- Email: [email protected]
composite skin hybrid ship hull model
ARTICLE IN PRESS
Marine Structures 19 (2006) 23–32 www.elsevier.com/locate/marstruc
Testing and analysis of a 6-m steel truss/composite skin hybrid ship hull model Jun Caoa, Joachim L. Grenestedtb,, William J. Marounc a
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA b Department of Mechanical Engineering and Mechanics, ATLSS Center Faculty Associate, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA c Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA Received 2 May 2006; received in revised form 4 July 2006; accepted 6 July 2006
Abstract A hybrid ship hull made of a steel truss and composite sandwich skins was investigated experimentally and numerically. A 6-m model was tested under hogging loads, after having previous been subjected to sagging loads. All loads were introduced as shear through brackets welded to bulkheads. The model was loaded to the design load, at which point there was plastic yielding of the steel truss. However, there was no indication of failure in any of the composite sandwich panels, nor in the adhesive bonds between the panels and the steel truss. The steel truss started to yield at lower strains than expected, a fact which was elucidated by manufacturing and testing subcomponents of the steel truss. Nonlinear elastic-plastic finite element analyses were performed on the complete hull. Results from the numerical analyses were compared with data from both sagging and hogging tests and good correlation was found. r 2006 Elsevier Ltd. All rights reserved. Keywords: Hybrid ship hull; Composite material; Stainless steel; Mechanical testing; Finite element analysis
1. Introduction Composites have a number of benefits such as light weight, high strength, corrosion resistance, etc., whereas steel has other benefits including high stiffness, ductility, simple Corresponding author. Tel.: +1 610 758 4129, fax: +1 610 758 6224.
E-mail address: [email protected] (J.L. Grenestedt). 0951-8339/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.marstruc.2006.07.001
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manufacturing, simple outfitting, etc. There is interest in combining steel and composites in a hybrid ship hull to achieve synergistic effects [1–4]. A hybrid ship hull concept with a steel truss and composite sandwich skins was investigated prior to current research [5,6]. A 142-m ship hull, similar to a destroyer in terms of size, weight and speed, was designed, finite element (FE) analyzed and optimized based on this hybrid hull concept. A 6-m ship hull specimen was subsequently developed, FE analyzed, manufactured and tested under sagging loads. The hull had a flat horizontal deck and a 201 deadrise bottom. This specimen consisted of a non-magnetic AL-6XN stainless steel truss, which was closed out with 60 glass fiber reinforced vinyl ester skin/foam core sandwich panels (Fig. 1). The panels were made from Hexcel 7725 glass fiber weave, vacuum infused with Derakane 8084 vinyl ester directly on 12.7-mm thick Divinycell PVC-based foam cores of four different densities (H130, H160, H200, H250). The panels were bonded to the steel truss using SIA E2119 epoxy adhesive from Sovereign Specialty Chemicals. The specimen was installed upside down and load was applied to simulate sagging. It was loaded to 36% above the design load, at which point there was substantial yielding and residual deformation of the steel truss. However, there was no indication of failure in any of the composite sandwich panels, nor in the adhesive bonds between the panels and the steel truss. In the present research, the 6-m ship hull specimen was turned back to its normal position and loaded to simulate hogging. Strain gage data indicated that plastic yielding of the steel truss initiated at strains considerably lower than in virgin AL-6XN tensile specimens. Subcomponent specimens, with the exact configuration of the longerons in the steel truss, were therefore manufactured and tensile tested to clarify the reason for the premature yielding. A uniaxial hardening constitutive model for the welded AL-6XN was developed from this test. This nonlinear constitutive relation of the steel after welding was then used in nonlinear elastic-plastic FE analyses of the hybrid ship hull model. The results from the nonlinear analyses were compared with the test results from both the sagging and the hogging tests.
Fig. 1. Six-meter hybrid ship hull specimen. The stainless steel truss was closed out with 60 composite sandwich panels. The load was fed into the specimen through 12 load brackets welded to bulkheads.
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2. Testing of subcomponents of the welded steel truss Sagging testing previously performed on the 6-m hybrid ship hull model showed that the stainless steel truss started to plastically deform at strains considerably lower than those expected in virgin steel [6]. For this reason, two identical subcomponent specimens with the same material (AL-6XN by Allegheny Ludlum Corp.), thickness (2 mm), geometry and manufacturing procedure (MIG welding) as the deck longerons of the steel truss were manufactured, instrumented and mechanically tested. The longeron specimens were 400 mm long. The longerons were box beams, where two of the sides of the box had protruding flanges that were manufactured with ‘‘fingers’’. These fingers were used to reduce the effective stiffness of the steel where the compliant composite panels were adhesively bonded to the steel longerons. One of the specimens can be seen in Fig. 2. At each end of the subcomponent specimens, a 9.5 mm thick stainless steel plate was welded perpendicular to the length of the specimen. Another plate of the same thickness was welded perpendicular to this plate and used for the tensile machine to grip the specimen. The load was centered over the centroid of the specimen. Four strain gages (Vishay CEA-06-250UN-350) were mounted at the center of each side of the specimens
Fig. 2. Welded stainless steel subcomponent specimen, simulating a section of a longeron.
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and oriented lengthwise. Two linear variable differential transformers (LVDTs) from Macro Sensors were mounted on each specimen to measure axial deformations (Fig. 2). Tension tests were performed in a SATEC 2700 kN (600 kips) test machine. National Instruments signal conditioners and data acquisition hardware were used together with a LabView program to record load, strains and displacements. The specimens were repeatedly loaded and unloaded in small increments, with a 0.25 mm/min loading rate. During the test, the specimen was loaded to 8888 N (2000 lbf) in the first load step, and then unloaded before proceeding to the next load level. The load increment between each load step was 8888 N (2000 lbf), and at each load step the specimen was loaded and unloaded before moving to a new load level. The test continued with same loading procedure until failure. The failure loads of the two specimens were 111.1 and 111.9 kN, respectively. In both specimens, cracks initiated between some of the fingers when the load was approximately 92 kN. Fig. 3 shows a load-strain graph from the test, where the strain is the average from the four strain gages. An FE model of the test specimen was made with a simple multi-linear isotropic hardening model. The properties of the constitutive model were adjusted such that the behavior of the FE model fit the experimental data. The resulting stress–strain relation was: E ¼ 210 GPa, ET ¼ 130 GPa from e ¼ 0.08%, ET ¼ 110 GPa from e ¼ 0.1%, ET ¼ 82.5 GPa from e ¼ 0.15%, ET ¼ 56 GPa from e ¼ 0.2%, and ET ¼ 18 GPa from e ¼ 0.3%, where E is Young’s modulus, ET are tangent moduli and e is strain. Young’s modulus E was obtained by linear regression of the test data during unloading. It should be pointed out that internal stresses due to welding were not considered per se, but rather this model for ‘‘effective properties’’ was developed.
Test results Ansys Results 80
Load [KN]
60
40
20
0 0.0%
0.2%
0.4%
Strain Fig. 3. Load versus strain of subcomponent specimen, obtained from experimental test and nonlinear elasticplastic FE analysis.
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The effective yield strain of the material that best fit the data was 0.08%, which is considerably less than the 0.2% of virgin AL-6XN. The reason is that the heavy weld bead creates large residual tensile stress in and adjacent to the bead, and compressive stress in the rest of the longeron, after cooling down; see e.g. [7] for a discussion. Upon tensile loading of the longeron, the material in and near the weld bead will yield at (additional) strains considerably lower than 0.2%. Likewise, upon compressive loading of the longeron, the steel farther from the weld bead will yield at (additional) strains considerably lower than 0.2%. The strain gage data from the previous sagging testing of the ship hull model behaved in a similar fashion [6]. Nonlinear elastic-plastic analyses of the complete ship hull specimen are performed and compared to experimental data from sagging and hogging tests in later sections. 3. Small scale ship hull hogging testing During the previous sagging testing of the 6-m ship hull model, described in detail in [5,6], the hull was mounted upside down in a six-point bend fixture. For the present hogging test, the specimen was turned to its ‘‘normal’’ position, with the deck up and keel down, and re-mounted in the fixture. The fixture consisted of an overhead support from which a single hydraulic jack was hung. A ‘‘wiffle tree’’ with three load spreader beams was attached to the jack through a load cell. Load was introduced to the specimen via eight loading arms, bolted to load brackets welded to the sides of the steel truss of the hull and connected to the spreader beams (Figs. 1 and 4). The specimen was supported by another four arms, bolted to load brackets welded to the hull on one end and constrained to floor mounts on the other (Fig. 4). There were bulkheads by all load brackets on the hull. All loads were thus introduced in shear to the hull girder. The six-point bend setup enabled the maximum bending moment and the maximum shear load according to ABS rules [8] to be reached simultaneously, but at different locations. The design load was 83,200 N, which gives the correct scaled bending moment and shear force as described in [6]. The steel structure of the full-scale hull was designed for a maximum stress corresponding to 95% of yield (380 MPa), i.e. 361 MPa. The small-scale hull specimen used steel slightly thicker than a perfect scale model would, and had a slight geometry change, which together reduced the maximum stress to approximately 345 MPa in the steel truss. The full-scale model used 63 mm thick steel in the longerons, which would correspond to 1.8 mm in the 1:35 model; however, 2 mm thick steel was used. The location of the maximum stress in the steel was the deck longerons. The hull model was instrumented with the 192 strain gages and 33 LVDTs that were previously mounted on the specimen for the sagging tests [6]. Six additional LVDTs were mounted on the hull for the hogging test as shown in Fig. 4. These new LVDTs measured cross section deformation. In particular, the compression-loaded keel could lead to ‘‘flattening’’ of the cross section and subsequent instability problems (in a sense similar to Brazier buckling). The previously used CR9000 Measurement and Control System, made by Campbell Scientific Inc., was utilized for the data acquisition. CR9050 Analog Input Modules and 4WFB350 Terminal Input Modules were used for all signals from the strain gages, LVDTs and the load cell. Test data was recorded by three personal computers. The zeroing of all gages was done using the same procedure as used for the sagging test [6]. Before any load was applied, all bolts between the four supporting arms and the lab
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Fig. 4. Hybrid ship hull specimen mounted in the six-point bend fixture.
floor were disconnected and the specimen was lifted by the hydraulic jack to allow the specimen to hang freely. The strain gages were then zeroed. When hanging freely, the gravity-induced bending moment in the hull was lower than when the hull was standing on the lower supports. The LVDTs mounted on the hull were also zeroed (but not the five LVDTs mounted between the hull and the lab floor). The specimen was then lowered until the four support arms fully supported the specimen, at which time the lower supports were connected. The jack was then further lowered until there was no load on the specimen, but the weight of the load tree was still carried by the jack (through the load cell). The load cell and the five vertical LVDTs mounted between the hull and the lab floor were then zeroed. The strain gages and the LVDTs on the hull were not re-zeroed at this time. With this setup, the strains recorded when the load read zero were mainly due to the dead weight of the specimen when sitting on the four lower supporting arms. During the hogging test, the load was applied in seven steps. At each load step the specimen was loaded and unloaded for three times before moving to a higher load level.
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Both the load and unload times were two minutes. Each occasion the specimen was loaded to a higher level, the specimen was visually checked for damage. The specimen was loaded to 13.3 kN (3000 lbf) in the first load step, and then to 26.7 kN (6000 lbf), 40.0 kN (9000 lbf), 57.8 kN (13000 lbf), 71.1 kN (16000 lbf), 77.8 kN (17500 lbf), and 83.2 kN (18700 lbf), in subsequent load steps. After the design load 83.2 kN (18700 lbf) was reached, the specimen was more carefully checked for damage. The specimen was loaded and unloaded three times to the design load and then the test was terminated. There was no indication of any failure in any of the 60 composite sandwich panels or in the adhesive bonds between the panels and the steel truss throughout the test. The test data of load–unload cycles clearly showed that there was plastic yielding of the steel truss before the design load had been reached and that there was quite substantial yielding and residual deformation of the hull girder at the final load step. 4. Small scale ship hull FE analyses Nonlinear elastic-plastic FE analyses were performed on the ship hull model. The FE model was first subjected to repeated sagging loads and then to hogging loads, in essence as done during the experimental testing except with much fewer unloadings. The FE results will be compared with the test results in the next two sections. The ANSYS FE package [9] was used for all analyses. An FE model of the subscale hull was created and analyzed, using the quasi-static loads that were applied during the test. Shell elements were used exclusively in the model, with sandwich-type shell elements for the composite sandwich panels. Effective nonlinear elastic-plastic material properties of welded stainless steel, obtained from the subcomponent tests previously described, were used for all steel in the FE model. J2 flow theory with kinematic hardening was assumed. Properties of the other materials were linear elastic and the same as in Ref. [6]. For the sagging analysis, the FE model was loaded twice: first to 60 kN, then unloaded, then reloaded to 120 kN, and finally unloaded. It was thus loaded slightly higher than the 112.9 kN the specimen was subjected to experimentally. The FE model was subsequently subjected to hogging loads. The model was loaded only once, to a level of 88.9 kN (20000 lbf), which is slightly higher than the 83.2 kN that the experimental specimen was subjected to. Strains and displacements obtained from the FE model were compared to experimental data, as discussed below. 5. Discussion of sagging Both sagging and hogging test results were compared with the results from the new elastic-plastic FE analyses. This section deals with sagging, described in more detail in [6]. Only elastic analyses were performed in [6]. In Fig. 5, the strain from strain gage 21, mounted at the middle of a deck longeron where the bending moment was the highest, is compared to the new FE results of the sagging test. This strain gage was mounted on the underside of a deck longeron, which is slightly less strained than the top of the deck longerons. In the nonlinear FE analysis, the specimen was first loaded to 60 kN and unloaded, and then re-loaded to 120 kN. The curves show a good match between the FE data and the test results. Equally good matches were obtained from other strain gages located on the (plastically deforming) steel longerons.
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Gage 21
FE analysis, loaded to 60kN then unload
FE analysis, loaded to 120kN
150
Load [kN]
100
50
0 -0.40%
-0.30%
-0.20%
-0.10%
0.00%
Strain
Fig. 5. Load–strain curves obtained from sagging test and elastic-plastic FE analysis. Gage 21 was located at the middle of a deck longeron where the bending moment was the highest. The load is the total load applied by the hydraulic jack.
Regarding strains measured by strain gages on bulkheads and on composite sandwich panels, there was no appreciable non-linear behavior. The same was true in the FE analyses. This suggests that the steel bulkheads remained elastic and that there was no damage even in the most highly shear-loaded composites side panels during the test.
6. Discussion of hogging After sagging loading up to 36% above the design load, the experimental hull model was turned over and loaded in simulated hogging. Plastic yielding was observed to initiate earlier than during the previous sagging tests, indicating that there is a Bauschinger-like effect, in particular in the steel longerons. The hull was repeatedly loaded up to the design load, after which the test was terminated. There was no indication of failure in any of the adhesive joints throughout the test, nor was there any indication of damage in any of the 60 composite sandwich panels. Fig. 6 shows the strain measured in strain gage 21 (see above), mounted at the middle of a deck longeron where the bending moment was the highest. The yield initiation loads in sagging and hogging were obtained as follows: the linear elastic part of the load–strain curves was obtained through a linear regression of the (elastic) unload portions of the test data. A line with 95% of the slope of the linear elastic part was drawn and the intersections of this line with the test data were defined as the yield initiation loads. This gave 56 kN in sagging and 24 kN in hogging, indicating a Bauschinger-like behavior. This is difficult to see in Figs. 5 and 6; however, the loads at 0.2% (absolute) strain differ as well. At 0.2% strain, the load in the sagging test was 86 kN while at 0.2% strain in the hogging test the load was 78 kN. Fig. 6 also shows the results of elastic-plastic FE analyses, which matched the test data very well.
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gage 21
31
FE analysis, loaded to 88.9kN
100
Load [kN]
80
60
40
20
0 0.00%
0.10%
0.20%
0.30%
Strain Fig. 6. Load–strain curves obtained from hogging test and FE analysis.
Regarding the steel bulkheads, there was no indication of nonlinear behavior during hogging either. The strains remained below 0.05%. The measured strains confirmed that the bulkheads deformed in an ‘‘S’’ shape, as also predicted by the FE analyses. The highest strains measured in the composites were in the side panels located in the highest shear load regions. The load–strain curves from both the test and the elastic-plastic FE analysis are straight lines, indicating absence of damage. There is a difference in slope between the experimental and numerical strains. The FE model utilized thin sandwich elements, which were non-symmetric but essentially loaded in their mid-planes. The sandwich panels in the experimental specimen were flat on the outside, whereas the sandwich core was beveled on the inside to create an edge around the panels with no core. This leads to a load offset in the panels, and subsequently bending due to in-plane loads. The inside and outside of the panels thus strained differently, as also seen from strain gages mounted on each side of certain panels. The experimentally measured strains were 5% and 9% lower, respectively, than the numerically calculated strains. Similar differences were also observed in the earlier sagging test [6]. It appears as if the stiffnesses of the composite panels were higher than those used for the numerical analyses. The stiffnesses of the composite had been determined experimentally using a vibration identification method [6]. With this method, there is a risk that the inhomogeneity of the glass fiber weave leads to an underestimation of the in-plane stiffnesses. The load–displacement curve measured from LVDTs mounted diagonally on side panels in the highest shear load regions also showed straight lines with no permanent deformation after unloading. These LVDTs indicated that the specimen was locally 4–7% stiffer than numerically calculated. There were residual strains after unloading in the composite deck and bottom panels located in the region with the highest bending moment. This was also observed in the earlier sagging tests [6]. These residual strains were not due to damage in the composite
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panels, but rather to yielding of the steel longerons to which the composite panels were bonded. Six newly mounted LVDTs measured the cross sectional deformation, and in particular the vertical displacement of the keel relative to the chine longerons. The maximum displacement was less than 0.5 mm, which is essentially negligible. Cross-sectional deformation was thus minimal. 7. Conclusion A hybrid ship hull model utilizing a steel truss, closed out with composite sandwich panels, was studied. A subscale model was tested under simulated hogging loads. The subscale model was loaded to the design load, at which point there was plastic yielding of the hull girder. However, there was no indication of any failure in any of the composite sandwich panels, nor in the bonds between the panels and the steel truss. Elastic-plastic behavior of welded stainless steel longeron subcomponents was investigated experimentally and numerically. Nonlinear elastic-plastic finite element analyses of the whole ship hull model were performed. Results from finite element analyses compared favorably with results from both sagging and hogging tests. The study indicates that a strong and lightweight ship hull could be made using this steel/composite hybrid concept. More studies will be performed in the near future to investigate how this hull concept stands up to extensive damage as well as fatigue. Acknowledgement This work was supported by ONR Grant N00014-03-1-0597, with Dr. Roshdy Barsoum as program manager. References [1] Barsoum R. The best of both worlds: hybrid ship hulls use composites and steel. AMPTIAC Q 2003;7(3):55–61. [2] Barsoum R. Hybrid ship hull. US Patent 6,386,131; 14 May, 2002. [3] Cao J, Grenestedt JL. Design and testing of joints for composite sandwich/steel hybrid ship hulls. Composites A: Appl Sci Manuf 2004;35:1091–105. [4] Thompson L, Walls J, Caccese V. Design and analysis of a hybrid composite/metal structural system for underwater lifting bodies. Department of Mechanical Engineering, University of Maine. Report no. UM-MACH-RPT-01-08, June 2005. [5] Cao J, Grenestedt JL, Maroun WJ. Steel truss/composite skin hybrid ship hull, Part I: design and analysis, submitted for publication. [6] Maroun WJ, Cao J, Grenestedt JL. Steel truss/composite skin hybrid ship hull, Part II: manufacturing and sagging testing, submitted for publication. [7] Masubuchi K. Models of stresses and deformation due to welding—a review. J Met 1981;33(12):19–23. [8] ABS. Guide for building and classing high-speed naval craft 2003, Part 3 hull construction and equipment. American Bureau of Shipping, 2003. [9] ANSYS. Version 9.0, Southpointe, 275 Technology Drive. Canonsburg, PA: Ansys Inc.; 2002. p. 15317.
Marine Structures 19 (2006) 23–32 www.elsevier.com/locate/marstruc
Testing and analysis of a 6-m steel truss/composite skin hybrid ship hull model Jun Caoa, Joachim L. Grenestedtb,, William J. Marounc a
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA b Department of Mechanical Engineering and Mechanics, ATLSS Center Faculty Associate, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA c Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA Received 2 May 2006; received in revised form 4 July 2006; accepted 6 July 2006
Abstract A hybrid ship hull made of a steel truss and composite sandwich skins was investigated experimentally and numerically. A 6-m model was tested under hogging loads, after having previous been subjected to sagging loads. All loads were introduced as shear through brackets welded to bulkheads. The model was loaded to the design load, at which point there was plastic yielding of the steel truss. However, there was no indication of failure in any of the composite sandwich panels, nor in the adhesive bonds between the panels and the steel truss. The steel truss started to yield at lower strains than expected, a fact which was elucidated by manufacturing and testing subcomponents of the steel truss. Nonlinear elastic-plastic finite element analyses were performed on the complete hull. Results from the numerical analyses were compared with data from both sagging and hogging tests and good correlation was found. r 2006 Elsevier Ltd. All rights reserved. Keywords: Hybrid ship hull; Composite material; Stainless steel; Mechanical testing; Finite element analysis
1. Introduction Composites have a number of benefits such as light weight, high strength, corrosion resistance, etc., whereas steel has other benefits including high stiffness, ductility, simple Corresponding author. Tel.: +1 610 758 4129, fax: +1 610 758 6224.
E-mail address: [email protected] (J.L. Grenestedt). 0951-8339/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.marstruc.2006.07.001
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manufacturing, simple outfitting, etc. There is interest in combining steel and composites in a hybrid ship hull to achieve synergistic effects [1–4]. A hybrid ship hull concept with a steel truss and composite sandwich skins was investigated prior to current research [5,6]. A 142-m ship hull, similar to a destroyer in terms of size, weight and speed, was designed, finite element (FE) analyzed and optimized based on this hybrid hull concept. A 6-m ship hull specimen was subsequently developed, FE analyzed, manufactured and tested under sagging loads. The hull had a flat horizontal deck and a 201 deadrise bottom. This specimen consisted of a non-magnetic AL-6XN stainless steel truss, which was closed out with 60 glass fiber reinforced vinyl ester skin/foam core sandwich panels (Fig. 1). The panels were made from Hexcel 7725 glass fiber weave, vacuum infused with Derakane 8084 vinyl ester directly on 12.7-mm thick Divinycell PVC-based foam cores of four different densities (H130, H160, H200, H250). The panels were bonded to the steel truss using SIA E2119 epoxy adhesive from Sovereign Specialty Chemicals. The specimen was installed upside down and load was applied to simulate sagging. It was loaded to 36% above the design load, at which point there was substantial yielding and residual deformation of the steel truss. However, there was no indication of failure in any of the composite sandwich panels, nor in the adhesive bonds between the panels and the steel truss. In the present research, the 6-m ship hull specimen was turned back to its normal position and loaded to simulate hogging. Strain gage data indicated that plastic yielding of the steel truss initiated at strains considerably lower than in virgin AL-6XN tensile specimens. Subcomponent specimens, with the exact configuration of the longerons in the steel truss, were therefore manufactured and tensile tested to clarify the reason for the premature yielding. A uniaxial hardening constitutive model for the welded AL-6XN was developed from this test. This nonlinear constitutive relation of the steel after welding was then used in nonlinear elastic-plastic FE analyses of the hybrid ship hull model. The results from the nonlinear analyses were compared with the test results from both the sagging and the hogging tests.
Fig. 1. Six-meter hybrid ship hull specimen. The stainless steel truss was closed out with 60 composite sandwich panels. The load was fed into the specimen through 12 load brackets welded to bulkheads.
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2. Testing of subcomponents of the welded steel truss Sagging testing previously performed on the 6-m hybrid ship hull model showed that the stainless steel truss started to plastically deform at strains considerably lower than those expected in virgin steel [6]. For this reason, two identical subcomponent specimens with the same material (AL-6XN by Allegheny Ludlum Corp.), thickness (2 mm), geometry and manufacturing procedure (MIG welding) as the deck longerons of the steel truss were manufactured, instrumented and mechanically tested. The longeron specimens were 400 mm long. The longerons were box beams, where two of the sides of the box had protruding flanges that were manufactured with ‘‘fingers’’. These fingers were used to reduce the effective stiffness of the steel where the compliant composite panels were adhesively bonded to the steel longerons. One of the specimens can be seen in Fig. 2. At each end of the subcomponent specimens, a 9.5 mm thick stainless steel plate was welded perpendicular to the length of the specimen. Another plate of the same thickness was welded perpendicular to this plate and used for the tensile machine to grip the specimen. The load was centered over the centroid of the specimen. Four strain gages (Vishay CEA-06-250UN-350) were mounted at the center of each side of the specimens
Fig. 2. Welded stainless steel subcomponent specimen, simulating a section of a longeron.
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and oriented lengthwise. Two linear variable differential transformers (LVDTs) from Macro Sensors were mounted on each specimen to measure axial deformations (Fig. 2). Tension tests were performed in a SATEC 2700 kN (600 kips) test machine. National Instruments signal conditioners and data acquisition hardware were used together with a LabView program to record load, strains and displacements. The specimens were repeatedly loaded and unloaded in small increments, with a 0.25 mm/min loading rate. During the test, the specimen was loaded to 8888 N (2000 lbf) in the first load step, and then unloaded before proceeding to the next load level. The load increment between each load step was 8888 N (2000 lbf), and at each load step the specimen was loaded and unloaded before moving to a new load level. The test continued with same loading procedure until failure. The failure loads of the two specimens were 111.1 and 111.9 kN, respectively. In both specimens, cracks initiated between some of the fingers when the load was approximately 92 kN. Fig. 3 shows a load-strain graph from the test, where the strain is the average from the four strain gages. An FE model of the test specimen was made with a simple multi-linear isotropic hardening model. The properties of the constitutive model were adjusted such that the behavior of the FE model fit the experimental data. The resulting stress–strain relation was: E ¼ 210 GPa, ET ¼ 130 GPa from e ¼ 0.08%, ET ¼ 110 GPa from e ¼ 0.1%, ET ¼ 82.5 GPa from e ¼ 0.15%, ET ¼ 56 GPa from e ¼ 0.2%, and ET ¼ 18 GPa from e ¼ 0.3%, where E is Young’s modulus, ET are tangent moduli and e is strain. Young’s modulus E was obtained by linear regression of the test data during unloading. It should be pointed out that internal stresses due to welding were not considered per se, but rather this model for ‘‘effective properties’’ was developed.
Test results Ansys Results 80
Load [KN]
60
40
20
0 0.0%
0.2%
0.4%
Strain Fig. 3. Load versus strain of subcomponent specimen, obtained from experimental test and nonlinear elasticplastic FE analysis.
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The effective yield strain of the material that best fit the data was 0.08%, which is considerably less than the 0.2% of virgin AL-6XN. The reason is that the heavy weld bead creates large residual tensile stress in and adjacent to the bead, and compressive stress in the rest of the longeron, after cooling down; see e.g. [7] for a discussion. Upon tensile loading of the longeron, the material in and near the weld bead will yield at (additional) strains considerably lower than 0.2%. Likewise, upon compressive loading of the longeron, the steel farther from the weld bead will yield at (additional) strains considerably lower than 0.2%. The strain gage data from the previous sagging testing of the ship hull model behaved in a similar fashion [6]. Nonlinear elastic-plastic analyses of the complete ship hull specimen are performed and compared to experimental data from sagging and hogging tests in later sections. 3. Small scale ship hull hogging testing During the previous sagging testing of the 6-m ship hull model, described in detail in [5,6], the hull was mounted upside down in a six-point bend fixture. For the present hogging test, the specimen was turned to its ‘‘normal’’ position, with the deck up and keel down, and re-mounted in the fixture. The fixture consisted of an overhead support from which a single hydraulic jack was hung. A ‘‘wiffle tree’’ with three load spreader beams was attached to the jack through a load cell. Load was introduced to the specimen via eight loading arms, bolted to load brackets welded to the sides of the steel truss of the hull and connected to the spreader beams (Figs. 1 and 4). The specimen was supported by another four arms, bolted to load brackets welded to the hull on one end and constrained to floor mounts on the other (Fig. 4). There were bulkheads by all load brackets on the hull. All loads were thus introduced in shear to the hull girder. The six-point bend setup enabled the maximum bending moment and the maximum shear load according to ABS rules [8] to be reached simultaneously, but at different locations. The design load was 83,200 N, which gives the correct scaled bending moment and shear force as described in [6]. The steel structure of the full-scale hull was designed for a maximum stress corresponding to 95% of yield (380 MPa), i.e. 361 MPa. The small-scale hull specimen used steel slightly thicker than a perfect scale model would, and had a slight geometry change, which together reduced the maximum stress to approximately 345 MPa in the steel truss. The full-scale model used 63 mm thick steel in the longerons, which would correspond to 1.8 mm in the 1:35 model; however, 2 mm thick steel was used. The location of the maximum stress in the steel was the deck longerons. The hull model was instrumented with the 192 strain gages and 33 LVDTs that were previously mounted on the specimen for the sagging tests [6]. Six additional LVDTs were mounted on the hull for the hogging test as shown in Fig. 4. These new LVDTs measured cross section deformation. In particular, the compression-loaded keel could lead to ‘‘flattening’’ of the cross section and subsequent instability problems (in a sense similar to Brazier buckling). The previously used CR9000 Measurement and Control System, made by Campbell Scientific Inc., was utilized for the data acquisition. CR9050 Analog Input Modules and 4WFB350 Terminal Input Modules were used for all signals from the strain gages, LVDTs and the load cell. Test data was recorded by three personal computers. The zeroing of all gages was done using the same procedure as used for the sagging test [6]. Before any load was applied, all bolts between the four supporting arms and the lab
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Fig. 4. Hybrid ship hull specimen mounted in the six-point bend fixture.
floor were disconnected and the specimen was lifted by the hydraulic jack to allow the specimen to hang freely. The strain gages were then zeroed. When hanging freely, the gravity-induced bending moment in the hull was lower than when the hull was standing on the lower supports. The LVDTs mounted on the hull were also zeroed (but not the five LVDTs mounted between the hull and the lab floor). The specimen was then lowered until the four support arms fully supported the specimen, at which time the lower supports were connected. The jack was then further lowered until there was no load on the specimen, but the weight of the load tree was still carried by the jack (through the load cell). The load cell and the five vertical LVDTs mounted between the hull and the lab floor were then zeroed. The strain gages and the LVDTs on the hull were not re-zeroed at this time. With this setup, the strains recorded when the load read zero were mainly due to the dead weight of the specimen when sitting on the four lower supporting arms. During the hogging test, the load was applied in seven steps. At each load step the specimen was loaded and unloaded for three times before moving to a higher load level.
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Both the load and unload times were two minutes. Each occasion the specimen was loaded to a higher level, the specimen was visually checked for damage. The specimen was loaded to 13.3 kN (3000 lbf) in the first load step, and then to 26.7 kN (6000 lbf), 40.0 kN (9000 lbf), 57.8 kN (13000 lbf), 71.1 kN (16000 lbf), 77.8 kN (17500 lbf), and 83.2 kN (18700 lbf), in subsequent load steps. After the design load 83.2 kN (18700 lbf) was reached, the specimen was more carefully checked for damage. The specimen was loaded and unloaded three times to the design load and then the test was terminated. There was no indication of any failure in any of the 60 composite sandwich panels or in the adhesive bonds between the panels and the steel truss throughout the test. The test data of load–unload cycles clearly showed that there was plastic yielding of the steel truss before the design load had been reached and that there was quite substantial yielding and residual deformation of the hull girder at the final load step. 4. Small scale ship hull FE analyses Nonlinear elastic-plastic FE analyses were performed on the ship hull model. The FE model was first subjected to repeated sagging loads and then to hogging loads, in essence as done during the experimental testing except with much fewer unloadings. The FE results will be compared with the test results in the next two sections. The ANSYS FE package [9] was used for all analyses. An FE model of the subscale hull was created and analyzed, using the quasi-static loads that were applied during the test. Shell elements were used exclusively in the model, with sandwich-type shell elements for the composite sandwich panels. Effective nonlinear elastic-plastic material properties of welded stainless steel, obtained from the subcomponent tests previously described, were used for all steel in the FE model. J2 flow theory with kinematic hardening was assumed. Properties of the other materials were linear elastic and the same as in Ref. [6]. For the sagging analysis, the FE model was loaded twice: first to 60 kN, then unloaded, then reloaded to 120 kN, and finally unloaded. It was thus loaded slightly higher than the 112.9 kN the specimen was subjected to experimentally. The FE model was subsequently subjected to hogging loads. The model was loaded only once, to a level of 88.9 kN (20000 lbf), which is slightly higher than the 83.2 kN that the experimental specimen was subjected to. Strains and displacements obtained from the FE model were compared to experimental data, as discussed below. 5. Discussion of sagging Both sagging and hogging test results were compared with the results from the new elastic-plastic FE analyses. This section deals with sagging, described in more detail in [6]. Only elastic analyses were performed in [6]. In Fig. 5, the strain from strain gage 21, mounted at the middle of a deck longeron where the bending moment was the highest, is compared to the new FE results of the sagging test. This strain gage was mounted on the underside of a deck longeron, which is slightly less strained than the top of the deck longerons. In the nonlinear FE analysis, the specimen was first loaded to 60 kN and unloaded, and then re-loaded to 120 kN. The curves show a good match between the FE data and the test results. Equally good matches were obtained from other strain gages located on the (plastically deforming) steel longerons.
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Gage 21
FE analysis, loaded to 60kN then unload
FE analysis, loaded to 120kN
150
Load [kN]
100
50
0 -0.40%
-0.30%
-0.20%
-0.10%
0.00%
Strain
Fig. 5. Load–strain curves obtained from sagging test and elastic-plastic FE analysis. Gage 21 was located at the middle of a deck longeron where the bending moment was the highest. The load is the total load applied by the hydraulic jack.
Regarding strains measured by strain gages on bulkheads and on composite sandwich panels, there was no appreciable non-linear behavior. The same was true in the FE analyses. This suggests that the steel bulkheads remained elastic and that there was no damage even in the most highly shear-loaded composites side panels during the test.
6. Discussion of hogging After sagging loading up to 36% above the design load, the experimental hull model was turned over and loaded in simulated hogging. Plastic yielding was observed to initiate earlier than during the previous sagging tests, indicating that there is a Bauschinger-like effect, in particular in the steel longerons. The hull was repeatedly loaded up to the design load, after which the test was terminated. There was no indication of failure in any of the adhesive joints throughout the test, nor was there any indication of damage in any of the 60 composite sandwich panels. Fig. 6 shows the strain measured in strain gage 21 (see above), mounted at the middle of a deck longeron where the bending moment was the highest. The yield initiation loads in sagging and hogging were obtained as follows: the linear elastic part of the load–strain curves was obtained through a linear regression of the (elastic) unload portions of the test data. A line with 95% of the slope of the linear elastic part was drawn and the intersections of this line with the test data were defined as the yield initiation loads. This gave 56 kN in sagging and 24 kN in hogging, indicating a Bauschinger-like behavior. This is difficult to see in Figs. 5 and 6; however, the loads at 0.2% (absolute) strain differ as well. At 0.2% strain, the load in the sagging test was 86 kN while at 0.2% strain in the hogging test the load was 78 kN. Fig. 6 also shows the results of elastic-plastic FE analyses, which matched the test data very well.
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gage 21
31
FE analysis, loaded to 88.9kN
100
Load [kN]
80
60
40
20
0 0.00%
0.10%
0.20%
0.30%
Strain Fig. 6. Load–strain curves obtained from hogging test and FE analysis.
Regarding the steel bulkheads, there was no indication of nonlinear behavior during hogging either. The strains remained below 0.05%. The measured strains confirmed that the bulkheads deformed in an ‘‘S’’ shape, as also predicted by the FE analyses. The highest strains measured in the composites were in the side panels located in the highest shear load regions. The load–strain curves from both the test and the elastic-plastic FE analysis are straight lines, indicating absence of damage. There is a difference in slope between the experimental and numerical strains. The FE model utilized thin sandwich elements, which were non-symmetric but essentially loaded in their mid-planes. The sandwich panels in the experimental specimen were flat on the outside, whereas the sandwich core was beveled on the inside to create an edge around the panels with no core. This leads to a load offset in the panels, and subsequently bending due to in-plane loads. The inside and outside of the panels thus strained differently, as also seen from strain gages mounted on each side of certain panels. The experimentally measured strains were 5% and 9% lower, respectively, than the numerically calculated strains. Similar differences were also observed in the earlier sagging test [6]. It appears as if the stiffnesses of the composite panels were higher than those used for the numerical analyses. The stiffnesses of the composite had been determined experimentally using a vibration identification method [6]. With this method, there is a risk that the inhomogeneity of the glass fiber weave leads to an underestimation of the in-plane stiffnesses. The load–displacement curve measured from LVDTs mounted diagonally on side panels in the highest shear load regions also showed straight lines with no permanent deformation after unloading. These LVDTs indicated that the specimen was locally 4–7% stiffer than numerically calculated. There were residual strains after unloading in the composite deck and bottom panels located in the region with the highest bending moment. This was also observed in the earlier sagging tests [6]. These residual strains were not due to damage in the composite
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panels, but rather to yielding of the steel longerons to which the composite panels were bonded. Six newly mounted LVDTs measured the cross sectional deformation, and in particular the vertical displacement of the keel relative to the chine longerons. The maximum displacement was less than 0.5 mm, which is essentially negligible. Cross-sectional deformation was thus minimal. 7. Conclusion A hybrid ship hull model utilizing a steel truss, closed out with composite sandwich panels, was studied. A subscale model was tested under simulated hogging loads. The subscale model was loaded to the design load, at which point there was plastic yielding of the hull girder. However, there was no indication of any failure in any of the composite sandwich panels, nor in the bonds between the panels and the steel truss. Elastic-plastic behavior of welded stainless steel longeron subcomponents was investigated experimentally and numerically. Nonlinear elastic-plastic finite element analyses of the whole ship hull model were performed. Results from finite element analyses compared favorably with results from both sagging and hogging tests. The study indicates that a strong and lightweight ship hull could be made using this steel/composite hybrid concept. More studies will be performed in the near future to investigate how this hull concept stands up to extensive damage as well as fatigue. Acknowledgement This work was supported by ONR Grant N00014-03-1-0597, with Dr. Roshdy Barsoum as program manager. References [1] Barsoum R. The best of both worlds: hybrid ship hulls use composites and steel. AMPTIAC Q 2003;7(3):55–61. [2] Barsoum R. Hybrid ship hull. US Patent 6,386,131; 14 May, 2002. [3] Cao J, Grenestedt JL. Design and testing of joints for composite sandwich/steel hybrid ship hulls. Composites A: Appl Sci Manuf 2004;35:1091–105. [4] Thompson L, Walls J, Caccese V. Design and analysis of a hybrid composite/metal structural system for underwater lifting bodies. Department of Mechanical Engineering, University of Maine. Report no. UM-MACH-RPT-01-08, June 2005. [5] Cao J, Grenestedt JL, Maroun WJ. Steel truss/composite skin hybrid ship hull, Part I: design and analysis, submitted for publication. [6] Maroun WJ, Cao J, Grenestedt JL. Steel truss/composite skin hybrid ship hull, Part II: manufacturing and sagging testing, submitted for publication. [7] Masubuchi K. Models of stresses and deformation due to welding—a review. J Met 1981;33(12):19–23. [8] ABS. Guide for building and classing high-speed naval craft 2003, Part 3 hull construction and equipment. American Bureau of Shipping, 2003. [9] ANSYS. Version 9.0, Southpointe, 275 Technology Drive. Canonsburg, PA: Ansys Inc.; 2002. p. 15317.