Effort is being made at the National Research Institute for Metals (NRIM) to establish reliable fatigue data for representative materials in the Japanese Industrial Standard (JIS). The present paper provides the results of statistical analysis of S-N data for three JIS carbon steels (0.35C, 0.45C, and 0.55C) and three JIS low alloy steels (0.40C-1Cr, 0.35C-1Cr-0.2Mo, and 0.40-1Cr-0.2Mo) tested for the NRIM Fatigue Data Sheets. Twelve different heats on average were examined for each steels at three quench-tempered states (550, 600, and 650°C tempered) using about twenty specimens each. The Probit analysis method using weighting was applied to this large number of small sample S-N data by pooling them on a stress scale relative to the tensile strength of each material. The analysis revealed that the relative fatigue limit was around 0.54 with the standard deviation near 0.02 of the tensile strength. An asymmetric fatigue strength distribution tailed in the weaker side was observed for the materials with their strength higher than 900N/mm2. The cause of this skewed distribution was discussed in relation to the pronounced influence of small defects on fatigue strength of higher strength materials.
Reliability analysis of structures based on fracture mechanics requires knowledge on statistical characteristics of m and C in the fatigue crack propagation law da/dN=C(ΔK)m. However, rather few experimental data have been reported on variability of m and C. In the present paper, axial fatigue tests were conducted on 30 specimens of 2024-T3 Al alloy under the same one condition. The values of m and C were determined for each specimen, and all the data were analysed statistically. The method for predicting the distribution of fatigue crack propagation life was also examined. The principal results are summarized as follows. (1) m follows a normal distribution approximately. (2) C follows a log-normal distribution approximately. (3) A strong linear correlation exists between m and log C, which is approximated by C=C0K0-m. (4) On the log da/dN-logΔK coordinates, the so-called pivot point (K0, C0) is considerably apart from the centroid of the data points, and therefore, it seems that the variation of m and C as well as their correlation do not arise from the intrinsic nature of the regression line. (5) Strictly speaking, C0 in the relation C=C0K0-m is not a fixed value but a random variable which is independent of m, and in the first approximation C0 follows a log-normal distribution. (6) The distribution of fatigue crack propagation life was calculated using the equation da/dN=C0(ΔK/K0)m on the assumption that m and log C0 are normally distributed random variables. The calculated distribution was in good agreement with the experimental distribution.
The present paper proposes a new model of fatigue process for smooth unnotched materials; namely, a Monte Carlo simulation model in which the fatigue fracture process of smooth unnotched materials is composed of the initiation, growth and coalescence of randomly distributed small surface cracks. Based on the model proposed, an analysis was made by using the experimental results on the initiation and growth behavior of distributed cracks in corrosion fatigue of smooth unnotched HT 60 steel. In the analysis, the statistical nature of small cracks in their initiation sites, surface lengths and growth behavior were taken into consideration. The proposed model and analysis may be applicable to the evaluation of fatigue damage accumulated in structures, and can be used in reliability analyses.
It has been recognized that a considerable number of structures require repairing or alteration from time to time. Under this situation, it is an emergent and important task to establish a method of evaluating the integrity of structures. However, analysis of structural integrity is very difficult, because the mechanism of damage assessment is complicated and concerned with various kinds of factors. In this paper, an attempt is made to develop a synthetic analytical method of structural integrity, based on the theory of fuzzy graph. At first, representative factors, which affect the structural integrity, are enumerated and integrated into a hierarchy system. By using the evaluating system, the analysis is performed through such linguistic variables as“large”, “medium”, “small”, etc. Information of the linguistic variables is transmitted from the input events to the top event, in which weightening is taken into account on the evaluation of each factor. The final result, which is obtained at the top event in the form of membership function, is interpreted by use of the concept of pattern recognition. The numerical results obtained confirm that (1) the method developed herein is available to introduce the engineering judgement into the integrity analysis, (2) the use of linguistic variables enables to merge the subjective assessment with the observation data or experimental results through simple matrix computations, and (3) the concept of pattern recognition is quite useful for classifying the degree of integrity of existing structures.
Static and cyclic fatigue tests were conducted on sintered silicon nitride at room temperature in air. The results were analysed through the fracture mechanics concept. Static tests were performed in a cantilever type bending state and the mean strength obtained was less than a half of that in the three-point bending tests on the same material. The decrease in strength was not explained satisfactorily only from the view point of size effect based on the weakest link model. Then, the fracture surface of the tested specimens was observed microscopically. The stress intensity factors evaluated for the observed flaws were smaller than the fracture toughness. The concept of equivalent crack length was introduced to represent the severity of flaw. The relation between fracture strength and this equivalent crack length obtained in the present experiment did not coincide with the expectation from the linear elastic fracture mechanics. This suggested that not all of the observed flaws were the fracture origin. Cyclic fatigue tests were conducted under fully reversed plane bending. Although a large scatter was observed in the relation between fatigue-life and stress-amplitude above 220MPa, the endurance limit at 107 stress-cycles was expected to be within the range of stress-amplitude from 170 to 200MPa. An attempt to explain these tendencies was made based on the distribution of inherent flaws and the relation of crack growth rate versus stress intensity factor.
Experimental studies have been performed on the residual strength degradation process of Glass/Polyester laminates under repeated tension and compression loadings. The validity of the model proposed in the previous paper was examined through the comparison with a sufficient amount of test data under both the perfectly reversed loading and the zero-tension loading conditions, for three kinds of specimens having different glass fiber contents. Good correlation was verified between the theoretical prediction and the test result of the residual strength as well as its statistical distribution. In addition to predicting the residual strength, the present model was used to evaluate the effect of proof loads. It was also shown that the correlation between the experimental results and the theory of proof tests was reasonable.
The impact tensile fatigue tests were conducted on alumina and silica filler reinforced epoxy resin castings. From the experiments, the properties of these resin castings under repeated impact tensile loads were clarified and the scatter properties of their strength were statistically analyzed. Safety factors and allowable stresses for resin castings under service impact tensile loading were studied on the basis of failure probability theory. The results were as follows: (1) The fatigue tensile strength σt of resin castings subjected to repeated impact tensile loading shows a scatter of logarithmic normal distribution and can be estimated statistically by the following formula. σtNfmt=ξDtμtStu where mt and Dt are the parameters of impact fatigue properties, Nf is the life to failure, μt and St are statistical values and u is the parameter of probability. (2) The strength constant Dt is closely related to the static tensile strength σB, and it can be estimated from the latter. (3) The safety factor and the allowable stress of these resin castings under service impact loads can be determined according to the expectative failure probability. It is useful for the most suitable structural design.
Composite materials are often combined with other materials such as foamed plastics and wood to make a sandwich-type component. In this case a designer is faced with a‘materials design problem’, that is the selection of the best combination of materials for a particular application and the determination of the thickness ratio of each layer and the fiber orientation angle. In this paper, an optimal design method of fibrous composite sandwich plates with required flexural stiffness is proposed. The sandwich plates were supposed to be limited in thickness and consist of a skin of angle ply laminate and a core of isotropic material. The effective Young's moduli E1f, E2f and E6f of the plate were considered as the flexural stiffness. The optimal value of the core thickness ratio, which gives the minimum cost or the minimum weight, and the fiber orientation angle for the skin were obtained under the condition of given flexural stiffness.
A new analysis method was presented to explain asymmetrical weld marks occasionally observed in the section of symmetrically molded products of FRP. At first, a possibility of initial deformation before material flow was calculated by eigenvalue analysis. Next, a model which could simulate the part of infinitesimal deformation was proposed, and by using this model the initial deformation mode was calculated by linear incremental analysis considering the above result. This showed that the material flow might be asymmetrical even if the flow canal is symmetrical. Finally, the flow analysis employing a conventional technique for composite materials was performed considering the above result of linear analysis. As an application of this method, the effect of interface which existed in hybrid lamination, on flow pattern was investigated numerically and experimentally. The numerical analysis that was developed in this paper could simulated the growth of weld line. The numerical model which contains isotropic lamina between each laminates was effective to simulate the behaviour of laminated materials such as hybrid lamination during compression molding process. And both are phenomenologically in good agreement. The numerical analysis also suggests that hybrid lamination, that is, the combined use of sheet molding compounds of different rigidity is a useful way to minimize weld marks in the molded product.
Recently, the hybrid composites containing various carbon clothes and glass mat in polyester matrix have attracted a special interest. This paper describes the flexural properties and the fracture behavior of the sandwich type hybrid composites in which three kinds of carbon cloth were used as facing material. These hybrid composites differ in the thickness ratio of CF part to GF part, and have the thickness from 1.68 to 4.03mm. Furthermore, the effect of thickness on the flexural strength was examined. The results obtained are as follows. (1) In all CF-cloth/GF-mat hybrid composites, the micro buckling of carbon fiber occurred in the compression side one by one with increasing load after the proportional limit, and in this place the whitening was observed. Consequently, the stress-strain diagrams like the teeth of a saw were obtained. The ultimate fracture occurred in the tension side of CF part. (2) The flexural strength of hybrid composites was considerably influenced by the thickness of specimen when it is under about 3.0mm, and the composite beam theory was corrected by considering such effect of thickness. However, the flexural strength of hybrid composites with more than 3.0mm in thickness could be estimated by using the common composite beam theory.
According to the development of various new kinds of fiber with high strength and high rigidity suitable for reinforcing materials, active studies on the hybrid composite structures containing such fibers are being carried out lately. On the other hand, the fracture of interlaminars of hybrid composites comes into a problem as the hybridization of these materials becomes common. Therefore, it is necessary to consider the interlaminar shear strength so far as the two-dimensional woven stuffs such as the mat or the cloth reinforcement are employed. So, in this paper, the interlaminar shear behavior of the carbon/glass hybrid construction (polyester matrix) consisting of symmetrical five laminations was studied. Since the interlaminar shear strength of hybrid composites generally depends on the combination of fiber reinforcement and resin matrix, the interlaminar shear stress in the CF/GF hybrid composites was analyzed by applying the composite beam theory and then the minimization of the shear stress of hybrid composites was examined. As the results, a design guide for minimizing the interlaminar shear stress of the CF/GF hybrid composites was obtained. Furthermore, the improvement of their mechanical properties was discussed.
Investigation was firstly made on the estimation method of fatigue life for FRP subjected to superimposed sinusoidal wave loads. Secondly, the fatigue life estimation was performed for three different load patterns programmed with triangular waves. Fatigue tests were conducted under both a constant stress amplitude and various programmed load patterns by a hydraulic fatigue testing machine. The test results showed that it is possible to make the fatigue life estimation for FRP under various superimposed sinusoidal wave loads based upon the frequency dependence of fatigue with the aid of the equivalent frequency method studied in the previous paper. The fatigue life under various load patterns can also be estimated to some extent by employing the equivalent stress range for the evaluation of stress value in random waves.
The dynamic fracture toughness of reinforced reaction injection molding polyurethane was experimentally studied using an instrumented impact tensile tester. In this paper, the effects of void diameter, void distribution and fiber content on the dynamic fracture toughness were discussed. The results obtained are summarized as follows. (1) Dynamic fracture toughness, Kd, decreased almost linearly with increasing void content irrespective of fiber content. (2) For the same void content, Kd was minimum at 5% of fiber content, beyond which it increased with fiber content. (3) Kd of R-RIM material was found to be lower than that of glass fiber reinforced polycarbonate (FRPC) but the energy release rate of R-RIM material was higher than that of FRPC. Thus, the R-RIM material has good energy absorption capacity.
The curing process of molding compounds such as BMC under compression molding is shown to be predictable by taking the following procedures. (1) The temperature-time curves of BMC are determined from a series of tests. (2) FEM analysis is applied to calculate heat conduction in the compound for the case that heat generation is neglected. (3) By combining above two results, the heat generation rate of BMC during the curing process is determined. (4) By employing the heat generation rate of BMC, FEM analysis is conducted to clarify the unsteady heat conduction in BMC during compression molding. The temperature vs. time curve thus obtained is in good agreement with the test result. (5) Finally, the curing process can be predicted by using the result of the analysis on the assumption that the resin cures sufficiently well when the cumulative heat generation reaches 80% of the total generation of heat.
The mechanical properties together with the tensile testing method of orthogonal and quasi-isotropic CFRP laminates made of finite number of unidirectional and cloth prepreg sheets were discussed. (1) Two different test specimens used in ISO and ASTM standards were checked. The dumbell-type specimen was found to be undersirable even for quasi-isotropic laminates, since the fracture usually takes place near the intersection of parallel and curved portions. The strip-type specimen with tabs at both ends recommended for oriented composites frequently yielded unexpected tensile fracture because of fracture near the tab end or in the grip. The specimen having a circular notch with large radius of curvature thicknesswise is recommended for the unidirectional composites. (2) The Young's modulus of orthotropic and quasi-isotropic laminates can be predicted by the lamination theory in good agreement with the experimental values independently of the type of prepreg sheets. However, the tensile strength of laminates made cloth prepreg is lower than that made of unidirectional prepreg because of the local high stress at the cross-over points. (3) It should be noted in the quasi-isotropic laminates that the in-plane elastic modulus is isotropic, but the tensile strength is different depending on the interval of lamination angle and on the tensile direction. These experimental results can be reasonably explained by considering that the fracture results from the tensile fracture transverse to fibers in a lamina.