Layer Approach to Model Fatigue Strength of Surface-Hardened Components

Abstract

This paper deals with a surface-hardened forged steel that is commonly used for powertrain components like gears, axles or crankshafts. In order to increase static and fatigue strength and to minimise wear, surface treatments like induction hardening lead to a significant microstructural change within heat-affected zones. The aim of this study was to elaborate a method for a reliable computational estimation of the local fatigue strength by considering local material properties. The method is based on experimental test results, where specimens were extracted from forged crankshafts and further heat-treated to investigate the fatigue strength of the unhardened and hardened material condition. The experimental test data were fundamental in defining elaborated Haigh diagrams, enabling a more reliable local fatigue assessment. The comparison of the component safety within the fatigue strength verification for a crankshaft section under alternate bending resulted in $28\%$-more progressive dimensioning of surface hardened layers.

1. Introduction

The current situation in the automotive industry is the claim of consistent lightweight design [1]. Hence, cost-efficient manufacturing processes, like surface hardening, have established themselves for highly stressed components, e.g., gears, axles or shafts [2,3]. These mass-production-suitable fabrication processes minimise wear and pitting [4] and increase fatigue strength [5]. Techniques causing further strength due to heat treatment are, e.g., nitriding, case and induction hardening [6]. This submitted paper focuses on an induction hardening process whereby the component surface is heated and quenched immediately, which significantly enhances the local fatigue strength, especially in cases of notched components [7]. An overview of the impact of induction-hardened crankshafts is presented in [8,9,10]. The use of thermal proceedings results in microstructure transformation within heat-affected zones, which can cause compressive residual stresses in the mentioned areas. In general, numerous finite element analyses-based residual stress studies for different heating processes [11,12,13] are applicable. The accordant state-of-the-art simulation is documented in [14]. Furthermore, the numerical methodology of residual stresses according to induction hardening is discussed in [15,16,17,18]. The change of microstructure leads to a significant impact on static and cyclic fatigue strength properties in the depth direction of structural components. In the majority of cases, the surface layer, however, has greater hardness and a significantly increased endurance limit in comparison to the subjacent ductile base material. Fatigue diagrams are used to depict endurance limits at different stress ratios, while visualisation according to Haigh is common. Points with equal stress ratio R values are revealed in linear relations through the coordinate origin ${\sigma }_a={\sigma }_m=0$. The following correlation was recommended by [19] to describe the slope between the two straight lines of alternating and pulsating stress ratios:

$$\begin{array}{cc}\hfill m& ={\displaystyle \frac{{\sigma }_a(R=-1)-{\sigma }_a(R=0)}{{\sigma }_a(R=0)}}\hfill \end{array}$$

(1)

As a consequence of microstructural change, the hardened surface area is more mean stress-sensitive, which can be established by an increase of overall tensile strength within the hardened surface area [20]. Because of the maximum compressive residual stresses underneath the surface, the durability of the hardened material rises slightly. As a result of the inner state of equilibrium of the stresses the development of tensile residual stresses leads to possible crack initiation in transition or base material layers. Figure 1 depicts the explained facts of the different distances from the components’ surface for one stress ratio in a comparison between load-induced stress and the material’s ability to withstand these load-induced stresses.

In relation to the presented studies and the conclusions made within [21,22,23,24,25], this paper scientifically contributes to the fatigue strength of surface-hardened steel layers by the following key topics:

• Experimental investigation of the cyclic fatigue strength properties of 38MnSiVS5 steel in two different microstructural states (untreated and martensitic microstructure) are discussed in detail in Section 2.
• Development of a depth-dependent fatigue stress diagram for surface-hardened components by the example of a crankshaft section.
• Validation study of a two-layer approach, in order to calculate the fatigue strength of an induction-hardened crankshaft section under alternate bending.

Figure 1. Mechanical load and durability of surface-hardened components adapted from [26].

Figure 1. Mechanical load and durability of surface-hardened components adapted from [26].

These effects regarding different hardening manufacturing processes are taken into account within fatigue design guidelines [20] and imply conservative component design by using technology factors. By exciting material properties, this paper presents a layer approach, e.g., see [27], considering different material properties of surface-hardened components for an engineering-feasible fatigue design concept.

2. Material and Methods

As a representative of induction surface hardening, including the produced metallurgical structure, crankshaft-bearing areas were studied. Figure 2 depicts a sectional view of a crankshaft where the cutting plane is located through both the main and the connecting rod bearings. The schematic figured martensitic microstructure was extended with microsection images. The resulting microstructure layers due to the induction hardening of the bearing surfaces can be determined:

The material investigated was AFP steel 38MnSiVS5, which is common for induction-hardened components, and is applied within the automotive field, e.g., high-pressure distributor systems [28] or crankshafts [29].

Table 1. Nominal chemical composition of 38MnSiVS5 in per cent by weight adapted from [29,30] (A) and nominal mechanical properties of 38MnSiVS5 adapted from [29] (B).

A
C	Si	Mn	V
0.34–0.41	0.15–0.80	1.20–1.60	0.08–0.20
B
Yield Strength $R_{p0.2}$ (MPa)	Ultimate Strength $R_m$ (MPa)	Elongation at rupture A (%)	Young’s modulus E (MPa)
≥580	≥850	≥10	210,000

(A) lists the as-per-standard permitted distribution for the chemical composition of the reviewed forging steel. The typical manufacturer specifications according to static-strength parameters are shown in Table 1(B).

To assess different microstructure behaviours for induction-hardened surface areas (see Figure 2) the following specimen preparation was partitioned into hardened and unhardened samples. The starting point of the manufacturing procedure was represented by a forged four-cylinder crankshaft. The first separation process comprised two cuts across parallel planes formed of main and conrod-bearing axes leading to a $20\mathrm{mm}$ thick middle part. The subsequently extraction of cuboids is depicted in Figure 3. The separation processes used were wire-eroding and waterjet cutting, due to time and economy concerns. The fabricated cuboids represented the foundation of the axisymmetric specimens. Machines with rotating tools will fabricate an unhardened specimen target form out of cuboids directly. The specimens representing hardened-surface-layer properties were transformed into a martensitic microstructure via oven hardening. Then, the cuboids were partially reworked by turning and grinding into an axisymmetric form plus an offset. This was followed by a two-hour heating at $850 °\mathrm{C}$ and an instant quenching procedure within a polymer-immersion bath. Downstream annealing at $220 °\mathrm{C}$ joined the tempering action. To receive final-specimen geometry identical to unhardened samples, one last machining process completed the manufacturing part.

These executed steps of production led to a martensitic microstructure which had to be contrasted with the serial components.

Figure 2(right) depicts the hardness depth profile along the direction presented in Figure 2(left). The measurement direction and length of the unnotched specimens were prepared along the smallest cross-section and total diameter. All length specifications were normalized to the available measurement depth. The comparison led to a very similar hardness level between the hardened samples and the surface-bearing areas. For the sake of completeness, however, the hardening profile of the unhardened specimen was noted. The microstructure analysis of the received samples can be found in Figure 4. For improved comparability, all forged crankshafts used were taken from the same production batch.

Figure 5 contains the dimensions of the axisymmetric specimens used for the fatigue testing. The shown dimensions were applied to both microstructures, whereby the critical diameter was $d=8\mathrm{mm}$. To transfer the supporting effect to the crankshaft, the notched geometry approximated the serial fillet according to the stress gradient, formfactor and highly stressed volume. Other geometrical parameters, e.g., length l or diameter D, were chosen in accordance with the volume availability of the crankshaft.

To receive different fatigue microstructure behaviour, the experimental action was based on uniaxial tension–compression, rotate bending and torsion S/N tests at partially different stress ratios. The point of interest was the statistical assessment of fatigue strength at N = 6,000,000 load cycles, which is characteristic for basic motor parts. To evaluate the endurance limit, the testing procedure included 15 specimens for each tension–compression and bending S/N curve. The torsional tests used eight samples per S/N curve. This led to a minimum need for 244 specimens according to the following testing scheme for testing alternating tension–compression, pulsating tension–compression, alternating bending, alternating torsion and pulsating torsion:

• Unnotched, untreated Rz1 specimen.
• Unnotched, hardened Rz1 specimen.
• Notched, untreated Rz1 specimen.
• Notched, hardened Rz1 specimen.

• However, to achieve a depth-dependent Haigh diagram, this paper derived from uniaxial unnotched tension–compression S/N curves.

3. Test Results

The fatigue investigations of the manufactured specimens were performed on force-controlled test machines at room temperature and under laboratory air. The runout level was estimated via procedure according to [31]. The slope of the S/N curve within the finite-life fatigue strength area was received via failures and re-tested runouts. Figure 6(left) displays the tension–compression S/N curves of the unnotched geometry at stress ratio $R=-1$ for both microstructures. The fatigue strength amplitudes were ${\sigma }_a\left(\mathrm{hardened}\right)=628.7\mathrm{MPa}$ and ${\sigma }_a\left(\mathrm{unhardened}\right)=318.2\mathrm{MPa}$. These two series of experiments were characterized by relatively low dispersion $T_{\sigma }\le 1:1.17$. Furthermore, the runout level of the hardened specimens was twice that of the initial ductile structure. To assess the fatigue strength at N = 6,000,000 load cycles according to [31], five unhardened and nine hardened runouts were used. Hence, those testing results are not fully statistically secure.

The fatigue test results for the pulsating-tension stress ratio of the unnotched specimens are illustrated in Figure 6(right). The evaluation of the runout levels resulted in fatigue strength of ${\sigma }_a=246.6\mathrm{MPa}$ (unhardened) and ${\sigma }_a=421.0\mathrm{MPa}$ (hardened). The proportional consideration provided a $1.7$ increase of pulsating tensile strength from the base material to the martensite microstructure. Characteristic rupture planes are depicted in Figure 7. The investigation of all the rupture planes revealed predominant crack initiation starting from the surface for the untreated specimens. However, due to small included imperfections from a former forging process, the majority of the hardened specimens started cracking below the surface. Figure 6 contains an exemplary description of all the test results, to maintain a proper overview. The main focus of the fatigue tests was on the fatigue strength for each microstructure state at N = 6,000,000 load cycles. The overall fatigue results for the uniaxial specimen tests are listed within

Table 2. Uniaxial fatigue testing results (nominal stress amplitude) adapted from [32].

		Tension–Compression		Bending	Torsion
	Stress Ratio	$\mathit{R}=\mathbf{0}$	$\mathit{R}=-\mathbf{1}$	$\mathit{R}=-\mathbf{1}$	$\mathit{R}=\mathbf{0}$	$\mathit{R}=-\mathbf{1}$
	Temperature	$\mathbf{20} °$C	$\mathbf{20} °$C	$\mathbf{20} °$C	$\mathbf{20} °$C	$\mathbf{20} °$C
Specimen
unnotched, untreated Rz1		$246.6$	$318.2$	$351.1$	$209.0$	$221.5$
unnotched, hardened Rz1		$421.0$	$628.7$	$773.3$	$334.4$	$497.4$
notched, untreated Rz1		$133.8$	$158.8$	$183.9$	$179.7$	$192.3$
notched, hardened Rz1		$280.1$	$346.9$	$530.9$	$284.2$	$401.3$

.

4. Model and Discussion

The development of the Haigh diagram rested upon the tensile strength, the yield strength and the fatigue strength at different stress ratios, including the constant mean stress sensitivity between the pulsating compressive and the tensile strength areas in conformity with the technical guidelines [20]. Both microstructure states resulted in a fatigue stress diagram according to Haigh (see Figure 8), which formed the basis for the development of the depth-dependent Haigh diagram. To assign methodology for the surface-hardened components the application followed the existing example of a conrod-bearing area. Computation of the typical material strength parameters was based on an approximation formula dependent on the local (measured) component hardness.

Within the academic literature [20,33,34], there exist numerous functional correlations between static fatigue strength parameters (e.g., tensile strength, yield strength) and material hardness for steel alloys. The documented data base of [33], including linear equations (see Equations (2) and (3)), should be compared to the present two microstructure states:

$$R_m=\left(3.373·\left(\mathrm{HV}\right)-99.8\right)\left(\mathrm{MPa}\right)$$

(2)

$$R_{p0.2}=\left(2.876·\left(\mathrm{HV}\right)-90.7\right)\left(\mathrm{MPa}\right)$$

(3)

Figure 9 displays the correlation between yield strength/tensile strength and hardness according to [33], including the static strength results of AFP steel 38MnSiVS5 for both the investigated microstructure states. However, minimal divergence from the literature occurred.

In addition to the left and right boundaries of the Haigh diagram, the knowledge of alternating fatigue strength and mean stress sensitivity played an important role. An exemplary approximation according to [20,34] is listed in Equations (4) and (5):

$${\sigma }_{T/C,a}=0.4·R_m\left(\mathrm{MPa}\right)$$

(4)

$$M=0.00035·R_m-0.1$$

(5)

The insertion of equation according [33] yields

$$\begin{array}{cc}\hfill {\sigma }_{T/C,a}& =0.4·\left(3.373·\left(\mathrm{HV}\right)-99.8\right)\left(\mathrm{MPa}\right)\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill M& =\left(0.00035·\left(3.734·\left(\mathrm{HV}\right)-99.8\right)-0.1\right)\hfill \end{array}$$

(7)

The comparison of the evolved equations, including hardness dependencies, with the testing results of AFP steel is visualised in Figure 10. Due to the fact that the literature references were based on approximations for various alloys, slight differences for both sampling points existed again. All the shown relations allow the development of a Haigh diagram, depending on the Vickers hardness (see Figure 11). In addition to approximation based on [20,33,34], linear interpolations of both microstructure sampling points of the AFP steel 38MnSiVS5 were integrated.

It was necessary to transform the crank pin depth measurement into a functional correlation between distance-to-surface and hardness. By way of example, linear or sigmoid (see Equation (8)) relations are common. Figure 12 provides the hardening depth path of the crankshaft section, including the mentioned approximations. The steady course of the sigmoid relation indicates good agreement between the measured hardness as a function of depth.

$$\begin{array}{cc}\hfill f\left(x\right)& =\mathrm{sig}\left(x\right)={\displaystyle \frac{1}{1+{\exp }^{-x}}}=\frac{1}{2}·\left(1+\tanh {\displaystyle \frac{x}{2}}\right)\hfill \end{array}$$

(8)

Calculated on the basis of [20,33,34], adjusted to the experimental results, Figure 13 shows a depth-dependent Haigh diagram according to the measured hardening profile for tension–compression. The above-described approach enabled data to be transferred over, e.g., alternating and pulsating torsional fatigue strength.

The available specimen results and depth-dependent Haigh diagrams represent the basis for the comparative computational fatigue approach according to [20]. The following study reduces the fatigue strength calculation to a simple crankshaft section under alternate bending. To replicate alternate bending, the material-fatigue-strength stress-gradient approach [35] based on the tension–compression test results was used. The component testing within this procedure led to pure bending in the crank pin area. The component test principle is schematically depicted in Figure 14. In total, eight crankshaft sections were fatigue-tested under pure alternating bending at three different load levels and the results were statistically evaluated by applying the approach given in [31]. As a real loadcase of a combustion engine, this represents a simple ignition time step.

The highly stressed component areas lie in the fillet areas of the crank pin bearings. The endurable cyclic bending moment at a defined number of N = 6,000,000 load cycles was statistically evaluated for a survival probability of $50\%$, which was subsequently applied as load for the numerical analysis of the crankshaft section. Hence, a direct evaluation of the safety factor by the presented approach was facilitated, whereby a safety factor of $S=1.00$ meant that the fatigue approach equalled the experimental component test. The result of the load-induced stresses was then used for three different material computational fatigue strength calculations:

• Variant 1 base material properties of 38MnSiVS5 (see Figure 8 untreated).
• Variant 2 base material properties of 38MnSiVS5, including surface treatment factor according to [20] and stress gradient dependency according to [36] for all bearing areas of the crankshaft section.
• Variant 3 two-layer approach (assignment see Figure 2) with base material properties of 38MnSiVS5, including martensite material properties (see Figure 8 hardened) within all bearing areas of the crankshaft section.

The computational fatigue strength calculation for such complex geometries without high-plasticity strain amounts in high-cycle fatigue based on local stress concepts like [35]. The computational proceeding according to [37], as a hybrid approach of [20] and other technical codes combined with empirical studies, was applied within a commercial software tool. The fatigue evaluation in the component fillet area was visualised with a safety value as a relation of local stress and local material strength for the most critical finite element node (see Figure 14).

Table 3. Calculated crankshaft section safety under alternate bending.

Safety S	Variant 1	Variant 2	Variant 3
Fatigue approach	$0.37$	$0.59$	$0.82$
Component test	$1.00$	$1.00$	$1.00$
Difference	$-63\%$	$-41\%$	$-18\%$

lists the calculation results. By including local fatigue strength information the results were closer to the target safety value of $S=1.00$ in compliance with the crankshaft section component test. This produced a more progressive design in comparison to [20] and allowed a more lightweight future component design.

5. Conclusions

Based on the presented fatigue test results and methodology in this paper, the following conclusions for a fatigue assessment of surface-induction-hardened 38MnSiVS5 steel crankshafts can be drawn:

• Uniaxial fatigue tests of unnotched round specimens under tension–compression loading at an alternating stress ratio of $R=-1$ show that the high-cycle fatigue strength of the hardened surface layer was higher by approx. a factor of 2 than the unhardened basic structure.
• Further fatigue investigations under tension–compression loading at a pulsating stress ratio of $R=0$ showed that the mean stress sensitivity of the hardened surface layer was higher by approx. a factor of $1.7$ than the unhardened basic structure.
• The reduction to a two-layer approach for the computational fatigue strength evaluation of a crankshaft section under alternate bending led to an $18\%$-more-realistic assessment, in accordance with the experimental test results.

• For further investigations, more analysis by including multiaxial [38] or local residual stress states [32] should be initiated. In general, different process parameters can lead to a significant variation in local residual stress states [39], whereas the presented approach acts as a feasible application-oriented method to assess the fatigue strength of induction hardened components, considering such effects. Other additional surface treatment methods like case hardening [40], shot peening [41], deep rolling [42] and superimposed treatment techniques [21] offer further potential for the presented approach, whereby additional effects, such as the surface treatment layer thickness [43], can be further investigated.