In isotropic materials, it is known that values of Poisson's ratio larger than one half are thermodynamically inadmissible, for such values would lead to negative strain energy under certain loads. Although a negative Poisson's ratio is not forbidden by thermodynamics, it is rare in crystalline solids. With the development of modem fiber reinforced composite materials, the effective Poisson's ratio of laminated fiber reinforced composites shows a peculiar behavior as it becomes larger than one half or less than zero. In this article, a study of negative in-plane Poisson's ratio for a general class of randomly-oriented composite laminates is presented. A simple random statistical analysis has been presented. It is demonstrated that composite laminates with negative in-plane Poisson's ratio could be achieved by using the specific values of independent elastic constants E1, E2, G12, and v12 in each lamina. Also, the influence of the lamina material properties to the negative in-plane Poisson's ratio of the composite laminates is presented. The results from this statistical analysis provide a set of general guidelines for designing composite laminates with a special character-the negative in-plane Poisson's ratio.
Composite materials can be regarded as structures, so there is a great opportunity to design a wide range of properties for such kind of material to meet the various application requirements, even a very particular one. A negative Poisson's ratio is an example. The mechanism of negative Poisson's ratio and the basic conditions for obtaining such a property were analyzed briefly, the formulas of optimal angle for designing minus Poisson's ratio were deduced, and the experimental results were given. The designed composite did show negative, but small Poisson's ratio.
A new criterion, which is named the quadric surfaces criterion for composite materials, is proposed based on the form of quadratic surface associated with a second-degree polynomial. The three interaction terms (i.e., σIσj, σIτij, and σjτij) are included in the quadric surfaces criterion completely. However, no more biaxial tests are required for the determination of those coefficients of the three stress interaction terms. Since the quadric surfaces criterion requires three yield strengths from simple tension, compression, and torsion tests, respectively, this criterion is applicable for ductile materials as well as brittle materials with different strengths in tension and compression. One unique feature of the quadric surfaces criterion is the ability to change its format depending upon what types of stresses are applied and what types of material strengths are considered. Thus, it is shown that the entire closed failure envelope of the quadric surfaces criterion is composed of piecewise quadric surfaces. For example, when a material is deformed in compression, the compressive strength should be the dominant critical strength, not the tensile strength. Accordingly, the failure function must be adjusted so that it can accommodate the compressive strength. The validity of the quadric surfaces failure criterion is examined with experimental results from off-axis uniaxial strength tests of unidirectional fiber composites, and angle-ply laminated composites. Comparisons were made with other well-known an isotropic strength theories as well.
A new criterion, which is named a sequential fiber failure criterion for the tensile fracture in notched fiber reinforced composite plates, is developed based on the combined micromechanical sequential fiber failure condition and the macroscopic Yeh-Stratton failure criterion. Since the sequential fiber failure behavior is considered, therefore, the failure mechanisms are included in this sequential fiber failure criterion. The fracture angle and damage zone can also be evaluated from this criterion. The fracture stresses predicted by the sequential fiber failure criterion are close to those stresses measured experimentally. The tensile failure of a laminate is governed by the failure of the plies having fibers parallel to the loading direction. These fibers fail sequentially by a process in which the failure of the fiber causes its neighbor to fail. Under the uniaxial tensile load, the fracture planes of all the plies are perpendicular to the tensile loading direction within the [90°/0°/±45°]s laminates containing a center crack.
In this paper an investigation of the through-the-thickness Poisson's ratio and the dilatation for a general class of randomly-oriented composite laminate is presented. A simple random statistical analysis has been used to demonstrate that under certain conditions, for instance, a laminate with 40 plies or more, the mean values of the through-the-thickness Poisson's ratio and the dilatation in the randomly-oriented laminate are close to those values evaluated from the analytical formulation. Also, the influence of the various lamina material properties E21E1, E31EI, G12/EI, v12, v31 and v32 on the through-the-thickness Poisson's ratio and the dilatation of the laminate are obtained. The results from this statistical analysis provide a set of general guidelines for designing the through-the-thickness Poisson's ratio and the dilatation of the composite laminates to meet various requirements in engineering applications.
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