Macroscopic behavior of solids is widely studied from microscopic viewpoints such as molecular dynamics and lattice dynamics. However, there are some dif®culties with the averaging methods in the microscopic expressions of stress, higher-order stress and heat¯ux. In this study, we discuss the microscopic expressions of macroscopic variables and macroscopic balance equations of a solid that is modeled as an assembly of atoms, on the basis of generalized Cosserat continuum theories. The concept of mesodomain is introduced to relate microscopic quantities of atoms to macroscopic quantities of continua. Microscopic expressions of stresses and heat¯ux are described as area averages of microscopic quantities such as velocities of atoms, interatomic potential forces. Balance equations for stress and higher-order stresses are derived from the equations of atomic motion. The energy equation, represented by the averages for the values in the mesodomain, is obtained by dividing the velocity of atoms into macroscopic motion and thermal motion. Since the generalized polar effects are taken into account in this model, derived macroscopic balance equations have the same form as the equations of generalized Cosserat continua. Moreover, microscopic descriptions obtained here show that the higher-order mechanical power of the generalized Cosserat continua is equivalent to the thermodynamic quantities of simple materials. The values of velocities of atoms calculated by molecular dynamics simulation are substituted into the newly obtained microscopic expressions of stress and higher-order stresses. The obtained values of stresses and the theoretical values derived from Eringen's formula correspond well, which demonstrates the usefulness of the present microscopic expressions for the practical application in computer simulations.
This paper describes the effect of large pre-strain on very high cycle fatigue strength of austenitic stainless steels that are widely used in nuclear power plants. Fatigue tests were carried out on strain-hardened specimens. The material served in this study was type SUS316NG. Up to ±20% pre-strain was introduced to the materials, and the materials were mechanically machined into hourglass shaped smooth specimens. Some specimens were pre-strained after machining. Experiments were conducted in ultrasonic and rotating-bending fatigue testing machines. The S-N curves obtained in this study show that an increase in the magnitude of the pre-strain increases the fatigue strength of the material and this relationship is independent of the type of the pre-strain of tension or compression. Although all specimens fractured by the surface initiated fatigue cracks, one specimen fractured by an internal origin. However, this internal fracture did not cause a sudden drop in fatigue strength of type SUS316NG. Vickers hardness tests were carried out to ascertain the relationship between fatigue strength and hardness of the pre-strained materials. It was found that the increase in the fatigue limit of the pre-strained materials strongly depended on the hardness derived from an indentation size equal to the scale of stage I fatigue cracks.
A safety assessment needs to be conducted to analyze the damage caused by an aircraft impacting into a concrete structure at a nuclear power plant. One of the analytical methods used for this issue is a numerical impact simulation conducted after aircraft and reinforced concrete (RC) models are determined. We established the RC model and aircraft model in this study and confirmed the applicability of an impact simulation. Validation of our RC model was confirmed by conducting impact simulations of an F4 Phantom engine (GE-J79) crashing into three different wall thicknesses of 900, 1150, and 1600 mm. The damages to the wall in the simulations agreed with the test results conducted at Sandia National Laboratory around 1990. We also conducted parametric impact simulations of a rigid missile crashing into a concrete wall, changing the impact speed, mass of the missile, and the wall thickness. The wall thickness required to prevent perforation in the simulations was close to that estimated by the empirical formulae, although the residual speeds of the missile after the perforation in simulation did not agree very well to the values obtained by empirical formulae. One of the reasons of the difference in the residual speed is that the speed of the ejected concrete was not considered in our RC model. An impact simulation of an F4 Phantom crashing into a RC wall was conducted for the validation of our aircraft model. The shape of the impact load and the state of the frames of F4 Phantom on impact were almost the same as those in the test results conducted at Sandia, which showed that the F4 Phantom model was valid.
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