Hybrid woven carbon-Dyneema composites under drop-weight and steel ball impact

Journal Pre-proofs Hybrid woven carbon-Dyneema composites under drop-weight and steel ball impact Y. Zhao, M. Cao, H.X. Tan, M. Ridha, T.E. Tay PII: DOI: Reference:

S0263-8223(19)31865-3 https://doi.org/10.1016/j.compstruct.2019.111811 COST 111811

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

20 May 2019 21 November 2019 16 December 2019

Please cite this article as: Zhao, Y., Cao, M., Tan, H.X., Ridha, M., Tay, T.E., Hybrid woven carbon-Dyneema composites under drop-weight and steel ball impact, Composite Structures (2019), doi: https://doi.org/10.1016/ j.compstruct.2019.111811

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Hybrid woven carbon-Dyneema composites under drop-weight and steel ball impact Zhao Y.a, Cao M.b, Tan H. X. a , Ridha M. *, a,Tay T.E. a * Corresponding author (Email: [email protected]) Affiliations a Department

of Mechanical Engineering, National University of Singapore, 117575, Singapore b College

of Textiles, Donghua University, Shanghai, China, 201620

Abstract In this study, the impact behavior and damage mechanism of novel carbon-Dyneema hybrid fabric reinforced plastic composites are investigated using drop-weight and steel ball impact tests. The force-displacement response, energy absorption and damage mechanisms of the hybrid composite were analyzed and compared with those of woven carbon laminates. The experimental results suggest that the impact resistance of the hybrid composites has been improved when benchmarked with carbon fiber composites. The Dyneema fibers suppress the splitting of bottom surfaces during impact but are susceptible to buckling due to the low compressive strength of Dyneema fibers. A multi-scale approach is proposed for modelling impact damage of hybrid woven composite accounting for the interweave patterns. A meso-scale representative volume element of the interwoven hybrid structure is analyzed and discretized into several sub-sections, each regarded as a type of laminate. Then, a macro-scale impact model is established based on the homogenized effective properties of the sub-sections using continuum shell elements. The failure of the material is modelled using energy-based continuum damage mechanics. Overall, the numerical simulations show good agreement with experimental data in terms of impact force history and damage features, providing insight into the impact damage behavior of hybrid composites.

Keywords Hybrid composites; impact; progressive damage; finite element method; multi-scale modelling

1

Introduction Although carbon fiber reinforced plastics (CFRPs) have been widely used for light-weight

structural applications because of the superior specific strength and stiffness, the relatively low

1

impact resistance of CFRP laminates has been a major concern due to their susceptibility to delamination. In recent years, researchers have been exploring fiber hybridisation to improve impact resistance while optimizing other properties of composites [1-5]. Many studies [6-11] suggested that placing tough high performance polymer fiber layers at the back and carbon layers at the front is beneficial to ballistic protection. Dyneema®, a type of ultrahigh molecular weight polyethylene (UHMWPE) fibers made by DSM, offers excellent energy absorbing capacity, high toughness, high specific strength and stiffness, but has low compressive and transverse strength properties. A previous study [8] showed that hybridization of carbon and Dyneema® fibers in interply configuration largely improves the high-velocity impact resistance.

However, the damage mechanism and

delamination area are found to be very sensitive to the stacking sequence. Most research work [2, 3, 12-15] focused on the effect of layup and stacking sequences on interply hybrid composites while studies [4, 16, 17] deal with the impact behavior of intraply hybrid composites are very limited. There is currently no study on the low–velocity impact performance of interwoven carbon-Dyneema hybrid composites. Recently, a novel carbon-Dyneema interwoven hybrid composite has been developed to improve the impact resistance, damping and vibration absorption of pure carbon fiber composites [18, 19]. Applications of carbon-Dyneema thermoset composites have been developed for automobile components, bicycle frames, and sports equipment. The study by Zhao et al. [20] showed that the intraply hybrid composite exhibit significant higher interlaminar fracture toughness compared to woven carbon composites in both mode I and mode II. The in-plane mechanical behavior of the hybrid composite has also been investigated by Cao et al [21] experimentally and numerically through a meso-scale progressive damage model. This paper studies the performance of the material under impact loading through modeling and experiments. Damage of composite laminate under impact load is a complex and challenging problem with various failure mechanisms, including fiber breakages, matrix cracking, fiber-matrix debonding and delaminations [22, 23] and melting [24]. Several methods were developed for impact simulation of woven composites [21-23, 25-42]. Meso-scale approaches model the yarns and matrix separately [21, 35-41]. In these approaches, yarns are often regarded as transversely isotropic material and the resin matrix as isotropic material. The interaction between yarns and matrix such as debonding and friction can be modelled as well. However, meso-scale models are usually very computationally demanding due to the details in the model. As a result, most works are limited to the static analysis of a representative volume element (RVE) of a woven composite [21, 35-39]. In contrast, macro-scale homogenized approaches are more computationally efficient. The woven ply is modeled as homogenized orthotropic materials with continuum damage mechanics using shell or solid elements [22, 23, 25-34]. The interfaces between the plies are usually modeled using cohesive elements or contact formulation based on traction-separation law. Although the macroscopic homogenized approaches are able to produce a fairly reliable prediction, they are unable to describe the variations in local stress and strain fields induced by the pattern of the fabric and resin rich area in the woven structure. For intraply hybrid composites, the RVE contains several subsections with distinctively 2

different fiber configurations. Therefore, it is critical for the numerical model to capture this feature especially when the size of a repeating unit in the hybrid composite is rather large compared to the size of the impactor. As a result, a multi-scale approach is proposed here for modelling impact damage of hybrid woven composite. This approach is able to take into account the meso-scale interwoven pattern of the hybrid structure with a reasonable computational cost. A meso-scale RVE of the interwoven hybrid structure is first analyzed and discretized into several sub-sections, each of which is homogenized as a type of laminate. Then, a macro-scale impact model is established based on the homogenized sub-sections using continuum shell elements and the fracture behavior of the material is modelled using energy-based continuum damage. In this study, the impact behavior and damage mechanisms of a novel carbon-Dyneema hybrid fabric reinforced composite are investigated experimentally through drop-weight and steel ball impact tests. Impact simulations based on the developed numerical model are conducted and validated with the experimental results in terms of impact force history and damage features.

2

2.1

Experimental study

Materials and specimens The fabric used for preparing the hybrid laminate in this study is Dyneema® SK75 + carbon 3K

twill 2/2 style fabric with 190 g/m2 (Figure 1). The hybrid laminate was fabricated by vacuum assisted resin infusion (VARI) with a low viscosity epoxy resin Epolam 5051. The panel was cured for 24 hours at room temperature (25OC) and then cut into specimen sizes by water-jet. The density of the hybrid specimen is around 1200 kg/m3 and the fiber volume fraction is 52%. The fabric has 200 tex carbon tows and 176 tex Dyneema tows, with a carbon Dyneema volume ratio of 0.6. The cross-section of the hybrid laminate was examined under a microscope and the cross section of a Dyneema yarn is found to be 1.5 to 2 times as large as that of a carbon yarn [20]. Pure woven carbon laminate specimens were also fabricated from plain woven fabrics as reference material, with the same lay-up and dimensions as the hybrid specimens. The detailed specifications of the drop-weight and steel ball impact specimens are presented in Table 1.

3

Figure 1 Hybrid carbon Dyneema® twill 2/2 of fabrics Table 1. Specifications of specimens Material Hybrid

Test method Drop-Weight

Layup

Dimensions

Thickness

Areal density

(mm)

(mm)

(kg/m2)

[(0/45)3]s

150 × 100

3.6

4.4

[(0/45)3]s

150 × 100

2.6

3.6

impact Carbon

Drop-Weight impact

Hybrid

Steel ball impact

[08]

100 × 100

2.4

2.9

Carbon

Steel ball impact

[08]

100 × 100

1.7

2.4

2.2

Drop-weight impact test Drop-weight impact tests were perform according to ASTM D7136 / D7136M standards [43]

as shown in Figure 2. A 16mm diameter hemispherical impactor was attached to a plate with customized lump mass weight. The falling impactor is able to slide smoothly along two rigid columns of the drop-tower. The impact force was measured by a piezoelectric force sensor connected to the impactor at 500 kHz for 20 ms. The specimen was placed on top of an impact frame with a rectangular cut-out of 125 mm by 75 mm. Four toggle clamps with rubber tips were used to secure the specimen to the impact frame. A high-speed laser triangulation sensor (Keyence LK-H152) was set up on a separate stand to measure the displacement and velocity of the impactor during the impact. The measuring range of the sensor is 80mm and the acquisition frequency is 50 kHz. In order to prevent multiple impacts, a wooden plate was slid under the impactor after the first strike. In this study, the total weight of the impactor is 9.92 kg and the drop height is adjusted based on the desired impact energy. The initial impact velocity (𝑣𝑖) and the rebound velocity (𝑣𝑟) were obtained through the laser measuring system. The displacement-time history 𝛿(𝑡) is calculated by Newton’s 2nd law [44]:

4

𝛿(𝑡) = 𝑣𝑖𝑡 +

𝑔𝑡2 ― 2

∫ [∫ 𝑡

𝑡′𝐹(𝑡′)

0

0

𝑚

]

𝑑𝑡′ 𝑑𝑡

(1)

where 𝐹(𝑡′) is the impact contact force, 𝑔 is the acceleration due to gravity and 𝑚 is the weight of the impactor. The velocity during the impact can also be obtained as: 𝑣(𝑡) = 𝑣𝑖 + 𝑔𝑡 ―

∫

𝑡 𝐹(𝑡′) 0

𝑚

𝑑𝑡′

(2)

Figure 2 Experimental setup for the drop-weight test

2.3

Steel ball impact test Steel ball impact tests were conducted by firing a stainless-steel sphere at the specimen with

a single stage nitrogen gas gun system shown in Figure 3. The hybrid composite specimens were placed on a solid metal ring (inner diameter = 80 mm) with the help of the Blu Tack®. The solid metal ring is mounted on a fixture which is designed to be perpendicular to the gun barrel. The center of the ring is aligned with the center of the muzzle. The low strength Blu tack® is used to hold the specimen on the ring support to impose a simply supported boundary condition. The steel ball has a diameter of 12.00 mm and a mass of 7.05 g. It was targeted at the center of the specimen with the impact velocity ranging from 50-150 m/s. The impact velocity of the steel ball is calculated from the time difference between the interruption of two laser gates separated by 100mm, which are positioned between the 5

gas gun muzzle and the target. The tests were recorded using a high-speed video camera running at a frame rate of 20000 fps. The residual speed of the steel ball after perforation or rebound were calculated based on the images captured by the camera.

Figure 3 Steel ball impact test setup

3

Modelling strategy Figure 4 shows a typical stress-strain curve of an intraply carbon-Dyneema laminate in a

uniaxial tensile test. The curve has two segments due to the hybrid structure, and the two peaks correspond to the failure of carbon yarns and Dyneema yarns, respectively. Unlike in pure woven fabric, intraply hybrid fabric composite is not homogeneous; there are areas occupied by only either one of the fiber types and there are also areas in which both types of fiber exist (Figure 1). A lot of information will be lost if the direct homogenization method is applied. To account for the heterogeneity in fabric structure, a multi-scale finite element model is proposed in this study to simulate the impact damage of the hybrid laminate. The framework of the method is described in the following steps: A meso-scale RVE model is generated based on the realistic geometry of the RVE of the hybrid laminate. The in-plane geometrical periodicity of the RVE is maintained through a set of periodic boundary conditions applied to the model. The meso-scale model is further discretized into four sub-sections so that each sub-section contains only one type of fibers in each principal direction. The elastic properties of the sub-section are obtained through local volumetric homogenization of the sub-section domain of the 6

RVE model. Now that the sub-sections are considered as homogenized orthotropic materials, a macro-scale laminate model for impact simulation is built with sub-sections and the damage of each sub-section is modeled with continuum damage mechanics.

Figure 4 Typical stress-strain curve of carbon-Dyneema laminates in tensile tests

3.1

Meso-scale model analysis An RVE of an interwoven hybrid layer was generated with detailed fabric geometry of yarns

and matrix (Figure 5) using the software TexGen [45]. Note that yarns in this model include resin between the fibers while the matrix is the resin rich volumes between the yarns. The RVE is an idealization of the actual single ply geometry of the hybrid woven composite. The volume fraction of the yarns and fiber volume fraction of the yarns are needed in order to build up the RVE model. In this study, the total fiber volume fraction is experimentally determined from dry fabric, while the yarn volume fractions and fiber volume fractions in each yarn are assumed. In the RVE model, the overall yarn volume fraction is calculated as 0.55, (with carbon yarns fraction 0.22 and Dyneema yarns fraction 0.33). The carbon fiber volume fraction (𝑣𝑐𝑓) in the RVE model is 0.176 while the Dyneema volume fraction (𝑣𝐷𝑓) is 0.297. Therefore, the overall fiber fraction in the RVE is calculated as 𝑣𝑓 𝑣𝑐𝑓

𝑣𝑐𝑓

= 0.47 and 𝑣𝐷𝑓 = 0.6. In comparison, the experimentally measured 𝑣𝑓 and 𝑣𝐷𝑓 of the material are 0.45 and 0.62 respectively. The model was meshed using linear tetrahedral elements C3D4 with one integration point. The material orientation of the elements in yarn structures were specified following the fiber directions. The yarns in the RVE is considered as transversely isotropic materials and the matrix is modeled as an isotropic material. The effective properties of yarns were calculated using the bridging model [21, 46] based on the constituent fibers and matrix properties. Table 2 lists the matrix

7

properties and the calculated yarn properties used for the RVE model. A set of equations representing the periodic boundary conditions [47] were imposed on the RVE.

Table 2 Material properties of carbon and Dyneema yarns calculated from bridging model Properties

Carbon yarns

Dyneema yarns

Fiber volume fraction*

0.8

0.9

𝐸11(GPa)

169.49

87.72

𝐸22 = 𝐸33 (Gpa)

10.18

3.21

𝐺12 = 𝐺13(Gpa)

5.32

2.47

𝐺23(Gpa)

3.78

0.60

𝜈12 = 𝜈13

0.28

0.2

𝜈23

0.41

0.2

*Assumed values

Figure 5 Meso-scale model of carbon/Dyneema Twill2/2 RVE The model was divided into four square sub-sections with the same dimension to account for the influence of the interwoven architecture of two different types of fibers. In this way, each subsection contains only one type of fibers in each principal direction. The approach is illustrated in Figure 6. The subsection CC contains only carbon yarns and subsection DD contains only Dyneema yarns. The subsection CD and DC, which have only one type of fibers in each direction, are the same but with a 90o difference in angle rotation. A uniaxial loading was applied to the RVE model in the

8

fiber direction and the simulation was solved using Abaqus/Standard. The subsections are assumed to be orthotropic and the effective elastic properties in the fiber directions were obtained using the volume averaging method [39], 𝜎𝑖 =

∫𝑉 𝜎𝑖𝑑𝑉𝑖 𝑖

(3)

∫𝑉 𝑑𝑉𝑖 𝑖

𝜀𝑖 =

∫𝑉 𝜖𝑖𝑑𝑉𝑖 𝑖

(4)

∫𝑉 𝑑𝑉𝑖 𝑖

where 𝑉𝑖, 𝜎𝑖 and 𝜀𝑖 are the volume, equivalent stress and strain of subsection 𝑖 respectively. The calculated effective moduli and properties of the sub-sections are listed in Table 4 . The overall stiffness obtained from the volumetric homogenization of the RVE shows good agreement with the stress-strain curve obtained from experiments (Figure 6).

Figure 6 Illustration of the sub-section scheme in the meso-scale model

Table 3 Tensile properties obtained for macroscopic models Properties Density Calculated Elastic modulus in fiber direction 1 Calculated Elastic modulus in fiber direction 2

Symbol

Intraply subsections DC

DD

CC

CD

𝜌 (kg/m3)

1220

1060

1400

1220

𝐸1(Gpa)

33.43

29.73

37.28

33.65

𝐸2(Gpa)

33.65

29.73

37.28

33.43

9

Poisson ratio

3.2

0.046 [34]

𝜈12

Macro-scale damage model for subsection In the macro-scale model, the damaged compliance of the homogenized material can be

represented as

𝐶𝑑 =

[

1 (1 ― 𝑑1)𝐸1 ― 𝜈21

― 𝜈12

𝐸2

𝐸1 1 (1 ― 𝑑2)𝐸2

0

0

0 0 1 (1 ― 𝑑12)𝐺12 ∗

]

(5)

where the damage factors 𝑑1 and 𝑑2 represent the damage of the yarns in the 1 and 2 directions respectively. The non-linear shear behavior and damage of the material is governed by the degraded shear modulus 𝐺12 ∗ and shear damage factor 𝑑12 (see Figure 7). 3.2.1

Fiber direction damage The material is considered to be elastic along fiber directions with same the modulus under

tension and compression before damage. The strain rate effect of carbon fibers is negligible [48]. Experiments by Russel et al. [49] and Sanborn et al. [50] show that Dyneema fibers are strain rate insensitive over the strain rate range of 10-5 s-1 to 103 s-1. Based on these studies and due to the absence of data at higher rates for Dyneema fibers, effect of strain rates is not considered in our model despite the fact that the strain rate may be more than 103 s-1 in certain areas of the specimen under the steel ball impact. A strain-based criterion is applied for the damage onset in fiber directions: ε 2 ε𝑖𝑂𝑇

( )

≥ 1, ε > 0 ;

( ) ε𝑖

ε𝑖0𝐶

2

≥ 1, 𝜖𝑖 < 0

(6)

where 𝜀𝑖 is the strain on the fiber directions (𝑖 = 1, 2). ε𝑖𝑂𝑇 and ε𝑖𝑂𝐶 are the failure initiation strains in tension and compression determined from experimental results of non-hybrid woven composites: X𝑇

X𝐶

ε𝑖𝑂𝑇 = 𝐸𝑖 ; ε𝑖𝑂𝐶 = 𝐸𝑖

(7)

where X𝑇 and X𝐶 are the tensile or compressive strength and 𝐸𝑖 is the modulus of the material. The inplane elastic modulus for non-hybrid woven carbon and Dyneema composites were experimentally measured as 58.9 ± 0.4 Gpa and 20.3 ± 0.9 Gpa in this study. The damage evolution follows a linear softening law and the effective damage factor 𝑑𝑖 for material degradation in fiber directions (𝑖 = 1, 2) can be written as: 𝑑𝑖𝑇 = 1 ―

(

ε𝑖𝑂𝑇 ε𝑖𝐹𝑇 ―𝜀𝑖 𝜀𝑖 ε𝑖𝐹𝑇 ― ε𝑖𝑂𝑇

)

, ε𝑖𝑂𝑇 < 𝜀𝑖 < ε𝑖𝐹𝑇, 𝜀𝑖 > 0

10

(8)

𝑑𝑖𝐶 = 1 ―

𝜀𝑖𝑂𝐶 𝜀𝑖𝐹𝐶 ― |𝜀𝑖|

(

)

|𝜀𝑖| 𝜀𝑖𝐹𝐶 ― 𝜀𝑖𝑂𝐶 𝑑𝑖 = 𝑑𝑖𝑇

〈𝜀𝑖〉 |𝜀𝑖|

, 𝜀𝑖𝑂𝐶 < |𝜀𝑖| < 𝜀𝑖𝐹𝐶, 𝜀𝑖 < 0

〈 ―𝜀𝑖〉

+ 𝑑𝑖𝐶

(9) (10)

|𝜀𝑖|

where ε𝑖𝐹𝑇 and ε𝑖𝐹𝐶are the final failure strain in tension or compression, respectively. The damage factor is zero in undamaged condition and set to be 1 when strain reaches the final failure strain. The final failure strain is determined by the critical energy release rate of the material and the crack band model [32]: 2𝑔𝑖𝑇

2𝑔𝑖𝐶

ε𝑖𝐹𝑇 = X𝑇 𝑙𝑒 ; ε𝑖𝐹𝐶 = X𝐶 𝑙𝑒

(11)

where 𝑔𝑖𝑇 and 𝑔𝑖𝐶 are intralaminar fracture toughness (𝑖 = 1, 2) of the woven composite under tension or compression loading, respectively, while 𝑙𝑒 is the characteristic length of the element which is defined as the square root of the planar area of the element. Following Huguet [34], damage carbon fibers caused by tension loading is assumed to have no effect on their behavior in compression, while the damage in compression loading would cause damage in tension as well. As a result, 𝑑𝑖𝑇 is set to be equal as 𝑑𝑖𝐶 if the calculated 𝑑𝑖𝐶 exceeds 𝑑𝑖𝑇 in carbon yarn directions. On the other hand, the damage caused by tension and compression is considered to be independent for Dyneema yarns. It is worth noting that the 𝑔𝑖𝑇,𝐶 and X𝑇,𝐶 obtained from experimental results of non-hybrid woven composites cannot be directly applied as material properties for the sub-sections models due to the large difference in fiber contents. However, failure initiation and final failure strain values are assumed to be constant for the same type of materials. Therefore, the failure strain values of the subsections in each fiber direction are calculated from the corresponding type of non-hybrid composite using Eqn. (7) and (11). The compressive failure strength of Dyneema fiber is measured from 100 Mpa [19] to 340 Mpa [51]. Consequently, the compressive failure strength of non-hybrid Dyneema composite is estimated as 23 Mpa to 78 Mpa using Eq. (7), as the linear modulus of the Dyneema fiber Sk76 is taken as 130 Mpa. In this study, the compressive failure strength of the non-hybrid Dyneema is set as 60 Mpa. The translaminar fracture toughness of woven Dyneema composite has not been reported in any literature. However, a recent study experimentally determined the translaminar fracture toughness of a woven Vectran/epoxy composite [52]. Vectran fibers, which are made from liquidcrystal polymer, have a similar mechanical property to Dyneema. Therefore, the translaminar tensile fracture toughness is taken from the value of the woven Vectran composite. The non-hybrid composite properties used in this study are summarized in Table 4.

3.2.2

Non-linear shear damage The Carbon/Dyneema hybrid composites in this study shows nonlinearity under shear

loading [21]. This nonlinear in-plane shear behavior of the material is modeled as an isotropic 11

hardening as shown in Figure 7. The Ramberg-Osgood equation is used to fit the loading curve [30, 34]: 1 𝜌 ―𝜌

( ( ))

∗ 𝜏12 = 𝐺012𝛾12 1+

|

𝐺012

|

∗ 𝛾12

𝑆∗

(12)

∗ where 𝐺012 is the initial shear modulus, 𝛾12 is the cumulative shear strain with plasticity taking into

account of cyclic loading history. 𝑆 ∗ and 𝜌 are the two parameters from curve fitting. In the case of ∗ unloading, the secant shear modulus 𝐺12 with respect to the shear strain is obtained through cyclic ∗ ±45o off-axis in plane shear test. The degraded shear modulus 𝐺12 is then fitted to a double

exponential law [53] ∗ 𝐺12 = 𝑐1𝑒

∗ | 𝑐2|𝛾12

+ 𝑐3𝑒

∗ | 𝑐4|𝛾12

(13)

The shear stress is then calculated as ∗ ( 𝜏12 = 𝐺12 𝛾12 ― 𝛾𝑝12)

(14)

where 𝛾𝑝12 is the transition point from unloading to reloading at current loading cycle. Therefore, the total response of the shear stress-strain curve contains the curve described by the Ramberg-Osgood equation during loading and a straight unloading path. The damage factor for the shear response is assumed as 𝑑12 = 1 ― (1 ― 𝑑1)(1 ― 𝑑2). The shear modulus 𝐺𝑑12 and permanent shear strain 𝛾𝑑12 are ∗ taken from 𝐺12 and 𝛾𝑝12 at the onset of damage. The shear stress after damage initiation can then be

written as 𝜏12 = 𝐺𝑑12(𝛾12 ― 𝛾𝑑12)(1 ― 𝑑12)

(15)

The parameters for modeling the non-linear shear behavior of the hybrid composite obtained through cyclic ±45o off-axis in plane shear tests are listed in Table 5. In this study, the shear behavior is assumed to be similar for all the sub-sections.

Figure 7 Illustration of non-linear shear damage

12

3.2.3

Interface modelling The interface between the plies is simulated with a cohesive zone model (CZM) and a general

contact algorithm implemented in Abaqus/Explicit. The initiation and propagation of delamination are modeled based on the quadratic stress criteria and an energy-based linear softening law. The mixedmode energy criterion is calculated by the Benzeggagh-Kenane (B-K) law[54]. The mode I and mode II fracture toughness of the hybrid interface were obtained experimentally through DCB and ENF tests [20]. The interlaminar strength is assumed to be 60 MPa for all delamination modes due to the lack of experimental values. The effect of the interlaminar strength on the result of the numerical simulation is discussed in 4.3. The properties for interface model are listed in Table 6. Table 4 Tensile properties for macroscopic models Properties

Non-hybrid woven laminate

Symbol

Carbon

Dyneema

Tensile strength in fiber

𝑋1𝑡(Mpa)

692

558

directions1

𝑋2𝑡 (Mpa)

692

558

Compressive strength in fiber

𝑋1𝑐 (Mpa)

689

60

directions

𝑋2𝑐 (Mpa)

689[33]

60

Crit. Energy release rate for tensile

𝑔𝑐𝑡1 (Mpa)

60[55]

145[52]

fracture in fiber directions

𝑔𝑐𝑡2 (Mpa)

60[55]

145[52]

𝑔𝑐𝑐1 (Mpa)

20[34]

0.52

𝑔𝑐𝑐2 (Mpa)

20[34]

0.52

Crit. Energy release rate for compressive fracture in fiber directions 1.

Measured in warp direction.; the strengths of both directions are assumed to be equal

2.

Assumed value (see 3.2,1)

Table 5 Shear properties for macroscopic models Properties

Symbol

Intraply

Shear modulus

𝐺12 (Mpa)

3556

Shear strength

𝑆12(Mpa)

28.34

Ramberg-Osgood equation

𝜌

0.912

parameters

𝑆 ∗ (Mpa)

32.74

𝐶1

884.15

Parameters fitted for the double

𝐶2

-11.14

exponential law (Eqn. 13)

𝐶3

704.86

𝐶4

0.994

13

Table 6 Interlaminar properties

3.3

Properties

Symbol

Mode I

Mode II

Penalty stiffness

𝐾 (N/mm3)

5×104

5×104

Interlaminar strength

𝑡 (Mpa)

60

60

Crit. Energy release rate

𝐺𝑐 (N/mm3)

1.1[20]

2.5[20]

Finite element model for impact tests The constitutive behavior described in the previous section is implemented in a VUMAT user

subroutine and the analysis is performed using Abaqus/Explicit. The subroutines were used to define the material behavior in both the drop-weight impact and the steel-ball impact models. Maximum stiffness degradation and element deletion algorithms were applied to the model to prevent any convergence issues. 3.3.1

Drop-weight impact model The assembly of the FE model of the drop-weight impact is shown in Figure 8. The target

hybrid laminate is 152 mm×104 mm and has a lay-up of [(0/45)3]s. It is worth noting that the dimension of the laminate in the numerical model is slightly different from that in the experiment (150 mm×100 mm). The adjustment is to keep an integer number of the sub-sections in the model. However, this would have little effect on the results as the adjustment is small compared to the overall dimensions and the dimension of the inner cut-out of the impact frame is still 125mm by 75mm, with the toggles in the same positions as in the experiment. The subsections of the meso-scale model shown in Figure 5 is translated into homogenized subsections in this macro model, depicted in different element colours. Each sub-section is modeled as an homogeneous orthotropic material using continuum shell elements (SC8R). Fine mesh with 1 mm x 1 mm SC8R elements is used to model the middle part of the model, covering an area of 40 mm x 72 mm of the plate. In this middle area, each subsection is represented by 4 x 4 elements. It is worth noting that the mesh in the model is aligned with the fiber directions except at the edges of the 45o plies. An enhanced hourglass control is employed to prevent the hourglass effect of the reduced integration element. Four rubber-tipped clamps are modeled by four cylinders. An approximately 1 kN total clamping force is exerted on the specimen in the simulation through a small displacement given to the cylinders. The clamps, the fixture, and the impactor are modeled by rigid bodies using R3D4 elements. A lumped mass of 9.92kg and an initial impact velocity is assigned to the reference point of the impactor. The fixture is fixed in all degrees of freedom. A general contact with a friction coefficient of 0.2 is defined for the laminate in contact with the impactor, the fixture, and the clamps. The effect of the friction coefficient value is presented in the sensitivity analysis in 4.3. 3.3.2

Steel ball impact model The assembly of the FE model of the steel ball impact is shown in Figure 9. The target hybrid

laminate is 100 mm×100 mm and each ply is divided into 4 mm×4 mm sections to represent the sub14

sections patterns. Similar to the drop-weight impact model, the composite laminates are also divided into subsections modeled using continuum shell elements (SC8R). The laminate consists of 8 plies and the ply thickness is 0.3mm. One element is used through the thickness direction for each ply. As shown in Figure 9, fine mesh with element size below 1 mm x 1 mm were used within an area of 40 mm x 40 mm in the middle of the model. The size of the element within this area is further reduced toward the middle and the smallest element is 0.5 mm x 0.5 mm at the middle of the impact point. The area away from the impact zone is gradually meshed with larger elements up to 1.5 mm × 1.5 mm. The enhanced hourglass control is also employed in this model. The steel ball and hollow frame are modeled using solid elements (C3D8R) with rigid body constraint. Various initial impact velocities are assigned to the steel ball. The hollow frame has a circular hole of 80 mm in diameter and is constrained in all directions. General contact is defined between specimen with the steel ball and fixture. The delaminated plies are also modeled using the general contact with the friction coefficient set as 0.2. 3.3.3

Maximum stiffness degradation and element deletion Stiffness degradation models are prone to excessive element distortions and other numerical

difficulties. These problems are mitigated in this study by limiting the stiffness degradation and deleting highly distorted elements. The maximum damage factor is set to a number very close to unity to avoid sudden element distortion due to zero stiffness in the element [33, 40, 56-59]. Following González et al. [22], the maximum damage factor for fiber directions (𝑑𝑖𝑇) is defined as 0.9999 to keep the residual stiffness of a fully damaged element as low as possible (less than 10 MPa) without causing numerical difficulties. On the other hand, the maximum compressive damage factor (𝑑𝑖𝐶) is set at 0.999 to avoid abortion of the simulation. These selected maximum damage factors do not add significant stiffness to the model [60]. In addition, a maximum shear strain value is set at 10% [34], beyond which the shear damage variable (𝑑12) is assigned the maximum damage value of 0.999. In addition to setting the maximum stiffness degradation factor, element deletion is implemented in this model to prevent excessive element distortion caused by damage. The element is deleted if both fiber directions completely failed in tension (damage variables = 0.9999), or the shear strain exceeds 100%. In addition, following Tan and Falzon [53], an element is removed if the determinant of the deformation gradient (𝑑𝑒𝑡 𝐹) is larger than 1.4 or smaller than 0.6. These values are chosen such that the elements are removed before they are excessively distorted and cause any convergence issue in the simulation.

15

Figure 8 Finite element model of drop-weight impact test

Figure 9 Finite element model of steel ball impact tests

16

4 4.1

Results and Discussions Drop-weight impact

Figure 10 Force-time history and force-displacement curves: (a)(b) carbon-Dyneema hybrid laminate; (c)(d) woven carbon laminate Figure 10 shows the force-time histories and force-displacement curves of the carbonDyneema hybrid laminates and the reference woven carbon laminates subjected to 30 J and 50 J impacts. The peak forces obtained from the same composite laminates are the same regardless whether the impact energy is 30 J or 50 J because damage has occurred in the specimens and the maximum force is dependent on the damage initiation and propagation in the specimens. Figure 11(a) and (b) presents the typical top and bottom view of the hybrid laminate after the tests. Figure 12 (b) shows a close-up view of the bottom surface of the hybrid laminate subjected to 50J impact. The bottom surface was found with little carbon yarn breakage and splitting. In contrast, the reference carbon laminates are all perforated under both 30J and 50J impacts due to brittle yarn breakage. This is because the localized splitting at the bottom surfaces of the hybrid laminate has been suppressed by the Dyneema yarns which have much higher strain to failure and fracture toughness in tension compared to carbon yarns. This mechanism also results in spreading the damage over a larger area and increase energy absorption. The penetration limit of the hybrid material is also increased and will be discussed further in section 4.2. It is worth noting that the Dyneema yarn is almost transparent in the pristine state and becomes whitened due to damage and matrix cracking (see Figure 12(a)). The whitened area on the surface indicates the approximate area of matrix and 17

Dyneema yarn damage. The front surface shows both carbon and Dyneema yarn compressive failure in the middle along the long side and a “cross” whitening mark due to the Dyneema damage and matrix cracking (Figure 11 (a)). Interestingly, in all the tests of the hybrid composites, the highest impact force occurs at around 7kN when localized buckling starts and the load suddenly drops. The localized buckling propagates from the impact point to a side of the specimen (yellow circles in Figure 11), mainly due to the low compressive properties of the Dyneema fiber, which makes the laminate very sensitive to the imperfection of the test setup. Therefore, the compressive strength of the Dyneema yarns in the laminate is the limiting factor of the strength of the hybrid composite under impact load.

Figure 11 Images of typical top (a) and bottom (b) surfaces of hybrid composite in the drop-weights impacts; top(c) and bottom (d) surfaces damage obtained by numerical simulation

18

Figure 12 (a) Whitening of impact area of the front surface of the hybrid laminate (b)The near impact center area of the bottom surface of the hybrid laminate subjected to 50J impact

The numerical simulation of the 50J impact tests is conducted using the model described in section 3.3. The post impact fracture surfaces of the numerical simulation are illustrated by the maximum compressive and tensile damage factor for the top and bottom surfaces respectively (Figure 11 (c) and (d)). These figures show that the damage morphology predicted by the numerical simulation bears a good resemblance to the experimental results (Figure 11 (a) and (b)). The white patches in the top surface of the model shown Figure 11 (c) are mostly caused by the compressive failure of the Dyneema rich sub-sections DD because the failure strength of Dyneema yarns are lower than that of the carbon yarns; these white patches matches with the whitened parts of Dyneema yarns in the experiment shown in Figure 11 (a). It should be noted that the early compressive failure of Dyneema yarns shown as white patches in Figure 11(c) would not have been captured by the simulation if the plies were homogenized using uniform properties. The proposed model presented here, however, is able to account for this phenomenon in the hybrid woven composite through subsectioning of the lamina and applying different properties to each subsection. Similarly, the white patch area on the bottom surface of the model (Figure 11 (d)), which represents the failure in both carbon and Dyneema yarns, also resemble the white patch area in the experiment Figure 11 (b). Figure 13 shows the predicted force-time history and force-displacement curves for both 50J and 30J

19

impacts. The simulations are generally in good agreement with the experiments and the load drop due to local bulking is captured with good accuracy. However, it is worth noting that the numerical model slightly underestimated the overall damage. Figure 14 shows a comparison between the damage progression in an 50J impact test as recorded by a high-speed camera and damage progression predicted by simulation. During the impact, compressive damage in the form of matrix cracking and Dyneema yarn failure was first initiated from the impact area and propagated to the side of the specimen. As the load increases, compressive damage of carbon yarn started to occur, and the top plies buckled under compression and caused a sudden drop in the force. The buckling started near the impact area and quickly propagated to one of the long edges. In the numerical model, this buckling is represented by element deletion triggered by large distortions in the elements, as determined by the deformation gradient criterion. These experimentally observed local ply buckling and the corresponding interlaminar damage from the simulation are shown in Figure 15.

Figure 13 Comparison of force-time history (a)(c) and force-displacement curves (b)(d) between experimental results and numerical simulations of 50J and 30 J drop-weight impacts

20

Figure 14 Development of the damage recorded by the high speed camera and numerical simulations (maximum compressive damage in yarn directions)

21

Figure 15 Experimentally observed (a) and simulated (b) interlaminar damage due to ply buckling

4.2 4.2.1

Steel ball impact Energy absorption and perforation resistance The results of the steel ball impact test of the carbon-Dyneema hybrid laminate and the

reference woven carbon-epoxy laminate are presented in Figure 16. The “HH” refers to the hybrid specimen used in the steel ball impact. The impact velocity of the steel ball was measured using laser sensors while the residual velocity after perforation or rebound was calculated based on the video captured using the high-speed camera. Since it is extremely hard to achieve a precise velocity at which the steel ball just perforates the target specimen and stops completely, The ballistic limit (𝑉𝐵𝐿) of the specimen was determined through curve fitting the residual velocity (with perforation) to impact velocity using the following equation [13, 14, 61] 1

𝑉𝑅 = 𝐴(𝑉𝑝0 ― 𝑉𝑝𝐵𝐿)𝑃

( 16)

where 𝑉𝑅 and 𝑉0 are the residual and impact velocity, and A and p are the fitting parameters. The calculated ballistic limits are presented in Table 7 . The test results of 8-layers pure Dyneema fabric/epoxy specimen impacted by a 12mm steel ball reported by Wang et al. [62] are included for comparison in Table 7 .

22

Figure 16 (a) Residual velocity vs. impact velocity (b) absorbed energy vs. impact energy Table 7 Ballistic limit results

Specimen type

Fitted

Estimated

Areal density

𝑽𝑩𝑳/areal

Parameters for

Ballistic limit (

(𝐤𝐠/𝐦𝟐)

density

Eq. 16

𝐦/𝐬)

(𝐦𝟑/𝐤𝐠·𝐬)

𝐴

𝑝

Carbon (CC)

1.271

1.345

60.9

2.4

25.4

Hybrid (HH)

0.992

2.014

98.7

2.9

34.0

Dyneema(DD)

-

-

>130

2.7[62]

>47.3

In Wang et al. [62], only two tests with perforation were recorded and so the ballistic limit is difficult to determine accurately. Nonetheless, the pure Dyneema composite performs best in the ballistic tests due to the high toughness of the Dyneema fibers. The ballistic limit of the Dyneema composite is at least 113% higher than that of the pure carbon composite, which has the lowest ballistic limit. The hybrid composite shows 62% improvements of the ballistic limit over the carbon composites. Since the carbon specimen (1.7mm) is thinner than the hybrid composite specimen (2.4mm), if the ballistic limit per areal density is computed, the improvement is about 34%. Numerical simulations are conducted at different initial velocities using the model proposed in this study. Figure 17 shows that the numerical model provides an accurate prediction of residual velocities for both impacts below and above the ballistic limit of the hybrid carbon-Dyneema composite. The ballistic limit is predicted to be 96.5m/s compared to the experimental value of 98.7m/s estimated by Eq. (16). It should be noted that, based on the simulation, the local strain rate may reach 105 s-1 in some areas of the test specimens when impacted by a 150 m/s steel ball. This is much higher than the highest strain rate in the experiments by Russel et al [49] and Sanborn et al [50], in which they examined the rate dependency of Dyneema properties. If test data at higher rate shows that the properties of Dyneema change with strain-rate, this model can be refined further to include this effect. However, in this work, this effect is assumed negligible. 23

Figure 17 Residual velocity measured from experiments and obtained from simulations 4.2.2

Impact damage evaluation The damage on the back face of the hybrid and the carbon composite after penetration

shown in Figure 18 appears to be highly localized. The carbon composite has two symmetrical axes of fiber breakage along warp and weft directions, resulting in orthogonal split fracture planes. The energy dissipation of the impact is mainly through the brittle failure of carbon fiber and matrix cracking [14, 29]. In contrast, the carbon-Dyneema composite exhibits a circular bulged shape at the back surface. Wang et. al [62] reported that the Dyneema/Epoxy laminate also shows a similar circular hole on the back surface after impact perforation. The diameter of this circular hole in the carbon-Dyneema composite is approximately the same size as that of the steel ball. However, the damage area indicated by the whitening of the surface is much larger. When the steel ball impacts the carbon-Dyneema hybrid composite, the steel ball tends to pull the Dyneema yarns towards the centre as it penetrates the laminate. Since the brittle carbon fibers will fail before the Dyneema fibers, this results in the pull out of the surface Dyneema yarns and subsequent breakage of the interlaced carbon yarns. The debonded Dyneema yarns form a permanently bulged shape with large transverse deformation and extended area of matrix damage (Figure 18), which contributes to the higher ballistic limit of the hybrid composites. With the increase of the impact velocity, the difference in the residual velocity between the hybrid and the carbon specimens becomes smaller. The damage becomes more localized when the impact velocity is much higher than the ballistic limit. Previous studies [14, 29] also show that the extent of damage usually decreases with the increase of impact velocity above the ballistic limit. Therefore, the difference in residual velocity between the hybrid and the carbon composites approaches a constant value at high impact velocity due to the change of damage mechanism Figure 16(a)).

24

Figure 18 Back surfaces of a hybrid specimen penetrated by steel ball at a speed of 100m/s (a) and woven carbon specimen (b) at a speed of 89m/s Micro-computerized tomography was used to examine the interior damage of the penetrated hybrid composite specimen. The damage contour and the cross-sectional images taken at different positions are presented in Figure 19. The delamination contour shown in the overview of the penetrated specimen was estimated by evaluating the extent of delamination and matrix cracks in the slice of the cross-sectional image. The measurement was taken every 1-1.5 mm from the center of the impact and the total damage area is around 660 mm2. In the cross-sectional view, the Dyneema yarn appears to be darker than the carbon yarn due to the difference in X-ray absorption by the fibers. The hybrid composite forms a circular hole around the perimeter of the steel ball. Discontinuous and diffused delaminations, as well as yarn debonding and pull-out can be found throughout the crosssection, which is related to the different fiber/matrix adhesion of carbon and Dyneema yarns. This phenomenon increases the energy dissipation of the hybrid composite during the impact and results in a higher ballistic limit.

25

Figure 19 Micro-CT images of top-view and cross-sectional slices of the hybrid composite after impacted at 100m/s Figure 20 shows the numerical results of a specimen subjected to an impact velocity of 100m/s in terms of maximum tensile damage in yarn directions and overall projected delamination area after perforation. The primary Dyneema yarns running directly under the impact area suffer extensive damage in weft and warp directions. This is similar to the damage observed in the experiment where the damaged Dyneema yarns whitened. Although the delamination area predicted by the simulation is slightly smaller than the delamination observed in the CT scan, the overall morphology is very similar if the elongated delamination in the weft and warp direction in the simulation is ignored. This elongated delamination in the weft and warp direction marks the debonding of the Dyneema yarns from the surrounding materials as they are being pulled out. Such debonding due to pull-out is difficult to identify in the Micro-CT scan as the feature is less than oneunit cell while the debonded yarns are still in contact with the surrounding material after.

26

Figure 20 Maximum tensile damage in yarn directions and delamination area of the hybrid laminate under a 100 m/s steel ball impact at 100m/s

4.3

Effect of friction coefficient value and interlaminar strength Frictional coefficients (µ) from 0.1 to 0.3 are generally measured or assumed in drop-weight

impact models for composite laminates in other studies [25, 32, 58, 60, 63]. In this study, a sensitivity analysis is conducted on the effect of the friction coefficient value used in the numerical model. Figure 21 shows the force-time response of the 50J drop-weight impact simulations with friction coefficient from 0.1 to 0.3. The initiation of the load-drop is delayed with the increase of the friction coefficient. The simulation results with friction coefficient of 0.1 and 0.2 are very similar while the load drop is significantly underestimated in the simulation with coefficient of 0.3. Due to the lack of material information, the friction coefficient is assumed 0.2 as it yields good agreement between numerical simulation and experimental results. The effect of the interlaminar strength used in the impact model is also examined. A previous study by Lu et al. [64] shows that the results are relatively strength-insensitive in problems with high stress concentrators. As shown in Figure 22, varying interlaminar strength value from 40Mpa to 80Mpa does not significantly affect the force-time response of the 50J drop-weight impacts. Models with strength value of 60Mpa for mode I and mode II delamination show good agreement with experimental results in this study.

27

Figure 21 Effect of friction coefficient on the force-time response of the 50J drop-weight impact model

Figure 22 Effect of interlaminar strength on the force-time response of the 50J drop-weight impact model

5

Conclusion In this study, the impact behavior and damage mechanism of a novel carbon-Dyneema

hybrid fabric reinforced composite have been investigated through drop-weight and steel ball impact tests. The force-displacement response and damage mechanisms of the hybrid composite were analyzed and compared with woven carbon laminates as the reference material. It was shown that

28

the hybrid composite shows significant improvements over the traditional carbon composites in both drop-weight and steel ball impacts. The Dyneema fiber with high toughness and failure strain prevents the splitting of bottom surfaces of the laminate during impact, which increases the penetration limit. In addition, the hybrid composite exhibits a large surface damage area and the micro-CT reveals dispersed internal delamination under steel ball impact. This increases the energy absorption ability of the material. Previous studies [20, 21] have found the hybrid composite exhibit significantly higher interlaminar fracture toughness and delay in final failure under the tensile loading. However, the hybrid composite laminate is found to be susceptible to ply buckling in drop-weight tests as the Dyneema fibers have a very low compressive strength. The tensile stiffness and strength of hybrid composites are 44% and 42% lower than the reference woven pure carbon laminates. The design of hybrid Dyneema and carbon fiber composites should therefore take into account desired combination of properties such as impact resistance, in-plane strength and stiffness. A multi-scale modeling approach has been proposed for modelling impact damage of hybrid woven composite taking into account the meso-scale interwoven pattern with reasonable computational costs. The employment of ply sub-sections to account for the variation in the mesoscale RVE of the hybrid composite, i.e. the existence of carbon rich area (CC), Dyneema rich area (DD), and the area that has both carbon and Dyneema yarns (CD and DC), has been shown to be critical in enabling the model to capture the correct damage behavior of the actual hybrid woven composite. The model is able to capture the early failure of Dyneema rich area under compressive stress and also an early failure of carbon yarns under tensile stress. This sub-sectioning method is also important because the size of the RVE subsection is rather large compared to the size of the impactor and therefore details will be lost if typical macro-scale homogenization were used.

6

Acknowledgement The support of NUS through research grant R265-000-523-646 is gratefully acknowledged.

7

Data availability The raw/processed data required to reproduce these findings cannot be shared at this time

due to technical or time limitations.

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Author statement Zhao Y.: Conceptualization, Methodology, Software, Writing - Original Draft, Visualization, Formal analysis, Visualization Cao M.: Investigation, Formal analysis, Visualization Tan H. X.: Investigation, Visualization Ridha M.: Writing – Review & Editing, Formal analysis, Visualization Tay T. E.: Writing – Review & Editing, Supervision, Funding Acquisition, Project Administration

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Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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