Advanced Thermal Mechanical Fatigue Life Simulation of ... · 2004 ABAQUS Users’ Conference 789...

2004 ABAQUS Users’ Conference 789

Advanced Thermal Mechanical Fatigue Life Simulation of Cylinder Heads

F. Zieher*, F. Langmayr, A. Ennemoser, A. Jelatancev, G. Hager, K. Wieser

AVL List GmbH, Graz, Austria

The demand for increased power and reduced emission levels for high-powered combustion engines, along with the reduction of development time, requires the deployment of advanced simulation methods in the engine development process. Thermal mechanical fatigue failure of cylinder heads, pistons, and exhaust manifolds has become one of the critical failure modes. This paper describes the deployment of a complete and advanced simulation process to predict thermal mechanical fatigue life for standardized engine test programs. It discusses the applications of viscoplastic material models for describing the complex material behavior of standard cylinder head materials such as cast iron and primary and secondary aluminum alloys. Finally, the deployment of different fatigue life models is addressed and an example of a fatigue life simulation for a cast iron cylinder head is shown.

1. Introduction

The demand for high power output for automotive engines has never been stronger than in today’s competitive engine business. The four-valve design has become the state of the art valve arrangement for passenger car and commercial engines from performance and emission point of view. The power output per liter has been increased to 65 kW/l for diesel engines and at the same time the peak firing pressure reaches levels of 170 bar and beyond for aluminum cylinder heads and 200 bar and beyond for commercial truck engines.

The common cylinder head materials for passenger car engines are aluminum alloys in various compositions, casting technologies and heat treatments. Cast iron in form of laminar or compacted graphite iron (CGI) are the most commonly used cylinder head materials for the commercial truck application.

In order to validate the engine design for the desired application and load profile, various durability tests are performed during the engine development program. For obvious reasons, those tests are positioned rather late in the development program after the performance and emission development steps are finished. Such durability tests range from 500 hours to 1000 (2000) hours for passenger car application and commercial truck engines, respectively. Considering the duration and the cost of each of these tests, it is of tremendous importance that the design has been thoroughly analyzed by simulation in order to minimize the risk for failing the test. In the case of

790 2004 ABAQUS Users’ Conference

failure, the development program is often delayed by several months and tool modification and procurement of new cylinder heads generate significant cost.

The present paper describes the process at AVL List GmbH on how to validate the cylinder head design for thermal mechanical fatigue based on simulation of durability testing, e.g. thermal shock or piston bowl crack testing. The example presented in this paper shows the lifetime simulation of a cast iron cylinder head for a general thermal-shock engine test. It describes the simulation of the heating and cooling conditions, the calculation of the transient temperature field, the analysis of the nonlinear stress strain response under thermal cycling, and the life time prediction until fatigue crack initiation.

2. Simulation process

AVL have implemented a simulation process for the virtual sign off for cylinder heads according to the process shown in Figure 1. This process rests on four cornerstones, which are CFD simulation for cooling and heat generation, FEA for heat transfer and structural analysis, material behavior testing and material simulation. Each of these steps is described subsequently in detail for the task of TMF life prediction, for which the process flow is detailed in Figure 2.

Mechanical BC’s Stress / strain analysis(durability testing, duty cycle)

Stresses /Strains

Gasket pressure

Durability(HCF, LCF, TMF) OK?

no

Heat transfer analysis(nucleate boiling)

Temperature fieldHeat flux OK?

Simulation variant

noSimulation variant

Engine simulation- thermodynamics- driving cycle

Material- filling & solidification- behavior, modeling- testing- process

yes

yes Design Release(Durability)

Deformations(liner, …)

Heat transfer BC’s

Engine Testing- Durability testing- Duty cycle

CFD simulationInner cylinder flow, coolant flow

Flow field(HTC, combustion) OK?

yes

noSimulation variant

CAE Models(FE-Model, complete engine), (CFD models coolant jacket, combustion chamber & ports)

Flow BC’s

Figure 1: Simulation process for design release of cylinder head.


Duty cycle / Durability test

Thermodynamicsimulation - BOOST

Coolant flowCFD simulation

(nucleate boiling) - FIRE

In cylinder flow CFD simulation

(combustion) - FIRE

Transient heat transfer FEA→ T(t) - ABAQUS

Material behavior/damage testing

Damage model parameter - ZEBULON

Material modelparameter - ZEBULON

Lifetime predictionNF

Nonlinear FEAABAQUS/ZEBULON

→ )(),( tt vpεσ

Figure 2: TMF lifetime prediction process and FE tools used. The TMF lifetime prediction process depends on the following process steps: 1. Calculation of transient temperature field conditions (for a given duty cycle). 2. Calculation of the cyclic stress strain response under thermal cycling. 3. Use of an appropriate material behavior model and identification of the material parameters

by applying a robust testing scheme. 4. Prediction of the number of cycles to crack initiation based on the stable cyclic stress strain

response. The software tools used in this process are AVL/BOOST, AVL/FIRE, ABAQUS, and the FE solver Zebulon from Northwest Numerics with the Zmat library for ABAQUS.

The following sections describe the details of the process steps shown in Figure 2.

3. Engine duty cycle

Several different test cycles are applied for engine durability testing. Up to now there is no standardized testing program for different engine applications such as passenger engine or truck engine. In general, the testing programs are designed for testing the field loads in a compressed time frame. This yields many different testing schemes at the OEM and suitability of these testing schemes for today’s requirements is more often questioned now. However, a test like the thermal shock test is performed in most cases. This type of test will be used in this paper for the demonstration of the analysis process. However, any other test can be analyzed using the principles described here.

A typical thermal shock test cycle consists of a variation in torque over the test cycle and a variation of the cooling temperature in order to bring the bulk temperature of the engine to a defined level at the end of each cycle.


A typical thermal shock test cycle is shown in Figure 12. It consists of a full load period and an idle period and a variation of the coolant temperature from 30 to 105 °C. This test cycle data is used to specify amplitudes in ABAQUS for the gas side heat transfer coefficients, gas temperatures and coolant temperature. Coolant mass flow and coolant pressure is derived from the water pump characteristics, which in turn is used to define amplitude curves for the coolant pressure and mass flow rate in the user subroutine (see section 4.1) for calculating the coolant side heat transfer coefficients over time.

4. Heat transfer simulation

4.1 Coolant side heat transfer

The complexity of the water jacket geometry comes from the four-valve design and the requirements for the installation of the fuel injector. This makes it often difficult to realize optimum cooling conditions throughout the cylinder head. Nucleate boiling processes play an important role at areas with only moderate flow velocities at high heat flux conditions and therefore must not be neglected in the simulation of the heat transfer problem. The model used and implemented in the CFD code FIRE and in ABAQUS (as user subroutine) is based on the “Bubble departure lift-off ” (BDL) model as presented in (Steiner, 2004).

The wall heat flux then reads according to the BDL formulation

( ) ( ) flowsubswnbbwfcw SSTThTThq −+−= , (1)

where fch is the forced convection heat transfer coefficient, wT is the wall temperature, bT is the bulk fluid temperature, nbh is the nucleate boiling heat transfer coefficient, sT is the saturation temperature of the fluid, subS and flowS are the subcooling and flow induced suppression factors, respectively. The forced convection heat transfer coefficients depends on the local flow parameters and is calculated from CFD flow simulation results. The nucleate boiling heat transfer coefficient implementation is according to the formulation by Forster and Zuber (Forster, 1955). It depends on fluid properties and on the local saturation pressure and temperature.

The current implementation of the BDL model can handle the regime of nucleate boiling efficiently. In case of the application for the coolant flow in engine coolant jackets it is important to stay below the “burnout point” (Figure 3) in order to avoid collapse of the heat transfer, and as a consequence overheating of the engine.

The contribution of nucleate boiling to the heat flux density increases with lower flow velocity (Figure 4). This effect is used to guarantee sufficient heat transfer even for cases of low or moderate flow velocity.

Because the nucleate boiling process is taken into account in ABAQUS, where the heat transfer problem is solved, the strong nonlinearity is iterated in one simulation run and another loop with the CFD simulation of the coolant flow field is often not necessary, because the influence of nucleate boiling on the flow field is generally small.


v = 0.5 m/s

v = 0.3 m/s

Figure 3: Nucleate boiling at the surface of an aluminum block (left) at constant pressure and general description of the nucleate boiling effect (right figure).

100 110 120 130 140 150 1600

1 .105

2 .105

3 .105

4 .105

5 .105

6 .105

7 .105

8 .105 2,0bar - 1,0m/s - 95°C

Oberflächentemperatur [°C]

Wär

mes

trom

dich

te [W

/m²]

Hea

t Flu

x D

ensit

y [W

/m²]

Surface Temperature [°C]100 110 120 130 140 150 160

0

1 .105

2 .105

3 .105

4 .105

5 .105

6 .105

7 .105

8 .105 2,0bar - 2,0m/s - 95°C

Oberflächentemperatur [°C]

Wär

mes

trom

dich

te [W

/m²]

Hea

t Flu

x D

ensit

y [W

/m²]

Surface Temperature [°C]

MeasurementCHEN ModelBDL Model

MeasurementCHEN ModelBDL Model

Figure 4: Measured heat flux density and comparison to BDL model prediction as implemented in form of an ABAQUS FILM user subroutine.

4.2 Gas side heat transfer

The derivation of the heat input generated during the combustion and gas exchange process over one engine cycle is usually based on 1D thermodynamic cycle simulation results. The difficulty here is to spatially distribute the heat transfer coefficient and gas temperature from 1D-simulation results in the combustion chamber. Therefore, AVL applies 3D CFD simulation of the combustion


and gas exchange process of one full engine cycle for calculating the spatial variation of the heat transfer coefficients and local gas temperatures.

The CFD analysis of the combustion and gas exchange process poses still several difficulties. These include efficient and rapid meshing for moving meshes, handling of the combustion process and efficient solver technology for rapid turnaround times. AVL/FIRE is specially designed to address all the relevant topics above and the use of CFD simulation has become the standard process for calculating the heat transfer coefficients and gas temperatures for high-powered engines. It takes into account the details of the FIE system and also of the piston bowl design, which is critical for the resulting heat transfer in the combustion chamber.

The time-resolved data, which is available at the boundary of the moving meshes of the combustion chamber, is transferred to a static FE mesh and then averaged on the time axes to obtain the cyclically averaged heat transfer coefficients and local gas temperatures. The averaging is done according to the following relation.

( ) ( )

( ) ( ) ( ) φφφ

φφ

dThh

T

dhh

gg xxx

x

xx

,,720)(

1

,7201

720

0

720

0

∫

∫

=

=, (2)

where h and gT are the locally time-averaged heat transfer coefficient and the effective gas temperature. Furthermore, h and gT are the time dependent heat transfer and local gas temperature on a fixed FE mesh.

4.3 Transient heat transfer simulation

The current implementation of the calculation of the heat transfer coefficients in the FILM user subroutine can handle steady state and transient conditions. In case of a transient heat transfer analysis, the coolant mass flow rate over time, the coolant temperature over time and a second convective flow field at another load point is required as additional input. The variation of the convective heat transfer coefficient is than defined according to the following formulation.

( )( )

0

0 )()(

),(

TTThTh

k

TTkhmmTmh

ref

ref

refrefref

−−

=

−−=

, (3)

where h is the heat transfer coefficient (W/m2K), m is the mass flow rate, T is the fluid temperature, ( refrefref Thm ,, ) are the corresponding quantities for a reference point. In addition, 0T is also a reference temperature for defining the temperature dependence of the heat transfer coefficients, which comes mainly from the influence on the viscosity of the fluid and is expressed


by the parameter k. The parameter k is evaluated individually for each boundary cell of the coolant jacket where film boundary conditions are applied.

The transient temperature field is obtained with little extra effort assuming that the gas side heat transfer coefficients and gas temperatures are proportional to the engine load. And the cooling side heat transfer coefficients can be determined over the whole temperature/pressure/mass-flow map of the coolant flow from knowing the mass-flow, coolant pressure and an additional set of heat transfer coefficients on the coolant side for a second temperature level.

It has been found that the cylinder head temperatures can be predicted repeatedly with a high accuracy. Differences in the temperatures across cylinders are captured correctly and with the use of CFD simulation for heat input and cooling conditions, the number of empirical parameters is reduced dramatically.

5. Material behavior

The materials used for cylinder head designs can be distinguished into cast iron and aluminum based alloys. Each of these materials poses certain difficulties in modeling the material behavior under the imposed loading conditions during thermal cycling. The following section briefly describes the typical gray cast iron behavior and modeling technique used at AVL for describing the material. Furthermore the AlSi7Mg alloy is addressed from a behavior and modeling standpoint because of its frequent use in high-powered passenger car diesel engines.

5.1 Cast iron cylinder head material

Cast iron used for cylinder heads (gray cast iron) is characterized by a perlitic matrix structure. Within the matrix a network of graphite flakes is embedded (Figure 5, left), which is responsible for the anisotropy in the macroscopic deformation behavior (Figure 5, right).

Typical microstructure for gray cast iron.

Figure 5: Gray cast iron microstructure (left) and anisotropy in tension and compression due to the effect of the graphite network (right).


Under cyclic loading this behavior is emphasized by a closure region under compressive loading direction with previous tensile loading direction. This has led us to formulate a damage based deformation behavior model for cast iron with a core elasto- viscoplastic Chaboche type model, which includes a Von Mises type yield criteria, isotropic and kinematic hardening and a Norton flow law. This standard model is enriched by a damage state variable depending on the maximum principal stresses (Zieher, 2002; Foerch, 2001).

A carefully balanced test matrix has been designed for thorough identification of the temperature dependent model parameters (11 for the base behavior). An example of the cyclic response of cast iron under isothermal conditions is given in Figure 6. The inflection point in the compressive loading direction is clearly visible, which is attributed to the closure of delaminations and voids from prior damage, which has been generated from loading in tensile direction. When changing the loading direction from compression to tension, the immediate action of damage is apparent by the change of the tangent modulus (elastic modulus).

The identification processes is completed and validated by simulations of the material response under anisothermal conditions and prescribed total strain conditions. This material response is recorded when performing TMF testing on specimen with a prescribed temperature profile and prescribed total strain. An example is shown in Figure 7, where the temperature varies between 50 °C and 370 °C and the total strain is zero during the cycling. The chosen temperature cycle is relevant for the desired application.

Compacted graphite iron (CGI) shows similar deformation behavior, although the damage created by tensile stresses has a much higher stress offset at the start of damage than gray cast iron. A comparison between gray cast iron and CGI when cycling between 50 and 370°C is given in Figure 8.

Strain

Experiment (T = 23 °C)

Simulation (T = 23 °C)

Strain

Experiment (T = 350 °C)

Simulation (T = 350 °C)

Figure 6: Isothermal cyclic test and simulation results at room temperature with hold time (left) and at 350 °C (right), respectively.


Temperature (°C)

Stress (MPa)

Time (sec) Mech. Strain

Figure 7: TMF simulation results for a given temperature cycle (center figure) for zero total strain condition. The TMF specimen used is shown at the left and the

stress/strain response to the described temperature is depicted on the right.

Gray cast iron Compacted graphite iron

Temperature (°C) Temperature (°C)

Figure 8: Stress response versus temperature for thermal cycling between 50 °C and 370 °C for gray cast iron (left) and CGI-450 (right).


5.2 Aluminum cylinder head material

Diesel passenger car engine cylinder heads are almost all made of aluminum alloys of different composition and final heat treatment. The two dominantly used families of aluminum alloys for cylinder heads are A319 (AlSi6Cu4) and A356 (AlSi7Mg). The A356 family has found great acceptance in the use for high-powered diesel cylinder heads together with a T6 or T7 final heat treatment process. This solution heat treatment is done in order to increase static strength and increase the yield strength of the material by precipitation hardening.

Both material classes exhibit strong aging-behavior over time when exposed to high temperature, i.e. 250 °C or above, which results in a modified microstructure with different mechanical properties and behavior. Several authors have addressed this behavior, e.g. Feikus (Feikus, 1999), Takahashi (Takahashi, 2002), or Cailletaud (Cailletaud, 2000).

From a continuum mechanics standpoint, the aging effect becomes apparent by an initial hardening and then followed by a softening behavior (Feikus, 1999), see Figure 10. Furthermore, the hardness is reduced and the fracture strain increased. The softening behavior clearly influences the fatigue life under thermal mechanical load conditions (Takahashi, 2002).

We have adopted the formulation from Cailletaud (Cailletaud, 2000) in describing the aging behavior in the context of the elasto-viscoplastic framework (Lemaitre, 1985), where an aging parameter is introduced affecting the softening and kinematic hardening behavior.

( )

( )

τζζζ

αζαζλ

−=

−==−+−+=

∞

−

2232

21132

1

*00

1,)1(1

CCReQRR b

XX , (4)

where ζ is the aging parameter varying between 0 (unaged) and 1 (fully aged) with saturation at

∞ζ . The rate with which the saturation value is approached is defined by the parameterτ . The amount of softening at fully aged condition is defined by *

0R . The remaining part of the model follows a classical viscoplastic formulation with Norton flow law and non-linear kinematic hardening for the back strain.

The test matrix for identification of the model parameters includes tensile tests at different strain rates, cyclic hardening tests (Figure 9), stepped creep tests at several temperature levels from room temperature to 300 °C. It is important to record the time history in order to determine the value of ζ at the beginning of each test.

For the calculation of the stress strain response on a cylinder head structure it is not feasible to run hundreds or even thousands of cycles, until stabilization occurs. In practice, the overaged material properties at the maximum temperature level are used.


Experiment (150 °C)

Simulation (150 °C)

Strain ()

Experiment (230 °C)

Simulation (230 °C)

Strain ()

Figure 9: Isothermal stress/strain cycling at 150 °C and 230 °C for AlSi7Mg-T7.

100

150

200

250

300

1000 10000 100000

Aging time (sec)

Rp0

,2 (M

Pa)

180°C200°C230°C

Strain ()

TMF−Experiment

TMF−Simulation

Figure 10: Softening (aging) of AlSi7Mg at different temperature levels (left) and stress/strain response of AlSi7Mg under thermal cycling between 50 °C and 280 °C

with a typical fracture of the specimen at the end of the cycling.


6. Fatigue life prediction models

The following basic assumption is used for calculating the thermal mechanical cycles to crack initiation:

,,111CHCFTMFfC

fHCFf

HCFcycleTMF

TMFff

DDDDorNN

NNN

++=++= − (5)

where the superscripts TMF, HCF, and C stand for the thermal mechanical fatigue, high cycle fatigue (gas pressure pulsation) and creep damage respectively. The base period in this formulation is one thermal mechanical cycle. The HCF damage over one thermal mechanical cycle is calculated based on classical fatigue life models, either stress based or strain based with mean stress corrections (Lemaitre, 1985). Considering a typical cycle as shown in Figure 12, the HCF damage is created during the hold time at high torque where peak pressure is high.

Creep damage is also calculated based on a classical damage formulation (Lemaitre, 1985). Creep damage plays an important role, when in-phase-loading conditions are acting. For cylinder heads, out-of-phase loading is the standard loading pattern due to the design principles, and therefore, creep damage is neglected in first order approximation of fatigue life prediction.

The anisothermal temperature condition throughout the cycle poses some difficulty in the choice of the model for damage calculation. It depends highly on the material type, temperature range and test data available. Cast iron for example, shows a rather weak dependency between temperature and the fatigue properties. On the other hand, it is highly sensitive to the maximum stress condition. We have opted for an energy-based formulation, which is assumed to be independent of the temperature history over the cycle (Skelton, 1991). Equivalently, a formulation based on the increment of the accumulated (visco-) plastic strain could be used.

( ) α−=∆ TMFfcycle NAW , (6)

were A and α are material constants and ∫=∆ εσ dWcycle : is the plastic work over one thermal shock cycle. This general setup is used for cast iron (Figure 11) and aluminum based alloys.

In the case of the aluminum alloys, in particular for the AlSi7Mg (A356) class of primary aluminum alloys, overaged data is used for identification of the model parameters. A similar approach has been described by Su et.al. (Su, 2002), where environmental effects had also been considered.

Note that for cast iron also a fatigue life prediction model based on the maximum and mean stress is adequate because of the small temperature influence and the sensitivity to tensile stresses.


100 1000 10000

Cycles to Failure

Plas

tic w

ork

(log-

scal

e)

Simulation of TMF-tests

Trendline

Trendline -50%

Trendline +50%

Simulation of TMF-tests

Figure 11: TMF damage model identification for gray cast iron (GJL-250).

7. Example: TMF life prediction for thermal shock testing

A typical example for a thermal shock test is given in Figure 12 with specification of engine load, engine speed, and coolant inlet temperature. We will use this test on a medium duty gray cast iron cylinder head in order to demonstrate the simulation process.

-50

0

50

100

150

0 2 4 6 8 10

Time (min)

Load

(%),

Spee

d (%

rate

d)

-60

0

60

120

180

Tem

pera

ture

(°C

)

Load [%]Speed (% rated)Coolant temperature (°C)

Figure 12: TS cycle with load, speed, and coolant temperature specification.

The simulation of the combustion and gas exchange process at the maximum load point returns the local (steady state) heat transfer coefficients and effective gas temperatures (Figure 13). It clearly shows the excess in heat input between the two exhaust valves (smaller sized valves) and a gradient in the heat input between the intake and exhaust valves.


384

552

720

888Local gas temperature (°C)

1240

1720

2200

2680Local heat transfercoefficients (W/m2K)

Figure 13: Local gas temperatures and local heat transfer coefficients for the cylinder head fire deck under rated power condition from 3D CFD simulation.

The transient temperature field is obtained according to the procedure described in section 4. The resulting temperature field is depicted in Figure 14, where the temperature variation over two thermal shock cycle is shown for the center positions of the valve bridges. The peak temperature exceeds 400 °C. More importantly however, the temperature levels between the intake and exhaust valve reach 330 °C (red curve). This temperature level is more critical than the 400 °C between the exhaust valves because of the mechanical constraints imposed during heat up.

Time (s)

Figure 14: Temperature distribution in cast iron cylinder head at maximum load condition (left figure) and transient temperature trace over two thermal shock

cycles at the center of the valve bridges (right figure).


In the next step, the transient temperature field is applied as thermal load until stabilization in the stress/strain response is reached. The rate of stabilization depends on the local stress/strain cycles and is typically reached within a few cycles at the severe loading locations. We limit ourselves here to define stabilization by the rate of change in size of the stress/strain path or by the rate of change in the accumulated viscoplastic strain, respectively. Figure 15 shows the stress/strain response at two locations at the cylinder head flame deck. The stress/strain condition between the intake and exhaust valve (right figure) shows the severe load this thermal shock cycle imposes on the material.

This response is characteristically for 4-valve cylinder head designs. The valve bridges, which are oriented in engine direction, are highest loaded although the temperature maximum often appears at a different location, i.e. in-between the two exhaust valves.

The stress response stemming from high frequency gas pressure cycling, which acts simultaneously, is linearly cumulated to the damage from thermal cycling. One should be aware that the linear accumulation might underestimate the damage created. More experimental work will be performed in order to obtain still more confidence in the prediction method.

Mech. strain (1)

s11−em11 @ 150906

s22−em22 @ 150906

Mech. strain (1)

s11−em11 @ 150867

s22−em22 @ 150867

Figure 15: Stress-strain response at the exhaust-exhaust valve bridge (left figure) and stress-strain response at the exhaust-intake valve bridge (right figure).

The stabilized stress/strain cycles are depicted in Figure 16 together with the cycles to crack initiation at the critical location. The prediction agrees very well with the observed thermal shock test results for this very aggressive load and design feature. It is interesting to notice that the crack initiation starts at the exhaust valve side towards the center of the valve bridge. Test observations support this simulation result, although it is often very difficult to identify crack onset in the case of cast iron.


Mech. strain (1)

sig−eps

me

@ 150906

sig−eps

me

@ 150867

sig−eps

me

@ 150692

sig−eps

me

@ 152766

2 53.5NF (log)

Figure 16: Stabilized stress/strain cycles at the valve bridge centers (in MPa) under thermal cycling (left) and log-cycles to crack initiation at the cylinder head

flame deck (right).

8. Summary and Conclusions

A complete simulation process for the TMF life prediction has been presented for typical cylinder head materials and test conditions. Cast iron as well as aluminum alloys exhibit a complex behavior under thermal mechanical cycling and require special treatment, which is often not available in standard industry FE codes. The use of ABAQUS together with Zebulon allowed for implementing the complete process.

The calculation of the transient heat transfer boundary and loading conditions in relation to a defined test cycle is one of the critical tasks. The implementation presented in this paper only needs a minimum set of 3D field boundary conditions, which are obtained by coolant flow simulation and combustion process simulation.

The presented fatigue life model has proven practical for engineering purposes. Further material testing will be performed to refine the model parameter base and improve the correlation between prediction and experimental results.

The analysis will be further extended to predict damage under field load conditions and to study the crack growth of the initiated crack. Already now designs are investigated, where cracks stop growing in a certain depth without propagating into the coolant jacket (which would cause fatale damage of the cylinder head).


9. References

1. Forster, H. K., Zuber, N., “Dynamics of Vapor Bubbles and Boiling Heat Transfer”, A.I.Ch.E. J. 1, pp. 531-535, 1955.

2. Chen, J.C. “A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow”, ASME preprint 63 HT34 presented at the 6th National Heat Transfer Conference, Boston, 1963.

3. Steiner, H., Kobor, A., Gebhard L., “A Wall Heat Transfer Model for Subcooled Boiling Flow”, ASME-ZSIS International Thermal Science Seminar (ITSS II), 2004.

4. Lemaitre, J., Chaboche, J.-L., “Mechanics of Solid Materials”, Cambridge University Press (1985).

5. Skelton, R.P., “Energy Criterion for High Temperature Low Cycle Fatigue Failure”, Mat. Sci. Tech. 7 427-439 (1991).

6. Su, X., Zubeck, M., Lasecki, J., Engler-Pinto Jr., C.C., Tang, C., Sehitoglu, H., Allison, J., “Thermal Fatigue Analysis of Cast Aluminum Cylinder Heads”, SAE technical paper 2002-01-0657, 2002.

7. Foerch R., Zieher F., “Damage Mechanics Based Modeling for Cast Iron TMF Applications”, Presented at USNCCM VI Dearborn, MI (2001).

8. Zieher, F., Langmayr, F., Foerch, R., Lampic, M., “TMF Life Prediction for Cast Iron Based on Damage Mechanics”, WCCM V, Vienna, 2002.

9. Zieher, F., Langmayr, F., “Engine Simulation in View of Reduced Development Time”, FISITA 2002, World Automotive Congress, Helsinki, 2002.

10. Cailletaud, G., Depoid, C., Massinon, D., Nicouleau-Bourles, E., “Elastoviscoplasticity with Aging in Aluminium Alloys”, in Maugin, G.A., Drouot, R., Sidoroff, F., Continuum Thermo-dynamics: The Art and Science of Modelling Material Behaviour (Paul Germain’s Anniver-sary Volume), Solid Mechanics and its Applications, pages 75-86. Kluwer Academic Publish-ers, 2000.

11. Gundlach, R.B., Hetke, A., Valtierra, S., Mojica, J.F., Ross, B., “Temperaturwechselbständig-keit von Untereutektischen Aluminium-Silicium-Gußlegierungen”, Giesserei-Praxis 11/12, pages 209-226, 1995.

12. Feikus, F.J., “Optimierung von Aluminium-Silicium-Gußlegierungen für Zylinderköpfe”, Giesserei-Praxis 2, pages 50-57, 1999.

13. Takahashi, T., Moizumi, K., Iida, M., Sasaki, K., Ohnuki, S., “Effect of Thermal Fatigue Phe-nomena of Aluminum Alloy by Artificial Aging”, SAE technical paper 2002-01-0584, 2002.

14. Smith, T. J., Hans, J. M. Sehitoglu, Fleury, E. and Allison, J., “Modeling High-Temperature Stress-Strain Behavior of Cast Aluminum Alloys”, Metallurgical and Materials Transactions, 1999, 30A, p133-145.

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