Anisotropy effects on crack path formation at atomistic-continuum scales
Anisotropy effects on crack path formation at atomistic-continuum scales
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Crystallographic and structural anisotropies are essential in governing the direction of crack propagation, particularly for brittle materials and their composites. However, capturing their combined effects and relative influence on crack-path formation at atomistic-continuum scales remains challenging. This paper presents a multiscale framework to capture the role of crystallographic anisotropy in controlling fracture in 3C-SiC and its composites. This framework decomposes the continuum media into a collection of 'Crystal symmetry preserved sub-domains' (CSPS) before finite element discretization. Interactions and continuum scale behavior of the CSPS are described by continuum scale parameters determined from atomistic simulations. The framework reproduces all essential features of atomic scale fracture, including bifurcation, arrest, renucleation, deflection, and penetration. Results reveal that 'crystallographic anisotropy' controls the local anisotropy in the propagation pathway, whereas 'structural anisotropy' controls the path deviation from the symmetry plane. The fracture pattern emerges from a competition between structural and crystallographic anisotropy effects and long-range elastic interactions among the stress-concentration sites. The underlying physics in high-symmetry configurations is well-explainable using 'bifurcation diagrams'.
Crystallographic and structural anisotropies are essential in governing the direction of crack propagation, particularly for brittle materials and their composites. However, capturing their combined effects and relative influence on crack-path formation at atomistic-continuum scales remains challenging. This paper presents a multiscale framework to capture the role of crystallographic anisotropy in controlling fracture in 3C-SiC and its composites. This framework decomposes the continuum media into a collection of 'Crystal symmetry preserved sub-domains' (CSPS) before finite element discretization. Interactions and continuum scale behavior of the CSPS are described by continuum scale parameters determined from atomistic simulations. The framework reproduces all essential features of atomic scale fracture, including bifurcation, arrest, renucleation, deflection, and penetration. Results reveal that 'crystallographic anisotropy' controls the local anisotropy in the propagation pathway, whereas 'structural anisotropy' controls the path deviation from the symmetry plane. The fracture pattern emerges from a competition between structural and crystallographic anisotropy effects and long-range elastic interactions among the stress-concentration sites. The underlying physics in high-symmetry configurations is well-explainable using 'bifurcation diagrams'.
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Unit cell for loading along (a) [110] direction in the xy-plane, (b) [100] direction in the xy-plane, (c) [111] direction in the xy plane, (d) [110] direction in the xz plane, (e) [111] direction in the yz plane, and (f) [111] direction in the xz plane. Cracks propagate in the directions parallel to the cyan-colored lines. The shaded regions represent the CSPS. They are constructed by joining the bisectors of the bonds surrounding an atom. The arrows indicate possible crack-propagation directions. The crack chooses to grow in one of the directions that require the minimum energy for material separation. (g) A continuum-scale representation of the atomistic domain for the [100] direction case shows a collection of CSPS. The red arrows identify two possible crack growth directions. The spacing h between the CSPS is the size of the finite element.
(Left panel) Crack paths and elastic fields for two different values of δ, representing the distance between the crack tip and the edge of the pore. The two crack-pore distances are δ = 40 nm and δ = 59 nm. The pore diameter is 15.5 nm, and the initial crack length is 20 nm. (Right panel) Zoomed in images show the atomic stress profile of the crack-pore interaction and the crack bifurcation diagram, highlighting the physical basis for crack arrest at the pore when δ = 40 nm and the crack path's insensitivity to the pore when δ = 59 nm.
(a) Initial atomistic and continuum scale configurations at a random point on the matrix-ellipsoid interface for five orientations of the interface relative to the x-direction (with loading applied along the y-direction). The effects of inclusion orientation on the crack path are shown in situations where the interface is (b) weak enough to cause deflection and (c) strong enough to cause penetration for five different orientations of the inclusion. The elliptical inclusion's minor and major axes are 200 Å and 800 Å, respectively, and the domain dimensions are 2000 Å by 2000 Å. Only part of the overall domain is shown for brevity. All parameters are kept unchanged except the inclusion orientation in each set.
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