A major part of bridge rating which is the kernel of bridge maintenance system is usually performed based on the subjective judgment of experts in the related fields. By considering the shortage of experts in the expanding field of bridge maintenance and need for the exact diagnosis of bridge condition, the systematization of bridge rating to replace the subjective information of bridge engineers such as professional experience, knowledge on bridge rating, etc. has become an important problem. The present paper is to introduce a newly developed expert system capable not only of various inferences and judgments for maintenance but also of output of estimation results of remaining life for existing bridges. Moreover, its application to some reinforced concrete T-beam bridges in service is also considered. For the construction of the knowledge base including the subjective information related to bridge rating, a concept of fuzzy set theory is adopted to deal with it. The final results produced by this system are represented by five elements of linguistic expressions with the fuzziness value which is the degree of subjective uncertainty.
It is an important problem for maintenance and rehabilitation of existing bridges to develop a method of evaluating safety such as remaining life and load carrying capacity of bridges. This paper describes a method of safety evaluation of concrete bridges in service together with verification of the evaluated results based on field tests. The field tests were performed under static loading by test trucks for application to the System Identification Method, and also under dynamic loading by falling mass for application to the Modal Analysis. The safety factors for flexural and shear failures were evaluated from the field tests. These results were verified through the ultimate load test carried out in field on the reinforced concrete main girders isolated by cutting off from the bridge system. Finally, remaining life of the bridge was predicted by application of fuzzy set theory which deal with the subjective information of bridge engineers.
Recently, fatigue failure has become frequent in RC (Reinforced Concrete) decks of urban expressway bridges, because of the increase of heavy vehicle transit and the deterioration of the structure itself. In a usual fatigue analysis of mechanical components and systems, their fatigue lives are estimated by using the simple law of cumulative damage. This law is based on the relation between the load intensity and its repeated cycles until failure. This relation is presented in the form of a so-called S-N curve which is determined from experiments. To obtain a reliable S-N curve, a great deal of experimental data should be collected. However, it is difficult to conduct a sufficient number of fatigue experiments on RC bridge decks, due mainly to the financial and technical restrictions. In this paper, an attempt was made to apply the fuzzy sets theory to the fatigue analysis of RC bridge decks. The S-N curve was modeled through the fuzzy regression theory instead of using probabilistic concepts. This was because the concept of frequency is useless in case of having few data, i.e., about ten samples. By using the fuzzy regression analysis, it was possible to develop a possibility model to draw up an S-N curve and to estimate the fatigue life of RC bridge deck in a more realistic and significant manner.
The present paper deals with the reliability-based fatigue-proof design based upon a practical viewpoint through correct evaluation of engineering uncertainties caused by use of a limited number of experimental data. To this end is first discussed the distribution properties of the statistical failure probability constructed with the aid of parameter estimators in the Weibull distribution. At the same time, the effect of sample size on the estimation of failure probability is also investigated. Comparison is made between shapes of the distribution function of the statistical failure probabilities based upon a Weibull and a log-normal model in order to clarify which is more practical as the fatigue life distribution model of structural components. Furthermore, discussions are made on how to determine the optimum sample size of the fatigue experiment in order to meet the prescribed level of reliability imposed on structural components. Finally, a simple but important design principle is proposed for the reliability-based fatigue-proof design of structural components with Weibull fatigue life distribution.
By using the fatigue crack growth test system developed in the previous study, statistical data of fatigue crack growth rate da/dN in 2024-T3 aluminum alloy were obtained. Eighteen specimens were tested. In the test system used, the crack length was measured using the DC electrical potential method and precise load control was made using a microcomputer. Thus, scatter in testing conditions and labor needed were decreased as compared with the previous test by the present authors in which the crack length was measured using a travelling microscope. From analyses of the experimental data, the coefficient of variation, ηΔN, of the number of stress cycles for crack growth from a given value of a to a+Δa (Δa=0.1mm) was found to be nearly constant independent of a. This implies that m in Paris' law da/dN=C(ΔK)m can be regarded to be deterministic in the present data. Then, the composite variability model as a stochastic model of da/dN proposed previously by the present authors was examined using the present data. In this model, C is treated as a random variable involving the inter-specimen variability and the intra-specimen variability, whereas m is treated as deterministic. From comparison of the model with the data, the inter-specimen variability was found to be considerably smaller in the present data than in the previous data. This seems to be due to the decrease of scatter in testing conditions. Furthermore, the correlation distance δ of the intra-specimen variability of C was found to be much smaller in the present data than in the previous data. The value of δ estimated from the present data was of the order of a grain size. This suggests that the intra-specimen variability of C occurs from grain to grain.
This paper deals with the sensitivity study on reliability or failure probability of uni-directional fiber reinforced composite laminates subjected to off-axial loads. Two kinds of new sensitivity measures, physical and stochastic sensitivity ones, were defined in the present first order reliability method (FORM). The former means the sensitivity measure which shows how the mean value of random parameters affect the safety index of laminates based on FORM. The latter is the variability sensitivity which is the measure how the standard deviations of random variables vary the failure probability of laminates. Both the sensitivities can be easily calculated analytically with safety index and standardized gradient coefficients on a design point by the present procedure. The proposed sensitivity measures have not only an advantage to be obtained analytically but also to offer more information on reliability than the conventional numerical procedure. Numerical analysis of graphite epoxy uni-directional composites laminates was performed for the various combination of off-axial loads. These results are useful for a designer to evaluate the quantitative characters of design parameters which contribute the stochastic material design of composite materials.
A Monte-Carlo simulation technique, using a shear-lag model, is proposed to elucidate the tensile fracture process and the tensile strength of unidirectional fiber reinforced metal matrix composite materials, on the condition that the fiber behaves elastically and the matrix metal is approximated as an elastic linear hardening plastic material in accordance with the kinematic hardening model. In the simulation procedure, a conventional technique is modified by γmin method based on the minimum value of the incremental ratios which can be calculated from the element strengths and the stresses working on each fiber element and each matrix element. The simulated results show that the average value and the coefficient of variation of tensile strength are improved by an increase in the Weibull's shape parameter of the fiber, although the average value does not reach the value estimated from a rule of mixture. Then, in order to investigate the validity of the present technique, the simulated strength data are compared with the theoretical cumulative distribution curve given by a recursion analysis technique. Additionally, it is shown that the structural uncertainty, e.g. random fiber spacing, lowers the composite average strength and increases its scatter.
A personal computer program of Finite Element Method was developed in the past in order to analyze the stresses in composite materials. Although the mechanical behavior of composite materials can be analyzed by such a developed computer program, the component construction of laminates can not be obtained because it is very difficult to optimize the computational results by using an ordinary F.E.M.. On the other hand, the ratio of layer components can be calculated by the method of optimization, but not the lay-up sequence of laminates. In this paper, the personal computer program of intelligent F.E.M. with a new concept has been developed in order to analyze the component and lay-up sequence of laminates which satisfy the design objects. As an example of analysis, the material for each layer of a laminated panel under bending condition was selected and the thickness of laminae under combined loads of bending and tension was determined. The computational results were very reasonable for the composite structure. Therefore, it was recognized that the proposed intelligent F.E.M. is very useful for the structure design of composite materials.
The method proposed previously by one of the authors for optimum design of fibrous laminated composite plates subjected to uniaxial compression has been proved to be applicable also to those subjected to biaxial compression. The proposed procedure consists of two methods. One is the Boundary Slope Method (BSM) and the other is the Critical Buckling mode Method (CBM). In order to apply these two methods, the range of the plate aspect ratio must be obtained because each method is valid only in its characteristic range of the aspect ratio. In comparison with the case of uniaxial compression, the transition of aspect ratio between BSM and CBM is somewhat complicated for the case of biaxal compression. However, the present procedure reduces computational time remarkably in comparison with numerical calculations.
Recently, in a mass production system, SMC is being applied for various products such as automobile parts, since it has advantageous mechanical properties. However, faults, such as sink marks, brittle resin rich regions and the reduction of strength at the weld line, are caused by its heterogeneous flow during the process of compression moulding. So it is very important to clear the flow process. In this paper, at first, in order to clarify the flow state changed by charge pattern, numerical analysis was executed by FEM based on a two-dimensional steady flow model, using the concept of branching flow according to the equivalence of stress gradient at the divergence point of the advance flow front to two-directions. In order to verify this numerical analysis, the visual observation was carried out. Parameters for the analysis were fillet radius and charge pattern. The results of the numerical flow analysis taking into consideration the distribution of flow rate at the divergence were good agreement with the experimental results, and so this analysis was found useful to various charge patterns in compression moulding.
The required properties of fiber reinforced composites such as bi-directional laminates may be obtained by changing the ply angle of laminae. But these laminates have distinct interfaces and so their properties are affected by the state of these interface stresses. Therefore, in the design of bi-directional laminates, it is very important to grasp the situation of interface stress. In this paper, the distortion behavior of bi-directional laminates under thermal residual stress, whose angle of principal axis in material properties was not 0°, was made clear by the experiments. In order to clarify the distribution of interface stresses, numerical analysis by finite element method (FEM) was carried out and the results were verified by the actual distortion behavior. A hybrid modeling with triangular shell and prismatic elements was used in the analysis. In the past, this modeling was found to be effective in the case of bi-directional laminates whose angle of principal axis in material properties was 0°. The following conclusions are obtained. (1) In the case that the angle of principal axis in material properties of laminates was not 0°, the experimental and numerical results showed quantitative accordance. So the hybrid modeling with triangular shell and prismatic elements was also effective in this case. (2) By using this modeling, the distribution of interface stress and the distortion behavior can be guessed in bi-directional laminates whose angle of principal axis in the material properties was not 0°.
In the present study the effect of a flawed part in the cylindrical adhesive-bonded joint of glass-fiber reinforced plastics on its mechanical property and the process to failure were investigated under combined bending and torsional loading conditions. Loading tests were performed in bending, torsional and combinded loading conditions in which the proportion of bending to torsional moment was set to 1:1 and 1:2. Both the area and the location of the flawed part of specimen were changed in two varieties. From the experimental results the followings became clear. (1) Even though two adhesive-bonded joints had the same area of the flawed part, the mechanical properties were quite different when the flawed parts were at different locations. (2) In the bending condition, the flaw reduced the stiffness of the specimen but affected the strength little. (3) Under the combined loading condition in which the proportion of torsional to bending moment was whithin a certain limit, the strength reduction ratio was higher than that in bending tests. However, in the condition of higher proportion of torsional moment the strength reduction ratio was lower than that in bending tests. The proportion of torsional moment at which the strength reduction ratio changed from that in bending tests to that in torsional tests increased with the area of the flawed part.
The strength by a short beam method of three point bending was measured for some CFRPs with varying fiber and matrix resin combination and their failure states were examined. The strength of every CFRP decreased linearly with increasing temperature. The strength retention at 200°C depended on the glass transition temperature of matrix resin. The retention for PMR-15 matrix resin was the highest, followed by MY720 resin and then EPIKOTE 828 resin. The failure mode of CFRP with EPI-KOTE 828 matrix resin tested at a cross head speed of 5mm/min was a mixture of shear and compression failure below 150°C, but pure shear failure at 200°C. Pure shear failure was also observed at cross head speeds less than 0.5mm/min, while compression failure in addition to shear failure was observed at cross head speeds more than 5.0mm/min. In CFRP with MY720 matrix resin, only shear failure was observed in the range of testing temperatures. In CFRP with PMR-15 matrix resin, buckling failure in addition to shear failure was observed up to 250°C. These differences in failure modes of different CFRPs were related with the ultimate strain of the matrix resin.
An investigation has been carried out concerning the influence of water absorption on the fatigue properties under completely reversed stress of 0° unidirectional and ±45° cross-ply composites of a Technola (HM50, Teijin)/epoxy and a Kevlar 49 (Dupont)/epoxy. The influence of water on the fracture mechanism was observed by a SEM. The ratio of fatigue strength under reversed tension and compression at N=106 in water to the one in air of the ±45° cross-ply composite was 0.61-0.66, and a remarkable decrease in fatigue strength was observed in water. In addition to the weakening of a fiber/matrix interface, local buckling of reinforcing fibers under compression due to the softening of water absorbed resin decreased the fatigue strength in water. The ratio of the fatigue strength in water to the one in air of the 0° unidirectional composite was 0.86-0.94, and the reduction of fatigue strength was moderate compared to that of the cross-ply one. This was due to the fact that the softening of resin not only increased the fatigue strength under tension but also decreased that under compression. Under reversed tension and compression, fiber splitting was decreased in water than in air in both types of composite. This was quite opposite to the case of pulsating tension, where the fiber splitting caused by water absorption reduced the fatigue strength in water.
The ENF testing for interlaminar fracture toughness is the most useful test method to evaluate the interlaminar fracture behavior of UDCF laminate. In this work, the sandwich ENF testing was presented as a new method to evaluate the interlaminar fracture behavior of various laminates, such as AF/AF, GF/GF, CF/GF, CF/AF, and AF/GF. The specimen consisted of a mid layer with a delamination crack to measure its interlaminar fracture behavior and two stiff outer layers to give adequate bending stiffness to the specimen. The sandwich ENF specimen showed good sensitivity to GIIC for laminates of various fiberous compositions. It was also founded that the change in chemical composition of the matrix resin system was effective to improve the interlaminar fracture behavior of UDCF/GFCSM hybrid laminate. As GIIC increased, the crack growth path shifted from UDCF intralayer to the interlaminar zone between UDCF and GFCSM layers.