Toshihisa Nishioka

Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements—Part 1: Formulation

An efficient numerical (finite element) method is presented for the dynamic analysis of rapidly propagating cracks in finite bodies, of arbitrary shape, wherein linear-elastic material behavior and two-dimensional conditions prevail. Procedures to embed analytical asymptotic solutions for singularities in stresses/strains near the propagating crack-tip, to account for the spatial movement of these singularities along with the crack-tip, and to directly compute the dynamic stress-intensity factor, are presented. Numerical solutions of several problems and pertinent discussions are presented in Part II of this paper.

Further studies on elastic-plastic stable fracture utilizing the T∗ integral

Abstract Herein, the T ∗ fracture parameter is shown to have relevance to the mechanics of elastic-plastic fracture. Specifically, it is shown to have certain advantages over the currently established plastic fracture parameters such as J and CTOA. Finite element analyses of experimental data were carried out as a means to obtain a comparison of the effectiveness of the plastic fracture parameters. T ∗ is clearly superior. A note on problems associated with satisfying the plastic incompressibility constraint is also included.

Dynamic fracture-path prediction in impact fracture phenomena using moving finite element method based on Delaunay automatic mesh generation

First, this paper presents the concept of mixed-phase simulation with fracture-path prediction mode which uses a postulated propagation-direction criterion together with experimentally obtained crack propagation history. Furthermore, this paper presents the development of an automatic moving finite element method that incorporates the Delaunay automatic triangulation. Using the automatic moving finite element method, the mixed-phase simulation with fracture-path prediction mode is carried out for mixed-mode impact fracture tests. Various dynamic fracture mechanics parameters are evaluated by the path-independent dynamic J integral. The moving finite element method in conjunction with the local symmetry (KII=0) criterion successfully predicts the numerical fracture path in excellent agreement with experimentally obtained actual fracture path.

Fracture of piezoelectric materials: energy density criterion

Abstract In this paper, the concept of energy density factor S for piezoelectric materials is presented. In addition to the mechanical energy the electrical energy is included as well. The direction of crack initiation is assumed to occur when Smin reaches a critical value Scr that can be used as an intrinsic materials parameter and is independent of the crack geometry and loading. The result agrees with empirical evidence qualitatively and explains rationally the effect of applied electric field on fracture strength: positive electric fields decrease the apparent fracture toughness of piezoelectric materials while negative electric fields increase it.

Analysis of Surface Flaw in Pressure Vessels by a New 3-Dimensional Alternating Method

An alternating method, in conjunction with the finite element method and a newly developed analytical solution for an elliptical crack in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. The problems considered in the present paper are: (/) an outer semi-elliptical surface crack in a thick cylinder, and (ii) inner semi-elliptical surface cracks in a thin cylinder which were recommended for analysis by the ASME Boiler and Pressure Vessel Code (Section III, App. G, 1977). For each crack geometry of an inner surface crack, seven independent loadings, such as internal pressure loading on the cylinder surface and polynomial pressure loadings from constant to fifth order on the crack surface, are considered. From the analyses of these loadings, the magnification factors for the internal pressure loading and the polynomial influence functions for the polynomial crack surface loadings are determined. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived by using the polynomial influence functions to check the internal consistency of the present analysis. These values agree excellently with the magnification factors obtained directly. The present results are also compared with the results available in literature.

Nonlinear electromechanical interfacial fracture for piezoelectric materials

Abstract This work is concerned with the analytical characterization of the electromechanical nonlinear effects on the fields surrounding the tip of an interface crack between ferroelectric-plastic bimaterials. A strip electric saturation and mechanical yielding model is developed for a mode III interfacial crack with electrical polarization reaching a saturation limit and shear stress reaching a yield stress along a line segment in front of the crack. The electrical saturation zone and mechanical yielding zone may have different length scales depending on loading conditions. This model may be considered as a generalization of the classical Dugdale model for plastic yielding near cracks in homogenous materials. The results reveal insight into the structure of stress and electric displacement fields for different load conditions. The energy release rate and COD δ III are also obtained, which indicates the possibility of fracture criterion based on the COD δ III .

An alternating method for analysis of surface-flawed aircraft structural components

A new alternating method for the analysis of a quarter-elliptical corner crack is developed. The completely general analytical solution for an embedded elliptical crack in an infinite solid, subject to arbitrary crack-face tractions, is implemented in the present alternating method. The present finite element alternating method results in an inexpensive procedure for the routine evaluation of accurate stress intensity factors for flawed structural components. The present alternating method is applied to the analyses of various shapes of quarterelliptical corner cracks: 1) in a brick subject to remote tension, 2) emanating from a hole in finite-thickness plates subject to remote tension as well as bearing pressure; and 3) emanating from a pin hole in aircraft attachment lugs subject to simulated pin loading. The results for problems 1 and 2 are compared with those available in literature, for problem 3 the stress intensity factors and their parametric variations for the corner cracks of various shapes are presented.

An intelligent hybrid method to automatically detect and eliminate experimental measurement errors for linear elastic deformation fields

In a previous study, to minimize or eliminate the errors and noises associated with a full-field experimental measurement and subsequent fringe analysis such as moiré interferometry, the authors derived a variational principle minimizing the experimental measurement errors. Furthemore, on the basis of this variational principle, the authors developed an intelligent hybrid method. In several test simulations, the method has demonstrated the automatic detection and elimination of randomly incorporated errors into known correct finite element displacement fields. In this study, a fringe analysis method is developed together with the two-dimensional fast Fourier transform method. Then, experimentally recorded moiré fringe patterns are analyzed by the fringe analysis method. The conventional and intelligent hybrid analyses are carried out using the analyzed fringe information as input data. The present method verifies the automatic detection of experimental errors and noises, and the simultaneous automatic elimination of those experimental errors. This method also makes it possible to obtain a fairly smooth visualization of higher order information such as the stress and strain distributions.

The use of the dynamic J integral (J′) in finite-element simulation of mode I and mixed-mode dynamic crack propagation

Abstract This paper summarizes recent theoretical and computational studies on the dynamic J integrals ( J′ ) and the moving-finite-element procedures for the simulation of dynamic crack propagation. The following topics are included: (i) invariance of the elastodynamic J integral ( J′ ), with respect to the shape of an infinitesimal process zone, (ii) a component-separation method for determining the mixed-mode stress-intensity factors using the path-independent integrals J′ k ( k = 1,2 ), (iii) the moving-finite-element method aided by computerized symbolic manipulation, and (iv) a concept of an element-controlling plane based on Lagrangian-element mapping, for the simulation of dynamic crack-curving. Pertinent numerical results in each topic are also included.

Analysis of Interaction Behavior of Surface Flaws in Pressure Vessels

The evaluation of stress intensity factors for surface flaw problems and, in particular, semi-elliptical surface cracks in cylindrical pressure vessels has been well developed using the finite element alternating method. Some of the examples presented here include the interaction effects due to multiple internal longitudinal surface cracks in cylinders as recommended for analysis in the ASME Boiler and Pressure Vessel Code (Section XI). For each crack geometry, several loading cases are considered including internal pressure and polynomial pressure loadings from constant to fourth order. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived using the polynomial influence functions. These influence functions give useful information for design purposes such as in the analysis of a thermally shocked cylinder. The problem of a single circumferential crack in a cylinder is also investigated using the finite element alternating method, and a number of results for such problems are also presented here.