Fiber length critical

In order to define the critical fiber length, it is necessary to know the shear stress (t) between the fibers and thermoplastic starch. Unfortunately, independent measurement of the value of t is impossible because of the lack of suitable measurement equipment. Because the problem of determining the value of steady stress between fibers and thermoplastic starch has only recently begun to attract interest, the scientific literature does not provide any definite data the approximate value of T was adopted from measurements reported by Morlin and Czigany [8]. In their research, they established that the shear stress between flax fibers and Mater-Bi (which is a variety of thermoplastic starch) amounts to 4.18 MPa. 

Oniszczuk [6] determined from these results that the critical fiber length for the flax fiber/thermoplastic starch combination is 951 jj.m. 

On examination of the samples with 5% flax fiber content, it can be noted that samples with higher glycerol content show shorter pull-out lengths and more breakage. Therefore it can be argued that an increase in glycerol content does not 

The mechanical properties of biocomposites depend on a number of factors. Firstly, these are the quantity and type of fiber added to the material, but the type and amount of plasticizers and the production temperature are also important parameters [14]. One of the parameters with a dominating influence on the mechanical properties of biocomposites is the quantity of both natural fiber and plasticizer [3, 4, 6]. It has been observed that the addition of fiber enhances the mechanical strength. The addition of extra plasticizer causes a decUne in the maximum sample stress. 

The same tendency can be seen in the case of samples obtained at different production temperatures. The highest mechanical strengths were displayed by moldings produced at a material injection temperature of 140 C (maxinial stress 27.8 MPa), whereas the lowest mechanical strengths were noted for moldings obtained at a temperature of 180 C (10.8 MPa). 

As mentioned in 10.2.3, super-strong polymeric, ceramic, metallic, and carbon fibers are now used to reinforce various t) es of composifes. However strong the fiber may be, fhe composite is no better than the bond between the fiber and its matrix. Consider a fiber of diameter D and length L, half of which is imbedded in a matrix along the z-axis. If a longitudinal force F is applied that tries to pull the fiber ouf of the matrix, the matrix will 

If the aspect ratio of the fibers is less than the critical value, the bond between the fibers and the matrix will fail before the fibers break and full advantage of the fiber s strength will not be realized. 

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In other words, the critical fiber length is a function of its strength, diameter and the shear strength at the filler-matrix interface. 

Another way to obtain the critical fiber length is to rearrange Equation (15.1) to give the following ... 

Lacroix, Th., Tilmans, B., Keunings, R., Desaeger, M. and Verpoest, F. (1992). Modelling of critical fiber length and interfacial debonding in the fragmentation testing of polymer composites. Composites Sci. Technol. 43, 379-387. 

Ohsawa, T., Nakayama, A., Miwa, M. and Hasegawa, A. (1978). Temperature dependence of critical fiber length for glass fiber-reinforced thermosetting resins. J. Appl. Polym. Sci. 22, 3203-3212. 

Mathematically the critical fiber length necessary for effective strengthening and stiffening can be described as follows ... 

Critical fiber length = [Ultimate or tensile strength times fiber diameter/2] times the fiber-matrix bond strength or the shear yield strength of the matrix— whichever is smaller... 

Fibers that have a length greater than this critical length are called continuous fibers, while those that are less are called discontinuous or short fibers. Little transference of stress and thus little reinforcement is achieved for short fibers. Thus, fibers whose lengths exceed the critical fiber length are used. 

V/ = volume fraction of glass fiber lc = critical fiber length la = actual fiber length d = fiber diameter t = shear strength of matrix resin a = ratio of actual to critical fiber length composite tensile strength a/ = fiber tensile strength... 

A similar balance can be made for fibers embedded in a matrix of a composite under tensile stress, but in this case we have to take into account that both ends on the fiber carry interfacial shear stress, so the critical fiber length will be... 

The critical fiber length, /c, is the minimum fiber length that will allow tensile failure of the fiber rather than shear failure of the interface. It can be calculated from Eq. (15.46) ... 

The critical fiber length for the fibers in the three different polymer matrices are shown in Table IV. Based on these critical lengths, both commercially treated fibers (XAS and AS-4) showed better adhesion to the polymer matrices than did the untreated fiber (AU-4). This can be explained in terms of the greater acid/base interactions of these two fibers with the matrices. 

The critical fiber length, can be derived from a similar force balance for an embedded length of IJ2. Thus,... 

So if the composite is to fail through tensile fracture of the fiber rather than shear failure due to matrix flow at the interface between the fiber and the matrix, the ratio IJd, known as the critical aspect ratio, must be exceeded, or, in other words, for a given diameter of fiber, d, the critical fiber length, / must be exceeded. 

The critical fiber length (L ) of programmed short SMPFs is estimated by the shear-lag theory [41] ... 

In self-healing with embedded short SMPFs, the fiber length plays a pivotal role in determining the crack width that can be closed. The critical fiber length has been a well-known concept in... 

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