Increasing the fatigue strength of high-strength steel grades

Introduction

The fatigue strength stands as a critical parameter for metals and alloys, profoundly influencing their potential applications as structural materials across diverse industrial sectors [1; 2]. Among the spectrum of structural metal alloys, steels persist as the most prevalent choice for fabricating a wide range of metal products and structures, especially those subjected to heavy-duty operations. In instances such as rail and spring steels enduring dynamic and fluctuating loads [3; 4], the fatigue strength assumes paramount importance, directly dictating the operational lifespan of metal products [5; 6]. It’s noteworthy that fatigue strength isn’t solely contingent upon the chemical and phase compositions of steel or its structural configuration [7; 8], but also on factors such as dimensions, non-metallic inclusion morphology, and operational conditions of the metal products [9; 10]. Notably, strain hardening emerges as a viable method to influence fatigue strength positively [11 – 13]. Consequently, enhancing steel’s fatigue strength remains a pressing research imperative in contemporary materials science endeavors [14].

Materials and methods

The known relationship σ_–1 = 0.5σ_u (where σ_–1 and σ_u is fatigue strength and σ_u is tensile strength) is valid for steel with the tensile strength not exceeding 900 MPa [15; 16]. However, as the strength surpasses this threshold, the actual values of fatigue strength significantly deviate from the calculated ones [17; 18] (Fig. 1). This study focuses on exploring the correlation between fatigue strength and tensile strength in spring steel using regression analysis methods. The specific values of tensile strength (σ_u) and fatigue strength limit (σ_–1) used in this study are extracted from [19 – 23] (refer to the Table).

The statistical regression model σ_–1 = 0.028σ_u + 566.4 is inadequate. Fisher’s criterion, at 0.206, falls below the significance value (0.657), indicating a low statistical significance. Additionally, the correlation coefficient stands at a meager 0.120.

The results of regression analysis reveal a lack of a meaningful relationship between the function and the parameter. Notably, there’s a noteworthy trend: as the tensile strength of steel escalates, the disparity between actual and calculated results widens.

Consequently, it can be inferred that the factor affecting the reduction of fatigue strength, contingent upon the tensile strength of the metallic matrix (MM), is subject to alteration. Steel products are typically designed considering the fatigue strength of steel. Under these circumstances, it becomes challenging to fully utilize the available strength potential (indicated by high σ_t and σ_u levels), thereby limiting the potential to reduce the material intensity of metal structures.

The papers [18; 24] demonstrate that in the non-metallic inclusion – metallic matrix (NMI – MM) system subjected to external impacts, shear stress occurs at their interface within the MM, while NMIs, acting as stress concentrators, have the potential to amplify the effects of these impacts.

Once the stress level attains or surpasses the yield strength under shear (τ), the local regions of the NMI – MM interface activate the Frank-Read sources [16 – 18]. This activation induces local plastic deformation within the metal. With the escalation of dislocation density in these zones, initial cracks begin to propagate, eventually reaching a critical size, thereby instigating material fracture.

The magnitude of resultant shear stresses is assessed using the following equation [18; 24]:

where τ is shear stress; σ_n is external tensile stress; Е_NMI and Е_ММ are modulus of elasticity of the NMI and the ММ, respectively; d is diameter (thickness) of the NMI; l_s is the sum of maximum lengths of the zone of shear stresses in the MM at the boundary with NMI.

Consequently, the factor \(\frac{{{E_{{\rm{NMI}}}}}}{{{E_{{\rm{ММ}}}}}}\frac{d}{{{l_{\rm{s}}}}}\) represents the stress concentration coefficient (SCС). The equations governing the fatigue strength limit are expressed as follows: \({\sigma _{ - 1}} = \frac{{{\tau _t}}}{{{\rm{SCC}}}}\) or \({\rm{SCC}} = \frac{{{\tau _t}}}{{{\sigma _{ - 1}}}}.\)

In instances where compressive stresses affect the NMI – MM system, shear stresses arise at their interface. However, their magnitude is significantly lower compared to tension scenarios [18]. Henceforth, only tensile forces are further considered.

A close statistical association is evident between the yield strength and tensile strength in spring grade steels (Fig. 2). The relationship is mathematically expressed as σ_Т = 1.08σ_u – 312, presenting the regression model’s statistical parameters as follows: a standard error of 104.5 MPa; a correlation coefficient of 0.94; Fisher’s criterion standing at 100.86, with a significance level of 9·10\(^–\)⁸. The dependences of the strength limit, yield strength under shear, and tensile strength of the steel are derived from the equation τ = 0.7 – 0.75σ_Т.

When τ is divided by σ_Т using the corresponding values of σ_u, a statistical model of the Stress Concentration Coefficient (SCC) dependency on steel strength is obtained (Fig. 3).

The model appears as follows

with statistical parameters indicating a Pearson coefficient is 0.70; a standard error of 0.31; and Fisher’s criterion measuring 15.98, showing a significance level of 0.00093.

Consequently, the SCС exhibits a fairly strong statistical association with the tensile strength of steel. It suggests that as the strength properties increase, so does SCС.

For specific thicknesses of NMIs (d) and their particular morphology, the equation is formulated as follows [18]

where \(\tau _{\rm{u}}^{{\rm{ММ}}}\) represents the MM strength limit during shear and \(\sigma _{\rm{u}}^{{\rm{NMI}}}\) denotes the tensile strength of the NMI.

Results and discussion

The theoretical analysis suggests that when identical NMIs of the same morphological type and the same size coexist within the steel, the relationship between SCC and the steel’s strength properties becomes functional. However, the observed variability in the actual SCС values (Fig. 3) is linked to the presence of diverse morphological types and sizes of NMIs within the metal. The morphology of internally formed NMIs during the steel’s deoxidation process is contingent upon the ratio of oxygen to aluminum dissolved within it [25 – 27]. These endogenous NMIs exhibit varying physical properties, which are notably influenced by the proportion of SiO₂ and Al₂O₃ basic oxides present in them. This variation spans from plastic aluminosilicates to brittle globules, which remain non-deformable during the rolling process, up to yielding pure alumina [28]. Each morphological type of NMI exhibits specific physical and mechanical properties, such as modulus of elasticity (Е_NMI), tensile strength (\(\sigma _{\rm{u}}^{{\rm{NMI}}}\)) resulting in diverse SCC.

Fig. 4 illustrates the derived relationships depicting the dependency of SCC on the tensile strength of steel concerning three potential elemental compositions of NMIs, %, along with sizes of 4.0, 5.8 and 7.0 μm:

Aluminosilicates falling within groups 1 and 2 of high-modulus NMIs, surpassing the typical modulus of elasticity within the MM (with an average value of 205 hPa, as indicated in the Table). Conversely, aluminosilicates categorized under group 3 demonstrate low-modulus traits.

SCC escalates proportionally with the increase in both steel strength and the diameter (or thickness) of the NMI. The rate of this rise in SCC depends on the size and elastic modulus Е_NMI of the NMI, dictated by the ratio of mass fractions of SiO₂ and Al₂O₃ oxides within the NMI (Fig. 5). It’s noteworthy that the average rate of change in SCC, calculated from experimental data using Equation (2), corresponds to analogous indicators for NMIs: 13 % SiO₂; 87 % Al₂O₃ (4.0 μm thick); 20 % SiO₂, 80 % Al₂O₃ (5.0 μm thick); 25 % SiO₂; 75 % Al₂O₃ (7.0 μm thick).

For example, in the context of producing spring grade steels by smelting and deoxidation processes (as indicated in the Table), where diverse high-modulus NMIs are formed, these inclusions significantly impact fatigue indicators. To enhance the steel’s fatigue strength limit, it becomes crucial to ensure the formation of NMIs with a modulus of elasticity not exceeding that of MM (Е_NMI ≤ Е_ММ) and a thickness (d) that does not surpass l_s.

As per [18], achieving involves the formation of NMIs in steel, comprising at least 60 – 65 % SiO₂, with the total content of high-modulus oxides like Al₂O₃, MgO not surpassing 35 – 40 %. These NMIs, when produced under these conditions, exhibit ductility at the heating temperature for metal rolling, allowing for easy deformation, resulting in the formation of thin filaments. For example, during rail rolling, aluminosilicate NMIs are generated within the rail head, measuring approximately 4.0 – 6.0 μm in diameter and having an average length of 40 – 50 μm. Fig. 6 illustrates the calculated maximum diameter (or thickness) for NMIs with the specified chemical composition and various levels of tensile strength within the MM.

Hence, as long as the NMI thickness does not exceed 8.5 μm (maintaining a d/l_s ≤ 1, E_NMI/E_ММ ≈ 1.0 [18], the SCC remains below 1.0, even with MM strength reaching 2000 MPa. In this context, the fatigue strength of the considered steel must be equal to or exceed the yield strength of the metallic matrix during shear.

Conclusions

To enhance the fatigue endurance of steel, particularly in high-strength conditions, employing aluminum-free metal deoxidation technology during smelting proves beneficial. This approach facilitates the creation of a desirable NMI morphology, ensuring that the SCC remains below 1.0. Achieving a fine-grained structure in steel post heat treatment is feasible by deoxidizing without the inclusion of aluminum, instead incorporating minimal amounts of vanadium, niobium, or titanium.