CHAPTER 3 Properties/ Dimension This chapter presents the geometries of the beam and plate samples, as well as the materials used for both four point bending and Hydromat Test System scenarios. An overview of four-point bend test (ASTM C393-94) [24] and HTS (ASTM D6416-99) [29] experimental setups are also presented. The experimental results are used to validate the numerical models results. 3.1 Beam and Plate Geometries The sandwich beam and plate geometries used in the analytical solutions and numerical models are based on the sandwich structure geometries used by Rao [22] and Eyre [25] in their respective experimental works. It is important to use the same dimensions and material properties in the analytical and numerical models to achieve meaningful comparisons. 3.1.1 Sandwich Beam Geometry The geometry of the beam specimen considered is based on the beam geometry used by Rao [22] in his study of core compression using Digital Image Correlation (DIC). The sandwich beams used by Rao were manufactured by the Gougeon Brothers Inc. in Bay City, Michigan. This specimen has Aluminum 2024-T3 face sheets and Herex C70.200 cross linked PVC foam cores. The face sheets are bonded on the top and bottom 41
sides of the foam core using ProSet 125/229 epoxy. Figure 3.1 shows the dimensions of the beam specimen used. These dimensions are provided by the ASTM C393-94 test standard [24] for sandwich beam in four-point bending. Face Sheets t Core L* c h b FIGURE 3.1 Sandwich beam dimension used for four point bend test. From Figure 3.1: L* = 304.8 mm b = 76.2 mm h = 27.5 mm t = 1.016 mm c = 25.4 mm 3.1.2 Sandwich Plate Geometry The selection of the sandwich plate geometry is based on the specimen geometry used by Eyre [25] in his work verifying the HTS for sandwich panels. The panel chosen is fabricated by AIREX AG of Sins, Switzerland. The selected panel consists of Airex R63.50 open cell foam core and 3003-H14 aluminum face sheets. The 42
face sheets are bonded adhesively to the foam core by using Sempafix I-112, a polyurethane based epoxy. Dimensions of the selected sandwich panel are shown on Figure 3.2. b a Face Sheets c Core t h FIGURE 3.2 Sandwich plate dimensions used for HTS. From Figure 3.2: a = 609.6 mm b = 609.6 mm h = 26.76 mm t = 0.98 mm c = 24.8 mm 3.2 Properties This subsection presents the material properties used to model the four-point bend test and HTS load scenarios in both numerical and analytical models. In both cases, 43
face sheets of the sandwich structures are assumed to remain elastic throughout the analyses. Therefore, only core materials require a good post yield behavior descriptions. In both load cases, the face sheets are assumed to remain elastic at all time. Therefore only elastic material properties are required for the face sheets. The core materials undergo plastic deformation during the four-point bend and HTS experiments, hence there is a need to obtain a full description of the core materials behavior upon yield initiation. In this research a first-order idealized core material property module suggested by Mercado and Sikarskie [3] is used. This first-order idealized module, also called the bi-linear model, describes the material properties of the core with the stressstrain curve as shown on Figure 3.3. Generally, the elastic slope, labeled as E c0 on Figure 3.3, is much higher then the plastic slope, E c1. The relationship between E c0 and E c1 can be related by a material parameter, K pl, as below: E = K E c1 pl c0 (3.1) V σ 0 E c1 E c0 H FIGURE 3.3 Idealized stress-strain diagram. 44
3.2.1 Sandwich Beam Properties Both material properties of the aluminum 2024-T3 face sheets and Herex C70.200 foam core were obtained from Rao s [22] work. Aluminum 2024-T3 has high machinability and provides good surface finish. Aluminum 2024-T3 is often used in aircraft applications. Herex C70.200 is an isotropic and rigid foam material with high stiffness and strength to weight ratios. The materials in Herex C70 family have excellent chemical resistance and low thermal conductivity and water absorption. The appreciation of these inherent properties of Herex C70 materials makes this material a popular choice for the core materials of structural sandwich structures in marine and railway applications. The elastic material properties of both aluminum 2024-T3 and Herex C70.200 foam core are presented in Table 3.1. Comparisons between experimentally obtained material properties and published values are also included. The Poisson s ratio of Herex C70.200 is an average value determined by averaging the ratios of the transverse and longitudinal strain values throughout the tension test conducted by Miers [14] and reanalyzed by Rao [22]. The bi-linear stress-strain curve of Herex C70.200 is summarized in Table 3.2. These material properties are based on the DIC analysis data presented by Rao [22]. 45
Table 3.1 Comparisons of sandwich beam material properties Aluminum 2024-T3 Aluminum 2024-T3 Herex C70.200 Herex C70.200 Property Source Young s Modulus Poisson s Ratio Shear Modulus 0.2% Offset Yield Strength Strain at Yield Point (mm/mm) Rao [22] 72,400 0.33 27,218 346.215 0.006782 Handbook [26] 72,400 0.33 27,220 345 Rao [22] 180 0.37 65.69 2.554 0.0162 Manufacturer [27] 180 75 Table 3.2 Post yield material property of beam core material Herex C70.200 Property Source E c0 K pl E c1 Rao [22] 180 0.075 13.5 3.2.2 Sandwich Plate Properties properties for the sandwich plate face sheets are taken from material handbook [26], whereas the material properties for the foam core are provided by Rao [22]. Aluminum 3003-T14 is a type of aluminum alloy that has high resistance to corrosion and is easy to weld. The 3003-aluminum family is normally used in the production of cooking utensils, chemical equipments, and pressure vessels. Airex R63.50 has high fatigue strength, high three-dimensional formability, and high resistance to dynamic loads. s in Airex R63 family are widely used in the production of marine hulls and lightweight cars due to the appreciation of their low density and high strength and stiffness to weight ratio. 46
The elastic material properties of the 3003-H14 aluminum face sheets and Airex R63.50 are presented in Table 3.3. The material properties of Airex R63.50 were investigated by Miers [14] through tension test, and the data obtained was reanalyzed by Rao [22]. Table 3.3 also presents comparison between the experimental values and the material property values provided by the manufacturer of Airex R63.50. Comparison could not be made for 3003-H14 aluminum due to lack of experimental data. Post yield properties of Airex R63.50 foam core is again described by a bi-linear stress-strain module reported by Rao [22]. Table 3.3 Comparison of sandwich plate material properties Aluminum 3003-H14 Airex R63.50 Airex R63.50 Property Source Handbook [26] Young s Modulus Poisson s Ratio Shear Modulus 0.2% Offset Yield Strength 69,000 0.33 25,000 145 Strain at Yield Point (mm/mm) Rao [22] 37.5 0.335 14.05 0.637 0.0190 Manufacturer [28] 30 30 Table 3.4 Post yield material property of plate core material Airex R63.50 Property Source E c0 K pl E c1 Rao [22] 37.5 0.0175 0.65625 3.3 Test Scenarios To make sure that the analytical model and numerical models fully describe the load cases, it is useful to understand the actual experimental setup of the four-point bend 47
test and HTS. This subsection provides an overview and brief description of the test setups for the four-point bend test and HTS. Detailed descriptions of the experimental setups, including the test fixtures, instrumentation and data acquisition, can be found in work by Eyre [25], Ahtonen [23], Miers [14], Rao [22], and Chintala [20]. 3.3.1 Four Point Bend Test The schematic of the four-point bend test setup is shown on Figure 3.4. Bolt Loading roller Test specimen Center LVDT Cross head Fixture loading side End LVDT Supporting roller Fixture support side Hemispherical head Adaptor Load frame base 44.5 kn (10,000 lb) load cell FIGURE 3.4 Schematics of four point bend test fixture setup [22]. 48
The four-point bend test fixture has two main parts: the loading side and the support side. The loading side of the fixture is fixed to the load frame cross head. By moving down the cross head, the loading fixture transmits load through the loading rollers to the sandwich specimen, hence applying line load on the top surface of the specimen. The support side of the fixture is mounted on a 44.5 kn (10,000 lb) load cell. Above the load cell is an adaptor and hemispherical head that ensures that the support side and load cell are aligned. There are two linear variable displacement transducers (LVDT) used. One of the two LVDTs is located at the mid-span region of the sandwich specimen to measure the mid-span deflection during the test. The other LVDT is placed at the end of the specimen, aligned with the supporting roller in order to measure the local compression due to the supporting rollers. The displacement data gathered by the mid-span LVDT is used to compare with the measured sandwich beam mid-span deflections with those predicted using analytical models and numerical models. 3.3.2 Hydromat Test System Hydromat test system is divided into three parts: the upper panel support frame (UPSF), lower panel support frame (LPSF), and the hydromat bladder. The schematic of the hydromat test system fixture is shown in Figure 3.5. The upper panel support is made of fiberglass covered douglas fir laminate and has a shape of tetrahedron. This upper panel support frame was originally designed by Gougeon Brothers Inc. of Bay City and then fabricated by Rau [21]. The upper support frame is attached to a 133.5 kn (30,000 49
lb) load cell, which is mounted to a crosshead load frame. The lower support frame is made of steel and offers support from the bottom of the sandwich panel specimen. 133.5 kn (30,000 lb) load cell Upper panel support frame Sandwich plate specimen LVDT Upper and lower journal bearings Hydromat bladder Pressure transducer Bladder support slab Corner bolt Lower panel support frame Clamping bars Bladder support slab FIGURE 3.5 Schematics of hydromat test system fixture setup [25]. 50
Corner bolts are used to fasten the upper and the lower panel support frame. As the corner bolts are tightened, the upper and lower support frames move closer to each other. This pushes the upper and lower journal bearings closer to the sandwich plate and eventually providing simply supported boundary condition to the specimen. The four pairs of aluminum journal bearings are situated at the four edges of the base of the tetrahedron, at top and bottom of the sandwich specimen. These pairs of bearing, with appropriate tightening of the corner bolts, will constrain the edges of the panel in a simply supported state during the test. This forced simply supported edge constraint is a better emulation of the actual marine hull condition in water. It also enabled the use of the same simply supported boundary condition in all the HTS numerical simulations. The downward movement of the crosshead that holds the load cell pushes the test specimen against the hydromat bladder. This movement thus applies a distributed load on the lower surface of the specimen. The skin of hydromat bladder is made of two pieces of reinforced vinyl conveyer belt material. The two pieces of skins are clamped at its four edges by four pairs of steel clamping bars. Filled with approximately 17 Liters (4.5 gallon) of pressurized water, the hydromat has a flexible loading surface that can conform to the shape change of the sandwich panel specimen, hence providing normal distributed load to the specimen at all times. 51