Surface Acoustic Wave Measurements of Surface Cracks in Ceramics

We have extended our earlier investigation of scattering from surface cracks. In particular, we have studied the change in the reflection coefficient of a Rayleigh wave incident on a half-penny shaped surface crack along with the corresponding change in the acoustic crack size estimates as the cracked sample is stressed to fracture. We have examined in this manner both cracks in annealed samples and as-indented cracks. We have found that the fracture behavior for cracks in these two types of samples differ quite significantly, with the cracks in the annealed samples exhibiting a partial crack closure characteristic and the cracks in the as-indented samples displaying both crack closure and crack growth effects. I NT RODUCT ION This work is an extension of our earlier studyl aimed at the establishment of procedures for locating and characterizing surface cracks in structural ceramics. The basic technique we have been using consists of launching a Rayleigh wave on the surface of the ceramic and observing the reflections of the acoustic surface wave from the crack. The particular type of crack we have been studying is a half-penny shaped surface crack introduced at a given orientation into the ceramic surface by a Knoop hardness indentor. In a pre,vious paper,1 we described a scattering theory valid in the low frequency regime based on the model of an open halfpenny shaped crack. This theory related the reflection coefficient measured in the experiment with the crack size and fracture stress of the cracked sample. The theory was shown there to give predictions for the fracture stress which were in good agreement with experimental results. However, predictions for the crack size were observed to be considerably less accurate, with crack size estimates for unstressed samples being smaller by factors of two to three than the actual crack sizes measured after fracture. Since that time we have extended the theory and correlated our results with what would be expected from fracture mechanics studies of ceramics. A series of experiments on annealed and unannealed samples has demonstrated the power of acoustic techniques for studying cracks in ceramics. The work indicates that cracks in annealed samples tend to be in contact over most of their crosssection and open up with applied stress. At the point of fracture, a very slight growth in crack radius is observed. On the other hand, cracks in unannealed as-indented samples exhibit partial closure at the sample surface. Upon application of stress, crack growth occurs, with crack radii tending to increase on the order of 50% . Upon release of stress, the cracks partially close, with their effective radii decreasing by less than 10% As stress is further applied, further crack growth 144 is observed, terminating in fracture at lower applied stresses than for equivalent annealed samples. This hysteresis effect has been observed for the first time acoustically. Both the initial crack radius, c0 , and final radius, Cm , can be measured after fracture. The results obtained can be predicted accurately via acoustic techniques and agree well with the predicti~n~ ~f earlier theories and experiments by Marshall. • • An important result of our work is the demonstration that it is highly desirable to anneal ceramics in which surface cracks are likely to be present. Annealing inhibits further crack growth by relieving the residual stresses that are present. As evidence, we note that when unannealed samples are stressed, the crack radius increases by a factor of approximately two. Annealing, however, causes an increase in the fracture stress observed by a factor of approximately 1.5 . THEORETICAL REVIEW A general theory of scattering from flaws developed by Kino and Auld5,6 forms the basis for our work. The scattering configuration considered is shown in Fig. 1. The reflection coefficient, Szl , is defined as the amplitude ratio of the reflected signal from the flaw, Az , received by transducer 2 , to the incident signal, A~ , transmitted by transducer 1 , at the term1nals of the transducers. In terms of the input power to the transmitting transducer, P , the Rayleigh wave displacement field when the rec~iying transducer is used as the transmitter, u\ZJ , and the applied stress in the vicinjty of theJflaw before the flaw is introduced, cr~j1J ' s21 is given by A2 = jw J u~2)cr~Pln.dS (1) S21 A 4P J 1 J 1 1 sc -----------------------------------·-·····--for the case where the flaw is a void. Here, the integral is taken over the entire surface of the void, Sc .