Coarse Graining Of Multiscale Crack Propagation Gages

The concept of multiscale architectured materials is established using composition and grain size gradients. Composition-gradient nanostructured materials are produced from coarse grained interstitial free steels via carburization and high-pressure torsion. Quantitative analyses of the dislocation density using X-ray diffraction and microstructural studies clearly demonstrate the gradients of the dislocation density and grain size. The mechanical properties of the gradient materials are compared with homogeneous nanostructured carbon steel without a composition gradient in an effort to investigate the gradient effect. Based on the above observations, the potential of multiscale architecturing to open a new material property is discussed.

After annealing, the HPT-processed materials of the carbon gradient had the grain size gradient, as depicted in Figs 3 and 4. The reason for these multiscale features is believed to be the difference in the thermal stability of the surface and center region, which originates from the carbon gradient because the carbon or fragmented carbide particles segregated in the subgrain/cell walls result in the material being resistant not only to dynamic recovery, but also to grain coarsening during annealing29,49.

The advantages of combining architecturing and nanostructuring are evident. First, MS-ArchiMat can exhibit significantly higher specific strength (or strength-to-weight ratio or strength/weight) because the masses are the same for their coarse-grained counterparts. Second, the predictable shortcoming of nanostructured materials could be compensated through architecturing with other materials. Finally, the numerous combinations of architecturing provide an avenue for multi-functional properties. Therefore, multiscale architecturing could be a promising method for designing advanced structural materials.

Fatigue cracking in polycrystalline NiTi was investigated using a multiscale experimental framework for average grain sizes (GS) from 10 to 1500 nm for the first time. Macroscopic fatigue crack growth rates, measured by optical digital image correlation, were connected to microscopic crack opening and closing displacements, measured by scanning electron microscope DIC (SEM-DIC) using a high-precision external SEM scan controller. Among all grain sizes, the 1500 nm GS sample exhibited the slowest crack growth rate at the macroscale, and the largest crack opening level (stress intensity at first crack opening) and minimum crack opening displacements at the microscale. Smaller GS samples (10, 18, 42, and 80 nm) exhibited nonmonotonic trends in their fatigue performance, yet the correlation was strong between macroscale and microscale behaviors for each GS. The samples that exhibited the fastest crack growth rates (42 and 80 nm GS) showed a small crack opening level and the largest crack opening displacements. The irregular trends in fatigue performance across the nanocrystalline GS samples were consistent with nonmonotonic values in the elastic modulus reported previously, both of which may be related to the presence of residual martensite only evident in the small GS samples (10 and 18 nm).

In this paper, a reduced order model for scale-bridging modelling of damage evolution in concrete is formulated. Figure 4 illustrates the proposed modelling procedure. First, we consider a representative elementary volume (REV) at the mesoscale. At this scale, the coarse aggregates are explicitly resolved. At each mesoscopic point, an associated microscopic representative elementary volume (REV) is incorporated. Hence, the REV at the mesoscale bridges the applied macroscopic loading at the macroscale and the growth of microcracks at the microscale. At the microscopic scale, the mortar solid consists of an intact mortar matrix and pre-existing microcracks as weak inclusions. The mortar solid is idealised as a multi-phase material with spherical fine aggregates embedded in the cementitious matrix. Microcracks are modelled using three-sets of mutually orthogonal penny-shaped microcrack families, see Section 3.2. At the mesoscale, concrete is explicitly represented in a computational model as a two-phase composite consisting of a mortar matrix and coarse aggregates. The aggregates are assumed to be linear elastic, while the nonlinear behaviour of the mortar matrix is modelled at the microscopic scale using a combination of continuum micromechanics and Linear Elastic Fracture Mechanics [25].

In this numerical experiment, the micro-cracked mortar REV is assumed to contain an initial microcrack volume fraction of 11.79% with aspect ratio 17. As a consequence of introducing initial microcracks, the mortar REV stiffness reduces to 26.9 GPa at the zero-stress state. Figure 5 top and bottom left show the stress and strain responses of the mortar REV subjected to uniaxial tension and compression, respectively. Under uniaxial tension, microcrack family 1, which is oriented in a direction perpendicular to the maximum stress, propagates. This microcrack propagation results in a significant reduction of the stiffness in a longitudinal direction (z-direction in this particular numerical example) and a slight reduction in the stiffness in the transversal directions. The volume fraction of microcracks belonging to family 1 grows with increasing loads while the volume fraction of the other (two families) remains constant. 2b1af7f3a8