Representative volume element for non-uniform micro-structure

A representative volume element (RVE) of micro-structure is an important input for computational-mechanics-based simulations of micro-mechanical response of heterogeneous materials such as composites. In this contribution, a methodology has been developed to arrive at a sufficiently small micro-structural window that can be regarded as a RVE of a non-uniform micro-structure of a ceramic matrix composite (CMC) containing a range of fiber sizes, and fiber-rich and -poor regions at the length scale of about 100 μm. The RVE contains about 250 fibers of 14 μm diameter average size. The absolute size of the RVE is 0.1 mm2. The methodology involves a unique combination of quantitative characterization of geometry and spatial arrangement of micro-structural features using stereological and image analysis techniques, development of computer simulated micro-structure model that is statistically similar to the real micro-structure, finite element (FE)-based simulations of micro-mechanical response on computer-simulated micro-structural widows of different sizes containing 60–2000 fibers, and FE-based simulations on large-area high-resolution digital image of the composite micro-structure containing about 2000 fibers. The RVE has the micro-structure that is statistically similar to that of the CMC having fiber-rich and -poor regions, its Youngʹs modulus is very close to that of the composite, and has local stress distribution that is comparable to that in the real composite under similar loading conditions. Therefore, such an RVE is useful for realistic simulations of damage initiation.