Time-dependent Stress Intensity Factor Research Articles

Elliptically polarized white light photoviscoelastic technique and its application to viscoelastic fracture

The present paper demonstrates the successful application of the photoviscoelastic technique using elliptically polarized white light to the stress field evaluation of the crack growth in a viscoelastic strip. Using the proposed technique, which can determine both isochromatic and isoclinic parameters simultaneously from a single color image, the time-dependent stress state around a slowly propagating crack tip in a viscoelastic strip plate is successfully analyzed. Then, the time-dependent stress intensity factor extended for linearly viscoelastic materials is evaluated from the experimental results using a method based on the least squares. The results show that the proposed critical stress intensity factor for fast crack growth may be considered as a characteristic property of the material under monotonically increasing load.

On the general treatment of a cracked multi-layered medium in antiplane viscoelasticity

An arbitrary crack lying in a viscoelastic multi-layered medium under an anti-plane concentrated load is discussed in this paper. The fundamental elastic solution is obtained as a rapidly convergent series in terms of complex potentials via successive iterations of the Möbius transformation in order to satisfy continuous conditions on multiple different interfaces. Based on the correspondence principle, the Laplace transformed viscoelastic solution is then directly determined from the corresponding elastic one. Using the singular integral technique, the time-dependent mode-III stress intensity factor of the crack tip can be solved numerically in a straightforward manner. Finally, some typical examples showing the effect of bonded layers and crack orientations on the stress intensity factor are also discussed. The results show that the stress intensity factor decreases monotonically with time if the bonded layer is stiffer than the cracked layer.

Stress intensity factors of a crack lying in a viscoelastic layer embedded in two different media under an anti-plane concentrated load

A general solution to the problem of a crack lying in a viscoelastic layer sandwiched between two different media under an anti-plane concentrated load is presented. The fundamental elastic solution is obtained as a rapidly convergent series in terms of complex potentials via successive iterations of Möbius’ transformation in order to satisfy continuity conditions on two different interfaces. Based on the correspondence principle, the Laplace-transformed viscoelastic solution is then directly determined from the corresponding elastic solution. Therefore, the time-dependent mode-III stress intensity factor (SIF) of the crack tip can be solved numerically in a straightforward manner. Furthermore, the viscoelastic moduli of polyurethane at various temperatures are regressed from a uni-axial test with a constant load while a standard solid model is applied to formulate the viscoelastic constitutive equation. Finally, the effects of working temperature, boundary conditions and the geometric relation on the SIF are also discussed.

Dynamic Fracture Mechanics Assessments for Cubic Ductile Cast Iron Containers

AbstractAn improved BAM safety assessment concept for the cask material ductile cast iron (DCI) to cover higher stresses in the cask body, highly dynamic load scenarios, and a broader range of material qualities will require more extensive fracture mechanics analyses based on a combination of material testing, calculation of applied stresses, and inspection standards. As an example, the brittle fracture mechanics assessment of a surface crack in a plate due to the dynamic load from the 5 m drop of a cubic container (not equipped with impact limiters) onto a reinforced concrete target is investigated. The numerically calculated time-dependent stress intensity factor is compared with a previous static solution with the same loading history inserted. For the scenario studied the differences between the curves are negligible because a dynamic load of the cask within a time scale of millisec9nds can be considered as a quasi static load for the crack.

線熱源による割断におけるき裂進展挙動

Electronic substrates on which precise circuits were already formed can be cleaved without leaving any micro-cracks on the cleaved surface by a thermal stress cleaving using a line heat source. In order to understand the crack extension behavior, time-dependent stress intensity factors of long and short cracks pre-induced from the end of a thin plate are analyzed when a thin plate is heated by a continual line heat source on the crack line. In the case of a long crack, the stress intensity factor is almost independent from the crack length but, in the case of a short crack, the factor is strongly dependent on the crack length. Accordingly, two different modes of crack extension appear. The condition, which mode appears, can be clarified from the comparison of stress intensity factors of two cases. With high heating power, a strip with narrow width can be cleaved stably. For stable cleaving, therefore, it is essential to use high heating power so long as the heat damage doesn't appear. This conclusion agrees well with experiments using glass plates.

Evaluation of Time-Dependent Fracture Mechanics Parameters of a Moving Crack in a Viscoelastic Strip.

The present work studies time-dependent stress fields around a moving crack tip in a viscoelastic strip and crack extension resistance. Photoviscoelastic technique is employed for the evaluation of the time-dependent stress state around a crack tip. For the fringe pattern analysis, a new technique using an elliptically polarized white light, which can determine isochromatic and isoclinic parameters simultaneously from a colored image obtained by a single acquisition, is applied. The time-dependent stress intensity factor K * I which is extended for linearly viscoelastic materials is evaluated using a method based on least-squares. The results show that the proposed crack extension resistance K* IC may be considered as a characteristic property of the material under monotonically increasing load.

線熱源による帯板の熱応力割断

A thermal stress field induced by a line heat source often causes crack extension. Taking advantage of this phenomenon, some glassy materials can be cleaved without leaving any microcracks on the cleaved surface. In the present paper, the time dependent stress intensity factor of a line crack pre-introduced from the end of a thin plate has been obtained when a thin plate is heated by a continual line heat source on a crack. The stress intensity factor is affected by the width of the strip and the ligament length but is almost independent from the crack length. The present analysis agrees well with the experimental results using glass plates. The section of the glass cleaved by a line heat source was extremely smooth. The surface roughness was within 0.02μm at Ra.

破壊力学 ぜい性薄板の熱線割断と寸法効果

A non-uniform temperature rise in the vicinity of crack tip often causes crack propagation. Taking advantage of this phenomenon, some brittle materials can be cleaved without any cutting tools but with an adequate controlling of a temperature distribution in the body.In the present paper, based on the linear fracture mechanics, a possibility of the thermal stress cleaving is discussed for a brittle rectangular plate which is heated along its symmetrical axis. A time dependent thermal stress intensity factor of an edge crack was analyzed systematically by changing the plate dimensions and crack length. Experimental findings were compared with the analytical results and good agreements were found.Especially, the crack extension characteristics in a cleaving test of a lime-soda glass can be well understood through the dependence of stress intensity factor on heating time and crack tip location.

帯板のレーザ割断における温度上昇の抑制

Brittle materials like semiconductor wafers and ceramic substrates are usually cut by diamond tools, where the generation of microcracks cannot be avoided. Recently, thermal stress cleaving of a thin strip using a point heat source is studied to cut brittle materials without leaving any microcracks on the cleaved surfaces. However, this method often causes thermal damages to the workpieces because of the very high temperature reached around the heating point. It is desirable to cut the electronic substrates, on which precise circuits were already formed, with minimizing the temperature rise. In the present paper, based on the plane thermoelasticity, the time dependent thermal stress intensity factor of a line crack has been obtained for two heating ways : by two point heat sources and a circular zone heat source located symmetrically with respect to the crack line. It was found that a zone heating is better than a point heating in the case of a thin strip cleaving under the restriction of the temperature rise. The most successful cleaving is generally achieved when a radius of a heating region is expanded up to the crack tip. The present calculation was compared with the experimental results and good agreement was found.

Viscoelastic composite with a cracked layer under anti-plane shear

A viscoelastic cracked sandwich composite under anti-plane load is presented via the application of the Laplace transform and the complex variable formulation. Using a special technique of analytical continuation associated with the method of image, the triple-layered problem is reduced to a singular function by simple algebraic manipulations. The superposition method and the singular integral equation is applied to deal with the concentrated load and crack problem. Finally, some typical viscoelastic models and its corresponding stresses and stress intensity factors are also discussed. The results show that the time dependent stress intensity factor is affected by the relative strength of creep compliances of each layer.

Transient SIF results for a cracked viscoelastic strip under concentrated impact loading—An integral-transform/function-theoretic approach

The diffraction of transient SH waves by a long crack in a strip of viscoelastic material is considered. These viscoelastic waves are generated by a pair of suddenly applied, equal but opposite concentrated anti-plane forces, which tend to separate the crack faces in a tearing mode. In this way, the present solution provides Green's function for the more general case of spatially non-uniform loading of the cracked strip. The diffraction problem, which contains two characteristic lengths, is solved asymptotically by a function-theoretic method in conjunction with a numerical technique for Laplace-transform inversion. Attention is focused on the time-dependent stress intensity factor (SIF). Extensive numerical results for the SIF dependence upon the viscoelastic material parameters and the ratio of characteristic lengths are provided.

Transient crack growth in a viscoplastic solid

Near-tip fields for transient crack growth in a material whose constitutive behavior is represented by the Bodner-Partom model are investigated for the case of plane strain mode I fracture under small-scale yielding conditions. At time t = 0, a load is applied to the cracked body. At the same instant, the crack starts to propagate with a constant velocity. A boundary integral equation method is used to compute the complete fields of stress and deformation. An expression for the near-tip time-dependent stress intensity factor has been derived and numerical results are presented for several crack tip speeds. Evolution of the stresses as the crack extends quasi-statically into the viscoplastic solid is also presented.

Propagating interface cracks with frictionless contact

R esults are presented for a study of the asymptotic stress and deformation fields around a crack that has frictionless crack surface contact, and is growing steadily along the interface of two dissimilar, homogeneous, isotropic and linearly elastic solids. A complete representation of Comninou-type (C omninou, J. appl. Mech. 44, 631, 1977) elastic crack tip fields is obtained using the method of analytic continuation. As in the case of stationary interfacial cracks, the crack tip stress singularity is found to be nonoscillatory and to resemble the classical mode II type singularity. The findings of this investigation form a basis for further theoretical and experimental studies on the subject, in cases where the notion of small-scale contact is invalid. Transient effects on the asymptotic crack tip fields, due to nonuniform crack velocity or time-dependent stress intensity factor, can be readily included, if desired, with a method developed recently by the current author (D eng, Int. J. Solids Struct. 30, 513, 1993).

The transient analysis of a subsurface inclined crack subjected to a buried dynamic dilatational source

The transient response of a subsurface inclined crack subjected to a buried dilatational source is analysed in this study. This investigation will be helpful in understanding the problems of seismology and waves generated by thermal loading in a cracked body. The solutions are determined by superposition of the fundamental solution in the Laplace transform domain. The required fundamental solution is the exponentially distributed traction on crack faces proposed by Tsai and Ma [1992a, ASME J. Appl. Mech. (in press)]. The exact closed form solutions of the time dependent dynamic stress intensity factors are obtained. These solutions are valid in the time interval from initial loading until the first wave scattered by the crack tip returns to the crack tip after reflection from the free surface. The direction of the crack propagation is predicted by different fracture criteria from the available stress intensity factors.

Unidirectional ceramic matrix composites under dynamic flexure

The impact response of a beam of unidirectionally fibre-reinforced ceramic matrix composites with matrix crack is modelled. Time-dependent stress intensity factors of the matrix crack and stresses in bridging fibres are obtained and their relationships with parameters such as crack lengths, interfacial bonding strengths, fibre diameters, beam configurations and loading rates are discussed in detail.

Boundary element analysis of cracks in thermally stressed planar structures

The evaluation of stress intensity factors is important for the assessment of structural integrity of flawed structures. The boundary element method is used in the present work for the computation of steady-state and time-dependent stress intensity factors of cracks in thermally loaded structures. While many boundary and volume integral based formulations are available for the treatment of thermoelastic problems in solids, the present analysis is based on a recently developed boundary-only formulation. Crack-tip elements that accurately model the behavior of displacement, temperature fields and singularity of traction, flux fields are used for the accurate evaluation of stress intensity factors.

Dynamic tensile‐failure‐induced velocity deficits in rock

Planar impact experiments were employed to induce dynamic tensile failure in Bedford limestone. Rock discs were impacted with aluminum and polymethyl methacralate (PMMA) flyer plates at velocities of 10 to 25 m/s. Tensile stress magnitudes and duration were chosen so as to induce a range of microcrack growth insufficient to cause complete spalling of the samples. Ultrasonic P‐ and S‐wave velocities of recovered targets were compared to the velocities prior to impact. Velocity reduction, and by inference microcrack production, occurred in samples subjected to stresses above 35 MPa in the 1.3 μs PMMA experiments and 60 MPa in the 0.5 μs aluminum experiments. Using a simple model for the time‐dependent stress‐intensity factor at the tips of existing flaws, apparent fracture toughnesses of 2.4 and 2.5 MPa m½ are computed for the 1.3 and 0.5 μs experiments. These are a factor of ∼ 2 to 3 greater than quasi‐static values. The greater dynamic fracture toughness observed may result from microcrack interaction during tensile failure. Data for water‐saturated and dry targets are indistinguishable.

Finite element solutions for propagating interface cracks with singularity elements

A finite element procedure has been developed to provide solutions for the state of stress, displacement and stress intensity factors for a propagating crack at the interface of two dissimilar anisotropic materials. In the finite element mesh the crack-tip is embedded in a singular element and the near-field state of stress and displacement described in our paper in Engng Fracture Mech. 36, 93/2-103 are used. The remainder of the body is filled with regular finite elements. The singular element formulation provides for the direct solution of the time-dependent stress intensity factors. The procedure for the finite element formulation including the development of the singular element matrices is presented. The element matrices are derived from a variational principle involving a modified functional for elastodynamic problems. The resulting discretized dynamic equations of motion are solved by an implicit method of time integration using Newmark-β formulas. Local asymmetries in the matrices which arise due to crack propagation are dealt with by modifying the finite difference formulation and by the use of an iterative procedure for convergence of the solution. Crack propagation is accomplished by moving the crack-tip inside the singular element according to a prescribed crack-tip position history. A local redefinition of the finite element mesh is required when the crack-tip reaches an extreme position inside the singular element. When the local mesh redefinition takes place, an extra node is created. This is accomplished using a double-noding technique. The accuracy of the finite element formulation is evaluated by solving problems for which analytical and numerical solutions are available. The solutions are found to compare well with solutions in the literature. The solution to some problems involving propagating and stationary cracks at the interface of two dissimilar orthotropic materials, for which there are no known solutions, are presented.

Crack extension induced by thermal stresses associated with uniform heating in a circle.

The time-dependent stress intensity factor of a semi-infinite crack has been obtained when an infinite plate is heated uniformly in a circle near the crack tip. The intensity depends on the heating location D and the radius R. But the radius dependence is small and the total amount of heat gives almost the same intensity as point heat as long as R/D remains small. This is preferable for cleavage cutting in which surface melting should be avoided. Glass plates were heated by an exposure of the CO2 laser beam and crack opening displacements were measured by an interference method. The measured crack deformation corresponds well with the thermal stress analysis. At the onset of the crack extension, similar stress intensity was attained for the same plate thickness irrespective of the heating intensity and location.

Fracture analysis of a single edge cracked strip under thermal shock

For a single edge crack in a long strip quenched on the cracked side, the time-dependent stress intensity factors have been calculated by means of the methods of weight functions, finite elements and boundary elements. These quantitative results support a recently developed heuristic fracture-mechanical approach to thermal shock damage due to single and multiple crack growth.