geometry of the specimen

The creep-thermal fatigue 119869-integral value in correspond-ing conditions can be obtained according to the modified J-integral method referred to in the front of the paper the datapoints of ln(119889119886119889119873) and ln 119869 are shown in Figure 15 hence



Table 3 The crack length is 07mm the maximum temperature is 210∘C

Holding time(min)

Size of plasticzone (mm)

Stress intensity factor(MPa sdotmmminus05)

Modified 119869-integral(J sdotmmminus2)

1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950

Table 4 The crack length is 07mm the insulating time is 80min

Maximumtemperature (∘C)

Size of plastic zone(mm)



1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148

Table 5 The maximum temperature is 200∘C the insulating time is 80min

Crack length (mm) Size of plastic zone(mm)



1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370

Figure 13 Specimen of creep-thermal fatigue

119899 = 251 119862 = 872times10minus6 can be obtained by some regressionanalysis of formula (10) using these data points

7 Conclusions

(1) The crack is closed under the compressive thermalstress during the heating and insulating processesBecause the inelastic strain generating in the two

0 200 400 600 800 10000

05

1

15

2

25

3

35

Number of thermal cycles

Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3

Figure 14 Propagation length of the CTFC

processes cannot be back by itself the tensile stressduring the late cooling process which is normal to thecrack faces makes the crack gradually open

(2) When the CTFC is opening the temperature of thematerial around it has become lower than the creep



119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3

Figure 15 (119889119886119889119873)mdash119869 data in double logarithmic coordinate

temperature therefore the creep fracture mechanismparameter 119862lowast is not applicable The stress intensityfactor and 119869-integral can be used as the controllingparameters The stress intensity factor can be usedonly with a short insulating time a low maximumtemperature and a deep crack The 119869-integral shouldbe modified in order to be applicable to the CTFCthat is to take the moment of opening as the startingof the strain energy density integral and eliminatethe effect of the residual compressive plastic strain by(7) It has been proved that the modified 119869-integralmethod is path independent and valid It is used fornot only theCTFCbut also any unloading crack or thecrack in the residual compressive plastic strain fieldThe stress intensity factor and 119869-integral increasewhen the insulating time prolongs the maximumtemperature rises and the crack grows

(3) Experimental results show that the modified 119869-integral can be used as the control value of the CTFCpropagation The research on the controlling param-eters of CTFC provides the theoretical basis for itsgrowth

Acknowledgments

This project is supported by the Natural Science Foundationof Liaoning Province (Grant no 201102167) Aeronautical Sci-ence Foundation of China (Grant no 20110450001) LiaoningExcellent Talents in University (Grant no LJQ2011012) andthe Science Program of Shenyang (Grant No F12-069-2-00)

References

[1] N Gao M Brown K J Miller and P A S Reed ldquoAn investiga-tion of crack growth behaviour under creep-fatigue conditionrdquo

Materials Science and Engineering A vol 410 no 25 pp 67ndash712005

[2] M F Geng ldquoAn idea for predicting crack growth time tofracture under creep-fatigue conditionsrdquoMaterials Science andEngineering A vol 257 no 2 pp 250ndash255 1998

[3] Y L Lu L J Chen P K Liaw et al ldquoEffects of temperature andhold time on creep-fatigue crack-growth behaviorrdquo MaterialsScience and Engineering A vol 429 no 1-2 pp 1ndash10 2006

[4] A T Yokobori and T Satoh ldquoThe characterization of creepcrack growth rate and its life of TiAl inter-metallic compoundwith full lamellar microstructurerdquo International Journal ofPressure Vessels and Piping vol 88 no 7 pp 435ndash440 2011

[5] G Marahleh A R I Kheder and H F Hamad ldquoCreep-lifeprediction of service-exposed turbine bladesrdquoMaterials Sciencevol 42 no 4 pp 476ndash481 2006

[6] V Maillot A Fissolo G Degallaix and S Degallaix ldquoThermalfatigue crack networks parameters and stability an experimen-tal studyrdquo International Journal of Solids and Structures vol 42no 2 pp 759ndash769 2005

[7] J Lansinger T Hansson andO Clevfors ldquoFatigue crack growthunder combined thermal cycling and mechanical loadingrdquoInternational Journal of Fatigue vol 29 no 7 pp 1383ndash13902007

[8] N Haddar A Fissolo and V Maillot ldquoThermal fatigue cracknetworks an computational studyrdquo International Journal ofSolids and Structures vol 42 no 2 pp 771ndash788 2005

[9] G T Yang Theory of Elasticity and Plasticity China BuildingMaterials Industry Press Beijing China 2005

[10] H Kraus Creep Analysis Wiley International Science Publica-tion New York NY USA 1980

[11] Z D Jiang A Zeghloul G Bezine and J Petit ldquoStress intensityfactors of parallel cracks in a finite width sheetrdquo EngineeringFracture Mechanics vol 35 no 6 pp 1073ndash1079 1990

[12] G Agnihotri ldquoStress analysis of a crack using the finite elementmethodrdquo Engineering FractureMechanics vol 44 no 1 pp 109ndash125 1993

[13] R Narasimhan and A J Rosakis ldquoA finite element analysis ofsmall-scale yielding near a stationary crack under plane stressrdquoJournal of the Mechanics and Physics of Solids vol 36 no 1 pp77ndash117 1988

[14] P Bensussan High Temperature Fracture Mechanisms andMechanic Mechanical Engineering Publications 2005



Table 1 Chemical composition (quality fraction) () of ZL111

Major elements ImpuritySi Cu Mn Mg Ti Fe Zn Sn Pb80 sim 100 13 sim 18 01 sim 035 04 sim 06 01 sim 035 lt04 lt01 lt001 lt005

Considering the bi-linear kinematic hardening and creepcharacteristic of the material the CTFC is analyzed by thefinite element method and its controlling parameters arestudied accordingly

2 Modeling and Material Properties

21 Modeling Assumption For convenience the actual com-ponent can be simplified to a rectangular plate (30mm times

10mm) fixed at both ends as shown in Figure 1(a) Assumethat the plate is in the plane stress state The temperature ofthe left side changes according to the curve shown in Figure 2and the temperature of the right side is always 30∘C A cracklies in the center of the left side and is enlarged in Figure 1(b)119877119860 and1198771198601015840 represent the crack faces (07mm)119877 is the cracktip

Generally in the finite element model the adjacentelements share one node to make the elements connect witheach other into a whole In the finite element model withcracks simulated crack elements have a fully coincidednode position on crack faces as is shown in Figure 1(b) theelements on both the up and down sides of the line AR Tosimulate the extrusion of the two crack faces during the heat-ing and insulating processes contact elements are used Tomeasure the singularity of the crack tip the elements aroundit should be quadratic with the midside nodes placed at thequarter points Such elements are called singular elements(Figure 1(c)) The mesh size at the crack tip is 003mm

22 Mechanical Properties of Material ZALSi9Cu2Mg (ZL111)is a kind of cast aluminumalloy and its chemical compositionis shown in Table 1 It is often used to cast the large dieselengine cylinder heads of naval vessels that are subject tothermal fatigue and creep damage in service

ZALSi9Cu2Mg (ZL111) has superior mechanical proper-ties under the room temperature and high temperature It isthematerial with bi-linear kinematic hardening [9] as shownin Figure 3 where OABC is the actual tensile curve and 119860is the yield point After yielding the relationship of stressand strain is nonlinear According to the bi-linear kinematichardening rule curve ABC can be replaced by straight lineAC and CDEF represents the unloading process

The creep equation of ZL111 is [10]

120576c= 119862112059011986221199051198623119890minus1198624119879

(1)

where 120576c is the creep rate (1119904)119862

119894(119894 = 1 2 3 4) are constants

From experiments 1198621= 05852 times 10

minus5 1198622= 2564 119862

3=

minus0764 and 1198624= 5196060 Other mechanical parameters

can be obtained by interpolation according to Table 2 119879represents the temperature (∘C)

119884

119883119874

(a)

119860(119860998400)119877

(b)

119874

119872

119873

119869

119870

119868 119875 119871

(c)

Figure 1 Finite element model

0 10 20 30 40 50 60 70 80 90 100Time (min)

230

210

190

170

150

130

110

90

70

50

30

Tem

pera

ture

(∘C)

Figure 2 Temperature curve






(MPa)20 186 71500 031 180 10840100 189 69800 031 168 8670150 200 68000 031 155 6720200 215 65000 032 141 4740220 220 63000 032 136 2040

119860

119861

119862

119863

119864

119865

119874

120590

1205901

1205902

1205760 1205761 120576 1205762






0 10 20 30 40 50 60 70 80 90 100

0

100

200

300

400

Stre

ss (M

Pa)



Time (min)

minus200

minus100







0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

Time (min)

Y co

mpo

nent

s str

ain



times10minus3

minus4

minus2


0 20 40 60 80 1000

20

40

60

80

100

120

140

160

180

Time (min)

Pres

sure

(MPa

)






0 20 40 60 80 100

0

2

4

6

8

Disp

lace

men

t (m

m)


Time (min)

times10minus3

minus4

minus2

119860 point119860998400 point


MNMX






0

1

2

3

4

0 20 40 60 80 100

Time (min)

times10minus3

minus3

minus1

minus2



Stra

in co

mpo

nent

s in119884

dire

ctio

n






119903119901

119886le 01 (2)




119869 = int120574

119908119889119910 minus int120574

T120597u120597119909119889119904 (3)


0

50

100

150

200

250

300

Stre

ss co

mpo

nent

s in

di

rect

ion

(MPa

)

minus200

minus150

minus100

minus50

0 20 40 60 80 100

Time (min)

119884




T120597u120597119909= (120590119909119899119909+ 120590119909119910119899119910)120597119906119909

120597119909+ (120590119910119899119910+ 120590119909119910119899119909)120597119906119910

120597119909 (4)



119908 = 119908119909119909+ 119908119909119910+ 119908119910119910

119908119894119895= int

120576

0

120590119894119895(119905) sdot 120576119894119895(119905) 119889119905

(5)




119909119909and 119908



119908yy = int1199052

1199051

120590119910119910(119905) sdot 120576119910119910(119905) 119889119905 (6)


2is the





as

120576119910119910(119905) = 120576

119890

119910119910(119905) + 120576

119901

119910y (119905) minus 1205761199010

119910119910 (7)

where 120576119890yy(119905) 120576119901






119869 =1198702

Ι

119864 (8)



5 Examples


119901 Clearly the







0 1 2

1

04

05

0402

06

06

07

08

08

09

12 14 16 18119903119903119901

119869(J

mmminus2)


++

1 2 3 4 5 6 7 8



119889119886

119889119873asympΔ119886

Δ119873=119886119894+1minus 119886119894

119873119894+1minus 119873119894

(9)




119889119886

119889119873= 119862119869119899

(10)






Holding time(min)




1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950






1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148





1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370



7 Conclusions


0 200 400 600 800 10000

05

1

15

2

25

3

35


Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3






119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References





















(MPa)20 186 71500 031 180 10840100 189 69800 031 168 8670150 200 68000 031 155 6720200 215 65000 032 141 4740220 220 63000 032 136 2040

119860

119861

119862

119863

119864

119865

119874

120590

1205901

1205902

1205760 1205761 120576 1205762






0 10 20 30 40 50 60 70 80 90 100

0

100

200

300

400

Stre

ss (M

Pa)



Time (min)

minus200

minus100







0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

Time (min)

Y co

mpo

nent

s str

ain



times10minus3

minus4

minus2


0 20 40 60 80 1000

20

40

60

80

100

120

140

160

180

Time (min)

Pres

sure

(MPa

)






0 20 40 60 80 100

0

2

4

6

8

Disp

lace

men

t (m

m)


Time (min)

times10minus3

minus4

minus2

119860 point119860998400 point


MNMX






0

1

2

3

4

0 20 40 60 80 100

Time (min)

times10minus3

minus3

minus1

minus2



Stra

in co

mpo

nent

s in119884

dire

ctio

n






119903119901

119886le 01 (2)




119869 = int120574

119908119889119910 minus int120574

T120597u120597119909119889119904 (3)


0

50

100

150

200

250

300

Stre

ss co

mpo

nent

s in

di

rect

ion

(MPa

)

minus200

minus150

minus100

minus50

0 20 40 60 80 100

Time (min)

119884




T120597u120597119909= (120590119909119899119909+ 120590119909119910119899119910)120597119906119909

120597119909+ (120590119910119899119910+ 120590119909119910119899119909)120597119906119910

120597119909 (4)



119908 = 119908119909119909+ 119908119909119910+ 119908119910119910

119908119894119895= int

120576

0

120590119894119895(119905) sdot 120576119894119895(119905) 119889119905

(5)




119909119909and 119908



119908yy = int1199052

1199051

120590119910119910(119905) sdot 120576119910119910(119905) 119889119905 (6)


2is the





as

120576119910119910(119905) = 120576

119890

119910119910(119905) + 120576

119901

119910y (119905) minus 1205761199010

119910119910 (7)

where 120576119890yy(119905) 120576119901






119869 =1198702

Ι

119864 (8)



5 Examples


119901 Clearly the







0 1 2

1

04

05

0402

06

06

07

08

08

09

12 14 16 18119903119903119901

119869(J

mmminus2)


++

1 2 3 4 5 6 7 8



119889119886

119889119873asympΔ119886

Δ119873=119886119894+1minus 119886119894

119873119894+1minus 119873119894

(9)




119889119886

119889119873= 119862119869119899

(10)






Holding time(min)




1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950






1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148





1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370



7 Conclusions


0 200 400 600 800 10000

05

1

15

2

25

3

35


Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3






119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References


















0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

Time (min)

Y co

mpo

nent

s str

ain



times10minus3

minus4

minus2


0 20 40 60 80 1000

20

40

60

80

100

120

140

160

180

Time (min)

Pres

sure

(MPa

)






0 20 40 60 80 100

0

2

4

6

8

Disp

lace

men

t (m

m)


Time (min)

times10minus3

minus4

minus2

119860 point119860998400 point


MNMX






0

1

2

3

4

0 20 40 60 80 100

Time (min)

times10minus3

minus3

minus1

minus2



Stra

in co

mpo

nent

s in119884

dire

ctio

n






119903119901

119886le 01 (2)




119869 = int120574

119908119889119910 minus int120574

T120597u120597119909119889119904 (3)


0

50

100

150

200

250

300

Stre

ss co

mpo

nent

s in

di

rect

ion

(MPa

)

minus200

minus150

minus100

minus50

0 20 40 60 80 100

Time (min)

119884




T120597u120597119909= (120590119909119899119909+ 120590119909119910119899119910)120597119906119909

120597119909+ (120590119910119899119910+ 120590119909119910119899119909)120597119906119910

120597119909 (4)



119908 = 119908119909119909+ 119908119909119910+ 119908119910119910

119908119894119895= int

120576

0

120590119894119895(119905) sdot 120576119894119895(119905) 119889119905

(5)




119909119909and 119908



119908yy = int1199052

1199051

120590119910119910(119905) sdot 120576119910119910(119905) 119889119905 (6)


2is the





as

120576119910119910(119905) = 120576

119890

119910119910(119905) + 120576

119901

119910y (119905) minus 1205761199010

119910119910 (7)

where 120576119890yy(119905) 120576119901






119869 =1198702

Ι

119864 (8)



5 Examples


119901 Clearly the







0 1 2

1

04

05

0402

06

06

07

08

08

09

12 14 16 18119903119903119901

119869(J

mmminus2)


++

1 2 3 4 5 6 7 8



119889119886

119889119873asympΔ119886

Δ119873=119886119894+1minus 119886119894

119873119894+1minus 119873119894

(9)




119889119886

119889119873= 119862119869119899

(10)






Holding time(min)




1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950






1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148





1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370



7 Conclusions


0 200 400 600 800 10000

05

1

15

2

25

3

35


Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3






119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References


















0

1

2

3

4

0 20 40 60 80 100

Time (min)

times10minus3

minus3

minus1

minus2



Stra

in co

mpo

nent

s in119884

dire

ctio

n






119903119901

119886le 01 (2)




119869 = int120574

119908119889119910 minus int120574

T120597u120597119909119889119904 (3)


0

50

100

150

200

250

300

Stre

ss co

mpo

nent

s in

di

rect

ion

(MPa

)

minus200

minus150

minus100

minus50

0 20 40 60 80 100

Time (min)

119884




T120597u120597119909= (120590119909119899119909+ 120590119909119910119899119910)120597119906119909

120597119909+ (120590119910119899119910+ 120590119909119910119899119909)120597119906119910

120597119909 (4)



119908 = 119908119909119909+ 119908119909119910+ 119908119910119910

119908119894119895= int

120576

0

120590119894119895(119905) sdot 120576119894119895(119905) 119889119905

(5)




119909119909and 119908



119908yy = int1199052

1199051

120590119910119910(119905) sdot 120576119910119910(119905) 119889119905 (6)


2is the





as

120576119910119910(119905) = 120576

119890

119910119910(119905) + 120576

119901

119910y (119905) minus 1205761199010

119910119910 (7)

where 120576119890yy(119905) 120576119901






119869 =1198702

Ι

119864 (8)



5 Examples


119901 Clearly the







0 1 2

1

04

05

0402

06

06

07

08

08

09

12 14 16 18119903119903119901

119869(J

mmminus2)


++

1 2 3 4 5 6 7 8



119889119886

119889119873asympΔ119886

Δ119873=119886119894+1minus 119886119894

119873119894+1minus 119873119894

(9)




119889119886

119889119873= 119862119869119899

(10)






Holding time(min)




1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950






1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148





1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370



7 Conclusions


0 200 400 600 800 10000

05

1

15

2

25

3

35


Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3






119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References



















as

120576119910119910(119905) = 120576

119890

119910119910(119905) + 120576

119901

119910y (119905) minus 1205761199010

119910119910 (7)

where 120576119890yy(119905) 120576119901






119869 =1198702

Ι

119864 (8)



5 Examples


119901 Clearly the







0 1 2

1

04

05

0402

06

06

07

08

08

09

12 14 16 18119903119903119901

119869(J

mmminus2)


++

1 2 3 4 5 6 7 8



119889119886

119889119873asympΔ119886

Δ119873=119886119894+1minus 119886119894

119873119894+1minus 119873119894

(9)




119889119886

119889119873= 119862119869119899

(10)






Holding time(min)




1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950






1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148





1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370



7 Conclusions


0 200 400 600 800 10000

05

1

15

2

25

3

35


Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3






119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References



















Holding time(min)




1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)0 00700 1944 05117 0531080 01050 09289150 01313 10750240 01570 11950






1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)180 0 239 00080 00082190 00630 1594 03440 03570200 00875 2115 05970 06285220 01778 14148





1198691015840

= (1198702

Ι119864)

(J sdotmmminus2)05 00623 0463309 01025 0702912 01220 0808815 01493 2526 08568 08965

02

02

3plusmn01

25plusmn01

25plusmn01

4

6

2

2

2

AAA

A A

002

002

002

002

6h7

20plusmn01

13 1370



7 Conclusions


0 200 400 600 800 10000

05

1

15

2

25

3

35


Crac

k pr

opag

atio

n ra

te (m

m)

1

2

3






119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References


















119869-integral100 101 102

10minus2

10minus3

10minus4

10minus5

1

2

3




Acknowledgments


References

















research on the controlling parameters of creep-thermal

Documents