Effect of Fibre Packing on Random Variability of Compressive Strength of Unidirectional Carbon Fibre Reinforced Plastic

XU Dong( )， HUANG Jin’e()， ZHANG Li( )， ZHANG Shufeng()

1 Naval Research Academy， Beijing 100161， China 2 Science and Technology on Integrated Logistics Support Laboratory， National University of Defense Technology， Changsha 410073， China

Abstract： Compression tests on twenty unidirectional(UD) carbon fibre reinforced plastic (CFRP) specimens are conducted， the statistics on the measured compressive strength is calculated， and the fracture surface is characterized. Two types of different fracture surface are experimentally observed， and they are corresponding to very different values on the compressive strength. A finite element (FE) analysis is conducted to investigate the influence of random fibre packing on the compressive strength. And a riks method (provided in ABAQUS software) is applied in FE model to analyze fibre buckling behaviour in the vicinity of compressive failure. The FE analysis agrees well with the experimental observation on the two types of buckling modes and also the partition of compressive strength. It is clearly shown that the random fibre packing lays a significant influence on the random variability of compressive strength of CFRP.

Key words： carbon fibre reinforced plastic (CFRP)； compressive strength； random variability； fibre buckling； finite element (FE)； reliability

Introduction

Carbon fibre reinforced plastic (CFRP) is becoming one of the most important materials in aerospace， aviation， marine， building and wind turbine engineering. The application of CFRP as main bearing structures in the airplane A350WXB and B787 marks a new milestone of the large consumption of CFRP in current industry. However， current CFRP structures still possess a large random variability on its mechanical properties such as the stiffness and strength. According to a recent publication[1-2]， the coefficient of variance (CV) of the CFRP stiffness is around 5%-10% while the CV of the strength is around 10%-20%， which is much larger than aluminum alloys. Among all the strengths of CFRP in different directions， the longitudinal compressive of the unidirectional (UD) CFRP shows the highest random variability[3]. The large random variability of the CFRP

properties leads to large safety factors in the structure design and hence the superior properties of the lightweight structure is significantly limited[4].

It has been widely accepted that the compressive failure of CFRP is mainly triggered by buckling of fibres. Based on observations from compressive experiments， Rosen proposed a analytical formula to predict the longitudinal compressive strength of UD composite[5]. Budiansky further improved Rosen’s approach and a new approach was proposed where the constituent nonlinear properties were taken into account[6]. The prediction of the above mentioned models could still be much higher than the experimental observation due to the neglect of defects in composite. Recently， Sutcliffe and Allixetal. adopted 2D finite element (FE) models to study the compressive behaviour of the UD CFRP where the fibre waviness was considered[7-8]. However， the fibre spacial packing status is not taken into account， which may have a crucial influence on the compressive strength prediction. The random fibre packing results in non-uniform distribution of the fibre volume fraction (FVR) which has a significant influence on the compressive strength. Meanwhile， the buckling of fibres which triggers the compressive failure very probably occurs in the 3D space instead of being limited to certain plane. Therefore the random fibre packing could heavily contribute to the large random variability of the compressive strength.

The objective of the present study is to achieve a comprehensive understanding about the influence of the random fibre distribution on the compressive strength of the UD CFRP. Compressive tests on CFRP specimens are conducted and the failure characteristic is investigated by measuring the shape of the fracture surface. Corresponding 3D FE models are constructed to study the buckling mode of fibres under a condition of random fibre distribution. It is shown that the random fibre distribution may result in different types of buckling mode. Different types of buckling mode further lead to very different values on the compressive strength.

1 Compressive Test on UD CFRP Specimens

1.1 Test set-up

The compressive test on UD CFRP was conducted strictly following the regulations defined in the American Standard Test Method (ASTM) D 6641. The specimen material is T 300/Epoxy with a fibre volume ratio (FVR) at 56%. The CFRP specimen dimension is 140 mm×13 mm×2.5 mm (length×width×thickness)， as shown in Fig. 1. CFRP specimens were cut from a large panel manufactured by the approach of prepreg consolidation. Aluminum end-tabs at a length of 63.5 mm were firmly bonded at the terminals of the specimen to prevent specimen squeezing and slipping from the grips.

Fig. 1 Shape and dimension of the specimen

The grip used to clamp the specimens are shown in Fig. 2. The specimen is clamped by two jaws which can only have relative motion in the vertical direction， and guided by 4 columns. The grip sits on the test machine by a plate which has a spherical surface on the downward side. This fixture eliminates any possible bending on the specimen due to the misalignment. The compressive load is introduced by moving the column downward.

The overall test apparatus is shown in Fig. 3. In the test machine， the cross head moves downward to introduce compression on the specimen. The test machine is equipped with a 50 kN load cell. The movement of the cross head is controlled by the controller， which is set at a speed of 0.5 mm/min. Load and cross head displacement are simultaneously recoded by the computer.

1.2 Test results

Twenty specimens are tested in total， and eleven tests are valid according to the ASTM D 6641， where the failure fracture occurs near the middle of the specimen (outside the aluminum end-tab)， and the other nine invalid tests are mainly due to debonding between the specimens and end-tabs. The compressive strength (stress at failure point) of the eleven valid test specimens is listed in Table 1. It can be seen that the compressive strength varies largely from 541.54 MPa to 812.31 MPa. The average value of the measured compressive strength is 708.32 MPa and theCVis 12.2%.

Fig. 2 Grips for clamping specimens

Fig. 3 Overall test apparatus

It is interesting to observe that there are two different types of the fracture surfaces， one (the left) is the fracture at both the inplane and transverse direction， and the other one (the right) is the fracture at the transverse direction， as shown in Fig. 4. In Fig. 4， the left fracture surface indicates that there are both in plane and transverse shear deformation induced by fibre buckling， but the right fracture surface indicates that only transverse shear deformation is induced. Among all the valid tests，

Table 1 Test results on the compressive strength

nine of the specimens failed by the fracture at both the inplane and transverse direction， and three of the specimens failed by the facture at the transverse direction. It can be seen that the compressive strength of the specimen failed at the transverse direction is much higher than that of specimens failed at both the inplane and transverse direction. Therefore， the random variability of the compressive strength of the CFRP not only depends on the defects such as misalignment， void， disbond between fibre and matrix (as conventionally accepted)， but also depends on the fracture surface type. The different fracture surface types could be caused by different fibre spatial buckling modes， as the widely-accepted 2D fibre buckling would result in only inplane or transverse fracture surface.

Fig. 4 Fracture surface characteristic

2 FE Model

3D FE models incorporating a region of fibre waviness are constructed to investigate the compressive behaviour of the UD CFRP， where the random distribution of the fibre is also taken into account. The matrix is modeled by 3D linear-elastic solid element (C3D20R in ABAQUS software)， afnd the fibre is modeled by the geometrically non-linear elastic beam element (B31 in ABAQUS software). Plastic deformation of matrix is not considered， and this FE model is more suitable for composite made of super-elastic matrix materials. The geometry mesh， constraint and load application are shown in Fig. 5. Mesh size of fibres is selected as 0.001 mm (along the length direction)， and the mesh size of matrix is 0.005 mm×0.005 mm×0.005 mm (X×Y×Z). For one single fibre， there are 200 elements over the length， which is fine enough to simulate the localized buckling. The nodes on the fixed surface are both restricted in 6 degrees of freedom， namely U1， U2， U3， UR1， UR2， and UR3， and displacement load is applied on the loading surface. An elaborate mesh convergence study concerning the counterforce at the fixed surface with a displacement load of 0.01 mm is conducted to ensure that a fully converged nonlinear FE solution is obtained. The fibre random packing is generated by the approach suggested in Ref.[5].The initial fibre waviness is defined in both the inplane (X-Z) and transverse direction (X-Y). The misalignment angle in the inplane is set as 1.12° and that in the transverse direction is set as 0.7°， according to the experimental measurement in Ref.[6]. Fibres in the FE model is shown in Fig. 6.

Fig. 5 Mesh， constraint and load in the FE model

Fig. 6 Fibre distribution in the FE model

Riks method (provided in ABAQUS software) is applied in FE model to analyse fibre micro-buckling behaviour in the vicinity of compressive failure. The compressive strength is determined at the vicinity when the fibre buckles.

Twenty FE analyses with different random fibre distributions are conducted. The results on the compressive strength are listed in Table 2. It can be seen that the derived compressive strength can be clearly divided into two different regions， one is around 1 900 MPa and the other is around 1 700 MPa. Similar as the observation from experiments， most of the derived compressive strength is around the smaller value. The spatial buckling modes corresponding to the two different compressive strength values are shown in Fig. 7.

Table 2 Compressive strength from FE analysis

In Fig. 7(a) or Fig. 7(b), the top graph shows the buckling shape of fibres projected in theY-Zplane, and the bottom graph shows the overall buckling shape of the composite block. Figure 7(a) shows that all the fibres buckle in the transverse direction， which is the buckling mode for Nos. 1， 12， 16 and 20 where the compressive strength is larger. The buckling mode introduces only the shear stress in the transverse direction， and it agrees well with the experimental observation listed in Table 1. Figure 7(b) shows that all the fibres buckle in both the transverse and inplane directions， which is the buckling mode for the FE model with smaller compressive strength. In Fig. 7(b)， the buckling mode results in both the inplane and shear stresses in the matrix， and it consequently leads to fracture surface with slops in both the inplane and transverse directions. This phonomenon agrees with the experimental observation as shown in Fig. 4. Overall， the FE analysis agrees well with the experimental observation considering the partition of the two different buckling modes. The compressive strength in the FE analysis is larger than the corresponding experimental observation， which could attribute to the neglect of voids， fibre/matrix interface disbond， possible large misalignment angles，etc.

(a)

(b)

Fig. 7 Buckling modes from the FE analysis：(a) fibre buckling in transverse direction；(b) fibre buckling in both transverse and inpalne directions

In a summary， it is clearly shown that the random fibre packing results in random variability of the compressive strength of the UD CFRP. Moreover， the random fibre packing leads to two different types of fibre buckling modes： only transverse or transverse and inplane. The transverse buckling mode results in larger compressive strength than the transverse and inplane buckling mode.

3 Conclusions

This study explored the intrinsic cause of the random variability of the compressive strength of the UD CFRP. Firstly， compression tests were conducted on twenty UD CFRP specimens， and theCVof the compressive strength was found to be 12.2%. Two different fracture surface characteristics were observed from the experiments， where the transverse buckling mode resulted in larger compressive strength. 3D FE analysis was conducted where the fibre was randomly distributed. The FE analysis agrees well with the experimental observation on the two types of buckling modes. It is clearly shown that the random fibre packing is a significant source for the random variability of CFRP， and the fibre buckling mode also varies depending on the fibre packing condition.