the mechanics of carbon-foams and design of module supports for the atlas-upgrade inner tracker
Koral Toptop is a PhD student in the research group Energy, Materials & Systems (EMS). His supervisor is prof.dr.ing. B. van Eijk from the Faculty of Science and Technology.
This dissertation aims to create a solid knowledge base regarding design issues in the ATLAS Inner Tracker, and presents technical information to be used in the design of the detector support structures. Studies are primarily based on computations conducted on developed finite element analysis (FEA) models. Experimental studies have been performed to confront the computational results for some cases. Overall, this research deals with three topics related to each other. The first subject is to improve the ATLAS Petal design in terms of its radiation length. The second subject focuses on the fracture mechanics of graphitic carbon-foam and its micro-scale computational model. The results of this model is then used to derive a macro-scale i.e. continuum model for a carbon-foam. The third topic investigates the foam-tube structure —an essential element of the Petal in terms of cooling performance— regarding the structural risks, and checks whether any fracture may occur.
Currently, the Large Hadron Collider (LHC) is operating. It is planned to be shut down in 2019 for improvements, and reoperate with higher luminosities (i.e. collisions per unit time). New conditions brought a need for replacing the entire innermost subsystem of the ATLAS detector, the Inner Detector, with a far higher radiation tolerant construction. In addition, new construction should minimise multiple scattering of the charged particles and other particle-matter interactions to increase accuracy in the reconstruction of particle trajectories. Both requirements can be achieved by reducing the fractional radiation length %X0 of the detectors, detector supports and services. Since detectors and electronics are not very flexible to reconfigure, most of the effort to lower %X0 is focused on the design of supports. Reducing %X0 simply means using low atomic number materials, such as carbon, and minimising the amount of all materials used. At the same time, supports must be rigid to prevent detector motion which would deteriorate the precision of position measurements of particles, setting a lower limit to material reduction.
The thermo-mechanical support units carrying detector modules are known as Petals. The petal is a sandwich structure, made of high-modulus thin facings glued on both sides of a light core material. The petals cool the detector modules with evaporative CO2 flow in a tube surrounded by carbon foam and embedded in the Petal’s core. While the facings and the core are essential elements for the structural rigidity, the tube-foam structure and the facings are prime elements to cool detectors.
The petal design was reduced to a rectangular sandwich beam model in combination with composite theory, and its three-point bending stiffness was formulated. The formula was used to compare two different prepregs with two different angular configurations for the facings along with varying core shear properties. Fig. 1 gives the longitudinal bending stiffness of the sandwich beam versus core shear modulus.
The current petal configuration (Nikhef LoI design) uses facings made of 3 plies of a 80 gsm K13D2U/RS3 unidirectional prepreg laid up in [60/0/-60]o angles from the petal longitudinal axis, and Nomex honeycomb core.
The target is to improve the bending stiffness, while reducing weight to reduce the radiation length of the structure. The angular configuration was replaced with [0/90/0]o, which almost doubled the longitudinal bending stiffness. The improvement in the facing rigidity allows thinner facings to be used, therefore 45 gsm K13C2U/EX1515 prepreg was used. Core shear modulus has a diminishing contribution to the bending stiffness; therefore it is not the predominant factor in determining bending stiffness of the petal beyond a specific modulus. After about 70MPa shear modulus, there is little improvement for the recommended facesheet material (continuous red line). Therefore, Plascore Kevlar honeycomb was chosen as an available core material on the market offering a moderate modulus (about 70MPa) and a lighter structure.
A FEA model of the Nikhef Petal prototype (LoI-design) was developed, which predicts the bending stiffness and the lowest modal frequencies within 5% agreement with the measurements. Later, this model was applied to the petal designed by the DESY group (LTF-design, which is the actual product being used for the future ATLAS tracker) and used to evaluate improvements resulting from the above material recommendations.
The recommended configuration gives a significant reduction in mass of about 30 g, resulting in 16% improvement in the fractional radiation length for the base petal. Through the analyses on the petal with conditions for use in the ATLAS detector (i.e. with modules mounted and constrained to the End-cap frame), the lowest natural frequency was evaluated at 64 Hz in the longitudinal bending mode, with a 5% improvement.
Graphitic carbon foam is used to transfer heat from electronics mounted on the facings of the petal to the cooling tube. The thermal contraction of the tube will exert forces on the carbon-foam. Early oversimplified calculations predicted fracture in the foam, and mechanical damage in the tube-foam interface can have adverse impacts on thermal transportation through the structure and its long-term reliability. This brought a need for a detailed study of fracture mechanics of the foam, and a FEA model of the tubefoam structure to further investigate this issue.
A series of destructive tests were performed to study fracture mechanics of Poco-HTC graphitic foam in compression and shear cases. The destructive compression (crush) tests were carried out in both out-of-plane and in-plane directions of the foam to characterise anisotropy. These tests were filmed to visually examine crack initiation and propagation at macro-scale.
The initial failure mode is cell-wall bending fracture (called Mode-I) followed by propagation to nearby cells up to complete material separation. Fig. 2 shows the crack lines for both crushing tests. In the out-of-plane (z) crushing, the fracture plane propagates diagonally in both in-plane directions (x and y) with a slightly larger component in the out-of-plane direction. This is very close to the 45o crack line in typical brittle shear failure. In the in-plane (x) crushing, the propagation is horizontal in the out-of-plane direction (z), while it is around 45o diagonal in the in-plane transverse (y) direction.
In the shear test (zx), cracks appear in the foam out-of-plane direction, as cleavages. These cleavages are probably due to separation of graphitic layers as a result of shear forces, and propagate along the planes. These observations showed that alignment of graphitic planes affects the behaviour of macro-cracks.
Then, scanning electron microscopy (SEM) images of fracture surfaces were recorded to examine post-failure formation of material at micro- and meso-scales. The SEM images indicate that the cracks initiate at cell-walls, becoming cleavages between graphitic planes at the junctions. These separations propagate along the planes and spread to neighbouring ligaments.
In another series of tests, cyclic compressive loads were applied in the elastic regime to characterise the elastic behaviour, such as measuring Young’s modulus and elastic limits. Also, strengths were measured by subjecting some samples to continuous compression load up to destruction after the cyclic test.
Poco-HTC shows highly anisotropic behaviour in both the elastic and fracture cases. Measurements showed that the local fractures start at 3.0 and 1.5MPa, and strengths are 5.3 and 3.5MPa in the out-of-plane and in-plane directions. The Young’s modulus was measured 113 and 75MPa in the same directions. The shear strength is 1.8MPa, measured with the Iosipescu shear test.
A computational micro-model for the porous graphite foam was developed to reproduce measured behaviour. The aim of the research was to improve existing models by taking local anisotropy and material failure into account. A geometric model was obtained by taking a prolate spheroid bubble as the unit-cell, and placing many cells in an enclosed volume via computer script by targeting a certain porosity. The cell dimensions were selected to match measurements on various Poco-HTC samples. Thus, topological anisotropy and cell irregularity were accounted. The generated geometry was discretized to small elements, and material directions (alignment of graphitic planes) were defined in each to introduce local anisotropy to predict macroscopic anisotropy. Here, plane orientations at each elements were formulated based on the wall formation of the nearest bubble. Failure criteria for finite elements are included in the model to predict strength. In-plane loads and curvatures result in a static loading term in the plane normal direction. A factor (called static bending moment factor) directly proportional to this static term was used to model cell-wall bending fracture, Mode-I, for linear static analysis case.
Fig. 3 gives the stress-strain graph for the crushing tests and analyses. The analyses predicted stress-strain characteristics relatively close to the measurements in both directions. The predicted compressive modulus in the in-plane direction was smaller than the measured values, leading to a higher foam elastic anisotropy. The predicted strength values in both directions were in good agreement with the measured ones, suggesting that the failure model works for the compression case. Increasing the foam edge size reduces the micro-structural effects and gives a higher in-plane modulus, bringing the prediction closer to the measurement. Although the anisotropy model shows weaknesses in predicting bulk elastic anisotropy and failure responses, the method presented here sufficiently extends current foam models, and gives a good basis for future work. Failure analysis was performed with an external code due to computational limits. If the failure model can be used within the finite element model, this could improve prediction accuracy.
The elastic constants found from measurements and computations with a micro-scale foam model were used to construct a macro-scale continuum model of the foam. This continuum model was used in a thermo-mechanical FEA model of the tube-foam structure to evaluate if any fracture occurs. According to analysis for a 60oC temperature drop, the current configuration of the structure is not expected to fracture, and will reliably maintain the performance.
Fig. 1: Three-point bending stiffness versus core shear modulus in the panel longitudinal direction. Vertical dashed-lines correspond to available core materials of interest. Filled-markers indicate the current and recommended material configurations.
Fig. 2: Failure initiation and growth during compression tests (out-of-plane in upper row and in-plane in bottom row). The compression direction is from up to down. Stress and strain (ε) increase from left to right. Red dashed lines highlight the crack paths in the out-of-plane case; ovals highlight the material separation. Yellow dashed lines highlight regions of cell collapse in the in-plane case, which propagate sideways. Direction of the foam is given with x, y and z-axis at sides.
Fig. 3: Stress-strain graph for crushing tests and analyses, performed in both directions, i.e. out-of-plane or z-direction, and in-plane or x-direction. The foam is stiffer and stronger in the z-direction.
