NUMERICAL STUDY ON RESIDUAL THERMAL STRESSES IN CARBON FIBRE PULLOUT

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1 28 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES NUMERICAL STUDY ON RESIDUAL THERMAL STRESSES IN CARBON FIBRE PULLOUT Y. -Y. Jia*, W.-Y. Yan*, H.-Y. Liu** *Department o Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800 Australia, **School o Aerospace, Mechanical and Mechatronic Engineering J07, The University o Sydney, Sydney, Australia yuan.jia@monash.edu;wenyi.yan@monash.edu Keywords: carbon ibre, pullout, residual stress, cohesive zone model Abstract This paper investigated the eect o residual thermal stresses on carbon ibre pullout by using cohesive zone modelling. The inite element method was applied to analyse the residual thermal stress components along the interace between the ibre and matrix due to curing. A comparison study on the anisotropic and isotropic material properties are considered using our typical carbon ibres, T300, AS4, T800HB-40B and. The results show that the simpliied isotropic ibres model would overestimate the compressive residual axial and interacial radial stress. The anisotropic material properties o the ibres should be considered in the theoretical study o carbon ibre pullout. The results also show that the inluence o the residual thermal stresses is signiicant at the stage o rictional sliding ater interacial debonding. 1 Introduction Carbon ibre used in advanced composites contains at least 92% carbon [1]. This type o material has generated a great scientiic and industrial interest due to its remarkable characteristics and properties, such as small size, high stiness, low thermal expansion and high strength. The properties o interace between the ibre and matrix oten inluence signiicantly the composite perormance in all types o composites, such as ailure mode and the racture toughness o composites. Interacial debonding is considered as an important mechanism o energy absorption during the ailure o a composite. Interacial shear strength, which controls the occurrence and evolution o ibre/matrix debonding, is one o the main properties used to characterise the interace. The single ibre pullout test is one o the most widely used techniques to quantiy the interacial strength. There are three stages during a single ibre pullout, which include elastic deormation stage beore debonding, debonding stage and sliding stage. In the irst stage, the ibre and the matrix are well bonded. As the pullout orce increases, a crack propagates along the interace between the ibre and the matrix, leading to a complete debonding, which is the debonding stage. In the last stage, the ibre slides out rom the matrix, with riction acting between the two newly ormed suraces. Several analytical and numerical models have been developed or the single ibre pullout test [2-5]. Residual thermal stresses are caused by the mismatch in the coeicient o thermal expansion between the ibre and matrix during the curing process. Residual thermal stresses play an important role in a mechanical perormance o a composite structure [6], which can have signiicant eects on the ibre-matrix interacial properties such as interacial debonding. The residual stresses developed at the ibre/matrix interace provide large rictional resistance in the pullout process, which increase the racture energy consumption [7]. Several studies have been carried out on the distribution o residual thermal stresses in a single ibre 1

2 Y.-Y. JIA, W.-Y. YAN, H.-Y. LIU composite [8-10]. To authors knowledge, the study on the eect o residual thermal stresses on ibre pullout is still insuicient. The purpose o this paper is to investigate the single carbon ibre pullout test under the inluence o residual thermal stresses by using cohesive zone modelling. Four typical commercial carbon ibres T300, AS4, T800HB- 40B and with anisotropic elastic and thermal properties embedded in epoxy matrix HY6010 are considered in this study. In this paper, a numerical model is irstly established, ollowed by the analysis o distribution o the residual thermal stresses along the interace between the ibre and matrix. Secondly, the results obtained rom the anisotropic material properties o ibre model with simpliied isotropic ibre model are compared. Finally, the eects o the residual thermal stresses on the ibre pullout test are examined. 2 Numerical Model The physical problem o a typical ibre pullout test can be treated as a cylindrical ibre embedded in a semi-ininite matrix, as shown in Fig. 1(a). The radius o the ibre is denoted as R and L is the total embedded ibre length. e In a ibre pullout test, a pullout orce with low pullout rate is applied uniormly on the top surace o the ibre in the axial direction. The commercial inite element package Abaqus was used to investigate the ibre pullout problem. Due to the symmetry o this problem, a twodimensional axisymmetric model was constructed in this inite element analysis. The radius and depth o the matrix are much larger than the dimensions o the ibre in the numerical models so as to simulate a semi-ininite matrix body. The bottom o the model is constrained in both the radial and axial directions. The vertical side along the axisymmetric axis is constrained only in the radial direction. A very ine mesh (element size: 1µm 1µm) is used in the area around the interace between the ibre and the matrix to ensure the accuracy o the numerical results, which is shown in Fig. 1(b). (a) Fig. 1. (a) A schematic diagram o the ibre pullout model; (b) Axisymmetric inite element model with a ine mesh around the interace. Cohesive zone (CZ) modelling [11] is a commonly used technique or investigating the racture ailure governed by crack or debonding propagation. It bridges the gap between the stress- and energy-based approaches. Cohesive zone model establishes the traction-separation relation or the interace. The traction across the interace increases and reaches to a peak value, then decreases and eventually vanishes, permitting a complete decohesion [12]. In this research, a bilinear cohesive law was implemented, which reduces the artiicial compliance inherent in the intrinsic cohesive zone model [13]. A small number o our-node, axisymmetric cohesive elements (COHAX4) were used to deine the cohesive zone. 3 Results and Discussion (b) 3.1 Distribution o Residual Thermal Stresses In the thermal stress analysis, there is no mechanical pullout orce. The loading is rom the change o the temperature during a curing process. A temperature change o T = -95 C was chosen in the inite element simulations, which corresponds to a typical curing process rom 120 C cooling down to the ambient temperature o 25 C. In the irst case study, carbon ibre T300 ( R = 3.5µm) embedded in epoxy matrix HY6010 with ibre embedded length L e = 100µm was considered. The mechanical and physical properties o the ibre and matrix are summarized in Table 1 and 2. 2

3 NUMETRICAL STUDY ON RESIDUAL THERMAL STRESSES IN CARBON FIBRE PULLOUT Table 1 Material properties o carbon ibres. [8, 15] T800H Parameter T300 AS4 B-40B Transverse Young s modulus (GPa) Axial Young s modulus (GPa) Axial shear modulus (GPa) Transverse shear modulus (GPa) Axial Poisson s ratio Fibre radius (µm) Transverse coeicient o thermal expansion (/ C) Longitudinal coeicient o thermal expansion (/ C) E E G G v R α 12 x x x x α -0.7x x x x Table 2 Material properties o epoxy. [15] Parameter Young s modulus (GPa) Poisson s ratio Coeicient o thermal expansion (/ C) Epoxy HY6010 E m 3.4 v m 0.36 α m 62 x10-6 The residual stresses ields at the interace rom the numerical simulation are plotted in Fig. 2, which presents the distribution o axial stresses and interacial radial and shear stresses along the interace between ibre and matrix. These plots only show the distribution o residual stresses along the interace rom z = 10µm to z = 90µm, which excludes the results around the singularity points. The singularity points, where the ibre intersects the matrix at the two ends ( z = 0 and z = 100µm), can be identiied by mesh sensitivity study. As shown in Fig. 2(a), the axial stress in the ibre near the interace is signiicantly dierent rom that in the matrix. The axial stress in the ibre is compressive and its value increases towards the ibre bottom end, while the axial stress in the matrix is tensile and small. A large matrix radius (here it s theoretically ininite) leads to small values o all the residual thermal stress components [9]. Fig. 2(b) shows that the interacial radial stress is also compressive and varies almost linearly rom MPa near the top end to -12MPa near the bottom end o the ibre. As discussed by Parlevliet et al. [14], the ibre always experiences compressive residual stresses in most polymer composite laminates. In contrast, the magnitude o interacial shear stress is very small. The distribution o residual thermal stresses obtained in this study exhibits similar trends as those reported in previous work [8, 9]. As the ibres loaded in compression along the interace, this may lead to interacial debonding and ibre microbuckling [15]. To improve the ibre-matrix bond strength, ibre treatment, such as ibre coating (sizing) are commonly used. (a) Residual axial stresses in ibre and matrix (b) Interacial radial and shear stress Fig. 2. Residual thermal stresses along ibre-matrix interace (T300). 3.2 Eect o Carbon Fibre s Anisotropy on Residual Thermal Stresses To apply this study to practical problems, our typical commercial carbon ibres, T300, AS4, T800HB-40B and embedded in epoxy matrix HY6010 were considered in this investigation. The material properties o the our 3

4 Y.-Y. JIA, W.-Y. YAN, H.-Y. LIU carbon ibres and matrix are listed in Table 1 and 2. As shown in Fig. 2, the residual axial stress in matrix and interacial shear stress are very small, thereore, only the residual axial stress in the ibre and the interacial radial stress will be presented and discussed in the ollowing section. As listed in Table 1, carbon ibres are transversely isotropic materials, whose elastic properties and thermal extension coeicient in ibre axial direction are signiicantly dierent rom those in transverse directions. Zhou and Mai [16] indicated that ibre anisotropy is an important actor to inluence the stress transer and the interacial debonding in both ibre pullout and pushout. In this study, it is hypothesized that the anisotropic behaviour o carbon ibres should aect the residual stresses due to curing. Due to the limitation o analytical solutions, carbon ibres were simpliied as isotropic materials in previous analytical studies [17-19]. To validate the hypothesis on the anisotropy eect, an additional set o simulations with simpliied isotropic carbon ibres were carried out. The real material data in the ibre axial direction were used in the isotropic study. The maximum residual thermal stresses in the our typical commercial carbon ibres are presented in Fig. 3, which compared with the results rom simpliied isotropic ibres. In the case o anisotropic real carbon ibres, the residual axial stresses in our ibres are compressive with a magnitude between -28MPa to -49MPa (Fig. 3(a)). Carbon ibre has the highest magnitude, ollowed by the ibre T800HB-40B. The magnitude o the residual axial stresses in the composites with ibre T300 and AS4 are similar. The dierence o the axial stress in these ibres is due to the smaller ibre radius and higher Young s modulus o the ibre and T800HB-40B, as listed in Table 1. It can also be seen clearly that the magnitude o the axial stress or anisotropic real carbon ibres are higher than that or their corresponding simpliied isotropic carbon ibres. The dierence in percentage varies rom 18% to 30%, which should not be ignored in composite design. Fig. 3(b) shows the dierence o the maximum interacial radial stress among these our real ibres is small. The averaged magnitude is around -16MPa in the case o anisotropic real carbon ibres, which may be due to the small dierences o coeicient o thermal expansion in these ibres. The magnitude o radial stress or anisotropic real carbon ibres is lower than the simpliied isotropic carbon ibres. The maximum dierence is 14%. Both Figs 3(a) and 3(b) indicate that the eect o anisotropic material property is signiicant on the residual thermal stresses. The simpliied isotropic ibres would overestimate both the interacial compressive axial and radial stress by up to 30%. The anisotropic material property o the ibres, instead o their simpliied isotropic material properties, should be used in the study o residual thermal stresses in composite and the consequent pullout test. Maximum residual compressive axial stress in ibre (MPa) Maximum interacial compressive radial stress (MPa) Anisotropic real carbon ibres Simpliied isotropic carbon ibres T300 T300 "T300" "T300" AS4 AS4 "AS4" (a) "AS4" T800HB -40B T800HB -40B "T800HB -40B" "T800HB -40B" Anisotropic real carbon ibres "" Simpliied isotropic carbon ibres "" (b) Fig. 3. (a) Maximum residual compressive axial stress in ibre and (b) maximum interacial compressive radial stress or our carbon ibres compared with their corresponding simpliied isotropic ibres. 4

5 NUMETRICAL STUDY ON RESIDUAL THERMAL STRESSES IN CARBON FIBRE PULLOUT 4 Eect o Residual Thermal Stresses on Fibre Pullout 4.1 Eect on Pullout Curve The maximum pullout orce ( F max ), the so called debonding orce, is one o the most important parameters recorded rom a pullout test, which is used to calculate the average interacial strength. In this study, the residual thermal stresses are introduced in the inite element simulation o ibre pullout. A carbon ibre T300 embedded in epoxy matrix HY6010 with an embedded length L e = 100µm is used. Comparison between the results rom the models with and without residual stresses is presented in Fig. 4. It can be seen that the inluence o the residual thermal stresses on the debonding orce ( F max ) is very small. But it is clear that the eect o residual thermal stress is signiicant ater initial debonding. In the debonded region, the rictional shear stress is governed by the radial compression, which provides a large resistance to urther debonding. Thereore, a larger applied orce is required to pull out the ibre even though the interace is debonded. F (N) Pullout without residual stress Pullout with residual stress Pullout displacement (µm) Fig. 4. Fibre pullout curve with and without residual stress. 4.2 Cases Studies on Pullout Force As shown in Fig. 5, the magnitude o the debonding orce or carbon ibre T300 and AS4 are highest, ollowed by T800HB-40B and. This is due to the larger ibre radius or T300 and AS4, see Table 1. As observed in previous work [20, 21], the eect o the ibre radius on the pullout orce was signiicant. The debonding orce F max increases linearly with ibre radius. The our cases presented in Fig. 5 urther conirm that the inluence o the residual thermal stress is insigniicant on the debonding orce. F max (N) T300 AS4 T800HB-40B Without residual stress With residual stress Fig. 5. Debonding orce or our carbon ibres with epoxy HY Conclusions In this paper, a single carbon ibre pullout under the inluence o residual thermal stresses due to curing process was numerically studied. The result showed that the residual thermal stresses depend on the material properties o ibre and matrix. The dierence o the residual stresses obtained rom the models considering carbon ibre s anisotropic material property and those simpliying carbon ibre as simpliied isotropic material is signiicant, which could aect the ibre pullout. Thus, the anisotropic material property o the ibres, instead o their simpliied isotropic material properties, should be used in the study o residual thermal stresses in composite. The case studies o ibre pullout show that the residual thermal stresses have negligible eect on the debonding orce, but they increase the resistance during the stage o ibre sliding ater interacial debonding. 6 Reerences [1] Fitzer E. Carbon ibres ilaments and composites. Kluwer Academic, Dordrecht, [2] Hsueh C-H. Interacial debonding and iber pull-out stresses o iber-reinorced composites. Materials Science and Engineering A, Vol. A123, No. 1, pp 1-11, [3] Liu H-Y, Zhou L-M and Mai Y-W. On ibre pull-out with a rough interace. Philosophical Magazine A, Vol. 72, No. 2, pp ,

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