Prediction of homogenized properties

In the current example, two representative volume elements are considered, the square and hexagonal arrays. However the self-consistent micromechanics method can be applied to other representative volume element geometries that meet the doubly periodic condition. Aschematic of each geometry is given in Figure 1. The first two columns in Table 1 are the input constituent […]

Representative volume element boundary conditions

The imposition of canonical states of strain upon the representative volume element utilizing finite-element analyses requires the development of a corresponding set of displacement boundary conditions. The representative volume element principal directions, (e1, e2, e3) are shown in Figure 1. Equation 10 defines the appropriate displacement boundary conditions for the prescribed extensional strain in the […]


approach, there are several shortcomings, which, if overcome, may provide increasingly accurate predictions of ultimate properties. The most apparent shortcomings of a homogenized analysis are: the modeling of fictitious interfaces; stresses and strains in the homogenized continuum exist in neither the fiber phase nor the matrix phase and the loss of the residual micromechanical thermal […]


The homogenization process seeks to obtain equivalent homogenous continuum properties for a medium composed of multiple phases of varying constitutive properties. For the current discussion, we will limit ourselves to a heterogeneous medium consisting of collimated, continuous fibers within an isotropic matrix. Many methods and closed-form expressions have been developed to achieve this goal (Pindera […]

Self-Consistent Micromechanical Enhancement of Continuous Fiber Composites

Andrew Ritchey1, Joshua Dustin1, Jonathan Gosse2 and R. Byron Pipes1 1Purdue University 2The Boeing Company USA 1. Introduction Much of the previous work in developing analytical models for high performance composite materials has focused on representations of the heterogeneous medium as a homogenous, anisotropic continuum. The development of the equivalent properties of the homogenous medium […]

Comparison of fatigue data at room temperature obtained by the authors and Hirano

As stated in the introduction, Hirano reported S-N test results at RT for a G40-800/5260 CF/BMI composite material using a small number of specimens (Hirano, 2001). This section will compare his data with those obtained in the present study. He used OH specimens 38.1 mm wide, and with other dimensions such as the hole diameter, […]

Effect of compression load cycles on tension-compression fatigue strength

The repeated stress range, Srange, of compression fatigue tests (R=10) in this study is calculated by Srange=-0.9xSmin. If the Srange-N relationships in Fig. 5 are noticed, it can be understood intuitively that they are very close to the tension-compression Smax-N relationships in Fig. 6. These relationships are discussed in detail below. Smax in tension-compression fatigue […]

Ratio of compression strength to tension strength in static and fatigue strengths

We now discuss the ratio of static compressive strength to static tensile strength in NH and OH specimens, and the ratio of compression fatigue strength (R=10) to tension fatigue strength (R=0.1) in OH specimens. That is, this section evaluates the weakness of the material tested for compression loading on the basis of the ratio of […]

Comparison of RT and 150°C strengths subjected to static or fatigue loading

To examine the high-temperature performance of the material tested, we will discuss the ratio of 150°C strength to RT strength when the specimens are subjected to either static or fatigue loading. This strength ratio, r150(N), is defined as r150(N) , 150°Cstrength(N) (4) RT strength (N) where static strength is given for N=1. Table 6 indicates […]