Analysis of the damage initiation in a SiC/SiC composite tube from a direct comparison between large-scale numerical simulation and synchrotron X-ray micro-computed tomography

Abstract

Analysis of the damage initiation in a SiC/SiC composite tube from a direct comparison between large-scale numerical simulation and synchrotron X-ray micro-computed tomography. AbstractDamage initiation is an important issue to understand the mechanical behavior of ceramic matrix composites. In the present work, a braided SiC/SiC composite tube was studied by FFT simulation tightly linked with micro-computed tomography (µCT) observations performed during an in situ uniaxial tensile test, which provide both the real microstructure, with a good description of local microstructural geometries, and location of cracks at the onset of damage. The FFT method was proven applicable to tubular structures and efficient to complete the large-scale simulation on a full resolution µCT scan (~6.7 billion voxels) within a short time. The edge effect due to the numerical periodic boundary conditions prescribed on the real and not rigorously periodic microstructure was quantified. The obtained stress field was compared to the cracks detected by the in situ µCT observations of the same composite tube. This one-to-one comparison showed that cracks preferentially initiated at tow interfaces, where sharp edges of macropores are mostly located and generate stress concentrations.

On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

“…Quasi‐Newton methods, such as Anderson acceleration and the Barzilai‐Borwein method, have attracted considerable attention for FFT‐based micromechanics. In contrast to the classical Newton method, these schemes do not require computing the Hessian.…”

“…One such algorithm is Anderson acceleration which was recently applied by Shantraj et al and Chen et al in the context of FFT‐based micromechanics. A general discussion of the scheme and its implementation is found, for example, in Walker and Ni or Kelley .…”

“…Note that for the given algorithm Anderson acceleration is applied for every iteration. In contrast, Chen et al only accelerate every third iteration and apply Moulinec‐Suquet's basic scheme otherwise.…”

“…To circumvent this problem, limited-memory Quasi-Newton methods were developed, which implicitly update the Hessian by storing a limited number m of recent iterates and gradients, with m commonly called the depth of the scheme. One such algorithm is Anderson acceleration 26 which was recently applied by Shantraj et al 3 and Chen et al 10,28 in the context of FFT-based micromechanics. A general discussion of the scheme and its implementation is found, for example, in Walker and Ni 59 or Kelley.…”

“…The algorithm is included in the software DAMASK as the nonlinear GMRES method. More recently, Chen et al successfully adapted the Anderson acceleration to simulate damage initiation and brittle fracture . Originally developed to accelerate general fixed‐point iterations, Anderson acceleration was linked to Quasi‐Newton schemes by Fang and Saad .…”