Keiji Yanase

Effective Elastic Moduli of Spherical Particle Reinforced Composites Containing Imperfect Interfaces

The effective elastic moduli of composite materials are investigated in the presence of imperfect interfaces between the inclusions and the matrix. The primary focus is on the spherical particle reinforced composites. By admitting the displacement jumps at the particle–matrix interface, the modified Eshelby inclusion problem is studied anew. To derive the modified Eshelby tensor, three approximate methods are presented and compared by emphasizing the existence of a unique solution and computational efficiency. Subsequently, the effective elastic stiffness tensor of the composite is formulated based on the proposed micromechanical framework and homogenization. Specifically, by incorporating imperfect interface, the modified versions of the Mori–Tanaka method, the self-consistent method, and the differential scheme are presented. By comparing these three methods, the effects of interfacial sliding and separation on the degradation (damage) of the effective elastic moduli of composites are analyzed and assessed. Finally, a critical aspect of the presented formulations is specifically addressed.

Micromechanical Elastoplastic Damage Mechanics for Elliptical Fiber-Reinforced Composites with Progressive Partial Fiber Debonding

By considering progressive interfacial partial debonding, a multi-level elastoplastic damage formulation is proposed to predict the overall transverse behavior of continuous elliptical fiber-reinforced metal matrix composites within the framework of micromechanics and homogenization. Based on the method of equivalent inclusion and taking the evolutionary interfacial debonding angle into consideration, partially debonded isotropic elliptical fibers are replaced by equivalent orthotropic yet perfectly bonded elliptical fibers. Three interfacial damage modes are considered. The Weibull’s probabilistic function is employed to describe the varying probability of progressive partial fiber debonding. The effective elastic moduli of four-phase composites, consisting of a ductile matrix and randomly located yet unidirectionally aligned elliptical fibers are derived via a micromechanical formulation. Further, the explicit exact exterior-point Eshelby’s tensor for an elliptical fiber is presented to investigate its effects upon inelastic responses of composites due to the cross-sectional shapes of fibers. In order to characterize the overall transverse elastoplastic damage behavior, an effective yield function is derived based on the ensemble-area averaging and the first-order effects of eigenstrains upon the overall yielding. Finally, comparisons between the present predictions and experimental data, and biaxial simulations are performed to illustrate the potential of the proposed framework.

Size-dependent Probabilistic Micromechanical Damage Mechanics for Particle-reinforced Metal Matrix Composites

A size-dependent micromechanical framework is proposed to predict the deformation responses of particle-reinforced metal matrix composites by incorporating the essential features of the dislocation plasticity. Within the framework of probabilistic micromechanical formulation, the damage caused by the manufacturing process and by the external mechanical loading in the presence of thermal residual stresses is considered. The effective elastic moduli of four-phase composites, consisting of a ductile matrix and randomly located spherical intact or damaged particles are derived. Subsequently, the size-dependent plastic deformation behavior of particle-reinforced metal matrix composites is predicted with a dislocation theory. Specifically, the density of dislocations due to the thermal contraction misfit and the plastic deformation misfit is taken into consideration within the micromechanical methodology to account for the dislocation strengthening. To predict the overall elastoplastic damage behavior of composites, a size-dependent hybrid effective yield function is presented on the basis of the ensemble-volume averaging and the modified matrix yield strength. The comparisons between our predictions and available experimental data illustrate the potential capability of the proposed framework. Numerical simulations are also performed to exhibit the salient features of the proposed methodology.

High-cycle fatigue threshold behaviors in notched plates

This article investigates the threshold behavior of fatigue crack emanating from an elliptical hole. The theoretical framework accounts for the presence of plastic zone ahead of the crack tip and the crack-closure development. To predict the threshold behavior, both the crack deriving force and the resisting force are considered. The crack deriving force (i.e. applied stress intensity factor) is calculated based on the plane elasticity theory and linear-elastic fracture mechanics. Based on the proposed computational framework, the fatigue limit, the length of non-propagating crack and the notch-size effect are simulated in a systematic manner. By conducting a series of comparisons between the theoretical predictions and the available experimental data, the predictive capability of the proposed method is examined and discussed.

Overall elastoplastic damage responses of spherical particle-reinforced composites containing imperfect interfaces

As a predominant damage mode, the interfacial damage between the reinforcements and the matrix is of importance for the composite materials. Correspondingly, in this paper, the effects of imperfect interfaces are systematically investigated in the framework of higher order micromechanics and homogenization. To examine the effects of imperfect interfaces, the equivalent stiffness of reinforcing particles is considered based on the spring interface model. By taking advantage of the equivalent stiffness, the effective stiffness and the effective yield function of a composite are systematically derived to study the overall elastoplastic damage behaviors of particle-reinforced composites. In the absence of damage, comparisons between the theoretical predictions and the available experimental data are presented to illustrate the predictive capability of proposed micromechanical framework. Subsequently, a series of parametric studies are performed to examine the characteristics of the proposed micromechanics-based damage formulation.

Toughening behavior of unidirectional fiber reinforced composites containing a crack-like flaw: Matrix crack without fiber break

The Mode-I stress intensity factors of unidirectional fiber reinforced composites are studied based on the framework of linear elastic fracture mechanics. As one of the dominant damage mechanisms, a matrix crack in the absence of fiber break is considered here. The bridging of crack faces is assumed a principal toughening mechanism in the unidirectional fibrous composites. Based on a frictional shear–slip relationship, the effect of fiber-bridging mechanism is reflected as the toughening mechanism of unidirectional fibrous composites. On computational scheme, Newton’s method is adopted to solve the governing simultaneous equations for the fiber-bridging stresses and the crack mouth opening displacements. By making use of the proposed computational framework, a series of parametric studies is carried out to examine the effects of key material parameters upon the toughening of fibrous composites in a systematic manner.

A New Fatigue Testing Machine for Investigating the Behavior of Small Shear-Mode Fatigue Cracks

The investigation of the behavior of small shear-mode fatigue cracks in the high-cycle fatigue regime is essential to understand the mechanism of rolling-contact fatigue failures, such as flaking in bearings and shelling in rails, from the fracture mechanics point of view. The stable growth of a shear-mode fatigue crack was achieved by applying static compression to a specimen in a cyclic torsion fatigue test. This loading condition is usually obtained by a combined tension-torsion testing machine with a servo-hydraulic control system. In this study, a new testing machine was developed and found to be superior to the servo-hydraulic testing machine in terms of price, operation/maintenance costs, operating speed, and installation volume. For substantiation and demonstration purposes, a shear-mode fatigue crack growth test with a bearing steel was also carried out using both the new and the conventional servo-hydraulic testing machines. The experiments revealed that under the same loading conditions, nonpropagating shear-mode cracks of similar size and geometry could be obtained by the respective testing machines. Thus, it was concluded that the new testing machine has equivalent capabilities to the servo-hydraulic testing machine in performing shear-mode fatigue crack growth tests.

A Study on the Multiaxial Fatigue Failure Criterion with Small Defects

This paper reexamines a multiaxial fatigue failure criterion in the presence of small defects. The criterion is based on the assumption that a Mode-I crack on a specified plane, termed a critical plane, plays a dominant role in the determination of fatigue strength. The present study extends previous research to propose a modified failure criterion in conjunction with a systematic computational scheme, and to conduct a detailed analysis of its predictive capability. Using the proposed computational scheme, the applied stress level for the multiaxial fatigue failure can be efficiently predicted for both in-phase and out-of-phase loadings. Additionally, a series of parametric studies was conducted to examine the materials sensitivity to the biaxial stress state with respect to the fatigue strength.

Analysis of the Notch Effect in Fatigue

The fatigue-crack propagation at stress concentrations is a topic of significant importance in a number of engineering applications. Further, it is recognized that the fatigue limit of notched components is dictated by the critical condition for either initiation or propagation of a small crack at the root of a notch. Moreover, because most fatigue cracks spend the vast majority of their lives as short cracks, the behavior of such a flaw is of significant importance. In the literature, McEvily and co-workers [McEvily, A. J., Eifler, D., and Macherauch, E., “An analysis of the Fatigue Growth of Short Fatigue Cracks,” Eng. Fract. Mech., Vol. 40, No. 3, 1991, pp. 571–584] developed a modified linear elastic fracture mechanics (LEFM) approach to tackle a number of fatigue problems, including the growth and threshold behavior of small fatigue cracks. In this study, a further extension is presented to deal with notch effects in fatigue. In this method, the elastic–plastic behavior and the crack closure are taken into account, as the major factors responsible for the peculiar behavior of small fatigue cracks emanating from notches. In the present paper, the notch effect in fatigue is systematically investigated by making use of a mechanism-based computational framework. A series of parametric studies demonstrate the predictive capability of the proposed framework. Based on the thorough investigation for notch-fatigue problem, the novelty of present study is illustrated.

An introduction to FE analysis with Excel-VBA

Aimed primarily for educational use, an effective platform for 2‐dimensional FE stress analysis was developed by making use of the Excel‐VBA program. With the undergraduate students as the target group, the educational emphasis was placed on the practical application of linear elasticity and the proper use of the FE method. As a part of the project, the students were requested to solve a stress concentration problem by conducting mesh convergence study using Excel‐VBA functionality. They generated the mesh manually by drawing the figures on the grid‐paper. This time consuming experience is usually sufficiently memorable to provide the student with the sense of the required mesh size for proper FE analysis. In addition, the use of tabular data in Excel allows the students to easily conduct the FE analysis. Further, the reports by students clearly manifest that the reliability of the FE method is highly dependent on the experience and the theoretical knowledge of the engineer. In sum, Excel‐VBA is a highly efficient tool for introducing the FE method and can motivate the students to study this subject further.