Research on the tension damage behavior of sandwich composite L-joints: Experiment and simulation

Composite Structures 232 (2020) 111566

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Research on the tension damage behavior of sandwich composite L-joints: Experiment and simulation

T

Qin Kaia,b, , Yan Renjuna,b, , Shen Weia,b, Hu Yaoyua,b ⁎

⁎

a

Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Ministry of Education, Wuhan 430063, China School of Transportation, Wuhan University of Technology, Wuhan 430063, China

ARTICLE INFO

ABSTRACT

Keywords: Sandwich composite L-joint Damage behavior Failure criterion

This article studies the failure process of Composite Sandwich L-joints under tension load. Test results show that damage has already taken place well before the loading force reaches the maximum. The failure process is divided into three stages based on the damage initiation force and damage expansion force identified through test data. A new failure criterion is proposed to describe the behavior of the laminate skin. The application of this criterion requires merely common engineering parameters. Simulation result using this new criterion matches both the failure load and the damage process of the experiment, while simulation using other mainstream criteria report much lower ultimate forces.

Matrix: Elastic Modulus

Em

Tension Fail Stress δtm

Fiber: Elastic Modulus Ef Tension Fail Stress δtf Skin: Skin Elastic Modulus Skin Matrix-Tension Fail Stress Skin Fiber-Tension Fail Stress Skin Matrix-Compression Fail Stress Skin Normal Direction Tension Fail Stress Skin Normal Direction Compression Fail Stress Fiber Layer Thickness Ratio Fiber Bundle Cross Sectional Area Ratio Fiber Bundle Cross Sectional Area Ratio inside Fiber Layer

Compression Fail Stress

δcm

Ex, Ey, Ez Xtm, Ytm Xtf, Ytf Xcm, Ycm Zt Zc η vfx = vfy = vf

vfx = vfy = vf /

1. Introduction Fiber reinforced sandwich composite materials are being widely adopted in modern naval vessels for its prominent performance in strength/weight ratio, design flexibility and electromagnetic properties [1]. Damage behavior of sandwich composite structures is a complex problem. Jiang [2] looked into the crack growth and crack blocking in sandwich composites. He developed a simple criterion that governs the two behaviors. He also claimed that there exists a critical facesheet thickness above which crack blocking is achieved and crack growth is prevented. Russo and Zuccarello [3] conducted a systematic experimental study and numerical simulation on the structure constituted by fiberglass laminate skins over PVC foam. They pointed out that the

⁎

failure modes are strongly influenced by the stresses orthogonal to the middle plane. Fan [4] investigated damage evolution in composite sandwich panels under quasi-static impact by using a progressive failure analysis methodology. Multiple failure criteria are adopted for different failure mechanisms. Basic components need to be connected to make a complete structure. Welding technology for conventional structural steel has been studied for decades, yet there still exist many problems waiting to be resolved. As one of the basic types of connection in composite structures, the performance of L-joint requires thorough research. Qiu [5] conducted bending test of a sandwich composite L-joints with stiffeners. Test phenomenon are described in detail and he claims that L-joint can maintain high load-bearing capacity with large deformations in structure. Zeng [6] looked into the tension and compression capability of a stiffened L-joint quite similar to the one in our research. With the help of progressive damage technique and finite element simulation, she proposes a numerical model to predict the failure load. Shen [7] focus his study on the fatigue life and fatigue failure mode of the same type of L-joints with Haiyan Zeng. He developed a fatigue life model for the joint and validated with test results. In 2019, a novel designed L-joint featuring a connector and a stiffener panel is mentioned in the work of Li [8]. After closely examined the damaging behavior through both test and simulation, he improved the design of the joint and increased its bending stiffness by 38.6%. Based on the previous work, the research described in this article concentrates on the damaging process and simulation method of the L-

Corresponding authors. E-mail addresses: [email protected] (Q. Kai), [email protected] (Y. Renjun).

https://doi.org/10.1016/j.compstruct.2019.111566 Received 6 June 2019; Received in revised form 9 October 2019; Accepted 11 October 2019 Available online 12 October 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

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Table 1 Material parameters. GFRP Facesheet

PVC Core

Elastic Modulus (MPa)

Tensile Strength (MPa)

Shear Modulus (MPa)

E11 E22 18,000 18,000 Compressive Strength (MPa)

E33 10,000

XT YT 488 488 Shear Strength (MPa)

ZT 100

G 3550 Composite Layup

XC 390

ZC 185

S12 160

S23 80

Orthogonal Fiber Cloth

YC 390

S13 80

Elastic Modulus (MPa)

Poison’s Ratio

Yield Stress (MPa)

E 135

μ 0.32

σs 3

joint under tension load. While adopting progressive damage method, a new failure criterion is proposed to describe the behavior of the facesheet laminates. Simulation results agree with the experiments. The damage process revealed by the simulation also help better understand the actual damaging process of the L-joint. 2. Test overview 2.1. Specimen The L-joint in this test consist of an “L” shaped rectangular sandwich plate and a strengthener in the middle. The facesheet are made of Glass Fiber Reinforced Plastic (GFRP) laminates and the core is polyvinyl chloride (PVC). Material parameters are listed in Table 1. The detailed sketches of the structure are shown in Fig. 1. The facesheet of the sandwich composite is 3 mm thick orthogonal fiber cloth.

Fig. 2. (a) Load conditions & specimen fixture; (b) 3D model of the L-joint.

2.3. Data collection 2.2. Load condition

Loading rate is controlled by the Test machine’s actuator and set at 3 mm/min. Load force and displacement data of the actuator are recorded directly by the test machine. Resistance strain gauges are glued on three key point locations on the surface of the facesheet shown in Fig. 1. Point D is in the middle of the curve length between point A and B. Point A and C are symmetrical. Each type of data is collected at the frequency of 5 Hz.

During the experiment, both ends of the joints are clapped by strengthened steel panels and fastened by bolts. The lower end is latched on the fixed workbench; the higher end is latched on the actuator, as is shown in Fig. 2(a). The actuator of the test bench provides the load force that pulls up the upper end. It is a typical loading scenario for an L-joint like this in service conditions.

Fig. 1. Diagrams and strain gauge locations of the stiffened composite sandwich L-joint (Unit: mm). 2

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Fig. 3. Experiment Results of Specimen 1. Fig. 4. Experiment Results of Specimen 2.

3. Experimental results & analysis It is common knowledge that the physical property of composite structures disperses greatly than conventional materials. Manufacturing process poses unneglectable influence on the experimental results. However, stress field redistribution accompanies damage occurrence and expansion. Although it is difficult to observe internal damage directly, but through monitoring strain variations at key points and fluctuations of load-displacement curves, we can indirectly understand the damaging process inside the composite joint. Experiment data from all three specimens are shown in Figs. 3–5. Throughout the loading process, we can recognize two feature points from the test data for all three specimens. Using the two feature points, we can divide the loading process into three stages. Irregular strain variations are always initially detected by strain gauges at point B, when displacement curve and strain data from other key points remain linear. This is the first feature point. This also indicates that at this stage, damage has appeared but limited only to a small area near point B. However, judging from the unaffected displacement curve, damage at this level does not poses perceivable influence to the overall structural response. The corresponding load force at the first feature point is the minimum force that can cause damage to the structure only detectable by strain sensors. It can also be regarded as damage initiation force. From this point forward during the test, we can hear small discontinuous noise coming out of the corner area of the joint. Accompanied with a louder crisp sound, the first fluctuation in displacement curves appear. This is the second feature point. From Fig. 6(b), we can only see minor color changes in the corner area. Some of the strain curves experience slope rate alterations, which means a large area of damage redistribution has happened. Judging from the “bump” of the displacement curve, damage have affected the overall structural response, but the corner joint still holds some reserved bearing capacity. After this point, the crisp noise becomes more frequent, and white areas become obvious on the strengthener of the joint. Finally, the noise grows extremely rapid and much louder. From the displacement curves, we can see that abrupt structural collapses take

Fig. 5. Experiment Results of Specimen 3.

place as load forces reach the maximum. The white areas quickly widen and stretch across the upper surface of the strengthener (Fig. 6c). As the joint continues to be pulled open, layers of the facesheet are pulled up, and then facesheet on the upper surface of the strengthener breaks and 3

Composite Structures 232 (2020) 111566

Q. Kai, et al. 2 xx

1,

Xtf

(

xx

> 0)

(2)

X direction Matrix Compression Failure: 2

xx

Xcm

2

xy

+

+

Sxy

2

xz

1,

Sxz

(

xx

< 0);

(3)

Y direction Matrix Tension Failure: yy

2

xy

+

Ytm

2

+

Sxy

yz

2

1,

Syz

(

> 0);

yy

(4)

Y direction Fiber Tension Failure: yy

2

1,

Ytf

(

yy

> 0);

(5)

Y direction Matrix Compression Failure: yy

2

+

Ycm

zz

zz

Zc

Xtm

Sxy

xz

Sxz

2

1,

(

xx

> 0)

(

yy

< 0);

(

zz

> 0);

(6)

+

xz

2

+

Sxz

yz

2

1,

Syz

(7)

2

+

xz

Sxz

2

+

yz

Syz

2

1,

(

zz

< 0)

(8)

Generally, when damage happens in one direction, the corresponding value of material properties must be degraded. Constant degradation of the elastic properties is selected rather than the continuous degradation approach, because constant degradation requires the lowest number of variables, it is mesh-size independent and more suitable for computational finite element adoption. When Eqs. (1), (3), (4), (6), (7) or (8) is met, material in the corresponding direction will completely lose its bearing capability. So, the degradation ratio for them is set as 0.1%. Nevertheless, along fiber direction, when matrix fails under tension load and fibers do not, the stiffness regression ratio k still needs to be determined. Table 2 lists all the stiffness regression ratio if any of the criterion is satisfied. The following content of this section describes an easy way to calculate the stiffness regression ratio in this scenario. Assuming that matrix and fiber bundles bond tightly. Fig. 7 shows the idealized basic unit of the GFRP skin. According to this model, we

In glass fiber reinforced plastic (GFRP) composites, matrix closely wraps up the fiber bundle. Matrix occupies most of the space, while its mechanical strength is far less than that of fiber. Our assumptions are that when structural damage occurs, matrix fails first. And after the matrix fails, if the damage area is under tension stress, the fiber bundles can still take on load until they finally break; if it is under compression, without the support of the matrix, fiber bundles cannot withstand any further compression or shear force. For the orthogonal GFRP cloth used in the corner joint, the failure criterion is described by the following Equations. X direction Matrix Tension Failure:

+

1,

Syz

4.2. Application of the new failure criterion and determining the stiffness regression ratio

4.1. A new failure criterion for resin matrix fiber reinforced plastic composites

2

2

Criterion for matrix tension failure on the fiber directions (Eqs. (1) and (4)) takes the same form of the fiber tension failure mode in Hashin Criterion [9]. It is an ellipse quadrant approximation that accounts for the mutual weakening effect of tensile and shear stress. After the matrix tension failure, the transverse interaction between the matrix and the fiber bundles are ignored. Therefore, the fiber failure in the next tension stage is solely dependent on the axial tension stress (Eqs. (2) and (5)). According to the assumptions, after the matrix fail under compression, fibers alone cannot withstand further load. So, Eqs. (3) and (6) are criteria for compression matrix failure that account for shear stress. Criteria for the layup direction is directly borrowed from the delamination tension (Eq. (7)) and compression (Eq. (8)) mode in ShokreihHashin [10] criterion. It should be noted that criteria for fiber-direction compression failure and layup direction failure have limited influence over the simulation results under tensile load, therefore they cannot be verified in this simulation or experiment.

Progressive failure method is adopted to simulate the failure process. Different components have different ways to describe their constitutive relations. As the major load-bearing component of the composite corner joints, skin is the main focus in our research. Therefore, foam core and the bonding layer are treated as ideal elastic-plastic materials. The problem we faced when trying to simulate the damaging process is that if we use conventional criterion for the skin, the Hashin Fabric [9] criterion for example, damage only occurs right before the final failure. This is a huge disagreement with the tests. In fact, strain data at point B shows that damage appears in the early stage of the loading process, when the stress level of the corner area is far less below the tensile strength of the skin. This is easily verified by a quick calculation using a pure elastic model. As a result, we have to make a few assumptions and develop a new failure criterion to describe this kind of behavior.

xy

Sxy

yz

Z direction Compression Failure:

4. Simulation methods

+

2

Zt

the crack runs down towards the base panel (Fig. 6d).

2

+

Z direction Tension Failure:

Fig. 6. Visible damage on the surface of specimen 1. (a). No damage state. (b). Feature point two, minor color changes. (c). Maximum force, apparent visible damage. (d). Final failure state.

xx

2

xy

(1)

X direction Fiber Tension Failure: 4

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Table 2 Stiffness regression ratios.

Ex =

Direction

Criterion

Material Parameters

Stiffness Regression Ratio

X

Eq. (1) Eqs. (2) and (3) Eq. (4) Eqs. (5) and (6) Eqs. (7) and (8)

Ex, μxy, μxz, Gxy, Gxz

k 0.10% k 0.10% 0.10%

Y Z

Ey, μxy, μyz, Gxy, Gyz Ez, μxz, μyz, Gxz, Gyz

(11)

f · Ef

Since the fibers are the only thing holding on the X direction before its final failure, then

Xtf =

(12)

f · tf

As for z direction, elastic modulus of the fiber layer is

Eflz = Ef ·Va + Em·(1

Va ),

where Va is the volume ratio of fiber bundles inside the fiber layer.

Va =

Vfx

+

Vfy

Vfx · Vfy 2

=

2Vf

V f2 (13)

2

Then

Ez =

Zc =

can calculate the x direction elastic modulus by means of elastic mechanics. In a matrix layer, elastic modulus is Em. When considering the elastic modulus of a fiber layer along x direction, the fiber layer can be divided into part a, which contains both resin and fiber, and part b, which only contains fiber. Along x direction, the elastic modulus of part a is fx

+ Em·(1

fx ),

Eax ·Ef Eax ·

fy

+ Ef ·(1

fy )

=

fy

=

f/

4.3. Finite element simulation model Simulation is conducted using Abaqus. The finite element model is a 3D model with C3D8R elements. Progressive failure is achieved by introducing USDFLD (User Defined Field). In order to focus on the transitional area and reduce computation labor, the model excludes part of the composite joint from both the fixture and the loading end. Then, each end face of the model is coupled with a single node at the corresponding loading or constraining location, as is shown in Fig. 8. Displacement load is added on RP-1 (reference point 1) node and the reaction force of RP-1 is the total load force. Additionally, quasi-static method is adopted to avoid possible convergence problem. But to ensure the accuracy, the simulation must be kept in a quasi-static state. Smooth step curve is adopted when adding displacement load. This can not only lessen the initial impact but also reduce the residual kinetic energy of the structure. Normally, a simulation can be considered as quasi-static when the kinetic energy of the system takes up less than 5% of the total internal energy. In this simulation, the ratio is kept below 0.5% all the time.

),

,

Then

Ex 2 f · Ef

+ (1

f

)

=

( ) ·E +( ) f

2

f

1

2 m

f

2

+

() f

· Ef +

2

f

·(1 +

()

f

f

2

f)

+ 1 · Ef ·Em

· Em (9)

When the unit is under tension load on X direction, if matrix failure is about to happen. The uniform stress on this section is

=

·Em·(1

fx )

+ · Ef ·

fx

= Xtm ,

Note that strain on this section is Then

Xtm =

tm·

1

f

+

Em · Ef

=

tm

Em

5. Simulation results & analysis

.

5.1. Simulation results using the new criterion Data extracted from the simulation results using the new criterion are presented in Fig. 9. Because the failure process of this simulation shares much resemblance with the experiment, we can also divide the

f

The same applies for compression

Xcm =

cm·

1

f

+

Em · Ef

f

(15)

cm

,

Note that the sectional area ratio of fiber bundles inside a fiber layer is 1/η times larger than the general ratio. fx

(14)

Va )

k = Ex' / Ex = 0.4917

Then, for the whole composite unit,

Ex = Eflx · + Em·(1

) + Em·(1

By combining Eqs. (10)–(15), we have established the relationship of some engineering constants between the composite unit and its constituents. Ex, Ez, Xtf, Xcm and Zc are given in Table 1. Additionally, we added Ef = 73100MPa as a known parameter. Other unknown values can be calculated (listed in Table 3). Therefore, when matrix fails under tension load along fiber direction, the stiffness regression ratio is

Elastic modulus of the fiber layer is

Eflx =

Va) + Ef ·Em· Va

When the unit is under compression load on Z direction, we believe that it is matrix compression failure that leads to the structure collapse. Then

Fig. 7. Idealized basic unit of the GFRP skin.

Eax = Ef ·

Em2 ·(1 Ef · Va·(1

Table 3 Calculated parameter results.

(10)

After the matrix fails, assuming that fiber bundles along Y direction would not affect the ones along X direction. The elastic modulus after the matrix fails is 5

νf

η

Em (MPa)

δtf (MPa)

E′x (MPa)

0.1211

0.2946

7201

4030

8851

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Q. Kai, et al.

Fig. 10. Matrix tension damage and Fiber tension damage in simulation. (a) Stage two starts and matrix tension damage appear. (b) Stage two ends with dispersed matrix damages. (c) Stage three starts and previously dispersed matrix tension damage merges. (d). Matrix tension damage at maximum load force. (e) Fiber tension damage after load force reaches maximum.

simulated loading process into the following three stages using the same two feature points as in the experiment. Stage one, no damage stage. Before any damage take place, strain and displacement values are linear to the loading force. Stage two, matrix tension damage appears and slowly extends. After load force reaches 42.34 kN, matrix tension damage starts to appear dispersedly along the edge of the upper surface of the strengthener’s corner (Fig. 10a). This clearly only affects strain at point B and makes it deviate from its linear path, which marks the first feature point. Stage three, matrix tension damage expands rapidly. After loading force reaches 53.71 kN, the damage area is large enough to affect not only all the strain readings, obvious fluctuations also start to appear on the displacement curve. This is the second feature point. Additionally, previously dispersed matrix tension damage now starts to merge (Fig. 10c) and continue to expand. Finally, fibers break and the structure completely fails (Fig. 10e). When loading force arrives at 70.29 kN, fiber tension damage occurs and almost instantly, multiple damage modes acutely expand across the strengthener and the joint completely fails.

Fig. 8. Couplings & Border Conditions.

5.2. Comparision between multiple criteria and the experiment For comparison, simulation using Hoffman, Tsai-Wu and HashinFabric criteria [9] is also conducted with the same model. In these simulations, the whole structure fails immediately after damage appears on the upper surface of the strengthener. Therefore, no damage stages can be identified. Fig. 11 compares the load-displacement curve between both experiments and the simulations. The overall stiffness of the simulations is larger than that of the experiment. This is because part of the two ends of the corner joint is excluded in the simulation model, which means their distortion is also excluded in the total displacement. Aside from the difference in displacement, simulation with the new criterion still agrees with the experiments in terms of load force. Fig. 12 compares the strain values at point B. It should be noted that

Fig. 9. Simulation Results of the New Rule.

6

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6. Discussion & conclusions Data in Fig. 13 compares the corresponding damage stages between the experiments and the simulations. Both the observed phenomenon and strain data collected from the experiment clearly show that damage initiates well before (at 57% of the ultimate force in average) the structure reaches its maximum bearing capacity. Simulation matches both the damage initiation force and the ultimate force in precise, and presents the damage expansion and failure process very similar to the experiment. The second feature point marks the turning point where the damage expansion starts to accelerate. From the experiment, we know that the load bearing force is noticeably affected and experimental phenomena (both noise and surface color changes) aggravate. Simulation tells us this is when initial dispersed damages begin to merge, which provides a reasonable explanation for the sudden changes in behavior. The result from the simulation using the new criterion is satisfying. Whereas simulations using other conventional criteria cannot reflect on any of the damage that happens before the abrupt final failure. Another huge difference of the simulations is between the ultimate forces. The local stress of the critical area prior to final failure is actually very similar, due to the insignificance of the transverse and normal stress. The difference is that in the simulation using the new criterion, large area around the final failure spot has already experienced matrix failure. Not only can it directly lessen the concentration of the local stress, but also the extra deformation shortens the arm of the load force. As a result, its ultimate force matches the experiment while other simulations fail under much lower load forces. Based on the simulation using the new criterion, we can now better understand how the damage initiates and expands for the corner joint. Additionally, application of this criterion does not require additional parameters other than conventional engineering ones. By adopting the same techniques, we are able to predict the tension damage behavior of other similar GFRP structures more accurately.

Fig. 11. Load-Displacement curves of simulations & experiments.

Declaration of Competing Interest

Fig. 12. Strain value at point B between simulations & experiments.

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. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51609185) and the Fundamental Research Funds for the Central Universities (Grant No. 2018-YS-023) . References [1] Santiuste C, Sánchez-Sáez S, Barbero E. A comparison of progressive-failure criteria in the prediction of the dynamic bending failure of composite laminated beams. Compos Struct 2010;92:2406–14. [2] Jiang H, Huang Y, Liu C. Fracture analysis of facesheets in sandwich composites. Compos B Eng 2004;35:551–6. [3] Russo A, Zuccarello B. Experimental and numerical evaluation of the mechanical behavior of GFRP sandwich panels. Compos Struct 2007;81:575–86. [4] Fan XL, Wang TJ, Sun Q. Damage evolution of sandwich composite structure using a progressive failure analysis methodology. Procedia Eng 2011;10:530–5. [5] Qiu JB, Xi Z, Mei ZY. Bending load-bearing capacity and damage mechanism of composite sandwich L-joint with stiffeners. J Naval Univ Eng 2015;27:23–7. [6] Zeng H, Yan R, Xu L. Failure prediction of composite sandwich L-joint under bending. Compos Struct 2018;197:54–62. [7] Shen W, Luo B, Yan R, Zeng H, Xu L. The mechanical behavior of sandwich composite joints for ship structures. Ocean Eng 2017;144:78–89. [8] Li H, Tu S, Liu Y, Lu X, Zhu X. Mechanical properties of L-joint with composite sandwich structure. Compos Struct 2019;217:165–74. [9] Klasztorny M, Nycz D, Labuda R. Modelling, simulation and experimental validation of bend tests on GFRP laminate beam and plate specimens. Compos Struct 2018;184:604–12. [10] Shokrieh MM, Rafiee R. Simulation of fatigue failure in a full composite wind turbine blade. Compos Struct 2006;74:332–42.

Fig. 13. Load stages comparison between experiments and simulations.

the strain data of point B from experiments is incomplete due to the limited measuring range of the resistance strain gauge. They stopped sending back data shortly after the first fluctuation in the displacement curve (which is also the second feature point). In the simulation using the new criterion, the first fluctuation of B strain curve marks the beginning of matrix tension damage. And its huge jump later matches the approximate timing when the strain gauges at point B break in the experiments. However, strain data of simulation using other criteria is still perfect linear before the abrupt failure.

7