This paper describes the application of the finite element analysis to some nonhomogeneous materials of simple structures with some distribution in elastic properties, such as Young's modulus, Poisson's ratio and principal directions of elasticity, by employing a stochastical simulation. It is well-known from the extensive laboratory tests that the properties of soil and rock show some kind of distributions. In this study, the variations of stress and deformation in the plate with a circular hole, the rectangular plate subjected to an uniaxial uniform load and the semi-infinite plate subjected to a concentrated load were analyzed on the assumption that the values of the above elastic constants varied randomly from one element to another according to the normal distribution function. The elastic constants for each element were generated by a random process using a probabilistic Monte-Carlo simulation. It has been found that the finite element analysis based on the randomized material constants for each element gives the mean values of stress and displacement which are not significantly different from those based on the fixed elastic constants, and yields a better prediction of a real structure. Thus, the safety factor used in the design of a structure can be estimated more adequately by considering the variations of stresses and displacements obtained by this process.
It is well known that the fatigue strength of machine parts is generally reduced by electroplating. This paper describes the summary of the data of fatigue strength for nickel plated steels obtained recently. The main results are as follows: (1) When carbon steel is nickel plated, the fatigue strength decreases as the current density or the thickness of plating increases. (2) The baking treatment at 200∼550°C after plating causes the reduction in the hardness of plating, but does not affect the fatigue strength. (3) The corrosion fatigue strength in 3% NaCl solution is slightly smaller than in air. Nickel plating gives only a little protective effect under the repeated stress condition, but prolongs the fatigue life of plated steel as compared with that of bare steel. (4) The fatigue strength of notched steel is also reduced by nickel plating, and the degree of loss can be estimated from the product of the individual reduction effects caused by plating and by notch. (5) The loss of fatigue strength of plated steel can be decreased by diffusion treatment at 700∼850°C. (6) Shotpeening, either before or after nickel plating, increases the fatigue strength considerably. These results suggest that the main cause for fatigue strength loss by nickel plating is not the internal stress nor absorbed hydrogen in the plated layer, but the low fatigue strength of the plated layer itself. The fatigue crack tends to form easily in plated layer, and acts as the source of stress concentration for crack propagation into steel similar to the double notch effect.
Many polymeric meterials such as rubbers and plastics show strong dependencies on strain rate and temperature, optically as well as mechanically. Therefore, it is difficult, in general, to perform the complete analysis of mechanical and optical behaviors of these materials mathematically. In this study, a method was proposed on the optical determination of strain energy stored in a linear viscoelastic material, based on the fact that the optical properties may be represented by such a spring-and-dashpot model, as the generalized Maxwell or Voigt model, in the same way as the mechanical properties. Then, the experimental strain energy analysis of polyurethane rubber under uniaxial tension was carried out by the use of both mechanical and optical coefficients. The results obtained from both experiments agreed qualitatively as well as quantitatively. Consequently, it is concluded that the optical method would be useful for the experimental determination of strain energy in the viscoelastic materials.
The effect of pressure on the yield behavior of polymeric solids was investigated at room temperature. Tests were carried out on samples of six thermoplastics; polycarbonate, polyvinyl chloride, polypropylene, polyethylene, nylon 6.6, and ABS plastics. An apparatus has been designed and constructed which allows the determination of the yield stress of a polymer specimen in thin-walled cylinder under internal pressure, while the sample is simultaneously subject to a hydrostatic external pressure. As the external pressure increases, the normal stress applied to the plane of the maximum shear stress in the thin-walled cylinder subjected to internal pressure changes from tension to compression. In the state of hydrostatic compression under high external pressure, the pressure dependence of yield stress fitted in well with Coulomb yield criterion. In the state of hydrostatic tension under low external pressure, the yield surface (the Mohr envelope for yielding) could not be explained by the Coulomb yield criterion. Furthermore, the deformation bands produced under hydrostatic pressure in polycarbonate have been examined by measuring the angles of bands after the load was removed. These bands were found to be inclined at 50° to the direction of the maximum principal stress. The angle of 50° was independent of hydrostatic pressure.
The purpose of this paper is to clarify the strength criteria and the mode of failure of orthogonally reinforced fiber composites under tension with emphasis on the effect of a circular hole on the tensile strength of these materials. It is well known that for the unidirectionally aligned fiber composites, the strength and the mode of failure are related quantitatively with the fiber orientation, and many investigations have been carried out on this problem. For the orthogonally reinforced fiber composites, these properties have also been determined and the results have been found to be in good agreement with the authors' calculation. It has been found that the Strength reduction. factor η=(σ-σi)/σ, Where σ and σi are the tensile strengths of specimens without and with a central hole, respectively, becomes minimum for the specimen having glass fabrics of a certain number of plies. An analysis has been presented here, which can explain the experimental results well. The effects of strain rate on the tensile strength and strength reduction factor of the glass fiber reinforced plastics have been studied also. Both the tensile strength and the strength reduction factor changed linearly with the logarithmic value of the strain rate.
The effect of the testing temperature on the strength reduction factor η, defined in the previous paper, was studied in the temperature range from 25°C to 125°C. In addition, the effects of the ratio of the diameter of the central hole to the breadth of the specimen, the direction of the reinforcement and the type of the cloth, on the tensile strength of the specimen were studied. At the elevated temperature around 125°C the specimen with a hole was stronger than that without a hole. Generally speaking, the strength of a specimen at 50∼75°C was higher than that at room temperature. These results were explained qualitatively.
The fracture criterion of low-cycle fatigue based on variable strains, which is represented as1/C0∫N0γpadn=1 for the varying plastic strain amplitude, has been verified experimentally by carrying out the low-cycle fatigue tests under the tension-compression and rotating bending conditions. The low-cycle torsional fatigue tests under multiple repeated loads were made on the 0.84% C piano wires and the applicability of the above mentioned criterion was examined. The main results obtained are as follows: (1) The experimental values of the cumulative damage obtained from the above criterion are larger than the values calculated from the linear damage criterion, and they scatter around in the vicinity of unity. (2) The test results indicate the existence of an exponential relationship between the equivalent stress amplitude τeq and the equivalent plastic strain amplitude γp.eq.