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1.
Biaxial tensile experiments with thin rubber sheets, containing an internal crack, reveal the possibility to simulate and readily check the exact linear-elastic crack-flank displacements. The resulting deformed shape and the final position during loading of an internal inclined crack in an infinite, biaxially loaded elastic plate, was defined by measuring the crack-flank displacements, and the deformation features of the internal crack in rubber sheets. The results were compared with the linear-elastic displacements and the respective features, which have been obtained from an infinitesimal elasticity theory.The calculation of these displacement and deformation properties for a given crack presupposes the determination of two parameters, which characterize the loading conditions of the boundaries of the elastic cracked plate. These parameters have been determined as Lagrangian or Eulerian ones from the homogeneous strains at the boundaries of the elastic sheet, assuming either a Hookean, or a neo-Hookean or a Mooney material behavior for the elastic sheet.It has been shown that, except for the vicinities of the crack tips and for the regions of the imposed boundary strains in the experiments, the observed crack-flank displacements agree satisfactorily with the respective displacements obtained from the infinitesimal theory, if the material behavior is assumed as a neo-Hookean one, and the boundary-loading parameters are calculated as Eulerian ones. 相似文献
2.
Dr. J. V. S. Krishna Rao Prof. N. Hasebe 《Archive of Applied Mechanics (Ingenieur Archiv)》1995,66(1-2):1-8
Summary A solution is derived from equations of equilibrium in an infinite isotropic elastic solid containing a penny-shaped crack where displacements are given. Abel transforms of the second kind stress and displacement components at an arbitrary point of the solid are known in the literature in terms of jumps of stress and displacement components at a crack plane. Limiting values of these expressions at the crack plane together with the boundary conditions lead to Abel-type integral equations, which admit a closed form solution. Explicit expressions for stress and displacement components on the crack plane are obtained in terms of prescribed face displacements of crack surfaces. Some special cases of the crack surface shape functions have been given in the paper. 相似文献
3.
The stereoimaging technique is an accurate, high-resolution means of measuring the in-plane displacements resulting from the deformation of a specimen so that the corresponding components of the strain tensor can be computed independently of the stresses. The example used in this paper is a fatigue-cracked specimen of a microscopically homogeneous experimental powder-metallurgy aluminum alloy, analyzed to determine the displacement and strain fields accompanying the opening of the fatigue crack. The displacement measurements are processed by a computer program which compensates for measurement fluctuations in the displacement data by smoothing, and derives the strain magnitudes. The principal strains and the maximum shear strain are determined using Mohr's circle, and the latter strain is then used to estimate the plastic-zone size. The crack-opening mode may be inferred from the displacement map, and the state of stress (plane stress or plane strain) inferred by applying the in-plane compatibility equation. 相似文献
4.
《International Journal of Solids and Structures》2005,42(24-25):6433-6456
A recently developed plate theory using the concept of shape function of the transverse coordinate parameter is extended to determine the stress distribution in an orthotropic functionally graded plate subjected to cylindrical bending. The transfer matrix method is presented to derive the shape function. The equations governing the plate deformation are then solved analytically using the transfer matrix method for arbitrary boundary conditions. For a simply supported functionally graded plate, a comparison of the present solution with the exact elasticity solution, the first- and third-order shear deformation plate theories is presented and discussed. It is demonstrated that the present method yields more accurate stresses than the first- and third-order shear deformation theories. The effect of boundary conditions and inhomogeneity of material on the displacements and stresses in functionally graded plates are investigated. A multi-span functionally graded plate with arbitrary boundary conditions is further considered to demonstrate the efficiency of the present method. 相似文献
5.
Sh. Hosseini Hashemi S. R. Atashipour M. Fadaee 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(5):677-698
In this article, the governing equations of motion of thick laminated transversely isotropic plates are derived based on Reddy’s
third-order shear deformation theory. These equations are exactly converted to four uncoupled equations to study the in-plane
and out-of-plane free vibrations of thick laminated plates without any usage of approximate methods. Based on the present
analytical approach, exact Levy-type solutions are obtained for thick laminated transversely isotropic plates and, for some
boundary conditions, the exact characteristic equations hitherto not reported in the literature are given. Also, the in-plane
and out-of-plane deformed mode shapes are plotted for different boundary conditions. The present solutions can accurately
predict both the in-plane and out-of-plane natural frequencies and mode shapes of thick laminated transversely isotropic plates. 相似文献
6.
John C. Amazigo 《International Journal of Solids and Structures》1974,10(9):1003-1015
The problem of a semi-infinite body with an edge crack subjected to far out-of-plane shear is solved by a transformation to a hodograph plane and the Wiener-Hopf technique. The material stress-strain behavior is governed by a pure power hardening relation and the results are valid for both deformation theory and flow theory of plasticity. Results are presented for crack opening displacement, path independent J integral and crack tip singularities for all finite values of the power hardening parameter. 相似文献
7.
David J. Unger 《Journal of Elasticity》2012,108(1):67-82
Two-dimensional problems of finite-length blunted cracks cut into infinite plates subject to remote tractions are solved using
complex variable theory. The slot geometry is composed of two flat surfaces connected by rounded ends. This special geometrical
shape was derived by Riabouchinsky in the study of two-dimensional ideal fluid flow around parallel plates. The simpler antiplane
slotted plate problem is addressed initially for this geometry. From this exact solution, the equivalent of a Westergaard
stress potential is found and applied to the two other principal modes of fracture, which are plane elasticity problems. For
a plate subject to uniform radial tension at infinity, an analytical solution is obtained that will reduce to the familiar
mode I singular crack solution as the separation between the parallel faces of the slot becomes zero. For finite-width mode
I slots, the rounded ends have tensile tractions which terminate at the adjoining flat surfaces of the slot, which remain
traction-free. In this respect, the finite-width mode I slot problem resembles a Barenblatt cohesive zone model of a plane
crack or a Dugdale plastic strip model of a plane crack, although the tractions will vary in magnitude along the slot ends
rather than remaining uniform as in the former type of crack problems. Similarly, in the case of the finite-width mode II
slot problem, the rounded ends of the slot have shear tractions, while the flat surfaces remain load-free. A distinguishing
feature of the mode II slot solution over the mode I slot problem is that the maximum in-plane shear stress is constant along
the rounded ends of the slot. Because of this, those particular regions of the boundary can represent incipient plastic yield
based on either the Mises or Tresca yield condition under plane strain loading conditions. In this way, the problem resembles
the plastic strip models of Dugdale, Cherepanov, Bilby-Cottrell-Swinden, and others. Notably, the mode III slot problem also
has a constant maximum shear stress along the curved portions of the slot, while the entire slot boundary remains traction-free,
unlike the mode II slot problem. Consequently, the mode III slot problem represents both a generalization of the standard
mode III crack problem geometry, while simultaneously satisfying the boundary conditions of a plastic strip model. 相似文献
8.
Study of a Crack at a Fastener Hole by Digital Image Correlation 总被引:1,自引:0,他引:1
P. López-Crespo R. L. Burguete E. A. Patterson A. Shterenlikht P. J. Withers J. R. Yates 《Experimental Mechanics》2009,49(4):551-559
In this work the efficacy of using digital image correlation to determine stress intensity factors for a crack emanating from
a fastener hole has been investigated. To this end a fatigue crack was grown in pure mode I from a 50 mm diameter hole in
an Al 7010 alloy plate test-piece. This crack was then loaded elastically under several combinations of mixed mode (I + II)
displacements. In each case, images of the sample surface before and after the deformation were recorded using a high resolution
digital camera. The surface preparation consisted only of scratching the surface lightly with silicon carbide abrasive paper.
The crack location and resulting displacements were then calculated using digital image correlation. The analytical displacement
fields for a traction free crack under arbitrary loading conditions based on the Muskhelishvili’s complex function approach
were fitted to the experimentally measured displacement fields and the mixed mode stress intensity factor was determined in
each case. Good agreement with the nominal applied values was obtained. The uncertainty of the crack tip position has a major
influence on the accuracy of the stress intensity factors and so the Sobel edge finding filter was successfully applied to
experimental displacement fields to establish precisely the crack tip location.
This paper was presented at the 2007 SEM Congress held in Springfield, Massachusetts, USA 相似文献
9.
David J. Unger 《Journal of Elasticity》2010,99(2):117-130
Within the context of plane stress assumptions and approximations, an analytical solution is derived for the finite deformation
of a traction-free elliptical hole in an infinite plate with tensile tractions at infinity. The plate is composed of a non-work-hardening
material satisfying the Tresca yield condition under a deformation theory of plasticity. The governing partial differential
equations are parabolic in nature and consequently have a single family of mathematical characteristics or slip lines associated
with them. Each particle of mass follows a rectilinear path in the plane defined by its slip line which emanates orthogonally
from the elliptical hole. By assuming a constant speed for each particle in the plane, a state of plane equilibrium is realized.
The originally elliptical hole expands in the shape of an oval which is a parallel curve to the original ellipse. The slip
lines remain orthogonal to the evolving oval hole as a necessary condition for a traction-free interior boundary. This solution
also satisfies the material stability criterion that the rate of plastic work be positive throughout the entire body for all
time. As this solution has some features associated with large deformation crack problems at elevated temperatures, possible
applications include secondary or steady-state creep. 相似文献
10.
Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic
speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever
square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI
method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally
at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped
edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with
the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack
locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless
frequency parameter (λ
2) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be
induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant
frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the
cracked plate will be safe. 相似文献
11.
Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones, notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode II component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass. 相似文献
12.
Pei-Wei Zhang Zhen-Gong Zhou Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(10):965-979
In this paper, the behavior of three parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic material plane
subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier
transform into three pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack
surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded
as a series of Jacobi polynomials. Finally, the relations among the electric displacement, the magnetic flux and the stress
fields near the crack tips can be obtained. The results show that the stress, the electric displacement and the magnetic flux
intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding
effect is present in piezoelectric/piezomagnetic materials. 相似文献
13.
Geometrical considerations are used to obtain quantitative data for the components of the displacement vector. Use is made of a dual-beam illumination and a variant is described, using point light sources and a single point of observation. Contour lines for the displacement vector in the viewing direction and in a perpendicular direction are obtained as the algebraic sum and difference of two interference patterns. Densification of the initial pattern is used to obtain moiré patterns for the out-of-plane and in-plane displacements of flat Surfaces and for the derivatives of these displacements. To determine the complete displacement field of objects of arbitrary shape, one holographic plate is sufficient, using two times two-point light sources. 相似文献
14.
The problem of the interaction of a crack and a dislocation in a medium with a nonlinear stress-strain law is considered for the case of a semi-infinite crack in a displacement loaded strip under longitudinal shear deformation. A power law stress-strain relation is considered and the dislocation is assumed positioned so that the net effect of its interaction with the crack is to produce a zero stress intensity factor when combined with the effect of the applied displacements. Thus the Atkinson-Kay superdislocation model of a relaxed crack tip is extended to the situation where the material satisfies a power-law stress-strain relationship. 相似文献
15.
Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic–viscoplastic constitutive relation with various hardening–softening–hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip.On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening(or softening–hardening) has a particularly strong effect on the near crack tip stress and deformation fields. 相似文献
16.
Zhen-Gong Zhou Pei-Wei Zhang Guoqiang Li 《European Journal of Mechanics - A/Solids》2009,28(4):728-737
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relation between the electric field and the stress field near the crack tips was obtained. The results show that the stress and the electric displacement intensity factors at the crack tips depend on the lengths and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric materials. 相似文献
17.
We use the Wiener-Hopf method to obtain exact solutions of plane deformation problems for an elastic wedge whose lateral sides
are stress free and which has rectilinear cracks on its axis of symmetry. In problem 1, a finite crack issues from the wedge
apex edge; in problem 2, a half-infinite crack originates at a certain distance from the wedge apex edge; and in problem 3,
the wedge contains an internal finite crack. 相似文献
18.
S. T. Lin 《Experimental Mechanics》2000,40(1):60-67
The in-plane method and the out-of-plane method are used to analyze blind-hole residual stress as measured by optical interferometry.
The in-plane method, which constructs a relation between the in-plane displacement field and the residual stress released
from blind-hole drilling, is applicable when the sensitivity vector of the interferometer used in the measuring system is
parallel to the object surface. Three in-plane displacements obtained from one interference pattern are sufficient to determine
the residual stress. The out-of-plane method, which establishes a new relation between the out-of-plane displacement field
and the released residual stress, is suggested when the sensitivity vector is perpendicular to the object surface. Two relative
out-of-plane displacements extracted from one interference pattern are sufficient to determine the residual stress. With the
adoption of these two methods, interpolating calculation is not needed to determine the fringe order of each data point, since
the selections of the required data points are flexible using these two methods. Two experiments, one for the in-plane method
and the other for the out-of-plane method, were carried out to illustrate the applicability and usefulness of these two methods. 相似文献
19.
Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is applied to measure the out-of-plane deformation of structures with one-shot projection.Through color fringe recognizing,decoding and triangulation processing for the captured images corresponding to each deformation state,the feasibility of the method is testified by the measurement of elastic deflections of a flexible square plate,showing good agreement with those from the calibrated displacement driver.The plastic deformation of two alloy aluminum rectangular tubes is measured to show the technique application to surface topographic evaluation of the buckling structures with large displacements. 相似文献
20.
S. K. Deb Nath S. Reaz Ahmed Sung-Gaun Kim 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(10):1125-1147
The present paper describes the advancement of displacement potential approach in relation to solution of plane problems of
structural mechanics with mixed mode of boundary conditions. Both the conditions of the plane stress and the plane strain
are considered for analyzing the displacement and stress fields of the structural problem. Using the finite difference technique
based on the present displacement potential approach for the case of the plane stress and the plane strain conditions, firstly
an elastic cantilever beam subjected to a pure shear at its tip is solved and these two solutions (plane stress and plane
strain) are compared with Timoshenko and Goodier cantilever beam bending solutions (Theory of elasticity, 2nd edn. McGraw-Hill,
New York, 1951); secondly the above-mentioned displacement potential approach for the case of the plane stress and the plane
strain conditions are applied to solve a one-end fixed square plate subjected to a combined loading at its tip. Effects of
plane stress and plane strain on the elastic field of the plate are discussed in a comparative fashion. Limitations of Timoshenko
and Goodier cantilever beam bending solutions (Theory of elasticity, 2nd edn. McGraw-Hill, New York, 1951) over the displacement
potential approach for the case of the plane stress and the plane strain conditions are not only discussed but also the superiority
of the present displacement potential approach for the case of the plane stress and the plane strain conditions are reflected
in the present research work. 相似文献