Experimental investigation of thermal effects in foam cored sandwich beams

ABSTRACT

Polymer foam cored sandwich structures are commonly used in applications where mechanical loads and elevated temperatures form the normal service conditions. The temperature sensitivity of the mechanical properties of the polymer foam cores leads to compromised mechanical performance of the overall sandwich structure at elevated temperatures. So far this phenomenon has primarily been investigated using analytical techniques. The present paper provides a basis for experimental studies of the temperature sensitivity of sandwich structures through the design of a test rig that can simulate the mechanical and thermal conditions experienced in service. The sandwich structure is modelled as a simple beam specimen with the mechanical load introduced using a standard servo-hydraulic test machine. A fixture has been specially designed that can apply a variety of constraints. A through thickness temperature gradient is introduced to the beam via an infrared (IR) radiator applied to one face sheet. The rig is designed to accommodate non-contact full-field techniques. An infrared detector is used to obtain the temperature field and high resolution white light cameras to capture the displacement using digital image correlation (DIC). An arrangement of mirrors enables both the face sheet and through-thickness surfaces to be viewed. The paper presents the design and evaluation of the rig, together with initial data obtained from a PVC foam cored sandwich specimen with aluminium face sheets.

KEYWORDS: Sandwich structures, thermal degradation, model validation

INTRODUCTION

Sandwich structures with polymer foam cores have been used extensively in the marine industry, and are finding increased use in wind energy and civil engineering applications where the low weight to stiffness ratio and cost effectiveness for manufacturing large structures with complex shapes is advantageous. In many cases the service environment includes a large range of temperatures and often temperature gradients. Surfaces exposed to direct sunlight can reach temperatures in excess of 60°C [1], leading to large thermal gradients through the thickness. Many polymeric foams start to loose stiffness at such temperatures; in the case of a cross linked PVC foam this loss in stiffness could be as much as 15% of its ambient temperature stiffness, as shown in Fig. 1 for an Divinycell H100 PVC foam by DIAB [2]. Due to the sensitivity of polymeric foams to changes in temperature, such service conditions present a challenge to designers when predicting the load response of a structure over the full range of service conditions to be expected. The loss in stiffness of the foam core changes the overall nature of the mechanical response of the sandwich structure. Simulations of a beam in three point bending with a temperature induced through thickness stiffness gradient using an analytical model developed in references [3, 4], predict a change in the mechanical behaviour from linear to nonlinear when the stiffness gradient in the core exceeds a threshold value. This change in behaviour is not currently considered in any design codes but it may lead to a significant change in the failure mode of a structure and possibly unexpected catastrophic failures in service. However, before the model predictions can be applied with confidence in practice, experimental validation is required.

Fig. 1 Degradation of moduli with temperature for Divinycell H100 PVC foam from DIAB [2]

The present paper describes the evaluation of a test rig designed to validate the analytical model from references [3, 4] (a model based on higher order sandwich panel theory (HSAPT)). The HSAPT model has shown that sandwich beam response is very sensitive to the applied mechanical and thermal boundary conditions. Three specific mechanical boundary conditions have been identified that show an especially interesting load / deformation response, two of which are presented in the current work. The rig has been designed to accommodate the use of full-field optical measurement techniques to monitor the temperature and displacement / strain fields on the specimen surface. Infrared thermography (IRT) is used to obtain the temperature field and digital image correlation (DIC) to provide displacements and strains. Both techniques are also used to assess the validity of the thermal and mechanical boundary conditions.

MECHANICAL BOUNDARY CONDITIONS

The three mechanical boundary conditions that have been defined for this study are illustrated in Fig. 2 and comprise simply supported lower face sheet with horizontal movement allowed (Fig. 2 a) – referred to as SS-1, simply supported lower face sheet with movement restraints in both the vertical and horizontal directions, while being able to rotate about its mid-plane (Fig. 2 b) – referred to as SS-2, and simply supported lower face sheet as in SS-2 but with the addition of a horizontal constraint to the upper face sheet, allowing vertical displacement and rotation about its mid-plane (Fig. 2c) – referred to as SS-3. Nominal specimen dimensions of 500 x 50 x 30 mm (length x width x thickness) were specified, with a variety of face-sheet materials and thickness from 0.5 to 2 mm. An end fixture was designed that could be used to apply the mechanical boundary conditions whilst allowing optical access to the specimen. The end fixture is mounted in a 200 kN Denison Mayes servo-hydraulic test machine as shown in Fig. 3. Two large beams with a T-section groove are bolted, one to the actuator and one to the test bed, and provide the interface with the end fixture shown in Fig. 4.

The beam specimens are mounted on a platform that is free to rotate about a horizontal axis, across the width of the beam as shown in Fig. 4. The height of the platform relative to the axis of rotation is adjustable so that the rotation axis always passes through the mid-plane of the lower face sheet, thereby enabling the rig to accommodate face sheets of different thickness. For SS-1, the specimen rests freely on the platform. Lubricant is used to avoid frictional effects constraining the specimen in the in-plane direction. For SS-2, the lower face sheet of the specimen is extended by 25 mm on either side, allowing the lower face sheet to be clamped to the platform as shown in Fig. 4 a), thereby constraining the beam in the vertical and horizontal directions but allowing in plane rotation. The edge of the clamp has a radius to provide a gradual introduction of the clamping loads into the face-sheet and minimises stress concentrations resulting from the clamping force.

Fig. 2 Schematic of boundary conditions to be applied; a) SS-1, b) SS-2 and c) SS-3

For SS-3, the upper face sheet is also extended either side. Two vertical supports are mounted on bearings on the shaft of the lower platform (as in Fig. 4 b)). A platform to which the upper face sheet can be clamped is mounted on bearings in a similar manner to the lower platform. These bearings, however, are set in long holes to enable vertical displacement while constraining the face sheet in the in-plane direction. A combination of shims is used to adjust the height of the clamping surface relative to the axis of rotation to accommodate different face sheet thicknesses. A counterbalance is fitted to both platforms to ensure that the centre of mass is vertically aligned with the rotational axes so that no bending moment is applied to the face sheets by the fixture.

In the configuration for SS-1 and SS-2, the whole length of the beam can be viewed for DIC and thereby the surface strain field can be evaluated right into the specimen corners enabling effects of clamping to be assessed. In the configuration for SS-3, the ends of the beam are slightly obscured, however, because the geometry of the clamping surfaces is the same as for SS-2 the clamping effect does not need to be investigated in this configuration. Furthermore, all components of the rig can be imaged and therefore the rig itself can be assessed to exactly quantify the mechanical boundary conditions.

ASSESSMENT OF THERMAL BOUNDARY CONDITIONS

The HSAPT model is a two dimensional model in the formulation presented in [3, 4]. As such, it is assumed that the temperature across the width of the specimen is uniform and the steady state temperature distribution through the thickness of the specimen is therefore linear. Experimentally, the temperature gradient is achieved by heating the upper surface of the specimen using an IR radiator, while maintaining the lower face sheet at ambient temperature by means of forced convection. The finite width of the specimen, however, leads to a non-uniform temperature distribution across the specimen width. This was shown by initial measurements of the through thickness temperature profile, obtained from the side of the specimen using IR thermography which revealed a strongly nonlinear temperature gradient, as shown in Fig. 5. This is due to heat losses at the specimen sides.

Fig. 3 Experimental arrangement, a) test machine and b) end fixture

Fig. 4 Overview of end fixture configurations a) SS-2 and b) SS-3

Fig. 5 Surface temperature profile of a specimen with a 30 mm thick Divinycell H100 foam core and 1 mm thick aluminium face sheets (data from IR thermography – Expt and FEA surface)

To assess the internal temperature field of the specimen, a two dimensional finite element model of the specimen cross-section was created using PLANE55 (4 node rectangular elements) in ANSYS 12. Material conductivity values were obtained from the manufacturer’s data sheet for the foam [5] and from reference [6] for the aluminium. The heat flux through the top surface was adjusted to control the top surface temperature. It was found that to achieve a good correlation with the experimental data, the conductivity in the foam core needed to be reduced from 0.032 to 0.028 Wm"1K"1. This provided good correlation with the experimental data over a range of temperature gradients, as shown in Fig. 5, although the model consistently under-predicted the lower surface temperature. In this configuration, a temperature difference of approximately 20°C exists between the centre of the specimen and the free edges (sides) of the specimen. Considering the stiffness degradation curve of the Divinycell H100 foam shown in Fig. 1, this would result in a 35% variation in stiffness across the width relative to the specimen mid-plane stiffness. To reduce the width-wise temperature gradient, insulation in the form of additional PVC foam was fixed to both sides of the specimen during the heating process. Due to the space available the practical limit of the thickness of the insulation was approximately 25 mm. The addition of insulation to the sides enabled a higher temperature to be achieved and provided a through thickness profile much closer to the desired linear distribution, as shown in Fig. 5 where the surface measurement is compared with the FEA.

Fig. 6 shows the temperature distribution across the specimen width. Again, the temperatures derived from the model were compared with temperatures obtained experimentally. To obtain the internal temperature through the width of the beam thermocouples were installed within the specimen as shown in the insert in Fig. 6. To facilitate this, 2 mm diameter holes were drilled to a controlled depth in the specimen. K-type thermocouples were pushed into the holes until the hot junction made contact with the end of the hole. The agreement between the FEA model and the thermocouple measurements is good, although the internal temperature measurements were slightly lower than the model predictions. This could be attributed to the conduction of heat out of the foam block due to the presence of the thermocouple wires which have a significantly higher conductivity than the foam.

Fig. 6 Comparison between thermocouple and FEA data across the specimen width, taken 3 mm below the specimen surface;the insert shows the thermocouple placement in the specimen

To observing the foam core behaviour, the foam insulation must be removed from one side of the specimen to enable images to be collected from the specimen side for DIC. The rate of convective cooling at the surface was measured using IR thermography. This indicated that 10 to 15 seconds were available (depending on the initial temperature condition) in which conduct the test. Hence a relatively high displacement rate of 20 mm / min is required for a test to failure.

INITIAL TEST RESULTS

Initial tests were conducted for the SS-1 and SS-2 condition at four temperatures between 25 and 90 °C. In both cases specimens of 450 x 50 x 27 mm (span x width x thickness) were used with a 25 mm thick PVC H100 foam core and 1 mm thick aluminium face sheets. A constant displacement rate of 20 mm / min was applied at the mid-span. The load was applied via a 12 mm diameter steel roller across the width of the specimen and the temperature of the top face sheet was monitored during the heating phase via a mirror attached to the actuator as shown in Fig. 3. When a steady temperature was reached (this took approximately 40 minutes depending on the temperature condition) the IR detector was moved to image the specimen side, to monitor the rate of cooling during the test. Images of the central portion of the beam were captured using a LaVision Imager E-lite (5 MPx 12 bit CCD camera) from which the displacements of both top and bottom face sheets were calculated using DIC.

Fig. 7 shows the force vs. displacement curves for the SS-1 condition to failure. A clear loss in overall stiffness is observed, most marked in the 90°C case, as would be expected based on the thermal degradation curve shown in Fig. 1. A difference can also be observed in the gradient of the curves for the upper and lower face sheets for all temperature conditions indicating a compressive strain in the foam core. Interestingly, the difference is most marked for the 25°C case and least observable in the 90°C case. Failure was defined as the point where the load decreases. Two types of failure mode were observed. At room temperature and 50°C failure occurred as a combination of indentation of the foam core and interfacial failure between the foam core and the face sheet in the region immediately adjacent to the load application. At 70°C and 90°C the failure mode changed to indentation of the foam core and plastic deformation of the aluminium under the roller only. No debonding was observed at these temperatures. At failure, the 90°C case shows the largest difference between the upper and lower face sheet displacements, indicating the largest core compression.

Fig. 7 Force vs. top and bottom face sheet displacement for SS-1

The load vs. displacement curve for SS-2 is shown in Fig. 8 for the lower face sheet only. The specimen shows a slightly higher stiffness and failure load than the SS-1 case. The same trend of loss of stiffness can be observed as for the SS-1 case. The most significant difference between the two boundary conditions was the failure mode. For SS-2 all specimens failed by failure of the interface between the face sheet and the foam core. Only minimal indentation was observed, mostly of the face sheet although at the higher temperatures a slight impression was also left in the foam core.

CONCLUSIONS

Initial work has been conducted to experimentally validate the HSAPT model using full-field measurement techniques. The challenge has been addressed to meet specific therrmal and mechanical boundary conditions through the design of a bespoke end-fixture that enables full optical access to the specimen throughout the loading. A compromise was required in the form of obscuring one side of the specimen during heating in order to achieve the very demanding thermal boundary conditions resulting from the limitations of a two dimensional model. However, it has been demonstrated that this does not present an obstruction to obtaining the images so that full-field displacement data can be obtained.

Obtaining accurate predictions of the mechanical and thermal performance of such a test setup using, for example, FEA techniques, is prohibitively complex due to the large number of surfaces in contact and the inherent nonlinearity and potential for stick-slip phenomena this implies. Instead, the full-field optical techniques used to measure the specimen deformations have been employed to assess the performance and provide information that can be fed back into the HASPT. Thereby it is possible to perform a valid comparison between calculated and measured data, despite the physical limitations of the experiment and the conceptual limitations of the model.

Fig. 8 Force vers. bottom face sheet displacement for SS-2

Preliminary data has been obtained for SS-1 and SS-2 that indicates a distinct progressive softening that resembles the predicted behaviour found using HSAPT. Observation of the full development of a nonlinear load-displacement curve has not been possible in these initial specimens due to the face / core interface failure that defines the maximum load. Optimisation of specimen geometry and materials combination is currently in progress using the experimental techniques laid out in this work. Ongoing work is focusing on conducting a systematic comparison of SS-1, SS-2 and SS-3 measurements with HSAPT and nonlinear FEA model predictions.