Yoichi Sumi

On crack path stability in a finite body

Abstract Theoretical and numerical investigations are made for crack path stability in a finite brittle solid under a predominantly Mode I loading condition. Based upon a first order perturbation solution, an“intermediate” range of stability (as compared with the “local” and “global” ranges) is introduced for the crack growth path. This theory is an extension of the stability concept proposed by Cotterell and Rice, but includes the effect of the change of the stability with increasing crack length along the curved trajectory. Four kinds of crack paths are identified: (i) stable, (ii) initially unstable but intermediately stable, (iii) initially stable but intermediately unstable, and (iv) unstable ones. The first two conditions may lead to stable (i.e. straight) crack growth, while the remaining conditions may lead to an unstable (i.e. sharply curved) crack path. Crack path stability is examined for a biaxially stressed Griffith crack. Then numerical results are given for compact tension and double-cantilever beam specimens for various initial crack lengths. In the numerical examples of compact tension specimens, crack paths are sometimes predicted as unstable by the Cotterell-Rice theory, while stable crack paths are always obtained by using the present theory. On the other hand. unstable crack paths are predicted for double-cantilever beam specimens, except for the eases with extremely long initial cracks. The numerical estimates of crack path stability presented here are in good agreement with experimental observations.

Computational crack path prediction

Abstract A computer program has been developed for the numerical prediction of curved crack growth paths under proportional loading conditions. The numerical prediction is performed by the step-by-step method in cooperation with the stress analysis ahead of the crack tip and the determination of the curved increment of the crack growth. The stress analysis is performed by the method of superposition of analytical and finite-element solutions, and the results are then utilized to determine the coefficients of the analytical expression of the curved crack path obtained by the first order perturbation method. The first numerical example is given for the crack path prediction in DCB-type specimen, where we often observe abrupt crack curving. Computational prediction is performed by introducing slight and small initial branching at the original crack tip. Within few steps of numerical calculations unstable crack curving is obtained, and the predicted path shows extremely good agreement with the experimentally measured path. The second numerical prediction is made for an edge crack approaching a circular hole, which may be considered as a crack arrester. In the present case the effect of the initially introduced slight kink diminishes with increasing crack length. The crack turns back to the original direction, resulting arrest at the hole.

Fatigue crack propagation and computational remaining life assessment of ship structures

The fitness for serviceability of structural members of marine structures in which fatigue cracks might be found during in-service inspection is investigated in order to prevent instantaneous failures of ships, as well as a loss of serviceability such as the oil- and/or watertightness of critical compartments. The essential features of fatigue crack propagation and the remaining life assessment are discussed in the first part of the paper, where the effects of weldment, complicated stress distributions including stress biaxialities at three-dimensional structural joints, structural redundancy, and crack curving are found to be of primary importance. The second part of the paper contains a discussion of an advanced numerical simulation method for the remaining life assessment, in which the above-mentioned effects of fatigue crack propagation are taken into account. The simulated crack paths and the fatigue crack propagation lives are found to be in fairly good agreement with the experimental results.

A finite-element simulation method for a system of growing cracks in a heterogeneous material

Abstract In this paper a numerical simulation method is proposed for the growth of interacting non-collinear cracks in a finite, heterogeneous, and two-dimensional elastic solid. The stress analysis is based on a step-by-step finite element method using the method of superposition of analytical and finite-element solutions accompanied by the quadtree automatic mesh generation algorithm. An incremental crack growth pattern is predicted considering the interaction of all growing cracks by the Schwartz–Neumann alternating procedure using a first order perturbation solution of slightly kinked and curved extension of all growing cracks, which analytically gives the mixed mode stress intensity factors at extending crack tips. The local symmetry criterion is used as the crack path criterion at the extending crack tips. Several numerical examples, including the avoidance of collinear edge cracks and cracks initiated at the ends of fibers show the validity of the present simulation method.

Morphological aspects of fatigue crack propagation Part II—effects of stress biaxiality and welding residual stress

In order to maintain structural integrity of welded structures, it is of great importance to evaluate the fitness for serviceability of the structural components, in which fatigue cracks are found during in-service inspections. Crack propagation paths are sometimes prerequisite for the proper estimation of fatigue crack propagation, because curved crack paths and sharp crack turning could occur at the intersections of structural members mainly due to stress biaxiality of repeated loads. In order to investigate this fatigue crack-growth behavior, fatigue crack-propagation tests and numerical simulation are carried out under various biaxial stress range ratios. Morphological mode transitions of fatigue failures are observed in experiments and also by computer simulation. Although simulated modes of failures are in fairly good agreement with the experimental results, discrepancies are sometimes observed for the crack-propagation lives. In order to investigate this problem, the welding residual stresses in the test specimens are measured, and the fatigue crack-propagation lives are quantitatively examined in terms of the combined effects of residual stress distribution and crack paths.

Morphological aspects of fatigue crack propagation Part I—Computational procedure

In the present paper a simulation method is proposed for the evaluation of paths and lives of fatigue cracks. The simulation is based on an incremental crack extension procedure. At each increment the stress analysis ahead of a crack tip is carried out by the finite element method, and the next incremental crack-growth path is predicted by the first order perturbation method with the use of the local symmetry criterion. From the computational viewpoint, the step-by-step rezoning of finite element mesh subdivision is one of the most difficult processes of the simulation procedure. In order to overcome this difficulty, we shall use the modified quadtree method as an automatic mesh generation technique. Considerations are made for the proper mesh arrangement in the vicinity of a crack tip, where a special fine mesh pattern is embedded so that mixed mode stress intensity factors and the higher order coefficients of the near tip stress field parameters can accurately be obtained. Using the proposed method, we simulate the branched and curved fatigue crack growth in three-point-bending specimens. They show fairly good agreement with the experimental results. The simulation procedure is also applied to biaxially loaded cruciform joints.

Thermally induced quasi-static wavy crack propagation in a brittle solid

Morphological aspects of thermally induced brittle cracks are revisited. The formation of a growth pattern of cracks, which are subjected to the thermal loading due to the penetration of surface cooling, has formerly been studied for a system of parallel interacting straight cracks. In the present paper, attention is focused on the transition from straight to wavy crack propagation. The incremental extension of a curved crack is predicted by using the local symmetry criterion, where the step-by-step stress analyses are carried out by the finite-element method with the aid of an automatic mesh generation which is based on the paving method. Varieties of numerical results are obtained so that the influencing factor which may control the wavy crack paths is identified. Discussions are also made by comparing the numerical results with experimental observation.

A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure

One of the demands for three dimensional (3D) finite element analyses is the development of an automatic hexahedral mesh generator. For this problem, several methods have been proposed by many researchers. However, reliable automatic hexahedral mesh generation has not been developed at present. In this paper, a new strategy of fully automatic hexahedral mesh generation is proposed. In this strategy, the prerequisite for generating a hexahedral mesh is a quadrilateral surface mesh. From the given surface mesh, combinatorial dual cycles (sheet loops for the whisker-weaving algorithm) are generated to produce a hexahedral mesh. Since generating a good quality hexahedral mesh does not depend only on the quality of quadrilaterals of the surface mesh but also on the quality of the sheet loops generated from it, a surface mesh modification method to remove self-intersections from sheet loops is developed. Next, an automatic hexahedral mesh generator by the improved whisker-weaving algorithm is developed in this paper. By creating elements and nodes on 3D real space during the weaving process, it becomes possible to generate a hexahedral mesh with fewer bad-quality elements. Several examples will be presented to show the validity of the proposed mesh generation strategy.

Analysis of the accident of the MVNakhodka. Part 2. Estimation of structural strength

In the early morning of January 2, 1997, a Russian tanker, the MVNakhodka, broke in two in the Sea of Japan. The fore part of the vessel drifted and was stranded on the coast of Japan, and the aft part sank. The coast of Japan was seriously polluted by spilled heavy oil. Following this disaster, the Japanese Government established a Committee for the Investigation of the Causes of the Casualty of theNakhodka. This paper deals with the structural strength of MVNakhodka at the time of the accident. First the structural characteristics of theNakhodka are described, and the reduction in thickness of the structural members are estimated based on the data measured on the fore part of the vessel which drifted ashose. Then the ultimate longitudinal strength of the hull girder at the time of the accident is evaluated by applying Smiths method, and the possibility of break-up collapse due to excess loads is discussed. The mechanism of fracture at the bottom plate is also discussed based on the observed fracture surfuce of the cross section. Finally an FEM (finite element method) simulation of the break-up of the hull girder is performed. It is shown that buckling/plastic collapse took place at the deck plate near Fr.153, which was followed by the successive buckling collapse of the side shell plate of the hull girder. Right after the collapse of the deck structure, the bottom plate fractured just in front of the transverse bulkhead at Fr.153.

Computational Crack Path Prediction Applied to Crack Arrestability by a Circular Hole

A computational scheme has been developed for the crack path prediction, which is performed by the step-by-step stress analysis ahead of the crack tip and the prediction of a curved icrement of the crack growth by the use of analytically expressed crack path in the neighbourhood of the crack tip. In this paper we consider the cases, where an edge crack in a plate has been initiated under tension and is approaching a circular hole. The present computational crack path prediction is applied to examine the crack arrestability by the hole. Crack paths observed in the corresponding experiments are found to be in good agreement with the computational predictions.