- Email: [email protected]
Ultimate strength analysis of composite typical joints for ship structures
Accepted Manuscript Ultimate strength analysis of composite typical joints for ship structures Wei Shen, Renjun Yan, Bailu Luo, Yingfu Zhu, Haiyan Zeng PII: DOI: Reference:
S0263-8223(16)32118-3 http://dx.doi.org/10.1016/j.compstruct.2017.02.008 COST 8225
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
11 October 2016 24 December 2016 1 February 2017
Please cite this article as: Shen, W., Yan, R., Luo, B., Zhu, Y., Zeng, H., Ultimate strength analysis of composite typical joints for ship structures, Composite Structures (2017), doi: http://dx.doi.org/10.1016/j.compstruct. 2017.02.008
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ultimate strength analysis of composite typical joints for ship structures Wei Shena,b, ∗, Renjun Yana, ∗, Bailu Luoc, Yingfu Zhuc, Haiyan Zenga a
Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Ministry of Education, Wuhan 430063, China. b
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. c China Ship Development and Design Center, Wuhan 430064, China.
ABSTRACT In order to solve the damage failure problem of composite L-joints for ship structures, the failures and ultimate strength of the composite L-joints for ship structures are researched by using the progressive damage analysis method and experimental method. A number of studies have been carried out on the structural failure process and failure strength of the joints under compressive loading. The experimental and numerical results show the axial displacement of sandwich plates under axial compressive loading increases slowly before reaching the limit, but the bearing capacity of the structure decreases rapidly once the load exceeds the ultimate load, with the slow increment of axial displacement until the sandwich plate cracks. The major failure modes of sandwich L-joints are the delamination between core and skin, fiber failure, base shear failure and PVC failure. There is a good agreement between the numerical results and the test results, which offers a guide in designing the structure of sandwich composite joint. Keywords: composite material; sandwich L-joint; ultimate strength; experimental research 1. Introduction As new kinds of functional materials, composites exhibit excellent performance such as high speed, low emission, long life and superior comfortability in the marine environment [1]. In addition, due to the lightweight and high specific strength, composites are gradually applied in ship building [2-5]. However, the anisotropic and brittle characteristics of composites make the stress distribution and failure modes of composite joints far more complex than metal structures [6]. Composite material failure is the process of the internal microscopic damage accumulation and material degradation. Due to the diversity of microscopic damages, the failure process is lack of regularity. Therefore, it is necessary to analyze the mechanical properties of the composite joint by experimental method. Smith and Dow [7] predicted the ultimate strength of hat composite stiffened plate under axial compressive load, ignoring the stiffness reduction of stiffened plate. Dow [8] completed a series of ultimate strength experiments on composite laminated plates and stiffened laminated plates of ship structure. Chen, et al. [9] analyzed the longitudinal ultimate strength and reliability of composite hull with beam-column theory and Smith’s method. Prusty [10] discussed the effect of reinforcement on the ultimate strength based on the first-order shear deformation theory and shear correction factor, but his research ignored the stiffness of destroyed layers within the elastic range. Tang, et al. [11,12] studied the compressive ultimate strength of stiffened laminated composite plates under axial load, then discussed the influence of layer, thickness on ultimate strength. However, only a few tests have been done to analyze the ultimate strength of sandwich composites. ∗Corresponding auther. E-mail address: [email protected].
1
Till now, the ultimate strength analysis of composite material structure is still in the stage of development, as material failure criterion is imperfect, the experimental data is not enough, and the progressive failure analysis method is flawed [13,14]. In fact, the failures of composite structures occur widely in practical engineering. During the initial loading, the weak part will be damaged first, which leads to stress redistribution. In fact, this kind of damage cannot be seen in macro. With the load increasing, the damage region will expand and the stiffness of structure will be degraded until the final failure happens. Considering the local failure and material degradation, progressive failure analysis method can better simulate the failure process and the ultimate failure load of composite material structure. Therefore, in this paper, experimental method and progressive damage analysis method will be compared to study the ultimate strength of sandwich L-joints in shipbuilding. 2. Experiment analysis Currently there is a wide range of naval structures being developed using composite materails. The applications examined inclued large patrol boats, hovercraft, mine countermeasure vessls and corvettes that are built completely of composite materials [15]. As shown in Fig. 1, the simplest type of plate girder structure consists of plates, stiffeners and brackets. Stress concentrations at these corners cause cracks initiate and propagate under static and cyclic loadings [16]. Therefore, several full scale sandwich L-joint were used in this paper to analyzed the ultimate strength in the corner. Schematic diagram of specimen sketches in Fig. 1, the corner is the stress concentration region when the hull is hogging or sagging.
Fig. 1. Schematic of the framwork for composite ships.
2.1. Specimen and equipment As shown in Fig. 2, sandwich L-joint specimens were used in the experiment. The main body was made by foam sandwich panel. Two sandwich plates were joined at 105°, the longitudinal reinforcement was joined by circular arc transition bracket along the corner, and the ends of L-joint were fixed with the vertical actuator and the base (see Fig. 3). To avoid the local failure, the both ends of the joint were designed as the solid core panels. Moreover, the transition region was also designed between the solid core panel and the sandwich panel. Considering such structural detail's actual boundary conditions, the L-steel plates were fixed in both two ends, and a vertical load was applied to the upper briquetting by the MTS actuator in Fig. 3.
2
Fig. 2. Geometry parameter of L-joint.
In order to reduce the influence of initial defects on experiment results, the initial appearance inspection was checked before the ultimate strength test. The vertical actuator g
The upper briquettin g
The lower briquettin g
Base
(a) (b) Fig. 3. Specimen and equipment: (a) specimen fixture; (b) test platform.
All the tests are conducted on the MTS322 test and analysis system. Vertical actuator is used to simulate the bending stress state. Specimen bottom is bolted with the fixed working platform, and the top bolted with the actuator (see Figs. 2-3). Five full-size L-joints under the same compressive load and boundary conditions are conducted in the test. Five groups of specimens are labeled as U1, U2, U3, U4 and U5. 2.2. Static strain measurement test In order to simulate the real stress state near the corner, strain measurement test and the linear analysis were conducted before the ultimate strength test. As shown in Fig. 4, 31 unidirectional strain gauges and 6 rectangular strain rosettes were arranged in the stress concentration areas near the corner. In order to increase the comparability of the data, the points 6-7, 12 and 15 are arranged symmetrically about the arc center point 10 (see Fig. 4a).
3
(a)
(b) Fig. 4. Stain measurement: (a) the arrangement of measuring points; (b) the specimen under test.
During the test, the compressive loads were loaded step by step with 15-20 levels, and the strain data was collected under a series of loads of 0kN, 2kN, …., 9kN, 10kN, ….until the fracture load, as shown in Table 1. Load level Load (kN)
Level 0-4 0-2-4-6-8
Table 1 The load under each step Level Level 5-8 9-12 9-10-11-12 12.5-13-13.5-14
… …
Level N Fracture
The main stress concentration points of specimen U1 are collected to monitor the strain change. As shown in Fig. 5a, the strain results of points 8,11 and 13 increase smoothly with the increase of load levels. As to the points 6,7,10,12 and 15, the strain values are symmetrical about the central point 10 (arc center, see Fig. 5b).
4
0 0
2
4
6
8
9
10
11
12 12.5 13 13.5 14 14.5 15 15.5 15.8
-1000
Strain/(µε)
-2000 -3000 -4000 -5000 -6000
point8 point11 point13
-7000 Load/(kN)
(a) 0 6
7
10
12
15
-2000
2kN 4kN 6kN 8kN 10kN 12kN 13kN 14kN 15kN 15.5kN 15.75kN
Strain/(µε)
-4000 -6000 -8000
10 12 15 7
-10000
6
-12000 -14000
Measuring points
(b) Fig. 5. The strain results of specimen U1 under different loads: (a) points 8,11 and 13; (b) points 6,7,10,12 and 15.
Strain/(µε)
Considering the individual differences, the load-strain curves of different specimens U1 and U2 are also compared in Fig. 6. There are certain differences in measured results between specimens U1 and U2, but the change trends are consistent. The results show that the strain changes of key points are reasonable. 0 -1000 0 -2000 -3000 -4000 -5000 -6000 -7000 -8000 -9000 -10000 -11000 -12000 -13000 -14000
2
4
6
8
point4-U1 point4-U2 point6-U1 point6-U2
Load/(kN)
(a)
5
10
12
14
16
0 -1000 0 -2000
2
4
6
8
10
12
14
16
Strain/(µε)
-3000 -4000 -5000 -6000 -7000 -8000 -9000 -10000 -11000 -12000 -13000
point7-U1 point7-U2 point10-U1 point10-U2
Load/(kN)
(b) Fig. 6. The load-strain curves of specimens U1 and U2: (a) points 4 and 6; (b) point 7 and 10.
Due to the complex stress state at the corner, 6 rectangular strain rosettes are also decorated symmetrically around the corner (see Fig. 4a). As to the rectangular strain rosette (see Fig. 7), the solutions of principal strains and corresponding strain direction result in the following values [17]: ε +ε 1 (1) (ε 0 − ε 90 ) 2 + [2ε 45 − (ε 0 + ε 90 )]2 ε 1 = 0 90 + 2
ε2 =
2
ε 0 + ε 90 2
−
tan 2θ =
1 (ε 0 − ε 90 ) 2 + [2ε 45 − (ε 0 + ε 90 )]2 2
(2)
2ε 45 − (ε 0 + ε 90 ) ε 0 − ε 90
(3)
Where ε 0 , ε 45 , ε 90 respectively represent the linear strain in the selected direction. For instance, the measurement results of rectangular strain rosettes under 4.0kN are collected in Table 2 and Fig. 8. As shown in Fig. 8, the directions of principal strains are almost along the edge of toggle plate, which may result in the local damage.
Fig. 7 Rectangular strain rosette.
6
Table 2 The measurement results of rectangular strain rosettes under 4.0kN Principal strain (µε) Measuring points
ε1
ε2
Direction (°)
21 22 23 24 25 26
522 544 943 466 1038 537
-1385 -972 -2204 -1593 -1432 -519
4.21 -0.76 -9.89 -13.85 32.14 -40.92
(a) (b) Fig. 8. The principal strains of rectangular strain rosettes: (a) points 21, 23 and 25; (b) points 22, 24 and 26.
3. Numerical analysis 3.1. Analysis process In this paper, progressive damage analysis was employed to simulate damage and failure process of sandwich joints under axial compressive load. The process is shown in Fig. 9. Failure of a composite structure initiates at lower load levels and develops in a progressive manner up to final failure. Therefore, progressive failure analysis methodology is developed and recommended for the analysis of sandwich joint. Based on a FE modeling and stress-strain analysis in ABAQUS, this methodology can predict the initiation and the localised progressive nature of damage, mode of failure and ultimate strength of the joint. It determines the damage initiation by failure criteria. If failure is detected, as indicated by a failure criterion, the material properties are changed according to a particular degradation model. Then, equilibrium of the structure needs to be re-established utilizing the modified material properties. The load step is then incremented until catastrophic failure of the structure is detected.
7
Fig. 9. The process of progressive failure analysis methodology.
3.2. Failure criteria Failure criteria for composite laminates are mainly analytical approximations or curve fittings of experimental results. Most failure criteria for composite material (Tsai-Hill, Tsai-Wu and Hoffman criteria) have been thought as an extension of the von Mises criterion to a quadratic criterion. The Hashin failure criteria [18] are interacting failure criteria as the failure criteria use more than a single stress component to evaluate different failure modes. The Hashin criteria were originally developed as failure criteria for unidirectional polymeric composites. Therefore, it is necessary to improve the Hashin criteria for laminate plates or non-polymeric composites. Shokrieh [19] presented the modified failure criteria in three dimensions, as shown in Table 3. Moreover, delamination failure should be also considered as it’s one of the most common failure modes [20]. Typical failure modes and criteria are summerized in Table 3. In these failure criteria, tensile and compressive failure in principle material directions (1-direction or 2-direction) as well as the fiber-matrix shear failure are donated by X , X , Y , Y , S , S and S . The stresses in the material coordinate system are simulated within the UMAT subroutine of ABAQUS using the given strains and the material stiffness coefficients at each material point. Based on the stress results, the stress-based failure criteria are evaluated and the material degradation is improved accordingly. T
C
T
C
12
13
23
Table 3 Failure modes and criteria
Failure modes Tensile failure in longitudinal direction
In-plane failure
Field variable
Failure criteria
σ τ τ + + X S S 2
2
1
12
13
T
12
13
σ X
2
≥ 1, σ > 0 1
FV1
2
Compressive failure in longitudinal direction
1
≥ 1,σ < 0 1
C
Tensile failure in transversal direction
σ τ τ + + Y S S 2
2
T
2
12
23
12
23
σ Y
Compressive failure in transversal direction
1
C
8
2
≥ 1,σ > 0
2
≥ 1, σ < 0 2
2
FV2
Fiber-matrix shear failure in transversal direction
σ τ τ + + X S S
Fiber-matrix shear failure in transversal direction
σ τ τ + + Y S S
Tensile delamination
σ τ τ + + Z S S
2
2
1
12
13
C
12
13
2
2
1
12
23
12
23
C
2
2
3
13
23
T
13
23
2
≥ 1,σ < 0 1
FV3
2
≥1,σ < 0 2
2
≥ 1, σ > 0 3
Delamination
FV4
τ τ + S S 2
Compressive delamination
13
23
13
23
2
≥1,σ < 0 3
3.3. Finite element model Three-dimensional FE model is necessary in order to have accurate progressive failure analysis predictions for the sandwich L-joint (see Fig. 10). An 8-node linear brick element with reduced integration and hourglass control (C3D8R) was adopted to simulate the fiberglass skins and PVC core. Adhesive layers between core and skin were modeled by COH3D8 elements. CHO3D8 is an 8-node three-dimensional cohesive element with double linear constitutive relationship. With the increase of load, the stress of cohesive element will linear rise first. After reaching the extreme value point, it will linear drop, eventually falls to 0.
Fig. 10. Finite element model.
This kind of sandwich L-joint was reinforced by an inner and outer GFRP skin, separated by and adhered to the PVC foam. The corresponding material properties of GFRP fabric and PVC foam are shown in Tables 4 and 5, respectively. The physical properties of GFRP are also given in Table 6. Table 4 Material properties of GFRP
Elastic modulus (GPa)
Shear modulus (GPa)
Poisson’s ratio
E11
E22
E33
µ12
µ13
µ 23
G
27
27
15
0.14
0.09
0.09
3.55
Table 5 Material properties of PVC foam
Elastic modulus (MPa)
Poisson’s ratio
Shear modulus (MPa)
Dessity (kg/m3)
Ec
µc
Gc
ρc
135
0.31
35
100
9
Table 6 The physical properties of GFRP
Tensile strength (MPa) XT
Compressive Strengt (MPa)
= YT
ZT
389
XC
20
= YC
212
Shear strength (MPa) ZC
S12
S13 = S 23
40
70.8
30.8
4. Experiment and simulation results 4.1. Strain comparision In order to simulate the real stress state, strain measurement test and FE analysis are compared at 2.0kN. A FE model was developed under the same compressive load 2.0kN (see Fig. 10). The strain results of the main monitoring points in the stress concentration areas are collected in Fig. 11. 0 5
6
7
10
12
15
16
-200
Strain/(µε)
-400 -600 -800 -1000 2.0kN-Measured values 2.0kN-FE values
-1200 -1400 -1600 Measuring points
Fig. 11. Strains of simulation and experiment values at 2.0kN.
Compared with the FE values and measured results, it is concluded that there is a good agreement in the change trend between the experimental strains and predicted strains. The change trend of strain values between the measured values and FE values are consistent, shaped as “W”. However, the predicted strains are smaller than the test results due to the differences between the actual structure and FE model. Among the main reasons for the difference is that the thickness is uneven around the corner due to the purely manual processing, as shown in Fig. 12.
(a) (b) Fig. 12. The appearance of the corner: (a) front view; (b) side view.
4.2. Failure strength analysis The ultimate load and stiffness of specimens U1-U5 are presented in Table 7. Due to the individual differences in manual processing, the initial size and stiffness may be slightly different. However, the 10
results are relatively close, so it is reasonable to take the average value as the final results. As shown in Table 7, the average ultimate load is 15.303kN, and the average stiffness is 441.4N/mm. Table 7 Experimental results of ultimate loads
Specimen
U1
U2
U3
U4
U5
The average values
Ultimate strength (kN)
16.001 14.941
14.798 14.966 15.809
15.303
Stiffness (N/mm)
391.76 377.35
407.58 512.54 517.58
441.4
Load and displacement curves are also compared in Fig. 13. In the initial stage, there is a good linear relationship between displacement and load. Displacement increases approximately linearly with increasing forces. With the increasing load, the compressive stiffness and load capacity decreases gradually.
(a)
(b)
Fig. 13. Load and displacement curves: (a) specimens U1-U3; (b) specimens U4-U5.
Fig. 14 shows the comparison of load and displacement curves between simulation and experiment results. The curve trends are very similar at 0-2kN (see Fig. 14b). With the increase of load, the difference between the curves increases gradually due to the differences between individuals.
(a) (b) Fig. 14. Load and displacement curves comparison of specimens U2 and U4: (a) load range: 0-16kN; (b) load range: 0-2kN.
4.3. Failure process analysis During the ultimate strength experiment, friction noise began to appear due to the internal failure and the increase of damping, under the load of 8.0-10.0kN. When the load was further increased, plastic deformation led to local failure and crack was visual near the corner. With the further extension of crack, specimen broke suddenly and the curve of displacement-force fell dramatically. The failure modes of specimens are shown in Fig. 15. In view of the differences of individuals, cracks mainly focus in the longitudinal stiffener or the arc bracket near the corner, and there is only one main crack. Meanwhile, a progressive failure analysis of the sandwich joint is also conducted, and the results are compared with the experimental results in Table 8. 11
(a) (b) (c) (d) (e) Fig. 15. Fracture of specimens: (a) specimen U1; (b) specimen U2; (c) specimen U3; (d) specimen U4; (e) specimen U5.
Typical failure modes are predicted in Table 8. The major failure modes of sandwich L-joints are the delamination between core and skin, fiber failure, base shear failure and PVC failure. Delamination failure (FV4) occured first at 1.90kN. With the increase of load, the failure area gradually expanded. When the load increased to 6.8kN, fiber failure in 2-direction (FV2), fiber-matrix shear failure (FV3) and foam failure appeared simultaneously. Fiber failure in 1-direction did not happen until 9.56kN. Moreover, failure in 2-direction initiated in the center of the arc bracket at the outer layer of the laminated plates, then extended to internal laminated plate. Fiber-matrix shear failure initiated in the center of the arc bracket firstly, and then extended to the ends of the arc bracket. Foam failure initiated and concentrated in the corner. Table 8 Failure modes and loads
Failure mode
Initial failure load (kN)
Fiber failure in 1-direction (FV1)
9.56
Fiber failure in 2-direction (FV2)
6.80
Failure area Initial failure
12
Final failure
Fiber-matrix shear failure (FV3)
6.80
Delamination (FV4)
1.90
Foam failure
6.80
5. Conclusions In the present paper, a 3D sandwich L-joint was modeled, and a progressive failure analysis methodology was developed to predict the strength of the joint. (1) Under axial compressive load, the failure process of composite joint can be divided into three stages: linear elastic stage, nonlinear stage and failure stage, and the failure modes include: skins and core delamination failure, fiber failure, fiber-matrix shear failure and foam failure. (2) In the initial stage, there is a good linear relationship between displacement and load. Displacement increases approximately linearly with increasing forces. When the load is further increased, plastic deformation leads to local failure and crack is visual near the corner. With the further extension of crack, specimen breaks suddenly and the curve of displacement-force falls dramatically. The final cracks mainly focus in the longitudinal stiffener or the arc bracket near the corner. (3) Numerical calculation results are consistent with the experimental results in the change trend. It shows that progressive damage analysis can be developed to simulate the damage process of sandwich joints. It is worth noting that there is a certain difference between numerical values and experimental values. The differences between the manual model and the numerical model may results in this prediction error. Therefore, the further work on the actual ship structure under complex stress state is also needed.
13
Acknowledgements The research project is supported by the National Natural Science Foundation of China (Grant No. 51609185) and the State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University (No. 1613). The support of China Ship Development and Design Center is also greatly appreciated. The authors wish to thank Dr. Yaoyu Hu and Feng He from Wuhan University of Technology, for the warm efforts about this test. References [1] Jones RM. Mechanics of composite materials. Flarida: CRC Press; 1998. [2] Slater JE. Selection of a blast-resistant GRP composite panel design for naval ship structures. Marine Structure 1994,7:417-440. [3] Benson JL. The AEM/S system, a pardigm-break mast, goes to sea. Naval Engineers Journal 1998; 110(4):99-103. [4] Mouritz AP, Gellert E, Burchill P, et al. Review of advanced composite structures for naval ships and submarines. Composite Structures 2001;53: 21-41. [5] Tiron R. Navy Gradually Embracing Composite Materials in Ships. National Defense 2004;89:28-29. [6] Jiang YP, Yue ZF. Numerical failure simulation of bolt-loaded composite laminate. Acta Material Composites Sinica 2005;22(4): 177-182. [7] Smith CS, Dow RS. Interactive bucking effects in stiffened FRP panels. In: Proceedings of the 4th International Conference on Composite Structures, Paisley,122-133, 1987. [8] Dow RS. Large scale FRP structural testing. In: International Conference Lightweight Materials in Naval Architecture, Transactions of the Royal Institute of naval Architects, 1996. [9] Chen NZ, Sun HH, Guedes SC. Reliability analysis of a ship hull in composite material. Composite Structures 2003;62(1):59-66. [10] Prusty BG. Progressive failure analysis of laminated unstiffened and stiffened composite panels. Composites Science and Technology 2004;64(3):379-394. [11] Tang WY, Chen NZ, Zhang SK. Ultimate strength analysis of stiffened laminated plates. Engineering Mechanics 2007;24(8): 43-48. [12] Cai ZY, Tang WY, et al. Ultimate strength analysis of composite laminated ship panels. International Journal of Ship Mechanics 2009;13(1):72-81. [13] YuY, Wang W. Investigation on the ultimate strength of sandwish plates in complex bending. Chinese Journal of Ship Research 2014;9(3):76-82. [14] Yang NN, Wang W, et al. Progressive damage analysis of steel-to-composite joints of radome. Journal of Harbin Engineering University 2014;35(10):1183-1188. [15] Mouritz AP, Gellert E, Burchill P and Challis K. Review of advanced composite structures for naval ships and submarines. Composite Structures 2001;53:21-41. [16] Shen W, Barltrop N, Yan RJ, et al. Stress field and fatigue strength analysis of 135-degree sharp corners under tensile and bending loadings based on notch stress strength theory. Ocean Engineering 2015;107:32-44. [17] Shen W, Yan RJ, et al. Application study on FBG sensor applied to hull structural health monitoring. Optik 2015;126:1499-1504. [18] Hashin Z. Failure criteria for unidirectional fiber composites. Journal of Applied Mechanics 1980; 47(2):329-334. [19] Shokrieh MM, Lessard LB. Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling. Journal of Composite Materials 2000;34(13):1056-1080. [20] Lin Y. Role of matrix resin in delamination onset and growth in composite laminates. Composites Science and Technology 1988;33(4):257-277.
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S0263-8223(16)32118-3 http://dx.doi.org/10.1016/j.compstruct.2017.02.008 COST 8225
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
11 October 2016 24 December 2016 1 February 2017
Please cite this article as: Shen, W., Yan, R., Luo, B., Zhu, Y., Zeng, H., Ultimate strength analysis of composite typical joints for ship structures, Composite Structures (2017), doi: http://dx.doi.org/10.1016/j.compstruct. 2017.02.008
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Ultimate strength analysis of composite typical joints for ship structures Wei Shena,b, ∗, Renjun Yana, ∗, Bailu Luoc, Yingfu Zhuc, Haiyan Zenga a
Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Ministry of Education, Wuhan 430063, China. b
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. c China Ship Development and Design Center, Wuhan 430064, China.
ABSTRACT In order to solve the damage failure problem of composite L-joints for ship structures, the failures and ultimate strength of the composite L-joints for ship structures are researched by using the progressive damage analysis method and experimental method. A number of studies have been carried out on the structural failure process and failure strength of the joints under compressive loading. The experimental and numerical results show the axial displacement of sandwich plates under axial compressive loading increases slowly before reaching the limit, but the bearing capacity of the structure decreases rapidly once the load exceeds the ultimate load, with the slow increment of axial displacement until the sandwich plate cracks. The major failure modes of sandwich L-joints are the delamination between core and skin, fiber failure, base shear failure and PVC failure. There is a good agreement between the numerical results and the test results, which offers a guide in designing the structure of sandwich composite joint. Keywords: composite material; sandwich L-joint; ultimate strength; experimental research 1. Introduction As new kinds of functional materials, composites exhibit excellent performance such as high speed, low emission, long life and superior comfortability in the marine environment [1]. In addition, due to the lightweight and high specific strength, composites are gradually applied in ship building [2-5]. However, the anisotropic and brittle characteristics of composites make the stress distribution and failure modes of composite joints far more complex than metal structures [6]. Composite material failure is the process of the internal microscopic damage accumulation and material degradation. Due to the diversity of microscopic damages, the failure process is lack of regularity. Therefore, it is necessary to analyze the mechanical properties of the composite joint by experimental method. Smith and Dow [7] predicted the ultimate strength of hat composite stiffened plate under axial compressive load, ignoring the stiffness reduction of stiffened plate. Dow [8] completed a series of ultimate strength experiments on composite laminated plates and stiffened laminated plates of ship structure. Chen, et al. [9] analyzed the longitudinal ultimate strength and reliability of composite hull with beam-column theory and Smith’s method. Prusty [10] discussed the effect of reinforcement on the ultimate strength based on the first-order shear deformation theory and shear correction factor, but his research ignored the stiffness of destroyed layers within the elastic range. Tang, et al. [11,12] studied the compressive ultimate strength of stiffened laminated composite plates under axial load, then discussed the influence of layer, thickness on ultimate strength. However, only a few tests have been done to analyze the ultimate strength of sandwich composites. ∗Corresponding auther. E-mail address: [email protected].
1
Till now, the ultimate strength analysis of composite material structure is still in the stage of development, as material failure criterion is imperfect, the experimental data is not enough, and the progressive failure analysis method is flawed [13,14]. In fact, the failures of composite structures occur widely in practical engineering. During the initial loading, the weak part will be damaged first, which leads to stress redistribution. In fact, this kind of damage cannot be seen in macro. With the load increasing, the damage region will expand and the stiffness of structure will be degraded until the final failure happens. Considering the local failure and material degradation, progressive failure analysis method can better simulate the failure process and the ultimate failure load of composite material structure. Therefore, in this paper, experimental method and progressive damage analysis method will be compared to study the ultimate strength of sandwich L-joints in shipbuilding. 2. Experiment analysis Currently there is a wide range of naval structures being developed using composite materails. The applications examined inclued large patrol boats, hovercraft, mine countermeasure vessls and corvettes that are built completely of composite materials [15]. As shown in Fig. 1, the simplest type of plate girder structure consists of plates, stiffeners and brackets. Stress concentrations at these corners cause cracks initiate and propagate under static and cyclic loadings [16]. Therefore, several full scale sandwich L-joint were used in this paper to analyzed the ultimate strength in the corner. Schematic diagram of specimen sketches in Fig. 1, the corner is the stress concentration region when the hull is hogging or sagging.
Fig. 1. Schematic of the framwork for composite ships.
2.1. Specimen and equipment As shown in Fig. 2, sandwich L-joint specimens were used in the experiment. The main body was made by foam sandwich panel. Two sandwich plates were joined at 105°, the longitudinal reinforcement was joined by circular arc transition bracket along the corner, and the ends of L-joint were fixed with the vertical actuator and the base (see Fig. 3). To avoid the local failure, the both ends of the joint were designed as the solid core panels. Moreover, the transition region was also designed between the solid core panel and the sandwich panel. Considering such structural detail's actual boundary conditions, the L-steel plates were fixed in both two ends, and a vertical load was applied to the upper briquetting by the MTS actuator in Fig. 3.
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Fig. 2. Geometry parameter of L-joint.
In order to reduce the influence of initial defects on experiment results, the initial appearance inspection was checked before the ultimate strength test. The vertical actuator g
The upper briquettin g
The lower briquettin g
Base
(a) (b) Fig. 3. Specimen and equipment: (a) specimen fixture; (b) test platform.
All the tests are conducted on the MTS322 test and analysis system. Vertical actuator is used to simulate the bending stress state. Specimen bottom is bolted with the fixed working platform, and the top bolted with the actuator (see Figs. 2-3). Five full-size L-joints under the same compressive load and boundary conditions are conducted in the test. Five groups of specimens are labeled as U1, U2, U3, U4 and U5. 2.2. Static strain measurement test In order to simulate the real stress state near the corner, strain measurement test and the linear analysis were conducted before the ultimate strength test. As shown in Fig. 4, 31 unidirectional strain gauges and 6 rectangular strain rosettes were arranged in the stress concentration areas near the corner. In order to increase the comparability of the data, the points 6-7, 12 and 15 are arranged symmetrically about the arc center point 10 (see Fig. 4a).
3
(a)
(b) Fig. 4. Stain measurement: (a) the arrangement of measuring points; (b) the specimen under test.
During the test, the compressive loads were loaded step by step with 15-20 levels, and the strain data was collected under a series of loads of 0kN, 2kN, …., 9kN, 10kN, ….until the fracture load, as shown in Table 1. Load level Load (kN)
Level 0-4 0-2-4-6-8
Table 1 The load under each step Level Level 5-8 9-12 9-10-11-12 12.5-13-13.5-14
… …
Level N Fracture
The main stress concentration points of specimen U1 are collected to monitor the strain change. As shown in Fig. 5a, the strain results of points 8,11 and 13 increase smoothly with the increase of load levels. As to the points 6,7,10,12 and 15, the strain values are symmetrical about the central point 10 (arc center, see Fig. 5b).
4
0 0
2
4
6
8
9
10
11
12 12.5 13 13.5 14 14.5 15 15.5 15.8
-1000
Strain/(µε)
-2000 -3000 -4000 -5000 -6000
point8 point11 point13
-7000 Load/(kN)
(a) 0 6
7
10
12
15
-2000
2kN 4kN 6kN 8kN 10kN 12kN 13kN 14kN 15kN 15.5kN 15.75kN
Strain/(µε)
-4000 -6000 -8000
10 12 15 7
-10000
6
-12000 -14000
Measuring points
(b) Fig. 5. The strain results of specimen U1 under different loads: (a) points 8,11 and 13; (b) points 6,7,10,12 and 15.
Strain/(µε)
Considering the individual differences, the load-strain curves of different specimens U1 and U2 are also compared in Fig. 6. There are certain differences in measured results between specimens U1 and U2, but the change trends are consistent. The results show that the strain changes of key points are reasonable. 0 -1000 0 -2000 -3000 -4000 -5000 -6000 -7000 -8000 -9000 -10000 -11000 -12000 -13000 -14000
2
4
6
8
point4-U1 point4-U2 point6-U1 point6-U2
Load/(kN)
(a)
5
10
12
14
16
0 -1000 0 -2000
2
4
6
8
10
12
14
16
Strain/(µε)
-3000 -4000 -5000 -6000 -7000 -8000 -9000 -10000 -11000 -12000 -13000
point7-U1 point7-U2 point10-U1 point10-U2
Load/(kN)
(b) Fig. 6. The load-strain curves of specimens U1 and U2: (a) points 4 and 6; (b) point 7 and 10.
Due to the complex stress state at the corner, 6 rectangular strain rosettes are also decorated symmetrically around the corner (see Fig. 4a). As to the rectangular strain rosette (see Fig. 7), the solutions of principal strains and corresponding strain direction result in the following values [17]: ε +ε 1 (1) (ε 0 − ε 90 ) 2 + [2ε 45 − (ε 0 + ε 90 )]2 ε 1 = 0 90 + 2
ε2 =
2
ε 0 + ε 90 2
−
tan 2θ =
1 (ε 0 − ε 90 ) 2 + [2ε 45 − (ε 0 + ε 90 )]2 2
(2)
2ε 45 − (ε 0 + ε 90 ) ε 0 − ε 90
(3)
Where ε 0 , ε 45 , ε 90 respectively represent the linear strain in the selected direction. For instance, the measurement results of rectangular strain rosettes under 4.0kN are collected in Table 2 and Fig. 8. As shown in Fig. 8, the directions of principal strains are almost along the edge of toggle plate, which may result in the local damage.
Fig. 7 Rectangular strain rosette.
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Table 2 The measurement results of rectangular strain rosettes under 4.0kN Principal strain (µε) Measuring points
ε1
ε2
Direction (°)
21 22 23 24 25 26
522 544 943 466 1038 537
-1385 -972 -2204 -1593 -1432 -519
4.21 -0.76 -9.89 -13.85 32.14 -40.92
(a) (b) Fig. 8. The principal strains of rectangular strain rosettes: (a) points 21, 23 and 25; (b) points 22, 24 and 26.
3. Numerical analysis 3.1. Analysis process In this paper, progressive damage analysis was employed to simulate damage and failure process of sandwich joints under axial compressive load. The process is shown in Fig. 9. Failure of a composite structure initiates at lower load levels and develops in a progressive manner up to final failure. Therefore, progressive failure analysis methodology is developed and recommended for the analysis of sandwich joint. Based on a FE modeling and stress-strain analysis in ABAQUS, this methodology can predict the initiation and the localised progressive nature of damage, mode of failure and ultimate strength of the joint. It determines the damage initiation by failure criteria. If failure is detected, as indicated by a failure criterion, the material properties are changed according to a particular degradation model. Then, equilibrium of the structure needs to be re-established utilizing the modified material properties. The load step is then incremented until catastrophic failure of the structure is detected.
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Fig. 9. The process of progressive failure analysis methodology.
3.2. Failure criteria Failure criteria for composite laminates are mainly analytical approximations or curve fittings of experimental results. Most failure criteria for composite material (Tsai-Hill, Tsai-Wu and Hoffman criteria) have been thought as an extension of the von Mises criterion to a quadratic criterion. The Hashin failure criteria [18] are interacting failure criteria as the failure criteria use more than a single stress component to evaluate different failure modes. The Hashin criteria were originally developed as failure criteria for unidirectional polymeric composites. Therefore, it is necessary to improve the Hashin criteria for laminate plates or non-polymeric composites. Shokrieh [19] presented the modified failure criteria in three dimensions, as shown in Table 3. Moreover, delamination failure should be also considered as it’s one of the most common failure modes [20]. Typical failure modes and criteria are summerized in Table 3. In these failure criteria, tensile and compressive failure in principle material directions (1-direction or 2-direction) as well as the fiber-matrix shear failure are donated by X , X , Y , Y , S , S and S . The stresses in the material coordinate system are simulated within the UMAT subroutine of ABAQUS using the given strains and the material stiffness coefficients at each material point. Based on the stress results, the stress-based failure criteria are evaluated and the material degradation is improved accordingly. T
C
T
C
12
13
23
Table 3 Failure modes and criteria
Failure modes Tensile failure in longitudinal direction
In-plane failure
Field variable
Failure criteria
σ τ τ + + X S S 2
2
1
12
13
T
12
13
σ X
2
≥ 1, σ > 0 1
FV1
2
Compressive failure in longitudinal direction
1
≥ 1,σ < 0 1
C
Tensile failure in transversal direction
σ τ τ + + Y S S 2
2
T
2
12
23
12
23
σ Y
Compressive failure in transversal direction
1
C
8
2
≥ 1,σ > 0
2
≥ 1, σ < 0 2
2
FV2
Fiber-matrix shear failure in transversal direction
σ τ τ + + X S S
Fiber-matrix shear failure in transversal direction
σ τ τ + + Y S S
Tensile delamination
σ τ τ + + Z S S
2
2
1
12
13
C
12
13
2
2
1
12
23
12
23
C
2
2
3
13
23
T
13
23
2
≥ 1,σ < 0 1
FV3
2
≥1,σ < 0 2
2
≥ 1, σ > 0 3
Delamination
FV4
τ τ + S S 2
Compressive delamination
13
23
13
23
2
≥1,σ < 0 3
3.3. Finite element model Three-dimensional FE model is necessary in order to have accurate progressive failure analysis predictions for the sandwich L-joint (see Fig. 10). An 8-node linear brick element with reduced integration and hourglass control (C3D8R) was adopted to simulate the fiberglass skins and PVC core. Adhesive layers between core and skin were modeled by COH3D8 elements. CHO3D8 is an 8-node three-dimensional cohesive element with double linear constitutive relationship. With the increase of load, the stress of cohesive element will linear rise first. After reaching the extreme value point, it will linear drop, eventually falls to 0.
Fig. 10. Finite element model.
This kind of sandwich L-joint was reinforced by an inner and outer GFRP skin, separated by and adhered to the PVC foam. The corresponding material properties of GFRP fabric and PVC foam are shown in Tables 4 and 5, respectively. The physical properties of GFRP are also given in Table 6. Table 4 Material properties of GFRP
Elastic modulus (GPa)
Shear modulus (GPa)
Poisson’s ratio
E11
E22
E33
µ12
µ13
µ 23
G
27
27
15
0.14
0.09
0.09
3.55
Table 5 Material properties of PVC foam
Elastic modulus (MPa)
Poisson’s ratio
Shear modulus (MPa)
Dessity (kg/m3)
Ec
µc
Gc
ρc
135
0.31
35
100
9
Table 6 The physical properties of GFRP
Tensile strength (MPa) XT
Compressive Strengt (MPa)
= YT
ZT
389
XC
20
= YC
212
Shear strength (MPa) ZC
S12
S13 = S 23
40
70.8
30.8
4. Experiment and simulation results 4.1. Strain comparision In order to simulate the real stress state, strain measurement test and FE analysis are compared at 2.0kN. A FE model was developed under the same compressive load 2.0kN (see Fig. 10). The strain results of the main monitoring points in the stress concentration areas are collected in Fig. 11. 0 5
6
7
10
12
15
16
-200
Strain/(µε)
-400 -600 -800 -1000 2.0kN-Measured values 2.0kN-FE values
-1200 -1400 -1600 Measuring points
Fig. 11. Strains of simulation and experiment values at 2.0kN.
Compared with the FE values and measured results, it is concluded that there is a good agreement in the change trend between the experimental strains and predicted strains. The change trend of strain values between the measured values and FE values are consistent, shaped as “W”. However, the predicted strains are smaller than the test results due to the differences between the actual structure and FE model. Among the main reasons for the difference is that the thickness is uneven around the corner due to the purely manual processing, as shown in Fig. 12.
(a) (b) Fig. 12. The appearance of the corner: (a) front view; (b) side view.
4.2. Failure strength analysis The ultimate load and stiffness of specimens U1-U5 are presented in Table 7. Due to the individual differences in manual processing, the initial size and stiffness may be slightly different. However, the 10
results are relatively close, so it is reasonable to take the average value as the final results. As shown in Table 7, the average ultimate load is 15.303kN, and the average stiffness is 441.4N/mm. Table 7 Experimental results of ultimate loads
Specimen
U1
U2
U3
U4
U5
The average values
Ultimate strength (kN)
16.001 14.941
14.798 14.966 15.809
15.303
Stiffness (N/mm)
391.76 377.35
407.58 512.54 517.58
441.4
Load and displacement curves are also compared in Fig. 13. In the initial stage, there is a good linear relationship between displacement and load. Displacement increases approximately linearly with increasing forces. With the increasing load, the compressive stiffness and load capacity decreases gradually.
(a)
(b)
Fig. 13. Load and displacement curves: (a) specimens U1-U3; (b) specimens U4-U5.
Fig. 14 shows the comparison of load and displacement curves between simulation and experiment results. The curve trends are very similar at 0-2kN (see Fig. 14b). With the increase of load, the difference between the curves increases gradually due to the differences between individuals.
(a) (b) Fig. 14. Load and displacement curves comparison of specimens U2 and U4: (a) load range: 0-16kN; (b) load range: 0-2kN.
4.3. Failure process analysis During the ultimate strength experiment, friction noise began to appear due to the internal failure and the increase of damping, under the load of 8.0-10.0kN. When the load was further increased, plastic deformation led to local failure and crack was visual near the corner. With the further extension of crack, specimen broke suddenly and the curve of displacement-force fell dramatically. The failure modes of specimens are shown in Fig. 15. In view of the differences of individuals, cracks mainly focus in the longitudinal stiffener or the arc bracket near the corner, and there is only one main crack. Meanwhile, a progressive failure analysis of the sandwich joint is also conducted, and the results are compared with the experimental results in Table 8. 11
(a) (b) (c) (d) (e) Fig. 15. Fracture of specimens: (a) specimen U1; (b) specimen U2; (c) specimen U3; (d) specimen U4; (e) specimen U5.
Typical failure modes are predicted in Table 8. The major failure modes of sandwich L-joints are the delamination between core and skin, fiber failure, base shear failure and PVC failure. Delamination failure (FV4) occured first at 1.90kN. With the increase of load, the failure area gradually expanded. When the load increased to 6.8kN, fiber failure in 2-direction (FV2), fiber-matrix shear failure (FV3) and foam failure appeared simultaneously. Fiber failure in 1-direction did not happen until 9.56kN. Moreover, failure in 2-direction initiated in the center of the arc bracket at the outer layer of the laminated plates, then extended to internal laminated plate. Fiber-matrix shear failure initiated in the center of the arc bracket firstly, and then extended to the ends of the arc bracket. Foam failure initiated and concentrated in the corner. Table 8 Failure modes and loads
Failure mode
Initial failure load (kN)
Fiber failure in 1-direction (FV1)
9.56
Fiber failure in 2-direction (FV2)
6.80
Failure area Initial failure
12
Final failure
Fiber-matrix shear failure (FV3)
6.80
Delamination (FV4)
1.90
Foam failure
6.80
5. Conclusions In the present paper, a 3D sandwich L-joint was modeled, and a progressive failure analysis methodology was developed to predict the strength of the joint. (1) Under axial compressive load, the failure process of composite joint can be divided into three stages: linear elastic stage, nonlinear stage and failure stage, and the failure modes include: skins and core delamination failure, fiber failure, fiber-matrix shear failure and foam failure. (2) In the initial stage, there is a good linear relationship between displacement and load. Displacement increases approximately linearly with increasing forces. When the load is further increased, plastic deformation leads to local failure and crack is visual near the corner. With the further extension of crack, specimen breaks suddenly and the curve of displacement-force falls dramatically. The final cracks mainly focus in the longitudinal stiffener or the arc bracket near the corner. (3) Numerical calculation results are consistent with the experimental results in the change trend. It shows that progressive damage analysis can be developed to simulate the damage process of sandwich joints. It is worth noting that there is a certain difference between numerical values and experimental values. The differences between the manual model and the numerical model may results in this prediction error. Therefore, the further work on the actual ship structure under complex stress state is also needed.
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Acknowledgements The research project is supported by the National Natural Science Foundation of China (Grant No. 51609185) and the State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University (No. 1613). The support of China Ship Development and Design Center is also greatly appreciated. The authors wish to thank Dr. Yaoyu Hu and Feng He from Wuhan University of Technology, for the warm efforts about this test. References [1] Jones RM. Mechanics of composite materials. Flarida: CRC Press; 1998. [2] Slater JE. Selection of a blast-resistant GRP composite panel design for naval ship structures. Marine Structure 1994,7:417-440. [3] Benson JL. The AEM/S system, a pardigm-break mast, goes to sea. Naval Engineers Journal 1998; 110(4):99-103. [4] Mouritz AP, Gellert E, Burchill P, et al. Review of advanced composite structures for naval ships and submarines. Composite Structures 2001;53: 21-41. [5] Tiron R. Navy Gradually Embracing Composite Materials in Ships. National Defense 2004;89:28-29. [6] Jiang YP, Yue ZF. Numerical failure simulation of bolt-loaded composite laminate. Acta Material Composites Sinica 2005;22(4): 177-182. [7] Smith CS, Dow RS. Interactive bucking effects in stiffened FRP panels. In: Proceedings of the 4th International Conference on Composite Structures, Paisley,122-133, 1987. [8] Dow RS. Large scale FRP structural testing. In: International Conference Lightweight Materials in Naval Architecture, Transactions of the Royal Institute of naval Architects, 1996. [9] Chen NZ, Sun HH, Guedes SC. Reliability analysis of a ship hull in composite material. Composite Structures 2003;62(1):59-66. [10] Prusty BG. Progressive failure analysis of laminated unstiffened and stiffened composite panels. Composites Science and Technology 2004;64(3):379-394. [11] Tang WY, Chen NZ, Zhang SK. Ultimate strength analysis of stiffened laminated plates. Engineering Mechanics 2007;24(8): 43-48. [12] Cai ZY, Tang WY, et al. Ultimate strength analysis of composite laminated ship panels. International Journal of Ship Mechanics 2009;13(1):72-81. [13] YuY, Wang W. Investigation on the ultimate strength of sandwish plates in complex bending. Chinese Journal of Ship Research 2014;9(3):76-82. [14] Yang NN, Wang W, et al. Progressive damage analysis of steel-to-composite joints of radome. Journal of Harbin Engineering University 2014;35(10):1183-1188. [15] Mouritz AP, Gellert E, Burchill P and Challis K. Review of advanced composite structures for naval ships and submarines. Composite Structures 2001;53:21-41. [16] Shen W, Barltrop N, Yan RJ, et al. Stress field and fatigue strength analysis of 135-degree sharp corners under tensile and bending loadings based on notch stress strength theory. Ocean Engineering 2015;107:32-44. [17] Shen W, Yan RJ, et al. Application study on FBG sensor applied to hull structural health monitoring. Optik 2015;126:1499-1504. [18] Hashin Z. Failure criteria for unidirectional fiber composites. Journal of Applied Mechanics 1980; 47(2):329-334. [19] Shokrieh MM, Lessard LB. Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling. Journal of Composite Materials 2000;34(13):1056-1080. [20] Lin Y. Role of matrix resin in delamination onset and growth in composite laminates. Composites Science and Technology 1988;33(4):257-277.
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