Anti-plane analysis of semi-infinite crack in piezoelectric strip

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Analysis of the cause of crack in cold rolling of QSn6.5-0.1 strip

In order to know the cause of cracks in cold rolling of QSn6.5 0.1 copper alloy strip, a lot of experiments and analysis were done. The microstructure changes of QSn6.5 0.1 were investigated by means of metallurgical microscope. The morphology of cracks and surface defects were examined using scanning electron microscope. Macroscopic residual stresses produced in every process during manufacturing in the QSn6.5 0.1 strip were measured by X ray diffraction method and hole drilling method. The results show that the cracks in the QSn6.5 0.1 cold rolling strip were caused due to the derivation of metallurgical defects, such as SnO 2, S, fine looses,the inverse segregation unable to clear up when milling, and the accumulation of all kinds of resi dual stresses. When the accumulation of the residual stress reaches the material′s breaking strength, the cracks will be generated. Several measures to avoid the development of these kinds of cracks were put forward, such as: controlling the casting technology, improving homogenization annealing procedure (680 ℃/7 h) and milling quality(using the second milling when necessary), working out a more reasonable rolling technology to ensure intermediate annealing in time.

DYNAMIC BEHAVIOR OF TWO PARALLEL SYMMETRIC PERMEABLE CRACKS IN A PIEZOELECTRIC STRIP

The dynamic behavior of two parallel symmetric cracks in a piezoelectricstrip under harmonic anti-plane shear waves is studied using the Schmidt method for permeable cracksuface conditions. The cracks are parallel to the edge of the strip. By means of the Fouriertransform, the problem can be solved with the help of two pairs of dual integral equations. Theseequations are solved using the schmidt method. The results show that the stress and the electricdisplacement intensity factors depend on the geometry of the cracks, the frequency of incidentwaves, the distance between cracks and the thickness of the strip. It is also found that theelectric displacement intensity factors for the permeable crack surface conditions are much smallerthan those for the impermeable crack surface conditions.

TORSIONAL IMPACT RESPONSE OF A PENNY-SHAPED CRACK IN A FUNCTIONAL GRADED STRIP

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and (strip's) highness on the dynamic fracture behavior. Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip's highness.

Analysis of strip edge cracks during cold rolling of thin strip

In this paper,the mechanics of strip edge cracks and its propagation has been studied,and the effects of strip edge drop and stress intensity factor(SIF) on edge crack defections during cold rolling of thin strip have been discussed.An experimental investigation was presented into the effect of strip edge drop on edge cracks during cold rolling of thin strip.The edge crack increases significantly due to more inhomogeneous deformation and work hardening at the strip edge.The effective stress intensity factor range is important as it represents the major physical cause of the crack propagation.The efficiency and reliability of the SIF analytical model has been demonstrated in the study.The proposed method for predicting strip edge crack is helpful in producing defect-free products and providing an understanding of the mechanics of edge crack propagation in cold rolling of thin strip.

TRANSIENT RESPONSE OF COPLANAR INTERFACIAL CRACKS BETWEEN TWO DISSIMILAR PIEZOELECTRIC STRIPS UNDER ANTI-PLANE MECHANICAL AND IN-PLANE ELECTRICAL IMPACTS

The dynamic response of multiple coplanar interface cracks between two dissimilar piezoelectric strips subjected to mechanical and electrical impacts is investigated.Solutions to two kinds of electric boundary conditions on crack surfaces,i.e.electric impermeable and electric permeable,are obtained.Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations, which can be solved numerically.The effects of electrical load,geometry criterion of piezoelectric strips,relative location of cracks and material properties on the dynamic energy release rate are examined.

TRANSIENT RESPONSE OF A CRACKED PIEZOELECTRIC STRIP UNDER ARBITRARY ELECTRO:MECHANICAL IMPACT

By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation of the crack depending on the time elapse since the application of the external electro-mechanical loads. (Author abstract) 9 Refs.

The Effect of Atmospheric Plasma Paint Stripping on the Fatigue Crack Growth Properties of Aluminium Substrates

Paint removal is a common maintenance requirement for aircraft as well as naval and land vehicles, since external paint gets damaged and loses much of its corrosion protection effectiveness with time. Paint removal is also conducted when metallic aircraft structures are inspected periodically for fatigue cracks and corrosion. The conventional methods of removing paint employed throughout the Canadian Forces mainly include chemical stripping and abrasive media blasting. Chemical stripping involves the use of hazardous chemicals, which are high in Volatile Organic Compounds (VOC) and Hazardous Air Pollutants (HAP). Abrasive media blasting typically results in a substantial quantity of solid waste consisting of paint and blast residues. Such waste is subject to control under increasingly stringent environmental and safety regulations and its disposal is costly. The new Atmospheric Plasma (AP) paint removal process purports to be a high chemical energy, low thermal energy (cold plasma process), that should not damage temperature sensitive substructures, such as heat treated aerospace aluminium alloys. Fatigue strength is one of the key properties in aircraft structures. In order for AP paint stripping to be accepted as an aerospace industry standard paint removal process, it must be thoroughly tested to demonstrate that it does not adversely affect the fatigue properties of the substrate. This paper investigates effect of the paint removal process on fatigue crack growth of 7075-T6 and 2024-T3 aluminium panels.

ANALYSIS OF A CRACK IN A FUNCTIONALLY GRADED STRIP WITH A POWER FORM SHEAR MODULUS

The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy＇s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line.

ELECTROELASTIC INTENSIFICATION NEAR ANTI-PLANE CRACK IN A FUNCTIONALLY GRADIENT PIEZOELECTRIC CERAMIC STRIP

Following the theory of linear piezoelectricity,we consider the electro-elastic prob- lems of a finite crack in a functionally gradient piezoelectric ceramic strip.By the use of Fourier transforms we reduce the problem to solving two pairs of dual integral equations.The solution to the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind.Numerical calculations are carried out for piezoelectric ceramics.The electric field intensity factors and the energy release rate are shown graphically,and the electroelastic interactions are illustrated.

SCATTERING OF ANTI-PLANE SHEAR WAVES IN A FUNCTIONALLY GRADED MATERIAL STRIP WITH AN OFF-CENTER VERTICAL CRACK

The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.

Analytical solution of multiple moving cracks in functionally graded piezoelectric strip

The dynamic behaviors of several moving cracks in a functionally graded piezoelectric （FGP） strip subjected to anti-plane mechanical loading and in-plane elec- trical loading are investigated. For the first time, the distributed dislocation technique is used to construct the integral equations for FGP materials, in which the unknown variables are the dislocation densities. With the dislocation densities, the field intensity factors are determined. Moreover, the effects of the speed of the crack propagation on the field intensity factors are studied. Several examples are solved, and the numerical results for the stress intensity factor and the electric displacement intensity factor are presented graphically finally.

Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips

The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.

Analysis of surface microcracks in low-carbon steel produced via twin-roll strip casting

In this study,morphological and microstructural analyses were conducted on net-shaped microcracks appearing on the surface of low-carbon steel manufactured via twin-roll strip casting. The fractograph and microscale distribution of elements in the cracked region were also analyzed. Results revealed that the cracked surfaces were characterized by slight pits,along with inclusions composed of manganese and silicon oxide distributed along both the sides of the cracks. Fractograph analysis revealed that the crack and smooth dendrite surfaces were oxidized. These phenomena indicate that microcracks on the cast strip surface form at the hightemperature stage of the solidification process during twin-roll casting and rolling. Microcracks were present in each region with pits in the cast strip and extended along the dendrite interface because of the combined effects of phasechange stress,thermal stress,mechanical stress,and fractional crystallization during the solidification process.

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum ＇anti-plane shear＇ stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.

STRESS ANALYSIS FOR AN INFINITE STRIP WEAKNED BY PERIODIC CRACKS

Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p ' in y_ direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T _stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.

Dynamic behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips

The dynamic interaction of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips subjected to the anti-plane shear harmonic stress waves was investigated. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is jump of displacement across the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter, the circular frequency of the incident waves and the thickness of the strip upon stress, electric displacement and magnetic flux intensity factors of cracks.

REPRESENTATION OF PLASTICITY AT AN INTERFACE CRACK BY INCLINED STRIP YIELD SUPERDISLOCATION MODEL

The basic equations of the representation of plasticity at an interface crack by an inclined strip yield superdislocation model are derived. With a special combination of the material properties and small-scale yielding case, the problem is reduced to an algebraic equation in an unknown, the ratio of the plastic zone size. Some discussions on the limitations of this model are presented.

The edge crack problem for an orthotropic functionally graded strip under concentrated loads

The plane crack problem of an orthotropic functionally graded strip under concentrated loads is studied. The edge crack is perpendicular to the boundary and the elastic property of the material is assumed to vary depending on thickness. By using an integral transform method, the present problem can be reduced to a single integral equation which is solved numerically. The influences of parameters such as the nonhomogeneity constant and the geometry parameters on the stress intensity factors (SIFs) are studied. It is found that the nonhomogeneity constant has important influences on the SIFs.