Quantitative characterization of microcracking in A533B steel by acoustic emission
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I.
INTRODUCTION
IN
a previous paper, I~j the authors reported acoustic emissions (AE) from microcrack formation at MnS inclusions during fracture toughness tests of A533B steel compact tension specimen. Three-dimensional locations of these microcracks were determined from an eightchannel recording system. We showed that most of the microcracks occurred outside the plastic zone when the normal tensile stress at each inclusion reached 400 to 800 MPa. In this paper, we report source characterization in terms of crack size, crack orientation, fracture mode, and time history of the microcrack formation, based on the experimental data reported in Reference 1. The microcracks are modeled by point moment tensors, each with six independent components which are related to the elastic moduli of the material, the orientation of the normal to the crack surface, and the discontinuous displacement vector across the crack. The theory of elastic wave radiation t2j is then applied to analyze the acoustic emission by a microcrack. To determine all components of the moment tensor and the time history, solving an integral equation of convolution is required, a process known as "deconvolution." Techniques of deconvolution have been developed only recently. [31 A simplified approximate method is developed here for the case when the complete Green's function is not available. In Reference 1, two types of sources, I and II, were identified from the waveforms recorded by the multichannel AE system. In this report, we show that the source of type I is indeed a tensile crack, the displacement vector being perpendicular to the crack surface, which is nearly parallel to the precrack. The time history of type I
is a ramp-step function with about 0.3 /xs rise time. Type II cracks are inclined with respect to the main precrack and contain both tensile and shear modes with a much longer rise time (about 1 /xs). This confirms the previous conjecture tl[ that type II sources are due to coalescence of microcracks.
II. THEORY OF AE SOURCE CHARACTERIZATION Toward the quantitative characterization of AE sources, the following key procedures have been developed in the past: (1) mathematical modeling of AE sources; [2] (2) evaluation of Green's functions in a bounded medium; [41 (3) calibration of transducers; tS'61 and (4) deconvolution techniques.[3.6 8] By applying all the existing procedures and newly developed ones, we are able to characterize the microcracks in a steel specimen. Since the basics of acoustic emission have been reviewed in a recent report, I91 we summarize in this section the theories needed for this investigation. The acoustic emission by a microcrack inside materials is modeled by a displacement discontinuity, [u] : u+ - u_, across a surface AA in an elastic body of volume V (Figure 1). If the largest dimension of AA is small compared to the distance between the source (at x') and receiver (at x) and to the shortest wavelength of interest, the crack then is approximated as a point source, which is characterized by a dipolar forc
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