HAL Id: jpa-00225396
https://hal.archives-ouvertes.fr/jpa-00225396
Submitted on 1 Jan 1985
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
REVIEW OF DEVELOPMENTS IN QUANTITATIVE ULTRASONIC NDE
D. Thompson, R. Thompson
To cite this version:
D. Thompson, R. Thompson. REVIEW OF DEVELOPMENTS IN QUANTITATIVE UL- TRASONIC NDE. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-835-C10-846.
�10.1051/jphyscol:198510182�. �jpa-00225396�
JOURNAL DE PHYSIQUE
Colloque C10, suppl6ment au no12, Tome 46, decembre 1985 page C10-835
REVIEW OF DEVELOPMENTS IN QUANTITATIVE ULTRASONIC NDE D.O. THOMPSON AND R.B. THOMPSON
Ames L a b o r a t o r y , Iowa S t a t e U n i v e r s i t y , Ames, I A 50011, U . S . A .
Risum6. C'est l e risum6 de 1 ' i n t e n t i o n e t l a m o t i v a t i o n dynamique pour une technologie d ' e v a l u a t i o n non-destructive (NDE) g u a n t i t a t i v e . Puis,
c ' e s t l a r e v i s i o n du l e p r o g r k s p i c i f i q u e q u i a 6 t e f a i t en l e cas ultrasonique.
Cet ouvrage comprend l e developpement des l e s modiles de d i s p e r s i o n d i r e c t e . pour ondes e l a s t i a u e d ' i n t e r a c t i o n de f e l u r e s , s o l u t i o n s aoproximatives du l e problime de 'dispersion i n v e r s e q u i pertnets l a d e t e r m i i a t i o n de l a
grandeur, l a forme e t 1 'o r i e n t a t i o n de l a f e l u r e , 1 'extension e t 1 'i n c o r p o r a t i o n de modiles de d i s p e r s i o n de f 6 l u r e pour l e t r a i t e m e n t de l a question de
l a p r o b a b i l i t i de l a d i t e c t i o n de f e l u r e s e t l e dessein de s y s t h e s (NDE) d ' u l t r a s o n i q u e , e t une d e s c r i p t i o n d'un s y ~ t 6 m e en diveloppment d e s t i n i a 1 ' i n c o r p o r a t i o n de beaucoup d'avances theoriques. La pub1 ic a t i o n c o n c l u t avec l a remarque de 1 1 a n c 6 t r e comune e n t r e l e s d6veloppments du l e groupe de True11 5 l a U n i v e r s i t i de Brown s u r NDE ult'rasonique q u a l i t a t i f r e c o n t i i c i e t quelques - uns d'ouvrage de c e t t e r i u n i o n sur a t t e n u a t i o n - f r i c t i o n i n t e r n e .
Abstract. The purposes and d r i v i n g m o t i v a t i o n s f o r a q u a n t i t a t i v e non- d e s t r u c t i v e e v a l u a t i o n (NDE) technology are sumnarized. S p e c i f i c progress t h a t has been made i n t h e u l t r a s o n i c case i s then reviewed. This work i n c l u d e s t h e development o f d i r e c t s c a t t e r i n g models f o r elastic-wave f l a w i n t e r a c t i o n s , approximate s o l u t i o n s t o t h e i n v e r s e s c a t t e r i n g problem which p e r m i t f l a w size, shape, and o r i e n t a t i o n t o be determined, extensions and i n c o r p o r a t i o n o f f l a w s c a t t e r i n g models t o deal w i t h questions of p r o b a b i l i t y o f f l a w d e t e c t i o n and u l t r a s o n i c NDE system design, and a d e s c r i p t i o n o f a system under development designed t o i n c o r p o r a t e many o f t h e t h e o r e t i c a l advances. The paper concludes by n o t i n g t h e common a n c e s t r y i n T r u e l l ' s group a t Brown U n i v e r s i t y o f t h e q u a n t i t a t i v e u l t r a s o n i c NDE developments r e p o r t e d here and some o f the i n t e r n a l f r i c t i o n - a t t e n u a t i o n work o f t h i s meeting.
I. INTRODUCTION
Nondestructive t e s t i n g (NOT) techniques have been a p p l i e d t o a v a r i e t y o f s t r u c - t u r a l systems f o r many years w i t h t h e primary goal o f ensuring system i n t e g r i t y and safety. While t h i s goal remains i n t a c t , c u r r e n t research i n nondestructive e v a l u a t i o n (NDE) has taken on an a d d i t i o n a l goal o f major importance, a goal d e r i v e d p r i m a r i l y from economic considerations. Conservative design p r a c t i c e s t h a t were adopted t o ensure r e l i a b i l i t y i n major s t r u c t u r a l systems have l e d t o an under u t i l i z a t i o n o f components w i t h major economic l o s s when they were implemented w i t h o u t concomitant advances i n i n s p e c t i o n techniques. NDE i s now being asked t o p r o v i d e a b a s i s f o r q u a n t i t a t i v e l y p r e d i c t i n g t h e s e r v i c e a b i l i t y o r remaining l i f e o f a s t r u c t u r e .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:198510182
C10-836 JOURNAL DE PHYSIQUE
The dual nature of these goals may be demonstrated by examples. One of these may be found in j e t engines dedicated t o m i l i t a r y aerospace applications. Present performance standards demand t h a t engines be designed so t h a t no more than one i n a thousand f a i l during the design 1 if e . After they have served t h i s one design l i f e , a l l p a r t s , regardless of t h e i r condition, are removed from service.
Obviously, many of the r e t i r e d components have large and unused remaining l i v e s t h a t a r e c h a r a c t e r i s t i c of the s t a t i s t i c a l d i s t r i b u t i o n s of lifetimes f o r nominally identical conponents. Economic estimates (1) show t h a t l i f e cycle cost benefits of $250 million d o l l a r s can be achieved over a 15 year period f o r a single engine model i f the overly conservative practice required f o r engine re1 i a b i l i t y could be safely abandoned. However, abandonment would require the introduction of appropriate quantitative inspection techniques t h a t a r e capable of sizing flaws and assuring t h e i r detection. Another example stands out in the nuclear power industry. I t has been estimated t h a t the cost of unscheduled downtime i n a 1000 Mw nuclear reactor i s $600,000 per day ( 2 ) . In some cases, t h i s downtime could be i n i t i a t e d by a nondestructive t e s t t h a t indicates a flaw's presence, but i s unable t o characterize i t s severity. Under these conditions a shutdown i s mandated under current procedures in order t o assure safety even though the flaw may be completely harmless under conditions of usual reactor operation.
These examples exemplify the need f o r quantitative inspection techniques from which remaining safe lifetime decisions can be made. Clearly, technical success i n achieving a predictable safe lifetime strategy will provide a way to assure an acceptable level of safety a t a minimum cost. This strategy i s r e a l i s t i c in recognizing t h a t absolute safety i n structures can only be achieved a t an i n f i n i t e cost.
Achievement of a quantitative capabi 1 i t y f o r nondestructive t e s t i n g has required very s i g n i f i c a n t extensions of existent c a p a b i l i t i e s i n multidisciplinary direc- tions. The prediction of remaining l i f e requires a knowledge of flaw s i z e and orientation, ways t o measure c e r t a i n f a i l u r e related material properties, appropriate f a i l u r e models, and a knowledge of the s t r e s s , temperature and environment in
which the part must operate (3). The t i g h t coupling of nondestructive measurement technique development -to f a i l u r e model development ' i s an essential element i n establishing a t r u e quantitative nondestructive evaluation (NDE) capability.
For example, f r a c t u r e mechanics (4) forms the basis of a f a i l u r e model f o r cracks, inclusions, voids, etc. Other f a i l u r e models f o r d i f f e r e n t f a i l u r e modes might include the dependence and e f f e c t s of embrittlement upon the amount of hydrogen present. In f a c t , the extensions required a r e so significant t h a t a new name, nondestructive evaluation (NDE) has come i n t o comnon useage t o delineate between the new quantitative technology and the older, q u a l i t a t i v e technology -(NDT).
The ultimate technical goal of any quantitative NDE research e f f o r t can be sumnarized by the curve shown in Fig. 1 (5). Operationally, the capability of a technique can be described by a probability of rejection curve a s shown in t h i s figure.
The ideal quantitative technique, indicated by the dashed l i n e would have a zero probability of rejecting a l l flaws l e s s than the c r i t i c a l s i z e a s determined by a f r a c t u r e mechanics analysis incorporating material and use conditions, and a unity probability of rejecting those l a r g e r than t h i s s i z e . Any real technique, however, i s broader than the ideal and will make e r r o r s , a s indicated by the solid curve. Some flaws l e s s than the c r i t i c a l , f a i l u r e producing s i z e will be rejected ( f a l s e r e j e c t s ) and some greater than t h i s c r i t i c a l s i z e will be accepted (fa1 se accepts).
A technical goal of research in quantitative NDE i s thus t o develop techniques t h a t a r e a s sharp a s possible in the probability of rejection characteristic.
The purpose of t h i s paper i s t o review a few of the r e s u l t s t h a t have been obtained t o e s t a b l i s h a quantitative ultrasonic technology. These topics include d i r e c t and inverse scattering, probability of detection, and an instrumental advance which provides a way t o u t i l i z e a major portion of the research r e s u l t s . Much of the work described has been done under the sponsorship of the Defense Advanced Research Projects Agency (DARPA) , the Air Force Wright Aeronautical Laboratories/
Materi a1 s Laboratory, and the Basic Energy Sciences Engineering Program (DOE-BES).
CRITICAL FLAW SIZE
$
FLAW SIZE
Fig. 1. P r o b a b i l i t y of r e j e c t i o n curve showing i d e a l technique (dashed curve) and r e a l i s t i c technique ( s o l i d curve). Shaded areas i n d i c a t e t o t a l p r o b a b i l i t i e s o f f a l s e l y accepting bad p a r t s (FA) and f a l s e l y accepting good p a r t s (FR).
I I. RESEARCH ADVANCES A. Methodology
A research p l a n used f o r t h e development o f a q u a n t i t a t i v e u l t r a s o n i c NDE technology i s shown i n Fig. 2 i n b l o c k form. The f i r s t b l o c k ( l a b e l e d 1 ) c e n t e r s on t h e development and v e r i f i c a t i o n o f t h e o r e t i c a l s c a t t e r i n g models which d e s c r i b e t h e i n t e r a c t i o n o f a s p e c i f i e d e l a s t i c wave w i t h a given f l a w and which p r e d i c t t h e way i n which t h e wave i s s c a t t e r e d as a f u n c t i o n o f t h e n a t u r e o f t h e f l a w and the p r o p e r t i e s o f t h e i n c i d e n t e l a s t i c wave (6). T h i s i n i t i a t i n g step i s key t o a l l subsequent work i n t h i s plan.
The second block, i n d i c a t e d by 2 i n t h e f i g u r e , embraces t h e i n v e r s e s c a t t e r i n g problem which i s o f g r e a t e r p r a c t i c a l importance t o q u a n t i t a t i v e NDE (5). The problem i n t h i s case i s t o determine t h e q u a n t i t a t i v e f e a t u r e s o f t h e f l a w ( s i z e , shape, o r i e n t a t i o n , v a l u e o f m a t e r i a l property, e t c . ) from a measurement o f t h e s c a t t e r e d e l a s t i c waves given a known i n c i d e n t e l a s t i c wave; s o l u t i o n s o f t h i s problem o f t e n depend upon d i r e c t s c a t t e r i n g r e s u l t s developed i n b l o c k 1 as kernels. Even under i d e a l c o n d i t i o n s , t h e mathematical s o l u t i o n o f t h e i n v e r s e problem i s more complex than t h a t o f t h e d i r e c t problem. I n r e a l p h y s i c a l s i t u a t i o n s , l i m i t a t i o n s on t h e angles and frequencies o f observation, noise, and numerical e r r o r s i n processing a l l c o n t r i b u t e t o t h e i l l - p o s e d n a t u r e o f t h e problem (7,8). Even so, t h e e x t r a c t i o n o f f l a w s i z e i s p a r t i c u l a r l y important.
T h i s p r o p e r t y a l l o w s t h e connection t o be made between q u a n t i t a t i v e u l t r a s o n i c s and f r a c t u r e mechanics as a f a i l u r e model; t o g e t h e r t h e y comprise t h e f a i l u r e p r e d i c t i v e technology mentioned i n t h e I n t r o d u c t i o n . Rational a c c e p t / r e j e c t c r i t e r i a can then be developed u s i n g t h i s i n f o r m a t i o n .
The t h i r d b l o c k o f major advances t h a t have been made i s shown i n t h e l e f t hand p o r t i o n o f F i g . 3. T h i s b l o c k focusses upon t h e development o f a methodology t o p r e d i c t t h e p r o b a b i l i t y t h a t a f l a w w i l l be d e t e c t e d i n a given t e s t s i t u a t i o n w i t h a g i v e n apparatus (9). Without assurance t h a t a f l a w can be detected i n t h e f i r s t place, a l l o t h e r e f f o r t s a t s i z i n g and c h a r a c t e r i z a t i o n are, o f course, useless. For l a r g e s t r u c t u r e s (e.g., n u c l e a r r e a c t o r s ) o r those w i t h complex geometries (e.g., a i r c r a f t components) t h e d e t e c t i o n problem can be a c h a l l e n g i n g o p e r a t i o n which may be f u r t h e r complicated by t h e e l a s t i c inhomogeneities i n t r i n s i c i n p o l y c r y s t a l l i n e metal components. A problem which has been a l l t o o f r e q u e n t l y encountered i n the l a s t decade i s t h e r e c o g n i t i o n , a f t e r t h e design and c o n s t r u c t i o n o f a s t r u c t u r e have been completed, t h a t t h e s t r u c t u r e i s uninspectable f o r
p h y s i c a l reasons which c o u l d have been a n t i c i p a t e d . As w i t h t h e i n v e r s e s c a t t e r i n g
C10-838 JOURNAL DE PHYSIQUE
work, t h i s block u t i l i z e s the d i r e c t scattering theories as necessary inputs.
I t i s a l s o d i r e c t l y related t o the development of a theoretical probability of rejection curve such a s i s shown i n Fig. 1 f o r a given technique and t e s t s i t u a t i o n and provides ways t o design new techniques t h a t approach the optimal conditions depicted in t h a t figure.
The following paragraphs provide examples of work completed in these various sectors, and concludes with an example of new instrumentation t h a t i s being developed t o implement these advances.
Fig.
i f f
FLAW SIZING PREMCTlONS
"Roadmap" showing blocks of research t o develop a quantitative NDE technique.
B. Direct Scattering
Over the l a s t decade, major progress has been made in the development and experimen- t a l verification of ultrasonic scattering theories. A t the beginning of t h a t time, attention had been given t o the problem of scattering of e l a s t i c waves from the most simply shaped objects such as spherical inclusions (10) and penny- shaped cracks (11). Further developments of the theory have followed two complemen- tary paths ( 6 ) . On the one hand, highly accurate but computationally intensive numerical techniques were developed for, a variety of selected flaw geometries.
Simultaneously, a s e r i e s of approximate techniques were developed which could be applied t o a wider range of flaw geometries with much l e s s computational e f f o r t . These were i n i t i a l l y guided strongly by comparison t o experiment.
After t h e i r development, the more exact solutions provided many important benchmarks.
These developments are summarized in Table I ; a region of a p p l i c a b i l i t y i s also specified in the case of the analytic approaches. Additional c i t a t i o n s may be found in the review a r t i c l e s found in Refs. ( 1 2 ) and (13).
Table I . Recent Elastic Wave Direct Scattering Techniques
Numerical Approximate Analytical Techniques
NAME
- Applicable Wavelength
Regime T-Matrix
Method of Optimal Truncation Boundary Integral
Finite Element Finite Difference Moment
Long wavelength Long
Quasi-static Long-Medi um
Born Medi um
Distorted Wave Born Med i um Physical Elastodynamics Short
Kirchhoff Short
Ray Solutions Short
Figure 3 provides an example of an e a r l y r e s u l t in t h i s development. Here, Tittmann (14) shows the angular scattering of a longitudional wave incident on a spherical cavity in titanium. Included a r e both the d i r e c t l y scattered longitudinal wave and the mode converted shear wave. Two theories a r e included.
As would be expected, the exact solution of Ying and True1 1, (10) obtained by
a separation of variables technique, i s i n excellent agreement with the measurements.
Not so obvious i s the excellent prediction of the angular dependence made on the basis of the Born approximation a s developed by Krumhansl, Gubernatis, and Domany (1 5 ) , particular1 y f o r the angles near backscattering. These comparisons would have been impossible without the a v a i l a b i l i t y of the diffusion bonding technique f o r sample preparation, a technique whereby s c a t t e r e r s of known shape were embedded in the i n t e r i o r of a metal polycrystal (16).
Fig. 3. Scattering radiation patterns f o r 50Dpm diameter spherical void in titanium a t 2.25 MHz for incident longitudinal waves.
Figure 4 presents comparable r e s u l t s f o r the case of an i n t e r i o r e l l i p t i c a l crack. Here Adler and Achenbach (17) have demonstrated the a b i l i t y of the elasto- dynamic Kirchhoff approximation t o predict the frequency dependence of the ultrasonic backscattering. For t h i s configuration, the specularly reflected wave does
not return t o the receiver; the modulation i s produced by the interference of rays diffracted from the two edges of the crack.
JOURNAL DE PHYSIQUE
EXPERIMENTAL -THEORETICAL (WITHOUT
ATTENUATIONI
THEORETICAL f CORRECTED FOR ATTENUATION) W
k 2
-1 W
a
0 2.0 4.0 6.0 8d 10.0 12.0 14.0 FREQUENCY ( MHz )
Fig. 4. Comparison o f experiment t o elastodynamic K i r c h h o f f approximation f o r L-L p i t c h - c a t c h (60") s c a t t e r i n g from an e l l i p t i c a l crack i n t i t a n i u m .
C. I n v e r s e S c a t t e r i n g
Despite t h e c o m p l e x i t i e s o f t h e i n v e r s e problem noted i n A above, a number o f f i r s t generation s o l u t i o n s have been demonstrated and a r e summarized i n Table 11. As i n Table I, t h e range o f u l t r a s o n i c a p p l i c a b i l i t y i s i n d i c a t e d t o g e t h e r w i t h a surmrary o f p r o p e r t i e s a v a i l a b l e from t h e procedure. I n a l l these techniques,
i t i s g e n e r a l l y necessary t o use a d i r e c t s c a t t e r i n g model as a kernel and t o make some a p r i o r i assumptions which reduce t h e t o t a l c l a s s o f a l l p o s s i b l e s c a t t e r e r s t o a s m a l l e r s e t o f p o s s i b i l i t i e s which can be l e v e r a ed by a v a i l a b l e data. An e x t e n s i v e s e t o f c i t a t i o n s can be found i n Refs. ( 5 ) , q l 3 ) , and (18).
Table 11. E l a s t i c Wave Inverse S c a t t e r i n g Models.
Name
- A p p l i c a b l e Wavelength I n f o r m a t i o n E x t r a c t e d
Regime
Long Wavelength Long o Combinations o f m a t e r i a l
p r o p e r t i e s o f f l a w (e.g mass defect, ( 2 x t 3 ~ ) . . . j
:
o Stress i n t e n s i t y f a c t o r
o Separation o f crack from v o l u m e t r i c flaw.
...
Born Med i um
o Geometrical f e a t u r e s o f f l a w
D i s t o r t e d Wave Born Medium
o Separation of crack from v o l u m e t r i c flaw.
U n i f i e d Long and Medium
...
F r o n t Surface Echo Analysis Short o Combination o f m a t e r i a l
p r o p e r t i e s
SAFT* Short o 2-D f l a w o u t l i n e
POFFIS** Short o 2-0 f l a w o u t l i n e
Elastodynamic Crack Edge Mapping Short o 2-D f l a w o u t l i n e
Imaging Short o 2-D f l a w o u t l i n e
- *Synthetic Aperture Focussing Techniques.
**Physical Optics Far F i e l d I n v e r s e S c a t t e r i n g .
F i g u r e 5 shows t h e r e s u l t s o f a p p l i c a t i o n o f the one-dimensiona1,inverse Born approximation t o t h e 3-0 f l a w r e c o n s t r u c t i o n problem (19,20). The s a l i e n t features o f t h e approach can be described as f o l l o w s . S c a t t e r i n g measurements a r e f i r s t made a t a v a r i e t y o f i n s o n i f i c a t i o n ( " l o o k " ) angles. The i n v e r s e Born technique
(19) i s then a p p l i e d t o these s c a t t e r e d waveforms and t h e d i s t a n c e from t h e plane o f wave f r o n t tangency t o t h e f l a w t o t h e c e n t r o i d o f the f l a w i s thereby determined. I t i s then assumed t h a t t h e f l a w has an e l l i p s o i d a l shape w i t h constant values f o r t h e moduli and d e n s i t y w i t h i n t h e e l l i p s o i d b u t w i t h yet-to-be determined values f o r t h e t h r e e semi-axes and t h r e e E u l e r angles t h a t describe
i t s o r i e n t a t i o n w i t h i n a l a b o r a t o r y reference system. A f t e r a s u i t a b l e transformation, a regression a n a l y s i s i s f i n a l l y used t o determine t h e s i x parameters t h a t describe the "best f i t " e l l i p s o i d t h a t approximates the f l a w (20). The r e c o n s t r u c t i o n o f an e l l i p s o i d a l i n c l u s i o n shown i n Fig. 5 demonstrates a r a t h e r remarkable s e n s i t i v i t y f o r small f l a w r e c o n s t r u c t i o n even though t h e u l t r a s o n i c wavelength i s o f the o r d e r o f the f l a w size. The small dimensions o f t h i s sample ( 5 0 ~ x 100pm) would have made r e c o n s t r u c t i o n by t r a d i t i o n a l imaging approaches, e. . ,
phased arrays, a c o u s t i c a l holography, and s y n t h e t i c a p e r t u r e techniques (sAFT~, q u i t e d i f f i c u l t a t s i m i l a r wavelengths.
Fig. 5. Cross s e c t i o n o f "equivalent" e l l i p s o i d f o r i n c l u s i o n (5011 x 10011).
S o l i d curve i s r e s u l t o f regression a n a l y s i s f o r best f i t e l l i p s o i d using inverse Born inputs; p o i n t s shown are experimental p o i n t s t h a t l i e i n plane o f cross section.
I I I , , , *Y'
Figure 6 presents a second example, t h a t o f r e c o n s t r u c t i n g the shape o f a two dimensional crack (21 ). T h i s r e s u l t , obtained by Ah1 berg, Tittmann, N o r r i s , and Achenbach, was based on t h e measurement o f t h e t i m e o f a r r i v a l o f s i g n a l s d i f f r a c t e d from t h e crack edges. The d i f f e r e n c e i n these times o f f l i g h t produced the modulations shown i n Fig. 4. The l o c a l crack edge mapping technique employed assumes t h a t a p o i n t c l o s e t o t h e crack i s known. The data are then used t o determine a s e t o f planes t a n g e n t i a l t o t h e crack edges. The edge o f t h e crack i s then determined as t h e envelope o f these planes. Included i s an i t e r a t i o n procedure which a l l o w s improvement i n t h e choice o f t h e i n i t i a l base p o i n t and subsequent i n v e r s i o n r e s u l t .
Actual Inclusion: -
a,= a,
= 5 0 ~-
aye
looptilt 7 O
JOURNAL DE PHYSIQUE
Fig. 6. Reconstruction o f e l l i p t i c a l crack i n t i t a n i u m using the crack-edge mapping method. The nominal crack major and minor axes were 2.57 and 1.41 mn, respectively.
0. P r o b a b i l i t y o f Detection
The development o f ways t o model and t o enhance the p r o b a b i l i t y o f d e t e c t i o n o f a f l a w i s f a i r l y new, b u t i s c l e a r l y a v i t a l step i n the o v e r a l l q u a n t i t a t i v e technology plan. As noted i n Fig. 2, block 3, t h i s modeling makes use o f d i r e c t s c a t t e r i n g t h e o r i e s t o synthesize waveforms t o be expected from a s p e c i f i c f l a w i n a given c o n f i g u r a t i o n by a given NDE apparatus. The r e a l i z a t i o n o f t h i s goal r e q u i r e s extensions of t h e d i r e c t s c a t t e r i n g models (which were generally derived f o r flaws i n unbounded media) t o i n c l u d e t h e e f f e c t s o f waveform, beam patterns, changes i n these patterns as the beam passes through various material i n t e r f a c e s on i t s way t o the flaw, and system noise (22-24).
The c a l c u l a t i o n described above y i e l d s a s p e c i f i c waveform determined by the physical parameters o f t h e u l t r a s o n i c system, p a r t , and flaw. However, i n practice, a d i s t r i b u t i o n o f signal strengths i s observed from flaws o f the same nominal size. These v a r i a t i o n s can be caused by v a r i a t i o n s i n the beam p o s i t i o n w i t h respect t o t h e flaw, v a r i a t i o n s i n the o r i e n t a t i o n o f t h e flaw, competing noise due t o r e f l e c t i o n s from g r a i n boundaries, o r other m i c r o s t r u c t u r a l inhomogeneities.
The problem then takes on a s t a t i s t i c a l character w i t h the requirement f o r e s t i - mating the p r o b a b i l i t i e s o f c o r r e c t detection, f a l s e detection, etc. The deter- m i n i s t i c models must then be recast i n a p r o b a b i l i s t i c format t o a l l o w these engineering parameters t o be estimated.
Figure 7 shows the r e s u l t s o f such a c a l c u l a t i o n (24). Here, the problem o f the d e t e c t i o n o f small cracks near t h e bore o f an a i r c r a f t t u r b i n e engine r o t o r component i s considered. The cracks are assumed t o have a c i r c u l a r shape.
The most probable o r i e n t a t i o n , due t o the d i r e c t i o n o f t h e f a t i g u e stresses, i s f o r t h e crack t o l i e i n a r a d i a l plane. However, i t i s assumed t h i s may
vary by *lo0 i n both the t i l t and skew d i r e c t i o n s , due t o m i c r o s t r u c t u r a l v a r i a t i o n s , stress variations, etc. I n addition, i t i s assumed t h a t t h e i n s p e c t i o n i s done by an automated system w i t h t h e inspections being performed on a c y l i n d r i c a l g r i d o f p o i n t s whose separations are determined by scan increments, probe scan speed, and pulse r e p e t i t i o n rates. I n Fig. 7a, t h e p r o b a b i l i t y o f d e t e c t i o n (POD) i s p l o t t e d as a f u n c t i o n o f crack s i z e f o r flaws a t t h r e e d i f f e r e n t depths f o r a postulated scan plan i n which the a x i a l and c i r c u m f e r e n t i a l increments are both 0.25cm (0.1 in.). The p r e d i c t i o n reveals a poor POD f o r t h e 2.54cm deep cracks. Analysis shows t h i s t o be the r e s u l t o f beam focussing a f t e r passage through t h e c y l i n d r i c a l bore surface, which leads t o a c i r c u m f e r e n t i a l beam e x t e n t l e s s than t h e scan increment. Figure 7b shows t h e performance o f an a l t e r n a t e scan plan, w i t h increments o'f D.5cm (0.2 in.) and 0.13cm (0.05 i n . ) , respectively, which overcomes t h i s problem w i t h no l o s s i n i n s p e c t i o n time.
POD POD
Crack Radius ( c m l Crack Rodius ( c m )
Fig. 7. Simulations o f p r o b a b i l i t i e s o f crack d e t e c t i o n on an a i r c r a f t engine t u r b i n e r o t o r bore.
a ) a x i a l and c i r c u m f e r e n t i a l scan increments o f 0.25cm.
b ) a x i a l and circumferencial scan increments o f 0.5cm and 0.13cm, r e s p e c t i v e l y .
E. New Instrumentation
An example o f new u l t r a s o n i c instrumentation t h a t i s under development t o implement t h e t h e o r e t i c a l advances described above i s shown schematically i n Fig. 8.
The f i g u r e shows s i x transducers arranged i n a r i n g about a c e n t r a l transducer w i t h a l l beams convergent upon the t a r g e t o f i n t e r e s t . By t a k i n g advantage o f various pulse-echo and p i t c h - c a t c h combinations, as many as 19 independent
"views" o f t h e t a r g e t f l a w can be e a s i l y obtained f o r each angle o f i n s o n i f i c a t i o n ( p o l a r angle) o f the t a r g e t flaw. M u l t i p l e "views1' a r e o f course necessary t o produce 3-D reconstructions.
Fig. 8. Schematic p l a n o f m u l t i v i e w i n g transducer.
Two views o f a f i r s t hardware version o f t h i s apparatus are shown i n Fig. 9a and b (25). Each o f t h e s i x p e r i p h e r a l transducers i s placed i n a gimbeled mount so t h a t t h e angle o f i n s o n i f i c a t i o n (defined as the angle between t h e normal t o t h e sample surface and t h e a x i s o f the transducer) may be v a r i e d from 0" t o 30' i n water. The s i x transducers are then coupled t o one d r i v e system
C10-844 JOURNAL DE PHYSIQUE
so t h a t a l l s i x transducers can be s e t t o t h e same angle ('1/4') simultaneously.
Since d i f f e r e n t i n d i v i d u a l transducers can be i n s e r t e d i n t o t h e assembly, the c a p a b i l i t i e s o f the m u l t i v i e w i n g probe can be t a i l o r e d t o i n s p e c t i o n requirements by a l t e r i n g o r m i x i n g i n d i v i d u a l probe frequencies and beam p a t t e r n s . The m u l t i - viewing assembly i s completely automated and placed under the c o n t r o l o f a desk t o p computer. Automation i n c l u d e s t h e s e l e c t i o n o f a data a c q u i s i t i o n p r o t o c o l , i n v e r s e wave form processing u s i n g t h e i n v e r s e Born approximation, a "best f i t "
e l l i p s o i d a l f l a w r e c o n s t r u c t i o n described above u s i n g a regression a n a l y s i s , and a d i s p l a y o f r e s u l t s format.
Fig. 9. Views o f m u l t i v i e w i n g transducer
a ) bottom view o f a d j u s t a b l e transducer a r r a y b ) assembled view.
111. SUMMARY
Many s i g n i f i c a n t advances have been made i n t h e development o f a q u a n t i t a t i v e u l t r a s o n i c NDE technology. These advances have been motivated by a d e s i r e t o improve c o n t r o l over b o t h t h e s a f e t y o f s t r u c t u r a l components and l i f e c o s t s associated w i t h those s t r u c t u r e s . This technology has been coupled w i t h f r a c t u r e mechanics t o p r o v i d e t h e framework f o r a l i f e p r e d i c t i o n s t r a t e g y . The advances o f the NDE technology, however, are n o t l i m i t e d t o d i s c r e t e f l a w s whose f a i l u r e p r o p e n s i t y i s described b y f r a c t u r e mechanics, b u t can i n c l u d e any f a i l u r e - r e l a t e d m a t e r i a l p r o p e r t y t h a t can be q u a n t i f i e d by an u l t r a s o n i c measurement and f o r which an a p p r o p r i a t e f a i 1 u r e model e x i s t s o r can be developed. Thus, t h e advances described a r e broad i n scope and i m p l i c a t i o n .
It i s worthwhile t o n o t e t h a t one o f t h e e a r l i e s t e f f o r t s i n t h i s area was nucleated a t Brown U n i v e r s i t y under t h e guidance o f Prof. R. T r u e l l (10). T h i s group
a l s o p r o v i d e d a n u c l e a t i o n seed f o r many s i g n i f i c a n t advances i n t h e understanding o f d i s l o c a t i o n and g r a i n boundary-generated c o n t r i b u t i o n s t o i n t e r n a l f r i c t i o n and u l t r a s o n i c a t t e n u a t i o n , t o p i c s o f s i g n i f i c a n c e t o t h i s conference. The
importance o f the i n i t i a l ~ o n t r i b u t i o n o f T r u e l l ' s group t o t h e p a r a l l e l development o f these two s u b j e c t s should be noted.
Refe
1. C. G. Annis, J. S. C a r g i l l , J. A. H a r r i s , Jr., M. C. Vanwanderham, "Engine Component Retirement-for-Cause: A Nondestructive E v a l u a t i o n (NDE) and F r a c t u r e Mechanics Based Maintenance Concept", i n , Nondestructive Evaluation:
M i c r o s t r u c t u r a l C h a r a c t e r i z a t i o n and R e l i a b i l i t y S t r a t e g i e s , 0. Buck and S. M. Wolf, Eds. (The M e t a l l u r g i c a l S o c i e t y o f AIME, Warrendale, PA, 1981), P. 53.
G. Dau, "NDE: In-Depth Search f o r Flaws", EPRI Journal 5 (July/August, 1980).
R. B. Thompson and A. G. Evans, "Goals and Objectives o f Q u a n t i t a t i v e U l t r a - sonics", IEEE Trans. on sonics and U l t r a s o n i c s SU-23, 292 (1976).
S. T. R o l f e and J. M. Barson, Fracture and Fatique Control i n S t r u c t u r e s : A p p l i c a t i o n s o f F r a c t u r e Mechanics ( P r e n t i c e - H a l l , Inc., Englewood C l i f f s , NJ, 1977).
R. B. Thompson and D. 0. Thompson, "New Techniques f o r Quantitative NDE", J. Metals 33, 29 (1981 1. A1 so pub1 ished i n extended form i n the book c i t e d i n Ref. 1.
D. 0. Thompson and R. B. Thompson, " Q u a n t i t a t i v e U l t r a s o n i c s " , P h i l . Trans.
R. Soc. Lond. A. 291, 233 (1979).
D. A. Lee, "111-posed and well-posed problems i n i n v e r s e elastodynamic s c a t t e r i n g f o r n o n d e s t r u c t i v e e v a l u a t i o n " , J. Nondestr. Evaluation 2, 161-172 (1981).
B r i a n DeFacio, "Rigorous r e s u l t s on i n v e r s e source and i n v e r s e s c a t t e r i n g theory", Review o f Progress i n Q u a n t i t a t i v e Nondestructive Eval u a t i o n 1, D. 0. Thompson and D. E. Chimenti, Eds. (Plenum Press, NY, 1982), p. 219.
R. B. Thompson and T. A. Gray, "Use o f u l t r a s o n i c models as t o o l s i n t h e design and v a l i d a t i o n o f new r o l e techniques", Presented a t t h e Royal S o c i e t y Discussion meeting on "Novel Techniques o f Nondestructive Examination and V a l i d a t i o n " , 9-10 J u l y , 1985 and t o be published i n P h i l . Trans. R. Soc.
C. F. Ying and R. T r u e l l , " S c a t t e r i n g o f a plane l o n g i t u d i n a l wave by a s p h e r i c a l o b s t a c l e i n an i s o t r o p i c a l l y e l a s t i c s o l i d " , J. Appl. Phys. 27,
1086 (1956). Also, R. T r u e l l , C. Elbaum, and B. B. Chuck, U l t r a s o n i c Methods i n S o l i d S t a t e Physics (Academic Press, NY, 1969), Ch. 3.
E. A. Kraut, "Review o f t h e o r i e s o f s c a t t e r j n g o f e l a s t i c waves by cracks", IEEE Trans. on Sonics and U l t r a s o n i c s SU-23, 102 (1976).
Y. M. Pao, " E l a s t i c Waves i n S o l i d s ' , J. Appl. Mech. 50, 1152 (1983).
R. B. Thompson, " Q u a n t i t a t i v e U l t r a s o n i c ~ o n d e s t r u c t i k Evaluation Methods", i b i d , p. 1191.
R. K. E l s l e y , J. M. Richardson, R. B. Thompson, and B. R. Tittmann, "Compari- son Between E x ~ e r i m e n t a l and C o m ~ u t a t i o n a l Results f o r E l a s t i c Wave Scat- t e r i n g " , i n , ~ c o u s t i c , ~ l e c t r o m a g n e t i c and E l a s t i c Wave S c a t t e r i n g - Focus on t h e T-Matrix Approach, V. K. and V. V. Varadan, Eds. (Pergamon Press, NY, 1980), p. 571.
J. E. Gubernatis, E. Domany, and J. A. Krumhansl, "Formal Aspects o f t h e S c a t t e r i n g of Ultrasound by Flaws i n E l a s t i c M a t e r i a l s " , J. Appl. Phys.
48, 2804 (1977).
- C. C. Bampton, " U l t r a s o n i c Test Samples", i n , Review o f Progress i n Q u a n t i t a t i v e Nondestructive E v a l u a t i o n 1, D. 0. Thompson and D. E. Chimenti, Eds. (Plenum Press, NY, 1982)., p. 315. Also, N.E. Paton, unpublished r e s u l t s .
L. A d l e r and J. D. Achenbach, " E l a s t i c Wave D i f f r a c t i o n bv E l l i ~ t i c a l Cracks:
Theory and Experiment", J. ~ o n d e s t r . Eval . 1, 87 (1980). -
R. B. Thompson and D. 0. Thompson, " U l t r a s o n i c s i n Nondestructive Evaluation", Proc. IEEE ( i n press).
J. H. Rose and J. A. Krumhansl, "Determination o f Flaw C h a r a c t e r i s t i c s from U l t r a s o n i c S c a t t e r i n g Data", J. Appl. Phys. 50, 2951 (1979).
D. K. Hsu, J. H. Rose, and D. 0. Thompson, J. A p p r Phys. 55(1), 162 (1984).
L. Ahlberg, B. R. Tittmann, A. N. N o r r i s , J. D. Achenbach,-Experimental
Results on Crack I n v e r s i o n " , i n , Review o f Progress i n Q u a n t i t a t i v e Nondestructive E v a l u a t i o n 3A, D. 0. Thompson and D. E. Chimenti, Eds. (Plenum Press, NY,
1985), p. 287.
C10-846 JOURNAL DE PHYSIQUE
22. K. W. F e r t i g and J. M. Richardson, "Computer Simulation of P r o b a b i l i t y
of Detection1', i n , Review of Progress i n Q u a n t i t a t i v e Nondestructive Evaluation ZA, D. 0. Thompson and D. E. Chimenti, Eds. (Plenum P r e s s , NY, 1983), p.
- 147.
23. K. W. F e r t i g , J. M. Richardson, and R. K. E l s l e y , " S t a t i s t i c a l Flaw Detection:
Theory", i b i d , Vol. 3A (1984), p. 65.
24. T. A. Gray, R. B. Thompson, and B. P. Newberry, "Use of Models t o P r e d i c t U l t r a s o n i c NDE R e l i a b i l i t y " , i b i d , Vol. 4 ( i n p r e s s ) .
25. D. 0. Thompson and S. J. Wormley, "Long and Intermediate Wavelength Flaw
~ e c o n s t r u c t i o n " , i n , Review of ~ r o q r e s s i n Q u a n t i t a t i v e Nondestructive.
Evaluation 4A, D. 0. Thompson and D. E. Chimenti, Eds. (Plenum P r e s s , d ~ ,
1985), p. 287.
