Koichi Goda

The evaluation of the strength distribution of silicon carbide and alumina fibres by a multi-modal Weibull distribution

The strengh distributions of silicon carbide and alumina fibres have been evaluated by a multimodal Weibull distribution function. This treatment is based on the concept that the fracture of the fibre is determined by competition among the strength distributions of several kinds of the defect sub-population. Since those fibres were observed to have two types of fracture mode, the evaluation of a bi-modal Weibull distribution was performed in comparison with the single Weibull distribution usually employed. The accuracy of the fit for these two distributions was judged from maximum logarithm likelihoods and cumulative distribution curves. The result showed that the logarithm likelihood calculated using the bi-modal Weibull distribution function gave a larger value, as compared with those using the single Weibull distribution function. The curve predicted from the former function was also in good agreement with the data points. In addition, the strength distribution and the average value at a different gauge length were extrapolated from the Weibull parameters estimated at the original gauge length. In this case, also, the bi-modal Weibull distribution gave a more accurate prediction of the data points.

Reliability approach to the tensile strength of unidirectional CFRP composites by Monte-Carlo simulation in a shear-lag model

A numerical technique based on the Monte-Carlo method in a shear-lag model is developed to simulate the tensile strength and fracture process for a unidirectional carbon-fiber-reinforced-plastic (CFRP) composite. The technique improves on the conventional approach by using an rmin method that can determine the stresses working on the fiber and matrix elements as the damage progresses. The rmin method is based on tracking the incremental ratio of the strength of an element to its stress. The present model includes the effect of the sliding frictional forces around fiber breaks caused by debonding between the fiber and matrix. Statistical properties of the tensile strength were obtained through simulation runs involving 100 samples for each value of the frictional force parameter. Also studied was the size effect in composite strength with increasing numbers of fibers, N, where it was found numerically that mean strength varies linearly as 1[ln(N)]12 and coefficient of variation varies linearly as 1ln(N), as suggested from a simple theory.

The role of interfacial debonding in increasing the strength and reliability of unidirectional fibrous composites

A Monte-Carlo simulation technique based on a finite-element method has been developed in order to clarify the effect of interfacial shear strength on the tensile strength and reliability of fibrous composites. In the simulation a boron/epoxy monolayer composite was modelled, and five hundred simulations were carried out for various interfacial shear strengths. The interfacial shear strength value which raised the average strength of the composite corresponded approximately to the value which reduced the coefficient of variation. This implies the existence of an optimum value of interfacial shear strength which can increase the strength and reliability. The simulated strength and reliability were closely related to the degree and type of damage around a fiber break. That is to say, large-scale debonding caused by a weak interfacial bond and matrix cracking caused by a strong bond reduced the number of fiber breaks accumulated up to the maximum stress, and decreased the strength and reliability. On the other hand, small-scale debonding promoted comparatively the cumulative effect of fiber breaks and played a key role in increasing the composite strength and reliability.

A new theory to obtain Weibull fibre strength parameters from a single-fibre composite test

A theory is developed to obtain the Weibull scale and shape parameters for in situ fibre strength utilizing the data obtained from a single-fibre-composite (SFC) test. It is well known that during the SFC test, the fibre fractures several times along its length at successive weak points that are randomly located. The SFC technique, although most commonly used for measuring the fibre/matrix interfacial shear strength, is an excellent way to determine the fibre flaw spacings and the in situ fibre failure stress at every fracture location. In the present technique, the SFC specimen is partitioned into a relatively large number of small sections of equal length such that each section will have either one or no fibre fracture point. Because all the sections may not include the fibre fracture points because of their random nature, the test data are regarded as “censored data”. In other words, the theory is constructed for the estimation of Weibull parameters that takes into account the censored nature of the data. The Weibull parameters predicted using the present theory are in the same range as those obtained from the single fibre tension tests. For several reasons the values obtained from the SFC test tend to be slightly higher than those obtained from the simple tension tests. However, the in situ fibre strength values obtained using SFC technique may be more realistic and thus may be more useful in modelling composite strength.

A new method of evaluating the interfacial properties of composites by means of the gradual multi-fiber fragmentation test

A new method for evaluating the interfacial properties of fibrous composites based on a fragmentation technique has been proposed by use of the gradual multi-fiber composite, in which the inter-fiber spacing is gradually changed. The results showed that as the inter-fiber distance increased, the aspect ratio of broken fibers decreased while the fibre/matrix interfacial shear strength increased. When the reciprocal of the inter-fiber distance was taken for the above relationships, both the aspect ratio and interfacial shear strength were found to show a saturated value. This means that the gradual multi-fiber composite indicates an upper bound in aspect ratio and a lower bound in interfacial shear strength, while the single-fiber composite shows a lower bound in aspect ratio and an upper bound in interfacial shear strength. It was concluded that this fragmentation test could be a new method for composite evaluation, since reducing the difference between these two bounds is effective for composite strengthening. In addition an elasto-plastic finite-element analysis was carried out to relate the above results with the fiber stress distribution around fiber breaks. It is proved that the bound obtained in the gradual multi-fiber composite test is closely concerned with stress concentrations caused by a group of multi-fiber breaks.

Considerations of the reliability of tensile strength at elevated temperature of unidirectional metal matrix composites

Abstract It is well known that the tensile strength of unidirectional metal matrix composites is somewhat decreased at elevated temperatures compared with that at room temperature. In order to elucidate this effect, a Monte-Carlo simulation has been carried out on the tensile fracture of unifirectional metal matrix composites by the use of a finite difference method based on the shearlag model. It was assumed that no reinforcing ceramic fibers were degraded, and only the shear yield stress of the matrix metal changed with temperature. The results showed that the average strength of the composites decreased slightly with temperature, and the variability increased. Such tendencies were also found by the recursion analysis technique based on the chain-of-bundle probability model proposed by Harlow and Phoenix.

Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage

Abstract A numerical simulation for predicting the axial creep-rupture lifetime of continuous fiber-reinforced metal matrix composites is proposed, based on the finite element method. The simulation model is composed of line elements representing the fibers and four-node isoparametric plane elements representing the matrix. While the fibers behave as an elastic body at all times, the matrix behaves as an elasto-plastic body at the loading process and an elasto-plastic creep body at the creep process. It is further assumed in the simulation that the fibers are fractured not only in stress criterion but time-dependently with random nature. Simulation results were compared with the creep-rupture lifetime data of a boron-aluminum composite with 10% fiber volume fraction experimentally obtained. The simulated creep-rupture lifetimes agreed well with the averages of the experimental data. The proposed simulation is further carried out to predict a possibility of creep-rupture for the composite without time-dependent fiber breakage. It is finally concluded that the creep-rupture of a boron-aluminum composite is closely related with the shear stress relaxation occurring in the matrix as well as time-dependent fiber breakage.

A strength reliability model of unidirectional fiber-reinforced ceramic matrix composites by Markov process

We propose a stochastic process analysis for predicting the strength and reliability of a unidirectional fiber-reinforced ceramic matrix composite. The analysis is based on a Markov process, in which it is assumed that a state of damage in the composite is developed with each fiber breakage. When the Weibull distribution is used to describe the strength distribution of the fiber, the probability of being in each state can be solved analytically in a closed form. Using the solutions of the probabilities, a discussion about damage tolerance of the composites is quantitatively developed, from the viewpoint of materials reliability engineering. To compare the proposed stochastic process analysis with previously proposed strength models in the basis of classical bundle theory, we obtained the expected value and variance in the composite stress from solutions of the probabilities of being in the states. The expected value and variance both consist of two terms, equivalent to the effects of both bundle structure and stress recovery in broken fibers. These are surprisingly in agreement with the solutions analyzed by Phoenix and Raj [9]. The effect of stress recovery in broken fibers produces a positive in the expected value and a negative in the variance and is thus a significant mechanism for increasing the strength and reliability of the composite. In addition we predicted the expected values of composite strengths and variances from the solutions. The corresponding value of normalized fiber stress to obtain the expected value in strength and the variance agreed relatively well with the value predicted by Hui et al. [13]. We further verified that the composite strength obeys a normal distribution, which has the expected value and standard deviation predicted above. Finally, we predicted the probabilities in strength of the composites with various sizes and concluded that the ceramic matrix composite is quite reliable in strength when the number of fibers corresponds to that in practical use.

Development and mechanical properties of bagasse fiber reinforced composites

Environment-friendly composites reinforced with bagasse fiber (BF), a kind of natural fiber as the remains from squeezed sugarcane, were fabricated by injection molding and press molding. As appropriate matrices for injection molding and press molding, polypropylene (PP) and polycaprolactone-cornstarch (PCL-C) were selected, as a typical recyclable resin and biodegradable resin, respectively. The mechanical properties of BF/PP composites were investigated in view of fiber mass fraction and injection molding conditions. And the mechanical properties and the biodegradation of BF/PCL composites were also evaluated. In the case of injection molding, the flexural modulus increased with an increase in fiber mass fraction, and the mechanical properties decreased with an increase in cylinder temperature due to the thermal degradation of BF. The optimum conditions increasing the flexural properties and the impact strength were 90°C mold temperature, 30 s injection interval, and in the range of 165 to 185°C cylinder temperature. On the other hand, as to BF/PCL-C fully-green composites, both the flexural properties and the impact strength increased with an increase in fiber mass fraction. It is considered that the BF compressed during preparation could result in the enhancement in mechanical properties. The results of the biodegradability test showed the addition of BF caused the acceleration of weight loss, which increased further with increasing fiber content. This reveals that the addition and the quantities of BF could promote the biodegradation of fully-green composites.

Biodegradation of Bagasse Fiber Reinforced Biodegradable Composites

Biodegradable composites made from bagasse fiber and biodegradable resin were prepared and the biodegradation were investigated by the soil burial test in terms of the effects of fiber content, alkali treatment to bagasse fiber and different soil. The biodegradable resin showed some extent biodegradation. The addition of bagasse fiber caused the acceleration of weight loss of the fiber reinforced composites in comparison with the neat biodegradable resin. The weight loss of the composites increased with the increase in the fiber content, which could attribute to the preferential degradation of bagasse fiber and the resin around the fiber. However there was no significant difference in weight loss between untreated and alkali treated fiber composites. Furthermore, it is noted that the weight loss drastically increased in the case of the composites buried in the microorganism enriched soil. This results from the increase of bacteria and fungi in soil. The photographs and SEM micrographs showed the degradation of the resin and the composites.