Lifetime and Damage Characterization of Compacted Graphite Iron During Thermo-mechanical Fatigue Under Varying Constraint Conditions


The cylinder head of heavy-duty fuel engines, made of compacted graphite iron, is sensitive to cracking as a result of a phenomenon called Thermo-Mechanical Fatigue (TMF) induced by subsequent start-up and shut-down cycles of the engine. Under laboratory conditions, various test setups were applied to reproduce the TMF behavior of the valve bridge areas, which are specifically prone to TMF. In these laboratory tests, various mechanical boundary conditions were applied including single and double constraints at low and high temperatures. The TMF lifetime is satisfactorily modeled based on the Paris Crack Growth Law. The reason why the law can accurately simulate the lifetime is due to the fact that this law allows for a description whereby plastically induced damage is gradually built up cycle by cycle, which eventually is reflected in the Cp parameter of the Paris equation. It was proven that the description is valid under partial constraint, full constraint, and over-constraint boundary conditions and even with varying constraint conditions at high and low temperature. Post-processing of the Paris Law model allowed defining an equivalent constraint value γ′, which is a single constraint that yields an identical lifetime as the experiment with double constraint at low and high temperature.

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a :

Defect size


As cast


Compacted graphite iron

Cp :

Paris’ crack growth law factor


Elastic modulus


Energy-dispersive X-ray spectroscopy


Finite elements

f g :

Shape factor


High cycle fatigue

KI :

Stress intensity factor


Low cycle fatigue


Linear elastic fracture mechanics

m :

Paris’ crack growth law exponent factor

N :

Number of cycles

N 10 :

Number of cycles to failure criteria

N f :



Out of phase

r :

Sample radius at the gauge length


Standard deviation


Thermo-mechanical fatigue


Total strain range


Valve bridge


X‐ray fluorescence analyzer

α :

Thermal expansion coefficient

γ :



Effective equivalent constraint

ε m :

Mechanical stain

Δε m :

Mechanical strain range

Δε p :

Plastic strain

\( {\overline {\Delta \varepsilon }_{\text{p}}} \) :

Average plastic strain constructed with Δεp values of cycles 4, 10, 20, 40 and N10

ΔT :

Temperature difference

σ :


ε th :

Thermal strain

ε E :

Elastic strain

ε total :

Total strain of the gauge length

\( {\varepsilon_{{\text{t}}{{\text{h}}_{\text{ref}}}}} \) :

Reference thermal strain

\( {\varepsilon_{{\text{total}}\_{\text{LT}}}} \) :

Total strain at minimum temperature

\( {\varepsilon_{{\text{total}}\_{\text{HT}}}} \) :

Total strain at maximum temperature


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M.Sc student Reinton Elise (TU-Delft) is acknowledged for her assistance with carrying out the experimental schedule.[30] The authors are also indebted to Dr. A.C. Riemslag for ample valuable discussions. The authors acknowledge and thank the contributions of Aslan Mohammadpour who performed Finite Elements calculations regarding temperature gradients at the sample gauge length during heating and cooling.


This research was carried out under project number F23.5.13484a. in the framework of the Partnership Program of the Materials Innovation Institute M2i ( and the Foundation of Fundamental Research on Matter (FOM) (, which is part of the Netherlands Organization for Scientific Research (

Author Contributions

Conceptualization: Edwin A. Lopez-Covaleda; Methodology: Edwin A. Lopez-Covaleda, Sepideh Ghodrat, and Leo A.I. Kestens; Formal Analysis: Edwin A. Lopez-Covaleda, Sepideh Ghodrat, and Leo A.I. Kestens; Investigation: E.A. Lopez-Covaleda; Resources: Leo A.I. Kestens; Data Curation: Edwin A. Lopez-Covaleda; Writing-Original Draft Preparation: Edwin A. Lopez-Covaleda; Writing-Review & Editing: Edwin A. Lopez-Covaleda, Sepideh Ghodrat, and Leo A.I. Kestens; Visualization: Edwin A. Lopez-Covaleda; Supervision: Sepideh Ghodrat and Leo A.I. Kestens; Project Administration: Leo A.I. Kestens; Funding Acquisition: Leo A.I. Kestens.

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Correspondence to Edwin A. Lopez-Covaleda.

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Manuscript submitted January 29, 2019.

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Lopez-Covaleda, E.A., Ghodrat, S. & Kestens, L.A.I. Lifetime and Damage Characterization of Compacted Graphite Iron During Thermo-mechanical Fatigue Under Varying Constraint Conditions. Metall Mater Trans A 51, 226–236 (2020).

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