Thermoplastics filled with short fibers have been used in injection moulding for more than ten years in order to improve or control mechanical properties of moulded parts such as mould shrinkage, stiffness, heat distortion, etc.. In the moulded parts of Fiber Reinforced ThermoPlastics (FRTP), the orientation of short fibers is determined by the flow of the molten resin and therefore their mechanical properties are highly dependent on the orientation state of fibers. For example, their elastic moduli and tensile strength in the oriented direction have been known to be greater than those in order directions. In FRTP composite industry, it is desired that the fiber orientation becomes predictable quantitatively and the mould design can be carried out to utilize the desirable orientation positively. This paper shows how to predict the fiber orientation distribution in injection moulded parts, from the modelling study on the flow properties of composites. In this model, it is assumed that the behaviour of fibers is completely governed by the flow state of matrix. This prediction might be limited to simple thin products, since the flow of the molten resin is considered to have 2-dimensional isothermal properties and the fibers have an in-plane orientation. The experimental results for a simple injection moulded plate revealed the process of the fiber orientation in short-shot samples. The numerical prediction is quantitatively in good agreement with the experimental results.
In general, laminated composite structures exhibit some coupling effect due to anisotropy and unsymmetric lamination. Thus, when the number of layers is low, they behave quite differently from the homogeneous orthotropic ones. In the present paper, the coupling effect on buckling pressure in the cross-ply and angle-ply laminated cylindrical shells subjected to external pressure was discussed based on the analysis by use of the Donnell-type equilibrium equations. The effects due to various factors such as stacking sequence, number of layers, lamination angle and dimension of cylinder, on the buckling pressure were clarified analytically. The principal conclusions are summarized as follows. (1) As for the effect of number of layers with equal thickness, N, the buckling pressure decreased very much when N is small in both cross-ply and angle-ply laminates because of the variation of cross-ply ratio and the coupling effect, respectively. (2) As for the effect of lamination angle, θ, in angle-ply laminates, the buckling pressure was minimum at θ=0° and maximum at θ=90° in both symmetric and antisymmetric laminates. (3) The coupling effect of laminates disappeared rapidly with an increase of the number of layers and their mechanical behavior became similar to that of homogeneous orthotropic laminates.
Optimum material design is of great importance when designers try to utilize the ‘designable’ characteristic of fibrous composite materials for developing the best product in terms of cost, weight or the combination of these. In this paper presented is an analytical method useful for designing optimum fibrous laminated sandwich plates which can stand a given compressive load. The sandwich plates considered in this study consisted of multidirectional balanced angle-ply laminated skin and isotropic core, and had a symmetric stacking sequence. The problem to be solved was the maximization of the core thickness ratio, which yields the minimization of cost of the plates, under the constraint of buckling load. The proposed method was based on the flexural lamination parameter diagram which shows the feasible design region for a possible stacking construction of the laminated sandwich plates. The feasible design region became smaller when the core thickness ratio increased, and the region finally reduced to a point. The optimum solution was obtained under this condition. It was found that the optimum stacking sequence of the skin was [(±θ)n] and the optimum fiber orientation angle varied with the aspect ratio of the plate and the ply material, but it did not vary with the buckling load. The optimum fiber orientation of the skin and the optimum core thickness ratio can be obtained easily by using the proposed method, but this method is limited to the aspect ratio less than unity.
Numerical analysis by the Finite Element Method has been carried out on the relaxation of stress concentration in FRP plates with a circular or square hole under uniaxial tension. As one of the successful ways to relax stress concentrations, it is conceivable to make two additional holes along the direction of tensile load. This paper deals with glass/epoxy and carbon/epoxy plates containing one original and two additional holes. The fibers were oriented parallel to the load direction. The relation between the pitch of hole and the hole size to optimize the relaxation of stress concentration was obtained. The result of FRP plate was compared with that of isotropic plate. It was found that the fiber reinforced composite plate showed a larger effect of relaxation than the isotropic plate. In FRP plate, the higher the fiber reinforcement, the more the effect of the relaxation of stress concentration. Also, the relaxation of stress concentration at a circular hole due to additional holes was more than that at a square hole having round corners.
The failure process of fiber reinforced composites is a complicated accumulation process of damage due to random failure of fibers, matrix and interfaces, which leads to a catastrophic fracture. A Monte Carlo simulation is one of the most effective methods to analyze such a complicated probabilistic phenomenon as a failure process of composites, and several investigations have been carried out in the past. In most of the past investigations, a simple failure model has been applied in which only random fiber break and stress concentration in the nearest fiber to the broken fiber are taken into consideration. This formulation, however, leads to no more than a flat cleavage plane of a specimen, which does not apparently agree with an actual observed phenomenon. The present paper proposes a new failure model considering interfacial debonding between fibers and matrix as well as fiber breakage. A tensile failure process simulation was carried out for unidirectional carbon fiber (C)/glass fiber (G) hybrid composites with two different kinds of hybrid constitution (concentrated versus dispersed) based on the proposed failure model. The simulation was compared with the observed results of hybrid model experiments based on an acoustic emission (AE) method. The present simulation showed a complicated zigzag cleavage plane in the specimen and also the clear difference in failure process depending upon hybrid constitutions. Furthermore, the simulated results agreed well in tendency with the model experiments in regards to the characteristic shape of stress-strain diagrams and AE properties.
Investigation was made on the fatigue crack propagation behavior of plain woven glass cloth FRP subjected to zero-tension cyclic loading, especially to clarify the effects of initial crack length, glass fiber content and stress ratio. As the result of this study, it was shown that the fatigue crack propagation of woven glass cloth FRP could be evaluated to some extent with the aid of the stress intensity factor modified by a compliance method. The effects of glass fiber content and stress ratio on fatigue crack propagation were discussed using the strain intensity factor and the maximum stress intensity factor, respectively.
Investigation was made on the estimation method of fatigue life for FRP under various random load patterns generated with a micro-computer. Both the constant stress amplitude and the random loading tests were carried out by a hydraulic fatigue testing machine. The distributions of peak stress amplitude and power spectral density were investigated in order to identify the statistical nature of random load being applied on the test specimen. The probability density distribution of peak stress was evaluated by the two-parameter Weibull distribution for convenience and the Zero-crossing method was used for counting the number of cycles of random load. The test results showed that the fatigue life under the Gaussian narrow-band and wide-band random loads could be estimated to some extent by the modified equivalent stress amplitude method based upon Miner's rule.
As Reinforced Reaction Injection Molding (R-RIM) Polyurethane has an excellent impact-proof properties, this material has been used for components in motorcars, and so the studies on fracture characteristics under impact loadings are needed. The aim of this work was to clarify the effects of void, fiber content and impact velocity on the dynamic fracture toughness. The dynamic fracture toughness values decreased with an increase in void content, and took a minimum value at 5% of fiber weight content and increased again with fiber content for impact velocity from 1.4 to 5.1m/s. It was found that the values increased with an increase of impact velocity and the stable crack extension appeared during impact. Therefore, it is concluded that the dynamic fracture toughness value corrected by the stable crack extension is almost constant in this impact velocity range.
A number of studies have been carried out in past years on optimum design under the condition of probabilistic constraints. For example, Switzky derived a probabilistic optimality criterion for the structural design with stress constraints. However, few attempts have been made to formulate the probabilistic optimality criterion for the displacement constraint. In the present study, an attempt was made first to derive the probabilistic optimality displacement criterion for the minimum weight design by using the Lagrange multiplier method. Then, a new probabilistic optimality criteria method was proposed, which unifies Switzky's probabilistic optimality stress criterion and the present probabilistic optimality displacement criterion by using the envelope method. Two design examples were presented to demonstrate the efficiency and convergency of the method developed herein. The results shows that the proposed method can be used to optimize the structure having probabilistic stress and displacement constraints only in few cycles of trials, and hence it has a good convergency in comparison with other probabilistic optimum design methods using mathematical programming.
This paper investigates the statistical distributions of surface length of multiple small cracks and their maximum length appearing in rotating bending fatigue of three different types of unnotched steels in air i.e., S45C steel, a degraded stainless steel with 10wt% σ phase in it, and a nondegraded stainless steel. The characteristics of these distributions were compared for these three types of steels, and the maximum surface length distributions were analyzed on the basis of the statistics of extremes in order to examine the possibility of the fatigue life prediction. The main results of the present investigation were as follows: (1) A great number of multiple small surface cracks were initiated in all three types of steels; i.e., approximately 400 cracks per cm2 in S45C steel, while over 1000 cracks per cm2 in the stainless steels. (2) Not only surface length but maximum surface length in the three types of steels followed the three-parametric Weibull distribution. In every case, the logarithms of the parameters varied linearly with load cycle ratio, N/Nf, and the variation of the maximum surface length distribution was greater than that of the surface length distribution. (3) Fatigue lives were predicted by the use of the return periods obtained from the maximum surface length distribution. They agreed well with the experimental results for all three types of steels.
This paper is concerned with the problem of how to take account of the variability of the fatigue crack propagation rate da/dN in the structural reliability analysis. Specifically, various methods for randomization of the parameters in the crack propagation law da/dN=C(ΔK)m or da/dN=C0(ΔK/K0)m were examined. These methods were divided into two classes. In the first class, randomization was made based on the inter-specimen variability of the parameters, whereas in the second class randomization was made based on the intra-specimen variability of the parameters. With respect to the first class, the following three methods were examined for da/dN=C0(ΔK/K0)m: (a) m and log C0 are treated as normal random variables independent of each other, (b) only m is treated as a normal random variable, and (c) only log C is treated as a normal random variable. By using each of the three methods, the variability of the crack propagation life N was analysed, where N was defined as the number of repeated cycles for crack growth from a=a1 to a=a2. In this calculation, a1 was fixed and a2 was varied. The results of the calculation as a function of a2 were compared with the authors' experimental result. It was shown that the method (a) was the most reasonable among the three methods. With respect to randomization based on the intra-specimen variability of the parameters, the method was examined in which only C0 was treated as a spatial random variable in da/dN=C0(ΔK/K0)m. It was shown that this method could also predict the experimental tendency of the variability of the crack propagation life as a function of a2.
Even in a structure manufactured under complete quality control, it is impossible to exclude some defects which initiate cracks in the early stage of their lives. Consequently, the non-destructive inspection (NDI) is ordinarily performed on the structures which require safety. In the present paper, by applying the initial crack distribution and the stochastic matrix (developed in the previous paper) to the crack propagation process during NDI, the probability of failure was calculated in both cases of “repair model” and “replacement model”. Then, the reliabilistic analysis was performed for a structure subjected to NDI, taken as a model of fracture. The effect of NDI as well as that of the variability in crack propagation on the propability of failure were also studied.
The impact fatigue tests were performed on alumina-filler reinforced epoxy castings at room and various high temperatures below the glass-transition point. From the experiments, the temperature-dependence of impact fatigue strength was clarified. The scatter property of this strength at each temperature was statistically analyzed and its temperature-dependence was also clarified. The safety factor and the allowable stress for the epoxy castings were studied with regard to the influence of circum-temperature used, on the basis of failure probability theory. The main results obtained were as follows: (1) The impact fatigue strength σt of the epoxy castings shows a scatter of logarithmic distribution at high temperatures below the glass-transition point as well as at room temperature and can be estimated failure-probabilistically by the formula of σtNfmt=DtμtStμ. (2) The parameters of impact fatigue property, mt and Dt, and their scatter St are dependent on temperature and increase with rise of temperature. (3) The safety factor and the allowable stress of epoxy castings under service impact loads can be determined according to the allowable failure probability with regard to the circum-temperatures practically used. It is very useful for the optimum structural design.
A simple and new statistical curve fitting method for the S-N type fatigue test, data has been proposed. The method utilizes a bi-linear type S-N curve comprising inclined and horizontal straight lines, and thus the data can be represented by 4 parameters, i.e., slope, knee, fatigue limit, and range of scatter. The principle of curve fitting for the inclined part is based on the principal component analysis technique and that for the horizontal part on the Probit analysis technique. 213 sets of small sample S-N data from NRIM Fatigue Data Sheets were analysed by the proposed method and correlations found between S-N parameters were discussed.