# Lifetime Assessment of Cylinder Heads for Efficient Heavy Duty Engines Part I: A Discussion on Thermomechanical and High-Cycle Fatigue as Well as Thermophysical Properties of Lamellar Graphite Cast Iron GJL250 and Vermicular Graphite Cast Iron GJV450.

INTRODUCTIONIncreasing the efficiency of heavy duty internal combustion engines is directly related to increasing specific power and, thus, increasing combustion pressure and temperature. One key component of the engine is the cylinder head which must withstand these higher temperatures and higher pressures. The path of increasing loads intensifies design conflicts, as e.g. associated with the fire deck of cylinder heads: the deck should be as thin as possible to avoid critical thermal stresses during the low frequency thermal transients but sufficiently thick to avoid failures due to the high frequency combustion pressure. A superficial solution of the design conflict is the usage of superior cast iron materials. Vermicular graphite cast iron show higher strength than the classically used lamellar graphite cast iron. However, due to the lower thermal conductivity of vermicular graphite cast iron (Figure 1), higher thermal stresses may arise.

Different cast iron materials are currently used for cylinder heads of efficient heavy duty engines. Further existing or soon-to-be developed cast iron materials are potential candidates for more efficient engines as well.. An appropriate choice of the material that can withstand the increased loadings and still meets the technological and economic requirements is hard to identify without numerous expensive and time-consuming bench tests. Reliable methods for materials characterization, materials selection and fatigue life assessment via finite-element calculations are necessary.

For the comparison of the behavior of different materials with respect to high-cycle fatigue (HCF), which is relevant for the water jacket side of the cylinder head, the elastic mechanical properties and corresponding stress-life fatigue curves including mean stress effects are required. For a comparison of the thermomechanical fatigue (TMF) properties, which are relevant for the fire deck, elastic and inelastic mechanical as well as thermophysical properties must be considered and a model for TMF life prediction is necessary. A simple approach to compare materials with respect to their high temperature performance is the thermal stress index [chi] [1]:

[chi]=[[[[sigma].sub.CY] * [lambda]]/[E * [[alpha].sub.T]]]. (1)

It considers thermophysical properties, namely the heat conductivity [lambda] and the coefficient of thermal expansion [[alpha].sub.T] as well as mechanical properties, namely Young's modulus E and the strength of the material, where the cyclic yield stress [[sigma].sub.CY] (0.2 %-offset yield stress obtained from stress-strain hysteresis loops) is used here. The higher the thermal stress index is (i.e. the lower E and [[alpha].sub.T] and the higher [[sigma].sub.CY] and [lambda]) the lower is the capability of the material to build up thermal stresses during transient thermal loading. A comparison of the temperature dependent properties and the resulting thermal stress indices for the lamellar graphite cast iron GJL250 and vermicular graphite cast iron GJV450 are shown in Figure 1.

The thermal stress index indicates that there might be a slight advantage for the vermicular graphite cast iron GJV450 compared to the lamellar graphite cast iron GJL250 for higher temperatures. However, the thermal stress index is just a simple phenomenological indicator of the high temperature performance of materials. In case of such slight differences, it does not allow for conclusions with respect to the TMF behavior. A more fundamental materials characterization and model is required for the comparison of the TMF performance of different materials.

For the assessment of TMF occurring at the fire deck, on the one hand the time and temperature dependent cyclic plasticity is important, i.e. besides E and [[sigma].sub.CY] also hardening and creep properties must be considered. On the other hand the time and temperature dependent growth of early initiated TMF cracks is the dominant damage mechanism [2, 3] so that also fatigue crack growth properties must be included in the choice of the material. Indeed, the loading situation at the fire deck is even more complicated due to HCF loads resulting from the combustion pressure that are superposing the TMF loads (TMF/HCF) and that might result in an increased crack growth rate [4, 5]. Thus, the TMF, TMF/HCF and HCF life prediction of cylinder heads and an appropriate choice of material and design is a challenging task.

It is the aim of this paper (Part I) to compare the TMF behavior of the lamellar graphite cast iron GJL250 and the vermicular graphite cast iron GJV450 for close-to-service loading conditions of efficient heavy duty engines. To this end, both materials are characterized in uniaxial low-cycle isothermal fatigue (LCF) and TMF tests. The experimental results are used to develop an advanced mechanism-based model for TMF life prediction for the material that is based on elastic-, plastic- and creep-fracture mechanics. Furthermore, the needs for an integrated material characterization are discussed, considering TMF, TMF/HCF and HCF as well as the thermophysical material properties. In Part II of the paper, the model for TMF life prediction is applied to assess the TMF life of cylinder heads by means of finite-element calculations.

EXPERIMENTAL

In this section, the investigated materials, the testing conditions for materials characterization and selected experimental results are presented.

Material

Round specimen with a diameter of 7 mm in the gauge length are used for the uniaxial LCF and TMF tests made of the lamellar graphite cast iron GJL250 and the vermicular graphite cast iron GJV450. The specimens are machined from material directly taken out from the fire deck valve bridge region of heavy duty engines cylinder heads. The surface finish for the specimens was done by lapping. Further finishing does not improve the surface quality due to the roughness caused by cutting graphite inclusions. Representative micrographs of both cast iron materials are shown in Figure 2.

Setup and Procedure

The experiments were performed with a universal servo-hydraulic testing machine of Instron Ltd. The elongation in the gauge length was measured with a Maytec extensometer, which comes into contact with the specimen with ceramic rods. The gauge length was 10 mm. The specimens are heated inductively. The temperature of the specimen is measured with three NiCr-Ni thermo-couples in the gauge length to monitor the homogeneity of the temperature distribution. Strain and temperature histories are controlled with self-made software programmed in LabView.

Strain-controlled isothermal complex low-cycle fatigue (CLCF) [6] tests were conducted at 20, 200, 300, 400 and 450 [degrees]C with both materials. The CLCF tests are composed of a non-periodical part and a periodical part. In the nonperiodical part, a few loading cycles are used with different strain rates and hold times in tension and compression. Based on the measured information on strain rate effects, stress relaxation and the hardening, the material properties of viscoplastic constitutive equations can be determined for application in finite-element calculations. The results of the non-periodic part of the CLCF tests are shown together with their description with the viscoplastic constitutive model in Part II of the paper. In the periodical part of the CLCF test, the specimen is cycled to failure with a constant strain amplitude under fully reversed loading with strain ratio of -1 and constant strain rate of [10.sup.-3] 1/s as usual for LCF testing. The strain amplitudes are chosen such that fatigue lives in the LCF as well as in the beginning of the HCF regime are obtained. The fatigue lives span over three orders of magnitudes so that the slope of life-curves can be reliably determined.

The isothermal CLCF tests are supplemented by strain controlled out-of-phase TMF tests, representing the situation of constraint thermal strains in the valve bridge region. The maximum temperature in all tests is 450 [degrees]C, while the minimum temperature is either 150 or 250[degrees]C. A hold time of 60 s is used at maximum temperature. The tests were performed according to the TMF standard ISO 12111. The cycle periods of the TMF tests were typically a factor 10 to 20 longer than those of the CLCF tests.

The fatigue life of the specimen is defined as the number of cycles corresponding to a decrease of 5 % in the stress value extrapolated over the tensile stress-number of cycles curve when the stress falls sharply. For the used geometry, this corresponds to the appearance of a semi-circular surface crack with a length of approx. 1 mm.

Results

In Figure 3, mechanical strain-life plots for the isothermal LCF and the TMF tests are shown for both materials. The symbol x indicates tests with failure outside the gauge length. Such failures only occurred for tests with GJL250 where also higher scatter is observed. The higher scatter is typical for lamellar graphite cast iron with the relatively sharp lamellar graphite inclusions acting as initial stress concentrations and, thus, as crack initiation sites.

GJV450 shows a stronger temperature dependency of the fatigue life for equal mechanical strain range than GJL250. Also the TMF tests for GJV450, all with maximum temperature of 450 [degrees]C, show lower fatigue life for the equal strain amplitude compared to the isothermal LCF tests at 450 [degrees]C.

For higher mechanical strain range GJV450 shows a higher TMF life than GJL250. For lower mechanical strain ranges, the data suggests the opposite behavior: the TMF lives are higher for GJL250 than for GJV450. However, on the basis of the relatively low number of tests, this cannot be validated.

TMF LIFE PREDICTION AND MATERIAL PROPERTIES

In this section, an advanced mechanism-based model for TMF life prediction is presented and the corresponding mechanical properties are shown. The properties for the lamellar graphite cast iron GJL250 and the vermicular graphite cast iron GJV450 are determined on the basis of the experimental data.

Mechanism-Based [D.sub.TMF] Model

The crack-tip blunting model is a reasonable mechanism-based approach to predict TMF lives of cast iron materials [2, 3, 4, 5]. The model assumes that the increment in crack advance per loading cycle, da/dN is correlated with the cyclic crack-tip opening displacement [DELTA]CTOD:

[da/dN] = [beta]*[DELTA]CTO[D.sup.B]. (2)

The proportionality factor [beta] and the exponent B are material properties. The analytical fracture mechanics based estimate

[DELTA]CTOD = [d.sub.n], * [D.sub.TMF] * a, (3)

where a is the crack length, is based on the cyclic stress intensity factor [DELTA]K, the cyclic J-integral and the C*-integral and, thus, accounts for contributions from elastic, plastic and time-dependent deformations to crack growth [2]. In case of Ramberg-Osgood behavior, where the relation between stress [sigma] and strain [epsilon] is described by

[delta][epsilon] =[[delta][sigma]/E]+0.002*[([[delta][sigma]/[[sigma].sub.CY]]).sup.[1/n']] (4)

and the Ramberg-Osgood hardening exponent n' describes a power law hardening stress-strain hysteresis loop (the symbol [delta] refers to the corresponding ranges of the quantities with respect to the point of load reversal), solutions of [d.sub.n], are available in [7], which can be described by the third order polynomial

[d.sub.n,] = 0.78627- 3.41692n'+6.11945[n'.sup.2] -4.2227[n'.sup.3], (5)

and the damage parameter [D.sub.TMF] for short semi-circular surface cracks and uniaxial loading conditions (as the case in the LCF and TMF tests) is

[mathematical expression not reproducible] (6)

[D.sub.TMF] can be interpreted as a measure of the damaging effect of a thermomechanical loading cycle, provided that failure occurs by fatigue crack growth. [DELTA][sigma] and [DELTA][[epsilon].sup.p] are twice the stress and plastic strain amplitudes of a saturated stress-strain hysteresis loop taken of a midlife cycle. The subscript eff indicates that mean stress effects due to crack closure are taken into account via Newman's crack opening stress equation [8]. Since the material properties E, [[sigma].sub.CY] and n' are temperature dependent, equivalent material properties are computed based on the integral means that refer to a non-isothermal loading cycle.

The stress and temperature dependent function F in equation (6) describes an increased damage due to creep at higher temperatures:

[mathematical expression not reproducible] (7)

The symbol [delta] again refers to the range with respect to the point of load reversal. R is the universal gas constant and [theta] the temperature in Kelvin. [Q.sup.cr] is the activation energy for creep and n is the Norton exponent according to Norton's law for the description of the strain rate due to creep:

[mathematical expression not reproducible] (8)

[B.sub.0] is a temperature independent creep property. The constant a' in the F-function can be directly related to [B.sub.0] in Norton's law [9]. The integral in equation (7) is evaluated between the time points [t.sub.0] and [t.sub.1] defining the stress and plastic strain ranges in equation (6). [t.sub.0] and [t.sub.1] are obtained in a minimization procedure to find the time points that minimize the fatigue life. To this end, for all time point combinations the fatigue life is computed and these time points are chosen that result in the minimal fatigue life.

Integration of the crack growth law in equation (2) from an initial crack length [a.sub.0] to the crack length at fracture [a.sub.f] yields the expression for the number of cycles to failure

[N.sub.f]=A*[([d.sub.n'] * [D.sub.TMF]).sup.-B]. (9)

A is a function of the initial and failure crack length and the proportionality constant [beta]: For B [not equal to] 1, one obtains

[mathematical expression not reproducible] (10)

The parameter A and the material property B are used as fitting parameters to adjust the calculated fatigue lives to the fatigue lives measured in LCF and TMF tests.

Mechanical Material Properties

In the model for TMF life prediction, the mechanical properties of the material directly affect the crack growth rate and, thus, the fatigue life. On the one hand, the Ramberg-Osgood properties E, [[sigma].sub.CY] and n' for cyclic plasticity and, on the other hand, the Norton properties [B.sub.0], [Q.sup.cr] and n for creep must be determined.

The Ramberg-Osgood properties are determined from measured stress-strain hysteresis loops at half fatigue life. The Ramberg-Osgood model description for the stress-strain hysteresis loops at half fatigue life of CLCF tests is shown in Figure 4.

The material properties of Norton's creep law are determined on the basis of the stress relaxation phases in the CLCF tests. Since stress relaxation is hardly observed for GJL250, creep is not considered for this material ([B.sub.0] = 0). For GJV450, the material properties are determined for temperatures higher than 300 [degrees]C, where stress relaxation occurs. The inelastic strain rate during the relaxation phase is plotted as function of the stress and shown together with description of Norton's law in Figure 5. The higher stress levels are assumed to lie in the power-law breakdown region so that the complete stress range cannot be described with Norton's law.

Fatigue Crack Growth Material Properties

The material properties related to TMF crack growth are [beta] and B. Generally fatigue crack growth tests can be used to determine these properties. Since these tests are elaborate and time consuming, the material properties are determined on the basis of the fatigue life data by fitting the parameter A instead of [beta].

For cast iron material with vermicular graphite inclusions B [approximately equal to] 2 and for lamellar graphite inclusions B [approximately equal to] 3 are typical values [10]. With these values, the slope of the [D.sub.TMF] fatigue life curve in Figure 6 can be described well for both materials. In the [D.sub.TMF]-life plot all isothermal tests as well as the TMF tests fall into a common scatter-band compared to the mechanical strain-life plot in Figure 3. Due to the different slopes B there is an intersection of the model lines at higher fatigue lives. This suggests that for lower loading levels GJL250 might have a better fatigue resistance that GJV450. However, for that range of cycles to failures there is no data to validate this behavior.

DISCUSSION

The mechanism-based [D.sub.TMF] model for TMF life prediction allows a very good description of the results of the isothermal LCF and TMF tests of both materials, the lamellar graphite cast iron GJL250 and the vermicular graphite cast iron GJV450. Hence, the effect of the material and different designs on the TMF life of cylinder heads can be assessed in finite-element calculations.

At first sight, the [D.sub.TMF] model seems to be a good indicator concerning the comparison of the TMF performance of both materials, since it includes mechanical material properties describing the elastic (E), plastic ([[sigma].sub.CY] and n') and time-dependent properties ([B.sub.0], [Q.sup.cr] and n). These material properties can be determined from standard tests and have a direct effect on the fatigue life. However, from the mechanical material properties alone it is not possible to conclude which material has a better TMF performance, since also fatigue crack properties (A and B) enter the model which strongly depend on the microstructure. A is directly depending on the initial crack length which is associated the characteristic length of graphite inclusions. The literature values of B lead to a good description of the sensitivity of the damage parameter to the fatigue life.

Moreover, for the comparison of the TMF performance of materials, the thermophysical properties are, besides the mechanical properties, also very important. The [D.sub.TMF] model only considers the mechanical properties and the effect of mechanical and thermophysical properties on the fatigue life is expected to be strongly dependent on the thermal loading history (e.g. heating and cooling rates) and the resulting thermal gradients. Hence, for the assessment of the TMF performance and the material selection for efficient heavy duty engines it is necessary to include thermal transients and gradients into the material characterization which are close to the loadings in the components. However, neither established methods nor adequate specimen geometries for such a characterization exist that allow a reliable and short-term assessment of different materials.

Besides the thermomechanical loads, the fire deck also experiences HCF loads from combustion pressure. A reduction of the fatigue life due to superimposed HCF on TMF was already measured on specimen and a mechanism-based model for the description of the reduction exists [5]. The underlying data base is, however, limited to some scientific investigations. In the light of the existing scatter of fatigue data, especially for cast iron materials with a relatively high characteristic length of the graphite inclusions, further investigations are necessary to identify the critical HCF loads resulting in a TMF life reduction.

The results of the fatigue tests of this paper show that there might be an intersection or coalescence of the mechanical strain-life curves as well as the [D.sub.TMF]-life curves of the investigated GJL250 and GJV450. Further tests are necessary to validate this since the HCF performance of the material is very important for the water jacket region. Indeed, there hardly exists any available HCF data for the cast iron materials that consider the effect of the relevant mean stresses. Even, the effect of the thin casting skin on the un-machined surface on the HCF life is neither known nor understood. Generally, a fatigue crack growth model as the [D.sub.TMF] model alone should only be applied for LCF and TMF conditions, where cracks initiate early. For HCF, also the crack initiation phase can constitute a significant portion of the fatigue life. Due to the graphite inclusions acting as initial cracks in cast iron materials, the crack initiation phase might be negligible also for higher fatigue lives so that the [D.sub.TMF] model could still be valid.

Currently, no validated integral concept exists for the material characterization of cast iron materials for efficient heavy duty engines that meets the requirements for HCF strength and TMF as well as TMF/HCF strength. All these fatigue loadings must be considered in the design and material selection for the cylinder head. Hence, a meaningful integral concept should consider mechanical properties, fatigue crack growth properties as well as the thermophysical properties of the material to assess the TMF and the TMF/HCF performance. Moreover surface and mean stress effects on HCF should be accounted for in the concept for a comprehensive lifetime assessment of efficient heavy duty engines.

SUMMARY/CONCLUSIONS

In this paper, the isothermal LCF and TMF properties of the lamellar cast iron GJL250 and the vermicular cast iron GJV450 are investigated in uniaxial tests and compared. A model for fatigue life prediction is developed that describes the measured fatigue lives very well and, thus, is used for the lifetime assessment of cylinder heads for efficient heavy duty engines by means of finite-element calculations in Part II of the paper. However, the material selection for cylinder heads of efficient heavy duty engines must also consider the thermophysical properties because they control the thermal stresses in the highly loaded fire deck region. Moreover the HCF properties of the materials must be considered, especially for the fatigue resistant design of the water jacket region. From the point of view of the multitude of available and currently or soon-to-be developed cast iron materials, a concept for an integral material characterization is necessary that allows to compare and select material for the application in efficient heavy duty engines

REFERENCES

[1.] Burgel, R., "Handbook high temperature materials engineering" (in German), 3rd edition, Vieweg & Sohn Verlag, 2006

[2.] Seifert, T. and Riedel, H., "Mechanism-based thermomechanical fatigue life prediction of cast iron. Part I: Models", International Journal of Fatigue 32, 2010, 1358-1367, doi:10.1016/j.ijfatigue.2010.02.004

[3.] Seifert, T., Maier, G., Uihlein, A., Lang, K.-H. and Riedel, H., "Mechanism-based thermomechanical fatigue life prediction of cast iron. Part II: Comparison of model predictions with experiments", International Journal of Fatigue 32, 2010, 1368-1377, doi:10.1016/j. ijfatigue.2010.02.005

[4.] Schweizer, C., Seifert, T., Nieweg, B., von Hartrott, P. and Riedel, H., "Mechanisms and modelling of fatigue crack growth under combined low and high cycle fatigue loading", International Journal of Fatigue 33, 2011, 194-202, doi:10.1016/j.ijfatigue.2010.08.008

[5.] Metzger, M., Nieweg, B., Schweizer, C. and Seifert, T., "Lifetime prediction of cast iron materials under combined Thermomechanical fatigue and high cycle fatigue loading using a mechanism-based model", International Journal of Fatigue 53, 2013, 58-66, doi:10.1016/j. ijfatigue.2012.02.007

[6.] Seifert, T., "A complex LCF test program for fast and cost-saving identification of material properties" (in German), in conference proceedings "Werkstoffprufung 2006", Borsutzki M., Geisler S. (Eds.), Bad Neuenahr, 2006, 409-414

[7.] Shih, C.F., "Tables of Hutchinson-Rice-Rosengren singular field quantities", Tech. rep. Brown University Report MRL E-147, 1983

[8.] Newman, J.C., "A crack opening stress equation for fatigue crack growth", International Journal of Fracture 24, 1984, 131-135, doi:10.1007/BF00020751

[9.] Schweizer, C., "Physics-based models for fatigue crack growth and fatigue life under thermal and mechanical loadings" (in German), Phd-thesis, Karlsruhe Institute for Technology (KIT), 2013

[10.] Metzger, M., "Microstructure- and mechanism-based models for the description of deformation and lifetime of thermomechanically loaded cast iron components" (in German), Phd-thesis, Karlsruhe Institute for Technology (KIT), 2016

ACKNOWLEDGMENTS

The authors would like to acknowledge John Deere for providing the funding of this project and for permission to publish this paper.

Thomas Seifert Offenburg University of Applied Sciences

Philipp von Hartrott Fraunhofer IWM

Kristopher Boss and Paul Wynthein John Deere Engine Works

doi:10.4271/2017-01-0349.