Interface temperature T and process time t p

The temperature T with time of the skin-to-core interface during processing is of major importance as it allows prediction of polymer mobility which enables polymer flow to achieve intimate contact and interdiffusion. Therefore, prediction of temperature evolution at the interface is necessary in order to determine the process time tp as well as to supply input for reptation time Tr and the viscosity η in Equation 14 and Equation 15. Both are highly dependent on the process temperature.

To describe the heat transfer from the heated skins into the foam core a simplified non-isothermal heat transfer model is used. The model is based on the manufacturing process which is schematically illustrated in Figure 45. Here, the focus lies on the heat transfer from skins into the core by means of heat conduction.

Figure 45: Non-isothermal compression moulding process This process contains the following steps:

Heating: The skin is placed on a transfer plate and heated in an oven until it reaches the pre-determined skin pre-heat temperature TSkinpre-heat.

Transfer: Skin and transfer plate are transferred into the press and integrated into a male mould. The transfer takes around 10 - 15 seconds and the heat loss during transfer is

~1.5 °C/sec. Pre-trials showed that the application of a transfer plate is necessary to reduce loss during transfer (more details in chapter Fehler! Verweisquelle konnte nicht gefunden werden.).

Pressing: The cold or pre-heated core is already positioned in the female mould which is installed on the upper press platen. Once transfer plate and skin are integrated into the male mould, the mould is closed and pressure is applied.

In this process the temperature evolution at the interface TInterface is mainly dependent on the skin pre-heat temperature TSkin pre-heat, transfer plate pre-heat temperature TTransfer plate, core temperature TCore as well as on temperatures of the periphery (e.g. press). The temperature evolution of the interface TInterface can be described dependent on the time t and the location (x,y,z) by applying a non-isothermal heat transfer equation [181].

𝜌𝑐𝜕𝑇

where λ is the thermal conductivity, ρ the density, c the specific heat capacity and Φ''' the heat generation (e.g. exothermal reactions). Equation 18 can be simplified for a two-dimensional case and without the additional heat generation to:

ρc∂T

∂t = [∂

∂x(λ∂T

∂x) + ∂

∂y(λ∂T

∂y)] Equation 19

The finite difference method is implemented to solve the numerical approach, where the derivatives are substituted by differential quotients. This leads to:

𝑇_𝑚+1,𝑛^𝑖+1 − 2 𝑇_𝑚,𝑛^𝑖+1+ 𝑇_{𝑚−1,𝑛}^𝑖+1

(∆𝑥)² +𝑇_𝑚,𝑛+1^𝑖+1 − 2 𝑇_𝑚,𝑛^𝑖+1+ 𝑇_{𝑚,𝑛−1}^𝑖+1

(∆𝑦)² =ρc

λ

𝑇_𝑚,𝑛^𝑖+1− 𝑇_𝑚,𝑛^𝑖

∆𝑡

Equation 20 where 𝑇_𝑚,𝑛^𝑖+1 is the temperature for the time point i+1 after the time step ∆t. ∆x and ∆y are the distances between two nodes, which are labelled with m und n (refer Figure 46).

Figure 46: Arrangement of elements and nodes

Reordering Equation 20 leads to the energy balance equation of every node 𝜆 ∆𝑦

∆𝑥 (𝑇_𝑚+1,𝑛^𝑖+1 − 𝑇_𝑚,𝑛^𝑖+1) +𝜆 ∆𝑦

∆𝑥 (𝑇_{𝑚−1,𝑛}^𝑖+1 − 𝑇_𝑚,𝑛^𝑖+1) +𝜆 ∆𝑥

∆𝑦 (𝑇_𝑚,𝑛+1^𝑖+1 − 𝑇_𝑚,𝑛^𝑖+1) +𝜆 ∆𝑥

∆𝑦 (𝑇_{𝑚,𝑛−1}^𝑖+1 − 𝑇_𝑚,𝑛^𝑖+1) =1

𝜏(𝑇_𝑚,𝑛^𝑖+1− 𝑇_𝑚,𝑛^𝑖 )

Equation 21

with

𝜏 = ∆𝑡

∆𝑥 ∆𝑦 𝑐_𝑝 𝜌 Equation 22

A relation between the individual energy balances of every volume element is achieved by the multiplication of a coefficient-matrix 𝐴 and the temperatures

∆

∆ m+1, n

m, n-1 m, n+1 m-1, n m, n

b = standards width

5 Process development 69 __________________________________________________________________________

𝑨 × 𝑻_𝑖+1= 𝑻_𝑖. Equation 23

In order to reduce the modelling extent, the following assumptions are taken into account:

• Skins and transfer plate are uniformly heated in a convection oven

• The core is kept at room temperature or heated up uniformly

• Skins and transfer plate cool down ~20 °C during transfer from the oven into the press (driven by convection and emissions)

• The model is effective after the press is closed and press platen, transfer plate, skin and core are in full contact.

• From here TSkin is referred to as the temperature of the skin in the press

• The model is implemented for one skin and the core up the core centre (mirror-line) because of the symmetric setup

• Heat loss to the environment at the periphery of the skins is neglected since the area of the skins is much larger than the thickness of the skins and transfer plate

• After several repetitions of the process, the press surface will warm up. This influences the heat transfer and might influence the bond strength development. However, for this study it is neglected and the surface press temperature is assumed to be at room temperature for every trial.

• Material properties (specific heat capacity, density, heat conductivity, etc.) are considered to be constant for a material phase

• The core area adjacent to the skin collapses at temperatures above Tg(PEI) and from then material properties are considered to be valid for a bulk PEI material

• The periphery is considered to be adiabatic

Figure 47 displays the manufacturing setup for the implementation of the heat model, with

• dx = node distance in x-direction

• hP = Height of press

• dhP = Node distance (Press elements)

• hT = Height of Transfer plate

• dhT = Node distance (Transfer plate elements)

• hS = Height of Skin

• dhS = Node distance (Skin)

• hc = Height of core

• dhc = Node distance core (Core)

• dhc,small = Node distance (Core, when compacted)

The values for the dimensions as well as material properties for the press, transfer plate, skin, core and compacted core material are given in Appendix A.

Figure 47: Discretisation of manufacturing setup

By formulating the energy balance for every element, the input of the boundary conditions and material data in Appendix A, Equation 23 can be solved and the temperature evolution with time at the interface predicted.

Experimental trials are conducted to validate the heat transfer model results. Thermocouples (Typ K, GG-KI-36-SLE-(*), Ø = 0.13 mm by Omega Engineering, Germany) are integrated into the skins, below the core surface (~1 mm below the core surface) as well as into the core centre (~2 mm – ~5 mm) and the temperature evolution of skins, core surface and core centre is recorded, see Figure 48. Due to the wire diameter and the manual integration, a hundred percent exactness of positioning cannot be assured, which can lead to deviations.

Figure 48: Integration of thermocouples to monitor heat flow from skin into core Core

Skin

Transfer plate Press

Thermocouples

~ 5 mm

~ 3 mm

~ 2 mm

Core Skin 1 mm below surface

Centre line

5 Process development 71 __________________________________________________________________________

Figure 49 shows a comparison of the predicted (dashed lines) and the experimentally determined (solid lines) temperature evolution for the skin, the core just below (~1 mm) the surface as well as for the core centre at different core depths. For purpose of simplification, the illustration of temperature evolution of the transfer plate and the periphery is omitted. The skin is pre-heated in an air-circulating oven to a temperature of 330 °C (TSkin pre-heat). The core is kept at room temperature. As the model is valid after the press is closed (see assumptions), where all parts are in close contact, the prediction starts with a temperature of 310 °C for the skin (TSkin). The temperature difference is related to the heat loss during transfer from the oven into the press, which is neglected in the model.

Figure 49: Temperature evolution (predicted and measured) of skin and core (at different core depths) for TSkin = 310 °C and TCore = 23 °C

Figure 49 shows that there is a reasonable agreement between predicted and measured temperature evolutions. Slight deviations between predicted and measured temperatures can be attributed to the assumptions (adiabatic periphery, material properties) in the model and inaccuracy of the thermocouple location. The higher starting temperatures of the measured temperature graphs can be explained by the heat conduction from the skin into the core before the press is fully closed. The unsteadiness of the predicted temperature profile of the core during the heating phase can be ascribed to the change of material properties between solid and softened aggregate state as well as core compaction which is considered by a change of the cell size in the model.

Since only the temperature evolution of the interface is relevant for the bond strength prediction, further temperature evolution graphs are simplified with focus on temperature

0

evolution of the skin and interface, see Figure 50. Here, the interface temperature is defined as an average temperature of skin and core surface temperatures.

In order to ensure correctness and reproducibility of the results, temperature measurements have been conducted multiple times and deviations during processing are determined, which are displayed with the red bandwidth in Figure 50. Except for the difference of the starting temperatures (caused by heat conduction from the skin into the core before the press is fully closed) the predicted temperature profile conforms to the measured temperature profile. A satisfying agreement between the temperature evolution prediction and measured temperature evolution is achieved. Therefore, the predicted temperature evolution depending on the skin and core temperature is used to supply input for the process time tp in Equation 14 and for the reptation time Tr (see following section) in the fusion bond modelling approach.

Figure 50: Skin and interface temperature evolution (predicted and measured) for TSkin = 310 °C and TCore = 23 °C

Im Dokument Thermoplastic composite sandwiches for structural helicopter applications (Seite 80-85)