journal of nuclear materials volume 212-215 issue part-p1 1994 [doi 10.1016_0022-3115(94)90102-3] j....

8/10/2019 Journal of Nuclear Materials Volume 212-215 Issue Part-P1 1994 [Doi 10.1016_0022-3115(94)90102-3] J. Bressers_

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ELSEVIER

Journal of Nuclear Materials 212-215 (1994) 448-452

Thermal fatigue crack growth: modelling

and experimental verification

J. Bressers, R.C. Hurst, D.C. Kerr , L. Lamain, G. Sordon, G.P. Tartaglia

Inst it ut e or Advanced M at eri als, JRC, CEC, P.O. Box 2, 1755 ZG Pett en, The Netherlands

Abstract

The first wall of tokamak type fusion reactors suffers from thermal fatigue damage as the result of discontinuous

loading due to plasma disruptions. The Institute for Advanced Materials launched a generic thermal fatigue research

project aimed at the numerical modelling, and at its experimental validation, of the lives spent in growing a crack to

failure in components subjected to cyclic temperature gradients typical of NET. The experimental testing facilities

consist of an out-of-pile and an in-pile rig for measuring the crack growth rate in tubular components exposed to

thermal fatigue conditions in a neutron free condition and under neutron irradiation in the HFR reactor,

respectively. Test results in the neutron free environment on 316L steel considered for first wall application in NET

serve as a thermal fatigue life data base, and as a basis for the verification of the model prediction of crack growth

rates under LEFM conditions.

1 Introduction

The anticipated presence of flaws in the first wall of

a fusion reactor, resulting from either manufacturing

defects or from plasma disruptions, suggests a fracture

mechanics approach for lifetime prediction purposes.

LEFM crack growth rates in thermal fatigue loaded

components can be predicted utilizing data bases of

crack propagation results determined isothermally on

standard fracture mechanics samples, provided that the

similarity concept is obeyed. Because of the differences

in environment at the crack tip between first wall

components and laboratory fracture mechanics speci-

mens in terms of temperature and irradiation condi-

tions, the similarity concept does not necessarily apply

and crack growth rate predictions need verification. On

the other hand the problem of determining stress in-

tensity factors of surface cracks, if present, adds to the

complexity of predicting lives in first wall structures.

1 Now at Imperial College, London.

3D analytical modelling, as well as finite element anal-

ysis of surface crack problems is time consuming in

terms of data preparation and computational time. In

engineering practice there is a great need for simpli-

fied solutions, but the assumptions made in the process

of simplified modelling need to be verified. In order to

address these problems the Institute of Advanced Ma-

terials started a generic thermal fatigue research pro-

ject aimed at the numerical modelling of the lives spent

in growing a crack to failure in components subjected

to cyclic temperature gradient fields, and its experi-

mental validation, both in a neutron irradiation envi-

ronment and in a non-nuclear testing rig. The experi-

mental testing rigs/methods, and the analytical ap-

proach adopted in the numerical model are briefly

reported. The potential of the model for predicting

crack growth rates in tubular components subjected to

cyclic temperature gradient fields is illustrated by

means of the outcome of a numerical example, and its

comparison with crack growth rates experimentally

measured in the non-nuclear testing rig. A more exten-

sive description of the model is given in Ref. [ll.

0022-3115/94/ 07.00 0 1994 Elsevier Science B.V. All rights reserved

XSDI 0022-3115(94)00123-6


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J. Bressers et al. Journal of Nucl ear M at eri aLs 212-215 1994) 448-452

449

2.

Testing rigs and methods

For the direct simulation of the conditions faced by

the first wall, two thermal loading test facilities have

been developed i.e. a non-nuclear testing rig designed

for generic thermal fatigue studies, and an in-pile rig in

the Petten High Flux Reactor for simulating the irradi-

ation environment. Three features critical to the design

and operation of first wall components have been

singled out as the essential elements for the design of

these experimental facilities. The thermal gradient and

thermal cycle are not only essential but also insepara-

ble because of their synergistic actions. Other workers

[2-51 have developed equipment for testing compo-

nents under thermal fatigue conditions but, for practi-

cal reasons, simultaneous in-situ measurement of the

crack growth is usually not performed. The assessment

of the resistance to crack growth from defects is the

other requirement.

For the achievement of a cyclic thermal gradient

condition, a thick walled (Ri = 12.5 mm, W = 9.5 mm

wall thickness) tubular geometry has been selected. In

the out-of-pile test rig the tube is coupled into a closed

loop water cooling system. The central section of the

test piece is heated using the coil of a 50 kW capacity

induction heating system, up to outside and inside

surface temperatures of T,,,, = 350 and 6OC, respec-

tively. Switching off the heater leads to cooling to

Tmin = 80C outside and 40C inside. Surface tempera-

tures are continuously monitored throughout each cy-

cle. The actual calculated temperature gradient through

the wall, required for analysis of the results, was veri-

fied from a specially instrumented test piece with

through-wall positioned thermocouples. In the in-pile

rig a column of four tubular specimens, similar to those

used in the out-of-pile rig is hosted in an irradiation

capsule. The tubes are internally cooled by flowing

water and externally heated by means of the radiant

heat supplied by a nuclear heated heavy molybdenum

shroud. Additional heating is through the nuclear heat-

ing of the tube material itself. This configuration cre-

ates the same temperature gradient, and similar inner

and outer wall temperatures through the wall thickness

of the tube as in the out-of-pile rig. The inlet water can

be pressurized and heated to achieve different temper-

ature limits. The cyclic thermal gradient field is estab-

lished by inserting and withdrawing the column of

tubular samples in and from the neutron field by

means of hydraulic actuators, thus enabling a heating-

dwell at T,,,,-cooling-dwell at Tmin cycle of 10 s-300

s-10 s-50 s, respectively, which is typical of NET 161.

The in-pile rig will be instrumented with thermocou-

ples and fluence monitors, enabling a continuous moni-

toring of temperatures and neutron fluences. The tem-

peratures are controlled by changing the composition

of the He-Ne mixture flowing in the gas gaps between

tubular samples and thimble, and by a vertical dis-

placement unit which can follow the changes of the

neutron fluence rate distribution curve during reactor

operation. The design of the in-pile rig for the mea-

surement of crack growth in situ in the High Flux

Reactor is ready. Construction of the device is sched-

uled to start in autumn 1993.

The out-of-pile rig is operational and a series of

preliminary experiments without dwell times have

yielded results which are reported below (heating and

cooling times of 5 and 21 s, respectively). The tubes are

notched to facilitate crack initiation during thermal

cycling. The crack growth is monitored by means of the

electrical potential drop method. In the out-of-pile rig

the dc method is used [7]. The number and the geo-

metric configuration of the dc probes attached to the

test piece for measuring crack extension depend on the

position and orientation of the crack. Calibration has

been realised by using crack depths measured on sec-

tions taken from the positions directly below PD probes

from completed experiments. During the experiments

the potential drop across the different probes is mea-

sured automatically at the same time in each cycle,

immediately after the induction heater turns off. The

ac potential drop technique was found to be more

suitable for application in a neutron field, because of

the low current density required to ensure adequate

signal recording and of the smaller calibration effort

181

3. Numerical modelling

The growth rate of longitudinal, semi-elliptical

cracks with a changing shape under cyclic thermal

gradient loading in the wall of the tube is predicted by

the code PREDI-N from the isothermal data base

determined on standard fracture mechanics samples

[9]. The code incorporates:

-

a module to calculate the temperature distribu-

tion in time and in space from the thermal boundary

conditions by means of a finite element formulation;

- a module to calculate the stresses in time and in

space, using a finite element formulation and tempera-

ture dependent material data;

- calculation of the cyclic stress intensity factor in

an arbitrary stress field, and of the resultant crack

growth rate at the deepest point of the crack through

the tube wall.

The tube wall is modelled by a row of ten one-di-

mensional finite elements, using a two-node element

and a three-node element with a l/r term in the

displacement field for the temperature and stress eval-

uation respectively. The l/r term is introduced to

obtain zero radial stress at the free surface of the tube.

The stress-strain part is solved by means of a two pass


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450 J. Bressers et al . Journal of Nu clear M at erial s 212-215 1994) 448-452

technique assuming generalized plane strain in the

axial direction. Plastic deformation can be taken into

account by means of a Prager kinematic hardening

model.

The line spring model is applied for evaluating the

effect of the changing, semi-elliptical shape of the

crack on the stress intensity factor at the deepest point

of the crack, because of its time saving nature as

compared to a general finite element code. The result

serves as the reference solution to the weight function

method [lO,ll], which offers an attractive and fast

route for calculating the stress intensity factors under

the arbitrary stress fields observed in thermal fatigue.

The line spring model is coded as described in Ref.

[12], yet the integration is performed over an open

interval in order to avoid singularities in the nodes.

The associated compliance coefficients for the line

spring are calculated using the stress intensity factor

coefficients of a ring as reported in Ref. [13]. Normal-

ized stress intensity factors at the deepest point of the

crack are calculated for a discrete series of tube ge-

ometries W/R, and for five different crack shapes,

ranging from a semi-circular to an infinitely long crack.

An interpolation technique is applied to cover other

tube geometry and crack shape combinations. The nor-

malized stress intensity factors are expressed in polyno-

mial form, suitable for input into the weight function

method. The weight function depends on the crack

face displacement U, which is usually not known. A

three-term approximation [14] is used which yields

results comparable to the two-term approach proposed

by Petroski and Achenbach [15] for small crack depths.

The extra term is based on the condition that the crack

flank curvature becomes zero at the crack mouth. For

larger crack depth/wall thickness ratios the three-term

approximation is more accurate.

4.

Results

In the literature a few references reporting stress

intensity factor solutions for semi-circular or semi-el-

liptical cracks in a tubular geometry exist, which have

been obtained using either the boundary integral equa-

tion method [16] or finite element analysis [17]. Com-

Table 1

Experimentally measured data

paring the PREDI-N solution with that of Ref. [16]

shows the stress intensity factors to be within 10% of

each other up to wall thicknesses of a/W = 0.8. A

similar conclusion is reached upon comparing the

PREDI-N calculation with the finite element analysis

of Raju and Newman [17] for internal and external,

semi-circular longitudinal cracks in a tube with

W/R,

= 1.25. A more elaborate analysis is given in Ref. [l].

The material used for the tube tests is ICL 167

SPH, a 316L type stainless steel, used as a reference

material in NET first wall studies. In order to support

the project in giving an indication of the crack growth

behaviour of the 316L stainless steel under mechanical

fatigue, a series of experiments have been carried out

using compact tension test pieces at the temperatures

of interest for the first wall application, namely 80 and

350C and at room temperature. Fatigue crack growth

measurements were achieved using the dc potential

drop method and the results correlated with the stress

intensity factor using the Paris law (see Table 1). In

addition to the data base covering the mechanical

fatigue behaviour of the material as obtained from

compact tension tests, a total of 20 thermal fatigue

tests have been carried out on the notched components

[18]. No dwell times have been incorporated as yet. In

the experiments on the longitudinally and circumferen-

tially notched components, the pair of dc potential

drop probes exhibiting the maximum change in poten-

tial in each test are selected for conversion to crack

length using the relationship established from the cali-

bration. The crack growth development through the

tube wall can be compared for an example of each of

the different defects in Fig. 1. Conclusions can be

drawn from this graph concerning the influence of the

starter notch depth, position, orientation and geome-

try. With the exception of the first half of the test on a

1 mm internally circumferentially notched test piece,

the depth of the starter notch has apparently little

influence, with the crack growth curves being approxi-

mately parallel. The internal longitudinal defects ex-

hibit slower crack growth than the external longitudi-

nal defects during the first 20 000 cycles. The maximum

stress generated during the cycle at the external sur-

face has been calculated to be approximately 5% in

excess of that at the internal surface, which, in con-

Test temperature (Cl

E-modulus (GPa)

Cyclic yield stress (MPa)

Paris law exponent, m

Paris law constant, C

20 80 300 350 500

200 196 186

220 190

3.35 3.20 3.35

1.53 x lo-4 3.74 x lo-l4 3.69 x 1OW4

Paris law da/dN=C(AKYwithda/dN inmm/cycle,AK inMPa&%


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J. Bressers et al. Journal of Nucl ear M at eri als 212-215 1994) 448-452

451

OO

I

I

I

I

I I I

20

LO

60

80

100

No of cycles xl0001

Fig. 1. Crack depth evolution with the thermal fatigue cycle

number in tubes with different internal and external notches.

junction with the higher yield stress at the cooler inside

surface, presumably leads to this slower crack growth.

The ratio of the thermally induced hoop stress over the

axial stress at the external surface is about 1.25, and

hence crack growth from the external circumferential

notch is found to be slower than that from the equiva-

lent 1 mm deep external longitudinal notch. The effect

of notch orientation and geometry at the internal sur-

face is less clear as the circumferential notch fails

repeatedly to initiate a crack until at least 40000 cy-

cles. As the axial stress at the inside surface is 1.1

times the axial stress at the external surface, this incu-

bation period must arise from the combined effects of

smoother notch section, the higher yield stress at the

cooler surface and the circumferential orientation.

The potential of the numerical model contained in

PREDI-N is illustrated by means of the example in

Figs. 2 and 3 for an internal, longitudinal crack. Tem-

peratures through the tube wall are calculated using

temperature dependent data of the stainless steel 316L,

taken from the producers data sheets. Data used for

2.5 50

75

95

Crack length mm1

Fig. 2. Stress intensity factors as a function of crack length in

a tube wall for internal, semi-elliptical longitudinal surface

cracks.

the stress calculations, and the coefficients of the Paris

law are determined from experiments, and are listed in

Table 1. The plastic hardening slope over the tempera-

ture range of interest is 2 GPa, with a pure kinematic

hardening behaviour. A converged stress-strain field is

arrived at after three cycles. The calculation shows

areas of reversed plasticity near the inner and outer

surfaces and an elastic zone in the middle of the tube

wall, with a shake down area in between. Although the

model adopts an LEFM approach, stress levels are

calculated elastoplastically, for two reasons. In combi-

nation with an isothermal Coffin-Manson type law, it

enables the code to be used for predicting the initia-

tion of engineering sized cracks in cases where re-

versed cyclic plasticity occurs. Moreover, when apply-

ing the weight function method, stresses are integrated

over the crack path in order to obtain the stress inten-

sity factor. In case (limited) plasticity occurs along the

crack path, yet far away from the crack tip as in the

tube loading example used here, a purely elastic calcu-

lation would yield too high values for the stress inten-

sity factors. The stress intensity factors for cracks of

different aspect ratios in Fig. 2 are based on the hoop

stress, which is the stress driving the internal longitudi-

nal crack to grow.

In particular for crack lengths in excess of approxi-

mately 1 mm the K factor reduces considerably with

decreasing l/a ratio. The corresponding cyclic stress

intensity factor is calculated as the difference between

K max

and

Kmin

over a cycle. Based on these values and

on the measured Paris law, the crack growth rates,

plotted as a function of the crack length in Fig. 3 are

calculated for various crack shapes. When taking the

changing crack shapes into account, the calculated

crack growth rate is within a factor of 2 of the mea-

sured rate. Typically the calculation time to yield the

crack growth rates is of the order of a few minutes on a

386 PC.

1.5.10-4

I I

0 I 25

I I

I

50

75 95

Notch-i

Crock length lmml

Intee

Tube wall thickness

YAnoI

Fig, 3. Comparison of predicted growth rates for a crack with

a changing aspect ratio a/l with experimentally measured

values.


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J. Bressers et al. Journal of Nucl ear M at eri als 212-215 1994) 448-452

Acknowledgement

The authors wish to express their appreciation for

the skilled technical assistance of Messrs. C. McGirl,

R. Metz and B. Eriksen.

[81

[91

1101

1111

1121

1131

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journal of nuclear materials volume 212-215 issue part-p1 1994 [doi 10.1016_0022-3115(94)90102-3] j....

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