Generating a Closed Simulation Chain for Hot Forged Aerospace Components to Optimize Fatigue Behaviour
H. Maderbacher1, M. Riedler2, B. Oberwinkler1
, H. -P. Ganser3, W. Tan1
, W. Eichlseder1
n Chair of Mechanical Engineering ,Montanuniversitiit Leoben, Franz-} osef-Stra[Je 18, 8700 Leoben ,Austria 2 > Bohler Schmiedetechnik GmbH&Co KG ,Mariazellerstra{Je 25, 8605 Kapfenberg ,Austria 3 > Materials Center Leoben Forschung GmhH ,Roseggerstra{Je 12, 8700 Leoben ,Austria
The general comprehension concerning tailor-made lightweight airplane components has changed and new standards were introduced in recent
years. Today, it is not only essential to find the best suited material with the best possible mechanical properties, but also the local material be
haviour must show optimal performance. Furthermore the design has to be observe the flow of force and keep the stress concentrations as low as
possible whilst minimizing the weight at the same time. In addition, it is necessary to select the surface treatment such that advantageous topo
graphical properties and residual stresses arise. So the design of components is no longer just the result of the subjective sensation of the desig
ner, but should become the end product of a well-defined optimization process. The present work depicts the possibility of optimizing heavy duty
aerospace components made of hot-forged titanium alloy with respect to their fatigue strength, regarding the entire design and manufacturing
process. To create these optimized components, an integrated optimization chain is proposed encompassing component design, manufacturing, and
strength evaluation. This chain comprises topology or shape optimization delivering the optimized geometry at minimized weight for the available
design space at defined loads. The core of the simulation chain is the forging and heat treatment optimization with respect to the fatigue strength
distribution in the component. To this purpose, the forging and heat treatment simulation is linked to an optimization tool which adjusts the local
microstructure such that the fatigue endurance is maximized. In the last step the component.optimized in terms of geometry and microstructure,
is subjected to a lifetime estimation. Here, in order to calculate damage or critical crack size, influence factors like stress amplitudes and mean
stresses (determined by finite element analysis) as well as the surface finishing are considered.
Keywords,Optimization,fatigue,simulation chain ,forging, Ti6. 4
1. Introduction
It is a matter of common sense that, for any prob
lem, the more detailed information is available, the bet
ter are the chances for finding the optimum solution. In
the case of the design and safety assessment of compo
nents against fatigue, the basic data to be known are
the local fatigue resistance of the material and the local
stresses due to the loading in service. However, by a more detailed comprehension of the complete system,
much more can be achieved than just a durability esti
mate. During the design process, each detail of the com
ponent can be tailored to the later demands in service.
From the force flow, stresses and distortions effected
by the loads,a geometry can be found that offers maxi
mum stiffness at minimum weight at the same time.
Moreover, the local material properties evolve during
the manufacturing process; so there lies an obvious op
timization potential in controlling the manufacturing
process so that the required material properties are at
tained throughout the component, and especially so in
the critical points of the structure. Finally the finishing process can be controlled in a manner that also residual
stresses and roughness have a positive influence on the fatigue behavior. An integrated simulation and optimi
zation chain for an engine mount link, a typical struc
tural aerospace component, can be seen in Figure 1. In
the initial step of the chain the design space of the com
ponent is re-defined iteratively by the use of topology
optimization to obtain the geometry with the ideal force
flow for a given load. In the following step the material
properties at the critical points have to be improved.
For this purpose the forging and heat treatment process is optimized, for which a process dependent mi
crostructure modelt> and a microstructure dependent
fatigue mode!2·3> are required. Subsequently, the param
eters for the finishing processes like turning, milling,
shot peening or rolling are chosen in a way that there is
no disadvantageous residual stress· or roughness in the critical regions. Finally, a fatigue assessment is carried
out using the stress results from the finite element analysis of the geo~etricafly optimized component, the
optimized microstructure from the forging simulation, the optimized surface conditions and the given load
spectrum. Experimental verification is performed by rig
testing.
2. Topology Optimization
To get the optimum geometry with respect to
stresses and weight, a topology optimization is conduc
ted. The schematic workflow of such a topology optimi
zation of the engine mount link with the software To
sca TM is shown in Figure 2. Figure 2, upper left, depicts
the unmachined forging serving as the design space. In
the design space the boreholes and surfaces which are
essential for the interface to the neighboring components are frozen to stay unchanged, while the remaining
geometry is varied throughout the optimization. The
forces are defined in accordance with the EASA air
worthiness certification specifications4> ; they consist of
thrust, inertia loads through turbulences, and cross
wind loads. The optimization objectives of the current
• 1966 • P roceedings of the 12'h World Conference on Ti tanium
De ign Space Topology Op1imiza1ion Geometry
Verification M icrostructure
Fatigue Assessment tress Calculation
. Bo~aP ·'.~ 1 ,. ; I~ ~ • •
Figure l. Simulation and optimization chain fo r hot-fo rged ae rospace components
Design pace Optimization FE Results
t: "' Vi l~lnput :
geometry, loads, boundaries
O utput : minimized weight , maximized stiffness
Comparison with Standard Part Deta il ed Des ign Proposed Geometry
Figure 2. Topology optimization
case are maximum stiffness at minimum weight, wi th an additional boundary condition given by the admissible stresses. For the tress analysis the finite element ( FE) package Abaqus™ is used; the FE results are subsequently evaluated by the topology optimization tool T osca™. This tool detects the elements which are nearly unloaded and assigns an elastic modulus and a density of zero to them , thereby modifying the structural properties of the component before re-submitting the component for FE analysis. This procedure is repeated until the desired weight is achieved while keeping the stiffness reduction as small as possible.
Figure 2 , upper right , shows the von Mises equiva-
lent stress after T osca™ has eliminated 40 % of the volume of the initial design space. T he proposal for the best geometry from the topology optimization can be seen in the picture below. On the basis of thi s proposal , a mount link wi th a geometry sui table for machining is designed and finally machined from the raw forging. The improvements resulting from the structural optimization are depicted in Figure 2 , bottom left; the final design has 10 % less weight while the maximum stresses under loading are reduced by approximately 20 % .
3. Forging Simulation
As the critica l loca tions for failure are known from
9. Aerospace Applications 1967 •
the FE ana lysis, it is important to ensure that the fatigue strength of the material is as high as possible a t
these locations exactly. The fat igue strength depends on the microstructure, whi le the microstructure itself is influenced by the forging and hea t trea tment process. Optimizing the fa tigue s trength therefore means optimizing the forging and hea t trea tment process. As the detai led investigation of the mount link forging is still in progress , the forging optimiza tion of a turbine disk made of lnconel 718 is regarded subsequently instead; th process is shown schematica ll y in Figure 3. The turbine disk is forged in 20 single steps by die fo rging because of the high demands in terms of fat igue behavior. Special parameters like initia l billet temperature,
severa l die speeds , rehea ting tempera ture or resting times between the single forging steps are allowed to be changed in a certain range depending on the forging
process window. Before attempting to optimize the fatigue strength of a forged component , a microstructure model has to be crea ted first which is able to predict the microstructure as a function of the many different quantities influenced by the forging process. T his microstructure model ll was implemented in the FE package D -form TM . Furthermore a microstructure-dependent fat igue model has to be found to estimate th material's S/ curve for an arbitrary microstructure5>. As an objective function for the numerica l optimization the inverse of the fa tigue strength was chos n to be minimized.
Standard Forging Process Microstructure Optimization
(IE1)•101
ObjF11c = -==---LS .. ,, Optimized Fatigue trength
lgc
lgN
process. design _.,,.... Input forg ing ~ variables DAKOTA ·~ Output max11rnzed
- .-~
fa ti gue strength at cnt1 ca l area •
Optimized Forging Parameters
I= Surrogate baMtd
optimiution
'·
r .. ....
Figure 3. Forging process optimization
The FE solver Deform TM was link d to the open
source optimization too l Dakota TM to optimize the forg
ing process. The present forging process consists of 7 variable parameters whose va lues have to be selected in a way that they result in advantageous fat igue properties. The challenge is now to find an appropria te opti
mization strategy which is not only able to find a loca l minimum but also the global one whi le having a high
convergence rate for acceptable computational cost. Generally, the number of variables, the smoothness of
the objective function, the numerica l noise and the com
putational effort per iteration depend on the choice of the optimization strategy. Gradient based as well as gradient free methods were investigated for the forging optimization. Either because of the large number of
variables or due to an unfavorab le choice of the start
values , the gradient based methods as well as other deterministic loca l methods did not produce satis fying re
sults. On the one hand, stochastic optimization strategies like evolutionary or genetic algorithms were able to find the vicini ty of the global minimum and showed a
high convergence rate at the beginning ; however, the
convergence rate decreased rapidly as the near-opti
mum values were approached.
Therefore, the best compromise between the se-
cure finding of the global minimum and rapid convergence was obtained by using a surroga te-based global optimization method6
' . In the present case thi method gives the randomized parameter set for 300 forging simulations by the aid of Latin hypercube sampli ng. 300 simulations seem to be very much but thi s is , in fact ,a moderate number for a set of 7 variables to b
optimized. In the next step a response surface is gener
ated for these 300 simulations such that the true points
(the simulation resul ts) are reproduced with the smallest variance possible. The virtua l optimizer then works
on this response surface , where the computational ef
fort is low. After the optimizer has made a proposal for the minimum on the response surface , a new forging simulation is sta rted with this parameter set. The ca l
culated objective is subsequently added to the set of the
300 true points. On this set of 301 true points, a new response surface is generated and the whole cycle is re
peated. By means of this strategy the global minimum can
be reached within 6 iterations after the sample for the first response surface has been created. As thi s sample is once
created it can be u ed for all subsequent optimization runs,
so a total of only 306 FE simulations ar necessary. In this
way, a fatigue strength increase by 15 % compared to th
result of the initial forging proces i obtained.
• 1968 • Proceedings of the 12'h World Conference on Titanium
4. Fatigue and Damage Tolerance Assessment
As the stresses resulting from the acting loads are already known from the FE calculations, exact knowledge about the frequency and the sequence of these loads - the load spectrum - is essential for the fatigue assessment. Load spectra for each of the acting loads were generated for mean stresses as well as for stress amplitudes in accordance with proposals from literature7' . By knowing the local microstructure and the ( microstructure-dependent) local S/ N curve in each
Stress Results Material
point, the stresses from the FE analyses, and the load spectra, the resulting damage or the admissible size of
local surface flaws can be calculated. For this purpose the postprocessor BoFaP (Boehler Fatigue Postprocessor) has been developed8
' , which is able to import stress results from AbaquslM or NastranlM as well as microstructure results from DeformlM(Figure 4). With these data, the spatial distribution of fatigue damage or of the admissible flaw size is obtained and can be visualized in the Abaqus 1M or Nastran 1M viewer. The fatigue
strength calculation is verified by component tests.
, .. t.__'_~_"_-_-_·_ ..
Surface Finish ~ ~
Damage ...
Load Spectrum
Load Spectrum I flight
Figure 4. Fatigue assessment
5. Conclusions
An integrated simulation chain for hot-forged titanium and Inconel aerospace components comprising design optimization, manufacturing process optimization and fatigue assessment has been developed. This chain consists of a topology optimization to get a geometry which is very stiff and lightweight at the same time. The next step is the numerical optimization of the forging process in order to obtain a microstructure with maximum fatigue strength in the critical locations. The influences of residual stresses and roughness caused by the forging and finishing processes will be regarded in more detail in future work. As the last step of the simulation chain, the postprocessor BoFaP has been developed for the fatigue and damage tolerance assessment of arbitrary hot-forged titanium and lnconel components, offering a unique capability of a fatigue and damage tolerance assessment by means of microstructuredependent fatigue models and direct result input from
forging simulations.
Acknowledgements Financial support by the Austrian Federal Govern
ment and the Styrian Provincial Government, represented by Osterreichische Forschungsforderungsgesellschaft
mbH and Steirische Wirtschaftsforderungsgesellschaf t mbH, within the research activities of the KZ Compe-
tence Centre on "Integrated Research in Materials, Processing and Product Engineering", operated by the Materials Center Leoben Forschung GmbH under the
frame of the Austrian COMET Competence Centre Programme, is gratefully acknowledged.
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