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Thomas Seifert - One of the best experts on this subject based on the ideXlab platform.
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a crack opening stress equation for in phase and out of phase Thermomechanical Fatigue loading
International Journal of Fatigue, 2016Co-Authors: Carl Fischer, Christoph Schweizer, Thomas SeifertAbstract:Abstract In this paper, a crack opening stress equation for in-phase and out-of-phase Thermomechanical Fatigue (TMF) loading is proposed. The equation is derived from systematic calculations of the crack opening stress with a temperature dependent strip yield model for both plane stress and plane strain, different load ratios and different ratios of the temperature dependent yield stress in compression and tension. Using a load ratio scaled by the ratio of the yield stress in compression and tension, the equation accounts for the effect of the temperature dependent yield stress and the constraint on the crack opening stress. Based on the scaling relation established in this paper, Newman’s crack opening stress equation for isothermal loading is enabled to predict the crack opening stress under TMF loading.
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assessment of Fatigue crack closure under in phase and out of phase Thermomechanical Fatigue loading using a temperature dependent strip yield model
International Journal of Fatigue, 2015Co-Authors: Carl Fischer, Christoph Schweizer, Thomas SeifertAbstract:Abstract In this paper Fatigue crack closure under in-phase and out-of-phase Thermomechanical Fatigue (TMF) loading is studied using a temperature dependent strip yield model. It is shown that Fatigue crack closure is strongly influenced by the phase relation between mechanical loading and temperature, if the temperature difference goes along with a temperature dependence of the yield stress. In order to demonstrate the effect of the temperature dependent yield stress, the influence of in-phase and out-of-phase TMF loading is studied for a polycrystalline nickel-base superalloy. By using a mechanism based lifetime model, implications for Fatigue lives are demonstrated.
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lifetime prediction of cast iron materials under combined Thermomechanical Fatigue and high cycle Fatigue loading using a mechanism based model
International Journal of Fatigue, 2013Co-Authors: M Metzger, Christoph Schweizer, Britta Nieweg, Thomas SeifertAbstract:Abstract In this paper the Fatigue life of three cast iron materials, namely EN-GJS-700, EN-GJV-450 and EN-GJL-250, is predicted for combined Thermomechanical Fatigue and high cycle Fatigue loading. To this end, a mechanism-based model is used, which is based on microcrack growth. The model considers crack growth due to low frequency loading (Thermomechanical and low cycle Fatigue) and due to high cycle Fatigue. To determine the model parameters for the cast iron materials, Fatigue tests are performed under combined loading and crack growth is measured at room temperature using the replica technique. Superimposed high cycle Fatigue leads to an accelerated crack growth as soon as a critical crack length and thus the threshold stress intensity factor is exceeded. The model takes this effect into account and predicts the Fatigue lives of all cast iron materials investigated under combined loadings very well.
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mechanism based Thermomechanical Fatigue life prediction of cast iron part ii comparison of model predictions with experiments
International Journal of Fatigue, 2010Co-Authors: Thomas Seifert, Gerhard Maier, A Uihlein, Karlheinz Lang, Hermann RiedelAbstract:In the present paper, predictions of mechanism-based models for cast iron are compared to experimental results obtained for the nodular cast iron EN-GJS-700, the vermicular cast iron EN-GJV-450 and the lamellar cast iron EN-GJL-250. A strategy is proposed to efficiently identify the model parameters based on isothermal experiments. In particular, complex low cycle Fatigue (LCF) tests, tension tests and compression tests are used to adjust the time and temperature dependent cyclic plasticity model. The time and temperature dependent Fatigue life prediction model is adjusted to LCF tests. For all investigated cast iron materials, good predictions of Thermomechanical Fatigue (TMF) tests are possible with the models. Additionally, the location of failure and Fatigue life of a Thermomechanically loaded double-sided notched specimen are predicted with high accuracy.
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Thermomechanical Fatigue of 1 4849 cast steel experiments and life prediction using a fracture mechanics approach
International Journal of Materials Research, 2010Co-Authors: Thomas Seifert, Christoph Schweizer, Michael Schlesinger, Martin Moser, Martin EiblAbstract:In this paper the Thermomechanical Fatigue properties of 1.4849 cast steel, which is used for exhaust manifolds and turbochargers, are investigated and a fracture mechanics based approach is used for Fatigue life prediction. Isothermal low-cycle Fatigue tests and Thermomechanical Fatigue tests are conducted in the temperature range from room temperature up to 1000°C. Fractographic investigations show that fracture occurs predominantly intergranularly at 600°C, whereas mixed transgranular and intergranular crack growth is found otherwise. The methodology for Fatigue life prediction is based on a time and temperature dependent cyclic plasticity model, which describes the transient stresses and strains, and on a law for time and temperature dependent microcrack growth. The crack growth law assumes that the increment in crack length in each cycle, da/dN, is correlated with the cyclic crack-tip opening displacement, ΔCOD. An analytical fracture mechanics based estimate of ΔCTOD is used, which is derived for non-isothermal loadings. The Fatigue lives of the low-cycle and the Thermomechanical Fatigue tests are predicted well with the model. Only predictions for the low-cycle Fatigue tests at 600 °C, where integranular fracture is predominant, are non-conservative.
R. W. Neu - One of the best experts on this subject based on the ideXlab platform.
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crack paths in single crystal ni base superalloys under isothermal and Thermomechanical Fatigue
International Journal of Fatigue, 2019Co-Authors: R. W. NeuAbstract:Abstract Fatigue crack paths in single-crystal Ni-base superalloys do not follow the classical Stage I/Stage II behavior. In fact, the opposite often occurs with cracks growing initially in Mode I opening and then later transitioning to crystallographic shearing. The crack paths under isothermal and Thermomechanical Fatigue (TMF) are influenced by several factors including temperature, strain range, dwells during the cycle, the microstructure and crystal orientation, the environment, the strain-temperature phasing in TMF, and frequency. The relative influences of the several crack growth parameters on the transition between Mode I opening and crystallographic shearing crack growth are graphically summarized.
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parameters influencing Thermomechanical Fatigue of a directionally solidified ni base superalloy
International Journal of Fatigue, 2015Co-Authors: M M Kirka, R. W. Neu, Stephen D Antolovich, K A Brindley, Sachin Shinde, Phillip W GravettAbstract:Abstract Thermomechanical Fatigue (TMF) is a low cycle Fatigue process in which material life is correlated to the mechanical strain amplitude. However, it is well known that several other factors influence this life. This paper examines several of these parameters and their influence on life using experiments conducted on a second generation directionally-solidified (DS) Ni-base superalloy. The parameters considered include the influence of the temperature extremums ( T max of either 750 or 950 °C and T min of either 100 or 500 °C), strain ratio ( R ∊ ), the strain-temperature phasing (in-phase (IP) and out-of-phase (OP)), the influence of dwells at the high temperature end of the cycle resulting in a creep–Fatigue (CF) interaction, and material anisotropy associated with the grain growth direction (longitudinal versus transverse). Results suggest that the phasing has a primary role in controlling the mechanism of degradation. IP TMF is dominated by crack formation in volumes surrounding debonded carbides for both continuously cycling (CC) and CF at 950 and 750 °C, while OP TMF is dominated by surface oxidation and repetitive cracking of the oxide that reforms at the crack tip at 950 °C. Decreasing the T max to 750 °C the environmental and creep effects are reduced resulting in virtually pure Fatigue exposure under OP conditions. With decreasing T min from 500 °C to 100 °C was observed an increase in inelastic strain amplitude and corresponding decrease in life. Variations in R ∊ were found to have no significant influence on life or stabilized stress behavior. TMF loading in the transverse orientation resulted in life reductions over the longitudinal orientation due to cracks propagating in a transgranular manner. Lastly, only in material exposed to CF with a T max of 950 °C rafting of the γ ′ precipitates was observed.
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influence of coarsened and rafted microstructures on the Thermomechanical Fatigue of a ni base superalloy
International Journal of Fatigue, 2015Co-Authors: M M Kirka, R. W. Neu, Stephen D Antolovich, K A Brindley, Sachin Shinde, Phillip W GravettAbstract:Abstract The aging of the microstructure of Ni-base superalloys during service is primarily characterized by coarsening and rafting of the γ ′ precipitates. The influence of these different aged microstructures on Thermomechanical Fatigue (TMF) under either continuously cycled (CC) and creep-Fatigue (CF) was investigated. Three different aged microstructures, generated through accelerated aging and pre-creep treatments, were studied: stress-free coarsened γ ′ , rafted with orientation perpendicular to loading direction (N-raft), and rafted with orientation parallel to loading direction (P-raft). Under most conditions, the aged microstructures were less resistant to TMF than the virgin microstructure; however, there were exceptions. Both stress-free coarsened and N-raft microstructures resulted in a reduction in TMF life under both CC and CF conditions in comparison to the virgin material. P-raft microstructure also resulted in reduction in TMF life under CC conditions; however, an increase in life over that of the virgin material was observed under CF conditions. These differences are discussed and hypothesized to be related to the interactions of the dislocations in the γ channels with γ ′ precipitates.
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influence of notch severity on Thermomechanical Fatigue life of a directionally solidified ni base superalloy
Fatigue & Fracture of Engineering Materials & Structures, 2014Co-Authors: Patxi Fernandezzelaia, R. W. NeuAbstract:The aim of this work is to understand the influence of notches under Thermomechanical Fatigue (TMF) in a directionally solidified Ni-base superalloy. Experiments were performed utilizing linear out-of-phase and in-phase TMF loadings on longitudinally oriented smooth and cylindrically notched specimens. Several notch severities were considered with elastic stress concentrations ranging from 1.3 to 3.0. The local response of the notched specimens was determined using the finite element method with a transversely isotropic viscoplastic constitutive model. Comparing the analysis to experiments, the locations observed for crack nucleation in the notch, which are offset from the notch root in directionally solidified alloys, are consistent with the maximum von Mises stress. Various local and nonlocal methods are evaluated to understand the life trends under out-of-phase TMF. The results show that a nonlocal invariant area-averaging method is the best approach for collapsing the TMF lives of specimens with different notch severities.
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Thermomechanical Fatigue and bithermal Thermomechanical Fatigue of a nickel base single crystal superalloy
International Journal of Fatigue, 2012Co-Authors: Robert L Amaro, R. W. Neu, Stephen D Antolovich, Patxi Fernandezzelaia, W HardinAbstract:Abstract Thermomechanical Fatigue (TMF) is a critical damage process incurred by turbine components. The most common methods for simulating the operating conditions of turbine components are either in-phase (IP) or out-of-phase (OP) TMF tests. However, due to the constantly changing temperature and applied load profile, it is challenging to decouple dominant damage mechanisms occurring in the material when relying solely on TMF test conditions. Further, the time to perform low(er) inelastic strain range TMF tests to failure can be cumbersome. This work proposes implementation of bithermal Fatigue (BiF) tests to address these issues. Out-of-phase BiF tests are strain-controlled Fatigue tests whereby a single cycle consists of an isothermal compressive half-cycle at the maximum temperature, followed by stress-free temperature change to the minimum temperature; the tensile half-cycle then occurs isothermally at the minimum temperature, followed by stress-free temperature change to the maximum temperature. Both conventional OP TMF and OP BiF tests were performed on nominally 〈0 0 1〉 oriented single crystal superalloy specimens. When plotting test results as inelastic strain range versus cycles to crack initiation, the OP BiF results exhibit a clear demarcation from the TMF data at a particular value of inelastic strain range; above which the results are primarily Fatigue dominated and follow the trend of the OP TMF tests while below the results are environmentally dominated, creating a separate trend. Thermally-activated base material degradation supports the theory of damage driver segregation. A relationship is proposed relating the inelastic strain of BiF to that of TMF, for identical lives, within the environmentally dominated Fatigue region. Finally, a life prediction model is proposed that includes Fatigue and environmentally assisted damage mechanisms, which enables the life estimation of either test type. These relationships enable the use of BiF tests in place of, or in conjunction with, TMF tests, thereby providing insight into the dominant damage mechanisms present during testing and simplifying life prediction for more complex TMF cycles.
Jianxin Zhang - One of the best experts on this subject based on the ideXlab platform.
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deformation twinning and twinning related fracture in nickel base single crystal superalloys during Thermomechanical Fatigue cycling
Acta Materialia, 2014Co-Authors: Fei Sun, Jianxin Zhang, Hiroshi HaradaAbstract:Abstract Thermomechanical Fatigue (TMF) tests in four 〈0 0 1〉-oriented nickel-base single-crystal superalloys were studied with the aid of microstructural investigation. Three experimental observation methods – optical microscopy, scanning electron microscope and transmission electron microscopy – were combined to obtain new insights into the microstructural and fractographic characteristics after TMF cycling with and without a compressive hold time. After the TMF cycling, the fracture surface shows different fractographic characteristics due to the introduction of the hold time. Fundamental differences in the crack propagation mechanisms have also been discovered under the influence of the compressive hold time. Without a compressive hold time, the crack propagates inwards perpendicular to the axial stress with the aid of oxidation. During the propagation, the crack reaches the twinning plate and propagates rapidly along it with the aid of the stress field at the crack tip. There appear to be obvious steps at this propagation stage. With a compressive hold time, the crack could only propagate in approximately one twinning plate. It appears in only one crystallographic fracture plane. Due to a few deformation twins being formed in this section, the crack propagation path may change to run along other twinning plates.
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Twinning Behaviors During Thermomechanical Fatigue Cycling of a Nickel-Base Single-Crystal TMS-82 Superalloy
Journal of Materials Engineering and Performance, 2013Co-Authors: Jianxin Zhang, Hiroshi HaradaAbstract:This paper provides further insight into the formation of deformation twins at different stages during the whole Thermomechanical Fatigue cycling in a nickel-base single-crystal TMS-82 superalloy. In general, it is found that twinning behaviors can always be associated with the applied stress orientation. The preferred twinning direction at the primary stage is 〈001〉-compression since the tangled dislocations which appear after the first plastic deformation provide an opportunity for twinning nucleation in compression. At the intermediate stage, the applied stress required for formation of twins in tension is much larger than that in compression; hence, twinning behaviors show distinct tension/compression asymmetry. A thick twin plate and a great many dislocations can be found after Fatigue failure, and one can rationalize the reason for this twinning being associated with the TMF procedure. Twins at the tip of the crack in tension occur owing to the existence of compressive strain field.
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Crack appearance of single-crystal nickel-base superalloys after Thermomechanical Fatigue failure
Scripta Materialia, 2009Co-Authors: Jianxin Zhang, Hirofumi Harada, Yutaka Koizumi, Toshiharu KobayashiAbstract:Thermomechanical Fatigue (TMF) testing was conducted on single-crystal nickel-base superalloys. Distinct cracking behaviors were found to occur under different cycling conditions. A crack generally initiates from the specimen surface. For the TMF cycling without a compressive hold time, the crack initially grows perpendicular to the stress axis and then propagates along a twin plate. For the TMF cycling with a compressive hold time, the main crack propagates directly along a twin plate until final failure.
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Thermomechanical Fatigue mechanism in a modern single crystal nickel base superalloy tms 82
Acta Materialia, 2008Co-Authors: Hiroshi Harada, Jianxin Zhang, Yutaka Koizumi, Toshiharu KobayashiAbstract:Abstract Thermomechanical Fatigue (TMF) in a 〈0 0 1〉 oriented nickel base single crystal TMS-82 superalloy was studied in an effort to clarify the mechanisms of stress relaxation and failure. Detailed observations of the microstructural evolution from the interior and outer surfaces of the specimens after TMF tests were made using transmission electron microscopy, scanning electron microscopy and optical microscopy. The stress relaxation took place during a hold time in compression at 900 °C, and the associated mechanisms varied with the following cycles. During TMF cycling, three stages of stress relaxations were identified: (1) primary stress relaxation; (2) steady stress relaxation; and (3) tertiary stress relaxation; each stage exhibits a distinct microstructural evolution. The first stage is related to the filling of dislocations in the γ channels; the second stage involves dislocation annihilation; and the final stage is associated with the de-twinning of deformation twins. The main crack was found to originate from the intersection of deformation twin plates with the specimen surface, and oxidation then assists the growth of the crack. The stress concentration at the crack tip results in a high density of deformation twins, and the propagation of the crack along the twin boundaries can lead to TMF failure of the specimen.
Johan Moverare - One of the best experts on this subject based on the ideXlab platform.
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Thermomechanical Fatigue crack growth in a single crystal nickel base superalloy
International Journal of Fatigue, 2019Co-Authors: Frans Palmert, Johan Moverare, David GustafssonAbstract:Abstract Thermomechanical Fatigue crack growth in a single crystal nickel base superalloy was studied. Tests were performed on single edge notched specimens, using in phase and out of phase Thermomechanical Fatigue cycling with temperature ranges of 100–750 °C and 100–850 °C and hold times at maximum temperature ranging from 10 s to 6 h. Isothermal testing at 100 °C, 750 °C and 850 °C was also performed using the same test setup. A compliance-based method is proposed to experimentally evaluate the crack opening stress and thereby estimate the effective stress intensity factor range ΔKeff for both isothermal and nonisothermal conditions. For in phase Thermomechanical Fatigue, the crack growth rate is increased if a hold time is applied at the maximum temperature. By using the compliance-based crack opening evaluation, this increase in crack growth rate was explained by an increase in the effective stress intensity factor range which accelerated the cycle dependent crack growth. No significant difference in crack growth rate vs ΔKeff was observed between in phase Thermomechanical Fatigue tests and isothermal tests at the maximum temperature. For out of phase Thermomechanical Fatigue, the crack growth rate was insensitive to the maximum temperature and also to the length of hold time at maximum temperature. The crack growth rate vs ΔKeff during out of phase Thermomechanical Fatigue was significantly higher than during isothermal Fatigue at the minimum temperature, even though the advancement of the crack presumably occurs at the same temperature. Dissolution of γ′ precipitates and recrystallization at the crack tip during out of phase Thermomechanical Fatigue is suggested as a likely explanation for this difference in crack growth rate.
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damage evolution in compacted graphite iron during Thermomechanical Fatigue testing
International Journal of Cast Metals Research, 2016Co-Authors: Viktor Norman, Peter Skoglund, Johan MoverareAbstract:Thermomechanical Fatigue properties of a compacted graphite iron in an out of phase configuration are investigated for different maximum temperatures and mechanical strain ranges. Furthermore, the stress–strain hysteresis loops are analysed, and, in particular, the unloading modulus, i.e. the elastic modulus measured during specimen unloading, is obtained from each cycle. This material parameter has earlier been explicitly related to the amount of microcracking in cast irons. The results show that the unloading modulus linearly declines with the numbers of cycles in all tests performed. In addition, the rate of change of the unloading modulus is closely related to the number of cycles to failure. Accordingly, it is concluded that microcracks are independently propagated by Fatigue until a point of rapid crack linking resulting in ultimate failure. This is supported by microstructural analyses consisting of optical microscope images taken at different stages throughout the life of a specimen.
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Thermomechanical Fatigue in single crystal superalloys
EUROSUPERALLOYS 2014 – 2nd European Symposium on Superalloys and their Applications 12-16 May 2014 Giens France, 2014Co-Authors: Johan Moverare, R C ReedAbstract:Thermomechanical Fatigue (TMF) is a mechanism of deformation which is growing in importance due to the efficiency of modern cooling systems and the manner in which turbines and associated turbomachinery are now being operated. Unfortunately, at the present time, relatively little research has been carried out particularly on TMF of single crystal (SX) superalloys, probably because the testing is significantly more challenging than the more standard creep and low cycle Fatigue (LCF) cases; the scarcity and relative expense of the material are additional factors. In this paper, the authors summarise their experiences on the TMF testing of SX superalloys, built up over several years. Emphasis is placed upon describing: (i) the nature of the testing method, the challenges involved in ensuring that an given testing methodology is representative of engine conditions (ii) the behaviour of a typical Re-containing second generation alloy such as CMSX-4, and its differing performance in out-of-phase/in-phase loading and crystallographic orientation and (iii) the differences in behaviour displayed by the Re-containing alloys and new Re-free variants such as STAL15. It is demonstrated that the Re-containing superalloys are prone to different degradation mechanisms involving for example microtwinning, TCP precipitation and recrystallisation. The performance of STAL15 is not too inferior to alloys such as CMSX-4, suggesting that creep resistance itself does not correlate strongly with resistance to TMF. The implications for alloy design efforts are discussed.
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Thermomechanical Fatigue crack growth in a cast polycrystalline superalloy
2nd European Symposium on Superalloys and their Applications, 2014Co-Authors: Johan Moverare, Sten Johansson, Paraskevas Kontis, R C ReedAbstract:Thermomechanical Fatigue (TMF) crack growth testing has been performed on the polycrystalline superalloy IN792. All tests were conducted in mechanical strain control in the temperature range between 100 and 750 °C. The influence of in-phase (IP) and out-of-phase (OP) TMF cycles was investigated as well as the influence of applying extended dwell times (up to 6 hours) at the maximum temperature. The crack growth rates were also evaluated based on linear elastic fracture mechanics and described as a function of the stress intensity factor K I . Without dwell time at the maximum temperature, the crack growth rates are generally higher for the OP-TMF cycle compared to the IP-TMF cycle, when equivalent nominal strain ranges are compared. However, due to the fact that the tests were conducted in mechanical strain control, the stress response is very different for the IP and OP cycles. Also the crack closure level differs significantly between the cycle types. By taking the stress response into account and comparing the crack growth rates for equivalent effective stress intensity factor rages Δ K eff defined as K max − K closure , very similar crack growth rates were actually noticed independent of whether an IP or OP cycle were used. While the introduction of a 6 hour dwell time significantly increased the crack growth rates for the IP-TMF cycle, a decrease in crack growth rates versus Δ K eff were actually seen for the OP-TMF cycle. The fracture behaviour during the different test conditions has been investigated using scanning electron microscopy.
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deformation and damage mechanisms in in792 during Thermomechanical Fatigue
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2011Co-Authors: Jan Kanesund, Johan Moverare, Sten JohanssonAbstract:Abstract The deformation and damage mechanisms arising during Thermomechanical Fatigue (TMF) of the polycrystalline superalloy IN792 have been investigated. The TMF cycles used in this study are in-phase (IP) and out-of-phase (OP). The minimum temperature used in all TMF-tests is 100 °C while the maximum temperature is 500 or 750 °C in the IP TMF-tests and 750, 850 or 950 °C in the OP TMF-tests. The majority of the cracks are transcrystalline, except for the IP TMF-test at 750 °C, where some tendency to intercrystalline crack growth can be seen. In all tests, the cracks were initiated and propagated in locations where deformation structures such as deformation bands have formed in the material. In the temperature interval 750–850 °C, twins were formed in both IP and OP TMF-tests and this behaviour is observed to be further enhanced close to a crack. Twins are to a significantly lesser extent observed for tests with a lower (500 °C) and a higher (950 °C) maximum temperature. Recrystallization at grain boundaries, around particles and within the deformation structures have occurred in the OP TMF-tests with a maximum temperature of 850 and 950 °C and this is more apparent for the higher temperature. Void formation is frequently observed in the recrystallized areas even for the case of compressive stresses at high temperature.
Hermann Riedel - One of the best experts on this subject based on the ideXlab platform.
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mechanism based Thermomechanical Fatigue life prediction of cast iron part ii comparison of model predictions with experiments
International Journal of Fatigue, 2010Co-Authors: Thomas Seifert, Gerhard Maier, A Uihlein, Karlheinz Lang, Hermann RiedelAbstract:In the present paper, predictions of mechanism-based models for cast iron are compared to experimental results obtained for the nodular cast iron EN-GJS-700, the vermicular cast iron EN-GJV-450 and the lamellar cast iron EN-GJL-250. A strategy is proposed to efficiently identify the model parameters based on isothermal experiments. In particular, complex low cycle Fatigue (LCF) tests, tension tests and compression tests are used to adjust the time and temperature dependent cyclic plasticity model. The time and temperature dependent Fatigue life prediction model is adjusted to LCF tests. For all investigated cast iron materials, good predictions of Thermomechanical Fatigue (TMF) tests are possible with the models. Additionally, the location of failure and Fatigue life of a Thermomechanically loaded double-sided notched specimen are predicted with high accuracy.
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mechanism based Thermomechanical Fatigue life prediction of cast iron part i models
International Journal of Fatigue, 2010Co-Authors: Thomas Seifert, Hermann RiedelAbstract:Abstract In the present paper, mechanism-based models are developed to describe the time and temperature dependent cyclic plasticity and damage of cast iron materials. The cyclic plasticity model is a combination of a viscoplastic model with kinematic hardening and a porous plasticity model to take the effect of graphite inclusions into account. Thus, the model can describe creep, relaxation and the Bauschinger-effect as well as the tension–compression asymmetry often observed for cast iron. The model for Thermomechanical Fatigue life prediction is based on a crack growth law, which assumes that the crack growth per cycle, da / dN , is correlated with the cyclic crack-tip opening displacement, Δ CTOD . The effect of the graphite inclusions on crack growth is incorporated with a scalar factor into the crack growth law. Both models can describe the essential phenomena which are relevant for cast iron materials.
