By definition, composite materials include two or more phases having different physical characteristics. Many composites incorporate fibers, typically of a relatively rigid material, in a matrix of another material which ordinarily is less rigid. For example, polymers are often reinforced with fibers of glass, ceramic or carbon, whereas metals may be reinforced with ceramic fibers.
Composites present unique problems not encountered with uniform, single phase materials. Practical processes for producing composite materials and forming them into the desired shapes impose limits and tradeoffs. It is often less expensive to make a fiber reinforced composite using relatively short fibers and with a relatively low ratio of fiber volume to matrix volume. Conversely, the physical properties of the composite such as tensile strength and tensile modulus often improve with increasing fiber volume and particularly with increasing fiber length. Design of a composite often involves balancing these competing considerations.
It has long been recognized that the length of the fiber influences the degree to which loads such as tensile loads are borne by the fiber as opposed to the surrounding matrix. This may be illustrated by considering the case of a fiber embedded in a surrounding matrix, the fiber having substantially higher modulus of elongation than the surrounding matrix material, and the entire assembly being subjected to a tensile load in the direction of the fiber. As loads can be transferred to the fiber only through the immediately adjacent matrix material, the total tensile force applied to the fiber is directly related to the load borne by the region of matrix material immediately surrounding the fiber. With a very short fiber, the region of matrix material which immediately surrounds the fiber is relatively small and hence the load transferred to the fiber for a given deformation of the matrix material is also relatively small. Thus, even where the matrix material has deformed to its breaking point, the amount of load transferred to the fiber may be very small. Conversely, for a very long fiber there is substantial region of matrix material surrounding the fiber, and the amount of load transferred to the fiber per unit deformation of the matrix material is correspondingly large. Therefore, substantial loads will be applied to the fiber even at relatively small deformations of the matrix material.
With very short fibers the fibers will remain unbroken when the composite is broken, whereas for very long fibers the fibers will be broken before the composite breaks. The term "critical length" is ordinarily used to refer to the fiber length forming the boundary between these two types of fracture behavior. For fiber lengths less than the critical length the matrix material will break leaving the fibers intact when the composite is stressed to failure, whereas for fiber lengths above the critical length the fibers will break before the matrix material breaks. The length of a fiber is often expressed in terms of its aspect ratio, i.e., the ratio between the length of the fiber in its direction of elongation and the diameter or largest dimension of the fiber in a direction perpendicular to its direction of elongation. The critical length can be stated as a critical aspect ratio.
Numerous attempts have been made at predicting the critical aspect ratio. One widely used predictive method is the so-called "shear lag" theory of Cox, BR. J. Appl. Phys. Vol. 3, p. 72 et seq. (1952). The shear lag theory makes certain simplifying assumptions about the system. As discussed in Asloun et al., Stress Transferred in a Single-fiber Composites: Effect of Adhesion, Elastic Modulus of Fiber and Matrix and Polymer Chain Mobility, J. Materials Sci. Vol.24, pp. 1835-1844 (1989) the Cox theory with refinements added by others leads to the conclusion that the critical aspect ratio is proportional to a constant times the square root of the ratio between the tensile elastic modulus of the fiber and the corresponding tensile modulus of the matrix material.
Termonia, J. Materials Sci. Vol. 22, pp. 504-508 (1987) applies a computer based nodal model. The model is based upon geometric conception of fibers embedded in a matrix as a two dimensional system and representation of that two dimensional system as a grid of theoretical points or "nodes" at rectilinear spacings. Node equations relate the forces acting between two adjacent points and the relative positions of these adjacent points. These equations incorporate certain properties of the materials present at those theoretical points. This model is then actuated by applying a theoretical deformation to the entire model and then determining the resulting locations for various nodes, and the deformations from the original starting positions, by a process of repetitive trial and error using known mathematical algorithms for solving large numbers of simultaneous conditions by approximation. The Termonia article does not disclose the equations relating the forces at individual points to relative deformations between those points. The Termonia model is further elaborated and discussed in additional articles by the same author, viz., Computer Model For The Elastic Properties Of Short Fiber And Particulate Filled Polymers, J. Materials Sci. Vol. 22, pp. 1733-1736 (1987); Tensile Strength Of Discontinuous Fiber-Reinforced Composites, J. Materials Sci. Vol. 25, pp. 4644-4654 (1990); and Computer Model For The Elastic Properties Of Short Fiber and Particulate Filled Polymers, J. Materials Sci. Vol. 22, pp. 1733-1736. The Termonia model generally leads to the prediction that the critical length is proportional to a constant times the ratio between the fiber elastic modulus and the matrix elastic modulus.
Attempts have been made towards enhancing the performance of composites by providing an "interphase" between the fibers and the surrounding matrix material. As distinguished from an interface of molecular scale dimensions, an interphase constitutes a distinct phase having physical properties different from those of the fiber and different from those of the matrix. European Patent Application 0,294,819 describes continuous fiber composites having high modulus fibers such as carbon, glass or aramid disposed in a relatively low-modulus matrix of an organic polymer and also having an interphase surrounding each fiber. The interphase has an elastic modulus intermediate between those of the fiber and those of the matrix.
Hobbs, U.S. Pat. No. 3,812,077 discloses composite materials incorporating a polymeric matrix and high-modulus fibers. The fibers are provided with a nucleating agent so as to promote crystallization of the polymer in planes perpendicular to the fiber axis during a manufacturing process in which the coated fibers are disposed in molten polymer and the resulting blend is cooled to solidify the polymer. Thus, the polymer in the vicinity of the fibers has a crystalline state different from the crystalline state of the surrounding matrix polymer. The specially crystallized material surrounding the fiber forms an interphase between the fibers and the surrounding matrix. The '077 patent refers to composites incorporating very short fibers, typically 0.01-025 inches and also to test samples incorporating apparently continuous fibers. It does not discuss the physical properties of the interphase in detail. Carvalho et al, Thermoplastic/fiber composites; Correlation Between Interphase Morphology and Dynamic Mechanical Properties, European Polymer Journal, Vol. 26, No. 7, pp. 817-821 (1990) also describes a system incorporating a polymeric matrix and an interphase of specially crystallized polymer created by use of a nucleating agent on the fibers. These composites are apparently continuous fiber laminate-type composites. Other references discussing composites with interphases formed by crystallization around the fiber include Kantz et al, J. Polym. Sci. Polym. Lett. Ed., Vol. 11, pp. 279-284 (1973); Kantz et al, Am. Chem. Soc. Div. Org. Coat. Plast. Chem. Pip., Vol. 34, pp. 361-365 and an abstract of a PhD dissertation of Melvin R. Kantz entitled, "Deformation Behavior of Continuous Thermal Plastic Fiber Reinforced Polypropylene Composites", Diss. Abstr. Int. B, Vol. B36, p. 389 (1975). Also, Kantz, "The Mechanical Properties of Organic Fiber Reinforced Polypropylene Composites, Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem., Vol. 14, pp. 447-452 discusses the properties of composites incorporating continuous organic fibers in an organic matrix. Campbell et al, Enhanced Fracture Strain of Polypropylene by Incorporation of Thermoplastic Fibers, J. Materials Science Vol. 12, pp. 2427-2434 (1977) discloses continuous fiber composites with polymeric matrices and with transcrystalline regions in the vicinity of the fibers. Huson et al, "The Effect of Transcrystallinity On the Behavior of Fibers in Polymer Matrices", J. Polymer Science, Polymer Physics Edition Vol. 23, pp. 121-128 (1985) describes the effect of transcrystallinity on experiments concerning pull-out of a single copper fiber from a polypropylene matrix.
F. J. McGarry, in a paper entitled, "Thin Elastomer Films in Glassy Polymers", p. 173 in "Rubber Toughened Plastics", Advances in chemistry series #222, The American Chemical Society, Washington, D.C., 1989, describes apparently continuous-fiber composites incorporating graphite fibers in an epoxy matrix. Certain of the composites described therein have a soft, rubbery interphase surrounding each continuous fiber.
Despite all of these developments in the art, there have been significant needs for still further improvements. Thus, neither of the aforementioned approaches to predicting critical length has been successfully applied to prediction in systems which include an interphase. Indeed, the work employing interphases has generally disregarded the concept of critical length. This work has been concerned either with continuous fiber composites having fiber lengths which vastly exceed the critical length or with discontinuous fiber composites having fiber lengths selected without regard for the concept of critical length. The resulting composites accordingly have not provided an optimum balance between processing and other considerations favouring short fiber lengths and advantages in physical properties attributable with long fiber lengths. For these and other reasons, there have been substantial needs for further improvements in composites and in methods of making composites.
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