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81.
FEA calculations have been carried out for a model rubber shear spring, consisting of a block of a highly elastic material, bonded between two rigid parallel plates and sheared by displacing one of the plates parallel to the other in its own plane. The block was prevented from deforming in the perpendicular direction, and thus was deformed in plane strain. Stress distributions along the bond-line and the center-line are reported and compared with those expected from the theory of large elastic deformations. Unexpected tensile stresses were found to develop in the interior of the sheared block. They are attributed to the absence on the end surfaces of the stresses needed to maintain a simple shear, causing a pronounced change in the reference pressure—a consequence that is usually overlooked. Because the internal stresses are governed by the boundary conditions, they were strongly affected by the shape of the end surfaces. In addition, they were reduced markedly by assigning values to Poisson's ratio slightly lower than 0.5, thus allowing some volume expansion of the rubber. Strain energy release rates were also evaluated for growth of a crack along the bond-line, starting at the edges, and compared with those reported previously by Lindley and Teo [Energy for crack growth at the bonds of rubber springs, Plast. Rubber Mat. Appl. 4 (1979) 29-37], Muhr et al. [A fracture mechanics study of natural rubber-to-metal bond failure, J. Adhes. Sci. Technol. 10 (1996) 593-616], Gregory and Muhr [Stiffness and fracture analysis of bonded rubber blocks in simple shear, in: D. Boast, V.A. Coveny (Eds.), Finite Element Analysis of Elastomers, Professional Engineering Publications, Bury St. Edmunds, UK, 1999, pp. 265-274] and Gough and Muhr [Initiation of failure of rubber close to bondlines, in: Proceedings of the International Rubber Conference, Maastricht, Netherlands, June 2005, IOM Communications Ltd., London, 2005, pp. 165-174]. They confirm that a long crack at the compression edge will grow faster than one at the tension edge, but the results for short cracks were inconclusive. 相似文献
82.
A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σns0. When σns0<60 MPa, the crack speed
mm/s and the crack is basically stationary; when 60 <σns0<95 MPa, then
mm/s the crack is in slow propagation; when σns0>95 MPa, then
mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation. 相似文献
83.
This work explores the edge agreement problem of second-order multi-agent systems with dynamic quantization under directed communication. To begin with, by virtue of the directed edge Laplacian, we propose a model reduction representation of the closed-loop multi-agent system depending on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent systems under directed graph are considered. The static quantizers generally contain a fixed quantization interval and infinite quantization level, which are, to some extent, inefficient and impractical. To further reduce the bit depth (number of bits available) and to obtain better precision, the dynamic quantized communication strategy referring to zooming in-zooming out scheme is required. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent systems under dynamic quantized effects with only finite quantization level can be guaranteed. Finally, the simulation of altitude alignment of micro air vehicles is provided to verify the theoretical results. 相似文献
84.
We analyze the detection and classification of singularities of functions , where and . It will be shown how the set ?S can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ?S is a dimensional piecewise smooth manifold with or 3, we will classify smooth and non-smooth components of ?S. This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in 3 dimensions by compactly supported shearlets. Finally, geometric properties of ?S such as curvature are described in terms of the continuous shearlet transform of f. 相似文献
85.
Vizing conjectured that every edge chromatic critical graph contains a 2-factor. Believing that stronger properties hold for this class of graphs, Luo and Zhao (2013) showed that every edge chromatic critical graph of order with maximum degree at least is Hamiltonian. Furthermore, Luo et al. (2016) proved that every edge chromatic critical graph of order with maximum degree at least is Hamiltonian. In this paper, we prove that every edge chromatic critical graph of order with maximum degree at least is Hamiltonian. Our approach is inspired by the recent development of Kierstead path and Tashkinov tree techniques for multigraphs. 相似文献
86.
High-speed holographic microscopy is applied to take three successive photographs of fast propagating cracks in Homalite 100 or in Araldite B at the moment of bifurcation. Crack speed at bifurcation is about 540 m/s on Homalite 100, and about 450 m/s on Araldite B. From the photographs, crack speeds immediately before and after bifurcation are obtained, and it is found that discontinuous change of crack speed does not exist at the moment of bifurcation in the case of Homalite 100, but exists in the case of Araldite B. From the photographs, crack opening displacement (COD) is also measured along the cracks as a function of distance r from the crack tips. The measurement results show that the CODs are proportional to √r before bifurcation. After bifurcation, the CODs of mother cracks are proportional to √r, though the CODs of branch cracks are not always proportional to √r. The energy release rate is obtained from the measured CODs, and it is found that energy release rate is continuous at bifurcation point in both cases of Homalite 100 and Araldite B. Energy flux that shows the energy flow toward a crack tip is also obtained. 相似文献
87.
Experiments on crack identification in cantilever beams 总被引:1,自引:0,他引:1
In this paper we present an experimental investigation of the identification of crack location and size. By providing the
first three natural frequencies through vibration measurements, curves of crack equivalent stiffness versus crack location
are plotted, and the intersection of the three curves predicts the crack location and size. In the experiments, the cracked
specimens were made using a wire-cut electrical discharge machine, and the cantilever beams were excited next to the free
end by means of an impulse force hammer. In order to obtain the accurate natural frequencies from the transient signal measured,
the method of zoom fast Fourier transform is adopted to improve frequency resolution. From experimental results, it is observed
that the identification errors of crack location and size are less than 2% and 4%, respectively. The effectiveness of crack
identification through vibration measurements is verified. 相似文献
88.
Sony Baby T. Balasubramanian R. J. Pardikar 《Theoretical and Applied Fracture Mechanics》2003,40(2):145-151
Embedded vertical cracks are very often encountered in structural components necessitating reliable procedure for determining their size. Specialized ultrasonic techniques are required for estimation of through thickness height of these cracks [Mater. Eval. (1970) 28; J. NDI 26 (1977) 320; NND (1975) 146]. The conventional pulse-echo technique has serious limitations for quantitative estimation of vertical cracks because it is subject to variations due to reflectivity, coupling factors etc. The present study aims to improve the accuracy of embedded crack height measurement based on transit time rather than the reflected amplitude [NDT Int. (1982) 315; J. JSNDT 27 (1978) 118]. A unique method has been developed for generating known sizes of fatigue cracks ranging from 2.5 to 18 mm in height and 15 mm in length. These cracks were generated in rectangular steel specimens and subsequently embedded at predetermined locations using welding. These welded specimens containing the embedded vertical cracks were examined using ultrasonic techniques based on transit time like (a) flaw tip echo method and (b) mode conversion method. Using both the techniques excellent agreement was obtained between the estimated crack height and actual crack height with an accuracy of ±1 mm. 相似文献
89.
Jean Marie Nianga 《Mechanics Research Communications》2006,33(5):747-752
This paper provides an analysis of the crack propagation criterion for a thin piezoelectric plate with a symmetry of order six. On the basis of Gol’denveizer’s asymptotic integration method or Destuynder’s unidirectional zoom technique, we obtain an extension of the purely mechanical J-integral to piezoelectric materials, with a dependence of the gradient of energy of the plate only on zeroth order terms of asymptotic expansions. 相似文献
90.