Tensile performance of basalt fiber composites with open circular holes and straight notches

Tensile performance of basalt fiber composites with open circular holes and straight notches

Journal Pre-proof Tensile performance of basalt fiber composites with open circular holes and straight notches Guangyong Sun , Linxin Wang , Dongdong...

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Tensile performance of basalt fiber composites with open circular holes and straight notches Guangyong Sun , Linxin Wang , Dongdong Chen , Quantian Luo PII: DOI: Reference:

S0020-7403(19)32887-5 https://doi.org/10.1016/j.ijmecsci.2020.105517 MS 105517

To appear in:

International Journal of Mechanical Sciences

Received date: Revised date:

5 August 2019 23 December 2019

Please cite this article as: Guangyong Sun , Linxin Wang , Dongdong Chen , Quantian Luo , Tensile performance of basalt fiber composites with open circular holes and straight notches, International Journal of Mechanical Sciences (2020), doi: https://doi.org/10.1016/j.ijmecsci.2020.105517

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Highlight 

Tensile properties of notched basalt fibers specimens are analyzed and compared to CFRP specimens.



The notch shape shows substantially negligible effect on tensile strength for BFRP and CFRP.



The characteristic parameters of the two stress criterion are associated with the size of the finite width notched laminate.



The characteristic parameters fitting curve is capable to predict tensile strength of notched laminates.

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Tensile performance of basalt fiber composites with open circular holes and straight notches Guangyong Sun1, *, Linxin Wang1, Dongdong Chen1, Quantian Luo2 1

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China

2

School of Mechanical and Mechatronic Engineering, University of Technology Sydney, NSW, 2007, Australia

Abstract Basalt fiber composites have attracted increasing attention in recent years due to their advantages over carbon fiber composites in many aspects such as lower cost, environmental friendliness, superior heat resistance and ductility. Notches in structural components are unavoidable in practical applications. In the present study, the effects of notch shape and size on the tensile properties of basalt fiber laminates were investigated by experiment, finite element analysis and theoretical calculation. Specimens were prepared using laminates reinforced by plain woven basalt or carbon fiber fabrics and machined with an open circular hole and straight notch. Standard tensile tests were conducted and recorded using digital image correlation, aiming to measure the full-field surface strain. Continuum damage mechanics based finite element models were developed to predict stress concentration factors and failure processes of notched specimens. The characteristic distances of the stress criterion models were calibrated by the experimental results of un-notched and notched specimens so that failure of basalt fiber laminates with circular and straight notches could be analytically predicted.

Keywords: Basalt fiber laminate, notched plate, digital image correlation, finite element modeling, damage mechanism.

* Corresponding Author: Tel: +86-13786196408; Email: [email protected].

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1 Introduction Use of composite materials to reduce structural weight is a favored approach to achieve energy saving and emission reduction and thus acts as a popular choice for automobiles and other applications [1, 2]. Notches such as holes and slots are inevitable in these structures during practical applications to assemble structural parts and to install accessary components, and may also be generated in service due to impact damage [3-5]. To ensure safety and reliability in service, quantification of residual properties and failure responses is thus highly important. It is inevitable that stress concentration problems will occur around holes, regardless of the applications of laminates as interior decoration, outsourcing parts or bearing parts [6-9]. It is also necessary in notch design to consider the effects on failure mode, mechanical performance and distribution of interlayer damage [10, 11]. In a review of literature concerning residual properties of structural applications, studies of notched laminates fall mainly into two aspects. Some authors have focused on the effects on mechanical performance of stacking configurations such as stacking sequence, layup thickness and laying angles. Wisnom and Hallett [12] studied the effects of plate thickness on the tensile strength and failure mode of quasi-isotropic carbon fiber laminates. They found that delamination played a crucial role in the in-plane strength and failure mechanism of the notched specimen in tension, which could lead to premature failure, especially in laminates with small holes and in thick ply blocks. Erçin et al. [13] performed an experimental study on the effect of notch sizes and layup sequences on tensile and compressive behaviors. They showed that the strength of the laminates decreased with an increase of pore size. In this study, a digital image correlation (DIC) technique was used to obtain the displacement field of the specimen by measuring its size change during the loading process. The DIC technique has been widely used to measure deformations of notched composite laminates [4, 7, 14, 15]. By using this technique, local stress concentration and damage development within an effective area can be evaluated. Other existing studies of notched laminates have focused on notch characteristics such as number, shape and size. Cunningham et al. [16] investigated the effects of hole 3

arrangement on the tensile performance with glass fiber reinforced composite plates. To analyze the stress concentration, strain distributions across horizontal sections were tested by the DIC method. Xu et al. [17, 18] investigated the effect of center notches and open holes with quasi-isotropic laminates. The stress concentration at the crack tip was analyzed via interrupted testing and X-ray computed tomography methods. Based on linear elastic fracture mechanics and the Weibull theory, O’Higgins et al. [19] comprehensively analyzed the effects of specimen dimensions on tensile performance. They found that carbon fiber reinforced plastic (CFRP) laminates were stronger and glass fiber reinforced plastic (GFRP) specimens had a greater ultimate strain; progressive damage mechanisms for CFRP and GFRP materials were similar [20, 21]. CFRP composite is an ideal material for many structural parts because of its high strength and high modulus [22]. As compared to CFRP, basalt fiber reinforced plastic (BFRP) composite shows better elongation, lower cost and more environmental friendly; therefore, it has been widely used in various fields [23]. Basalt fiber has been considered a substitute for fiberglass because of its similar mechanical properties, greater usability, and environmental friendliness [24-26]. Various studies of mechanical performance of notched BFRP laminates have been published in recent years, covering low velocity impact behaviors, interlaminar shear and flexural properties of BFRP laminates [27-30]. Also, a number of thin-walled structures made from basalt materials such as composite tubes [31, 32] and biomimetic fully integrated honeycomb [33] have been proposed in recent years. In this manuscript we investigate tensile failure behaviors of notched laminates with different notch shapes, notch sizes, and material types. First, BFRP and CFRP specimens were manufactured with different notch configurations. Then tensile testing was conducted for notched and un-notched specimens, in which the full-field surface strain was measured using the DIC technique. Tensile performance of the notched specimens was analyzed by experiment and finite element analysis (FEA) in terms of strain distribution, strength degradation and failure evolution. Crack initiation and propagation were further studied by FEA simulation. Finally, the experimental results for the notched and un-notched samples were used to calibrate characteristic lengths of two stress criterion fracture models. The 4

fitting curves and formulations of the characteristic lengths were obtained, aiming to predict the failure of BFRP laminates with circular and straight notches.

2 Experiment 2.1 Materials and specimen fabrication Reinforcements for the composite laminates were adopted with plain weave fabrics: carbon fiber (T300, 3K) and basalt fiber supplied by Weihai Guangwei Group Co., Ltd and Sichuan Aerospace Tuoxin Basalt Industrial Co., Ltd respectively. Resin systems of EPOLAM 5015 (epoxy resin) and EPOLAM 5014 (hardener) were provided by Sino Composite Co., Ltd. The resin-to-hardener mix ratio of 3:1 was adopted. Detailed information of the commonly used fibers and matrix has been summarized in our previous studies [34], as shown in Table 1. The basic chemical components of glass and basalt fiber are SiO2, Al2O3, CaO, B2O3. Glass has less diverse chemical composition than basalt fibers. Also, some compounds, e.g. Fe2O3, K2O, MgO, Na2O and TiO2 (the glass fiber also contains TiO2 compound, but the content is less than 1%), could be found in basalt fiber. The differences between basalt and glass fibers are thus determined by these chemical compounds [35]. Fig. 1 shows specimens composed of different raw materials with plain weave structures and schematic illustration of the vacuum assisted resin transfer molding (VARTM). The laminates were prepared with VARTM technology, which was categorized in [30, 36]: (1) the plain weave fabric layers were first placed on a flat mold cleaned with acetone; (2) the corresponding flow guiding medium and vacuum film were laid; (3) the mold was sealed in a vacuum bag with sealing tape and the vacuum pump was opened. The resin was injected under constant negative pressure until the shaped layer was sufficiently wetted. The pump provided a suitable negative pressure to meet the curing conditions of the resin. Finally, the specimens were machined after curing at ambient temperature for 27 hours.

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Fig. 1. Specimen fabrication: (a) raw materials and layup structure and (b) schematic illustration of the VARTM [36]. Table 1 Specifications of fibers and matrix provided by the manufacturers [34].

Carbon fiber Glass fiber Basalt fiber Epolam

Diameter (μm)

Density (g/cm3)

Tensile strength (MPa)

Tensile modulus (GPa)

Elongation to fracture (%)

7 12 13 /

1.78 2.56 2.80 1.1

3800 3120 2100 80

238 73 105 3.1

1.6 2.0 2.6 7

2.2 Geometry of specimens Specimens for tensile tests were machined with the dimension of 250 mm×36 mm according to ASTM D5766 [37] as shown in Fig. 2(a). The total thickness of the composite laminates was 2 ± 0.4 mm. The diameter of the standard round hole was 6 ± 0.06 mm. Clamping portions with 50 mm length were reserved on each side of the specimen. Fig. 2(a) 6

also shows the configurations for testing of an un-notched (UN) specimen, an open circular hole (OH) specimen, and a straight notched (SN) specimen. To facilitate analysis, a uniform labeling system was used. In the label BF-OH-3, BF indicates a basalt fiber reinforced composite material. The notch shape is represented by OH. Number 3 indicates the diameter for the open hole. In the label CF-SN-3, CF stands for CFRP; SN indicates the straight notched shape. The diameter of an open hole and the crack length were abbreviated as D and L and adopted with values of 3, 6, 12, and 18 mm respectively. For each scheme, three repeat tests were conducted.

Fig. 2. Tensile test information: (a) sketch of specimens (reference points 1 and 2 for measuring extension) and (b) labeling system.

All specimens were machined using a computerized numerical control milling machine. It was essential to pay attention to several details during the preparation. First, the composite laminated plates for machining had to be checked to avoid defects, with a smooth surface (so as not to affect subsequent speckle treatment) and good quality. Before machining of the hole to standard values, a small round hole was drilled with 2 mm diameter drill, aiming to ensure the accuracy of hole position and to avoid impact damage and delamination caused by the 7

tool movement. For the SN specimen, an end mill with 1 mm diameter was used. Holes were then expanded to their required shapes and dimensions using different drill bits.

2.3 Tensile test Fig. 3 shows the experimental setup for the axial tensile tests. Here the DIC method was used to capture spots on the specimen surface with the capture speed of 180 frames/minute. Full-field surface strain was measured in real time using the ARAMIS v6.3.1 (GOM mbH, Germany) and VIC-2D (CSI, USA) DIC systems [38]. The axial tensile test was conducted in an INSTRON machine (Instron 5985, USA), using the displacement controlled mode at the speed of 2 mm/min (based on ASTM Standards [37, 39]). The environmental temperature and humidity were 25 °C and 33%RH respectively.

Fig. 3. Schematic diagram of tensile testing setup.

To ensure testing precision, the speckle pattern size varied between 2 to 4 pixels [40] and specimens were pre-processed before testing: they were first degreased with acetone to remove the surface oxide layer and oil stain; after a drying process, a special gun was used to spray black and white pigments onto a test area to form a speckle pattern. It should be noted that debugging of camera equipment and speckle accuracy are important in DIC measurement and the imaging camera should be set to have sufficient resolution and cover the entire sample area [16]. Also, the facet size and facet step should be 8

set based on the resolution and the average speckle size. The two reference points identified in Fig. 2 were used to record the overall longitudinal strain and the relative extensions. The full-field strain was recorded by tracking measurement the length between the reference points.

3 Analytical and finite element models 3.1 Stress based analytical models Two stress criterion models proposed by Whitney and Nuismer [41] were considered to analytically predict the strength of the BFRP laminates with open holes and straight notches. The absolute error minimization method was used to determine the relevant parameters [42].

3.1.1 Stress concentration factor The Y-axis was along the loading direction and the X-axis was the lateral loading direction, as indicated by subscripts 1 and 2, respectively. By assuming linear elastic behavior, the finite-width stress concentration factor (SCF) along the X-axis could be expressed as [5]:

K t ( x)  RK

 

R 2 R 4 R 8   R 6  2  ( )  3( )  ( KT  3) 5( )  7( )   , R  x  (W / 2) 2  x x x   x

(1)

where x is the distance from the center of the OH or SN specimen [4]; KT and RK are the SCFs of an infinite plate laminate and finite-width modification factors [5]:

 2  A11 A22 -A122 K  1  A A  A   11 22 12 2 A66  A22   T

1/2

   

2R   3(1  )  K 1 2R 2R   W RK  T    ( M ) 6 ( K T  3) 1  ( M ) 2   W K T  2  (1  2 R ) 3 2 W   W  

(2) 1

(3)

in which W is the width of the laminated plate and Aij comprises the plane stiffness matrix. The parameter M is calculated by:

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M2 

 3(1  2 R / W )  1 8  1  1 3  2  (1  2 R / W )  2  2R / W 

(4)

2

3.1.2 Stress criterion models Whitney and Nuismer [41] developed two stress criterion models for orthotropic plates contaning a circular hole or a straight crack to predict failure of such notched plates. The first model assumed that failure occurred if the stress of the notched plate at distance d0 from a hole or a crack was equal to the un-notched plate strength, referred to as the point stress criterion (PSC), as shown in Fig. 4(a) and 4(c); the other assumed that failure occurred if the average stress over distance a0 was equal to the un-notched plate strength, denoting the average stress criterion (ASC), as illustrated in Fig. 4(b) and Fig. 4(d). It was also assumed in [41] that the characteristic length d0 or a0 was a material property, independent of geometry and stress distribution.

Fig. 4. Schematic representation of characteristic lengths: (a) point force of an OH, (b) 10

average force of an OH, (c) point force of a SN and (d) average force of an SN.

3.1.2.1 Open circular holes The PSC for a laminate with an OH was derived as:

  2 /2  12  314  ( KT  3)(516  718 ), 1  R /( R  d 0 ) 0

(5)

The ASC for a laminate with an OH was given by:

  2(1  2 ) /2  22  24  ( KT  3)(26  28 ),  2  R /(R  a0 ) 0

(6)

where   is the uniformly applied stress parallel to the y-axis at infinity of the notched laminate and  0 is the uniform tensile stress of the un-notched laminate.

3.1.2.2 Straight notches In the SN specimens with a straight notch (a=0.5L = C), stress y ahead of the crack tip was approximated as [42-44]:

 y ( x, 0) 

KI x

 a( x 2  a 2 )



x a( x 2  a 2 )

a  x  1.1a

(7)

where K I is the stress intensity factor. The PSC for a laminate with a straight notch could be expressed as:

  (1  32 )1 / 2 , 3  C /(C  d0 ) 0

(8)

The ASC for a laminate with a straight notch was:

 1/ 2  (1   4 ) /(1   4 ) ,  4  C / C  a0 0

(9)

In this study, BFRP laminates with notches were the main focus and CFRP laminates were considered for comparison. The elastic material properties are listed in Table 2, where subscripts 1 and 2 represent the longitudinal and transverse directions respectively [36, 42].

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Table 2 Mechanical properties of basalt fiber and carbon fiber reinforced composites. Modulus (GPa)

Poisson’s ratio

Fracture energies (kJ/m2)

Strength (MPa)

Material

E1  E2

G12

12

X1+=X2+

X1-=X2-

S

Gf  Gf

CFRP BFRP

50.38 19.09

1.70 1.54

0.052 0.09

504 413

320 200

31 23

62 88

1

2

1

G f G

2 f

86 120

3.2 Finite element model In previous studies, a combination of a cohesive zone model (CZM) and a continuum damage mechanics (CDM) model was often adopted to simulate the progressive damage mode in CFRP structures [45]. To simulate the progressive damage process, the BFRP laminate was meshed with each composite ply treated as a single layer, as shown in Fig. 5. Intralaminar failure was modeled with a CDM-based homogeneous orthotropic model to consider fiber damage under tensile and compressive damage and in-plane shear damage. Delamination failure was modeled by the CZM with zero-thickness cohesive elements embedded between adjacent layers.

Fig. 5. Finite element model of the BF/CF-OH-6.

The basic FEA model using ABAQUS/Explicit 6.13-4 was studied and validated in Refs. [46, 47]. Based on the mesh sensitivity analysis in [46], a finer element size of approximately 0.72 mm was adopted for the central area. The 8-node reduced integration continuum shell element (SC8R) was used with one element through the thickness for each ply, and the total number of elements was 5268. Displacement in the X-direction of a reference point at the end of the specimen was constrained to apply tensile load to simulate the test. A multipoint 12

constraint algorithm was employed between the reference point and a meshed area of 50 mm, with the aim of simulating the constraints applied by fixtures.

3.2.1 Intralaminar failure modeling and failure criteria The intralaminar failure model of composite materials proposed by Sokolinsky et al. [47] was considered in the present study. By utilizing a user subroutine VUMAT in ABAQUS/Explicit, damage mechanisms including fiber damage, matrix crack, and delamination were considered in this study. The constitutive stress-strain relationship was expressed in a local Cartesian coordinate system with a basic vector that was consistent along the fiber direction. The intralaminar stress-strain relationship was:

 1   11   (1  d1 ) E1      21  22     el   E 2  12   0 

 12 E1 1 (1  d 2 ) E 2 0

    11     0   22    12  1  (1  d1 2 )2G12  0

(10)

where σ   11  22  33  is the stress vector; ε  11  22  33  is the elastic strain vector; E1 , E 2 and G12 are initial in-plane stiffness parameters; 12 is the in-plane Poisson’s ratio. Degradation of mechanical properties is governed by three damage evolution variables d1 , d 2 , and d12 , where d1 and d 2 are damage variables accounting for the effects of fibers on mechanical responses once fiber damage is initiated; d12 is a matrix failure parameter under shear loading. The computational parameters in a previous study [36] are listed in Table 2. To describe material failure, the damage threshold function was defined as [47]:

Fi  

ˆ ˆ i  , F12  12 S X i

(11)

where Fi  and F12 are the failure coefficients in different failure modes. If the failure threshold is less than 1, no damage appears and the mechanical state remains elastic. Xi  13

and S denote the tensile and shear strengths, respectively. The effective stresses ˆ i  and

ˆ 12 are defined as: ˆ i  

 ii 1  d i

, ˆ 12 

 12

(12)

1  d12

The evolution of the damage variables could be expressed as (  1  , 2  ) [48]: d  1 

  2g  L 1 exp   0 c (r  1) r  G f  g 0 Lc 

(13)

where Lc is the characteristic length of the element; G f is the fracture energy per unit area under uniaxial tensile or compressive loading; and g 0 is the elastic energy per unit volume (elastic energy density) at the point of damage initiation. The r in Eq. (13) is the damage threshold introducing different failure modes [49]:

r  max( F ,1)

(14)

It is known that the shear response of fiber reinforced composites is dominated by nonlinear plastic behavior of matrix and fiber fracture is the major failure mode, particularly for axial tensile loading. Therefore, only the linear elastic shear response was considered and the effect of plasticity was neglected in the present study. The evolution of damage was modeled as sudden degradation, reflecting that when d  1 , the associated element was 12

completely degraded and was no longer able to carry in-plane shear loads.

3.2.2 Delamination modeling The built-in bilinear traction-separation law was used for cohesive elements to simulate delamination behavior. The initiation of delamination was considered with a quadratic nominal stress failure criterion as in [50]. The Benzeggagh-Kenane law based progressive failure process was used to characterize the evolution of interlaminar damage [36]. 2

2

2

tn  ts   tt   0    0    0  1 t n  t s  tt 

(15)

where t n0 , t s0 and t t0 are the peak values of these stresses when the separation is purely 14

opening, purely shearing or purely tearing, respectively. The corresponding values are 12 MPa, 26 Mpa, and 26 MPa, respectively. The B-K evolution law is:  G S  Gn G  G  (G  G )  G S  G n  Gt C

C n

C S

C n

  



(16)

where GnC and G sC are the corresponding critical fracture energies with values of 0.50 N/mm and 1.57 N/mm respectively; G C is the total critical mixed-mode fracture energy. In this numerical study, each ply of the fiber reinforced composite laminates was modeled as a homogeneous orthotropic material. The fracture process from damage to collapse predicted based on the present FEA was discussed in Section 4.6.2. Computational parameters required in the numerical simulation are listed in Table 2 [36].

4 Results and discussion 4.1 Tensile load–extension curves The purpose of this experiment was to evaluate the tensile strength and strain distribution in un-notched and notched specimens. Fig. 6(a) shows the tensile load–extension curves of all UN and the SN BFRP specimens. It can be observed that the tensile load increases linearly to the peak point and then drops catastrophically when it exceeds the peak load. Similar phenomena are also observed for the plates containing OH, as shown in Fig. 6(b). After reaching the peak load, the BFRP specimen experienced rapid tensile failure, causing a sharp drop in load carrying capability. The results for the CFRP specimens are shown in Fig. 6(c). It is worth noting that the peak load decreases with an increase in crack size, regardless of material types or notch shapes. It can be seen from Figs. 6(a) and 6(c) that the slope of the load–extension curves decrease for cracks of different sizes compared with the UN specimens. The slopes of specimens with crack lengths of 12 mm and 18 mm are less than those of the 3 mm and 6 mm specimens. When the crack length is less than 6 mm, the effect of notch size on the specimen’s rigidity can be ignored because it can be considered as a deformation feature in an infinite plate (based on ASTM D5766 Standards). The decrease 15

of the slope of the specimens with gaps of 12 mm and 18 mm is related to the decrease in the average modulus of the defective plate.

Fig. 6. Comparison of the tensile load–extension curves for different notch shapes and notch sizes: (a) BF-SN, (b) BF-OH, (c) CF-SN and (d) CF-OH.

4.2 Notched specimen characteristics Key parameters were extracted for quantitative analysis to better explain the influence of the notch characteristics. Fig. 7 summarizes the experimental data for composite laminates with OH for comparison with SN specimens. It can be seen from Fig. 7(a) that the tensile strength is strongly related to the notch size but not the notch shape. The BFRP and CFRP specimens showed similar patterns. The effect of the notch shape on the tensile test specimens is discussed in Section 4.4. Because the notch shape showed little effect on the tensile strength (seen from Fig. 7), one of the notch sizes was used to indicate the influence on the tensile strength. Fig. 8(a) shows the tensile strengths for the SN specimens with diameters of 3, 6, 12, and 18 mm. The 16

strength values decrease by 77.6% and 67.7% for the CFRP and BFRP specimens respectively when the hole diameter increases from 3 mm to 18 mm. The ultimate strength values vary greatly with the notch size, and the laminate strength decreases as the notch size increases in both materials. To better understand the strength degradation, further analysis of notch sensitivity and strain field distribution around the notch is presented in Section 4.3. Fig. 8(b) shows the average of failure strain of the SN specimens with notch lengths of 3, 6, 12, and 18 mm under peak load.

Fig. 7. Different notch shapes of the tensile strength ratio: (a) BFRP and (b) CFRP.

Fig. 8. Comparison of different materials: (a) average tensile strength  and (b) average strain Eyy.

Table 3 shows tensile strength ratios of the laminated plates with different notch shapes and notch sizes. It can be seen that minor differences exist in the tensile strength ratios 17

between OH and SN specimens of the same notch size. The notch sensitivity is inversely proportional to the intensity and is expressed as  b /  bH . The tensile strength of the UN specimen is used as the reference value in Table 3. The notch sensitivity of both open hole and SN specimens increases with the increasing of notch size, indicating that notch size affects the strength degradation of laminates. However, the notch sensitivity of the OH plates and SN plates shows 44.4% and 54.9% increase when the notch diameter increases from 3 mm to 18 mm. The notch sensitivity of the SN plates is slightly greater than that of the OH plates. It is believed that the notch shape affects the stress state of the specimen.

Table 3 Tensile strength ratios and notch sensitivity of BFRP with different sizes and shapes. Specimens

Peak load ratio

BF-OH-3 BF-OH-6 BF-OH-12 BF-OH-18

0.60 0.56 0.41 0.32

 b /  bH 1.70 1.76 2.36 3.06

Specimens

Peak load ratio

BF-SN-3 BF-SN-6 BF-SN-12 BF-SN-18

0.66 0.56 0.38 0.29

 b /  bH 1.49 1.78 2.49 3.30

Note: peak load ratio and notch sensitivity value of BF-UN-0 specimen are 1.

4.3 Analysis of progressive failure in notched specimen Crack initiation and propagation during a progressive damage process were captured using the DIC method. Each notch shape of the BFRP specimens contained four notch sizes, of which two were selected for analysis due to their similar failure processes, as seen in Figs. 9-10. It can be seen from Fig. 9(a) that the first visible crack appears near the upper left side of the hole at 86% of the peak load, and then the crack propagates perpendicular to the loading direction with a new crack forming on the right side. When the load reaches 99%, clear fracture zones perpendicular to the load direction can be observed. In Fig. 9(b), BF-OH-3 shows similar progressive damage behaviors under the same strain concentration pattern. A certain angle inclination appears between cracks and the loading direction, which is different from that for the BF-OH-3 shown in Fig. 9 (a). Similarly, the specimen results with the notch diameters of 12 mm and 18 mm show a similar situation, although the direction and angle of crack inclination are not quite the same. 18

This may be because, with the larger notch size of the OH specimen, the likelihood of mechanical damage during processing is greater and eventually the specimen breaks first at the damage. Furthermore, from comparisons of Fig. 9(a)-(b), it can be found that with the increase in hole diameter, the allowable fracture zone length decreases gradually, indicating the influence of hole size on tensile strength of the specimen. As the failure process of CFRP specimens was similar to that of BFRP specimens, one CFRP specimen was chosen for analysis, as shown in Fig. 10. Fig. 10(a) shows the failure process of BF-SN-3. Visible cracks near the notch appear when the applied force increases from 90% to 99% of peak load and then the crack propagates perpendicularly to the loading direction, causing final fracture of the specimen into two pieces. In comparison with BF-SN-3, CF-SN-3 shows no clear cleavage marks when the tensile load reaches 99% of the peak load. Before failure at the 99% load level, the damage area is still limited to the vicinity of the notch, indicating the brittle damage mechanism in Figs. 9-10.

Fig. 9. Comparison of surface cracks and fracture morphology of BFRP: (a) gradual loading of BF-OH-3 and (b) gradual loading of BF-OH-6.

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Fig. 10. Comparison of surface cracks and fracture morphology of BFRP and CFRP: (a) gradual loading of BF-SN-3 and (b) gradual loading of CF-SN-3.

4.4 Strain distribution in notched specimen Fig. 11 shows the strain distribution for specimens with typical notch shapes and sizes. It can be observed that OH specimens show relatively even strain distribution around the holes, whereas the strain distribution of the SN specimens is more concentrated. In the strain level for the 18 mm straight notches, fiber breakage and debonding from the matrix occur and develop quickly. It can be seen from Fig. 11 that the strain concentration areas on both sides of the defect are not completely symmetrical, especially in specimens with larger notch size. The strain distribution away from the holes is also uneven. It is evident that the longitudinal strain at the right side of the hole is more concentrated than that at the left side. It can be seen from the contour lines in Fig. 11 that the strain distribution around the hole is uneven due to the appearance of transverse cracks on the hole opening edge. The magnitude of Eyy is slightly greater on right hand side of the hole than on the left hand side. This could be due to heterogeneous material, non-uniform plate thickness, uneven damage caused by defect processing, or misalignment of the specimen. It was also difficult to completely correlate the loading direction with the length edge of specimens, resulting in slightly asymmetric loading.

20

Fig. 11. Strain values and distributions of the BFRP and CFRP specimens measured by the DIC.

The strain distribution in OH and SN specimens during the tensile failure process was studied using DIC and FEA techniques. The average longitudinal strain distributions at different time points are shown in Fig. 12. Here, the Y direction was taken as parallel to the loading direction. For the sake of clarity, only a typical change image of the strain field is shown. Both qualitative and quantitative comparisons of strain were assessed between experiment and FEA. The plots of strain and local strain measurement graphs were used for the comparisons between experimental and finite element data. For the direct comparisons, the scales of the FEA contour plots were kept the same as those of the DIC plots. The gray areas on the plot represent oversaturation of scales, indicating that part of strain is beyond the upper limit value of the DIC contour line at the hole edge. The hole edge part of the specimen ruptured at this load time, causing inaccurate capture of the strain field. The presence of a hole in the specimen complicates the strain field and causes a highly localized strain zone around it. The maximum strain is observed around the transverse edge of the hole that is 21

perpendicular to the loading direction. The minimum strain is across the longitudinal edge of the hole parallel to loading direction. Fig. 13 illustrates the strain distribution of the BF-SN-3 specimens. The Exy strain field in Fig. 12(c)-(d) shows an x-shaped strain distribution around the defect. In the OH and SN specimens, the shear strain Exy drives an axial split that is parallel to the loading axis.

Fig. 12. Comparison of engineering strain fields obtained by FEA and DIC methods for the specimen BF-OH-3.

22

Fig. 13. Comparison of engineering strain fields obtained by the FEA and DIC methods in the BF-SN-3 specimen.

4.5 Local strain measurement Figs. 14-15 show the variation in strain Eyy over the width of the specimens. As can be seen from Fig. 14, the peak strain appears at the edge of the hole and gradually decreases toward the edge of the sample. As the load increases, the strain field concentration around the hole becomes more serious, especially at the edge of the notch. Near the peak load, obvious cracking near hole edge can be seen at the curve where the final failure occurs (17.2 kN curve 23

in Fig. 14). At this time, the strain value at the edge of the hole is inaccurately recorded by the DIC method. The SN specimen also produces a similar situation and the strain value cannot be accurately obtained at the edge of the notch. Therefore, the strain value were adopted from the finite element results when the edge of the output hole breaks (when the element is not deleted) in this paper, as shown in Fig. 15. The value predicted by FEA was approximately 20% greater than that measured by DIC. Moreover, the strain value corresponding to the data point slightly away from the edge of the hole was approximately the same as that measured by the DIC method. Therefore, the FE simulation more accurately measured the true strain value of the sample near the edge of the hole, to some extent.

Fig. 14. Strain Eyy across the mid-section of specimen BF-OH-6: (a) strain field coordinate system of DIC and (b) strain value of data point.

24

Fig. 15. Strain Eyy across the mid-section of specimen BF-SN-6 obtained by DIC and FEA methods: (a) strain field coordinate system of DIC and FEA and (b) strain value of data point.

4.6 Failure properties 4.6.1 Experimental failure mode Partial views and microscope images of typical areas around failure regions are shown in Fig. 16, which depicts the major damage features of laminated specimens, including delamination, fiber breakage and matrix fractures. The tensile failure modes of un-notched CFRP/BFRP laminates are shown in front and local side views. The failure mode of the specimens is basically fiber breakage; matrix cracking occurs when the peak load is reached along the vertical tensile loading direction. A small delamination can be observed in the enlarged side views. The micrograph Fig. 16(a) clearly shows the partial delamination and fiber breakage fracture of the BFRP specimen. The right side is a sectional view of a carbon fiber specimen. It can be seen from micrograph Fig. 16(d) that fiber brittle fracture and matrix crack dominate the failures of the CFRP specimen without delamination, indicating different mechanisms from those occurring in the BFRP laminate.

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Fig. 16. Failure modes of UN specimens in multiple views of BFRP and CFRP.

Fig. 17 shows typical failure modes of UN and SN specimens. It can be seen that the fracture surfaces are perpendicular to the static loading direction. This is due to the stress concentration that causes minor cracks to initiate around the hole edge. For specimens with larger diameters, both fiber breakage and fiber–matrix interface failure occur at this stress level (that is, the average nominal breaking stress, which is calculated from the actual specimen width and the nominal thickness of the specimen). As the notch size increases, initial cracks appear first near the hole edge, where defects could be introduced by processing or manufacturing. In the final failure mode, the cracks on the left and right sides are not parallel. As compared to the UN specimen, the BF-OH specimens show a larger amount of fiber draw (the amount of protrusion when the fiber is broken) than the CFRP specimens, showing that the toughness of the BFRP specimens is greater than that of the CFRP specimens.

26

Fig. 17. Photographs of the fracture in notched specimens: (a) BF-OH, (b) BF-SN and (c) CF-SN (unit: mm).

4.6.2 Simulation results Finite element analysis was performed to simulate the deformation and failure behavior of BF-OH-6 and BF-SN-6. Fig. 18 shows the fiber damage (SDV3) and final failure of the specimens. Failure states at three different applied loads (80%, 85% peak load, and failure) were obtained from FEA for BF-OH-6. The obvious damage area that could be observed is recorded in Fig. 18(a), which shows the fiber damage distribution in the BF-OH-6 specimen in the longitudinal direction before the peak load is reached, obtained by FE simulation. The most severe fracture occurs in the high strain area at the edge of the hole. Fig. 18(b) shows the damage area of the BF-SN-6 specimens. Compared with the experimental images (gray), the FE simulations (blue) obtained more accurate images of the deformation process and the damage distribution and they showed more clearly the moment when damage first appeared.

27

Fig. 18. Comparison of final failure between experiment and FE method simulation for (a) BF-OH-6 and (b) BF-SN-6.

5 Prediction of characteristic variables Fig. 19 shows the SCF values calculated by Eq. (1) and measured by the DIC technique. The DIC curves of Fig. 19 fluctuate near the notches as it is difficult to measure the true strain value accurately in the vicinity of notches due to the high stress concentration. The SCF value reaches its maximum at the tip of the damage crack and then gradually decreases. Minor differences appear in SCF values away from the defect, as predicted by the theory and measured by the DIC method. It should also be noted that the strain obtained by the DIC measurement method is the average strain. This can be the reason why there is a certain error between the strain at a specific point and the value given by the analysis. At the same time, local defects and minor drilling damage cannot be obtained by elastic analysis.

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Fig. 19. SCF measured by DIC along a hole: (a) BF-OH-3 at load of 18.7 kN and (b) BF-SN-3 at load of 20.9 kN.

The modified PSC and ASC were validated with the experimental data. The values of the characteristic distances d0 and a0 were estimated using the experimental tensile strength of the UN and notched specimens, as shown in Fig. 4. The characteristic lengths of the OH and SN specimens could be obtained as specific values. Table 4 gives the characteristic parameters of the notched BFRP specimens. Fig. 20 shows the least square curves for relationships between the characteristic length and the size of the finite-width notched laminates, which are obtained based on these parameters. The fitted curve can be used to predict the characteristic length of a specimen containing a notch of any size within a certain range, and is applied to Eqs. (5)-(9) for strength prediction.

Table 4 Characteristic distances of the BFRP laminates with different notch sizes. D(L)/W

Characteristic distance d 0

Characteristic distance a0

Experimental values (OH)

Experimental values (SN)

0.08 0.17 0.33 0.50

0.52 0.62 0.55 0.45

2.49 2.75 2.32 1.83

0.60 0.56 0.41 0.32

0.66 0.55 0.38 0.29

FEA values (OH)

FEA values (SN)

0.65 0.56 0.51 0.37

0.76 0.62 0.37 0.32

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Fig. 20. Values of characteristic distance according to D(L) /W for OH/SN specimens: (a) functional expression of d0 and (b) functional expression of a0.

For any material system, the d0 and a0 (constant parameters) in both stress criteria are determined by testing un-notched and notched specimens. In this study, the hole diameter (D) or straight notch length (L) to the specimen width (W) ratio was D(L)/W < 0.6. It has been shown [5, 42-44] that the length d0 or a0 depends on material and geometry. Thus, for the finite width of the notched laminate, the original constant value cannot accurately evaluate the strength of the different sizes. In this paper, the parameters d0 and a0 of multiple sets of finite-width notched laminates are combined, and the corresponding curves are fitted to predict the parameters of the notched laminates with other sizes of BFRP. On the basis of standard ASTM D5766, comparisons between experimental testing and FEM findings were undertaken with four specimen types, each with hole diameters of 3, 6, 12, and 18 mm. The results can be observed in detail in Figs. 21-22. For the test results of 3 mm holes, the PSC curve and the ASC curve were calculated using the values of d0 and a0 obtained by the two fitting curves in Fig. 20, respectively. The characteristic distances were about 0.54 mm for the point stress model and 2.56 mm for the average stress model. Fig. 21 shows the comparison between the experimental and theoretical results for specimens with circular holes. The experimental points in the photos are the mean values calculated from the 30

three repeated experimental datasets. As can be seen from the OH specimens of Fig. 21, there are errors between the point stress model and the average stress model prediction curve compared with the experimental values, but the average stress model predicts more accurately. Fig. 22 shows the comparisons in the case of notched line. It can be seen from Fig. 22 of SN specimens, for points less than 6 mm, the point stress model is closer to the experimental value. For points greater than the standard value, the average stress model prediction curve matches the experimental value more closely, and the largest error results are less than 5 %.

Fig. 21. Relationships between hole diameter and strength ratio of BF-OH.

Fig. 22. Relationships between straight notch length and strength ratio of BF-SN.

6 Conclusions In this study, the effects of notch shape and notch size on tensile performance were investigated in carbon and basalt fiber composites. Tensile strengths were predicted by analytical approaches, the FEA and experiment. Based on the experimental and numerical 31

investigations, the following conclusions can be drawn: (1) The un-notched and notched CFRP laminate showed higher tensile stiffness and strength and lower failure strain than the BFRP laminate. (2) Two distinct failure modes occurred in the notched composites: brittle fracture failure in the CFRP composite and fiber draw dominated mode in the BFRP composite. (3) With the increase in notch size from 0 mm to 18 mm, the tensile strength showed 69.64% and 69.78% reduction in BF-OH and BF-SN respectively, levels which were slightly greater than the reductions in the CFRP (68.27% and 68.32%). The notch shape had a significant influence on the strain distribution but negligible effect on the strength. (4) The strain distribution measured by the DIC method agreed well with that predicted by the analytical formula. (5) Relationships between the characteristic length and sizes of the finite-width notched laminates were determined based on the two existing stress criteria by the curve fitting using the least square method. The predicted tensile strengths agreed well with the experimental and FEA simulation results. (6) The CDM-based FEA showed good accuracy in terms of failure mode, strain distribution, and peak force of the specimens with different notches.

Acknowledgements This work is supported by the National Natural Science Foundation of China (51575172) and the Hunan Provincial Innovation Foundation for Postgraduate (CX2018B198).

Conflict of interest The authors declared that they have no conflicts of interest to this work.

Author contributions section 32

Guangyong Sun and Linxin Wang designed the experimental scheme and wrote the manuscript, Linxin Wang conducted the experimental tests, Dongdong Chen and Quantian Luo analyzed the experimental results, Quantian Luo revised the manuscript.

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Graphical abstract 1. Specimen preparation and test methods

Materials

Specimens

Test methods

2.Model validation and strain analysis

Tensile test Experiment

DIC

FEA

Strain Eyy across the mid-section

3. Mechanism and theories

Failure mechanism

Strength prediction

36