THE NUMERICAL SIMULATION OF CRACK GROWTH IN WELD … · stress corrosion, fatigue and unstable crack propagation. The solution procedure and the individual results are first presented

LEVYEL: V"THE NUMERICAL SIMULATION OF CRACK GROWTH

IN WELD-INDUCED RESIDUAL STRESS FIELDS

by

M.F. Kanninen, F.W. Brust, J. Ahmad, and I.S. Abou-Sayed

C~)

A STRESS ANALYSIS AND FRACTURE SECTION

BATTELLE* • Col umbus Laboratories

.1 505 King AvenueColumbus, Ohio 43201

July, 1981 DTICSELECTEI

,: ~JAN 5 19M2

Invited paper for the 28th Army Sagamore Research Ccnference, Lake Placid,?c New York, July 13-17, 1981. To appear in the Conference Proceedings.

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THE NUMERICAL SIMULATION OF CRACK GROWTH IN InterimWELD-INDUCED RESIDUAL STRESS FIELDS 6. PERFORMNO ORAG. REPORT NUMBER

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M.F. Kanninen, F.W. Brust, J. Ahmad, and

I.S. Abou-Sayed N00014-77-C-0576 - Battelle

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Paper was presented at the 28th Army Sagamore Researh Conference, Lake Placid,

New York, July 13-17, 1981.

1I1. KFY WORDS (Continue on reverse side Ii necessarytend id•yI@ t. by bl.oc numbser)

Stress Corrosion Cracking; Fracture; Dynamic Crack Propagation, Finite Element

Analyses

V0. ABSTRACT (Continue on reverse side It neoessary aald identity by bloc.k numb*t)

A marriage of elastic plastic fracture mechanics techniques with thermoplasticfinite element analyses is developed to examine crack growth in the presence ofweld-induced residual stresses. A hypothetical crack growth relation based onthe crack tip opening displacement is used. Three problem areas are studied:stress corrosion cracking in a girth-welded pipe, fatigue crack growth undercyclic loading in a butt-welded plate, and dynamic crack propagation under impactloading in a butt-welded plate. Comparisons with computations carried out underconventional linear elastic assumptions are made. It is found that, ir. all three

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IVcases, neglect of the plaiatc deformation caused by the welding processappears to be anti-conservative. It is concluded that more realisticcomputations for crack growth in and around welds than are commonly usedmay be t.eeded for realistic structural in~egrity assessments.

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1'

THE NUMERICAL SIMULATION OF CRACK GROWTH

IN WELD-INDUCED RESIDUAL STRESS FIELDS

M. F. Kanninen, F. W. Brust,J. Ahmad, and I. S. Abou-SayedStress Analysis and Fracture SectionBattelle Columbus LaboratoriesColumbus, Ohio 43201

ABSTRACT

A marriage of elastic-plastic fracture mechanics techniqueswith thermoplastic finite element analyses is developed to examinecrack gruith in the presence of weld-induced residual stresses. Ahypothetical crack growth relation based on the crack tip openingdisplacement is used. Three problem areas are studied: stresscorrosion cracking in a girth-welded pipe, fatigue crack growthunder cyclic loading in a butt-welded plate, and dynamic crackpropagation under impact loading in a butt-welded plate. Compari-sons with computations carried out under conventional linear elas-tic assumptions are made. It is found that, in all three cases,

neglect of the plastic deformation caused by the welding processappears to be anti-conservative. It is concluded that more realis-tic computations for crack growth in and around welds than are com-monly used may be needed for realistic structural integrityas se ssme nt s.

INTRODUCTION

A significant proportion of all structural failures cin betraced to cracks emanating in and around welds. Crack grow.'ý inwelded regions must be strongly affected by the presence of theplastically deformed material indigenous to the welding process.Yet, present day fracture mechanics analysis procedures, which arelargely based on linear elastic conditions, do not directly treatsuch complications. While elastic-plastic fracture mechanics anal-ysis procedures have been developed, they have previously been

2.

applied to account only for crack tip plasticity itself. Recently,a further step has been taken by the authors through the use ofpostulated elastic-plastic crack growth relations for crack growthin weld-induced plastic deformation fields 1 "3 . This work is sum-marized and assimilated in this paper.

The immediate objective of the work reported in References 1-3was to critlcally examine the assumptions of linear elastic mate-rial behavior commonly made in analyzing weld cracking problems.Three separate problems were addressed. As shown in Table 1, theseincluded two different welded structures - a girth-welded pipe anda butt-welded plate - and three different crack growth mechanisms -

stress corrosion, fatigue and unstable crack propagation. Thesolution procedure and the individual results are first presentedin what follows with general conclusions for future progress in theanalysis of crack growth in the presence of weld-induced residualstress drawn from them.

Table 1. Problems Examined

SimulatedCracking

Structure Material Applied Loading Mechanism

Girth-welded Type 304 Constant Tension Stress Corrosionpipe with circum- Stainlessferential crack Steel(axisymmetry)

Butt-welded HY-80 Steel Cyclic Tension Fatiguewith edge crack(Plane Strain)

Butt-welded plate HY-80 Steel Impulsively Dynamic Fracturewith edge crack Applied Tension(Plane Strain)

THE ANALYSIS PROCEDURE

The analysis procedure followed in this work, which is basi-cally the same for all three problems examined, consists of threemain steps:

.. °

3

The residual stress field induced in a welding process iscomputed using an incremental thermoplastic finite elementanalysis procedure.

2. Crack growth is simulated by sequential node release alonga pre-set crack plane located In the weld heat-affectedzone.

3. A postulated elastic-plastic crack growth relation is usedto infer crack length as a function of time or loadinghistory to simulate a particular crack mechanism.

A comparison with a computational result made using a commonlyaccepted linear elastic approach is then made to assess the signif-icance of the linear elastic 'assumption and the essential neglectof residual plasticity inherent in such an approach.

Residual Stress Analysis

The residual stress analysis procedure is one that has been

used successfully at Battelle in a variety of appl1 ications4-6 .

It consists of two parts. First, a thermal analysis is made toIobtain the time-temperature history for each point in the body foreach individv'al welding pass. Then, these histories ore used asinput to an incremental elastic-plastic finite element model todetermine the stress and deformation state of the weld and the basematerial as the weld is deposited. Because tach welding pass isconsidered on an individual basis, the residual stress and strainstate that exists at the completion of one weld pass constitutesthe initial condition for the next. The final residual stressstate is that which exists at the completion of all of the weldpasses*

In the work deascribed here, the finite element models for thewelding analysis were d.ýslgned with a line of double nodes along apre-set crack plane. This had no effect on the residual stress dis-

tribution as it was assumed that an initial (small) crack appearedafter the welding process was complete'. The potential crack planewas located In the heat-affected zone ~ut was otherwise arbitrary.

The two welded structures examined in the work reported here-a girth-welded pipe and a butt-welded plate - are shown in Figures1 and 2, respectively. The corresponding finite element models areshown in Figures 3 and 4.. It can be seen that a nmuber of simpli-fications have been introduced for computation convenience. Theseinclude:

4

FIGURE 1. CROSS SECTION OF A SEVEN-PASS GIRTH-BUTT WEIDIN A 4-INCH DIAMETER SCHEDULE 80 TYPE 304STAINLESS STEEL PIPE

730

13

1 4

FIGURE 2. CROSS SECTION OF AN 18-PASS BUTT WELDIN AN HY-80 STEEL SHIP STRUCTURE

155

1. t

44~ 0

6

I -- L" I IV

~Line of

CoupledNodes

rr

- \ 4

FIGURE 4. FINITE ELEMENT MODEL FOR A BUTT-WELDED PLATE(PLANE STRAIN)

7

* weld line symmetry

* two-dimensional deformation (i.e., axisymuetry or planestrain)

• one-dimensional crack growth (i.e., concentric orcollinear).

Note that, because the cracks are not supposed to be at the centerof the weld (cf, Figures 3 and 4), the first of these simplifyingassumptions means that two cracks exist In the analysis.

The temperature-dependent &.,arial properties used in the anal-yses of the pipe weld are those of Type 304 stainless steel shownin Figure 5. The properties for the butt-welded plate are those ofthe ship structure steel HY-80 given in Figure 6. In the firitproblem, the heat inputs were taken from an actual experience"while in the second, typical values were used. These together withthe weld pass and structure geometry, suffice to determine theresidual stress distribution. The normal stresses acting on theprospective crack plane for the two welded configurations are shownin Figures 7 and 8. It can be seen that, while these are quitedifferent, they share a high tensile stress near the surface.Thus, an edge crack would be likely to grow, particularly when theresidual stresses are abetted by a tensile applied stress.

Subcritical Crack Growth Analysis

The equivalence between the crack tip opening displacement(CTOD) and the stress intensity factor in small-scale yielding iswell known. Recent progress in elastic-plastic fracture mechanicshas further revealed the distinctive role played by the crack tipcrack op~ning displacement in crack initiation and stable growthin large scale yielding conditions 8 "10 . Specifically, for theinitiation of crack growth, the CTOD can be expressed as

a small-scale yielding

6 - (1)

dn deformation plasticity

n

where K is the stress intensity factor, J Is the J-integral param-ster, E is the elastic modulus, Y is the yie7.d stress while t andd. are numerical constants on the order of unity. In addition,for extended stable crack growth, the CTOD appears to take on aconstant value. While certainly not conclusive evidence that the

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FIGURE 8. RESIDUAL STRESS CN POTENTIAL CRACK LINE IN A 1-INCH THICKBUTT-WELDED PLATE OF HY-80 STEEL

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12

CTOD is the controlling parameter for subcritical crack growth aswell, for lack of an alternative, it will be so taken in this work.Note that, because of the equivalence represented by Equation (1),this choice is not inferior to one based on either K or J in anyevent.

Starting from an assumed initial crack, crack growth is simu-lated in each of the finite element models by sequential node re-lease along the line of double-noded elements. Each node. pair isreleased by diminishing the initial force that exists between themto zero. This is done over from five to ten load increments. Thevalue of 6 for a given crack length is then the value of the CTODthat exists when the load has vanished. Hence, it is a value atone finite element spacing behind the actual crack tip. The re-suits obtained from the finite element models are shown in Figures9 and 10. Note that in the latter problem two solutions are shown:one with no applied stress, the second with an applied tensilestress normal to the crack plane of 67 percent of the room tempera-ture yield stress of HY-80 steel (80 ksi).

Figures 9 and 10 contrast the CTOD values obtained by advanc-ing the crack through the finite e.,.ement model under two differentconditions. First, the computed weld-induced plastic deformationis left unaltered and an incremental plasticity computation made.This is the elastic-plastic analysis. Second, a simplified ap-proach is followed wherein (1) only the normal component of theresidual stress acting on the potential crack plane is retained,and (2) linear elastic behavior is assumed. This is denoted as thesimple elastic analysis and typifies that commonly used for thiskind of problem.

Stress corrosion cracking is often supposed to occur accordingto a power law relation of the type

da .CKm (2)dt

where a denotes the crack length, t is time, while C and m arematerial constants. Because this relation is clearly valid onlyunder small scale yielding conditions, the relation between K and 6expressed by Equation (1) can be used to cast it into the equiva-lent form

da C1,6m/2t" (3)

where C' is also a material constantI. Having 6 - 6 (a) fromFigure 9, Equation (3) can be integrated numerically to find thecrack length in terms of a dimensionless time t*

13

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0.0 Crock Growth, Au, InchI I I

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600

IEgo 400

C

300d8 200

100

j 00 a I I I2 4 6

Crack Growth, AG, mm

FIGURE 9. CTOD CALCULATED AS A FUNCTION 0� CRACK GROWTH (na) FOR4-INCH DIAIIETER TYPE 304 STAINLESS STEEL PIPE SUBJECTEDTO WELDING INDUCED RESIDUAL STRESSES A�D ZERO APPLIEDSTRESS

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where h denotes the wall thickness. The result is shown inFigure 11.

Notice that the results given in Figure 11 were obtained with-out the imposition of an applied stress. Thus, despite the factthat the residual stresses are self-equilibrating, catastrophiccrack growth can occur. The reason is that the stresses are redis-tributed as crack growth occurs and, at least until a net compres-sive force is freed by the growing crack, a positive crack drivingforce exists; cf, Figure 9. Of more importance, the results ofFigure 11 indicata that the simple elastic analysis predicts ananti-conservative result in that the time-to-failure iF greaterthan in the more rigorous elastic-plastic an.alysis.

Fatigue crack growth under a uniform cyclic loading can oftenbe adequately characterized in the form

dai"C(K -Kn)m (5)FN C(max -KMIX

where N denotes a load cycle number and C and m are materialconstants. Again introducing the CTOD from Equation (1) gives

da . (61/2 - 6n1/2 (6)dN min min

where 6 jax and 6min are the CTOD values that would be attainedunder the maximum and minimum load levels, respectively. Conse-quently, the number of cycles required to achieve a given cracklength can be found by integrating Equation (6) via

1 a daSN' J f (7)a (o1/2 1/2

max min

The results, using the CTOD values given in Figure 10, are shown inFigure 12. It can be seen that the simple elastic analysis is onceagain anti-conservative.

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Dynamic Crack Propalation Analysis

The governing relations for unstable crack propagation andarrest in elastodynamic conditions are

Ka KD , 0 (8)

K < KD a 0

where KD is known as the dynamic fracture toughness. Once again,so long as small scale yielding conditions are satisfied, suchrelations are equivalent to those couched in terms of the CTOD. Inparticular, the critical CTOD value for dynamic crack propagationwould then be simply

2

6 - a (9)

Clearly, if a time varying loading is imposed on a crackedbody, the CTOD value will also vary. So long as 6 < 6 D, thecrack tip will be stationary. If 6 becomes equal to 6D, crackgrowth will occur at a rate such that the equality is maintained.Arrest occurs when the equality can no longer be satisfied.

A dynamic computation was performed in which the ship struc-ture shown in Figure 2 was subjected to a suddenly imposed load of42 ksi, about 50 percent of the room temperature yield stress.This load was held for 30 usec and then dropped to zero. A valueof Kc - 37.9 ksivan. was used to reflect the lower toughnessexisting in the heat-affected zone. Using Equation (9), this gavea critical CTOD value of 0.0006 inch. Both a linear elasto-dynamic and an elastic-plastic dynamic calculation were made. Theelastic-plastic analysis was based on the entire residual stressand deformation field together with incremental dynamic plasticity.However, in accord with common practice, the residual stresses werecompletely ignored in the elastic analysis. The computed CTODvalues for the two analyses are shown in Figure 13.

It can be seen in Figure 13 that the elastic-plastic analysispredicts that unstable crack growth would quickly occur (at approx-imately 15 psec). It also predicts that the crack would penetratethe wall. In contrast, the elastic analysis does not predictinitiation of growth until much later (about 40 usec) and predictsarrest soon thereafter. Consequently, the simpler procedure isonce again found to be anti-conservative.

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19

rPredicted Crock InitictionA elostic-plostic analysis Predictea Crack Initiation

_n elastic analysis

Predicted Crack Arrest06 Iin elastic analysis06

05-

N04-

£ Elastic

Plastic0 03k Analysis

ElOstic

02 Analysis

0'

C - -

0 tO 110 60 40 50 60 ?C 80 90Time, u sec

FIGURE 13. COMPARISON OF ELASTIC AND ELASTIC-PLASTIC SOLUTIONSFOR DYNAMIC CRACK PROPAGATION IN THE HEAT AFFLCTEDZONE OF AN INITIALLY CRACKED BUTT-WELDED PLATE

S.. . ... ... . - . . . • 2 1 -. '• a ' '".'' '' '-•---

20

DISCUSSION

It is important to recognize that the price purpose of thiswork was not to arrive at quantitative results for different typesof materiaTbehavior. Rather, it was to critically examine a setof assumptions that are commonly used in analyzing a class of prob-lets fo~r given material behavior. The specific materials consid-ered in this study are very ductile and tough (eog., Type 304stainless steel, EY-80 steel) which undoubtedly exacerbates thedifferences that were found* It Is quite possible that othermaterials--and, perhaps more importantly, residual stress fieldsinduced without large-scale plastic deformations--would show ion-siderably less difference. Of equal importance, since the elastic-plastic crack growth criteria needed for the purposes of this studyhave not been established, a pragmatic approach was taken to obtaincomparative results. All of these factors would be borne In mindin interpreting the results given in this paper.

The basic assumption that has been called Into question hereis the applicability of linear elastic fracture mechanics in thepresence of weld-induced residual stress fields. This has beenaddressed by performing two parallel computations where thisassumption has and has not been made. Hence, while there areundeniably many aspects of the calculations that can be improvedupon, because the two computations were otherwise performed onexactly the same basis, these cannot be of critical Importance.Indeed, the comparison has revealed such wide disparities, that,neglect of the inelastic deformation accompanying welding wouldappear to be unequivocally incorrect.

Conversely, the work presented in this paper shoul.d not betaken As a blanket indictment of LEFM-based crack growth predic-tions. The mathematical convenience of LEFM is too useful to notplay an important part in the assessment of weld cracking. Whatappears to be needed is some sort of plasticity-enhanced LEFI.procedure, possibly calibrated with the more rigorous analysesdescribed in this paper, that can be confidently applied even inthe presence of large-scale plasticity and its attendant residualstress fields. How this can best be done is an open question atthis time. However, as the work reported herein so strongly sug-gests, the necessity for it is not.

CONCLUJSIONS

Elastic-plastic fracture mechanics research has identified theC'rOD as a key crack growth parameter. The use of this finding inconjunction with thermoplastic finite element analysis procedureshas enabled more realistic computations of crack growth in the

21

presence of weld-iriduced residual deformation and stresses to bemade. Comparisons of these results with commonly used approachesbased on linear elastic fracture mechanics indicate that the lattercould be highly anti-conservative.

ACKIJOWLEDGEHENT

This paper was prepared with support from the structuralmechanics program of the Office of Naval Research under ContractNumber N-00C14-77-C-0576. The authors would like to express theirgratitude to Drs. N. Perrone and Y. Rajapakse of ONK for supportingtheir work.

REFERENCES

1. I. S. Abou-Sayed, Js Ahmad, F. Wo Brunt, and Mo F. Kanninen,"An Elastic-Plastic Fracture Mechanics Prediction of StressCorrosion Cracking in a Girth-Welded Pipe", 14th ASTMNational. Symposium on Fracture Mechanics, Los Angeles, June30 to July 2, 1981.

2. F. W. Brust, J. Ahmad, V. Papaspyropoulos, and M. F. Kanninen,"An Elastic-Plastic Fracture Mechanics Prediction ofFatigue Crack Growth in the Heat-Affected Zone of a Butt-Welded Plate", manuscript in preparation (July, 1981).

3. J. Ahmad, F. W. Brust, and M. F. Kanninen, "Dynamic CrackPropagation in the Heat-Affected Zone of an Impact-LoadedButt-Welded Plate", manuscript in preparation (July, 1981).

4. E. F. Rybicki, D. W. Schmueser, R. G. Stonesifer, J. J. Groom,and H. W. Mishler, "Residual Stresses at Girth-Butt Weldsin Pipes and Pressure Vessels", Battelle's ColumbusLaboratories Report to the U.S. Nuclear RegulatoryCommission, NUREG-0376 (November, 1977).

5. F. W. Brust and R. B. Stonesifer, "Effect of Weld Parameterson Residual Stresses in BWR Piping Systems", Battelle'sColumbus Laboratories Report to the Electric Power ResearchInstitute on RP1174 (June, 1980).

6. M. F. Kanninen, T. E. Barber, F. W. Brust, and H. W. Mishler,"Controlling Residual Stresses by Heat Sink Welding",Battelle's Columbus Laboratories Report to the ElectricPower Research Institute on RP1576-1 (December, 1980).

7. W. J. Shack, W. A. Ellingson, and L. E. Pahis, "The Measure-ment of Residual Stresses in Type 304 Stainless Steel PipeButt Weldments", Argonne National Laboratory Report to theElectric Power Research Institute on RP449-1 (December,1978).

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8. M. F. Kanninen, et al, "The Development of a Plastic FractureMethodology", Battelle's Columbus Laboratories Report tothe Electric Power Research Institute on RP601-1, EPRINP-1734 (March, 1981).

9. C. F. Shih, et al, "Methodology for Plaptic Fracture", GeneralElectric Company Report to the Electric Power ResearchInstitute on RP601-2, EPRI •TP-1735 (March, 1981).

10. H. F. Kanninen, C. H. Popelar, and D. Brook, "A CriticalSurvey on the Application of Plastic Fracture Mechanics toNuclear Pressure Vessels and Piping", Battelle's ColumbusLaboratories Report to the U.S. Nuclear RegulatoryCommission, NUREG CR-2110 (May, 1981).

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