Unidirectional shear

The first term on the right-hand side is a term of energy production by the gradient of the turbulence-average flow. Considering the equation for k, for a sheared, unidirectional averaged flow Ux z), the production term reduces to... 

Fig. 3.13 Variation in direct and shear strains for unidirectional composite loaded axially...

It is also worthy of note that large values of Poisson s Ratio can occur in a laminate. In this case a peak value of over 1.5 is observed - something which would be impossible in an isotropic material. Large values of Poisson s Ratio are a characteristic of unidirectional fibre composites and arise due to the coupling effects between extension and shear which were referred to earlier. 

Figure 2-13 Unidirectional Lamina Shear Behavior (2) Relation of E45. to E. ...

D. F. Adams and D. R. Doner, Longitudinal Shear Loading of a Unidirectional Composite, Journal of Composite Materials, January 1967, pp. 4-17. 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

A simplified performance index for stiffness is readily obtained from the essentials of micromechanics theory (see, for example. Chapter 3). The fundamental engineering constants for a unidirectionally reinforced lamina, ., 2, v.,2, and G.,2, are easily analyzed with simple back-of-the-envelope calculations that reveal which engineering constants are dominated by the fiber properties, which by the matrix properties, and which are not dominated by either fiber or matrix properties. Recall that the fiber-direction modulus, is fiber-dominated. Moreover, both the modulus transverse to the fibers, 2, and the shear modulus, G12. are matrix-dominated. Finally, the Poisson s ratio, v.,2, is neither fiber-dominated nor matrix-dominated. Accordingly, if for design purposes the matrix has been selected but the value of 1 is insufficient, then another more-capable fiber system is necessary. Flowever, if 2 and/or G12 are insufficient, then selection of a different fiber system will do no practical good. The actual problem is the matrix systemi The same arguments apply to variations in the relative percentages of fiber and matrix for a fixed material system. 

Tests by Roe et al. [63] with unidirectional jute fiber-reinforced UP resins show a linear relationship (analogous to the linear mixing rule) between the volume content of fiber and Young s modulus and tensile strength of the composite over a range of fiber content of 0-60%. Similar results are attained for the work of fracture and for the interlaminate shear strength (Fig. 20). Chawla et al. [64] found similar results for the flexural properties of jute fiber-UP composites. 

The theoretical basis for spatially resolved rheological measurements rests with the traditional theory of viscometric flows [2, 5, 6]. Such flows are kinematically equivalent to unidirectional steady simple shearing flow between two parallel plates. For a general complex liquid, three functions are necessary to describe the properties of the material fully two normal stress functions, Nj and N2 and one shear stress function, a. All three of these depend upon the shear rate. In general, the functional form of this dependency is not known a priori. However, there are many accepted models that can be used to approximate the behavior, one of which is the power-law model described above. 

The failure of a simple structural element under unidirectional stress (tensile or compressive) is easy to relate to the tensile strength of the material, as determined in a standard tensile test, but for components subjected to combined stresses (normal and shear stress) the position is not so simple, and several theories of failure have been proposed. The three theories most commonly used are described below ... 

Experimental results are presented that show that high doses of electron radiation combined with thermal cycling can significantly change the mechanical and physical properties of graphite fiber-reinforced polymer-matrix composites. Polymeric materials examined have included 121 °C and 177°C cure epoxies, polyimide, amorphous thermoplastic, and semicrystalline thermoplastics. Composite panels fabricated and tested included four-ply unidirectional, four-ply [0,90, 90,0] and eight-ply quasi-isotropic [0/ 45/90]s. Test specimens with fiber orientations of [10] and [45] were cut from the unidirectional panels to determine shear properties. Mechanical and physical property tests were conducted at cold (-157°C), room (24°C) and elevated (121°C) temperatures. 

ISO 14130 1997 Fibre-reinforced plastic composites - Determination of apparent interlaminar shear strength by short-beam method ISO 15024 2001 Fibre-reinforced plastic composites - Determination of mode I interlaminar fracture toughness, GIC, for unidirectionally reinforced materials... 

The short beam shear test designated in ASTM D 2344 (1989) involves loading a beam fabricated from unidirectional laminate composites in three-point bending as... 

Therefore, the unidirectional translaminar (i.e. through-thickness) shear strength can be obtained for the maximum load and the in-plane shear modulus of elasticity, Gu, taken from the initial linear portion of the unidirectional shear stress-shear strain (ti2 - y 2) curve ... 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

ASTM D 3518 (1991). Practice for in-plane shear stress-strain response of unidirectional reinforced plastics. 

Petit, P.H. (1969). A simplified method of determining the in-plane shear stress-strain response of unidirectional composites. In Composite Materials Testing and Design, ASTM STP 460, ASTM, Philadelphia, PA, pp. 83-93. 

Pindera, M.J., Choksi, G., Hidde, J.S. and Herakovich, C.T. (1987). A methodology for accurate shear characterization of unidirectional composites. J. Composites Mater. 21, 1164-1184. 

Rosen, B.W. (1972). A simple procedure for experimental determination of the longitudinal shear modulus of unidirectional composites. J. Composites Mater. 6, 552-554. 

Fig. 7.25. Impacl fracture toughness (O) and interlaminar shear strength (ILSS, ) of unidirectional carbon fiber-epoxy matrix composites as a function of expanding monomer (spiro) content. After Lim...

The rule of mixtures generally provides a poor estimate of the bulk and shear moduli in both the axial and transverse directions, respectively, in unidirectional, discontinuous-fiber-reinforced composites. 

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