Hirofumi Minamoto

Viscoplastic Effects Occurring in Impacts of Aluminum and Steel Bodies and Their Influence on the Coefficient of Restitution

Generally speaking, impacts are events of very short duration and a common problem in machine dynamics. During impact, kinetic energy is lost due to plastic deformation near the contact area and excitation of waves. Macromechanically, these kinetic energy losses are often summarized and expressed by a coefficient of restitution, which is then used for impact treatment in the analysis of the overall motion of machines. Traditionally, the coefficient of restitution has to be roughly estimated or measured by experiments. However, more recently finite element (FE) simulations have been used for its evaluation. Thereby, the micromechanical plastic effects and wave propagation effects must be understood in detail and included in the simulations. The plastic flow, and thus the yield stress of a material, might be independent or dependent of the strain-rate. The first material type is called elastic-plastic and the second type is called elastic-viscoplastic. In this paper, the influence of viscoplasticity of aluminum and steel on the impact process and the consequences for the coefficient of restitution is analyzed. Therefore, longitudinal impacts of an elastic, hardened steel sphere on aluminum AL6060 rods and steel S235 rods are investigated numerically and experimentally. The dynamic material behavior of the specimens is evaluated by split Hopkinson pressure bar tests and a Perzyna-like material model is identified. Then, FE impact simulations and impact experiments with laser-doppler-vibrometers are performed. From these investigations it is shown that strain-rate effects of the yield stress are extremely small for impacts on aluminum but are significant in impacts on steel. In addition, it is demonstrated that it is possible to evaluate for both impact systems the coefficient of restitution numerically, whereas for the aluminum body a simple elastic-plastic material model is sufficient. However, for the steel body an elastic-viscoplastic material model must be included.

The Mechanical Behavior Analysis of CFCC with Overall Anisotropic Damage by the Micro-Macro Scale Method

In this paper, a micro-macromechanical approach is used to establish the macroscopic constitutive model with anisotropic damage in continuous fiber reinforced ceramic matrix composites (CFCC). For microlevel analysis of unit cell, the homogenization method based on double-scale asymptotic expansion is used to derive the material properties of composites. The macrolevel analysis is conducted to compute the macrostresses and strains with anisotropic damage. The two analyses are conducted by using Finite Element Method (FEM). An overall anisotropic damage tensor for the whole composite is used to describe all types of damage that composite undergoes, such as matrix cracking, fiber breakage, and interfacial damage between matrix and fiber. The damage evolution equation is obtained by using thermodynamic theory. The numerical calculation is carried out to investigate and to predict the onset and evolution of anisotropic damage for composites with different types of laminate. The damage material parameters are determined by fitting the numerical results to the experimental data, and some results are compared well with experimental results in the literature [Wang, S.W. and Parvizi-Majidi, A. (1992). Experimental Characterization of the Tensile Behavior of Nicalon Fiber-Reinforced Calcium Aluminosilicate Composites, Journal of Materials Science, 27: 5483-5496.]. By using the proposed model, the stiffness and nonlinear stress-strain response of brittle composite materials are predicted, and the macroscopic elastic brittle anisotropic damage behavior is also described

EFFECTS OF STRAIN RATE DEPENDENCY OF MATERIAL PROPERTIES IN LOW VELOCITY IMPACT

Impact processes are often analyzed using the coefficient of restitution which represents the kinetic energy loss during impact. In this paper the effect of strain rate dependency of the yield stress on the coefficient of restitution is investigated experimentally and numerically for the impact of a steel sphere against a steel rod. Finite Element simulations using strain-rate dependent material behavior are carried out. In addition, Finite Element simulations with elastic-plastic material behavior, which ignore the strain rate dependency, are carried out as well as elastic material behavior. Comparisons between the experiments and the simulations using strain-rate dependent material behavior show good agreement, and also prove the strong dependency of the coefficient of restitution on the strain rate dependency of the yield stress for steel. The results from both, the experiments and the simulations show also the strong influence of the wave propagation in the rod on the coefficient of restitution.

Influence of Sports Equipments on Human Arm

Impacting on muscles is a normal phenomenon when a ball strikes a racket or a bat during playing tennis or baseball. It causes vibration, which propagates to human body, especially, hand and arm. Vibration is not desired because it may be a cause of the tennis elbow injury or fracture. So, designing of sports equipments is very important to avoid these injuries of players. In this study, the influence of sports equipments on the muscles and skeleton of human arm during impact is focused. A case is considered where a ball strikes against a tennis racket, which is fixed by hand and arm. A multi-degree-of-freedom model of the ball and racket is constructed by finite element method, and human hand, lower arm and upper arm are considered as an individually rigid linked model. The joint moments are calculated when a ball strikes against a racket using modal analysis technique. Then, some muscles are adopted and a musculoskeletal model is constructed. The muscular forces are identified such as to satisfy the joint moments by the optimization method. Finally, the influence of property of racket on the muscles is investigated.

Experimental and Numerical Analysis of Repeated Impacts between Two Spheres

The impact of spheres and bodies with spherical surfaces is frequently occurring in engineering applications. Only little research on repeated impacts of spheres is available and the variation of the COR (Coefficient of Restitution) due to repeated impacts is not fully understood yet. Further, the variation of the COR for impact repetition of visco-plastic materials, such as steel, has not been investigated in full detail yet. Therefore, the aim of this study is to investigate the behavior of steel spheres during repeated impact in detail in both, experiments and numerical simulations. In the experiments, two steel spheres are suspended like pendula, and the two spheres collide at the same position with the same initial velocity for every repeated impact. The COR is obtained from the velocity change of the spheres which is measured by LDVs (Laser Doppler Vibrometers) set at both sides of the spheres. The static and dynamic material properties are obtained from material tests and are incorporated into an FEM (Finite Element Method) analysis. The experimental results and the FEM results agree fairly well. It is observed that the COR increases toward to 1 by the repetition of impacts, indicating decreasing amount of plastic deformation in the successive impacts.

Rebound Property in Low Velocity Impact of Two Equivalent Balls

The present study focuses on an impact phenomenon of two spheres and its rebound property. The collision of two spheres is a fundamental problem with impact phenomenon. The coefficient of restitution characterizes the property of impact phenomenon and has been estimated in general by experiment. In addition, it has been tried to estimate the coefficient by analytical and numerical methods. Considering body deformation, the body is deflected rapidly in collision and the strain rate occurred in the body is significantly high. It is well known the yield stress of the specific industrial material depends on the strain rate. However, it has not been proved the relationship between the coefficient of restitution and the strain rate in details yet. The present paper discusses the coefficient of restitution in low velocity impact of two equivalent balls. The impact experiments were conducted for the balls with different diameters by a pendulum impact apparatus. And the balls are numerically analyzed based on the finite element method considering the dependence of yield stress on strain rate as the material property of the balls. In conclusion, the strain rate decreases with the increment of the ball diameter and, it causes the coefficient of restitution to decrease.

Stepwise Diagnosis for Rotating Machinery Using Force Identification Approach

Machine condition monitoring and diagnosis have become increasingly important, and the application of these processes has been widely investigated. The authors previously proposed a stepwise diagnosis method for a beam structure. In that method, the location of the abnormality is first estimated using the force identification approach, and then the cause of the abnormality is identified. In this study, the stepwise diagnosis method was improved specifically for rotating machinery. The applicability of the proposed method was checked by using the experimental data. In the case of a rotor system with unbalance, it was shown that the location of the abnormality and its severity could be identified, and, in the case of a rotor system with stationary rubbing, the location of the abnormality could be accurately identified. Therefore, it was confirmed that the proposed diagnostic method is feasible for actual application.

Influence of the Discretizing Method on the Identified Results in Boundary Value Inverse Analysis by the Boundary Element Method

In this study, the influence of the discretizing method, such as a constant element or a linear element, on the accuracy of the identified results is investigated in the boundary value inverse analysis by the Boundary Element Method. For the regularization of the inverse analysis, the combination method is used ; the one that the fundamental solution in B.E.M. is selected adequately and the one that the rank of the coefficient matrix is reduced. The optimum condition for solving the inverse problem is found by two performance indexes which are the condition number of the coefficient matrix and the residual norm caused by the rank reduction of the matrix. In a numerical example, the inverse problem governed by two-dimensional Laplace equation is treated. As a result, the identified result obtained using the linear element has almost the same accuracy as the one using the constant element while the accuracy using the constant element is often better, and the selection method of an adequate fundamental solution is very effective for the inverse analysis. Thus, the inverse analysis may be carried out using the constant element and the adequate fundamental solution selected.