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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