Akihide Saimoto

Effectiveness of Two-Dimensional Versatile Program Based on Body Force Method and its Application to Crack Problems

Body force method (BFM) was originally proposed in 1967 as a general technique for the stress analysis of notch and crack problems. The concept of BFM is to express the stress fields of elastic problems by means of superposition of point force solutions. BFM has been provided a number of highly accurate solutions of practical problems by developing special programs suitable for individual problems. In 1990, a versatile program based on BFM for general 2D problems was developed by considering the research fruits obtained until then. Due to the exploitation of this versatile program, it became possible to obtain highly accurate solutions of various 2D elastic problems even by using standard PCs. This paper describes how useful the versatile program based on the BFM is. As numerical examples, several solutions of selected problems including crack propagation/coalescence analysis are demonstrated. Introduction Body Force Method (BFM) is a boundary type technique for stress analysis originally proposed by H. Nisitani[1, 2]. The most distinguished characteristic of the BFM is its numerical accuracy. A proper BFM program provides the practically-exact solution even using the relatively coarse mesh division. Some of the fruits obtained through the studies of the BFM have been inserted in technical documents or handbooks. For example, the stress intensity factors handbook Vol.1 edited by Y. Murakami et. als.[3] gives 265 crack solutions totally and quotes 71 crack solutions from technical papers based on the BFM. In this paper, firstly, the basic concept of the BFM is described by taking a problem of an elliptic hole as an example. Then the characteristics of the versatile program for 2D-elastic problems named BFM2D is mentioned[4]. In this versatile program BFM2D, various techniques which improve the accuracy of solutions and save the calculation time as well as the memory space of computer are used. Finally, numerical solutions of selected problems are shown. BFM2D works well on standard PCs and actualizes highly accurate analyses especially for crack problems. Basic concept of the BFM The original paper of the BFM published in 1967 paid attention mainly to how to calculate the 2D stress concentration problem by using a digital computer. Then the BFM was extended so as to apply various situations such as the 3D-problems, the elastic–plastic problems[5], elastodynamic problems[6], thermoelastic problems[7] and so on. In the BFM, an elastic boundary value problem is transformed into the form of integral equation. The transformation is conducted intuitively and concisely by means of the principal of superposition. Taking Fig.1 as an example, the procedure of transformation is explained. The purpose of the transformation is to determine the stress at P of Fig.1(a). The original shape of elliptic hole is denoted by Γ and its deformed shape by Γ respectively. In order to analyze this problem, the following two regions Key Engineering Materials Online: 2003-10-15 ISSN: 1662-9795, Vols. 251-252, pp 97-102 doi:10.4028/www.scientific.net/KEM.251-252.97

Development of a magnetic sensing device for tooth displacement under orthodontic forces

The authors are developed a system for measuring tooth displacement from orthodontic force. Eight small magnetic sensors and a magnet are combined to measure three-dimensional displacement. Sensors, arranged cubically in the three planes of space, are placed in the mouth and fixed to the posterior teeth by a splint. A magnet is placed in the center of the 8 sensors and attached to a front tooth that is subjected to orthodontic force. Sensors detect the magnets movement as target tooth displacement. The system was designed to achieve displacement resolution of 1 /spl mu/m. The mean percentage of measurement errors was determined to be less than 1% in a 600-cubic-/spl mu/m volume from calibration. The system was tested clinically on human teeth. Although the oral environment, with high temperature and humidity, was not agreeable with the sensors, this system was stable and accurate enough for quantitative measurement of tooth displacement. The advantage of this system is the ability to detect tooth trajectories by decomposing displacement into translation and rotation and to determine the position of the center of rotation from these parameters.

Accurate Solutions of Stress Intensity Factors of Standard Fracture Test Specimens

Practically exact solutions of stress intensity factor for several two-dimensional standard specimens were calculated and shown in numeric tables. The solutions were confirmed to converge until 6 significant figures through a systematical computation of discretization analysis. The convergence analyses were carried out by using a general purpose program based on a body force method.

Crack Growth Behavior in Overloaded Specimens with Sharp Notch in Low Carbon Steel

The purpose of the present study is to evaluate fatigue crack propagation after tensile overloading. A 6-mm long u-shaped notch was cut in the center section of the specimen. Notch root radii of 0.1, 1, and 2 mm were chosen for ρ. These were regarded as center-notched specimens. The crack propagation behavior of these specimens was compared with a center-cracked specimen. Push-pull fatigue tests were carried out under stress ratios R=0, −1, and −1.5. A special investigation was made into the results for ρ=1 mm. After overload, retardation of crack growth was observed under R=0 and −1 for the notched specimens and center-cracked specimens. However, where R=−1.5, crack growth acceleration was observed after overload in both types of specimens. Even though crack growth was accelerated or decelerated, the rate was able to be evaluated by the effective stress intensity factor range after 0.2 mm of crack growth from the notch root.

Short history of body force method and its application to various problems of stress analysis

Body force method (BFM) was originally proposed in 1967 as a general technique for the stress analysis of notch and crack problems. The concept of BFM is to express the stress fields of elastic problems by means of superposition of point force solutions. In principle, any problem of individual shape and boundary conditions is transformed into a problem of an infinite region without any holes, cracks or external boundary. BFM has provided a number of highly accurate solutions. Some of these have been inserted in technical documents or handbooks. In this paper, firstly, a short history of BFM is described. Then the fundamental principle of BFM is explained. As numerical examples, some useful solutions of 2D and 3D crack problems are shown.

The Genesis of Echelon-Mode-I Cracks in the Neighbourhood of a Mode-II-Crack Tip under Uniaxial Compression

Abstract. The mechanical background why the compressed brittle material fails in a shear mode is studied. Compression-induced shear fracture was experienced in a standard compression test of cylindrical mortar sample whereas a mode I crack branching almost parallel to compression was dominant in a cracked specimen. In a uniaxial compression test of artificially-flawed PMMA plate, formation of a number of minute-surface cracks (en echelon cracks) as well as growth of wing cracks emanated from the artificial flaw tips were observed. The damage zone composed by en echelonmode-I cracks can be considered as a possible source of the macroscopic shear faulting. The relevance between the genesis of en echelon cracks and the compression-induced shear failure is discussed based on experimental observations and numerical analyses.

The Critical Angle for Perforation versus Ricochet of a .38 CAL. LRN Bullet on a Windshield.

From forensic point of view, it is important to clarify the condition whether ricochet or perforate for a bullet fired toward the automobile windshield. The purpose of this study was to specify the critical angle at which the ricochet of the fired bullet takes place. To estimate the result of firing, a rigid‐body dynamics simulation of the bullet together with the test‐firing using .38 CAL. LRN bullet was examined. It was found both from numerical simulation and firing test that when the incidence angle is <45°, a complete perforation of the windshield was observed, whereas the bullet ricocheted remaining a characteristic damage on the windshield when the incidence angle is >60°. To measure the static failure resistance of various windshields, static indentation test was also examined.

Evaluation of Accuracy for 2D Elastic–Plastic Analysis by Embedded Force Doublet Model Combined with Automated Delaunay Tessellation

An embedded force doublet (EFD) model is proposed to express the presence of permanent strain in body force method (BFM). BFM is known as a boundary type method for elastic stress analysis based on the principle of superposition. In EFD model, the permanent strain is replaced by distributed force doublets. In an actual elastic–plastic analysis, the plastic region whose shape is not clear a priori, have to be discretized into elements where the magnitude of embedded force doublets is unknown to be determined numerically. In general, the determination process of magnitude of EFD is considerably difficult due to nonlinear nature of yield criterion and plastic constitutive relations. In this study, by introducing the automated Delaunay tessellation scheme for discretizing the prospective plastic region, appreciable reduction in input data was realized. Adding to this, in order to improve the computational efficiency, influence coefficients used for determining the magnitude of EFD are stored in a database. Th...

An eigenstrain-based model for residual stress arising from transient local surface heating

We present a model for approximating residual stresses arising from thermally induced plasticity and apply it to a simple two-dimensional (plane strain) test problem of transient heating. The model uses stress fields derived from simple eigenstrains to perturb an initially elastic-only solution in a way that mimics plastic flow. The plane strain condition of the test problem gives rise to plastic strains in the out-of-plane direction, owing to constraints on thermal expansion. However, the model is able to cope with the challenges this poses and also encapsulates the time-dependent nature of the problem. We show that the model agrees well with finite-element simulations under moderate strength heat sources provided that appropriate plastic flow rules are used. There exists sufficient generality in the model to allow its extension to more realistic scenarios.

Simulation of Propagation and Localization of Minute Cracks Near a Mode II Crack Tip under Compressive Stresses

The failure behavior of brittle solids under compressive stresses is discussed. It is known that the failure mode of brittle solids under compressive stresses depends strongly upon specimen geometry and loading conditions. A plate specimen often exhibits a split-type fracture characterized by mode I cracks that propagate almost parallel to the direction of compression. On the other hand, a pseudo-mode II fracture in which the failure plane is inclined from the axis of compression can be observed in a compression test of a cylindrical specimen. In the uniaxial compression test of plate-type mortar and PMMA specimens, the macroscopic fracture was dominated by the appearance of mode-I wing cracks and their propagation. However, in a neighborhood of an artificial crack tip, a considerable damage zone was also observed. In order to investigate the mechanism for a formation of damage zone, numerical analyses base on the linear elastic fracture mechanics were carried out. It was found that the damage zone is composed of an echelon of mode I micro-surface cracks and the inclination of the damage zone is about 30° from the axis of compression.