Non-dimensional Stress Intensity Factor Research Articles

An Electroelastic Problem of Two Interface Cracks between Matrix and Inhomogeneity Subjected to Anti-Plane Shear Stress and In-Plane Electric Displacement.

In this paper, we study a two-dimensional electroelastic problem of two interface cracks between matrix and an inhomogeneity subjected to anti-plane shear stress and in-plane electric displacement. We formulate the stress intensity factor (SIF) and electric displacement intensity factor (EDIF) analytically. The SIF and EDIF are formulated by the potential functions representing the electroelastic field. These potential functions are obtained as the solutions of the Hilbert problems. The non-dimensional SIF and EDIF can be expressed by the product of two simple functions: one is the function of the non-dimensional lengths of the cracks, the other is the function of the non-dimensional material properties and the loads at infinity. The behavior of these functions, which characterize the effects of crack lengths, material properties and the loads at infinity on the SIF and EDIF, is examined for some cases.

Compact solutions for the corner singularity in bonded lap joints

This paper presents compact solutions of the corner singularity at the adhesive/adherend interface in a bonded lap joint. Two configurations of special importance to evaluating joint strength are considered: corners pertaining, respectively, to a square edge and a spew fillet. The stress intensity factors are determined for the limiting case of rigid substrates by means of a numerical matched asymptotic expansion method. The non-dimensional stress intensity factor depends only on the Poisson's ratio of the adhesive, and this variation is characterised in a convenient analytical form by polynomial expressions. Comparison with finite-element results of a bonded joint obtained using fine mesh near the corner points confirms that the present analytical solutions provide very good representations of the singular stress fields at adhesive/substrate corners.

An extended equivalent domain integral method for mixed mode fracture problems by the p ‐version of FEM

A new path-independent contour integral formula is presented to estimate the crack-tip integral parameter, J-value, for two-dimensional cracked elastic bodies which may quantify the severity of the crack-tip stress fields. The conventional J-integral method based on a line integral has been converted to an equivalent area or domain integral (EDI) by the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of domain integrals are readily available in a finite element analysis. The details and its implementation are extended to the p-version FE model with hierarchic elements using integrals of Legendre polynomials. By decomposing the displacement field obtained from the p-version finite element analysis into symmetric and antisymmetric displacement fields with respect to the crack line, the Mode-I and Mode-II non-dimensional stress intensity factors can be determined by using the decomposition method. The example problems for validating the proposed techniques are centrally oblique cracked plates under tensile loading. The numerical results associated with the variation of oblique angles show very good agreement with the existing solutions. Also, the selective distribution of polynomial orders and the corner elements for automatic mesh generation are applied to improve the numerical solution in this paper. © 1998 John Wiley & Sons, Ltd.

Experimental stress intensity factors for cracks in a thin plate with stiffeners

The problem of cracked plates stiffened by three-dimensional stringers is investigated using transmission photoelasticity. Models were produced of the hole-in-the-plate geometry stiffened by a combination of stringers transverse and/or parallel to the applied tensile load. Cracks of different lengths emanating from one edge of the hole and approaching a stringer were examined. These cases represent geometry and loading conditions for which it would normally be very difficult to obtain results using analytical methods. The stringer-stiffened plates show a consistent reduction in the non-dimensional stress intensity factor of about 20 per cent irrespective of the arrangement of stringers.

Analytical/numerical solutions for a single hole-edge crack in a narrow plate under pure bending

The problem of a crack emanating from a hole in a plate has been widely studied. However, almost all studies to date assume the loading to be in the form of a uniform far-field tensile stress in the plane of the plate. This study examines the case of a far-field uniform bending moment acting on a finite plate/strip weakened by a crack emanating from the hole. Both on-center and off-center holes are considered. Stress intensity factors are determined for a variety of geometries. These computations are performed both analytically and numerically (finite element method). These computations are compared with each other and with experimental results obtained from cold-drawn 2024-T3 aluminum alloy plates. Statistical variations in the experimental results are estimated by using replicated tests. On average, analytical values of the non-dimensional stress intensity factors are 16% lower than the experimental values. There is also some deviation between the analytical and numerical results, and the reasons for these deviations are discussed in the paper.

じん性を変えた注型用エポキシ樹脂の耐熱衝撃性評価

Previously the present authors proposed the testing method of thermal shock resistance using a notched disk type specimen of brittle type epoxy resin and its evaluation method based on fracture mechanics. In order to examine their applicability, some practical epoxy resins for casting were tested in this study.For brittle alicyclic epoxy resin, irrespective of the cooling bath temperature, the nondimensional stress intensity factor calculated by the experimental results agreed well with that of theoretical estimation.In the case of mixed resin of bisphenol A epoxy having certain toughness and very brittle alicyclic epoxy, the critical temperature difference ΔTC was clearly recognized for all resin systems with various mixture ratios, and the resin with higher bisphenol A epoxy content showed higher thermal shock resistance. For the bisphenol A type epoxy resin with longer molecular chains (larger number of repeated units) indicated higher resistance. The analysis agreed well with the experiments for these both resin systems.For the epoxy resin modified with a low content of plasticizer, the same evaluation method of thermal shock resistance was found to be applicable. But over 20phr content, plastic flow occurred markedly, and so the critical temperature difference could not be obtained. For such cases, it is still possible to evaluate the thermal shock resistance by using a large size specimen.

Boundary element analysis for standard specimen configurations in the ISRM suggested methods for determining fracture toughness of rock

In order to provide an analytical basis for the current “Suggested Methods for Determining the Fracture Toughness of Rock” [1] (referred to hereafter as Suggested Methods) proposed by ISRM, a 3-D boundary element analysis was carried out for standard configurations of two specimen types: chevron bend and short rod. From the results, it is shown that the non-dimensional stress intensity factor described in the Suggested Methods for the chevron bend specimens is approx. 10% greater than that determined in this work. This new calibration constant gives a more realistic fracture toughness for Ogino tuff. Good agreement was obtained with the Suggested Methods for the short rod specimen.

Thermal shock problem of a hollow circular cylinder with a crack.

This paper deals with the thermal shock problem of a hollow circular cylinder with an edge crack, initially at uniform temperature, being suddenly cooled on the circular surfaces. It is asuumed that the thermal disturbance near the crack surface may be neglected in the analysis of the temperature field of the elastic solid with a crack, because thermal shock occurs rapidly. We analyzed the transient thermal stress problem of a hollow circular cylinder with a crack and determined the stress intensity factor at the crack tip. The nondimensional maximum transient stress intensity factor is expressed as a function of Biot's number and the nondimensional crack length. We then proposed a simplified formulation of the nondimensional maximum transient stress intensity factor as a function of Biot's number and the nondimensional crack length.

Thermal shock problem of a hollow circular cylinder with a crack

This paper deals with the thermal shock problem of an infinitely long, hollow, circular cylinder with an edge crack on the outer surface, initially at uniform temperature, being suddenly cooled on the circular surface. It is assumed that the thermal disturbance near the crack tip may be neglected. The transient thermal stress problem of the elastic solid with a crack is analyzed and the stress intensity factor at the crack tip determined. Simplified formulations of the nondimensional maximum transient stress intensity factor as a function of Biot's number, the nondimensional crack length, and the ratio of the inner radius to the outer radius are proposed.

THERMAL SHOCK PROBLEMS OF ELASTIC BODIES WITH A CRACK

This paper deals with thermal shock, problems of elastic bodies with a crack. The case considered is that of an infinitely long circular cylinder with an edge crack, and a homogeneous flat plate with an edge crack initially at uniform temperature and suddenly immersed into a medium of lower temperature. The thermal disturbance near the crack tip is assumed to be neglible in the analysis of the temperature field because thermal shocks occur very quickly. We analyze the transient thermal stress problems of elastic solids with a crack and determine the stress intensity factor at the crack tip. The nondimensional maximum transient stress intensity factor is expressed as a function of the Biot number and the nondimensional crack length. Then we propose simplified formulations of the nondimensional maximum transient stress intensity factor as a function of the Biot number and the nondimensional crack length.

Thermal shock problem of a circular cylinder with a crack.

This paper deals with the thermal shock problem of a flat plate with an edge crack, initially at uniform temperature, being suddenly cooled on the plate surfaces. It is assumed that the thermal disturbance near the crack surface may be neglected in the analysis of the temperature field of the elastic solid with a crack because thermal shock occurs rapidly. We analyed the transient thermal stress problem of a flat plate with a crack and determined the stress intensity factor at the crack tip. The nondimensional maximum transient stress intensity factor is expressed as a function of Biot's number and the nondimensional crack length. We then proposed a simplified formulation of the nondimensional maximum transient stress intensity factor as a function of Biot's number and the nondimensional crack length.

Stress intensity factor determination of radially cracked circular rings subjected to tension using photoelastic technique

A parametric study was carried out to determine the Stress Intensity Factor (SIF) in a cracked circular ring by using the photoelastic technique. The stress intensity factors for mode I deformation were determined by subjecting the specimens to the tensile loading from inner boundary and through the holes. The results of Non-Dimensional Stress Intensity Factor (NDSIF) variation with non-dimensional crack length for both methods of loading are compared with each other and with published results.

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N1(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.

Transient Thermal Load Effects on Coatings Bonded to Cylindrical Substrates and Containing Circumferential Cracks

The effect of a transient thermal load on a coating which is bonded to a cylindrical substrate is analyzed using fracture mechanics by considering the presence of a circumferential edge crack normal to the inner boundary of the coating. The solution is obtained using the finite element method and is compared to the exact solution of the problem. The analysis is then used to show that smaller heat transfer rates at the boundary result in smaller stress intensity factors. For three different materials combinations, including two ceramic coatings on metal, the nondimensional stress intensity factor has a similar magnitude for short crack lengths, but varies appreciably as the crack length becomes longer. It is also determined that inner coatings result in smaller or comparable stress intensity factors than thicker ones.