Measurements of Crack Growth in a Solid at Elevated Temperature by Holographic Interferometry

Paper desc r ibes an inves t iga t ion into the poss ib i l i t y of mon i to r i ng c rack g rowth over a p ro longed per iod of t ime and at e l eva ted tempera tu re , using rea l - t ime ho log raph ic i n te r fe romet ry

by T.R. Hsu, R. Lewak and B.J.S. Wilkins

ABSTRACT--Real-time holographic interferometry was used Experimental Procedure to follow the crack-opening displacement (COD) of a compact tension specimen of zirconium 2.5-percent niobium subjected The cold-worked; Zr-2.5 wt.% Nb specimen is shown to a constant tensile load at 120~ for a period of 860 h. This was made possible by a dimensionally stable Invar plate placed beside the specimen as the reference for the alignment of holograms. A finite-element elasto-plastic stress-analysis code and measurements on a duplicate specimen with a clip gage were used to correlate the measured COD and the corresponding crack growth.

Introduction

Slow cracking induced by hydrogen can occur in cold- worked Zr-2.5 wt .% Nb. ' This paper describes an investi- gation into the feasibility of monitoring such cracking, over a prolonged time period and at elevated temperatures, using real-time holographic interferometry. The main purpose was to develop ways of determining the threshold values of stress-intensity factor below which either cracking will not initiate or where crack-growth velocity is small, i.e., < 10 -'2 ms -1. The holographic method was pursued because of its high sensitivity and because it does not require physical contact with the specimen. The latter characteristic is important for it means that the cracking process need not be disturbed and measurements at high temperatures are possible. 2'3

The essence of the technique is the making of a sequence of holograms from which specimen dimensional changes, reflecting crack growth, are followed. In this instance, crack-opening displacement (COD) was measured. Later, COD and crack growth were correlated by examining the specimen-fracture surface. In addition, COD was correlated to crack growth by an established finite element, thermo- elastic-plastic stress-analysis code named T E P S A 4,' and by clip-gage measurements on other duplicate specimens at room temperature.

T R. Hsu and R. Lewak are Professor and Research Associate, respectively, Department o f Mechanical Engineering, University o f Manitoba, Winnipeg, Manitoba, Canada R3T 2N2. B.J.S. Wilkins is Research Officer, Whiteshell Nuclear Res'earch Establishment, Atomic Energy o f Canada Limited, Pinawa, Manitoba, Canada, ROE ILO.

Original manuscript received : July 11, 197Z Revised version received : September 8, 197Z

in Fig. 1. It was of the compact-tension type with a 2-mm- long fatigue crack at the tip of the Vee notch. The arrangement of the apparatus is shown in Fig. 2. To minimize movement , the optical components were fastened rigidly to a heavy steel plate which rested on a sturdy optical bench. The oven was equipped with a double-pane glass window (216 mm x 203.2 ram) set at an angle to avoid reflection of the laser beam onto the film plate. The double gl~ing was used to reduce distortion of holograms due Io hol air rising from the outer surface of the window.

Since real-time holography was involved, the reference holograms had to be placed each time in their original positions. Alignment of the holograms to the unconstrained lnvar plate adjacent to the specimen was achieved by an

~

40.64 , ]

E 50.8 I- J

ALL DIMENSIONS IN MILLIMETER

Fig. 1--Dimensions and geometry of notched specimens

Experimental Mechanics �9 297

(a)

(b)

l - - |

[ ]

@

I

/ / I I I I I I I I 17111111 I I I I

(~ He Ne LASER

(~) BEAM SPLITTER

(~) LENS

(~) MIRROR

(~) INVAR PLATE

(~ NOTCHED SPECIMEN

(~ OVEN

(~) FILM PLATE

(~) CAMERA AND MOUNT

(~ LOADING LEVER

(~) DEAD WEIGHTS

Fig. 2--(a) Photograph of apparatus; (b) general arrangement of apparatus

t rr7

Q

adjustable, water-immersion type of photographic-plate holder.

The specimen was polished, then fixed in position in the apparatus. A tensile load of 1794 N was applied to it by

adding weights over a period of 15 min. Next, the oven was turned on. Temperature was recorded by two iron- constantan thermocouples attached to the back of the specimen. When the temperature had stabilized at 120~

298 �9 August 1978

Fig. 3--Typical interference fringes

14.0

E ~?

0 12.0

I--- z IO.O LIJ

h l (.2 <[ 8.0 &_ o9

6 0 (.9 Z Z la.J 4,0 0

< 2.0 rr (._)

A P P L I E D LOAD P : 1 7 9 4 N /

0 I I I I I I I I I I I I I I I I I I 0 I00 200 500 400 500 600 700 800 900

TIME ( H O U R S )

Fig. 4 - - C r a c k - o p e n i n g d i s p l a c e m e n t s o f a n o t c h e d s p e c i m e n

Y

Z P o r i g i n a l p o s i t i o n on specimen P ' - d i s p l a c e d p o s i t i o n on specimen S - p o s i t i o n o f l i g h t source (beam

s p l i t t e r ) H - o b s e r v a t i o n p o i n t on hologram

P ' ( X + U , Y + V , Z + W )

(X , Y , Z )

k , Y k ' Z k ) S (X o , Y O , Z o )

Fig. 5 - - S c h e m a t i c d i a g r a m f o r fringe i n t e r p r e t a t i o n s

Change in Pa th Leng th = S P ' + P ' H - - SP + P H

Experimental Mechanics �9 299

Fig. 6--(a) Finite-element model for the notched specimen-- Region 1; (b) finite-element model--Region 2

(a)

SYMMETRY LINE

ACK TIP REGION 2 FOR THE CROSS - SECTIONED AREA

a hologram was made. The time period elapsing between the start of heating and the making of the hologram was one hour. For the experiment, the making of the hologram was taken as time zero.

After 149.5 h, sufficient fringes had developed for a good estimate of the change in COD to be made. Photo- graphs were made through each of nine separate observa- tion points on the hologram and the shifts of fringe order were determined. This was facilitated by an adjustable camera mount. Figure 3 shows a typical fringe distribution seen on the specimen. Using the method described by Dhir and Sikora, 6 the displacement of points on the speci- men surface was determined and the COD wag calculated. The procedure was repeated at 192, 268, 316, 364, 456 and 527 h into the experiment. The temperature was maintained at 120~

Between 316 and 527 h, no significant change in fringe order was detected. This was interpreted as meaning tha t crack propagation had become extremely slow or had ceased. To stimulate further cracking, the specimen temperature was cycled at 300~ and back to 120~ between 528 and 538 h. Additional changes in fringe order were observed. A new hologram was made at 552 h. Further photographs of fringes were made at 788 and 860 h. The manner in which COD varied with time during the experiment is shown in Fig. 4.

(b)

Estimation of COD by Holography The 2-mm-long fatigue crack at the tip of the specimen

Vee notch could not be resolved on the hologram. Hence, the COD, i.e., the distance between points PI and P2 in Fig. 1, was measured and later was correlated to the crack length.

According to the method of Dhir and Sikora, 6 the three displacement components at points P, and P2 can be calculated by the shifting of fringes viewed from at least four points on the hologram. This is expressed in the following equations :

( A k - Ak§ + ( B k - Bk§ V + ( C k - Ck.,) W

= (n~ - n~.,) k (k = 1, 2, 3)

where X - X o X - X ~

A ~ - + Ro R~

Y - Y o Y - Y k Bk - - - - + - -

Ro Rk Z - Z o Z - Z ~

Ck - - + - - R~ R~

in which U, V and W were the three components along the x, y and z coordinates, respectively, and Ro and R~ are defined in Fig. 5. The term nk refers to the fringe-order counting bright fringes from a fixed point on the specimen using a single observation point, k, on the hologram. In

300 �9 August 1978

9 . 0

%

o o

,b

w

I -

8 0

7.0

6.0

5.0

4 0

3.0

2 0

1.0

%i0o

EE"

,.r L(I-v

E= 1836.38 MN/m 2 E'= 7,67 MN/m 2

I~K= 16.376 MN/m 2

n = 10

I I I I I I I I I 0 0 4 0.08 012 0 1 6

EFFECTIVE STRAIN, ~-

I 1 . J 0.20 0 24

Fig. 7--Stress and strain relation for zinc.niobium at 120 ~

this experiment, for more consistent results, nine observation points (i.e., k = 1, 2 . . . . 9) were taken. Consequently, the three displacement components were solved from a set o f eight overdetermined simultaneous equations by a least- squares technique.

Correlation of Crack Extension and COD A thermoelasto-plastic stress-analysis computer code,

TEPSA, based on the finite-element principle was used to correlate the COD and the crack extension in the notched specimen shown in Fig. 1. This code uses constant stress- strain elements and is capable o f calculating the elasto- plastic deformation in a solid subject to various combinations o f thermal and mechanical loads. The detailed derivation of mathematical formulations o f this code can be found in Refs. 4 and 5. The finite-element grids used for the present investigation are shown in Figs. 6(a) and 6(b) with an effective stress ~ vs. effective strain ~-relation of the material shown in Fig. 7. Since only constant stress-strain elements were used in the computation, very small elements had to be used near the crack tip as indicated in Figs. 6(a) and (b). The relationship as estimated by TEPSA code for

E 5e

o_ 54

u.l ~ 5 2 uJ

~ 5C

c ~ 4 8

z 4 6

o ~ 44

0c- CD

6 0

5 8 -

4C

5 8 [ l I l

15 2 0 2 5 I I I I I I I I I I 1 I I

3 0 3 5 4 ,0 4 5 5 0 5 5 6 . 0

CRACK LENGTH (C) x 10-Sm

Fig. 8--Analytical relation between COD and crack length in a notched specimen

m E I O

o

(.9

(D

3 0

2.5

2 0

1.5

10

0.5

O0 o

RATES OF CRACK GROWTH, m / s

17x I0 -9 .j..

leO 200 5 0 0 4 0 0 i I I

500

0 4 6 xlO 9 1 .79x i0 -9

APPLIED LOAD = 1794 N

I I I I I I 600 700 800

T I M E , HOUR

900

Fig. 9- -H is to ry of crack growth

Experimental Mechanics �9 301

Fig. lO--Fracture surface of the notched specimen

a load of 1794 N at 120~ is shown in Fig. 8. The estimated crack length and growth velocities at various stages during the test were obtained by combining Figs. 4 and 8, and are shown in Fig. 9. These results predict that crack growth velocities in the 0.5 x 10 -9 to 1.8 x 10 -9 m.s -~ range occurred during the test. Also, they indicate that the crack extended approximately 3 mm to produce the 1.4 • 10 -4 m total COD observed by holography.

The direct physical measurements of COD were made at room temperature, with a clip gage, on a specimen identical to that used in the holography experiment. The output of the gage was recorded continuously as the tensile load was increased from zero to 2224 N. This was repeated twice at each of four different crack lengths ranging from 2 to 5 mm. Between each pair of tests, the crack was extended further by fatigue loading. The result was a series of straight-line plots of tensile load vs. COD at various crack lengths. From this, it was calculated that a crack extension of approximately 2.2 mm was required to produce a COD of 1.4 • 10 -4 m.

The actual crack extension is shown clearly by fracto- graphy to be approximately 1,2 mm (see Fig. 10). In this figure, from left to right, is shown the Vee notch, the original fatigue crack (2 mm in length), two bands of slow crack growth (1.2 mm total width) and the fracture surface produced by breaking open the specimen.

Discussion The COD changes measured by holography paralleled

the crack growth behavior in the specimen. For example, the two periods of growth indicated are seen in the speci- men fracture surface in Fig. 10. The line separating the growth bands is a stretch band introduced by the thermal cycle. The total crack extension during the experiment was 1.2 ram. The crack extensions predicted by the TEPSA code and the clip-gage measurements, from the COD changes measured by real-time holography, are 3 mm and 2.2 mm, respectively. The discrepancy between the predicted and actual crack extension is not large con- sidering the nature of the experiment. Also the clip-gage

experiment and TEPSA code estimation were intended only to yield an approximation of the test-specimen behavior. However, the results suggest that not all the COD increase was due to crack extensions. Possibly some of the increase was due to creep.

Conclusions This work has demonstrated, for the first time, the

practicability of using holographic interferometry to measure slow crack growth in solids. This was made possible by the use of a dimensionally stable reference plate of Invar placed next to the specimen. The success of the experiment has considerably increased the possible scope of laser holographic interferometry to include measurements of strain changes over extended time periods.

Acknowledgment The authors wish to acknowledge the financial support

of this investigation by Atomic Energy of Canada Limited. Thanks are also due to J. Boulton of AECL for his continuous encouragement of this project.

References 1. Jackman, A.H. and Ounn, J.T., "Delayed Hydrogen Cracking o f

Zirconium Alloy Pressure Tubes," Atomic Energy o f Canada Limited Rep. AECL-5691 (Oct. 1976).

2. Hsu, T.R. and Moyer, R.G., "'Application o f Holography in High-temperature Displacement Measurements, "' EXPERIMENTAL MECHANICS, 12 (9), 43,-432 (Sept. 1972).

3. Hsu, T.R. and Lewak, R., "'Measurements o f Thermal Distortion o f Composite Plates by Holographic Interferometry, "" EXPERIMENTAL MECHANICS, 16 (5), 182-187 (May 1976).

4. Hsu, T.R. and Bertels, A .W.M. , "Propagation and Opening o f a Through Crack in a Pipe Subject to Combined Cyclic Thermochemical Loading, "" J. Pressure Vessel Tech., Trans. ASME, 17-25 (Feb. 1976).

5. Hsu, T.R., Bertels, A.W.M. , Banerjee, S. and Harrison, W.C., "'Theoretical Basis for a Transient Thermal Elastic-plastic Stress Analysis o f Nuclear Reactor Fuel Elements, "" Atomic Energy o f Canada Limited Rep. AECL-5233 (Jul. 1976).

6. Dhir, S.K. and Sikora, J.P., "'An Improved Method for Obtaining the General-displacement Field f rom a Holographic Interferogram," EXPERIMENTAL MECHANICS, 12 (7), 323-327 (Jul. 1977).

302 �9 August 1978