Numerical Characterization of the In-plane Shear Behaviour of Non-Crimp Fabric Composites

J. Appl. Compu . Mech., 11(2) (2025) 439-450 DOI: 10.22055/jacm.2024.47328.4695 ISSN: 2383-4536 jacm.scu.ac.i Published online: Augus 28 2024 Shahid Cham an Uni e si y o Ah az Jou nal o Applied and Compu a ional Mechanics Resea ch Pape Nume ical Cha ac e iza ion o he In-Plane Shea Beha iou o Non-C imp Fab ic Composi es L.M. Fe ei a 1,2 , E. G aciani 2 , F. Pa ís 2 1 G upo de Elas icidad y Resis encia de Ma e iales. Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa. Camino Descub imien os, S/N 41092 Se illa, España, Email: lma [email protected] 2 Escuela Poli écnica Supe io , Uni e sidad de Se illa. C/ Vi gen de Á ica, 7, Se illa, 41011, España, Email: eg [email protected] (E.G.); pa [email protected] (F.P.) Recei ed July 02 2024; Re ised Augus 13 2024; Accep ed o publica ion Augus 13 2024. Co esponding au ho : L.M. Fe ei a (lma [email protected]) © 2024 Published by Shahid Cham an Uni e si y o Ah az Abs ac . Expe imen al o -axis ensile es s aimed a cha ac e ising he in-plane shea beha iou o biaxial non-c imp ab ic (NCF) composi e lamina es ob ained om di e en di ec ions wi hin he same panel (wa p and we ) e eal no ewo hy a ia ions. The in-plane shea modulus, shea s eng h, and shea s ain a ailu e a e signi ican ly highe in he we di ec ion compa ed o he wa p di ec ion. To gain insigh s in o he unde lying easons o hese disc epancies, a pa ame ic s udy is pe o med. This nume ical s udy u ilises mesoscopic 3D ini e elemen (FE) models, ep esen ing he uni cell o a [+45,-45] 2S NCF lamina e. The analysis indica es ha nei he he p esence o s i ching ya ns no he ou -o -plane ib e c imp induced by he ya ns accoun o he subs an ial di e ences obse ed in he expe imen al indings. The maximum ini ial angen in-plane shea modulus (G xy ), due o ou -o -plane ib e c imp is only 2%. Howe e , his di e ence inc eases o app oxima ely 6.1% when s i ching ya ns a e also included in he FE model. Mo eo e , i is ound ha ib e olume ac ion o he ows and he non-linea beha iou negligibly impac he in- plane shea pe o mance o he NCF lamina e in bo h di ec ions. In con as , he s udy e eals ha he p ima y ac o con ibu ing o he di e ences be ween he wa p and we di ec ions is ela ed o misalignmen be ween he nominal 45° ows wi hin he NCF composi e lamina e panels. The misalignmen obse ed in he expe imen ally es ed specimens is app oxima ely 6°, leading o an 8.5% dec ease in he G xy o SP lamina e (wa p di ec ion) compa ed o ST lamina e (we di ec ion). Keywo ds: In-plane shea beha iou ; Composi es; Non-c imp ab ic; Fini e elemen analysis; Fib e c imp. 1. In oduc ion Non-c imp ab ic (NCF) composi es ep esen a signi ican al e na i e wi hin he ealm o high-pe o mance composi e applica ions. The de ining ea u e o NCF composi es esides in he a angemen o unidi ec ional ib e ows, which a e no wo en bu ins ead posi ioned side by side and held in place by s i ching ya ns [1, 2]. The alignmen o ib es pe mi s he cus omisa ion o mechanical pe o mance, enabling he op imisa ion o s eng h and s i ness in mul iple di ec ions, hus accommoda ing speci ic load-bea ing equi emen s [3]. Mo eo e , NCF composi es o e se e al ad an ages o e adi ional wo en ab ics, p ima ily due o hei lowe c imp, which leads o enhanced mechanical p ope ies. The alignmen o ib es wi hou he in e lacing ypically seen in wo en ab ics educes s ess concen a ions and po en ial weak poin s wi hin he composi e ma e ial. This esul s in be e load dis ibu ion and highe ensile s eng h, making NCF composi es pa icula ly sui able o applica ions equi ing high pe o mance unde complex loading condi ions. In he ae ospace and au omo i e indus y, o example, he use o NCF composi es allows o he c ea ion o ligh weigh componen s, con ibu ing o uel e iciency and o e all pe o mance [4-7]. Simila ly, in ma ine applica ions, he esis ance o a igue and en i onmen al ac o s. The manu ac u ing p ocess o NCF composi es is ano he c i ical aspec ha se s hem apa . The use o s i ching ya ns o hold he ib es in place be o e esin in usion allows o be e con ol o e ib e o ien a ion and placemen , leading o mo e consis en mechanical p ope ies h oughou he ma e ial. This p ocess also acili a es he p oduc ion o la ge, complex shapes. Despi e hei ad an ages, he manu ac u ing p ocess o NCF composi es in oduces ce ain challenges, such as he po en ial o in-plane and ou -o -plane ib e c imp and he c ea ion o esin- ich a eas, all o which can impac he o e all pe o mance o he composi e. The ib e c imp o he ows is in luenced by se e al ac o s, including he ension in he s i ching ya ns, and he nes ing o he ows du ing layup [8-13]. Addi ionally, esin pocke s o m be ween he ows du ing manu ac u ing, u he complica ing he in e nal s uc u e [14-16]. Collec i ely, hese mesoscale geome ic ea u es con ibu e o a complex h ee-dimensional (3D) in e nal a chi ec u e ha signi ican ly impac s he mechanical pe o mance o NCF composi es. The goal o his wo k is o add ess he challenges posed by his complex in e nal a chi ec u e in accu a ely modelling NCF composi es using Fini e Elemen (FE) me hods. Some ea lie ep esen a i e s udies employed a 2D modelling app oach [11, 17-21]. Howe e , he mesoscopic a chi ec u e o hese ma e ials is no ully cap u ed by a 2D FE model [22], as i exhibi s conside able 440 L.M. Fe ei a e al., Vol. 11, No. 2, 2025 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 i egula i y along all ma e ial di ec ions, leading o inaccu acies in s ess and s ain p edic ions. Consequen ly, he li e a u e has seen he de elopmen o se e al 3D FE models designed o eplica e he in ica e in e nal s uc u e o NCF lamina es [14, 23-27]. The modelling s a egy adop ed in his s udy builds upon he app oach in oduced by [24] and u he de eloped in subsequen wo ks [25, 26, 28], which ocused on p edic ing he comp essi e esponse o NCF composi es h ough nume ical analysis. This app oach in ol es modelling he ows using a geome ically s aigh 3D FE mesh, wi h ib e c imp accoun ed o by o a ing he elemen s’ coo dina e sys em o align wi h he ac ual ib e di ec ion. This me hod has been no ed o i s simplici y in modelling he ow geome y and i s pa ame iza ion [22]. Howe e , i also highligh s he ongoing ension be ween model ideli y and compu a ional e iciency, a ecu ing heme in he li e a u e [24, 29-31]. This s udy builds on he expe imen al cha ac e isa ion o NCF composi es ha was ca ied ou in [32, 33], whe e di e ences in he in-plane shea beha iou o [+45,-45] 2S lamina es we e obse ed du ing o -axis ensile es s in di e en loading di ec ions (wa p and we ). To unde s and he unde lying causes o hese expe imen ally obse ed di e ences, a pa ame ic s udy was pe o med using a mesoscopic scale 3D FE model o a [+45,-45] 2S NCF composi e lamina e. The FE model speci ically conside ed ou -o -plane ib e c imp induced by non-s uc u al s i ching ya ns, a po en ial ac o in luencing he mechanical esponse o he lamina es [34, 35]. Pa ame e s analysed included he e ec o ib e c imp due o he s i ching, a ia ions in ib e olume ac ion, he non-linea beha iou o bo h ows and esin, and he o ien a ion o he ows. The s udy sys ema ically explo ed how hese ac o s con ibu e o he di e ences in mechanical pe o mance be ween lamina es cu in he wa p and we di ec ions. The indings we e hen compa ed and co ela ed wi h he expe imen al esul s epo ed in [32, 33] o deepen he unde s anding o he s uc u al beha iou o NCF composi es and o iden i y c i ical ac o s in luencing hei in-plane shea esponse. In his way, he no el y o his s udy lies in i s ex ended pa ame ic analysis using a mesoscopic-scale 3D ini e elemen model o explo e he impac o se e al di e en pa ame e s, on he in-plane shea beha iou o NCF composi es, p o iding new insigh s in o he causes o expe imen ally obse ed di ec ional di e ences in mechanical pe o mance. Addi ionally, his wo k is mo i a ed by he need o b idge he gap be ween he cu en modelling app oaches and he complex eali y o NCF composi es, aiming o de elop accu a e and compu a ionally e icien FE models. In his con ex , ou app oach aligns wi h ecen ends in he li e a u e ha seek o enhance model accu acy wi hou p ohibi i e inc eases in compu a ional cos [31, 36, 37]. The documen is s uc u ed as ollows: Sec ion 2 showcases he expe imen al indings, emphasising he dispa i ies obse ed in lamina es cu in wo di e en di ec ions. Sec ion 3 de ails he de eloped nume ical models, co e ing he geome ic pa ame e s, ma e ial p ope ies, bounda y condi ions, and elemen ypes. Sec ion 4 p esen s he esul s om he pa ame ic s udy, examining he in luence o ac o s such as ib e c imp, non-s uc u al s i ching, ib e olume ac ion o he ows, nonlinea ma e ial beha iou o he ows, and ows misalignmen . Subsequen ly, Sec ion 5 jux aposes he nume ical esul s wi h he expe imen al e idence. Finally, he s udy’s main indings a e p esen ed in Sec ion 6. 2. Expe imen al E idence To cha ac e ise he in-plane shea p ope ies o NCF composi es, expe imen al ensile o -axis es s we e ca ied ou acco ding o he EN6031 s anda d [38] on [+45,-45] 2S NCF lamina es as pa o he “Failu e, pe o mance and p ocessing p edic ion o enhanced design wi h non-c imp ab ic composi es p ojec (FALCOM)” [39]. The layou o he 8-ply s anda d es ed specimens is shown in Fig. 1(a), ea u ing a leng h o 250 mm, a wid h o 25 mm and a hickness o 3 mm, as de ailed in Table 1. As i is possible o obse e, longi udinal s ain was measu ed using an ex ensome e a ached o he specimen, while ans e se s ain was measu ed wi h a s ain gauge glued o he specimen. The specimens we e cu in wo dis inc o ien a ions: one aligned wi h he s i ching ya ns, deno ed as “SP” (wa p di ec ion), and he o he pe pendicula o he s i ching ya ns, e e ed o as “ST” (we di ec ion). A ep esen a ion o SP and ST specimens is depic ed in Fig. 1(b), p o iding an illus a ion o he di e ences be ween he wo o ien a ions. (a) (b) Fig. 1. (a) Layou o he s anda d es ed specimen, (b) di e ences be ween SP and ST specimens. Table 1. Speci ica ions o he es ed specimen. Layup Leng h [mm] Wid h [mm] Thickness [mm] Fib e olume ac ion 𝑉 𝑓 𝑙 [+45,-45]2S 250 25 3 60% Nume ical Cha ac e iza ion o he In-Plane Shea Beha iou o Non-C imp Fab ic Composi es 441 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 Table 2. Expe imen al esul s o Gxy and Sxy wi h s anda d de ia ions, ob ained o di e en NCF lamina e con igu a ions [31, 34]. Layup Specimen Gxy [GPa] Sxy [MPa] [+45,-45]2S SP 4.95±0.29 62.27±1.25 ST 5.43±0.29 80.54±1.83 This s udy u ilised NCF lamina es manu ac u ed om biaxial Tenax ® HTS ca bon ib e 5632 12k ab ic, wi h a weigh o 534 g/m 2 . Resin ilm in usion (RFI) using he HexFlow ® RTM6 esin sys em was employed [33, 40]. Nons uc u al Sin e ama Ze bion ® 50 d ex polyes e s i ching ya ns we e added o main ain he ab ic’s s uc u al in eg i y. The NCF lamina es exhibi ed a ib e olume ac ion o app oxima ely 𝑉 𝑓 𝑙 = 60%. Gi en ha he specimens we e ex ac ed om a common panel, simila esul s we e expec ed o bo h di ec ions. Howe e , he ST specimens demons a ed supe io shea modulus, shea s eng h, and shea s ain a ailu e compa ed o hei SP coun e pa s. Cha ac e is ic shea s ess-s ain cu es ob ained o he o -axis ensile es s in bo h o ien a ions a e p esen ed in Fig. 2 along wi h he uppe and lowe limi s o he expe imen al da a. Resul s pe aining o ini ial angen in-plane shea modulus G xy and in-plane shea s eng h S xy a e ou lined in Table 2. No ice ha he x-axis and y-axis co espond o he ans e se and longi udinal di ec ions o he specimens, espec i ely, as shown in Fig. 1. The longi udinal and ans e se s ains we e measu ed in he specimens using s ain gauges posi ioned a 0° (longi udinal) and 90° ( ans e se) di ec ions. In his way, 𝜎 𝑥𝑦 was calcula ed using Eq. (1): 𝜎 𝑥𝑦 = 𝑃 2 𝑤𝑡 (1) whe e, P ep esen s he applied ensile load, and w and deno e he wid h and hickness o he specimen, espec i ely. S xy was calcula ed conside ing he highes ensile load P max sus ained by he specimens du ing es ing. Rega ding G xy , i was de e mined by applying a s anda d linea i ing p ocedu e o he s ess-s ain cu e wi hin he ange o 0.1% o 0.4% shea s ain. I is possible o obse e ha in he case o G xy , he di e ences be ween specimens ST and SP can each a ound 9%. In he case o S xy , he di e ences a e mo e p onounced, eaching app oxima ely 25%. No ewo hy, his mechanical beha iou o he biaxial NCF specimens, when cu in wo di e en o ien a ions wi hin he same panel, was also epo ed by González e al. in [41]. 3. Nume ical Model A mesoscopic scale 3D FE model was de eloped o he ep esen a i e uni cell (RUC) o a [+45,-45] s NCF lamina e using ANSYS FE code [42]. The RUC comp ises o ou laminas s acked wi h co esponding +45° and -45° o ien a ions, and each lamina ea u es wo hal - ec angula c oss-sec ion ows wi h esin ich a eas be ween hem, as shown in Fig. 3. Wi h e e ence o he local coo dina e sys em, he RUC’s plane co esponds o he 12-plane, wi h di ec ions 1 and 2 co esponding o he ib e di ec ion and in-plane di ec ion no mal o he ib e. Di ec ion 3 ep esen s he h ough- hickness di ec ion o he lamina e. Non-s uc u al s i ching ya ns, along wi h he ou -o -plane ib e c imp hey induce ac oss he leng h o he ows, we e also inco po a ed in o he nume ical model. Since a s aigh 3D FE mesh was employed, he ou -o -plane ib e c imp was modelled ollowing he app oach ou lined in [24] and which has p o en success ul in p e ious s udies [25, 26, 28]. Each colou used in he RUC depic ed in Fig. 3 ep esen s a dis inc ib e o ien a ion angle, deno ed as α. In his s udy, a linea a ia ion in ib e c imp angle is assumed. Consequen ly, he heo e ical and he app oxima e o a ions a e de e mined based on he y-coo dina e o he poin . Figu e 3(c) illus a es he a ia ion o he ib e o ien a ion angle α conce ning he maximum c imp angle β o each column o elemen s along he leng h o he RUC (in he y-di ec ion). I ’s impo an o no e ha he o a ion o he elemen ’s axis is execu ed abou he x-axis. The modelling app oach used enables he de ini ion o bo h cons an and a iable ou - o -plane ib e c imp angles, as well as dis inc c imp o ien a ions o each lamina (ei he cu ed upwa ds o downwa ds). Howe e , o he pu pose o maximising he impac o ib e c imp, all laminas we e uni o mly cu ed o he same side, cha ac e ised by a consis en h ough- hickness angle β. As men ioned be o e, he e a e wo p ima y ac o s con ibu ing o ib e c imp: he p esence o esin pocke s, which may lead o he nes ing o ows, and he exis ence o s i ching ya ns wi h a de e mina e s i ching ension. I ’s wo h no ing ha p e ious s udies p edominan ly ocused on ou -o -plane ib e c imp esul ing om he p esence o esin pocke s [24–26, 28]. Howe e , in his s udy, his ib e c imp is o e looked, and he ocus is on examining he “s i ching ya ns” ib e c imp. Fig. 2. Typical shea s ess-s ain cu es ob ained om he o -axis ensile es s [31, 34]. 442 L.M. Fe ei a e al., Vol. 11, No. 2, 2025 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 Fig. 3. 3D FE model o he RUC o a [+45,-45]s NCF lamina e: (a) Shape o he ows, (b) comple e RUC, including s i ching and ou -o -plane ib e c imp, (c) geome ic pa ame e s o he comple e RUC illus a ed h ough de ailed d awing iews. The geome y and mechanical p ope ies o he cons i uen s o he laminas we e pa ame ically de ined, enabling he s udy o he e ec o dimensions and mechanical p ope ies on he in-plane shea beha iou o he NCF lamina e. Figu e 3(c) depic s he geome ical pa ame e s employed, wi h a ep esen ing he leng h o he RUC, deno ing he hickness o each lamina, and g indica ing he wid h o he gap be ween wo adjacen ows o each lamina. In his s udy, he nume ical alues o he geome ic pa ame e s we e de e mined o a 𝑉 𝑓 𝑙 = 60%, and hey we e es ima ed based on he in e nal geome y and ib e con en o he ma e ials analysed in [33]. Consequen ly, he speci ic pa ame e alues we e ob ained: a = 3.67 mm, = 0.24 mm and g = 0.26 mm. 3.1. Ma e ial P ope ies The ows we e modelled as a homogeneous ans e sely iso opic elas ic ma e ial wi h bilinea shea beha iou . This non- linea i y mani es s in he longi udinal and ans e se h ough- hickness planes, speci ically he 12-plane and 13-plane, whe e he esponse o he ows o shea loads is in luenced by he non-linea beha iou o he esin [11,17]. To inco po a e his non-linea i y in o he nume ical model, a bilinea 𝜎 12 /𝛾 12 ela ionship was in oduced. The s ess-s ain cu e by Di che [43] was used as a e e ence. The ansi ion om he ini ial slope o he second slope occu s a 𝜎 12 ∗ = 𝜎 13 ∗ = 60 MPa and 𝛾 12 ∗ = 1.4%. Acco dingly, he ollowing alues we e assigned o he ini ial slope 𝐺 12 𝑖 = 𝐺 13 𝑖 = 4.03 GPa and second slope 𝐺 12 𝑖𝑖 = 𝐺 13 𝑖𝑖 = 0.75 GPa o he shea moduli. Con e sely, he esin- ich a eas we e ea ed as a homogeneous iso opic ma e ial. The elas ic cons an s o he esin- ich a eas (𝐸 𝑟 , 𝜈 𝑟 and 𝐺 𝑟 ) and o he s i ching ya ns (𝐸 𝑠 , 𝜈 𝑠 and 𝐺 𝑠 ) we e ob ained om [44, 45]. The mechanical p ope ies employed in he pa ame ic a e summa ised in Table 3, along wi h he co esponding sou ce e e ences. 3.2. Bounda y Condi ions and Elemen Types The applied bounda y condi ions on he aces o he RUC aim o eplica e he ensile es in bo h he SP and ST di ec ions. Fo he case in which he load is applied in he SP di ec ion, a symme y condi ion was imposed on one o he aces pa allel o he yz- plane (𝑢 𝑥 = 0, and 𝜎 𝑥𝑦 = 𝜎 𝑥𝑧 = 0), and a pu e longi udinal ensile s ain was applied along he x-axis on he opposi e ace (𝜀 𝑥 = 3%, and 𝜎 𝑥𝑦 = 𝜎 𝑥𝑧 = 0). When he load is applied in he ST di ec ion, a symme y condi ion was assumed on one o he aces pa allel o he xz-plane (𝑢 𝑦 = 0, and 𝜎 𝑥𝑦 = 𝜎 𝑥𝑧 = 0), and a pu e longi udinal ensile s ain (along he y-axis) was applied on he opposi e ace (𝜀 𝑦 = 3%, and 𝜎 𝑥𝑦 = 𝜎 𝑥𝑧 = 0). In bo h cases coupling bounda y condi ions we e applied in he emaining aces and poin suppo s we e used o a oid igid body mo ion. In his way, he in-plane shea s ain 𝛾 𝑥𝑦 o he SP and ST lamina es was calcula ed as he di e ence be ween he longi udinal s ain and he ans e se s ain. Table 3. Mechanical p ope ies assigned o he ib e ows, esin- ich a eas and s i ching ya ns. Mechanical p ope y Uni s Value Fib e ows [24, 26] 𝐸 11 𝑡 GPa 167.6 𝐸 22 𝑡 = 𝐸 33 𝑡 GPa 11.44 𝜈 12 𝑡 = 𝜈 13 𝑡 - 0.3 𝜈 23 𝑡 - 0.42 𝜎 12 ∗ = 𝜎 13 ∗ MPa 60 𝐺 12 𝑖 = 𝐺 13 𝑖 GPa 4.03 𝐺 12 𝑖𝑖 = 𝐺 13 𝑖𝑖 GPa 0.75 𝐺 23 𝑡 GPa 4.03 Resin- ich a eas [44, 45] 𝐸 𝑟 GPa 3.5 𝜈 𝑟 - 0.42 𝐺 𝑟 GPa 1.23 S i ching ya ns [44, 45] 𝐸 𝑠 GPa 61 𝜈 𝑠 - 0.29 𝐺 𝑠 GPa 2.9 Nume ical Cha ac e iza ion o he In-Plane Shea Beha iou o Non-C imp Fab ic Composi es 443 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 The ows and he esin ich a eas we e modelled u ilising linea solid elemen s (SOLID45) wi h eigh nodes and h ee deg ees o eedom a each node ( ansla ions in he di ec ions 1, 2 and 3). The non-s uc u al s i ching was implemen ed using 3D spa elemen s (LINK180). This elemen wo ks as a uniaxial ension-comp ession elemen , p o iding h ee deg ees o eedom a each node: ansla ion in he nodal x, y, and z di ec ions. This app oach was employed in a ious s udies using s i ched composi es [46- 49]. The con igu a ion o each NCF lamina, deno ed as [+45,-45], equi es he duplica ion o s i ching ya ns in he middle o he lamina e hickness. As a esul , he c oss-sec ional a ea o he spa elemen s be ween wo consecu i e -45° laminas is wice ha o he emaining elemen s. I is no ewo hy ha a ious s i ching pa e ns we e es ed, bu no signi ican changes in he esul s we e obse ed. As indica ion, he comple e nume ical model is composed o 65,600 elemen s and 68,901 nodes. 4. Resul s o he Pa ame ic S udy A pa ame ic s udy was conduc ed o examine he impac o a ious pa ame e s on he in-plane shea beha iou o a [+45, -45] n NCF lamina e. Pa ame e s unde analysis encompassed ou -o -plane ib e c imp, non-s uc u al s i ching, he non-linea beha iou o he ows, lamina ib e olume ac ion, and ows misalignmen . The goal was o iden i y po en ial ac o s con ibu ing o he obse ed di e ences in in-plane shea pe o mance be ween he SP and ST lamina es, as indica ed in he expe imen al e idence. Fo his pu pose, he nume ically p edic ed alues o he in-plane shea s ess 𝜎 𝑥𝑦 a e plo ed agains he in-plane shea s ain 𝛾 𝑥𝑦 . Conside ing he geome ic pa ame e s de ined in he nume ical model depic ed in Fig. 3, 𝜎 𝑥𝑦 was compu ed using Eq. (2). No ice ha he di e ence be ween Eqs. (1) and (2) a ises because he o al hickness in he nume ical model is de ined as 4 , as shown in Fig. 3(c), whe eas in he expe imen al samples, i co esponds o he o al lamina e hickness. 𝜎 𝑥𝑦 = 𝑃 8 𝑎𝑡 (2) 4.1. E ec o he Ou -o -Plane Fib e C imp The modelling app oach employed o he ou -o -plane ib e c imp enables he speci ica ion o ei he cons an o a iable ou - o -plane angles, while also allowing dis inc c imp o ien a ions o each lamina, as illus a ed schema ically in Fig. 4. Ne e heless, i was ound ha hese a ia ions exe ed a negligible in luence on he nume ical p edic ions. In his con ex , he same ib e c imp o ien a ion and angle β was assumed o all laminas. To assess he e ec o β on esul s in bo h SP and ST lamina es, a ious c imp angles ( anging om 0° o 45°) we e conside ed. Fo cla i y, only he esul s ob ained wi hou s i ching ya ns, and wi h ib e c imp angles o β = 0°, 15°, and 45° a e p esen ed. Al hough β = 45° may be conside ed a high c imp alue, i was chosen as a e e ence o clea ly disce n i s e ec on esul s be ween SP and ST lamina es. Figu e 5 depic s he in-plane shea s ess 𝜎 𝑥𝑦 plo ed agains he in-plane shea s ain 𝛾 𝑥𝑦 . The indings e eal ha , unless un ealis ic high ib e c imp angles a e conside ed, almos no di e ences can be app ecia ed in he in-plane shea pe o mance be ween SP and ST lamina es. This is e iden in Fig. 5, whe e he esul s ob ained wi h β = 15° closely esemble hose wi h pe ec ly s aigh ows, and some di e ences only eme ge be ween SP and ST o β = 45°. The esul s indica e ha his dispa i y inc eases upon eaching he second pa o he bilinea shea cons i u i e equa ion o he ows. Addi ionally, i is obse ed ha bo h o ien a ions demons a e almos iden ical ini ial angen in-plane shea modulus 𝐺 𝑥𝑦 . Speci ically, o β = 45°, he 𝐺 𝑥𝑦 alue o ST lamina es is app oxima ely 2% highe compa ed o SP lamina es. While he nume ical p edic ions sugges enhanced in-plane shea pe o mance in ST lamina es, aligning wi h expe imen al obse a ions, i can be concluded ha inco po a ing ou -o -plane ib e c imp has a ma ginal e ec on he o e all in-plane shea pe o mance o bo h SP and ST lamina es. No iceably, Yin e al. [14] simila ly obse ed he negligible in luence o ib e c imp on he in-plane shea s eng h o NCF composi es. Thei analysis employed 3D mesoscale FE models inco po a ing ow wa iness angles anging om 1° o 3°. 4.2. E ec o he Non-S uc u al S i ching The analysis in his sec ion aims o assess he e ec o non-s uc u al s i ching ya ns on he obse ed expe imen al di e ences be ween SP and ST lamina es. Fo his pu pose, assuming β = 45°, he in-plane shea s ess-s ain cu es ob ained wi h and wi hou s i ching ya ns a e compa ed in Fig. 6. In e ms o modelling, he inco po a ion o non-s uc u al s i ching ya ns is accomplished h ough he u ilisa ion o 3D spa elemen s, speci ically he LINK180, as de ailed in sec ion 3.2. Consequen ly, he FE model wi hou s i ching ya ns does no include hese elemen s. I is no ewo hy ha despi e conside ing la ge s i ching ya n a eas and di e en s i ching pa e ns, no signi ican impac was obse ed on he nume ical p edic ions. The in oduc ion o s i ching ya ns con ibu es o a sligh inc ease in he s i ness o he NCF lamina e, pa icula ly o ST. Consequen ly, he ini ial angen in-plane shea modulus o ST wi h s i ching ya ns is abou 6.5% highe han wi hou s i ching ya ns, while o SP, his di e ence is app oxima ely 2.2%. Mo eo e , he p esence o s i ching ya ns con ibu es o an inc ease in he di e ences ound in 𝐺 𝑥𝑦 be ween SP and ST. Speci ically, wi h he inclusion o s i ching ya ns, he maximum di e ence obse ed is abou 6.1%, whe eas wi hou s i ching ya ns is 2%. These indings sugges ha he inco po a ion o non-s uc u al s i ching in he nume ical models, coupled wi h ou -o -plane ib e c imp, in ensi ies he obse ed di e ences in in-plane shea pe o mance be ween SP and ST lamina es. Fig. 4. Schema ic ep esen a ion o he ou -o -plane c imp o ien a ions conside ed o he NCF laminas: (a) cons an ou -o -plane ib e c imp wi h iden ical o ien a ion, (b) cons an ou -o -plane ib e c imp wi h dis inc o ien a ions, (c) a iable ou -o -plane ib e c imp wi h dis inc o ien a ions. 444 L.M. Fe ei a e al., Vol. 11, No. 2, 2025 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 Fig. 5. In-plane shea s ess 𝜎𝑥𝑦 s. he in-plane shea s ain 𝛾𝑥𝑦 o SP and ST wi h a maximum c imp angle β = 45°, 15° and 0°. Fig. 6. In-plane shea s ess 𝜎𝑥𝑦 s. he in-plane shea s ain 𝛾𝑥𝑦 o SP and ST wi h and wi hou s i ching ya ns and conside ing β = 45°. Fig. 7. In-plane shea s ess 𝜎𝑥𝑦 s. he in-plane shea s ain 𝛾𝑥𝑦 o SP and ST wi h 𝑉𝑓 𝑙 = 60%, 65% and 70%, conside ing β = 45° and s i ching ya ns. 4.3. E ec o he Fib e Volume F ac ion Lamina ib e olume ac ions o 𝑉 𝑓 𝑙 = 60%, 65% and 70% we e conside ed o assess hei impac on he in-plane shea beha iou o SP and ST lamina es. Fo his pu pose, he RUC wi h a ib e c imp angle β = 45° and inco po a ing s i ching ya ns was u ilised. In Fig. 7, he in-plane shea s ess 𝜎 𝑥𝑦 is plo ed e sus he in-plane shea s ain 𝛾 𝑥𝑦 o he di e en lamina ib e olume ac ions. As could be expec ed, inc easing he lamina ib e olume ac ion 𝑉 𝑓 𝑙 enhances he ini ial angen inplane shea modulus 𝐺 𝑥𝑦 o bo h SP and ST lamina es. Fo example, aising 𝑉 𝑓 𝑙 om 60% o 65% esul s in a 16% inc ease in 𝐺 𝑥𝑦 . Howe e , al e ing he ib e olume ac ion o he lamina does no accoun o he expe imen al disc epancies be ween he wo lamina es. In ac , an inc ease in 𝑉 𝑓 𝑙 educes he di e ences ound be ween ST and SP. Fo example, inc easing 𝑉 𝑓 𝑙 o 65% and 70% esul s in di e ences o app oxima ely 5.3% and 4.6%, espec i ely. Nume ical Cha ac e iza ion o he In-Plane Shea Beha iou o Non-C imp Fab ic Composi es 445 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 Table 4. Pa ame e s used o analyse he e ec o he in-plane shea moduli 𝐺12 𝑖𝑖 = 𝐺13 𝑖𝑖 . 𝜎 12 ∗ = 𝜎 13 ∗ (MPa) Fi s Slope 𝐺 12 𝑖 = 𝐺 13 𝑖 (GPa) Second Slope 𝐺 12 𝑖𝑖 = 𝐺 13 𝑖𝑖 (GPa) 60 4.03 0.10 0.75 1 Table 5. Pa ame e s used o analyse he e ec o he in-plane shea s esses 𝜎12 ∗= 𝜎13 ∗. 𝜎 12 ∗ = 𝜎 13 ∗ (MPa) Fi s Slope 𝐺 12 𝑖 = 𝐺 13 𝑖 (GPa) Second Slope 𝐺 12 𝑖𝑖 = 𝐺 13 𝑖𝑖 (GPa) 40 4.03 0.75 60 80 4.4. E ec o he Non-Linea Beha iou o he Tows To assess he e ec o he non-linea shea beha iou o he ows, h ee di e en alues o he second slope o he in-plane shea moduli 𝐺 12 𝑖𝑖 = 𝐺 13 𝑖𝑖 we e analysed. Addi ionally, h ee dis inc alues o 𝜎 12 ∗ = 𝜎 13 ∗ , co esponding o he in-plane shea s ess alues a which he bilinea ma e ial cu e ansi ions o i s second slope. I is impo an o no e ha , o all con igu a ions, he ini ial slope o he in-plane shea moduli was kep cons an . The nume ical models also accoun ed o he p esence o he s i ching ya ns and a ib e c imp o β = 45°. The pa ame e s used in his s udy a e de ailed in Tables 4 and 5. The e ec o a ying he second slope o he in-plane shea moduli on he on he in-plane shea s ess-s ain cu es is illus a ed in Fig. 8(a). As p e iously no ed, he ini ial slope emains cons an ac oss all con igu a ions. Mo eo e , he pe cen age di e ence be ween he cu es o ST and SP lamina es emains la gely unchanged, wi h a consis en alue a ound 6%. The in luence o he s ess alue a which he cu e ansi ions o he second slope is shown in Fig. 8(b). The esul s clea ly demons a e ha choosing di e en s ess alues a ec he lamina es esponse, bu do no con ibu e o he obse ed di e ences in he in-plane shea pe o mance o SP and ST lamina es. The di e ence be ween he in-plane shea moduli o ST and SP lamina es emains consis en h oughou he en i e cu e, wi h ST alues consis en ly abou 6% highe han hose o SP. O e all, he pa ame ic s udy e eals ha al e ing he non-linea beha iou o he ows has no signi ican impac on he in-plane shea pe o mance o SP and ST lamina es. 4.5. E ec o he Misalignmen o he Tows Va ious phases in he manu ac u ing p ocess o NCF panels can impac he o ien a ion o he ib e ows, leading o a ce ain deg ee o o a ion o misalignmen conce ning he p ojec ed o ien a ion. This phenomenon is e iden in he C-Scan images o he NCF panels es ed in [50], as illus a ed in Fig. 9. Upon isual inspec ion o he panels, a misalignmen be ween he nominal di ec ion o he ows was obse ed, as shown in Fig. 10. The p e ailing misalignmen was a ound 6° and displayed a nea -symme y wi h espec o he di ec ion o he s i ching ya ns. This misalignmen in oduced a de ia ion om heo e ical uni o mi y in he lamina es. The smalles angle be ween he ows consis en ly appea ed in he loading di ec ion o he ST lamina es, esul ing in he highes angle in he loading di ec ion o he SP lamina es, as ep esen ed in Fig. 11. By applying he Classical Lamina e Theo y (CLT) [51, 52], i becomes possible o assess he impac o misalignmen o he ows on 𝐺 𝑥𝑦 . Fo ins ance, i he misalignmen o 6° is aken in o accoun , co esponding o a SP lamina e wi h a s acking sequence [+42, -42] S and a ST lamina e wi h [+48, -48] S as shown in Fig. 11, 𝐺 𝑥𝑦 inc eases by 12% o ST and dec eases by 7% o SP when compa ed o pe ec ly aligned ows, i.e., SP = ST = [+45, -45] S . The esul s om he CLT unde sco e he impac o misalignmen on he in-plane shea modulus. Ne e heless, i is essen ial o no e ha hese esul s do no conside he ou -o -plane ib e c imp o he p esence o s i ching ya ns, bo h o which, as p e iously demons a ed, can also sligh ly con ibu e o he obse ed di e ences be ween he wo lamina es. (a) (b) Fig. 8. In-plane shea s ess   e sus he in-plane shea s ain   o SP and ST conside ing β = 45° and s i ching ya ns: (a) 𝐺12 𝑖𝑖 = 𝐺13 𝑖𝑖 = 0.1 GPa, 0.75 GPa and 1 GPa, (b) 𝜎12 ∗ = 𝜎13 ∗ = 40 MPa, 60 MPa and 80 MPa. 446 L.M. Fe ei a e al., Vol. 11, No. 2, 2025 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 Fig. 9. C-Scan images o NCF lamina e panels [50]. Fig. 10. Misalignmen o ows ound in SP and ST lamina es. Fig. 11. Schema ic ep esen a ion o a misalignmen o 6° be ween he ows in SP and ST lamina es. To p edic how he misalignmen angle o he ows in luences in-plane shea pe o mance, new 3D FE models o he RUC we e gene a ed wi h misalignmen angles o 2°, 4°, and 6°. As a esul , he FE models we e modi ied o adop a ec angula shape o ep esen he angle o misalignmen . The e o e, he wid h a used in Eq. (2) o calcula e 𝜎 𝑥𝑦 was adjus ed o i he ec angula shape o he RUC. Figu e 12 illus a es he new 3D FE model, inco po a ing he ele an geome ic pa ame e s, wi h a misalignmen o 6°. This con igu a ion co esponds o an SP lamina e wi h a s acking sequence o [+42, -42] S and an ST lamina e wi h [+48, -48] S , as shown in Fig. 11. To acili a e he unde s anding o he nume ically p edic ed in-plane s ess s ain cu es, Fig. 13 only showcases he cu es co esponding o 2° and 6°. The esul s unde sco e he impac o ows misalignmen on he in-plane shea pe o mance o bo h ST and SP lamina es. Fo example, when an angle o 2° is conside ed, he in-plane shea modulus (𝐺 𝑥𝑦 ) o SP expe iences an 8.5% dec ease ela i e o ST. This pe cen age change becomes mo e p onounced wi h inc easing angles, eaching app oxima ely 11.8% and 15.1% o 4° and 6°, espec i ely. I is impo an o highligh ha hese esul s we e de i ed unde he condi ions o an ou -o - plane ib e c imp angle o 45° and he inclusion o s i ching ya ns. No ably, when hese ac o s we e no conside ed, he p edic ions exhibi ed less p onounced e ec s. Nume ical Cha ac e iza ion o he In-Plane Shea Beha iou o Non-C imp Fab ic Composi es 447 Jou nal o Applied and Compu a ional Mechanics, Vol. 11, No. 2, (2025), 439-450 Fig. 12. Geome ic pa ame e s o he 3D FE model o he RUC gene a ed wi h a misalignmen angle o 6° be ween he ows, including ou -o -plane ib e c imp and s i ching ya ns. Fig. 13. In-plane shea s ess 𝜎𝑥𝑦 e sus he in-plane shea s ain 𝛾𝑥𝑦 o SP and ST wi h misalignmen angles o 2° and 6°, conside ing β = 45° and s i ching ya ns. Fig. 14. Nume ical-expe imen al co ela ion o he In-plane shea s ess 𝜎𝑥𝑦 e sus he in-plane shea s ain 𝛾𝑥𝑦. Table 6. Pa ame e s used o adjus he nume ical p edic ions o he expe imen al e idence. 𝜎 12 ∗ = 𝜎 13 ∗ (MPa) Fi s Slope 𝐺 12 𝑖 = 𝐺 13 𝑖 (GPa) Second Slope 𝐺 12 𝑖𝑖 = 𝐺 13 𝑖𝑖 (GPa) 55 5.57 0.45