6.2 Cure Cycle Optimization of 823-1 Laminates
6.2.1 Single Zone Optimization
The choice of the weighing factors as well as the constants of the individual ob-jective evaluation function is critical for the resulting optimal temperature cycle.
In this thesis, the values were chosen with consideration of the industrial back-ground of the case study in Chapter 7 and are shown in Table 6-2. All introduced individual criteria try to distinguish between a "better" and "worse" and compro-mises in-between different contradicting criteria are made in the summation to one final fitness value. However, the maximum resin temperature criterion has to be fulfilled and builds the upper limit of the temperature cycle optimization search. The weight loss investigation in Chapter 3 showed an increasing mass loss above 160 ◦C indicating thermal instability above that temperature and the maximum temperature criterion was set in accordance. Increasing laminate thickness lead to an increasing risk of temperature overshoot and, thus, thermal and degree of cure gradients within the curing laminate. This is especially the case for the resin system investigated with the reported high cure rate change with temperature. Each laminate can be perfectly homogeneously cured if the cure cycle time is elongated long enough. Thus, the objective of a cycle time restriction is the natural antagonist to the objective of a reduction in laminate
temperature and degree of cure gradients during the production of thick lami-nates. Hence, the cycle time restriction completely defines the optimization and only cure cycles of similar duration should be compared. The time restriction was thus set up to lead to similar cycle times as the standard cure cycle based on the manufacturer’s recommended cure temperature, which was used in the validation experiment (see Chapter 3). The chosen weighing factorωtrepresents the importance of the time criterion. Given that the part has to be close to fully cured within this time the corresponding weighing factorωfcwas raised as well.
Table 6-2Objective function constants and weighing factors for the optimization of 823-1 lami-nate manufacturing.
Constant Jfc JT Jgel J∆T J∆α Jt
Ai 1 1 1 1 1 1
Bi 1 1 0.618 1 1 1
Ci -3 3 140 6 6 6
Di - - -0.618 15 0.06
-Other: αult αmin Tmax Tmin - - - tmax tmin
0.95 0.9 175◦C 165◦C - - - 14000 s 12000 s
ωi 2 1 1 1 1 4
The target application for the optimized cure cycle is a part produced by a CFRP tooling. Hence, the thermal FDM model for the cure cycle optimization study in part thickness direction is required to feature not only the part, but also the tool material until the location of heat introduction, which is the middle plane of the tooling shell. Due to the low transverse conductivity of the CFRP tool, this 5 mm tool material between heat introduction plane and curing part surface effectively acts as an additional insulation layer and, thus, has a significant impact on the temperature evolution within the part since cure cycle target temperature does not equal part surface temperature. Consequently, the FDM model for the optimization study includes 5 mm CFRP tool laminate between the temperature boundary conditionsTset−pointand the curing part’s surface at the top and bottom side, as shown in the sketch in Figure 6-4.
The target application for the optimized cure cycles features varying part lam-inates thicknesses of up to 30 mm in the CFRP section and up to 15 mm in the GFRP spar. Three thicknesses were investigated for both material combinations.
The material models of Chapter 3 were used to model the evolution of material properties of the CYCOM 823-1 resin system. The curing laminate’s fiber prop-erties are given in Table 3-11 for the HTS40 carbon fiber and in Table 6-3 in case of the S2 glass fiber. Given the stochastic nature of the genetic algorithm as well
Laminate CFRP tool
CFRP tool
5 mm
5 mm
Varying laminate thickness and material (HTS40 carbon fiber, S2 glas fiber) Part surface
Part center
Tset-point(t)
Tset-point(t)
Figure 6-4Sketch of the FDM temperature cycle optimization laminate set-up.
as the complexity of the search domain, the global optimum is not guaranteed to be found by each run. Therefore, 25 optimization runs were conducted for each thickness and material combination.
Table 6-3Properties of the S2 glass fibers [20].
Mechanical properties Thermal properties
E 93.8 GPa ρ 2488 [kg/m3]
ν 0.23 k 1.45 [W/m/◦C]
CTE 1.6E-06 [1/◦C] cp 737 [J/kg/◦C]
In Figure 6-5, the resulting laminate surface and center evolution of temperature and degree of cure for the CFRP set-ups (see Fig. 6-5 (c), (e) and (g)) and GFRP set-ups (see Fig. 6-5 (d), (f) and (h)) with optimized set-point temperatureTset−point
are shown. The results of the thickest set-ups, 30 mm in case of CFRP and 15 mm in case of GFRP, with the standard temperature cycle base on the manfucturer’s recommended cure temperature applied are shown for reference in Fig. 6-5 (a) and (b).
Naturally, the thickest laminate featuring 30 mm CFRP showed the highest tem-perature overshoot with an optimized temtem-perature cycle and, thus, was the most critical case regarding thermal and degree of cure gradients. The optimized cure cycle for this laminate is therefore discussed in detail in the following (see Fig. 6-5 (c)).
a)
Time [s]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
0 2000 4000 6000 8000 10000
Temperature [°C]
Figure 6-5Standard (a-b) and optimized (c-h) cure cycle of the HTS40- and S2-laminate for different thicknesses.
The optimization results of the 30 mm CFRP laminate in Figure 6-5 (c) showed, that no gradient-free temperature cycle is possible for the contemplated cycle time of ∼10000 s in combination with the material thickness. The optimal tem-perature cycle found is defined by several trends: an elongated dwell time at a relatively low temperature of 99◦C, which lasts for half of the total cure cycle time. This temperature acts as a limit for a controlled cure reaction, in which the transport effects still dominate the temperature profile in thickness direction.
Hence, the exothermic reaction energy can still be transported into the tool lead-ing to low temperature and degree of cure gradients at this stage. Thus, the more energy is released at this temperature the more energy is taken out of the system and the lower will be the final temperature spike in the middle of the laminate at the end of the cure cycle.
At the end of the first dwell at 5100 s, the temperature deviation between surface and center is 3.4◦C and the following second ramp is chosen to increase the part surface temperature to part center temperature. This enables a close to uniform cure until the point of gelation at 6200 s, where the degree of cure deviation between part laminate center and surface is ∼ 3%. This time also indicates the starting point of a significant increase in center and surface temperature devi-ations up to ∼ 8◦C compared to set-point value at 7900 s. As the temperature and degree of cure deviations between center and surface at this time are getting too large, the tool surface temperature is subjected to a steep temperature ramp resulting in higher heating rates in the part’s surface than in the center of the laminate. This steep heating ramp results in a decrease in the degree of cure gradient. The higher the final temperature level of the third dwell is elevated, the lower the resulting degree of cure gradients. However, higher final dwell temperature also lead to elevation of the final laminate center temperatures, which are required to stay below 160◦C due to thermal stability reasons. The final dwell temperature of 139◦C leads to laminate center peak temperatures of 153◦C, which is well below that threshold. The maximum values for the peak temperature, thermal and degree of cure discrepancy between laminate center and surface for this optimized temperature cycle in comparison to the cure cycle based around the manufacturer’s recommended cure temperature is presented in Table 6-4.
Table 6-4Numerically determined overall improvement of optimized cure cycle for a 30 mm CFRP laminate.
Fitness value time [s] Tmax[◦C] ∆maxT[◦C] ∆maxα[-]
Std. cure cycle 7.22 10900 175.3 33.9 0.354
Opt. cure cycle 0.445 10240 152.7 8.0 0.138
Although this optimized cure cycle does lead to gradients in temperature and degree of cure as well as a final temperature overshoot, it significantly reduces these gradients as well as the final temperature overshoot in comparison to the standard cure cycle, given in Figure 6-5 (a). The optimization shows, that for the 30 mm carbon laminate the projected cycle time is not sufficient if a close to gradient-free cure is targeted. If smaller gradients or lower final temperatures are required in the 30 mm carbon fiber laminate, the overall cycle time has to be increased.
The optimization of CFRP with lower thicknesses as well as GFRP laminates, shown in Figure 6-5 (d) to (h), follows a similar trend and general explana-tion to the ones presented in detail for the 30 mm laminate, albeit with more homogeneous results thanks to more prominent transport effects in thickness direction apparent in thinner laminates. Gelling occurs in all optimized cycles in the second dwell stage.