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This study demonstrates the effect of weak-link scaling on the tensile strength of bamboo fibers. The proposed model considers the random nature of fiber strength, which is reflected by using a two-parameter Weibull distribution function. Tension tests were performed on samples that could be scaled in length. The size effects in fiber length on the strength were analyzed based on Weibull statistics. The results verify the use of Weibull parameters from specimen testing for predicting the strength distributions of fibers of longer gauge lengths.

In recent decades, natural fiber reinforcement has gained much attention as realistic, environmental-friendly alternatives to synthetic fibers. As typical biological materials with unique multiscale structures, natural fibers approximate or even exceed the specific mechanical properties of man-made fibers [

Fibers are the main load-bearing elements of a fiber-reinforced composite, which means that most of the mechanical properties of fiber-reinforced composites are primarily affected by fiber strength distribution [

The aim of the present paper is to investigate the scaling effects involved in predicting the ultimate tensile strength of bamboo fibers. Tension tests were performed to describe the statistical strength distributions of bamboo fibers. The measured fiber strengths at different gauge lengths were analyzed according to a two-parameter Weibull distribution. Thus, we established a method for determining statistical parameters used for characterizing strength distribution. Fibers 20, 30, 40, 50, and 60 mm long were used to investigate the dependence of strength on fiber size. The accuracy of using weak-link scaling statistics for fiber strength was also examined.

The bamboo fibers were produced by Ban Ltd., Tokushima, Japan. The scanning electron micrograph of the longitudinal section of a bamboo fiber measured in the present study is shown in Figure

Longitudinal photomicrographs of bamboo fiber.

To fix the fiber as straight as possible between the clamps, a fiber specimen is mounted on a paper frame that matches the gauge length chosen for the test. The ends of the fiber were glued to the tab using a double-sided adhesive. The frame was cut after clamping in the jaws of the testing machine. The opening of the paper frame determined the gauge length. For this experiment, the gauge lengths were set to 20, 30, 40, 50, and 60 mm. Fifty individual fibers were tested at each of the five gauge lengths. Fiber length was measured to an accuracy of ±1 mm at each end. Tests were performed on a variety of lengths to investigate the effects of fiber length on tensile strength. To prevent additional flaws caused by the clamping force, samples broken near the edge of the clamps were excluded from the analysis.

Fiber specimens were mechanically tested on a WDW3050 computer-controlled universal testing machine. All static tests were conducted in displacement control mode at a rate of 0.5 mm/min and at ambient temperature under atmospheric pressure. All samples were maintained under load until mechanical failure occurred, with failure being defined as the point in which the laminate no longer supported the externally applied load. The forces applied and the testing machine displacements were directly recorded by an acquisition system and on a chart recorder. Therefore, tensile strength was taken as the ratio of the maximum load applied to the cross-sectional area of the specimen. Based on a typical load-displacement response shown in Figure

The experimental results of a classical load-displacement curve of bamboo fiber.

Brittle fibers typically exhibit wide variability in strength, which is determined by the microstructural flaws that act as stress concentrations. These internal defects occur randomly along the length of the fiber. Fracture stresses measured on specimens with identical dimensions have a statistical distribution because of the widely varying severity of flaws caused by variability in shape, size, and location with respect to stress state [

Since

Figure

Weibull distribution of fiber strength.

Expressing (

Hence, a plot of

Weak-link theory, which accurately describes the failure of many brittle materials, is based on the assumption that the material can be divided into smaller linked elements and that the fracture of a specimen is identified with the unstable propagation of the most “critical” crack [

Based on the weakest link theory, Weibull [

If the diameter,

From (

If the strength of a material is determined by weak-link statistics, longer fibers have a larger number of links than shorter fibers and have a higher probability of encountering a more severe flaw along the fiber [

Considering (

The work by Curtin [

With constant fiber diameter, (

Figure

The experimental probability density function for ultimate strength of bamboo fiber.

A typical Weibull plot of bamboo fracture strength at 20 mm gauge length based on (

Strength distributions of bamboo fibers with

The relationship between the mean tensile strength of bamboo fiber and the testing gauge length is plotted on Figure

Length dependence of the mean tensile strength of bamboo fibers.

If the characteristic strength at a given gauge length is known, the mean strength at other gauge lengths can be calculated based on (

Comparison of measured and predicted fracture strengths of bamboo fibers.

Fiber test length (mm) | Tensile strength | Difference (%) | |
---|---|---|---|

Measured by experiment* (MPa) | Predicted by ( | ||

20 | 555 | — | — |

30 | 523 | 502 | 4.26 |

40 | 492 | 467 | 5.35 |

50 | 451 | 442 | 2.12 |

60 | 442 | 422 | 4.60 |

Predictions of the tensile strengths were made by size scaling data from samples of longer gauge lengths to access the accuracy of weak-link scaling. An example comparing the experimental and predicted bamboo strength distribution for

Strength distributions for bamboo fibers with

The tensile strength distribution of fibers is a key constitutive property of fiber-reinforced composites. Thus, understanding the scaling effects in the tensile properties of natural fibers is important. In the present study, bamboo fibers were tested with tension at several different gauge lengths. For each gauge length, 50 individual fibers were measured. The experimental fiber strength values were compared with the predicted values through weak-link scaling. The following conclusions were drawn.

Tensile strength of bamboo fibers exhibits statistical Weibull-type distribution, which is not necessarily constant. The two statistical parameters,

Ultimate fiber strength depends on specimen length, which is dominated by flaws statistics. This dependence is due to the increased probability of flaws that cause failure with larger material volumes. The gauge length effect on bamboo fiber strength can be predicted through weak-link scaling.

The simulated cumulative failure probability from the scaling model is consistent with the test data. These results verify the use of Weibull parameters from specimen testing for predicting the strength distributions of fibers of longer gauge lengths.

The authors gratefully acknowledge the financial support of National Science Foundation of China under Grant no. 11102169, National Science Foundation Project of CQ CSTC under Grant no. 2012JJA70002, and Fundamental Research Funds for the Central Universities under Grant nos. XDJK2013B019, XDJK2013D011.