A stochastic model for predicting the strength and reliability of a unidirectional fiber-reinforced ceramic matrix composite is proposed, based on the Markov process model. In the proposed model, stress distributions in the composite follow the Curtin's assumptions, of which validity is examined by using the FEM model consisting of fiber, matrix and interface elements. It is further assumed that a state of damage in the composite is evolved with each fiber breakage. Then, the damage evolution process is governed by simultaneous first-order differential equations. When the Weibull distribution is used as a strength distribution of the fiber, each state probability is analytically obtained as a function of stress. The expected value and variance of the composite stress were estimated from the state probabilities. Additionally the maximum stress of the expected value, i.e. the strength, was predicted together with the coefficient of variation. The results showed that, even if broken fibers are imperfectly recovered in stress on the fiberaxis away from the breakage points, the composite exhibits a higher strength and reliability than that of bundle structure. Finally, it is concluded that stress recovery in broken fibers is a significant mechanism to increase the strength and reliability of the composite.
The residual stress, which generated by thermal expansion coefficient mismatch between ceramics and metals, is an important problem on strength in ceramic/metal joints. An interlayer, which is a ductile metal, is inserted between ceramics and metal in order to relax the residual stress. In this study, first of all, the analysis of the residual stress produced in joint-cooling process and 4-point bending tests were carried out. Next, from a viewpoint of experimental and fracture mechanics, the effects of interlayer thickness on joint strength in ceramic/metal joints were discussed considering the superposed stress distribution of the residual stress and the bending stress. In addition, the estimation of joint strength was tried to do from viewpoints of fracture mechanics and probability of strength by considering the superposed stress, size and position of potential defects in the ceramics. From the above-mentioned, it is found that the optimum thickness is 0.2mm in this specimen. Joint strength in various interlayer thicknesses can be estimated as normalized strength of ceramics by arranging joint strength to normalized strength considering the scatter of joint strength and the effective volume.
Static and cyclic fatigue strength in porous SiC ceramics were evaluated using quasi-static and cyclic tests, i.e. load, P, increasing and load range, ΔP, increasing tests, respectively. The evaluation method used Weibull distribution, in which the fracture parameters are stress at failure, σf, for quasi-static loading and maximum stress at failure, σmax, f, for cyclic loading. The results revealed that the static fatigue behavior had an important role on the fatigue strength. Statistical characteristics of the fatigue strength were expressed by P-S-N curve estimated by the results of ΔP-increasing tests. During the fatigue experiments, crack nucleation was detected using acoustic emission (AE), and the fracture surfaces were observed by SEM. Based on these results, fracture mechanism of the porous SiC ceramics was discussed in detail.
A large scale database MSDRD on mechanical properties of structural materials was constructed by the Research Group for Statistical Aspects of Materials Strength. In order to extract and analyze the material strength data from MSDRD, a software of STANAD was also developed by this research group. In the present study, fatigue data of aluminum alloys such as 2024-T4 and 5083BE-O were newly analyzed by the same software. Paying particular attention to the statistical feature of the crack initiation and propagation behaviors, statistical fatigue properties (P-S-N characteristics) were theoretically analyzed for smooth and notched specimens. Total fatigue life Nf is given by sum of the crack initiation life Ni and the crack propagation life Np. Thus we can derive the distribution function of Nf from the respective probability density functions of Ni and Np by applying the convolution integral. It was finally found that distribution characteristics of fatigue lives in a wide stress range were well explained by the present analytical model.
A new probabilistic model describing the random fatigue crack growth is proposed based upon a spatially random differential equation driven by a random field. First, a basic equation to describe the random crack growth is formulated as a system of spatially random differential equations by modeling the random propagation resistance in the well-known Paris law as a homogeneous random field. The probability of failure against the fatigue crack growth is then formulated as a functional integral form by the use of its solution. Next, validity of the proposed model is quantitatively verified by comparing with statistical experimental data reported by Ichikawa et. al. Next, an importance sampling simulation scheme is constructed by the use of the Girsanov theorem to make an efficient esimtation for the probability of failure. A numerical example is finally given, which shows that the proposed simulation scheme can give accurate estimation for extremely small probability of failure.
This paper describes a newly developed probabilistic evaluation system of seismic damage states for bridge structures. At first, non-linear dynamic response analyses for the reinforced concrete bridge pier system were performed and the response values were calculated. And also, the probability of the first excursion for the threshold that corresponds to multiple damage states was calculated for each response value by the application of threshold-crossing in random vibration theory. Next, the damage transition probability matrix was constructed on the basis of probability of the first excursion. Then, the damage transition probability matrix conducted the damage transition model that included the damage interaction between elements. Finally, based on resulting probabilities of multiple damage states of structure elements, both functional and social damage states of the bridge structures damaged by earthquakes were evaluated. In addition, the development of a program for visualizing damage transition over time with graphical user interface made it possible to check the transition of structural damage easily in the behavior of the entire bridge structure during an earthquake. Then, by comparing cases with and without seismic retrofits, the effects of different seismic retrofit measures on seismic performance were evaluated.
It is important for the evaluations of safety and reliability of chemical plants to estimate the diffusion of storage subjects because of the prevention of the occurrence of fire or explosion. Therefore, we have developed the computer simulation program in order to make clear the effects of storage's outflow, evaporation and gas diffusion on the dangerous area in a plant. A probabilistic estimation approach of the risk considering the effect of wind condition on gas diffusion is proposed in this paper. As the result of numerical examples, the risk in process with time can be compared quantitatively, even if the volume and the location for tanks differ each other. These results indicate that the proposed method is useful for the evaluation of reliability for chemical plants.
Rubber-modified epoxy resin is widely employed as a base for adhesive compositions and as a matrix material for glass and carbon-fiber composites. A damage zone is generated around a crack tip before fracture. This damage zone is caused by the deformation of rubber particles dispersed in the matrix resin. Its size is closely correlated with the fracture toughness of the resin. In this study, we investigate the deformation of rubber particles inside a damage zone and the relation between the fracture toughness and the size of a damage zone around a crack tip, that is, the length, width, and area under mixed mode condition. The fracture toughness (KIC) and the fracture energy (GC) are measured using an end notched circle type (ENC) specimens. The damage zones around crack tips of damaged specimens are observed by a polarization microscope. As a result, the fracture energy (GC) of rubber-modified epoxy resin has close relationship with the area of damage zone. The rubber particles are deformed elliptically due to the difference of the components of principal stress in the specimen whose load angle is 30 degree.
A theoretical model for attenuation behavior of ultrasonic waves is formulated for unidirectional fiber-reinforced polymer-based composites consisting of viscoelastic matrix and elastic fibers. The model accounts for energy losses due to wave scattering by the fibers and viscous absorption in the matrix, where the scattering loss is evaluated on the assumption of single and independent scattering. Using this theoretical model, the overall attenuation coefficient of the composite can be connected to its microstructure and the constituent properties. Numerical analysis is carried out for attenuation behavior of longitudinal wave in a unidirectional CFRP. When the frequency is sufficiently low or when the incident wavelength is sufficiently large compared to the fiber diameter, the analysis reveals that the CFRP exhibits less attenuation than the epoxy matrix. On the other hand, as the frequency is increased so that the fiber diameter approaches the wavelength, the attenuation of the CFRP may exceed that of the matrix due to significant scattering. The frequency dependence of attenuation in the CFRP is described in detail based on the findings of the present analysis and discussed in the light of the corresponding experimental results.
Fatigue tests were conducted on a βTi-15Mo-5Zr-3Al alloy and a (α+β)Ti-6Al-4V alloy in air and in 3%NaCl solution to clarify the effects of specimen thickness and environment on fatigue crack propagation (FCP) behaviour. Specimens with three different thicknesses, i.e. 0.5, 2 and 10mm, were employed in the present study. In both environments, the FCP rates in Ti-15Mo-5Zr-3Al alloy were almost the same for all the thicknesses in high ΔK region, but were enhanced in low ΔK region with decreased thickness. On the other hand, in Ti-6Al-4V alloy, the da/dN-ΔK relationships in air were similar for all the thicknesses, while in 3%NaCl solution, FCP rates were enhanced with decreased thickness in high and low ΔK region. It was found that the FCP resistance of Ti-15Mo-5Zr-3Al alloy was inferior to that of Ti-6Al-4V alloy, except for high ΔK region in 3%NaCl solution.
Residual stresses arise in fiber-reinforced metal matrix composites due to the thermal expansion mismatch between the matrix and fibers after cooling the composites from elevated temperatures. The residual stresses in a 6061Al alloy unidirectionally reinforced with 140-μm diameter SiC fibers were measured during thermal cycling, and after heat-treating, of the composite. While relative changes of the fiber residual stress were estimated from measurements of the change in length of the heat-treated composite, matrix residual stresses were measured by X-ray diffraction. The X-ray triaxial stress analysis, where the measured value of a stress-free interplanar spacing d0 was discussed to be reliable, showed that a stress state in the matrix surface layer sampled by the X-ray was biaxial and that the longitudinal residual stress parallel to the fibers was the maximum principal stress. It was found that the residual stresses were independent of cooling rates of the composite and that changes of the longitudinal residual stress in the matrix and in the fibers balanced each other in the heat-treated composite. The X-ray biaxial stress measurements during thermal cycling between room and aging temperature of the aged composite revealed that the matrix tensile residual stresses decreased linearly with increasing temperature. The reduction could be well described by using an elastic concentric cylinder model.