Development of an acoustic microscope to measure residual stress via ultrasonic Rayleigh wave velocity measurements

Abstract

c write(6,25)xO,zO,xll,zll c c 25 format(lx,5fl0.4) c c 30 continue c x0=x*0.03175 thetalO=asin(xO / ak) phiO=asm{c2*sin(thetalO) / c 1) thetaO=thetalO-phiO c zO=-s(j)+ak*(l .-cos(thetalO)) c f=ak*sin{thetalO)/sin(thetaO) b=f-s(j) am=(b-20)/(O.O-xO) c al=l.+am*am a2=2.*am*(b-s(j)+ak) a3=b*b+2.*b*ak-2.*b*s(j)-2.*ak*s(j)+s(j)*s(j) c xll=(-a2-sqrt(a2*a2-4.*al*a3))/2./al Xl2=(-a2+sqrt(a2*a2-4.*al *33)) /2. / al zll=am*xll+b zl2=am*xl2+b thetall=atan(xl 1 / (zl l-(s(j)-ak))) c tr=2.*sqrt((xll-x0)*(xll-x0)+(zll-z0)*(zll-z0))/c2 * +2.*(s(j)-abs(zO))/cl+2.*thetall*ak/vr c tsp=4.*s(j)/c2 deltat=tr-tsp write(6/)deltat 200 continue stop end Third reflection case c This program finds the relationship between the time difference c and ^e lift-off for the 3rd reflection data c IMPLICIT REAL-^S (A-H,0-Z) real*8 low, high dimension s(50) c c Pertinant constants (distances espressed in mm) c c's are velocities and ak is the radius of curvature of the lens c write(6/)"enter Rayleigh velocity" read(5,*)vr cl =5.969 bb=thetalow-slope*ilow x=(theo-bb)/ slope c 30 continue c c x0=x'^0.03175 x0=x*0.03073 thetalO=asin(xO/ak) phi0=asin(c2*sm(thetal0) / cl) thetaO=thetalO-phiO c zO=-s(j)+ak*(l.-cos(thetalO)) f=ak*sin(thetaIO)/sin(thetaO) b=f-s(j) am=(b-20) / (O.O-xO) c al=l.+am*ain a2=2.*am*(b-s(j)+ak) a3=b*b+2.*b*ak-2.*b*s(j)-2.*ak*s(j)+s(j)*s(j) c xl 1=(-a2-sqrt(a2*a2-4.*al*a3)) /2. / al Xl2=(-a2+sqrt(a2*a2-4.*al*a3)) /2. / al 2ll=am*xll+b zl2=ain*xl2+b c thetall=atan(xll/(zll-(s(j)-ak))) thetr=2.*thetall+theta0 amnew=tan(thetr) bnew=xl l-amnew*zl 1 c tlens=2.*(s(j)-z0) / cl tr=2.*sqrt((xll-xO)*(xll-xO)+(zll-zO)*(zll-zO))/c2 * +2.*sqrt((bnew-xll)*(bnew-xll)+zll*zll)/c2+bnew*2./vr * +2.*(s(j)-abs(z0))/cl sl=sqrt((xll-xO)*(xll-xO)+(zll-zO)*(zll-zO)) s2=sqrt((bnew-xl 1) *(bnew-xl 1)+zl 1 *zl 1) tsp=6.*s(j)/c2 deltat=tr-tsp write(6,*)deltat 200 continue stop end

Issues in the High Resolution Acoustoelastic Measurement of Stress

“…Considerable effort has been expended in trying to pin down the difficulty, with the results discussed in detail in Ref [4]. Two classes of errors can be considered: systematic effects and random effects.…”

“…Figure 3b shows a typical result [2], which also indicates that this slope could be determined quite accurately, to about 0.2% in the case shown. The Rayleigh wave velocity can be computed fromm using a simple formula [2][3][4][5].…”

“…When the Rayleigh velocity was plotted as function stress, the data could be fitted to a straight line, as expected. However, the slope observed varied significantly from run to run, even changing sign [4]. As an example, Fig 4 shows the last two sets of data, which were taken on two different days and not exactly the same position on the sample Each point is derived from plots such as those shown in Fig.…”

“…This, in turn, places tighter tolerances on the absolute time and distance measurements required to achieve a given precision in velocity measurement. The authors have been engaged in a program addressed at the latter problern [2][3][4]. In particular, we have chosen to make a very localized measurement of the Rayleigh wave velocity using an acoustic microscope.…”

“…Part (a) shows the electronic timing circuit that was used to synchronize the transducer to the clock of the digitizer. This was done to eliminate problems associated with "trigger jitter" [5] and led to a significant improvement in the time resolution for a fixed number of averages of the received signal [3,4]. Part (b) shows the apparatus which was used to study the stress dependence of the Rayleigh wave velocity, as measured with the acoustic microscope.…”