Makoto Obata

Branched cracks in anisotropic elastic solids

Branched crack problems are analyzed in two-dimensional, anisotropically elastic homogeneous solids. The method of analysis is based on the complex variable approach of Savin and Lekhnitskii. The Hilbert problem in an anisotropic body is defined, and a pair of singular integral equations are derived for dislocation density functions associated with a branched crack. For both symmetric and nonsymmetric geometries, and under symmetric and antisymmetric loads, the stress intensity factors and the energy release rate are computed numerically by extrapolation for infinitesimally small lengths of branched cracks. The results are compared with those of the isotropic case given in the literature and the effects of anisotropy are discussed.

On Stress Field Near a Stationary Crack Tip

Abstract It is well known that the stress and elastic-plastic deformation fields near a crack tip have important roles in the corresponding fracture process. For elastic-perfectly-plastic solids, different solutions are given in the literature. In this work we examine and compare several of these solutions for Mode I (tension), Mode II (shear), and mixed Modes I and II loading conditions in plane strain. By consideration of the dynamic solution, it is shown that the assumption that the material is yielding all around a crack tip may not be reasonable in all cases. By admitting the existence of some elastic sectors, we obtain continuous stress fields even for mixed Modes I and II.

Alternative solution methods for crack problems in plane anisotropic elasticity, with examples

Two-dimensional crack problems of homogeneous, anisotropic, linear elasticity are solved using the Riemann‐ Hilbert method. To this end, the Riemann‐Hilbert problem of line-discontinuity is formulated for anisotropic plane problems and the necessary parameters and functions are identified. For illustration, the method is applied to obtain the complete stress field and the stress intensity factors for a crack in an infinite anisotropic plate which is loaded on a part of one of its faces. Then, the well-established method of continuously distributed edge-dislocations is considered and illustrated via some example problems; e.g., an infinite anisotropic plate under uniform farfield loads containing: 1. a closed frictional crack and a pair of arbitrarily-located single edge-dislocations, and 2. an infinite row of equally-spaced parallel open cracks. The illustrative examples reveal that the first method oAers an eAective solution technique for problems where unbalanced tractions are applied on crack surfaces, whereas for problems with self-equilibrating loads applied on the crack faces, the second method is generally well suited. In addition, the method of resultant forces along the crack is discussed and its formulation in terms of the dislocation density functions and also the crack-opening displacements (which is new) is presented. The solutions to some of the example problems are provided in some detail, and for others, just the key formulae (e.g., stress functions and stress intensity factors) are calculated and analyzed. In brief, this paper presents the generalization of the Riemann‐Hilbert method from isotropic to anisotropic in-plane elasticity problems, and also provides a collection of certain basic two-dimensional anisotropic crack problems; some of the results here are also new. 7 2000 Elsevier Science Ltd. All rights reserved.

The failure mechanism and the pull-out strength of a bond-type anchor near a free edge

A bond-type anchor bolt has been used as a post-installed type anchor. Recent developments in construction technology have diversified the use of this type of anchor even in a new construction site. Since this type of anchor exhibits a complex failure mode involving cone and bond failure, its design method is still to be investigated in depth. Among the various conditions to be considered, we focus on the effect of a free edge on the pull-out strength both experimentally and analytically. We propose a new method to estimate the cone failure strength using the theory of linear fracture mechanics. The experimental results coincide well with the analytical estimation. The reduction of the strength is much larger than expected by the analysis based on the current design method.

Ultimate State of Thin-Walled Circular Steel Columns under Bidirectional Seismic Accelerations

The effects of coupling of two horizontal seismic acceleration components are investigated for the ultimate states of thin-walled circular steel columns used as bridge piers. Ultimate states of these columns are mainly governed by the instability caused by the local buckling at the lower part of the columns. First, an accurate bidirectional pseudodynamic experiment is carried out to examine their ultimate seismic behaviors as well as to confirm the accuracy of our nonlinear dynamic FEM shell analysis. The experiment showed that the columns under bidirectional seismic excitations suffer larger local buckling deformations than those under unidirectional excitations. Furthermore, the experimental results agree well with those obtained by the FEM analysis. Based on the so-called pushover analysis under monotonically increasing unidirectional horizontal displacement, two types of circular ultimate interaction curves for columns are derived in terms of two horizontal restoring force components and two sway displacement components. The validity of these two interaction curves is examined by the nonlinear dynamic shell analyses under various bidirectional seismic excitations. In this analysis, the ultimate states of columns are identified by the elastic-plastic stability theory. The numerical analysis shows that the ultimate interaction curves expressed by the horizontal restoring force components give a good prediction of the ultimate states of columns. For the sake of practical applications, a formula is derived to provide the ultimate interaction curves for arbitrary thin-walled circular columns.

Micromechanical consideration on the theory of elasto-plasticity at finite deformations

Abstract J 2 -based phenomenological plasticity has unchallengedly dominated the scene of the practical applications. However, when the finite deformations are involved, the proper way to generalize the theory is still under the debate. The objective of this work is to examine the phenomenological theory of elasto-plasticity at finite deformations in view of micromechanical plasticity which is based on the crystal plasticity and the averaging procedure. Both macro and macroscopic constitutive relations are discussed in terms of the multiplicative decomposition of deformation gradient. Plastic spin and backstress in phenomenological plasticity are investigated as the averaged quantities of microscopic counterparts. Instead of using the mathematical representation, a certain kinematic condition is assumed to define plastic spin. We, then, discuss the relation between the phenomenological and the micromechanical theories of elasto-plasticity.

A rigorous method for the analysis of localization of axisymmetric buckling patterns in thick cylindrical shells

This paper theoretically investigates the localization of axisymmetric buckling patterns in cylindrical shells because this phenomenon has a large influence on the strength degradation in the post-buckling range. The localization behavior is caused by a plastic bifurcation on the decreasing equilibrium path subsequent to the maximum load point. Thus, we first show a rigorous numerical method based on the finite-element method technique for analysis of plastic bifurcation under two-axial stresses. Then, using this method, we examine how the structural parameters, constitutive models and boundary conditions affect the deformation capacity of cylindrical shells.

Numerical simulation of adhesion of sea-salt particles on bridge girders

It is important to estimate corrosion environment of steel bridges for a proper corrosion prevention and maintenance program. The governing factors of corrosion are temperature, humidity and various dusts on the surfaces. Among them, the adhered sea-salt particulate matter (SSPM) is most important and therefore airborne SSPM near a bridge site must be considered in its design. To prevent degradation of protective paint, removal of adhered SSPM by wash out has been tried in some bridges. To this end, it is better to know the adhesion behaviour of SSPM to bridge girders. The objective of this manuscript is to pursue numerical method to simulate the adhesion behaviour of salt particles oriented from sea surface. Specifically, two scale approach is proposed. Mesoscale meteorological analysis and Lagrangian type two phase flow analysis are used in global and local analyses respectively. The comparisons between the numerical and observed results showed that the numerical analysis can reproduce essential behaviours of airborne SSPM.

On the analysis of fracture phenomena observed in steel structures during the Kobe earthquake

Publisher Summary During the Kobe earthquake, brittle fracture occurred in some of the steel structures. From the observation of fracture surface, the process of the brittle fracture is considered to occur as a sequence of three events: ductile crack initiation, ductile crack growth, and brittle crack propagation. This implies that the ductile crack initiation plays an important role in the brittle fracture. As a first step to assess the brittle fracture, this chapter examines the applicability of a finite element method (FEM) analysis based on the void damage theory to the simulation of the initial ductile failure. To deal with the ductile fracture under cyclic loads, such as seismic loads, the conventional void damage theory based on the Gurson model is modified to take into account the kinematic hardening rule in addition to the isotropic hardening rule for the constitutive relation of the base material. By the comparison between the FEM analysis and experiment, the chapter shows that the location of the ductile fracture in steel columns can be predicted by the FEM analysis based on the void damage theory. This implies that a lot of improvisation is needed in order to quantitatively predict the process of the ductile fracture under cyclic loading.

Numerical Estimation of Corrosion Environment by Airborne Sea Salt Particles

Anticorrosion of steel bridges has been an increasingly important problem in Japan. For a proper anticorrosion and maintenance program, it is important to estimate corrosion environment of steel bridges. In Japan, airborne sea salt generated from ocean is a predominant factor. Authors have been working on establishing a consistent framework to estimate corrosion environment numerically. It consists of a local and a global approach. While adhesion of airborne sea salt particles to bridge structures are simulated locally by a CFD analysis, the large scale analysis yields a boundary conditions of the local analysis and is given by a part of a mesoscale meteorological analysis. The objective of this work is to numerically investigate reliability of such large scale analysis in estimation of corrosion environment caused by airborne sea salt particles.