Effective modulus of 3D-printable curvilinear fiber reinforced composites
Effective modulus of 3D-printable curvilinear fiber reinforced composites
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This study explores the intricate relationship between curvilinearity and effective modulus within a diverse range of mathematically admissible high-symmetry and low-symmetry fiber architectures. By decomposing the contour of the fiber into unidirectional short segments, an innovative integration scheme, combining theoretical analysis and finite element simulations, is employed to determine the effective modulus. Results highlight the nonlinear variation in the modulus of low-symmetry sinusoidal and hyperbolic tangent fibers, influenced by the orientation and segments with the smallest direction cosine relative to the loading direction. The study further uncovers a critical fiber-orientation angle of 60 degrees in unidirectional fiber-reinforced composites, where the modulus reaches a minimum, distinguishing load-bearing dominance between fibers and matrix. The developed integration scheme holds promise for determining the effective modulus of composites featuring fibers with arbitrary geometries and orientations, with potential applications in advancing the design of complex, additively manufactured composite structures.
This study explores the intricate relationship between curvilinearity and effective modulus within a diverse range of mathematically admissible high-symmetry and low-symmetry fiber architectures. By decomposing the contour of the fiber into unidirectional short segments, an innovative integration scheme, combining theoretical analysis and finite element simulations, is employed to determine the effective modulus. Results highlight the nonlinear variation in the modulus of low-symmetry sinusoidal and hyperbolic tangent fibers, influenced by the orientation and segments with the smallest direction cosine relative to the loading direction. The study further uncovers a critical fiber-orientation angle of 60 degrees in unidirectional fiber-reinforced composites, where the modulus reaches a minimum, distinguishing load-bearing dominance between fibers and matrix. The developed integration scheme holds promise for determining the effective modulus of composites featuring fibers with arbitrary geometries and orientations, with potential applications in advancing the design of complex, additively manufactured composite structures.
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High-symmetry architecture reveals both macroscopic and local patterns. In the actual short-fiber composite depicted in (a), there are three straight-fiber (SF) segments (AB, DE, and GH) and two curved-fiber (CF) segments (BD and EG). Meanwhile, (b) showcases the continuous representation of the short-fiber composite alongside its homogenized counterpart, consisting of a series of parallel blocks on different isotropy planes. The homogenized counterpart has the same effective modulus compared to the short-fiber composite, and its modulus can be theoretically calculated using the energy conservation principle and Hooke’s law.
(a–b) Multisegment curvilinear fiber reinforced (CFR) composites exhibit varying choices of 𝛼 and 𝛽, where 𝛼 denotes the change in curvature at the transition regime, and 𝛽 represents the orientation of the top and bottom of the domain. (c–d) Depicting the 𝜎𝑦𝑦 stress field for different values of 𝛼 and 𝛽 at a given loading state, with stress ranging from 0 GPa (blue) to 1 GPa (red). (e) Explores the impact of 𝛼 on modulus at a constant 𝛽, (f) examines the effect of 𝛽 on modulus at constant 𝛼, and (g) analyzes the combined effects of 𝛼 and 𝛽 on the effective modulus.
(Top) Fiber configurations and (Bottom) 𝜎𝑦𝑦 stress field for six orientations at a given load for sinusoidal carbon fiber reinforcement composites.
(Top) Fiber configurations and (Bottom) 𝜎𝑦𝑦 stress field for six orientations at a given load for hyperbolic tangent carbon fiber reinforcement composites.
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