Composite material analysis

J. E. Ashton. J. C. Halpin, and P. H. Petit. Primer on Composite Materials Analysis, Technomic, Westport, Connecticut, 1969. See also J. C. Halpin, Revised Primer on Composite Materials Analysis, Technomic, Lancaster, Pennsylvania, 1984. 

Vectors are commonly used for description of many physical quantities such as force, displacement, velocity, etc. However, vectors alone are not sufficient to represent all physical quantities of interest. For example, stress, strain, and the stress-strain iaws cannot be represented by vectors, but can be represented with tensors. Tensors are an especially useful generalization of vectors. The key feature of tensors is that they transform, on rotation of coordinates, in special manners. Tsai [A-1] gives a complete treatment of the tensor theory useful in composite materials analysis. What follows are the essential fundamentals. 

Halpin, J.C. Primer on Composite Materials Analysis Technomic Publishing Co., Lancaster, PA, 1984. 

Ashton JE, Halpin JC, Petit PH. Primer on composite materials analysis. Technomic 1%9. 

Halpin, J. C. 1992. Primer on Composite Materials Analysis. Lancaster, U.K. Technomic. 

Gillespie Jr, J.W., Shuda, L.J., Waibel, B., Garrett J.J. and Snowden J., CMAP—Composite materials analysis of plates. Report CCM 87-45, University of Delaware, Center for Composite Materials, Newark, USA, 1987. 

J.E. Ashton, J.C. Halpin and P.H. Petit, "Primer on Composite Materials Analysis", Technomic Publishing Co., Stamford, Conn., 1984. 

Halpin, J.C. Tsai, S.W. Environmental factors estimation in composite materials design. AFML Trans. 1967, pp. 67-423. Halpin, J.C. Primer on Composite Materials Analysis, 2nd ed. Technomic Publishing, Lancaster, PA, 1992. 

S.M. El-Haggar and M.A. Kamel in Advances in Composite Materials -Analysis of Natural and Man-Made Materials, Ed., P. Tesinova, InTech, Rijeka, Croatia, 2011. 

Kaminski BE (1973) Effects of specimen geometry on the strength of composite materials. Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP 521, pp 181-191... 

J. Ashton, J. Halpin and P. Pett. Primer on composite materials Analysis. Technomic Publishing. Co. Stanford, Conn. (1969). 

Ashton JE, Halpin JC, Petit PH (1969) Primer on composite materials. Analysis Technomic, Stamford, p 77 Barsoum RS (1989) J Adhes 29 149 Brinson HF (1974) In Kausch H et al (eds) Deformation and fracture of high polymers. Plenum, New York... 

Current Efficiency. Current efficiency for caustic production in diaphragm and membrane cells can be estimated from collection of a known amount of caustic over a period of time and from a knowledge of the number of coulombs of electricity passed during that time period. An alternative method involves analysis of the gases evolved during electrolysis and determining the anolyte composition. Material balance considerations (7) show the expression for the caustic efficiency for membrane cells to be... 

Crystallinity. Generally, spider dragline and silkworm cocoon silks are considered semicrystalline materials having amorphous flexible chains reinforced by strong stiff crystals (3). The orb web fibers are composite materials (qv) in the sense that they are composed of crystalline regions immersed in less crystalline regions, which have estimates of 30—50% crystallinity (3,16). Eadier studies by x-ray diffraction analysis indicated 62—65% crystallinity in cocoon silk fibroin from the silkworm, 50—63% in wild-type silkworm cocoons, and lesser amounts in spider silk (17). 

K. Kabe, M. Koishi, and T. Akasaka, "Stress Analysis for Twisted Cord and mbbet of FRR," presented at 6th Japan—U.S. Conference on Composite Materials, Odando, Fla., June 1992. 

A composite material used for rock-drilling bits consists of an assemblage of tungsten carbide cubes (each 2 fcm in size) stuck together with a thin layer of cobalt. The material is required to withstand compressive stresses of 4000 MNm in service. Use the above equation to estimate an upper limit for the thickness of the cobalt layer. You may assume that the compressive yield stress of tungsten carbide is well above 4000 MN m , and that the cobalt yields in shear at k = 175 MN m . What assumptions made in the analysis are likely to make your estimate inaccurate ... 

Photoluminescence is a well-established and widely practiced tool for materials analysis. In the context of surface and microanalysis, PL is applied mostly qualitatively or semiquantitatively to exploit the correlation between the structure and composition of a material system and its electronic states and their lifetimes, and to identify the presence and type of trace chemicals, impurities, and defects. 

XPS has been used in almost every area in which the properties of surfaces are important. The most prominent areas can be deduced from conferences on surface analysis, especially from ECASIA, which is held every two years. These areas are adhesion, biomaterials, catalysis, ceramics and glasses, corrosion, environmental problems, magnetic materials, metals, micro- and optoelectronics, nanomaterials, polymers and composite materials, superconductors, thin films and coatings, and tribology and wear. The contributions to these conferences are also representative of actual surface-analytical problems and studies [2.33 a,b]. A few examples from the areas mentioned above are given below more comprehensive discussions of the applications of XPS are given elsewhere [1.1,1.3-1.9, 2.34—2.39]. 

If the rf source is applied to the analysis of conducting bulk samples its figures of merit are very similar to those of the dc source [4.208]. This is also shown by comparative depth-profile analyses of commercial coatings an steel [4.209, 4.210]. The capability of the rf source is, however, unsurpassed in the analysis of poorly or nonconducting materials, e.g. anodic alumina films [4.211], chemical vapor deposition (CVD)-coated tool steels [4.212], composite materials such as ceramic coated steel [4.213], coated glass surfaces [4.214], and polymer coatings [4.209, 4.215, 4.216]. These coatings are used for automotive body parts and consist of a number of distinct polymer layers on a metallic substrate. The total thickness of the paint layers is typically more than 100 pm. An example of a quantitative depth profile on prepainted metal-coated steel is shown as in Fig. 4.39. 

In this book, attention will first be focused on macromechanics because it is the most readily appreciated of the two and the more important topic in structural design analysis. Subsequently, micromechanics will be investigated in order to gain an appreciation for how the constituents of composite materials can be proportioned and arranged to achieve certain specified strengths and stiffnesses. 

Robert M. Jones ar Harold S. Morgan, Analysis of Nonlinear Stress-Strain Behavior of Fiber-Reinforced Composite Materials, AIAA Journal, December 1977, pp. 1669-1676. 

J. M. itney, D. L. Stansbarger, and H. B. Howell, Analysis of the Rail Shear Test - Applications and Limitations, Journal of Composite Materials, January 1971, pp. 24-34. 

A strong background in elasticity is required for solution of problems in micromechanics of composite materials. Many of the available papers are quite abstract and of little direct applicability to practical analysis at this stage of development of elasticity approaches to micromechanics. Even the more sophisticated bounding approaches are a bit obscure. 

Thomas [3-18] successfully applied Equations (3-72) and (3-73) to analysis of the stiffness of glass-ribbon-reinforced composite materials. 

The preceding analysis is premised on having continuous fibers of equal strength all of which fracture at the same longitudinal position. However, fibers under tension do not all have the same fracture strength nor do they fracture in the same place. Rather, because surface imperfections vary from fiber to fiber, the individual fibers have different fracture strengths. A statistical analysis is then necessary to rationally define the strength of a composite material. 

The micromechanics approaches presented in this book are an attempt to predict the mechanical properties of a composite material based on the mechanical properties of its constituent materials. In nearly all fiber-reinforced composite materials, there is considerable difference between expectation and reality. Thus, we must ask what is the usefulness of micromechanical analysis beyond gaining a feeling for why composite materials behave as they do Basically, there are two answers one related to designing a material and one related to designing a structure. 

The reader should be exposed to both micromechanics and macromechanics in order to function effectively in either material design or structurai design. The main thrust of this book is in iine with structurai design and analysis requirements. Thus, the point of our addressing micromechanics is to better understand how and why composite materials function. 

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