Measurement of energy release rate and energy flux of rapidly bifurcating crack in Homalite 100 and Araldite B by high-speed holographic microscopy

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.     

Experiments on crack identification in cantilever beams

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.     

Ultrasonic sizing of embedded vertical cracks in ferritic steel welds

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.     

Modelling of flow pattern in a shallow aquifer affected by reservoirs

A compartmental model is developed to estimate flow parameters of a shallow aquifer affected by water loads in surface reservoirs and to evaluate its nonsteady flow distribution. The method incorporates temporal piezometric head measurements and sampling of water for dissolved chemicals and isotopes analyses. Each compartment is governed by a set of equations describing the conservation of linear momentum and mass balance expressions for water, isotopes, and dissolved chemicals. The number of compartmental balance expressions always must be greater than that of the unknown flow parameters associated with each compartment. An optimization method is described to yield spatial distribution of aquifer storativity, transmissivity, porosity, leakage, and compliance coefficients and fluxes leaking into an aquifer's lower boundary. Future predictions of an aquifer's piezometric head distribution in a compartmental system is formulated on the basis of the estimated flow parameters and the leakage components.Compartmental modelling which incorporates concentrations of environmental tracers, may yield efficiency in computing resources and accuracy enhancement for predicting an aquifer's flow regime.     

Forced oscillations of a layer of a viscoelastic material under the action of a convective pressure wave

The longitudinal and transverse components of deformation of the surface of a flat layer of a viscoelastic material glued onto a solid base under the action of a traveling pressure wave are determined. The coating compliance is described by two components corresponding to two components of surface displacement. The dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wave length to the layer thickness λ/H, and the ratio of the wave velocity to the velocity of propagation of shear oscillations V/C _t ⁰ . Data on the dynamic compliance are presented for 0.3 < λ/H < 30 and 0.1 < V/C _t ⁰ < 10. The compliance is demonstrated to be determined by its absolute value and by the phase lag of strain from pressure. The effect of viscous losses in the material and compressibility of the latter on the dynamic compliance is analyzed. An anomalous behavior of the compliance with the wave velocity being greater than a certain critical value is explained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 90–97, March–April, 2007.     

An extension of the J-integral to piezoelectric materials

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.     

A delta-function method for the n-th approximation of relaxation or retardation time spectrum from dynamic data

A function series g(x; n, m) is presented that converges in the limiting case n and m = constant to the delta-function located at x = = 1. For every finite n, there exists 2n+1(–nmn) approximations of the delta-function _(n)(x–x _n,m ). x _n,m is the argument where the function reaches its maximum. A formula for the calculation is given.The delta-function approximation is the starting point for the approximative determination of the logarithmic density function of the relaxation or retardation time spectrum. The n-th approximation of density functions based on components of the complex modulus (G*) or the complex compliance (J*) is given. It represents an easy differential operator of order n.This approach generalizes the results obtained by Schwarzl and Staverman, and Tschoegl. The symmetry properties of the approximations are explained by the symmetry properties of the function g(x; n, m). Therefore, the separate equations for each approximation given by Tschoegl can be subsumed in a single equation for G and G, and in another for J and J.     

淮河大堤老应段土体蠕变特性研究及工程应用

本文依据工程需要, 采取淮河大堤老应段的原状和扰动土样, 在室内对堤体及堤基土的剪切蠕变和拉伸蠕变特性进行了试验研究。粘土的蠕变剪切强度远低于瞬时剪切强度, Ｃ∞值仅是Ｃ值的４０％左右;相同含水条件下粘土的长时抗拉强度大于瞬时抗拉强度, 长时拉伸应变量远大于瞬时拉伸应变量, 约为２倍。     

Interface crack between two shear deformable elastic layers

An improved method based on the first-order shear deformable plate theory is developed to calculate the energy release rate and stress intensity factor for a crack at the interface of a bi-layer structure. By modeling the uncracked region of the structure as two separate Reissner-Mindlin plates bonded perfectly along the interface, this method is able not only to take into account the shear deformation in the cracked region, but also to capture the shear deformation in the uncracked region of the structure. A closed form solution of energy release rate and mode decomposition at the interface crack is obtained for a general loading condition, and it indicates that the energy release rate and stress intensity factor are determined by two independent loading parameters. Compared to the approach based on the classical plate theory, the proposed method provides a more accurate prediction of energy release rate as well as mode decomposition. The computational procedures introduced are relatively straightforward, and the closed form solution can be used to predict crack growth along the layered structures.     

Application of material forces to fracture of inhomogeneous materials: illustrative examples

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.