M. S. Hughes Iowa State University See next page for additional authors
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Ultrasonic NDE of thick composites Abstract
A series of ultrasonic techniques being developed for the characterization of thick composites are described. Techniques for the in-situ measurements of elastic constants on thick-walled cylinders based on the times of a variety of ultrasonic modes of propagation are first presented, followed by discussion of the determination of the porosity from measurements of the frequency dependence of the attenuation. Two techniques for imaging delamination are then discussed. The first involves inferring size from plots of reflected signal amplitude versus lateral position of the transducer with a model for beam propagation in anisotropic media used to deconvolve the effects of the distant and direction dependent beam width. The second makes use of synthetic aperture techniques. Keywords
Center for Nondestructive Evaluation Disciplines
Materials Science and Engineering | Mechanical Engineering | Structures and Materials Authors
R. Bruce Thompson, Donald O. Thompson, David K. Holger, David K. Hsu, M. S. Hughes, Emmanuel P. Papadakis, Yu-Min Tsai, and Loren W. Zachary
This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/aere_conf/21
NDE-Vol. 10, Enhancing Analysis Techniques For Composite Materials ASME 1991
ULTRASONIC NDE OF THICK COMPOSITES R. B. Thompson, D. 0 . Thompson, D. K. Holger, D. K. Hsu, M. S. Hughes, E. P. Papadakis, Y.-M. Tsai, and L. W . Zachary Department of Aerospace Engineering/Engineering Mechanics Center for NDE Iowa State University Ames, Iowa
Three types of measurements are discussed. In Section II, techniques for the determination of the anisotropic elastic constants are presented. Knowledge of these constants is necessary as an input to predictions of macroscopic structural response, e.g. buckling analysis, to external loads (Chin and Prevorsek, 1989; Greszczuk et al., 1971). They are also needed to properly interpret a variety of ultrasonic measurements. The section opens with a summary of determinations of the elastic constants on small test-specimens cut from thick composite plates and cylinders. Although these results were obtained destructively, they are included as they provide a frame of reference for t he rest of the section which describes several schemes for determining the elastic constants in-situ. Included are .discussions of the uses of surface waves, Lamb waves, and obliquely propagating bulk waves.
ABSTRACT A series of ultrasonic techniques being developed for the characterizaton of t hick composites are described. Techniques for the in- situ measurements of elastic constants on thick-walled cylinders based on the times of a variety of ultrasonic modes of propagation are first presented, followed by discussion of the determination of the porosity from measurements of the frequency dependence of the attenuation. Two techniques for imaging delamination are t h en discussed. The first involves inferring s i ze from plots of reflected signal amplitude versus lateral position of the transducer with a model for beam propagation in anisotropic media used to deconvolve the effects of t he distant and direction dependent beam width . The second makes use of synthetic aperture techniques.
The elastic cons tants can also provide information about fabrication errors such as wavy fibers and fiber disbonding. Other important micr ostructural information is provided by attenuation and backscattering measurements. Section III discusses an example, the inference of porosity from the frequency dependence of the attenuation.
As a consequence of t he ir tailored internal structure, e.g. reinforcing fibers i n particular geomet~ical arrangements , composites exhibit de~irable mechan1cal properties, e.g. high strength-to-wetght ratios. These internal structures and the resulting properties, are strongly influenced by a variety of processing variables. Hence the nondestructive characterization of composites is particularly impor~ant. In one application, the use of composite matertals in thick-walled submersible vessels, one needs to obtain in-situ e~timates of anisotropic elastic constants in order to predict the macroscopic structural respo~se to external loads, an important example being buckltng analysis. In addition distributed or localized defects must be detected and characterized to predict degradations in the performance of the structure.
Interply delaminations, as well as the presence of foreign objects, constitute macrosc~pic defects. Two techniques for determining defect stze are presented in Section IV. In one, knowledge of the anisotropic elastic constants is used to correct C-scan images so that the flaw size can be quantitatively determined from the spatial variation of the C-scan image intensity. In the other, synthetic aperture techniques are employed to reconstruct B-scan representations of the flaw ' s shape. In this work, two sample geome~ries will be considered. The ultimate objective 1s the nondestructive evaluation of uncut filament wound composite cylinder s illustrated in Fig. 2. However, due to the limited availability of samples, most of the measurements were performed in the flat plate geometry and include samples fabricated by other techniques.
This paper describes a variety of ultrasonic techniques which are being developed for the chara~terization of thick filament wound composites, . ispectally those designed to withstand large compresstve oads. As in many classes of composite materials, the e~~stence of an elastic anisotropy is a major factor ~itch must be taken into consideration. This leads to a illectionally dependent wave speed ( Auld, 1973), as di ustrated in Figure 1, for the case of a sample ~cussed in greater detail in Section II. The ~~~stence.of such a strong anisotropy in velocity ferenttates composites from many other classes of materials and is essential to many of the ultrasonic ~ho~destructive evaluation (NDE) techniques discussed in Ls paper.
DETERMINATION OF ELASTIC CONSTANTS Oriented fibers cause the macroscopic physical and mechanical properties of a compos i te to be highly anisotropic. One example is the elastic constant tensor Cij r elating stress o, and strain eJo (1)
" 7 ~7.0 ·5.0
·l.O ·1.0 1.0 3.0 5\.0WI'IESS ALONG XI
Slowness surface for a filament-wound composite, experimental rocket c ase. The 3 direction is normal to the fib er s.
Radial ( 3)
Graphite - Epoxy Fiber Resin
Cylindr i cal geomet ry of a fil ament wound composite.
Elastic Constant Determination
1 tic constants are, in general, described by a Th~r~ha~ank tensor. However, various symmetries in the fo and strain tensor allow the elastic constant s tres~ to be replaced by a symmetric, 6x6 matrix as tens~ d b the reduced notation used in Equation (1) ~~~ide 19~3). Hence t here are generall y 21 independent constants. Material symmetry further reduces 1 tic ~h!~ number, with the number of independent el astic stants being two, five and nine for isotropic, ~~~nsversely isotropic, and orthotropic materials, respectively.
The most direct way of determining elastic constants is by making measurements on parallelipipe~ removed from a large specimen. If certain symmetries can be assumed, the techniques are analogous to those employed in the determination of the elastic constants of single crystals. Such studies are described elsewhere, with a typical result shown i n Table I (Papadakis, et al., 1991). Here the elastic constants are presented for a filament-wound c omposite experimental rocket cage section prepared by Herculespie Orthotropic symmetry is present. The h ighly anisotr~o nature of the elastic constants is evide nt, l eading in the slowness surface shown in Fig. 1 fo r directio~~le the X1-X3 plane. The X2·X3 picture is similar, w the X1·X2 is more circular.
A composite, of course, has internal structure at a v ariety of scales, ranging from fiber-matrix interface regions having dimensions of nanometers through fibers with dimensions on t he order of mi crometers to pl ies with dimensions on the order of millimeters. In this work, we will assume that the ultr asonic wavelength is large with respect to all of these scales , t hus justifying the use of the macroscopic elastic constants. The macroscope symmetry depends on the details of the lay-up.
In-Situ Measurements of Elastic Constants A practical NDE technique requires t he t determination of elastic constants in-situ on uncu one samples. There are two categories of approaches.
Elastic Constants of Thick, Filament-Wound Experimental Rocket Case Section (GPa)
can either make measurements utilizing modes of propagation that are guided by the surface of the sample (i.e. Rayleigh or Lamb modes), or one can make measurements using ultrasonic beams that propagate through the bulk and are reflected by the surfaces (i.e. angle beam measurements). A theoretical foundation for the former case is first presented, followed by a presentation of both theore tical and experimental results for the latter case.
surface wave is much stronger than the wave packet strength which is represented by the first term on the right hand side of the equation. In view of the above wave properties, an experimental measurement of the speed of the first arriving wave will determine the elastic constant C 11 • The wave-peak speed will determine the surface wave speed. The value y is the root of the Rayleigh characteristic equation, and is a function of CII,Czz,c ... and C 12• The dependence of the surface wave speed on the material constants is used later to determine the off- diagonal constant C 12•
Use of Guided Modes. Guided modes can consist of either Rayleigh or surface waves confined to one surface on the sample, or vibrations in which the energy is distributed through the sample wall thickness and strongly influenced by boundary conditions at both surfaces. In the former case, theoretical guidance can be obtained from solutions describing the radiation of a line source on a half-space, as presented below, to determine the influence of the elastic constraints on the radiation characteristics (Tsai, et al ., 1991) .
The application of a line surface load along a principal direction tangent to the orthotropic half-space is expected to produce a shear wave. For the case of a tangent line load (Figure 3b) Fourier and Laplace transform techniques have been used to solve the equations of moti on and to satisfy the boundary conditions. Note that different coordinate systems were chosen in the normal and tangent loading cases for convenience in analysis. Results for other cases can be obtained by rotation o.f coordinates. The disturbance produced by the tangent loading in the case shown is 112 found to travel at the shear wave speed c•• /p) • An experimental measurement on the wave speed will determine the shear constant C 66 •
The response of an orthotropic half-space to a normal periodic surface load is first investigated to identify the type of waves propagating in the free surface. The coordinates , x, y, and z are along the three principal material axes (Figure 3a). The normal load is uniformly distributed along the z-axis and acts in the direction of the y-axis, which is directed into the material half-space.
A proper combination of the above results for the surface normal and tangential line loadings (involving multiple directions of propagation on multiple surfaces), will achieve a nondestructive evaluation of all the nine elastic constants. However, for many structural components, there are only two mutually perpendicular surfaces available for experimental measurements. As an example, the upper surface in Figure 4 represents an available surface while the right surface is another available surface. The measurement of the speed of the first arriving wave produced by a normal load along line [D) propagating in the !-direction determine the diagonal constant C 11 • Similarly, the normal loads applied along lines (D'] and [E) respectively determine the other two diagonal compressional constants C 22 and C3:1, respectively. The application of a surface tangent load along (E']-line produces shear waves propagating in the 2-direction. The measurement of this shear wave speed determines the constant c... Similarly, surface tangent loads along [D) and [D'] can be used to obtain C" and c .. respectively . The amplitude of the [D)-i~~ited shear wave is inversely proportional to (C44 C66) I , and the amplitude of the shear wave produced by the tangential load along the [D') - line is inversely proportional to (Css C66)1/2. Thus the ratio of the two amplitudes will be a check upont Cs5· The measurement procedures and operations for all the six diagQnal constants are summarized in Table II.
. The equations of motion and the boundary condttions are satisfied by using the Fourier transform technique. In the transformed complex plane, the inversion integrals involve branch points and simple roles. The contributions of the singular points are all ncorporated into a complete contour integration of the 1nversion integral. An exact expression for the ~angential displacement in t he free surface in a direction perpendicular to the line load and offset by a w stance, x, is obtaine d in the form of propagating aves as follows: u•
J.:li Fn ·
xvc 6 )]d~ + H(y)exp[lw(t- xy/C 6 )] (2)
where P_is the material density. The integrands F(~. w) and H(y) are functions of the wave frequency w and the related material constants, C 11 .C 22 .C 66 , and C,z. The above results indicate that the wave group with the speed ~C 11 /p•f!> 112 C 6 first arrives at the ~hsition x. The second term on the right hand side of e above equation is the surface wave propagating at the speed c.ty, which is less than the shear wave speed i•· This is consistent with the results obtained by sal and Kolsky (1967, 1968) . The strength of the
Coordinate systems used in analys is of dynamic line loading. (a.) Dynamic normal loading .
y Figure 3
Coordinate systems used in analysis of dynamic line loading. (b.) Dynamic tangent loading . TABLE II
Scheme for Determining 9 Elastic Constants of an Orthotropic Composite from the Response to Line Source Excitations on Two Orthogonal Surfaces. Type of Load
Distribution in Fig. 4
Measurement of t he speed of the Rayleigh wave launched by the normal line load can be used to determine the rema i ning off-diagonal elastic constants. For exampl e , the Ray leigh frequency equation for r adiation from a normal load along [E-) involves only f our e lastic constan t s Cll• C22. C66. and Cl2· If the constants Cll • C22 • C66 and the surface wave speed are measured, the fre quenc y equation can be used to determine t he elas t ic constant Cl2· Therefore, the measurement of t he t hree properly related surface wave speeds will determine the three off-diagonal constants c 12 c13 and C23· The types of loading and the elastic con~tants to be deter mined in this way are also summarized in Table I I .
a speed of 0.206 % 0.002 em/~. and t he other transve r se mode with its propagation and polarization direc tions both normal to the fibers had a wave speed of 0 . 155 • . 0. 001 em/~. Combined with a measured density of l. 586 g/cm3, the three elastic constants values were: C2214.95 GPa, e55- 6.73 GPa, and C44- 3.81 GPa. To determine the remaining two constants, c11 and e12. a method was developed to extract t he constants from the times - of-flight of the acousto·ultrasonic signals. In thin composite laminates the acousto-ultrasonic (Duke, 1980, Vary , 1982) signals are complex mixtures of unresolved echoes of many dif~erent modes and are very difficult to analyze quantitat1vely . In thick laminates, however, these different modes become temporally resolved and the signals are amenable to quantitative analysis (Hsu and Margetan, 1990) .
The above scheme is suitable for measurements made on uncut cylinders at high frequencies, such that the wavelength is short wit h respect to the wall thickness and the radius of curvature. At lower frequencies ( l onger wavelength ), wave speeds depend not only on mat erial constants but also on the geometry of structural components or specimens, and the curvature mus t be explicitl y taken into consideration. For a hol low composite cylinder both the cylinder rad~us and t he wall thicknes s have effects on the propagat1on of str ess waves. To study the interactive effects between t he cyl i nder geometry a nd the w~ve len~th, longitud~nal moti on of a thick t r ansversely 1sotrop1c hollow cyl1nder has r ecen tly been investigated (Tsai, in press). The frequency equation whi ch results from satisfyin~ the s t res s - free inner and outer cylindrical boundar1es has been obtained in an exact expression in terms of the wave length, the cyl i nder radii and the material constants . The frequency equation reduces to an expr ession which is the product of the frequency equations for symmetrical and antisymmetrical motions of t hick composite plates when the wave length is smal~ and t he difference between the cylinder radii has a fin1te val ue. I f the wave length is small compared to the shell thi ckness, t h e s hell frequency equation becomes t he corresponding surface wav e equation. For long wave length , the anisotropic shell frequency equation predicts a wave speed which reduces to the rod wave speed for aniso t ropic material.
In making acousto-ultrasonic measurements, two transducers were coupled to the same side of the plate and the times-of- flight of the various obliquely bounced echoes are measured as a function of the transducer separation distance. To determine C11 and Cl2• the time - of-flight of the quasi-longitudinal (QL-+ QL) echo was used. In an anisotropic solid the speed of sound is a function of propagation direction as was illustrated by Fig. 9, and the time -of-flight of the oblique l y bounced QL-+ QL echo may be computed from the slowness surfaces of the material. This relationship i s now utilized in an inverse manner for the determination of the elastic constants e11 and C12 from the experimental acousto-ultrasonic time-of-flight data. Figure 6 shows the time-of-flight versus ~he transducer separation for a 2.54 em (1") thick graphltejepoxy laminate. To determine the values of C12 and C22 iteratively, initial guess values were chosen for them and together with the other three elastic constants alr~ady measured, the slowness surfaces of the mate rial were computed. Using the slowness surfaces and the transducer separation distance, the time-of-flight of the QL-+ QL echo was computed for each separation distance . The computed and meas ured times-of-flight were compared and the values of C11 and e12 we re changed; the process was r e peated until t~e computed times-of- flight came closest to the expe r1mental da t a , in the least squares sense . The c11 and c12 that produced the best fit were taken to be the answe r. Using this method , the full set of stiffness constan~s for the unidirectional graphite/epoxy was dete rmined , the results for a 2.54 em ( l") thick unidirectional specimen were: e11 - 130.0 GPa, e22 - 14.95 GPa , C44 3 . 81 GPa, C55- 6.73 GPa, C12- 6.85 GPa.
The phase v eloci ty of the fundamental mode has been calcul ated f rom t he frequency equation for some composite shells f or a wide range of the wave l engths and cylinder radii . The results are shown in Figure 5. The fundamenta l phase veloc ity varies significantly ~~th respect to the ratio between the inner and outer rad11 a~d the material ani sotropy. The spread of the d1s persion curves for anisotropic composite shells is. seen i n Figure 5 to be much wider than the correspond1ng curves for an iso tropic material.
The stability of this iterative method for extracting c11 and e12 from the acous to - ultrasonic data was evaluated. It was found tha t small systematic errors in the time-of-flight data can lead to very large errors in the iteratively determined e11 and Cl2· systematic errors were present and were believed to be mostly due to the finite size of the transducers . A number of ways were tried to reduce the systematic errors; the most successful scheme involved extrapolating the acousto-ultrasonic QL-+ QL time-of-flight to zero separation distance be t ween the transducers. Using a rational function extrapolation routine the time-of-flight for zero s eparation was de termi~ed. This time-of -flight was t hen_compared to the actual measured pulse-echo time - of-fl1ght for normally incident longitudina l wav e . The diffe rence between the two was subtrac t ed f r om t he acousto ultras onic time-of-fligh t befor e t he i ter ati on p r ocess.
Us e of Acousto-l!ltra s onjcs . An alternative method of measuring the anisotropic elastic stiffness constants uses the times-of-fl i ght of acousto-ultrasonic echoes from only one s i de access. The method grew out of a previ ous s tudy of t h e quantitative interpretation of acousto-ultrasonic s i gnals in thick composites based on t he slowness surfaces (Hsu and Margetan, 1990). Experiments were conducted on unidirectional thick laminates wher e the anisotropy effect i s t he ~reatest. Although the verification was performed on th1ck flat P~ates , the method s hould also be applicable to large d1amete r cyl inder s on which regular transducers may be used to conduct acousto-ultrasonic measurements along t he axial directi on. Unidi rectiona l composites with the fibers o~iented along t he x -direct ion have five independent elast1c sti ffness con stan t s: c 11 , c 22 , C44, C55. and Cl2· Due to symme try, t h e f ollowing relationships exi st: C22 er3 • el? - C13, e 55 - C66. and e23 - C22 - 2e44. For a P ate Wlth unidirec t i onal fibers lying in the plane, thr ee of t h e e lastic constants, C22• C44 and C55. can be de~ermined by measuri ng the speed of sound i n the t hlckness direction (normal to the fibers) for one longitudinal wave and two transverse waves. Such measurements have bee n made in the usual pulse-echo mod~. For the 2. 54 em (1") thick graphite/epoxy lamlnate s t udied in this work the longitudinal wave speed normal to t he fiber dir~ction was measured to be 0.307 ~ 0.003 emf~. The transverse wave propagating normal t o t he f i be r s and polarize d along the fibers had
The experiment on t h e unidirec tional laminate showed that anisotropic e lasti~ cons t ant s of thick composites may be determined w1th one- s ide access and without cutting the specimen. EVALUATION OF POROSITY The presence and severity of porosi ty in a thick osite depend on the manufacturing process a nd may be ~om~ality reliability concern in some applications. In th~ 5 work methods developed previously for thin com osite~ were tested in samples of a 3.56 em (1.4" ) thi~k filament wound case (FWC) as an example of a t hick section composite structure.
Orientation of line sources for generation (and reception) of longitudinal, shear, and surface Rayleigh waves on orthogonal accessible faces of a sample. The particle motion directions and the constants to be measured are given in Table II .
Acousto-ultrasonic t i me-of-fligh t data on a 2.54 em (1" ) thick unidirectional graphite/epoxy l aminate. The solid line is a fit to the experimental data. the estimated void contents of the samples were 2.6 to 3.6% if t he voids were f l at long cylinders, or approximately 5.2 to 7.2% if the voids were all spherical. Examinations of the void morphology using an optical microscope and a method of pyrolytic deploy (Freeman, 1984) on an adjacent piece revealed a great variety of void sizes and shapes . Acid dige stion of an adjacent piece showed a void content of approximately 4 .4 percent. The complexity of void morphology was believed to be t he principal difficulty in estimating the porosity content using ultrasound . However, consistent with the expected trend based on void morphology, the acid d igestion val ues fell between the two extremes and were closer to those for flat , long voids . More wor k is clearly needed in order to improve the quantitative evaluation of porosity content in thick composites .
198 ) ~f previous studies (Nai r, et . al ., 1989; Hsu , 8 attenuatiporosity quantification by ultrasonic fr on measurements, it was found that the la:f~e~cy dependence of attenua tion in composite linea~ ~~ ~hntbainding por os ity was usually approximately the e an width of t he t ransmitted pulse. For secttases studied, the s l ope ( daj df) of the linear the vor of fthe attenuati on was found to correl ate with 0 ume raction of porosity: Void content (%) .. k( d aldf)
where dajdf · ( em HHz)- 1 . The numerical value of th i s expressed 1n void mor h constant k in thin lami nates depends on the 0 ogy; it i s approximately equal to 4 for spheric compos i ~e loits (e.g. t hos e often occurri ng in woven flat elonga~mdnates) and approximately equal to 2 f or uni directi el voids ( e. g . , those in lami nates made of ona prepreg tapes . )
FUW SIZING C-scan Corrected by Beam Model
compos~:ssamples used i n the study of porosity i n t h ick wound case (~~) pifces of a graphi te/epoxy fil ament 0 1986) Th a large rocket motor (Poe , et. al ., s l igh t c e sampl es were 3. 56 em (1.4") thick, with a (hoop) u~ature, and t he fiber directions were at 900 The ult~n • 33.50 from t he axial direction of the case. through ~sonic attenuation was measured using the immersionr~nsmission of a broadband pulse in an diameter an~s~ ~;tup. Pa irs of 1 MHz , 2 . 54 em ( 1") t r ansducer s · MHz , 1.27 em (0.5" ) d i ameter results sh w~rehused in dat a acquisiti on. Measurement with fre owe t at t he a t tenuation was quite linear most of ~h:n~y over the range of 0.3 to 1.5 MHz where however th nergy of t he transmitted pulse reside; f rom lo~atie slope of a t tenua tion varied considerably on to location . Using the simple r elation,
The sizing of flaws, such as de laminations, in an elastically anisotropic composite is more difficult than t hat in an isotropic solid. Due to the anisotropy, the flaw shape and size as seen in a regular ul t rasonic C-scan are distorted and dependent on flaw depth. In this work, the f l aw size is determined from the way the flaw echo amplitude change s as a transducer is scanned over it. (Both t he flaw and the transducer are assumed The amplitude ver sus lateral distance t o be circul ar.) curve is usually bell- shaped, as shown in Fig. 7, but the distance between the half- amplitude points may be quite different from the flaw diameter. Quantitativel y the shape and width of thi s curve depend on a number of pa rameters, including the transducer size, the flaw
0.0 -+----r----.-----r----r----.-----r---......------J -0.5 0.0 0.5 -1.0 1.0 X & Y Coordinate (Cm) Figure 7
Results obtained from scans along fibers and normal to fibers over a 0.635 em (0.25 inch) delamination embedded 2.72 em inside a unidirectional graphite/epoxy composite . Plotted are the 2 MHz component of an echo obtained with a 2.25 MHz, 1.27 em (0.5 inch) diameter transducer. the acquisition of ultrasonic data is being developed. Associated processing algorithms to condition and analyze ultrasonic data to obtain images of flaws in anisotropic composites have also been developed.
size, the frequency, the flaw depth, and the elastic nisotropy of the material. A method has been ~evelope d (Hsu and Minachi, 1990) in which the flaw size is varied iteratively until the computed echo amplitude versus lateral distance curve is closest to the measured rve in the least squares sense. The computation ~~kes'into account the experimental parameters and is based on a Gauss-Hermite model for the ultrasonic beam ropagation (Newberry and Thompson, 1989; Margetan et P1 1989 Margetan, et al., 1989). The computation !1~~ inco~porates the slowness surfaces of the composite
As a first step towards obtaining accurate ultrasonic imafes of defects in thick composites, we have obtained mages of known defects using both conventional B-scan presentation and synthetic aperture images. The potential of SAFT for imaging in thick composites is investigated via parameter studies of images of known defects in isotropic materials and anisotropic composites. To date our studies have concentrated on two samples one made of plexiglas and the other of graphite/ epoxy (Oo/90• layup), with . identical defects. The geometry of these samples 15 f h shown in Figure 8 . The dimensions and placement 0 t ~t defects in both samples are identical in order to pe~ qu~ntitative investigation of possibl e effects of Both an1sotropy on the SAFT reconstruction algorithm. samples were insonified using a 5 0 MHz center f 1 frequency, 2.54 em (1") diameter, ·6.35 em (2. 5") ocf length immersion transducer focused on the surface 0 the sample. Data were acquired inC- scan format on 0.0127 em (0.005") centers (-k/4 ins i de samples at At center frequency) at a digitization rate of 50 MHz. each point in the C-scan 200 rf time-domain traces were averaged together (into a lG bit word) and the resulting averafe traces stored on disk for later off-line analys s. for the Figures 9a, 9b, 9c and 9d all present data plexiglas sample. Figure 9a contains the raw data of presented in B-scan format. The downward concavit~ult the defects shown in the B-scan is the expected red by and arises from the increased path length traverse All the insonifying beam as it sweeps over the defects. defects are evident in the image at depths that lie the within 1% of the values shown in Fig . 8. However, ure widths of the defects are clearly exaggerated. Fig FiS· 9b is a surface plot of a subsection of the data 0 9a plotted with the relevant spatial axes. The reconstructed SAFT image is shown in Fig . 9c. A11 d7pths are correct to within 1%. In addition, thethose w1dths of the defects are noticeably smaller than i~ t~e B-scan image, as they should be, and agreeu~face w1th1n 5% of the actual values. Figure 9d is a s inS plot of a subsection of the same data. The flatten
material. Experiments were performed on a 0.635 em (0.25") diameter Teflon insert simulated delamination in a nidirectional graphite/epoxy composite laminate. Extra uieces of unidirectional graphite/epoxy were added on ~ to vary the effective depth of the flaw. This flaw w~~ sized using the method of C-scan corrected by the beam model. Since the flaw was circular, only a line-scan was made through the center of the flaw. Table I I I shows the sizing results (Minachi and Hsu, 91). The data shows that the effect of the anisotropy 19 increases with increasing flaw depth, as evidenced by the increasing discrepancy between the apparent sizes (distance between h alf-amplitude points) in scans along the fiber and normal to the fiber direction. When the flaw sizes were det:rmined by applying the iterative method on the exper1mental data, the results were much less dependent on the scan direction and the size e stimates were closer to the nominal flaw diameter . The experimental verification of t he iterative f law sizing method showed that the sizing accuracy for flaws in thick composites was much improved by taking into account the diffraction (beam spreading) effect and the elastic anisotropy of the material. SYnthetic Aperture Focussin& (SAfT) Ima&in& An alternative approach to the sizing of flaws makes use of imaging techniques. In this section we cons ider the synthetic aperture focussing (SAFT) technique (Seydel , 1982), which is of interest because of its potential for incorporation of algorithms to correct for various sources of image distortio 1 order to investigate the potential of SAFT to n sizing in thick composites, an experimental syst:: for
Apparent and computed flaw sizes using t he 2 HHz component of a 2.25 HHz, 1.27 em (0.5 inch) diameter transducer. The del amination is a circular 0.635 em (0.25 inch) diameter Teflon implant in a unidirectional graphite/epoxy composite. Scan Direction Along Fiber Sizing Method Direction
Normal to Fiber Direction
Apparent Size Computed Size
0.303" 0 . 289"
Apparent Size Computed Size
2. 72 em
Apparent Size Computed Size
1. Elongated Flat-Bottom 2. Slot across material 3. Side-drilled across material 4. Flat-bottom 5. Flat-bottom
0.5'' Figure 8
t---- -- -1
I I I I 1_1
Plexiglas™ and graphite/epoxy sample geometry.
Images of Plexiglas sample: (a.) Raw B-scan data
ions for the flat bottom holes is evident of the indicat consistent with the fact that the in this figur~ture is focussed at each point of the synthetic ape image . lOa lOb lOc and lOd all present data for Figui~! sample. 'Figure lOa contains the raw data the compos n B-scan format. The downward concavity of presented i shown in the B-scan is again apparent as are the deiec~: . from the image their depths are all found all de ec hin lX of the values shown in Fig. 8. to lie wi;s in Fig. 9, the width s of the defects are However,ted Figure 10 shows a subsection of the image exaggeralOa. plotted as a surface plot. Relevant spatial in Fig.e also shown. The reconstructed SAFT image is 8 axes In Fig. lOc. Once again, all depths are correct sho~thin lX. Furthermore, the widths of the defects tow oticeably smaller, as they should be. In fact, are ndiffer from the actual values by less than SX they FWHM criteria), which is surprising since the (usi~fal is anisotropic and our reconstruction algorithm mat: not yet account for this effect. We speculate that doe (0 90] layup may approximate an isotropic medium thi 1 e~ough to permit this level of agreement at the i!mited aperture used in the reconstruction. Some differences from the isotropic case, however, are evident as shown more clearly in Fig. lOd, which is a surface plot of a subsection of the data in Fig. lOc . The flattening of the indications for the flat bottom holes is less evident in this figure than it was in the plexiglas sample. This may be due to the effects of
anisotropy, which tend to defocus t h be ~ynthetic investigated aperture. This effect is presently e ~ les The fact further using uniaxial graphite/epoxyh s lzing accuracy that the anisotropy did not degrade e ;esently being is a somewhat surprising resul t and s P s These 1 examined more closely using uniaxia~ ~am~r~h~gonal samples have identical flaws aligne n n The directions r e lative to the fiber directi~~ samples reconstructed images of data from. these n of the effects should permit quantitative determ1natio lgorithm· of anisotropy on the SAFT reconstruction 8
CONCLUSIONS the Considerable progress has been rna de f in material f nondestructive evaluation for a varie~l 0 measurement 0 properties in thick composites, inclu ng d discrete anisotropic elastic constants, poros~ty 8 ~s should plaY flaw sizes. It is believed that sue toolo ment an important role in future material d~ve c~erize the·es programs; as they provide a means to cha~lcal propertl material and better understand the mec 8 and structural response to large loads. ACKNOWLEDGMENT
throu~h) This work w. supported by the U· S Navy _86-K-079 the Univers ity of linois (Contract #NO014 I wa St ate and was performed \ the Center for NDE at ~endations t University. The fit. . gs, opinions fan~ r=~~hors and no expressed in this paper are those o t e
Images of Plexiglas sample: (b.) Surface plot of B-scan
Images of Plexiglasfs;:tr image (d. ) Surface plot 0
Images of compos i te sample : ( a .) Raw B-scan data 54
Images of composite sample: (b.) Surface plot of B-scan
!mages of composite sample: (c.) Reconstructed SAFT image
Scan Post.tt·on (t·n.) 55
Images of compos.te sample: (d ) Surface plot of SAFT image
of the University of Illinois or the necessarily ~~~s~f the authors (D. K. Hsu) expresses his U.S. Navy. LTV Aerospace Dallas, Texas and Hercules gratitude t~ na Utah for'providing composite specimens AerospaceH, ag s'for performing the acid digestion and for ercule tests. REFERENCES
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ANALYSIS TECHNIQUES FOR COMPOSITE MATERIALS
presented at THE WINTER ANNUAL MEETING OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS ATLANTA, GEORGIA DECEMBER 1-6, 1991 sponsored by THE NDE ENGINEER ING DIVISION, THE APPLIED MECHAN ICS DIVISION, AND THE AEROSPACE DIVISION, ASME edited by LEN SCHWER APTEK, INC. J. N. REDDY VIRGINIA POLYTECHNIC INSTITUTE AND STAT E UNIVERSITY AJIT MAL UNIVERSITY OF CALIFORNIA
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