Statistical Analysis of Mechanical Stressing in Short Fiber Reinforced Composites by Means of Statistical and Representative Volume Elements

Abstract

Analyzing representative volume elements with the finite element method is one method to calculate the local stress at the microscale of short fiber reinforced plastics. It can be shown with Monte-Carlo simulations that the stress distribution depends on the local arrangement of the fibers and is therefore unique for each fiber constellation. In this contribution the stress distribution and the effective composite properties are examined as a function of the considered volume of the representative volume elements. Moreover, the influence of locally varying fiber volume fraction is examined, using statistical volume elements. The results show that the average stress probability distribution is independent of the number of fibers and independent of local fluctuation of the fiber volume fraction. Furthermore, it is derived from the stress distributions that the statistical deviation of the effective composite properties should not be neglected in the case of injection molded components. A finite element analysis indicates that the macroscopic stresses and strains on component level are significantly influenced by local, statistical fluctuation of the composite properties.

A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution

“…The additional information is lost when working with a closure approximation (2.19). Yet, working with closure approximations is the rule rather than the exception [50,62,63], both for process simulations and mechanics. The success of closure approximations lies in their construction which accounts for constraints imposed by the underlying physics and selects suitable "plausible" fourth-order fiber-orientation tensors.…”

Toward stochastic multiscale methods in continuum solid mechanics

“…It can be seen that, for such a sample cut from a plate manufactured by injection moulding, the distribution of fibres is not uniform along the cross-section of the plate: whilst at the lower and upper skin the fibres tend to orient themselves with the injection direction, at the core the fibres orientation exhibits more randomness. Breuer et al (2021) have extracted the aspect-ratio distribution of the fibres, or more exactly the fibre length distribution and fibre diameter by incinerating a sample of SFRP and measuring the fibres exposed with an optical microscope. The correlation, if any, with the orientation distribution function (ODF) π P (p) is however lost by the process.…”

An algorithm for generating microstructures of fiber‐reinforced composites with long fibers

“…Also, the influence of the fiber orientation is pronounced. [17][18][19] Algorithms for generating discontinuous composites essentially come in two flavors: sequential insertion algorithms and collective rearrangement algorithms. The former handle each fiber individually, adding the fibers one by one to the volume.…”

“…As an example, it is difficult to estimate the fiber‐length distribution from micrographs, see Hessman et al 16 for a discussion. Also, the influence of the fiber orientation is pronounced 17‐19 …”