Crack Propagation in Rock Plates Loaded by Projectile Impact
Paper by L.A. Glenn and H. Jaun was published in EXPERIMENTAL MECHANICS,
January 1978, Pages 35-40
Discussion by H.P. Rossmanith The discusser read the paper with great interest. The authors describe "apparent supervelocity cracks" which they have observed in dynamically impacted rock specimens using the methods of dynamic photoelasticity. In following the authors' work, the discusser believes that an inaccurate terminology has been used throughout the paper; no difference is made between the classical crack propagation and the progressive joining of intrinsic flaws due to dynamic excitation (flaw coalescence). Whereas in the classical theory, the crack-propagation velocity is limited by the velocity with which new crack surfaces are generated (terminal velocity) there is no upper limit for the coalescence velocity. Recent experiments were conducted by the discusser at t h e University of Maryland where the dynamic behavior of square glass plates under explosive excitation was studied a n d the resulting crack pattern was recorded using high-speed photography.' It was found in the discusser's experiments that fracture i n glass essentially occurs by anticipated retrogression of activated surface flaws ahead of the crack tip. Surface flaws seem to 'explode' under the excitation of the stress field generated by the tensile pulse of the incident,P-wave and form symmetrical multibifurcated crack patterns termed cascadations. Post-mortem observations of fracture surfaces revealed that coalescences exhibit an entirely different surface structure than the classical fracture surfaces. Coalescence-fracture surfaces show a chain of activated and extended surface flaws, whereas the classical-fracture surface exhibits a certain regular change of surface structure which is observed in a periodic sense when multiple branching occurs. The results of experiments conducted at the University of Maryland suggest that the 'sudden' appearance of the central crack in the authors' Fig. 6 is due to the joint action of two different phenomena. During high-velocity impact, the subsurface shear-stress maximum exceeds the fracture strength of the material and initiates the median crack. Tensile PP-waves reflected from the finite boundaries of the specimen interact with the lower crack tip and assist further crack propagation)-' This is confirmed numerically by data given by the authors. The discusser believes that statistical concepts may be introduced on the basis of a statistical distribution of preexisting surface flaws. This approach should lead to dynamic statistic coalescence with a mean coalescence velocity, which would be more meaningful than applying the measured results directly to a characteristic crackvelocity concept. The authors may like to comment on the following points : (1) Nonsymmetrical experimental setup as well as nonsymmetrical impact causing bending influence the crack pattern generated. Glass plates (450 • 230 x 6.3 mm in dimensions) modeling a halfplane excited explosively at the center of one edge exhibited a concentric crack of radius 90 mm with center at the point of explosion. This 1t.t). Rossmanith is Visiting Professor at the Glehn L. Martin Institute of Technology Department of Mechanical Ensineering, University of Maryland, College Park, AID 20742.
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crack was partially a not-through crack being more developed on the tension side. Such a circumferential crack appears in Fig. 5 of the authors' paper. (2) Some discrepancies in the wave propagation as well as crack patterns related to the back side and front side of the specimen-coating composite arrangement are reported. However, the paper does not discuss the different behavior of photoelastic coating and the rock material due to impact. Moreover, is the possibility of impacting the coating as well as the rock sample exCluded? (3) It seems that, in some circumstances, strain in the rock sample was below a.certain sensitivity threshold for the coating to respond to fracture, although successful fracture of rock has been achieved.
References 1. Rossmanith, H.P., "'Dynamic Fracture in Glass, "" N S F Report, Univ. o f Maryland, College Park, M D (Apr. 1978). 2. Kolsky, H., Stress Waves in Solids, Dover Pub. Inc., Table 1 and p. 192 (1963). 3. Knight, C.G., Swain, M. V. and Chaudhri, M.M., "Impact o f Small Steel Spheres on Glass Surfaces, "' J. Mat. Sci., 12, 1573-1586 (1977). 4. Lawn, B.R. and Evans, A.G., "',4 Model f o r Crack Initiation in Elastic~Plastic Indentation Fields, "" J. Mat. Sci., 12, 2195-2199 (1977).
Authors' Closure In following the nomenclature suggested by Schardin, we leave to the reader the judgment as to whose terminology more accurately represents the phenomena in question. The whole point of our report was to contrast cracks formed by the interaction of strong tensile and shear waves with those formed by the application of quasistatic loads. It is the former that dominate in most rock mechanics and geophysics applications. With regard to the items enumerated : (1) We certainly agree that unsymmetrical impact can effect bending moments in plates impacted on edge. Although great care was taken to align the gun barrel and target in our experiments, it was not possible to completely eliminate this kind of loading and we were much concerned about these effects until we were able to view both sides of the plates simultaneously. The figure presently labeled Fig. 7 in our paper clearly demonstrates that the main cracks are caused by in-plane loading. This question may have been motivated by an unfortunate error in the original labeling of the captions for Figs. 7 and 8 which have been interchanged. We trust that the error is obvious to most readers. (2) When the rock plates were impacted on edge, both the base and the coating were simultaneously struck. Since the mechanical impedance of the rock is many times that of the coating, the displacement of the latter is clearly limited by that of the former, unless massive failure occurs. Such 'shattering' of the base material was evidenced only in the experiments with glass. (3) If the coating is not properly bonded to the base material (or becomes unbonded in the loading sequence), the coating response will be unsatisfactory. This will also be the case if too thick a coating, or the wrong coating, or the wrong adhesive, is employed.
