T. Nishioka

Analytical solution for embedded elliptical cracks, and finite element alternating method for elliptical surface cracks, subjected to arbitrary loadings

Abstract The complete solution for an embedded elliptical crack in an infinite solid and subjected to arbitrary tractions on the crack surface is rederived from Vijayakumar and Atluris general solution procedure. The general procedure for evaluating the necessary elliptic integrals in the generalized solution for elliptical crack is also derived in this paper. The generalized solution is employed in the Schwartz alternating technique in conjunction with the finite element method. This finite element-alternating method gives an inexpensive way to evaluate accurate stress intensity factors for embedded or elliptical cracks in engineering structural components.

Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics

In this paper the following topics are addressed: (i) the physical meaning of pathindependent integrals for elastodynamically propagating cracks introduced earlier by Atluri, Bui and Kishimoto et al. (ii) the relation of these integrals to the energy release rates, for propagating cracks and (iii) the relation between these integrals and the time-dependent stress-intensity factors KI(t), KII(t) and KIII(t) in general mixed mode dynamic crack propagation. Finally, a new path-independent integral which has the meaning of energy-release-rate for a propagating crack, is introduced.

Incremental path-independent integrals in inelastic and dynamic fracture mechanics

Abstract Certain incremental path-independent integrals, of relevance in the mechanics of fracture of elastic-plastic materials described by a classical flow theory of plasticity, are presented. Both quasi-static as well as dynamic fracture situations are considered. The topics discussed include: (i) incremental path-independent integrals that characterize the crack-tip fields in elastic-plastic materials; (ii) incremental integrals related to the incremental total potential energy difference; and (iii) the complementary or dual representations of these integrals. The use of these integrals is illustrated through some numerical examples. Comments are made on the utility of these integrals in postulating rational fracture criteria.

Multiple surface cracks in pressure vessels

Abstract An alternating method, in conjunction with the finite element method and a solution for multiple coplanar elliptical cracks in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The solution technique for multiple cracks in an infinite body has recently been developed by the present authors which implements a well-known analytical solution for a single crack in an infinite body. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. Numerical examples are presented for the situation of two equal surface cracks in a pressure vessel. Comparison is made between these results and the procedure for multiple cracks in the ASME Boiler and Pressure Vessel Code.

Numerical Analysis of Dynamic Crack Propagation: Generation and Prediction Studies.

Abstract Results of “generation” (determination of dynamic stress-intensity factor variation with time, for a specified crack-propagation history) studies, as well as “prediction” (determination of crack-propagation history for specified dynamic fracture toughness vs crack-velocity relationships) studies of dynamic crack propagation in plane-stress/strain situations are presented and discussed in detail. These studies were conducted by using a transient finite element method wherein the propagating stress-singularities near the propagating crack-tip have been accounted for. Details of numerical procedures for both the generation and prediction calculations are succinctly described. In both the generation and prediction studies, the present numerical results are compared with available experimental data. It is found that the important problem of dynamic crack propagation prediction can be accurately handled with the present procedures.

Stress analysis of holes in angle-ply laminates: An efficient assumed stress “special-hole-element” approach and a simple estimation method

Abstract In the present paper, the development of “special hole-elements”, to enable an efficient and accurate analysis of stress concentration around through-thickness holes in angle-ply laminates, is presented. In these “hole-elements”, the development of which is based on a modified complementary energy principle, the analytical asymptotic solutions for the stress-state near the hole are embedded. The fully 3-D stress-state in the laminate is accounted for, and the interlaminar traction reciprocity is satisfied a priori , while the interelement reciprocity condition is satisfied a posteriori through a Lagrange multiplier method. In addition, a simple method of estimation of stress concentration factors is also given. Results obtained from the present “special-hole-element” procedure are compared with the solutions by the present simple estimation method as well as other available solutions in literature.

Finite element simulation of fast fracture in steel DCB specimen

Abstract Results of a numerical simulation, based on an energy consistent moving singularity dynamic finite element procedure, of fast crack propagation and arrest in a high strength steel DCB specimen are presented. The influence of material properties of high strength steel on dynamic crack propagation and arrest is investigated. The influence of the loss of constact of specimen with the loading wedge is also critically examined. The present numerical results are compared with available experimental data. It is found that the present results agree well with available experimental data, and the crack arrest toughness values obtained in the present analysis correlate well with the ratio of the maximum kinetic energy of the specimen to the input energy.

An evaluation of several moving singularity finite element models for fast fracture analysis

Abstract In this paper, several formulations of moving-singularity finite element procedures for fast fracture analysis are evaluated as to their accuracy and efficiency.

Crack-tip parameters and temperature rise in dynamic crack propagation

Abstract This paper presents a discussion of (i) possible crack-tip parameters that may govern elastodynamic crack propagation in the presence of nonuniform temperature fields, material inhomogeneity, etc.; (ii) possible crack-tip parameters in elastoplastic dynamic fracture; and (iii) the temperature field near the crack tip due to the propagating inelastic zone in which heat is generated.

A method for determining dynamic stress intensity factors from cod measurement at the notch mouth in dynamic tear testing

Abstract A formula is derived for determining dynamic stress intensity factors directly from crack mouth opening displacements in dynamic tear test specimen. The results obtained by the present estimation method for stationary as well as propagating cracks agree excellently with those directly obtained through a highly accurate moving-singularity finite element method. The present method can also be applied for other types of specimen which have a relatively short edge crack without any loading on the crack surface. The present simple estimation method should be of great value in the experimental measurement of dynamic stress-intensity factors for propagating cracks in (opaque) structural steel dynamic tear test specimens.