4. List major sentence patterns worth learning

01.     The design and development of high-performance materials requires a thorough understanding and careful control of microstructure and its effect on properties.

02.     Modeling and prediction of the overall elastic-plastic response and local damage mechanisms in heterogeneous materials, in particular particle-reinforced composites, is a very complex problem.

03.     While these models provide bounds on composite behavior, they are not able to capture precisely the experimentally observed behavior of the composite, because the microstructure of the composite is not really considered.

04.     For multiphase materials, numerical modeling techniques, such as the finite element method (FEM), are often more effective than analytical modeling since these materials lack the structural simplicity of continuous fiber composites or laminates and hence are not readily amenable to closed-form theoretical analyses.

05.     Unit cell models have been employed to model fracture of the ceramic reinforcement [10–12], void nucleation, and growth and coalescence of voids within a metallic matrix [7], and/or decohesion and crack growth along the particle/matrix interface [13].

06.     Modeling of damage in the composite was conducted on two-dimensional (2D) sections by approximating the particle morphology as ellipsoids, so the deformation assumed a 2D stress state (plane stress, plane strain, or modified plane strain).

07.     Thus, it was shown that for a given far-field applied stress in highly clustered composites, a given particle locally may have a much higher stress deviation from the average stress, and, thus, be more prone to fracture.

08.     A survey of the modeling approaches and results in the literature indicates that while conventional numerical modeling is reasonable for modeling simple shapes, such as cylindrical fibers, the unit cell models approximate the highly variable and irregular angular structure of particles by using simplified particle geometries such as spheres, ellipsoids, or cubes.

09.     These models consider the inherent particle morphology and clustering of particles, as a basis for analysis using finite element techniques, with minimal approximations.

10.     Currently, models have been used to conduct 3D microstructure simulations, by obtaining 2D images from serial sectioning, reconstruction of the 3D virtual microstructure, and incorporation of the 3D model into a FEM analysis [22].

11.     It should be noted that other techniques, such as X-ray tomography [24,25] and holotomography [26], simulated microstructures [27–29], and multiphase elements [30], have also been incorporated into FEM analysis.

12.     It will be shown that these simplified models severely underrepresent the local and macroscopic stresses and strains, which are only accurately represented by the microstructurebased models.

13.     Uniaxial tension experiments, to correlate with the simulated response, were carried out at room temperature on a precision-aligned servohydraulic load frame in strain control at a strain rate of 10^-3/s.

14.     A volume of 100×100×20μm³ yields approximately 100 particles, assuming that the SiC particles are approximately 6-8 lm in diameter, for a volume fraction of 20% SiC.

15.     This volume served as a starting point for determining a “representative”number of particles for the FEM simulated response.

16.     The effect of microstructure volume on predicted deformation response of the composites was confirmed, to ensure that the volume being modeled was representative of the deformation behavior of the material.

17.     The sample was secured using a mounting fixture to minimize translational and rotational misalignments between sections.

18.     One of the challenges of using a microstructure-based approach is that a very large number of elements and a highly refined mesh are required to conform to the heterogeneous nature of the microstructure.

19.     The larger the degree of simplification of the microstructure, of course, the more efficient the computation

20.     The stress in the spherical particles is quite uniform, while that in the angular particles is not.