The prediction of fatigue life under varying stress amplitude is usually done from the S-N curve in the fatigue tests of constant stress amplitude by using Miner criterion. However, it has not been clarified whether the mean and the variance of the Miner damage values should result from only the central tendency and the dispersion of the S-N curve, or from the change in stress amplitude from constant to varying. In the present paper, the above-mentioned problem is studied by using Bayesian analysis in reliability engineering on the fatigue test data under constant and varying-stress amplitudes.
It is one of the most fundamental steps to clarify the parameters of the initial distribution of structural member's fatigue life, whenever the reliability of any structure is analized using the reliability theory. Whittaker and others reported some studies on fatigue life distributions accepting the Weibull distribution with two parameters but without the location parameter. However, the Weibull distribution with three parameters including the location parameter should be considered as the distribution function at a stress level near the fatigue limit of a material. Since structures are designed often based on the fatigue limit of the members, it is important for the reliability analysis of the structures to clarify the fatigue life distribution at such stress levels. From the above viewpoint, the estimation of three parameters of the Weibull distribution was made in this study by means of several methods. Before the estimation was performed, Monte Carlo technique was applied to prepare many experimental data of fatigue life governed by the Weibull distribution with three known parameters. Then the values of each parameter estimated by several methods were compared with the true values given in advance, and the applicability of these estimating methods was examined. Furthermore, the sample size necessary to estimate the parameters of the initial distribution was discussed quantitatively.
Repeated rotating bending fatigue tests were carried out on the notched specimens of Cr-Mo steel, SCM 4, especially at and near it's fatigue limit, and its statistical fatigue properties were investigated. The distributions of the number, depth and length of microcracks being developed were determined at various steps of fatigue lives, and the distribution shapes of fatigue lives were obtained. A new model which can explain the statistical properties of microcracks and fatigue lives was proposed, and a new method to evaluate the distribution of lives at and near the fatigue limit was established. The new method was essentially based on the consideration of properties of microcracks and the distribution of crystallographical properties. This new method of statistical evaluation presents the so-called variable finite extreme value distribution function. The tested lives were analysed by this evaluation method. It was revealed that the distributions of lives calculated at and near the fatigue limit were in good agreement with the test results.
The impact tensile strength and impact tensile fatigue strength of non-woven polyester cloth reinforced epoxy resin were investigated by using a repeated impact tensile loading apparatus. The allowable stress and the safety factor under repeated impact tensile loading were analysed on the probability theory of failure. The results obtained are summarized as follows; (1) Both the impact strength σf and the impact fatigue strength σ are represented by a logarithmic normal distribution and can be estimated as the probability values by the following formula. σf=(A+Bεn)μσfsσfu, and σNfm=Dμσsσu where ε is the strain rate, Nf is the fatigue life to failure, μ is the mean value, s is the standard deviation, u is a parameter of probability, m, n, D, A and B are the material constants, and the suffixes σf and σ denote the impact test and the impact fatigue one, respectively. (2) The effect of strain-rate on the impact fatigue strength can be estimated by σNfm=A+B(σ/ET)n where E is elastic modulus of the material and T is the time during stress rising by the impact loading. (3) It is found that the material can be used as a structural element of high reliability.
As composite materials became widely applied to structure members, the dispersion of strength for composite materials has become a centre of great interest. There are many factors affecting the dispersion, because composite materials are produced by the combination of various materials. For example, the distributions of modulus of elasticity, void and another defects in a composite material are some of those, but their complexity makes this field of research difficult. In this paper, the finite element method was applied to investigate the dispersion of strength, because it is a very useful technique for numerical analysis of mechanical behaviors. Fiberglass reinforced plastic was chosen as a sample and the Weibull-distribution of modulus of elasticity was set up as the factor which influences the dispersion. The mechanical behavior was simulated by the finite element method. The results showed that dispersions of the strength and modulus of elasticity obtained by choosing the coefficient of variation for the Weibull-distribution as parameter agreed qualitatively well with the experimental results obtained by Coleman. It was recognized that the present method is very useful for the investigation of dispersion of strength for composite materials.
Fatigue tests have been conducted to investigate the fatigue properties of various types of laminated composites and some statistically meaningful inference was drawn from these results. The materials used in the experiment were 4 different kinds of FRP laminates, satin woven FRP, plain woven FRP, roving woven FRP and SMC laminated FRP. Sufficient data were accumulated to produce the P-S-N diagrams for each type of laminates. A statistical approach based on the Weibull distribution was applied to the test data to evaluate the dispersion in the fatigue life of the materials. The dependences of fatigue life and its dispersion on the applied stress level, specimen size and fiber content in the specimen were discussed. The test results showed a wider experimental scatter particularly at the life range of 105 to 106 cycles than that observed on conventional metallic materials. Thus, it is emphasized that a larger reduction of design life is necessary for FRP to assure the same level of confidence and reliability as other materials.
As a basic study on fatigue damage accumulation of structural members subjected to service load, fatigue tests under superposed stress and varying stress amplitude have been carried out in the past, and various fatigue life prediction methods have been proposed. To investigate the applicability of six different cycle counting methods to more complicated stress pattern than the superposed stress, the in-plane bending tests were carried out on the specimens made of low carbon steel S10C under the combined superposed stress having such a pattern that the maximum stress amplitudes of two superposed stresses were varied stepwise or that the superposed stress and sine wave were mutually repeated. The cycle counting methods investigated were zero cross range pair mean method (ZRPM), range pair mean method (RNPM), peak method (PEAK), range pair method (RNPR) among others. The modified Goodman's method was used to evaluate the effect of mean stress on stress amplitude. The lives estimated by using the linear cumulative fatigue damage law were compared with the experimental lives, and the applicability of the cycle counting methods was examined. The results obtained were as follows; (1) For the superposed stress wave, the ratio of the experimental life (N) to the estimated life (Nes) was within the range of 1/3≤N/Nes≤3 except the PEAK method. (2) For the combined superposed stress wave and the superposed-sine stress wave, the ratio of the experimental life (N) to the estimated life (Nes) was within the range of 1/3≤N/Nes≤3 except the PEAK and RNPR method. The PEAK method showed a conservative life against the experimental results, but RNPR method was not. (3) The scatter band of the estimated-experimental life ratio by the ZRPM and RNPM method was smaller than that of the other 4 kinds of cycle counting methods.
This paper describes the irradiation effects on the tensile characteristics of welded polypropylene and on the adhesiveness of this material. Polypropylene plates of 2mm in thickness were butt welded by using a semiautomatic heating plate welder and exposed to various irradiation doses of neutron. Tensile characteristics of these specimens were examined and measurements of melting point, dissolution rate and molecular weight were made. Examination of X-ray diffraction patterns was also made during tensile tests on neutron-irradiated specimens. Furthermore, the adhesive strength, infrared spectra and surface appearance of neutron-irradiated specimens were examined, and the irradiation effect on the adhesiveness of this materials was also discussed. The results obtained were summarized as follows; (1) The irradiation effects for the welded part are similar to those for the base material of polypropylene, that is, tensile strength decreases with excessive irradiation and brittleness becomes greater with an increase of irradiation dose. (2) The irradiation effects on the melting point, dissolution rate, molecular weight and molecular orientation tendency are correlative with those on the tensile characteristics of neutron-irradiated materials. (3) The adhesive strength of polypropylene increases with irradiation of neutron. This increase seems to be caused by polarization due to irradiation.
To investigate the effect of atmospheric-corrosion on the early stage fatigue cracks, fatigue tests were made in air and in vacuum (3×10-3mmHg) on α-brass under push-pull loading, and both external and fractured surfaces were observed by means of optical and scanning electron microscopy. It was found that fatigue lives, compared with the case iron, were much longer in vacuum than in air, and the improvement in life increased as the stress amplitude was reduced. The number of cycles up to fatigue crack nucleation in vacuum was found to be about 44 times longer than that in air. Crack nucleation in vacuum occurred predominantly along the slip bands. The number of intercrystalline fracture surfaces increased as crack length and stress amplitude increased. The morphology of transcrystalline fracture surfaces in vacuum was similar to that in air. On the other hand, in vacuum, intercrystalline fracture surface was not observed within the interior of the specimen and few near the specimen surface. Striations observed in vacuum were not clear.
Fatigue crack growth behaviors of an explosively-bonded naval brass-steel clad plate and roll-bonded nickel-steel and naval brass-steel clad plates were examined. Micro- and macroscopic observations of crack growth, when a crack approaches the bond interface, were carried out. Effects of initial residual stresses and K-value anomalies due to bonding of dissimilar materials on crack growth were studied.
The Thin Wafer method for determining the dynamic stress-strain relation of materials has been examined on the basis of wave propagation in a specimen. The analysis was done for an elastic-plastic rate independent material and rate dependent elastic-viscoplastic or elastic-viscoplastic-plastic materials. Stress history at both ends of the specimen was taken as a measure of uniformity in the deformation of the specimen. The stress-strain curves obtained from the conventional Thin Wafer method were compared with those calculated from the average strain rate by the constitutive equations. It is concluded that the Thin Wafer method is a valid means for obtaining the stress-strain relation of materials at high strain rates.