The fatigue crack growth behavior in glass mat reinforced polyester laminate was investigated by macroscopic observations and discussed from the view point of fracture mechanics. The main fatigue crack was found to propagate after the debonding between fibers and resin took place and the damage zone increased at the fatigue crack tip. The fatigue crack length was determined by the compliance method, since the fatigue crack tip was not clear. The fatigue crack growth law was easily determined by ΔK-controlled tests of the materials. It was found that the crack growth rate of the specimen containing thick fibers was lower than that of the specimen containing fine fibers at the same stress intensity factor range and the same fiber content in weight.
FRP has the nature of visco-elasticity and this has various effects on the mechanical behavior of FRP. In estimating the fatigue life of FRP under random load, the frequency dependence is one of the most important subjects. From this standpoint, investigations were made on the fatigue properties of satin woven glass cloth FRP under six different sinusoidal wave loads at frequencies of 0.1, 1, 5, 10, 15, 20Hz. Both the constant stress amplitude and the programmed loading tests were carried out by a hydraulic fatigue testing machine. As a result of this paper, it was shown that the fatigue life of FRP is affected strongly by the change in repeated frequency, and the following experimental equation was obtained to represent the S-N relationship for the different repeated frequencies; σ0.91f+9.79×Nf=100.86f+16.2 where σ is the applied stress, Nf the expected fatigue life and f the repeated frequency, respectively. The fatigue life under programmed loads at various frequencies could also be estimated to some extent by using the weighted mean of material constants.
Previously, in the case that both the fiber/matrix and the FRP/FRP interfaces were constructed with the same matrix, the temperature dependence of the strength of roving glass cloth FRP in the flatwise direction was reported. In this paper, two types of matrices having properties different from those of the matrix used in roving glass cloth FRP, were applied at the FRP/FRP interface, so as to construct the fiber/matrix and the FRP/FRP interfaces with different matrices. The relation between the fiber/matrix and the FRP/FRP interfaces and its dependence on matrix were studied by changing the fiber/matrix ratio, the condition of heat treatment and the temperature. The results obtained are as follows. (1) The temperature dependence of the fracture behavior (brittle or ductile) of the interface was changed by both the type of matrix and the condition of heat treatment. But it was not affected by the location of the weakest interface. (2) The temperature dependence of the location of the weakest interface was affected by both the type of matrix and the condition of heat treatment. But the influence of the fiber/matrix ratio on the temperature dependence of the location of the weakest interface varied with temperature. (3) The temperature dependence of the bond strength was affected by the type of matrix, the condition of heat treatment and the location of the weakest interface. But the influence of the fiber/matrix ratio on the temperature dependence of the bond strength was changed by the type of matrix and the condition of heat treatment. (4) In spite of the type of matrix examined, the bond strength varied with the temperature dependence of the bond strength for fiber/matrix ratio=100/0 and the bond strength varied with the temperature dependence of the location of the weakest interface for fiber/matrix ratio=0/100.
This paper deals with SMC (Sheet Molding Compound) laminate which is one of the useful fiber reinforced plastics manufactured by press-molding. In order to examine the influence of quantity of the component on the mechanical properties of SMC, SMC were molded in the square shaped plates and tensile strength at various points in the plate was measured. The glass-fiber contents of SMC were 30, 55 and 65wt.%. The main results obtained in this work are summarized as follows; (1) The complicated flow of the dispersed materials in SMC occured during molding due to localized phenomena at the edge of squre plate. The tensile strength of SMC plate except that at the edge part increased with increasing fiber content but the increase of strength stopped at the fiber content over 55wt.%. The tensile strength at 55wt.% was as high as 20.9kg/mm2. The variation of the tensile strength of SMC plate except that at the edge part decreased with increasing fiber content. The minimum coefficient of variation was 7.4%. It seems to suggest that the SMC with high fiber content is very usefull. (2) The variation of the tensile strength of SMC plate including that at the edge part has the minimum value at the fiber content of 55wt.% and the filler content of 10wt.%. This seems to be influenced by the effect of filler which prevents the fiber alignment at the edge part and makes the fiber orientation distribution not uniform.
Two important problems are discussed in this paper with respect to the material design of composite laminates. One of them is the selection of optimal constitution of laminates from the viewpoint of the statistical variation of orientation angle. The other is concerned with the problem of the degree of accuracy of lay-up fabrication process. The variation sensitivity of in-plane elastic properties was studied statistically. The effect of the variation of orientation angle on effective engineering elastic constants is investigated by the partial derivative and Monte Carlo simulation technique. In addition, the effect of number of plies on standard deviation of in-plane elastic constants was studied. These sensitivity studies are summarized as follows. (1) The difference in constitution of laminates considerably affects the sensitivity of the variation of effective engineering elastic constants to the orientation angle. Therefore, from these equivalent constitutions, one can select the optimal constitution taking account of statistical sensitivity of in-plane elastic constants. (2) The procedure to evaluate the influence of the number of plies on the standard deviation of elastic constants was presented. (3) The proposed evaluation procedure suggests a method how to fabricate the composites having the variation of elastic constants less than a required value.
The molding of composite materials using BMC and SMC contributes greatly to mass production technology. However, the products made by this molding process have some problems. For example, in the case of a product with rib part, a hollow occasionally appears at the opposite surface of the rib. Furthermore, the strength of rib is reduced at the resin rich corner of rib. In order to solve these problems, it is necessary to investigate the flow state of BMC during the molding process by experimental and numerical analyses. In this paper, the dependence of flow state of BMC on the length of fiber involved was investigated. The experiments were carried out at room temperature so as to avoid the effect of polymerization. In the numerical analysis, a model consisting of isotropic laminae between each prepressed BMC laminates was used to simulate slippage in the specimen. The experimental and analytical results showed that the resin rich part at the corner of rib became larger as the fibers in BMC became shorter. The higher the height of rib, the larger the distortion of flow pattern and the variation of the strength of this part.
By using Fokker's Bond Tester (FBT, a resonance-impedance method) and the Image Analyzer System (IAS), the resonance characteristics and areas of defects of fiber reinforced plastic (FRP) sheets with a defective infiltrated layer were experimentally studied. The shear strength was also measured to compare with the values obtained by FBT and IAS. One type of defect in a layer was found to be wide-spread crowd voids and the other was locally distributed crowd voids. Although the wide-spread microscopic defects varied in size, quantity and configuration, three experimental values measured by FBT, IAS and shear tests on an arbitrarily selected place in FRP sheets were closely related eath other. In the case of local defects, the values by IAS could be related differently to the shear strength. But more detailed examinations about the local defects are needed to prove FBT and IAS to be useful devices to inspect FRP with defective infiltrated layers.
Although fatigue life distributions are often represented by the Weibull distribution with three parameters, the properties of these parameters have not been clarified. In this study, the fatigue tests were conducted on JIS S 35 C steels with two different grain sizes at stress levels near each fatigue limit by using a Wöhler type fatigue testing machine. The property of each parameter in Weibull type representation was discussed from the viewpoints of its dependency on the grain size and microscopic observations. The value of the scale parameter was larger for the material with larger grain size. The value of the shape parameter was roughly proportional to the applied stress for the material with larger grain size, while it was almost constant independently of the applied stress for the material with smaller grain size. From the microscopic observations of the crack growth behavior, it was suggested that the value of the location parameter might correspond to the number of stress cycles where the transition from stage I type crack to stage II type takes place. At stress levels near the fatigue limit of each material, the relationship between the applied stress σ and the fracture probability Pf could be approximated by the following linear equation, Pf=Aσ+B where A and B were material constants, and A increased as the grain size became larger. The evaluation of the safety factor was discussed on the basis of the above relation.
Fatigue tests under rotating bending and torsion were conducted in air, in distilled water and in 3 percent saltwater, using smooth specimens of a high strength low alloy steel. In each case, the fatigue crack length distributions were examined at the fixed cycle ratios, and the dependences of a parameter in the distribution function on cycle ratio and stress level were discussed. It was found that the fatigue crack length distributions under both loading conditions were well approximated by a three-parameter Weibull probability model in all environments, as same as the previous results on low carbon steel. The dependence of shape parameter on cycle ratio was not recognized, but that on stress level was more remarkable in distilled water than in other environments. These trends of the results were approximately in agreement with those of low carbon steel.
The impact fatigue tests were conducted on several kinds of laminates such as non-woven polyester cloth or glass cloth reinforced epoxy resins. From the experiments, the properties of impact fatigue strength for these laminates were clarified, and the scatter properties of these strengths were statistically analyzed. The safety factor and the allowable stress for laminates under service impact loadings were studied on the basis of failure probability theory. The results were as follows: (1) The fatigue strength (σt, τs) of the laminates subjected to repeated impact tensile or shear loads show the scatters of logarithmic distribution and can be estimated as the probability values by the following formula, respectively, σtNfmt=Dtμsu, τsNfms=Dsμsu where (mt, Dt), (ms, Ds) are the parameters of impact fatigue properties, Nf is the life to failure, (μ, s) are statistical values and u is the parameter of probability. (2) Both strength constants (Dt, Ds) are closely related to the static monotonic strength (σB, τf) and can be estimated from these values. (3) The safety factor and the allowable stress of these laminates under service impact loads can be determined according to the expectative failure probability. It is very useful for the fittest structural design.
A residual strength degradation model of FRP has been proposed based on the assumption that the residual strength decreases monotonically with increasing number of stress cycles. An experimental test program using plain woven laminated FRP has been conducted to generate statistically meaningful data. Good correlation has been verified between the theoretical predictions and the test results of the statistical distributions of residual strength. It is of great interest to note that the statistical distribution of fatigue life has been derived to be a well-known double exponential distribution by the proposed model. It is also shown that the model could be extended easily to reflect the engineering reality for other kinds of composites under different loading conditions.
Reliability analysis was conducted for the static fracture of circumferentially wound FRP flywheels. The carbon-epoxy and the glass-epoxy flywheels were considered. The probability of failure Pf was calculated assuming that both the longitudinal (circumferential) and transverse (radial) strengths have a two-parameter Weibull distribution and that failure obeys the maximum tensile stress criterion. Residual stresses were taken into consideration. The energy density ew (stored energy per unit weight) was evaluated as a function of Pf. The relation between Pf and the factor of safety was also examined. The principal results are summarized as follows. (1) The energy density ew decreases with a decrease in the allowable value of Pf. This tendency gets stronger as the ratio of the inner radius to the outer radius λ decreases. (2) The energy density ew for a specified value of Pf decreases as λ decreases. However, since the influence of λ is not large when λ_??_0.9, λ≅0.9 is close enough to satisfying the optimal design condition. (3) The energy density ew for a specified value of Pf decreases with a decrease in mθ and mr, which are the shape parameters of the longitudinal and transverse strength distributions, respectively. The influence of mθ is remarkable when λ is large, and that of mr becomes stronger as λ decreases. (4) When λ is small, the energy density ew of the glass-epoxy flywheel for a specified value of Pf can be higher than that of the carbon-epoxy flywheel. This is due to the presence of residual stress. (5) The radial safety factor Sfr is considerably greater than the circumferential safety factor Sfθ when λ=0.9. Even though a state of Sfθ≅Sfr may be ensured for a smaller λ, such a λ will be far from satisfying the optimal design condition.
This paper proposes a method to evaluate the reliability of structures by using moments up to the fourth-order, which are the minimum number of terms reflecting the shape of probability distributions. The one-dimensional cumulative distribution function (c.d.f.) is asymptotically expanded into Edgeworth's series expressed in terms of moments up to the fourth-order. The expanded c.d.f. gives a negative value at the tail of the distribution for some cases of the combination of skewness and kurtosis. Modification is made in the approximation formula to remedy this draw-back, thus making it possible to evaluate any general non-Gaussian c.d.f. The proposed method is applied to the reliability analysis of typical frame structures where the random variables follow non-Gaussian probability distributions. It is shown that the proposed method is very effective for evaluating quantitatively the effects of probability distributions on the resulting structural reliability or failure probability.