PSI - Issue 54

Isyna Izzal Muna et al. / Procedia Structural Integrity 54 (2024) 437–445 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 3 ‡ Šƒ‹ ƒŽ „‡Šƒ˜‹‘” ‘ˆ ƒ ‘’‘•‹–‡ „› ‘•‹†‡”‹‰ –Š‡ ‹ˆŽ—‡ ‡ ‘ˆ ‡ƒ Š ‘•–‹–—‡– ȋ ‡Ž”‘ǡ ʹͲͳ͸ȌǤ The approach used in current work is a based on a Representative Volume Element (RVE) or unit cell concept which is representative of the entire microstructure. The boundary value problem on the structural scale and in the microstructural scale (RVE) is solved by the Finite Element (FE) method. Within this approach, the chosen RVE method is using non-homogenization where the RVE is not being solved each time before performing the macrostructural model but rather a separate modelling step. The elastic properties of each constituent are computed for solving the microstructural mechanical performance. Compared to the homogenization methods where the elastic properties of the microstructure are obtained solving the microstructural problem, their computational cost for a non-linear analysis is high because it is required solving the RVE in every integration point at the macrostructural problem. 2.1. Unit Cell generation The unit cell generation is created based on regular square packing for the unidirectional (UD) composites with ordered fiber distribution with transverse isotropy behavior which most such UD composites possess owing to the fiber distribution in the matrix over the cross-section perpendicular to fibers. The square packing has been chosen to minimise the size of the unit cell using the reflectional symmetries, however, loads in terms of macroscopic stresses or strains can only be applied individually and an arbitrary combination of the macroscopic stress components is usually not allowed. In this simulation, the simplest case with circular fiber and perfect bonding will be considered. A general scenario has been sketched in Fig. 1 in which regular fibre cross-section is illustrated schematically. &ŝŐ͘ ϭ͘ ƌĞŐƵůĂƌ ƉĂĐŬŝŶŐ ŽĨ ƐƋƵĂƌĞ ƵŶŝƚ ĐĞůů͘ ‘ ‘””‡ –Ž› ’”‡†‹ – –Š‡ ‡ Šƒ‹ ƒŽ „‡Šƒ˜‹‘” ‘ˆ ƒ ‘’‘•‹–‡ ’Ž›ǡ –Š‡ ‹†‹˜‹†—ƒŽ ‘†‡Ž• ˆ‘” –Š‡ ‘•–‹–—‡–• – Š —‡ • – „ ‡ ‘ƒŽ ’—‘Ž ƒ• –‹ –‡‡† ’’Ž”›‘ ’‹ ‘ ”– –Š‹ ‹‘• ”ƒ‡Ž •– ‡‘ ƒ –”Š ‡Š ˜™‘ Žƒ—• • ‡‹  ˆ ”’ƒŽ ‹ ˆ–‹‹‡‘† ƒ‘•ˆ –ƒŠ ‡” ‡ ˆ ‰‹ „—‡Ž ƒ” ”–ǡ ‘ • ‰“‡—ƒ‡” ”‡ƒ ƒ– ‡” ”–ƒŠ›‡ ˆ ‹ „ ‡ ”Ǥ ƒ ”Š”‡ƒ ‰‹ ‡ ” ‘‡• – ”– — ƒ – —†” ‡‹ • ‘ ƒˆ ‹ ‘–‡ ”ˆ ƒ‘ ‡ ǡ ƒ Ž ƒ › ‡‰”‡ ‘‘ ˆ ‡‡Ž –‡”› ‡–‘– •” ‡™’ƒ”•‡ • ‡” ‡ ƒ– – ‡ † ƒ ” ‘‘ — ’†‘ •‡ ‹ƒ– ‡Š• ˆȋ‹ „ ‡ƒ”Ž Ǥ‹ ‰ ‹ ‰‘—ǡ ”ʹ‡Ͳ ͳͲ ͻ• ŠȌ Ǥ‘ ™ ‘• –‡Šš‡’ Ž†‹ ‡ ‹––ƒŽ ‹›Ž ‘†ˆ‡ –ˆŠ‹ ‡‡ ƒ  † — • ‡‘†† ‹‡Ž ––ŠŠ‹ ‡• ”ƒ‡•••‡—ƒ”‹Š‰Ǥ –ŠŠ‡‡ †ƒ‹”ƒ‡ƒ ‡‘–ˆ‡ ”–Š ‘‡ˆ –—Š‡‹ –ˆ ‹„‡‡ŽŽ” •‹• – ‘ „α‡ Ž‡‰–Š ȋ Ȍ š ™‹†–Š ȋ ȌǤ Š‡ ˆ‹„‡”• ƒ”‡ ‘ˆ ƒ ‹” —Žƒ” ”‘••Ǧ•‡ –‹‘ǡ ǡ –Š‡ ˆ‹„‡” ˜‘Ž—‡ ˆ”ƒ –‹‘ ȋ Ȍ ˆ‘” –Š‹• ’ƒ ‹‰ ƒ „‡ ‰‹˜‡ ƒ• α 2 4 Ǣ –Š—• =√ 4 Š‡ ˜‘Ž—‡ ˆ”ƒ –‹‘ ȋ Ȍ ‘ˆ –Š‡ ƒ”„‘ ˆ‹„‡” ”‡‹ˆ‘” ‡‡– ‘–‡– ™ƒ• ͳͺǤʹΨǤ ‘ ’”‘˜‹†‡ ƒ ‹†‡ƒ ‘ˆ –Š‡ ‘’ƒ –‡•• ‘ˆ –Š‡ ’ƒ ‹‰ ‹ –Š‹• ƒ•‡ǡ –Š‡ ƒš‹— –Š‡‘”‡–‹ ƒŽŽ› ƒ Š‹‡˜ƒ„Ž‡ ˆ‹„‡” ˜‘Ž—‡ ˆ”ƒ –‹‘ ‹• ˆ α /4 ≈ ͹ͺǤͷͶΨ ™Š‡ ”ƒ†‹—• ‘ˆ –Š‡ ˆ‹„‡”• α ŠƒŽˆ ‘ˆ –Š‡ •’ƒ ‹‰ „‡–™‡‡ ˆ‹„‡”•Ǥ 2.2. Materials parameters The material parameters considered in numerical simulation is based on materials used for printing process. The reinforcement material used is continuous carbon fiber (CCF) T300D-3000 from Toray and the matrix material used is polylactic acid (PLA) from Natureworks. The CFRP composites are printed unidirectionally and have dimensions 439