Bi-material Plate Research Articles

Three-dimensional analysis of bimaterial cracked plates

Three-dimensional analysis of bimaterial cracked plates

Stress analysis of finite interfacially cracked bimaterial plates by using the variational method

The problem of finite bimaterial plates with an interfacial crack subject to a uniaxial loading was studied by using the eigenfunction expansion variation method (EEVM). Interfacial stress intensity factors (ISIFs) associated with the stress and displacement fields were determined. The effects of material properties and crack geometry on ISIFs and stress distributions were investigated. Finally, a simple expression of ISIFs for finite bimaterial plates is proposed.

Application of the electrical analog technique in fiber-reinforced composites

The electrical analog technique which has been previously used for the determination of normalized stress intensity factors in isotropic plates and in bimaterial plates is extended to the case of fiber-reinforced composites. The technique is based on the similarities between electrical and certain mechanical problems. Specifically, the fact that electric potential in a conductor as well as displacement in two dimensional elasticity problems in antiplane loading both obey the Laplace equation is made use of in determining normalized stress intensity factors ( K N ) in bimaterial plates and in fiber-reinforced composites. The K N determined by the electrical analog technique corresponds to the anti-plane problem. Since the behavior of cracks in the vicinity of interfaces is qualitatively similar in both plane and antiplane loading, the K N determined by the electrical analog technique provides useful information for the design of composites. This paper uses the electrical equivalence of the J- integral for the determination of K N . The specific problems examined include cracks in bimaterial plates, the behavior of a crack in the vicinity of fibers of higher modulus than the matrix, and the role of debonding and fiber fracture on K N . Fiber-reinforced composites and bimaterial plates were electrically simulated by electroplating copper or nickel on part of the surface of steel foils. The electroplated regions have higher electrical conductivity than the unplated regions and simulate materials of higher modulus in the corresponding mechanical problems.

Boundary element analysis of stress intensity factors for bimaterial interface cracks

The stress intensity factors for bimaterial interface cracks are determined by the boundary element method employing the multi-region technique and the double-point concept. A formula relating the stress intensity factors to the crack surface displacement, which is applicable to both the homogeneous and the bimaterial systems, is derived. The accuracy of the numerical results obtained using the formula is shown to be satisfactory within 5% when compared with the pre-existing analytic solutions. The stress intensity factors for the edge-cracked and the center-cracked bimaterial plates are computed with various crack lengths and shear modulus ratios under the biaxial and the uniaxial loadings, respectively.

A numerical study of the transient behavior of an interfacial crack in a bimaterial plate

In this paper we developed a numerical method to determine the transient stress intensity factor and crack opening displacement of an interfacial stationary crack in a bimaterial plate subjected to time dependent anti-plane shear stress on the surfaces of the plate. A bimaterial plate of finite length of dissimilar elastic, isotropic laminae with Griffith type of crack at the interface is analyzed. For the numerical method the finite element equations are derived in the frequency domain from a variational principle. The stress intensity factors in the frequency domain are evaluated from the displacements, which are obtained upon solving the finite element equations. The transient stress intensity factor is then obtained by numerical Fourier inversion technique using the Fast Fourier Transform (FFT) routine. Quarter point elements and transition elements are used to model the crack tip singularity.

Crack deceleration and arrest phenomena at an oblique bimaterial interface

The method of caustics with high-speed photography was employed to study the dynamic behavior of a transverse crack in bimaterial plates, with slant interfaces. Both phases of the specimens were fabricated from epoxy-polymers by casting the one phase successively after the other along its oblique boundary.The results have shown that the cracks propagate, in general, under mode-I conditions and that the interface acts as a decelerator for the propagating crack, which, after passing the obstacle of the interface region, accelerates. The observed decelerations and accelerations were always greater in the brittle phases than those of the ductile ones.The influence of the interface region to the crack propagation velocities was found to be more intense, when the crack propagates from a more brittle to a more ductile phase, than in the opposite case.The zone of interaction of the crack with the interface was wide in the case of the inclined interface, increasing with the angle between interface and the loading axis. In this zone the stress intensity factor at first increases, then decreases to a minimum value on the interface and again increases, as the crack enters in the second phase. The crack paths were always slightly curved with a discontinuous tangent at the interface.

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The complex potentials Φ(z) and Ψ(z) describing the stress-field due to a concentrated force, or a dislocation, applied at some point at the interior of either of the half planes bonded together, or being under some kind of contact between them, are calculated. By using these potentials as Green's functions we have reduced the problem of crack and/or holes existing in either of these half-planes to an integral equation along the cracks or holes. The advantage of the method is that the integral equation along the interface between the two half-planes (y=0) is canceled out. Thus, the numerical evaluation of the state of stress is considerably reduced and simplified. The respective integral equations corresponding to some characteristic cases of bimaterial plates were derived. Finally, examples of cracked half-planes, either stressor displacement-free, or bonded with other half-planes, indicated the potentialities of the method.

Failure of a bimaterial plate with a crack at an arbitrary angle to the interface

A thorough analysis of the fracture behaviour of a bimaterial plate, with a crack in one of its constituent materials and arbitrarily oriented with respect to the interface, was undertaken. The loading of the plate consisted of a uniform compressive or tensile stress applied along the crack surfaces. The influence of the crack position and orientation with respect to the bimaterial interface, as well as the elastic constants of the materials of the composite plate, on the critical stress required extension from the appropriate crack tip and the crack extension angle was studied. The characteristic cases of a single cracked plate with a stress-free and a rigid boundary, as well as the bimaterial plate with various material combinations of its constituents, were analysed. From the whole study interesting results were derived.

Crack-arrest at a bimaterial interface

A study of the behavior of a transverse crack propagating at right angles through the interface of a bimaterial plate was undertaken by means of the method of high-speed photography along with the optical method of transmitted caustics. The investigation was mainly concentrated on the changes of the stress intensity factor at the tip of a moving crack when reaching the bimaterial interface. The investigation was also extended to duplex plates consisting of the same material in both phases of the duplex.The results have shown that the process of crack arrest at the interfaces of duplex specimens depends mainly on the material discontinuity that this interface region presents on the process of crack propagation and not on the abrupt change of the mechanical properties of the materials of the phases.Therefore, the dynamic problem of a crack reaching an interface can in no way be appropriately approached by means of only the results of the static analysis.By studying the dynamic process of crack arrest at an interface we have formulated a rule for the experimental determination of the stress intensity factor during the whole process of crack arrest.Finally and in relation with the above experimental evidence, the dependence between crack propagation and stress wave emission from the tip of a moving crack was also discussed.

Crack propagation velocities in bi-phase plates under static and dynamic loading

An investigation of the dependence of the crack-propagation velocity in complex bimaterial plates at different loading rates was undertaken. The specimens were fractured under the influence of both static and dynamic loadings and the crack-propagation velocities were detected by high speed photography with the optical method of caustics. The investigation was concentrated in detecting the influence that the different loading rates have on the fracture velocities in both phases of the plates and how this influence interferes—counteracting or superimposing—with the other factors that determine the crack propagation process in bi-material specimens. These factors are the effect of interface, the influence of the mechanical characteristics of each phase on the crack-propagation velocity etc. The results show that for constant and given material characteristics of the bi-phase plate the crack propagation velocity in the first (notched) phase tends to increase with increasing strain rates. The same is valid for the crack propagation velocity in the second phase, but only for the case when fracture occurs under the influence of a dynamic load. A significant discrepancy of the latter statement occurs, however, in the case of fracture under a continuously-increasing static load. In this case the crack-propagation velocity in the second phase reaches some remarkably high values, which are of the order of high strain-rate dynamic crack propagation velocities. In this way, the crack-arrest effect on the crack propagation velocity appears to be more significant in the case of a static loading than it is for the case of dynamic loading.

Collocated interfacial stress intensity factors for finite bi-material plates

This paper deals with elastic stress intensity factors associated with stress fields near partially debonded interfaces in finite, bi-material plates. Bi-materiai stress intensity factors K 1 and K 2 are not associated, respectively, with symmetric and skew-symmetric loading and are functions of an arbitrary length parameter. Any fracture condition involving bi-material stress intensity factors must be independent of the arbitrary length parameter and must be consistent with experiment. We define a new parameter K i called the interfacial stress intensity factor which satisfies the former condition. A truncated Williams power series stress function for stresses in a cracked bi-material plate, as modified by Sih and Rice, is used with a modified boundary collocation procedure to generate interfacial stress intensity factors for finite bi-material plates. This modified collocation technique eliminates the need for tuning the boundary points. The method is exemplified by application to a centrally cracked bi-material plate and to a partially debonded composite laminate.

A finite element stress analysis of a crack in a bi-material plate

A stress analysis is presented for the problem of a crack in one material of a bi-material plate located perpendicular to the material interface. A numerical solution using the finite element techniques to determine the force displacement relationships is used. Knowing this, a work integral method is used to determine the stress intensity factors for the crack. Since the work integral is independent of path, the path of integration can be chosen far enough away from the crack tip to avoid the complications of the crack tip singularity. The problem is studied for a number of cases where the crack length to plate width ratio, distance from crack tip to material interface, and the ratio of material constants were varied as parameters.

Cracks and screw dislocation arrays in anisotropie bimaterial plates

This article examines the equilibrium configuration of dislocation arrays in anisotropic bimaterial plates. Both components in the plate are assumed to be orthotropic with respect to plate axes. Forces on dislocations due to external loadings are found in closed form.Image forces due to phase boundary and free surfaces are also taken into consideration.Discussions on the behavior of screw dislocation arrays can be easily extended to the behavior of antiplane shear cracks. The crack opening displacements for several biomaterial systems have been calculated. In these systems, the crack opening displacements are found to be insensitive to the variation of plate thickness. However, they are strongly affected by the relative magnitude of elastic constants of the component phases. This is demonstrated in several diagrams.

Stress Distribution in a Bimaterial Plate under Uniform External Loadings

The elastic fields in a bimaterial plate under uniform compressive and anti-plane shear loadings are analyzed. Explicit expressions for the stresses are obtained. Interfacial shear stresses are found to be induced when the plate is subjected to anti-plane shear loading. In the compressive case, both normal and shear components of stress are introduced near the phase boundary. These stresses decrease expo nentially with the distance from the interface. Some implications with respect to dislocation pileups and interface failure are presented. Under a uniformly applied shear stress the effect of the inhomogeneity is to cause screw dislocations to pile up only in the phase with the comparatively higher shear modulus.

Circular-arc cracks in bi-material plates under bending

On the basic of the Poisson -Kirchhoff theory of thin plates, boundary problems of bi-material plates bonded along circular arc segements are reduced to the solution of the non-homogeneous Hilbert problem in complex function theory. The unbonded portions of the interface may be regarded as flaws or crack-like imperfections of some kind. Using the properties of Plemelj formulas and Cauchy integrals, sectionally holomorphic functions are obtained for one or more cracks distributed along the circumference of a circle dividing two different materials. The results suggest the possibility of using current fracture theories to predict the failure of thin plates containing circular inserts of another material partially joined along a finite number of arcs. For illustration, stress-intensity factors employed in the Griffith-Irwin theory of fracture are computed.