Effect of Thermal Expansion Mismatch on Thermomechanical Behaviour of Compacted Graphite Iron

Abstract

Compacted graphite iron (CGI) attracts significant attention in the automotive industry thanks to its suitable thermomechanical properties and cost-effectiveness. A primary fracture mechanism at the microscale for CGI involves interfacial damage and debonding between graphite inclusions and its metallic matrix, which can occur under high-temperature service conditions due to a mismatch in the coefficients of thermal expansion between these two phases. Such microscopic interfacial damage can initiate macroscopic fractures in cast-iron components subjected to thermal loading. While this phenomenon was studied in various composites, there remains a lack of detailed information for CGI, especially related to the complex morphology of its graphite inclusions. This study investigates the influence of graphite morphology and type of matrix on the thermomechanical performance of CGI at high temperatures. A set of three-dimensional finite-element models were developed in the form of unit cells with a single graphite inclusion embedded within a cubic domain of the metallic matrix. Elastoplastic behaviour was assumed for both phases in the numerical simulations. The study is focused on the response of the constituents in CGI to pure thermal loading in order to explore the relationship between graphite morphology and fracture mechanisms. The findings aim to enhance understanding of how graphite morphology affects the behaviours of CGI under high-temperature conditions.

1. Introduction

Cast iron with high wear resistance, mechanical properties and economic benefits is an important material in engineering. In 1948, compacted graphite iron (CGI) was initially applied in the industry as a type of cast iron [1]. Its industrial applications include exhaust manifolds [2], cylinder heads, blocks and brake drums [3] in automotive engineering.

At the microscale, CGI can be regarded as a metal–matrix composite consisting of graphite inclusions and a metallic matrix (Figure 1). Based on their morphology, the graphite inclusions in CGI are classified into three types—nodular graphite, vermicular graphite and flake graphite [4]. The metallic matrix of CGI is composed of ferrite, pearlite or a mixture of both, with different types of CGI having different mechanical properties [5].

Among the main factors affecting the thermomechanical behaviour of cast irons are the graphite morphology and matrix microstructure [6]; this explains the use of various types of cast irons. The advantages of CGI over grey cast iron include higher tensile strength, a greater strength-to-hardness ratio and increased ductility and toughness. Compared to spheroidal graphite cast iron, CGI offers a lower coefficient of thermal expansion, better heat conduction, greater resistance to thermal shock and superior damping capacity [7]. CGI (with its 247 HV) has approximately ten times better wear resistance than spheroidal graphite iron, which has a lower hardness of 172 HV [7,8]. Typical CGI features a ferrite, ferrite/pearlite, or pearlite matrix. Due to the extensive contact surface between graphite inclusions and the matrix in CGI, there is a strong tendency for the formation of a ferrite matrix [9]. It is a soft and ductile phase in cast irons with high toughness and excellent machinability but lower strength. In contrast, pearlite consists of alternating layers of ferrite and cementite, creating a microstructure that combines higher strength and hardness with good toughness and wear resistance. A pearlite matrix is achieved by adding pearlite-stabilizing alloying elements such as Cu, Sn, Cr or Ni [10]. Among the various types of CGI materials in class 450 with different pearlite contents, CGI GJV-450 with 84% pearlite demonstrates greater hardness but a shorter tool life compared to CGI GJV-450 with 89% and 90% pearlite [10]. During CGI milling, the tool life of coated cemented carbide tools was found to be around 73 min for CGI with 86% pearlite, whereas it exceeded 140 min for CGI with 21% pearlite [11]. It was found that the interlamellar distance in pearlite did not have as significant an impact on the physical properties of the material or machinability compared to the pearlite content [11].

Although CGI has been widely used in various industrial applications, its fracture behaviour at the microscale is still insufficiently studied. Graphite particles play an important role in the fracture process due to their soft and brittle nature, with a low coefficient of thermal expansion (CTE). Under heating, these particles typically exhibit limited expansion, unable to match the level and rate of that for the surrounding matrix. This mismatch in deformation can lead to interfacial debonding, with the inclusions separating from the surrounding matrix at, or close to, the interface [2,12]. The fully debonded inclusions can no longer support load and effectively function as voids. Furthermore, the debonding at the graphite–matrix interface can initiate the formation of microcracks in the deformed metallic matrix that may eventually merge, leading to the development of primary macrocracks [13]. Graphite inclusions separate from the ferrite matrix at stress levels around 320 MPa, while separation from the pearlite matrix occurs at stress levels exceeding 770 MPa in ductile iron [13,14]. However, the effect of the ferrite matrix and pearlite matrix on the behaviour of CGI is not yet fully understood.

In industrial applications of cast iron, components in diesel engines are exposed to high temperatures, typically ranging from 400 °C to 600 °C [15]. In such an environment, CGI experiences softening, and the interfacial debonding initiates at lower stress levels compared to its behaviour at room temperature. Interfacial debonding occurs at stress levels below 50 MPa at 723 K (450 °C), while at room temperature, it was observed at stress levels exceeding 495 MPa [16,17,18]. This process is additionally affected by residual stresses introduced in casting. As spheroidal graphite iron cools from casting to room temperature, thermal residual stresses increase due to the disparity in thermal expansion [19]. So, even pure thermal loading conditions can cause interfacial debonding, but this phenomenon—caused by a thermomechanical mismatch of CGI constituents—has not been fully studied.

Recent studies on the thermomechanical performance of cast irons mainly utilize two approaches for numerical simulation: phenomenological and micromechanical models. The former scheme typically overlooks the specific contributions of the phases, focusing instead on representing the material’s overall behaviour by adjusting macroscopic parameters such as the yield surface and hardening characteristics to reflect the effects of microstructure and fracture mechanisms [20,21,22,23,24]. In contrast, micromechanical models directly incorporate microstructural parameters into simulations to assess their effects on mechanical responses [2,25]. In such simulations, the material components are typically assumed to display elastoplastic behaviour [26] or anisotropic properties [27]. When evaluating the effects of different factors and assumptions related to inclusions on microstructural behaviour, the matrix is usually simplified, commonly modelled as either ferrite or pearlite with elastoplastic properties.

This study analyses the phenomenon of graphite debonding under pure thermal loading, focusing on evaluating the influence of graphite morphology and matrix properties on its initiation and progression. The evaluation is carried out using three-dimensional numerical simulations, with key model inputs obtained from statistical analyses of scanning electron microscope (SEM) images and mechanical testing across different temperatures [28].

2. Numerical Simulations

2.1. Geometry

Complex shapes of graphite inclusions in CGI require direct introduction of the microstructure into numerical analyses to assess their response to purely thermal loading conditions, typical for many applications. Based on in-house micrographs obtained with SEM [29] and the microstructure characterization analysis [28], a single-inclusion representative volume element (RVE) was developed for this study. The three-dimensional model consists of single graphite inclusion and the surrounding matrix area (Figure 2).

For comparability, specific dimensions of the particles were used in this study: the diameter of a nodular graphite particle (Nod_N)—15 μm—was equal to the length of the major axis of vermicular graphite inclusions. The volume of nodular graphite was 6.5%, within the typical volume fraction range for CGI [30]. Vermicular graphite was assumed as an oblate spheroid with a minor axis length of 8 μm and oriented in different directions with regard to main axes related to the cubic matrix. The model with the major axis of vermicular particle oriented perpendicular to the top surface of the cubic matrix is denoted as Ver_VV, while that with the major axis aligned parallel to the top surface of the metallic matrix (i.e., parallel to the XY plane, Figure 2) is referred to as Ver_VH. The effect of interaction between graphite inclusions was not considered in this study. This approach enables the evaluation of the impact of both matrix phases on graphite debonding. To account for the remaining graphite inclusions, the metallic matrix was modelled with effective properties of the metallic (ferrite or pearlite) matrix.

It is important to consider that, in practical CGI components, numerous graphite inclusions are dispersed throughout the matrix. Their distribution and interactions can significantly alter the stress and strain fields within the material. Overlapping stress concentrations from nearby inclusions can amplify local stresses, potentially accelerating damage initiation and crack propagation [31]. Additionally, the collective thermal and mechanical behaviour of multiple inclusions contributes to the development of complex internal stresses during service [32]. While this work provides insights into the fundamental mechanisms around individual inclusions, future work should incorporate models with multiple inclusions to more accurately reflect the material’s microstructure and predict its macroscopic behaviour under operational conditions.

2.2. Constitutive Behaviours

There is a considerable spread in the data available for both the graphite and matrix in CGI. Due to their inherently soft and brittle behaviour, graphite particles have traditionally been modelled with limited plasticity in prior numerical studies [33,34,35]. For the thermal properties of graphite, constant CTE (C-CTE) [28] and temperature-dependent (T-CTE) [19] coefficients of thermal expansion were considered (See Figure 3a). In this analysis, the inter-particle distances within CGI were smaller than the model dimensions, prompting the assignment of effective properties to the metallic matrix domain, consistent with those applied in our previous two-dimensional studies [36,37]. These matrix properties accounted for the microstructure of the studied CGI, which included the contributions of the ferrite and pearlite phases. The properties of the (effective) matrix were selected from our previous study based on a representative experimental stress–plastic strain curve for CGI (Figure 3b) and was employed in this work. The case of the matrix with effective properties is compared with cases of pure ferritic [38] and pearlitic [39] matrices. Generally, the ferrite phase is much softer than the pearlite one; it also demonstrates a higher extent of thermal extension at the entire temperature range under study. The J2 flow theory was adopted to characterize the mechanical behaviour of both the metallic matrix and the graphite inclusions [30].

A ductile damage criterion was considered in this study. Ductile fracture includes three stages: voids, microcracks and macrocracks [40]; it is suitable for cast irons and has been used in previous research [41]. The numerical assessment of damage was conducted by evaluating the damage variable ${\omega }_{\mathrm{D}}$ at all Gauss points in a finite element. This variable denotes the proportion of stiffness reduction following the initiation of material mechanical degradation. Hence, an element was deemed damaged when ${\omega }_{\mathrm{D}}$ became non-zero at any Gauss point, while element deletion occurred when the critical damage value was exceeded at all integration points. The fundamental equations governing the chosen damage criterion are as follows [42]:

$${\omega }_{\mathrm{D}}=\int {\displaystyle \frac{d{\bar{\epsilon }}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}}{{\bar{\epsilon }}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}\left(\eta ,{\dot{\bar{\epsilon }}}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}\right)}}=1,$$

(1)

$$\mathsf{\Delta }{\omega }_{\mathrm{D}}={\displaystyle \frac{\mathsf{\Delta }{\bar{\epsilon }}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}}{{\bar{\epsilon }}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}\left(\eta ,{\dot{\bar{\epsilon }}}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}\right)}}\ge 0,$$

(2)

where ${\bar{\epsilon }}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}$ represents the equivalent plastic strain at the onset of damage, expressed as a function of stress triaxiality $\eta$ (ratio of hydrostatic pressure to the von Mises equivalent stress) and equivalent plastic strain rate, ${\dot{\bar{\epsilon }}}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}$. The parameter ${\bar{\epsilon }}_{\mathrm{D}}^{\mathrm{p}\mathrm{l}}$ for graphite was assigned the value corresponding to the strain at yield (0.184%), based on the assumption that graphite is highly brittle and cannot undergo significant plastic deformation [33]. Consequently, ${\omega }_{\mathrm{D}}$ was computed at each increment, and the damage criterion required the difference between successive increments ($\mathsf{\Delta }{\omega }_{\mathrm{D}}$) to be non-negative.

2.3. Boundary and Loading Conditions

As mentioned previously, the high-temperature service condition of CGI utilized in automotive engineering can exceed 400 °C. Components are often subjected to combined thermal and mechanical stresses in real-life applications; however, to study the individual effect of high temperature on the thermomechanical behaviour of CGI at the microscale, pure thermal loading was applied to all unit cells, with a temperature history of 20 °C–500 °C–20 °C. The analysis in numerical simulations was quasi-static, reflecting relatively low heating and cooling rates used in the experiments, without any thermal shocks. The combined action of mechanical and thermal loadings will be studied in the future.

Generally, representative volume elements (RVEs) are considered the smallest microstructural components capable of effectively representing the entire structure, particularly when they exhibit a regular pattern [43]. Nodular graphite inclusions with simple spherical shapes were easily modelled in RVE simulations for ductile cast iron [19,44]. However, in CGI, the complex shape of three types of graphite particles was mainly applied to 2D studies [19] or single-particle 3D unit cells [45]. Elastoplastic behaviours of the matrix were extensively studied with unit cells for various materials such as cast irons [21,45,46] and steel [39]. Accurately modelling an RVE requires ensuring the continuity of both displacements and tractions across its adjacent edges. This continuity is achieved by applying periodic boundary conditions (PBCs) at the edges of the RVE, which allows precise simulations of the deformation field [47]. In this study, PBCs were applied to the pairs of side surfaces. The top surface was free to deform, and the bottom surface was constrained with (U1 = U2 = UR3 = 0) where the bottom surface can deform in the XY plane.

The elongation of the developed unit cell under thermal loading was calculated and compared to the literature data, showing the reasonably close position of the curves (Figure 4).

3. Results and Discussion

3.1. Effect of CTE of Matrix on Damage Distribution

In this part of the study, C-CTE was assigned to graphite inclusions, whereas three types of the metallic matrix were considered, as discussed above—common (effective), pearlite and ferrite. The distribution of damage in graphite inclusion at different temperatures after the heating and cooling stages was analyzed for the outer surface of particles, where the highest levels were found (Figure 5). The damage distribution, recorded from all the elements on this surface of the particle, was summarized in two subgraphs representing the end of the heating (Figure 5a) and cooling (Figure 5b) stages. The maximum damage values are crucial as they clearly indicate the potential failure regions in the material. While average damage values provide a general overview of its evolution on the outer surface of inclusions, the maximum values specifically highlight the areas of greatest vulnerability, essential for understanding the most severe damage effects under thermal loading conditions. The temperature increase from 20 °C to 500 °C caused different levels of thermal expansion of the inclusion and the matrix as a result of the CTE mismatch. The induced interfacial interaction between the two domains triggered the damage formation in graphite.

In all the studied unit cells, the maximum level of damage in the spherical inclusion was higher than in the vermicular ones because of its larger volume. At 500 °C, after the heating step, the maximum damage in spherical graphite approaches 0.33 in the case of the common matrix, increasing to 0.55 after the cooling stage. A higher level of maximum damage was observed in the Ver_VV unit cell at 500 °C. After the cooling step at 20 °C, both the average and maximum values of damage increased for the vermicular particles (Figure 5).

With the lowest stiffness curve and the largest CTE, the maximum damage in graphite inclusion surrounded by the ferrite matrix was higher than that in the case of the pearlite and common matrices. The maximum damage level for the spherical particles (0.55, Figure 6) was also larger than for the vermicular particles (0.5 for Ver_VV and 0.25 for Ver_VH) at 500 °C. The damage also accumulated during the cooling stage, with its maximum level achieving 1 in the spherical particle (Figure 6c); hence, some parts of the contacting area were fully damaged and could not carry load. The maximum damage level for Ver_VV was also close to 1 and higher than for Ver_VH (0.5).

The damage levels in graphite inclusions surrounded by the pearlite matrix were lower than for the ferrite one because of pearlite’s relatively higher stiffness and lower CTE (Figure 7). The volume affected the damage in graphite inclusion significantly as it was always higher in spherical graphite particles than in the vermicular ones. For the same volume of vermicular inclusions, the damage in graphite was higher at its contact with the metallic matrix at the narrow edge (Ver_VV), resulting in stress concentration.

Clearly, the morphology and size of graphite inclusions play crucial roles in determining the material properties of CGI. Different graphite shapes—such as flake, spheroidal, and vermicular—and a change in their sizes can lead to variations in stresses, also affecting the thermal expansion behaviour, damage, and crack-initiation sites. While this study was focused on specific cases of the morphology and sizes of graphite particles for purposes of clarity and comparability (as well as model validation), future research will explore a broader range of shapes and dimensions of inclusions (i.e., their volume fraction) to fully understand their impact on CGI’s thermomechanical performance.

3.2. Effect of CTE of Matrix on Stress Distribution

The distribution of von Mises stresses is measured and summarized in Figure 8 and Figure 9 for path AB (see Figure 2) from the graphite–matrix interface on the top surface of the metallic matrix to the edge of the model. As discussed, the major axis length of the vermicular graphite particle was equal to the diameter of the nodular inclusion (15 μm), while the length of the cubic model was 30 μm. Thus, the length of the path in the metallic matrix was 7.5 μm (the position with 0 μm corresponds to the interface). The domain was stress-free before the thermal loading.

Under PBCs, both the graphite particle and the metallic matrix were free to expand in the Z direction. When the temperature of the model increased and approached 500 °C, two domains in all three types of unit cells expanded, causing different levels of displacement because of different CTEs. The most significant interaction between the constituents caused by the mismatch of CTEs was observed at the location close to the graphite–matrix interface. For PBCs, the levels of von Mises stress decreased along path AB. The CTE of the standard matrix was the lowest, smaller than that of pearlite and ferrite matrices. This resulted in lower interaction between the graphite particles and the matrix, leading to the lowest levels of damage (Figure 5) compared to the ferritic (Figure 6) and pearlitic (Figure 7) matrices at 500 °C. The load-bearing capacity of graphite particles decreased as damage grew, causing the maximum von Mises stress levels to be highest in the standard matrix, followed by pearlitic and then ferritic matrices. This phenomenon was observed in all unit cells with different types of graphite inclusions. The particle morphology affected the level of stresses in the matrix, with the highest magnitudes observed for the VV particle and the lowest ones for the VH case (the nodular particle caused somewhat higher stresses).

During the cooling stage when the temperature dropped from 500 °C back to 20 °C, von Mises stress in all three types of matrices decreased because of a shrinkage phenomenon (Figure 9). The interaction between the graphite particles and the metallic matrix became less strong. With the same volume but different orientations of vermicular graphite particles, the von Mises stress levels were higher in VV unit cells compared to VH cells, while for the nodular particle they were close to those for VH due to the similar volume of graphite on the top surface. Still, the case with the nodular inclusion demonstrated a higher sensitivity to the matrix type than VH: the variation in von Mises stress near the graphite–matrix interface was much lower for the vermicular (VH) particle.

3.3. Effect of CTE of Graphite on Damage Evolution

The evolution of maximum damage in graphite inclusions with different CTEs but with the same material of metallic matrix is summarized in Figure 10. Although the matrix material, volume, and morphology of the graphite inclusions remained consistent, the mismatch in the CTEs between the two material domains is an important factor for all the unit cells. The maximum damage level of the graphite with T-CTE was consistently larger than for the case of C-CTE.

The maximum damage in the vermicular particle Ver_VV with T-CTE approached 0.63 and was higher than for C-CTE (0.24) after the thermal load at 20 °C. Graphite with a lower T-CTE generated greater strain differences at the inclusion interface during the heating and cooling stages. This triggered damage initiation in inclusions, with damage accumulated even during the cooling stage with decreasing temperature. The higher induced plastic strains at these interfaces render the low-CTE graphite more vulnerable to damage under thermal loading for the vermicular particles with the same volume.

With a relatively flat interface between the graphite and the matrix, the maximum damage levels in Ver_VH were smaller than those in Ver_VV with the narrow edge for all temperatures and CTEs. With its rounded interface with a larger contact area, the maximum damage level in the spherical particle was higher than in the vermicular ones because of the higher volume of graphite.

4. Conclusions

In this study, the thermal expansion mechanism in micro-structured CGI was investigated for pure thermal loading of CGI. A set of three-dimensional numerical models were developed using the concept of RVEs. The morphology of a graphite inclusion embedded within a cuboid domain of the metallic matrix, assuming perfect bonding between the phases, was considered.

The significantly higher coefficients of thermal expansion of the matrix than of the graphite cause larger strains in the matrix than that of graphite inclusions and the damage in graphite was caused by the thermal expansion mismatch between the phases. Under the PBCs, the damage appears at the free top surface of the model. A higher volume of the nodular particle showed a more significant effect on the damage in the unit cell.

For the same morphology and behaviour of inclusions, the highest damage level in graphite was observed for the unit cell with a softer matrix (i.e., ferrite). So, the matrix material with higher stiffness provides better protection against damage in graphite inclusions. The smaller damage resulted in a higher load-bearing capacity of graphite particles causing higher residual stress in the matrix. With more thermal cycles, stress might accumulate and exceed the yield strength of CGI. With the increased use of components (i.e., larger number of thermal cycles), growing different displacements of constituents can create some irregularities on the surfaces as a result of their nonuniform expansion and contraction. This effect may accelerate wear, particularly in components with significant contact surfaces, like engine blocks or brake discs, ultimately shortening their operational lifespan.

For the same materials of the phases, the morphology of particles affected the damage in the unit cell. The maximum damage in the nodular inclusion was larger than that in the vermicular ones because of the higher graphite volume. However, for the same morphology but different orientations of vermicular particles, the effect of the narrow edge in Ver_VV on damage was more significant than the flatter edge of Ver_VH.

Although the volume fraction of graphite was significantly lower than that of the metallic matrix, the type of thermomechanical behaviour of inclusions still affected the response of the matrix to the thermal loading. For the vermicular Ver_VV, both the affected area and the maximum levels of strains of the matrix were larger than those in Ver_VH. Compared to C-CTE, the lower thermal expansion of graphite in the T-CTE case caused larger graphite damage but lower stress in the metallic matrix.

It is important to note that in automotive applications, engine components experience cyclic stresses caused not only by thermal loading but also from mechanical loads during operation. Time-dependent factors such as creep [49], fatigue [50] and oxidation effects [51] under prolonged high-temperature service conditions play significant roles in material degradation and failure mechanisms. Although this study focused on pure thermal cycles to provide some insights into microstructural effects on the thermomechanical performance of CGI, future work will incorporate these factors in order to more accurately simulate the operational conditions and to develop a comprehensive understanding of the material behaviour and its evolution.