Tooth Root Bending Fatigue Strength of High-Density Sintered Small-Module Spur Gears: the Eﬀect of Porosity and Microstructure

Article Tooth Root Bending Fatigue Strength of High-Density Sintered Small-Module Spur Gears: The Eﬀect of Porosity and Microstructure

Vigilio Fontanari 1,*, Alberto Molinari 1, Michelangelo Marini 1, Wolfgang Pahl 2 and Matteo Benedetti 1

1 Department of Industrial Engineering, University of Trento, via Sommarive 9, 38122 Trento, Italy; [email protected] (A.M.); [email protected] (M.M.); [email protected] (M.B.) 2 GKN Sinter Metals, via Delle Fabbriche 5, 39031 Brunico (BZ), Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-0461-282-430

Received: 26 April 2019; Accepted: 22 May 2019; Published: 24 May 2019

Abstract: The present paper is aimed at investigating the effect of porosity and microstructure on tooth root bending fatigue of small-module spur gears produced by powder metallurgy (P/M). Specifically, three steel variants differing in powder composition and alloying route were subjected either to case-hardening or sinter-hardening. The obtained results were interpreted in light of microstructural and fractographic inspections. On the basis of the Murakami √area method, it was found that fatigue strength is mainly dictated by the largest near-surface defect and by the hardness of the softest microstructural constituent. Owing to the very complicated shape of the critical pore, it was found that its maximum Feret diameter is the geometrical parameter that best captures the detrimental effect on fatigue.

Keywords: small-module gears; tooth root bending fatigue; powder metallurgy; microstructure; porosity and defectiveness

1. Introduction The automotive industry is being steadily pushed to pursue economic and environmental efficiency. Powder metallurgy (P/M) offers a powerful means to achieve this target, as (near) net-shape mechanical components can be fabricated on a large scale, with high geometrical accuracy and minimum waste of raw material compared to conventional chip-generating machining processes. Flodin [1] reviewed the increasing employment of P/M parts in automotive transmissions, mainly in the form of synchronizer sleeves, shift fingers, carriers of epicyclical automatic transmissions, and oil pump gears. Attempts are now made to replace conventionally machined gears with P/M gears, at least in the least-loaded gear stages of car transmissions. However, bringing the mechanical performance of P/M gears to the level of their wrought counterparts is a tremendous technological challenge because this particular manufacturing route inevitably affects the resulting microstructure and mechanical properties. The main microstructural characteristic that differentiates P/M from wrought parts is residual porosity. Despite constant improvements in the compaction and sintering of metallic powders, P/M parts still display a relative density lower than 1. This clearly impacts on the stiffness, tensile, fatigue and wear properties of such components [2–4]. In the context of P/M gears, (i) the lower stiffness is detrimental to the mesh precision and mesh power loss factor [5], (ii) inferior fatigue properties negatively affect tooth root bending fatigue strength [6] and pitting resistance [7], and (iii) sintered tooth flanks have higher wear rates [8]. To combat these adverse effects, many treatments have been devised so far, such as shot peening [9], surface rolling [10], sinter-forging [11], and the double press double

Metals 2019, 9, 599; doi:10.3390/met9050599 www.mdpi.com/journal/metals Metals 2019, 9, 599 2 of 14 sinter process [12]. These treatments lead to tooth flank and root densification, which significantly improves the gear load capacity [13,14]. However, both bulk and surface densification treatments have a cost that is not always sustainable if compared to the profit margin of these automotive components. In this framework, the leanest and most cost-efficient process is powder compaction followed by sinter-hardening. Thereby, two processes are done in one single step, thus reducing the manufacturing time and cost. In addition, since martensite is directly formed during the cooling stage of the sintering process, no quenching is required, thus, problems related to oil retention and distortions associated with severe cooling rates are avoided [15]. To facilitate the formation of a martensitic or lower 1 bainitic microstructure at cooling rates (1–10 ◦C s− ) typical of the sinter-hardening process, special pre-mixed, diffusion-bonded or pre-alloyed powder blends have been devised to achieve adequate hardenability through the control of carbon content and the addition of alloying elements, such as Mo, Ni, and Cu. However, during sintering these elements are not distributed uniformly along the sinter-necks, resulting in a heterogenous microstructure. For instance, the slow diffusion rate between iron and nickel leads to the formation of nickel rich areas (NRAs), which are a combination of soft austenite and hard martensite [16], in general surrounding critical pores [17]. From the above discussion, it is clear that the tooth root bending fatigue strength of P/M gears, the focus of the present article, is the result of a complex interplay between porosity and microstructural constituents. Devising suitable fatigue calculation tools that are able to capture these phenomena is therefore of paramount importance for the fatigue prognosis of such P/M parts. In this regard, Danninger and Weiss [18] carried out fundamental investigations on the influence of porosity on the mechanical properties. They found that up to relative density levels of 94%, the porosity is mostly or completely open and interconnected, forming a spongy structure with a continuous pore network. However, at higher density levels, the structure is composed of isolated and more or less rounded pores in a continuous matrix. This means that in the former case, the sintering contacts are isolated and the area of the real metallic contacts, the ‘load bearing cross-section’ Ac is markedly smaller than the volume fraction of the metallic phase. In [18], the authors were able to rationalize the fatigue endurance of high-strength steels just by scaling the fatigue strength of the fully dense reference material by Ac. In such spongy materials, fatigue damage usually occurs very early and is located at the necks between powder particles, which are the weakest point of the microstructure. In this way, the fatigue is diffused rather than localized as it is in conventional materials and proceeds until eventual failure by coalescence of widespread defects [19,20]. In this context, it is clear that the key parameter for improving fatigue performance is the increment in relative density. Accordingly, when the porosity drops to levels below 6%, fatigue damage is delayed and localized in the correspondence of isolated pores with low shape factor or clusters of near-superficial pores [21]. Under these circumstances, fatigue calculation models originally developed for bulk metallic materials, can be applied to P/M steels. In this regard, the pores are treated in some papers [18,22,23] as pre-existing cracks and a linear-elastic fracture mechanics approach is applied for identifying the propagation conditions of crack-like defects. Furthermore, the Murakami model [24], initially proposed for determining the fatigue limit of steels containing inclusions, has been successfully applied to predict the fatigue strength of P/M steels [22,23] and additively manufactured metals [25]. In its most general formulation, this approach permits the estimation of the fatigue limit of the material with the following equation, which also includes the effect of the load ratio R:

HV + 120 1 Rα σ = F − (1) W loc 1/6 2 √area where the microstructure-dependent mechanical properties of the material are quantified by the Vickers hardness (HV), and the detrimental effect of the fatigue damage triggering defect is expressed by its area projected on the plane experiencing the highest normal stress. The location factor Floc is related to the defect location with respect to the outer surface, being equal to 1.41 and 1.56 for surface and internal Metals 2019, 9, 599 3 of 14 defects, respectively. The exponent α is also a function of the material microhardness, being expressed as α = 0.226 + HV 10 4. × − Since the Murakami model was devised for materials whose fatigue strength is dictated by isolated defects, Bergmark [22] proposed an adaption of its formulation when applied to P/M materials affected by widespread defectiveness by introducing a corrective factor. This is a function of the loss in elastic modulus with respect to the fully dense material, which is in turn, a measure of the material porosity. In this way, it is possible to link the Murakami model, which is suitable for continuous materials, to the Ac model devised in [18] for sponge materials with interconnected porosity. Nevertheless, it is still Metalsunclear 2019 how, 9, x toFOR define PEER REVIEW the critical pore and the material hardness to be considered in the application3 of 14 of such a model to P/M materials. and internalTo shed defects, further respectively. light on this researchThe exponent topic, theα presentis also a paper function investigates of the material the tooth microhardness, root bending beingfatigue expressed strength ofas smallα = 0.226 module + HV high-density × 10−4. spur gears produced by P/M using different pre-alloyed powdersSince and the subjected Murakami to diversemodel heatwas treatments.devised for The materi mainals goal whose of this fatigue paper isstrength to understand is dictated whether by isolatedsinter-hardening defects, Bergmark is able toimpart [22] proposed fatigue properties an adaption comparable of its formulation to those achieved when applied by conventional to P/M materialscase-hardening affected post-sintering by widespread treatments. defectiveness Moreover, by introducing the paper a corrective investigates factor. the This synergic is a function effect of ofpore the structure loss in elastic and heterogeneous modulus with microstructurerespect to the fully (typical dense ofsinter-hardened material, which materials)is in turn, ona measure the fatigue of thestrength. material Therefore, porosity. the In fatiguethis way, behaviour it is possible was examined to link the by Murakami starting with model, an in-depth which is fractographic suitable for continuousanalysis aimed materials, at exploring to the Ac the model influence devised of porosity in [18] andfor sponge microstructure materials on with the nucleationinterconnected and porosity.propagation Nevertheless, of cracks. Special it is still care unclear was taken how toto adaptdefine the the formulation critical pore of and the Murakamithe material model hardness so as to to becapture considered the particular in the application characteristics of such of thea model sintered to P/M materials. materials. To shed further light on this research topic, the present paper investigates the tooth root bending fatigue2. Materials strength and of Methods small module high-density spur gears produced by P/M using different pre- alloyedThe powders experiment and wassubjected carried to out diverse on small-module heat treatments. spur The gears main that goal are usedof this in paper automotive is to understandapplications. whether Their main sinter-hardeni constructiveng characteristics is able to impart are summarized fatigue properties in Table1 andcomparable their geometry to those is achievedschematically by conventional sketched in case-hardening Figure1. post-sintering treatments. Moreover, the paper investigates the synergic effect of pore structure and heterogeneous microstructure (typical of sinter-hardened materials) on theTable fatigue 1. Main strength. geometrical Therefore, data for the the fatigue investigated behaviour small-module was examined spur gears. by starting with an in-depth fractographic analysis aimed at exploring the influence of porosity and microstructure on the nucleation and propagation of cracks.Parameter Special care was Value taken to adapt the formulation of the Murakami model so as to capture theNormal particular module characteristics (mm) 0.71 of the sintered materials. Number of teeth 20 2. Materials and Methods Pressure angle (◦) 20 Pitch diameter (mm) 14.2 The experiment was carried Outsideout on diametersmall-module (mm) spur 15.8 gears that are used in automotive applications. Their main constructiveRoot characteristics diameter (mm) are summarized 12.4 in Table 1 and their geometry Gear thickness (mm) 5.37 is schematically sketched in Figure 1.

Figure 1. Geometry of the powder metallurgy (P/M) small-module spur gears. Image taken from [26]. Figure 1. Geometry of the powder metallurgy (P/M) small-module spur gears. Image taken from [26].

Table 1. Main geometrical data for the investigated small-module spur gears. Parameter Value Normal module (mm) 0.71 Number of teeth 20 Pressure angle (°) 20 Pitch diameter (mm) 14.2 Outside diameter (mm) 15.8 Root diameter (mm) 12.4 Gear thickness (mm) 5.37

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The gears were fabricated through the conventional P/M route using three types of pre-alloyed or diﬀusion bonded powders, whose nominal compositions are listed in Table2.

Table 2. Nominal compositions of the powders. Table taken from [26].

Powder Label Composition (wt%) Powder Type Carbon Content (wt%) A85Mo05 0.85 Mo, Fe bal. pre-alloyed 0.25 DHP 1.5 Mo, 2.0 Cu, 4.0 Ni, Fe bal diﬀusion bonded 0.15 DDH 1.5 Mo, 2.0 Cu, Fe bal diﬀusion bonded 0.15

During the blending phase, carbon was added in the form of graphite in an amount of 0.25 wt% for A85Mo05 and 0.15 wt% for DHP as well as DDH. The gears were manufactured by GKN Sinter Metals. The powders were compacted by single pressing to achieve a green density exceeding 7.2 g/cm3. The green compacts were sintered at 1120 ◦C for 30 min in a controlled atmosphere of endogas, and then subjected to different thermochemical treatments. Conventional case-hardening was applied to the A85Mo05 variant. This consists of austenizing at 860 ◦C followed by oil quenching. Sinter-hardening was instead applied to DDH and DHP variants. Thereby, the gears were cooled through forced convection of endogas from 1120 ◦C to 300 ◦C. The endogas atmosphere in sinter-hardening was set with a 0.8% carbon potential to enrich the carbon content of the surface layer, thus making possible the martensitic transformation upon cooling. The hardening effect is comparable to that of the more conventional case hardening. Final stress-relieving was carried out at 180 ◦C for 1 h. Total and open porosity were measured through the Archimedes’ method according to standard ASTM B311. For a deeper analysis of the permeability of the pore network during carburization the He pycnometry is preferable [27], however, this paper is more focused on the role of the pore network in dictating the fatigue crack propagation. For this reason, these measurements were complemented by image analysis of micrographs taken by optical microscopy, in order to investigate the morphology and spatial distribution of the pores located at the tooth root, inside the tooth and in the gear body. Tooth root bending fatigue tests were conducted in a laboratory environment with a resonant Rumul Mikroton testing machine equipped with a 20 kN load cell. This was operated in load control with a load ratio R = 0.1 at a frequency of about 150 Hz. Fatigue tests were interrupted after 1 Hz frequency drop or survival of 3 106 cycles. The test configuration is shown in Figure2, that is, × two anvils apply a pulsating load to two teeth encompassing 3 unloaded teeth. The anvils were designed so that when their stem is in contact with two teeth, the load is applied along a direction inclined of about 2◦ (with respect to the normal) to the contact point. In this way, a low friction coefficient (on the order of 0.05) is sufficient to prevent loss of contact during loading. This test configuration fails to apply the fatigue load along the line tangent to the base circle and passing to the tooth tip as prescribed by ISO6336. For this reason, rather than the formula available in this standard and used for instance in [28], the stress state in the critical location of the tooth root was evaluated through a finite element (FE) analysis able to reproduce the actual testing configuration. The FE model employs quadratic 20-node brick elements. To increase the computational efficiency, the local stress field in the most critically stressed teeth was evaluated from a sub-model, shown in Figure3, whose boundary conditions were imposed by the interpolated displacements of the general model. The adopted mesh was refined with the ISO 6336 loading configuration as a reference. The final refinement proved capable of estimating the FE tooth root bending stress of the ISO 6336 loading configuration with a better than 2% accuracy. Metals 2019,, 9,, 599x FOR PEER REVIEW 55 of of 14 Metals 2019, 9, x FOR PEER REVIEW 5 of 14

Figure 2. Tooth bending fatigue testing conﬁguration. Detail of the anvils and the gear under testing. Figure 2. Tooth bending fatigue testing configuration. Detail of the anvils and the gear under testing. FigureImage 2. taken Tooth from bending [26]. fatigue testing configuration. Detail of the anvils and the gear under testing. ImageImage taken taken from from [26]. [26].

FigureFigure 3. 3. Sub-model Sub-model of of the the finite finite ﬁnite element element (FE) (FE) analyses analyses carried carried out out to to estimate estimate the the tooth tooth root root bending bending stress.stress. The The applied applied loads loads are are represented represented by by the the red red arrows. arrows.arrows. Image Image taken taken from from [26]. [[26].26].

6 TheThe fatigue fatigue strength strength at at 3 3 × × 10 106 cycles cycles was was determined determined using using a a staircase staircase procedure procedure based based on on at at × 6 least 15 tests withwith 0.050.05 kNkN loadload increments.increments. TheThe choicechoice ofof 33 × 106 cyclescycles is is compliant compliant with the ISO6336 least 15 tests with 0.05 kN load increments. The choice of 3 ×× 10 cycles is compliant with the ISO6336 standard,standard, which whichwhich prescribes prescribesprescribes an an enduranceendurance endurance factorfactor factor equalequal equal to to to one one one in in in the the the design design design formula formula formula for for for this this this fatigue fatigue fatigue life. life.Thelife. The rationaleThe rationale rationale for for exploringfor exploring exploring the the fatiguethe fatigue fatigue behaviour behaviour behaviour of Pof of/M P/M P/M gears gears gears up up toup to such to such such a fatiguea a fatigue fatigue lifetime lifetime lifetime will will will be bediscussedbe discussed discussed below. below. below. The The The ﬁnite finite finite life fatiguelife life fatigue fatigue regime regi regi wasmeme exploredwas was explored explored through through through 15–20 tests15–20 15–20 performed tests tests performed performed at diﬀerent at at differentdifferent stress stress levels. levels. The The results results were were interpolat interpolateded through through least least square square fitting fitting the the Basquin Basquin law law reportedreported in in Equation Equation (2): (2):

Metals 2019, 9, 599 6 of 14 stress levels. The results were interpolated through least square fitting the Basquin law reported in Equation (2): 1 σa N m = C (2) · f where σa is the stress amplitude and Nf the number of cycles to failure. The uncertainty range was assumed to be constant for different fatigue lives and approximated by its centroid value. The ratio between the stress amplitude corresponding to 90% and 10% probability of failure was taken as a measure of the results scatter: σa,90 Tσ,10:90 = (3) σa,10 Optical inspections of the crack path and electron scanning microscopy (SEM) observations of the fracture surfaces complemented the material characterization. The former was conducted after sectioning the tooth along a plane orthogonal to the gear axis. The SEM observations were carried out to analyze the critical defect in terms of size, shape and location. Microhardness HV0.5 profiles were measured at the gear tooth root sampling points along the direction of the maximum bending stress (viz. perpendicular to the tangent line inclined by 30◦ with respect to the radial direction). Each microhardness value was obtained by averaging the results of five indentation tests.

3. Results

3.1. Microstructure and Porosity Tables3 and4 lists the mean porosity values calculated according to ASTM B311 and the results of the image analysis measurements, respectively. The porosity has a non-homogeneous distribution in the gear volume, especially in the A85Mo05 variant, which exhibits the lowest total porosity among the three variants. However, in the vicinity of the tooth root, viz. the most stressed region during the fatigue tests, the three variants exhibit a similar porosity value of around 7%.

Table 3. Mean density, total porosity and open porosity following ASTM B311. Table taken from [26].

Quantity A85Mo05 DHP DDH 3 Density (g cm− ) 7.55 7.35 7.41 Total porosity (%) 4.09 7.56 6.36 Open porosity (%) 0.60 1.39 0.96

Table 4. Mean porosity values in diﬀerent regions of the gear measured using image analysis on metallographic sections. Table taken from [26].

Porosity % A85Mo05 DHP DDH Tooth body 7.13 8.85 7.63 Tooth root 6.29 7.99 6.20 Gear body 3.04 7.15 4.17

The microstructures of the three variants are illustrated in Figure4. It can be noted that A85Mo05 (Figure4a) is characterized by irregularly shaped pores, the microstructure is prevalently martensitic in the surface layer with a limited presence of bainite and retained austenite, whereas in the core, it consists of a mixture of lower bainite and martensite. The DHP variant exhibits a more homogeneous pore distribution. The heterogeneous microstructure (Figure4b) is composed of austenite (white areas), lower bainite (light grey areas) and martensite (dark grey areas). It appears that this microstructure is the result of the inhomogeneous distribution of the alloy elements in the diffusion bonded powders, and of the incomplete diffusion of Ni and Cu into the base powders (1.5% Mo Pre-alloyed iron) during sintering. The Ni-rich austenite is Metals 2019, 9, x 599 FOR PEER REVIEW 77 of of 14 is Metalspredominantly 2019, 9, x FOR locatedPEER REVIEW around the pores [16]. The martensite is richer in Cu, whereas 7the of 14base powder,predominantly which locatedis poor aroundin Ni and the Cu, pores is mostly [16]. The bainitic. martensite is richer in Cu, whereas the base powder, is predominantly located around the pores [16]. The martensite is richer in Cu, whereas the base which is poor in Ni and Cu, is mostly bainitic. powder,Similar which to isA85Mo05, poor in Ni theand Cu,pores is mostly are irregulabainitic.rly distributed in the DDH variant. The microstructureSimilarSimilar to toA85Mo05,(Figure A85Mo05, 4c) the is mainly poresthe pores are martensitic irregularly are irregula in distributedthe rlysurface distributed inlayer the with DDH in some variant.the tracesDDH The ofvariant. microstructurelower bainite,The whereas(Figuremicrostructure4 c)the is mainlycore (Figure microstructure martensitic 4c) is mainly in consists the martensitic surface mostly layerin theof withsurfaceupper some bainite.layer traces with Even ofsome lower in traces this bainite, case,of lower the whereas bainite, diffusion the bondedcorewhereas microstructure Cu the doescore microstructurenot consists completely mostly consists ofdiffuse upper mostly bainite.into of the upper Even base inbainite. thispre-alloyed case, Even the in dithispowdersffusion case, bondedtheand diffusion the Cu doesfinal microstructurenotbonded completely Cu does diis ffcharacterizeduse not into completely the base by the pre-alloyed diffuse inhomogene into powders theous basedistribution and pre-alloyed the final of microstructure Cu, powders indeed Cu-richand is characterizedthe areas final are stillbymicrostructure the present inhomogeneous after is sintering characterized distribution and assume by the of inhomogene Cu,a martensitic indeedous Cu-rich microstructure distribution areas are of upon stillCu, presentindeedcooling. Cu-rich after sintering areas are and assumestill present a martensitic after sintering microstructure and assume upon a martensitic cooling. microstructure upon cooling.

(a) (b) (c) (a) (b) (c) Figure 4. Microstructure of the investigated material variants. (a) case-hardened A85Mo05, (b) sinter- FigureFigure 4. 4.Microstructure Microstructure ofof thethe investigated material material variants. variants. (a ()a case-hardened) case-hardened A85Mo05, A85Mo05, (b) (sinter-b) sinter- hardened DHP, (c) sinter-hardened DDH. hardenedhardened DHP, DHP, (c ()c sinter-hardened) sinter-hardened DDH.DDH.

FigureFigure 55 illustrates5illustrates illustrates thethe the in-depthin-depth in-depth microhardnessmicrohardness pr proﬁlesprofilesofiles measured measuredmeasured in inin the thethe three threethree material materialmaterial variants. variants. It Itcan can be be be noted noted noted that that that all all all the thethe materials materialsmaterials exhibitexhibit exhibit aa a surfacsurfac surfaceee layer layer layer with with with hardness hardness hardness higher higher higher than than than that that that of theof of the thecore. core. core.

FigureFigure 5. 5.Microhardness Microhardness profiles profiles measured measured atat thethe geargear toothtooth root.root. Each point represents the the average average of Figure 5. Microhardness profiles measured at the gear tooth root. Each point represents the average fiveof five measurements. measurements. of five measurements. TheThe A85Mo05A85Mo05 alloyalloy receivedreceived a case-hardening treatment, treatment, which which is isable able to toincrease increase the the microhardnessmicrohardnessThe A85Mo05 of of the the alloy outerouter received layerslayers significantlysignificantly a case-hardening above above that that treatment, of of the the two two materialwhich material is variants variantsable to produced producedincrease by the by microhardnesssinter-hardening.sinter-hardening. of Despitethe Despite outer the the layers low low initial initialsignificantly carbon carbon content, contenabove t,that these these of variants variantsthe two were werematerial ableable tovariantsto hardenharden produced thanksthanks toto theby sinter-hardening.carbonthe carbon pickup pickup from Despite thefrom endogas thethe endogaslow atmosphere. initial atmosphere. carbon In conten fact, In atfact,t, highthese at high temperature, variants temperature, were carbon able carbon to can harden rapidlycan rapidly thanks diffuse to theintodiffuse carbon the pore into pickup networkthe porefrom and network the then endogas into and the thenatmosphere. microstructure, into the Inmicrostructure, fact, thus at favoring high temperature,thus the favoring martensitic carbon the transformationmartensitic can rapidly diffuseeventransformation though into the the evenpore resulting though network hardness the resultingand incrementthen hardness into th is incremente lower microstructure, than is lower that ofthanthus the that case-hardenedfavoring of the case-hardened the martensitic A85Mo05 A85Mo05 alloy. Interestingly, the depth of the hardened layer is about 0.5 mm in all three conditions. transformationalloy. Interestingly, even the though depth the of resulting the hardened hardness layer increment is about 0.5 is lower mm in than all three that of conditions. the case-hardened The two The two sinter-hardened conditions displayed a significantly larger dispersion of the microhardness A85Mo05sinter-hardened alloy. Interestingly, conditions displayed the depth a of significantly the hardened larger layer dispersion is about 0.5 of mm the in microhardness all three conditions. value value as a result of the more heterogeneous microstructure, wherein soft phases are interspersed in Theas a two result sinter-hardened of the more heterogeneous conditions displayed microstructure, a significantly wherein larger soft dispersion phases are ofinterspersed the microhardness in the the martensitic or lower bainitic matrix. valuemartensitic as a result or lower of the bainitic more matrix.heterogeneous microstructure, wherein soft phases are interspersed in the martensitic or lower bainitic matrix.

Metals 2019, 9, 599 8 of 14 Metals 2019, 9, x FOR PEER REVIEW 8 of 14

3.2. Fatigue Curves and Fractographic Analyses Figure6 6a–ca–c illustrates the the fatigue fatigue data data collec collectedted for for A85Mo05, A85Mo05, DHP, DHP, and and DDH, DDH, respectively. respectively. The Thedata data were were interpolated interpolated using using Equation Equation (2). The (2). Thebest-fit best-ﬁt coefficients coeﬃcients are listed are listed in Table in Table 5. 5.

Figure 6. 6. ResultsResults of the of thefatigue fatigue tests. tests. (a) Case-hardened (a) Case-hardened A85Mo05, A85Mo05, (b) sinter-hardened (b) sinter-hardened DHP, (c) sinter- DHP, (hardenedc) sinter-hardened DDH. The DDH. run-out The samp run-outles are samples indicated are indicated by arrows. by arrows.

Metals 2019, 9, 599 9 of 14

Metals 2019, 9, x FOR PEER REVIEW 9 of 14 Table 5. Best-ﬁt coeﬃcients of the fatigue curves (Equation (2)). Table 5. Best-fit coefficients of the fatigue curves (Equation (2)).

- σa,3 106 @ 50% (MPa) Tσ,10:90 C (MPa) m - 𝝈𝒂,𝟑∙𝟏𝟎𝟔 ·@ 50% (MPa) 𝑻𝝈,𝟏𝟎:𝟗𝟎 C (MPa) m A85Mo05 321 1.42 3163 5.90 A85Mo05 321 1.42 3163 5.90 DHP 307 1.26 2858 5.71 DHP DDH307 262 1.591.26 3846 5.002858 5.71 DDH 262 1.59 3846 5.00

The fatigue strength data are comparable with those published in [11,12,28] for similar The fatigue strength data are comparable with those published in [11,12,28] for similar microstructures.microstructures. Even though the the porosity porosity foun foundd here here may may differ differ from from that that measured measured in in the the abovementionedabovementionedpapers, papers, itit cancan bebe notednoted thatthat thethe fatiguefatigue strength is is not not very very sensitive sensitive to to relative relative porosity,porosity, as as long long as as it it is is higher higher than than 90%.90%. Conversely, below this limiting value, value, the the decrease decrease in in fatigue fatigue resistanceresistance is is very very remarkable. remarkable. Interestingly,Interestingly, thethe fatiguefatigue curves of all all the the explored explored material material variants variants clearlyclearly show show evidence evidence of of a a knee, knee, that that is,is, aa markedmarked changechange in the slope of of the the SN SN curve curve at at fatigue fatigue lives lives 6 muchmuch shorter shorter than than 10 106cycles—a cycles—a fatiguefatigue behaviourbehaviour typically ex exhibitedhibited by by high-strength high-strength steels steels [29,30]. [29,30 ]. 6 This outcome suggests that the choice of 3 10 6cycles as the survival lifetime of run-out specimens is This outcome suggests that the choice of ×3 × 10 cycles as the survival lifetime of run-out specimens adequateis adequate for for characterizing characterizing the the high-cycle high-cycle fatigue fatigue behaviour behaviour ofof thethe investigated materials. materials. Clearly, Clearly, thisthis evidence evidence is notis not suffi sufficientcient to assume to assume infinite infinite fatigue fatigue life at life stress at levelsstress belowlevels suchbelow fatigue such strength,fatigue thereforestrength, we therefore strongly we advise strongly against advise extrapolating against extr suchapolating fatigue such data fatigue at very data high at fatigue very high lives, fatigue as also discussedlives, as inalso [31 discussed], whose explorationin [31], whose would explorat requireion additional would require and time-consumingadditional and time-consuming experiments. experiments.The highest fatigue limit exhibited by the case-hardened A85Mo05 variant is consistent with the lowestThe porosity highest and fatigue highest limit microhardness exhibited by the found case-h inardened Section 3.1A85Mo05. Unexpectedly, variant is theconsistent fatigue with strength the oflowest the DHP porosity variant and is highest higher microhardness than that displayed found byin Section DDH, even3.1. Unexpectedl though they, former the fatigue shows strength similar microhardnessof the DHP variant and slightly is higher higher than relative that display porosityed by at theDDH, tooth even root. though the former shows similar microhardnessTo shed light and on slightly these higher issues, relative fractographic porosity at analyses the tooth were root. carried out on fatigued teeth. The representativeTo shed light imageson these are issues, shown fractographic in Figures 7anal–10yses for thewere three carried material out on variants. fatigued teeth. The crack The pathrepresentative typically displayed images are by shown A85Mo05 in Figures (Figure 7–107a) is for characterized the three material by little variants. evidence The of deflectionscrack path inducedtypically by displayed porosity, by resulting A85Mo05 in (Figure a fairly 7a) straight is characterized trajectory. by Figurelittle evidence7b shows of deflections a surface pore induced that probablyby porosity, triggered resulting the crackin a fairly initiation. straight In thetrajecto samery. region, Figure evidence 7b shows of a intergranular surface pore fracturethat probably can be attributedtriggered to the grain crack boundary initiation. embrittlement In the same region, due to ev cementiteidence of precipitation intergranular promoted fracture bycan case be attributed hardening andto grain the resulting boundary carbon embrittlement enrichment. due to cementite precipitation promoted by case hardening and the resulting carbon enrichment.

(a)

(b)

Figure 7. Fractographic inspections of A85Mo05: (a) crack path (LOM), (b) crack initiation site (SEM). Figure 7. Fractographic inspections of A85Mo05: (a) crack path (LOM), (b) crack initiation site The trajectory typically followed by the critical(SEM). fatigue crack in DHP (Figure8a) and DHH (Figure9a) conditions seems to be more influenced by the presence of pores. Accordingly, the crackThe path trajectory tends totypically interconnect followed such by pores the critical resulting fatigue in a verycrack serrated in DHP geometric (Figure 8a) configuration. and DHH A(Figure concomitant 9a) conditions effect of the seems microstructure to be more influenced heterogeneity by the cannot presence be excluded of pores. as Accordingly, will be discussed the crack below. SEMpath inspections tends to ofinterconnect the fracture such surfaces pores of bothresulting material in a variants very serrated (Figures geometric8b and9b) attestedconfiguration. to cracks A nucleatedconcomitant preferentially effect of the in microstructure the vicinity of heterogene surface poresity cannot with very be excluded articulated as morphology.will be discussed In addition, below. SEM inspections of the fracture surfaces of both material variants (Figures 8b and 9b) attested to

Metals 2019, 9, x FOR PEER REVIEW 10 of 14 Metals 2019, 9, x FOR PEER REVIEW 10 of 14 Metalscracks2019 nucleated, 9, 599 preferentially in the vicinity of surface pores with very articulated morphology.10 ofIn 14 cracksaddition, nucleated such inspections preferentially revealed in the that vicinity fatigue of damagesurface pores is not with localized very inarticulated a single criticalmorphology. crack but In addition,proceeds suchin a inspectionsmuch more revealed diffused that fashion fatigue throug damageh multiple is not localized crack initiation in a single followed critical crackby crack but suchproceedscoalescence. inspections in a much revealed more that diffused fatigue fashion damage throug is not localizedh multiple in crack a single initiation critical crackfollowed but proceedsby crack in acoalescence. much more diﬀused fashion through multiple crack initiation followed by crack coalescence.

(a) (b) (a) (b)

FigureFigure 8. 8.Fractographic Fractographic inspectionsinspections ofof DHP:DHP: (a) crack path (SEM), (SEM), ( (bb)) crack crack initiation initiation site site (SEM). (SEM). Figure 8. Fractographic inspections of DHP: (a) crack path (SEM), (b) crack initiation site (SEM).

(a) (b) (a) (b) Metals 2019Figure, 9, x 9. FORFractographic PEER REVIEW inspections of DDH: (a) crack path (SEM), (b) crack initiation site (SEM).11 of 14

Figure 9. Fractographic inspections of DDH: (a) crack path (SEM), (b) crack initiation site (SEM). Figure 9. Fractographic inspections of DDH: (a) crack path (SEM), (b) crack initiation site (SEM). This scenario is further confirmed by SEM examinations of small cracks nucleated at pores in the immediateThis scenario neighborhood is further confirmed of the tooth by SEMsurface examin (Figureations 10a,b of smallfor DDH cracks and nucleated DHP, respectively). at pores in theWhile immediate the first stageneighborhood of fatigue of damage the tooth consists surface of multiple(Figure 10a,b crack for initiation DDH andand DHP,coalescence respectively). to form Whilethe main the crack, first stage the cracks of fatigue not involved damage in consists this proc ofess, multiple such as crack those initiation shown in and Figure coalescence 10 stop growing to form theand main become crack, non-propagating. the cracks not involved This observation in this proc agreess,es such with as those those reported shown inelsewhere Figure 10 in stop the technicalgrowing andliterature become [5,8,12,13]. non-propagating. This observation agrees with those reported elsewhere in the technical literature [5,8,12,13].

(a) (b)

Figure 10. Non-propagating cracks found by SEM inspection in the DDH variant. (a) Cluster of pores

interconnectedFigure 10. Non-propagating by the crack, (cracksb) single found pore. by SEM inspection in the DDH variant. (a) Cluster of pores

interconnected by the crack, (b) single pore.

4. Discussion From the above discussion, it is clear that the fatigue damage mechanism is triggered by the most critical pore. For this reason, the Murakami fatigue model expressed by Equation (1) seems to offer an appealing interpretation tool for the fatigue results collected so far. However, this fatigue model was devised by Murakami [24] to predict the fatigue strength of steels and cast irons, whose fatigue behaviour is dictated by isolated defects with an approximately rounded shape, for instance in the form of hard inclusions [29] or shrinkage microporosity [32]. Conversely, in the present case, the critical defect is, in most cases, represented by a cluster of near-surface pores, whose spatial arrangement is 3D rather than 2D, and whose jagged shape likely results in a stress intensity factor much more severe than that predicted by the area formula. For this reason, we propose in the present paper, to estimate the critical defect size to be incorporated into Equation (1) by: (i) using SEM fractographic images, which are much more effective to describe the 3D geometry of the pore cluster with respect to the conventional metallographic section, and (ii) estimating the defect area considering the convex contour that circumscribes the real defect area. In a first simplified attempt to estimate such a geometrical parameter, the critical defect size is assumed to be the area of the circle having a diameter equal to the maximum Feret diameter of the pore cluster, as schematically illustrated in Figure 11. Accordingly, the circular shape satisfies the condition of a convex boundary and the Feret diameter is a geometrical parameter that can be easily calculated by common image analysis software.

Metals 2019, 9, x FOR PEER REVIEW 11 of 14

Metals 2019, 9, 599 11 of 14

This scenario is further confirmed by SEM examinations of small cracks nucleated at pores in the immediate neighborhood(a) of the tooth surface (Figure 10a,b for DDH and DHP,(b) respectively). While the first stage of fatigue damage consists of multiple crack initiation and coalescence to form the main crack, the cracks not involved in this process, such as those shown in Figure 10 stop growing and Figure 10. Non-propagating cracks found by SEM inspection in the DDH variant. (a) Cluster of pores become non-propagating. This observation agrees with those reported elsewhere in the technical interconnected by the crack, (b) single pore. literature [5,8,12,13]. 4. Discussion 4. Discussion From the above discussion, it is clear that the fatigue damage mechanism is triggered by the From the above discussion, it is clear that the fatigue damage mechanism is triggered by the most most critical pore. For this reason, the Murakami fatigue model expressed by Equation (1) seems to critical pore. For this reason, the Murakami fatigue model expressed by Equation (1) seems to offer offer an appealing interpretation tool for the fatigue results collected so far. However, this fatigue an appealing interpretation tool for the fatigue results collected so far. However, this fatigue model model was devised by Murakami [24] to predict the fatigue strength of steels and cast irons, whose was devised by Murakami [24] to predict the fatigue strength of steels and cast irons, whose fatigue fatigue behaviour is dictated by isolated defects with an approximately rounded shape, for instance behaviour is dictated by isolated defects with an approximately rounded shape, for instance in the form in the form of hard inclusions [29] or shrinkage microporosity [32]. Conversely, in the present case, of hard inclusions [29] or shrinkage microporosity [32]. Conversely, in the present case, the critical the critical defect is, in most cases, represented by a cluster of near-surface pores, whose spatial defect is, in most cases, represented by a cluster of near-surface pores, whose spatial arrangement is 3D arrangement is 3D rather than 2D, and whose jagged shape likely results in a stress intensity factor rather than 2D, and whose jagged shape likely results in a stress intensity factor much more severe area muchthan that more predicted severe bythan the that√area predictedformula. by For the this reason, formula. we propose For this in the reason, present we paper, propose to estimate in the presentthe critical paper, defect to estimate size to be the incorporated critical defect into size Equation to be incorporated (1) by: (i) using into SEM Equation fractographic (1) by: (i) images, using SEMwhich fractographic are much more images, effective which to are describe much themore 3D effe geometryctive to ofdescribe the pore the cluster 3D geometry with respect of the to pore the clusterconventional with respect metallographic to the conventional section, and (ii)metallogr estimatingaphic the section, defect areaand considering(ii) estimating the the convex defect contour area consideringthat circumscribes the convex the realcontour defect that area. circumscribes In a first simplifiedthe real defect attempt area. to In estimate a first simplified such a geometrical attempt to estimateparameter, such the a critical geometrical defect parameter, size is assumed the critical to be the defect area size of the is assumed circle having to be a diameterthe area of equal the circle to the havingmaximum a diameter Feret diameter equal ofto thethe poremaximum cluster, Feret as schematically diameter of illustrated the pore incluster, Figure as 11 .schematically Accordingly, illustratedthe circular in shape Figure satisfies 11. Accordingly, the condition the of circular a convex shape boundary satisfies and the the condition Feret diameter of a convex is a geometrical boundary andparameter the Feret that diameter can be easily is a geometrical calculated by paramete commonr that image can analysis be easily software. calculated by common image analysis software.

Figure 11. Sketch illustrating the procedure for evaluating the characteristic dimensions of the pore, deﬁned by the maximum Feret diameter. Image taken from [26].

Beside the size of the critical defect, the other key parameter controlling the fatigue strength as expressed by Equation (1) is the microhardness. As shown in Figure4 and discussed in Section3, the microstructure of the material variants is highly non-homogeneous. Therefore, we expect large fluctuations in the local values of microhardness, resulting in large dispersion bands in the microhardness profiles plotted in Figure5. For this reason, we followed two approaches in incorporating the microhardness value into Equation (1): either (i) considering the average value measured in the surface layer where crack initiation occurs, or (ii) considering the hardness of the softest microstructural Metals 2019, 9, 599 12 of 14 constituent found in the vicinity of the critical defect. The results of these two approaches are summarized in Tables6 and7, respectively. Comparing Tables6 and7, it can be noted that a significant improvement in the estimation of the fatigue strength is achieved by incorporating the local hardness into Equation (1). This result emphasizes, even considering the approximations introduced for the evaluation of the critical defect size, the crucial role played by the microstructure in the vicinity of the critical pores. From another point of view, it can be noted that the critical crack spends most of the fatigue life nucleating and propagating through the microstructural phases enveloping the pores.

Table 6. Fatigue strength estimated with the Murakami model considering the average microhardness. Table taken from [26].

Variant HV (Mean) √area (m) σW (MPa) σa (MPa) Err (%) A85Mo05 873 111 524 321 +63 DHP 744 152 437 307 +42 DDH 758 136 452 262 +73 6 σ : high-cycle fatigue strength predicted by Equation (1); σa: experimental fatigue limit @ 3 10 cycles. W ×

Table 7. Fatigue strength estimated with the Murakami model considering the microhardness of the softest microstructural constituent. Table taken from [26].

Variant HV (Local) √area (m) σW (MPa) σa (MPa) Err (%) A85Mo05 515 111 345 321 +7 DHP 325 152 233 307 24 − DDH 378 136 264 262 +1 6 σ : high-cycle fatigue strength predicted by Equation (1); σa: experimental fatigue limit @ 3 10 cycles. W ×

To conclude, it is worth advancing a plausible explanation of the diﬀerent errors obtained for the three variants. The overestimation in the fatigue strength of the A85Mo05 variant can be attributed to the fact that the grain boundary embrittlement occurring in the case-hardened layer is not considered by the Murakami fatigue model. On the contrary, such a model tends to underestimate the fatigue strength of the sinter-hardened DHP material, characterized by soft retained austenite enveloping the critical pores. Its negative eﬀect on the fatigue strength may be at least partially attenuated by stress-induced transformation into harder martensite. In addition, the resulting local volumetric increment produces crack closure that is able to slow down or even arrest the fatigue crack propagation. Further investigations are required to support these hypotheses.

5. Conclusions The present paper investigated the tooth root bending fatigue strength of high-density P/M gears produced from high strength pre-alloyed powders. The key conclusions that can be drawn from this study are as follows:

1. The fatigue curves of all explored material variants show evidence of a knee at fatigue lives well shorter than 106 cycles. This outcome suggests that the choice of 3 106 cycles as the survival × lifetime of run-out specimens is adequate for characterizing the high-cycle fatigue behaviour of the investigated materials. Nevertheless, the fatigue strength at 3 106 cycles does not represent × the fatigue limit of the material, but highlights the signiﬁcant change in the slope of the S-N curve. Additional tests at longer fatigue lives are required to conﬁrm the existence of a material fatigue limit. 2. The main fatigue crack seems to be the result of the coalescence of multiple cracks nucleated in the vicinity of the most stressed and largest pores. Metals 2019, 9, 599 13 of 14

3. The fatigue strength is the result of a complex interplay between porosity and microstructure; the former factor essentially depends on the size and shape of the critical pore leading to crack initiation, the latter is related to the microhardness of the softest microstructural constituent surrounding the critical defect. 4. SEM fractographic inspections are more suitable for identifying the critical defect than conventional metallographic sections. In fact, the size of the defect detected in this way is a more faithful representation of the concept of a defect surface projected on the critical plane, as required by the Murakami model. In addition, fatigue strength data are better rationalized by this fatigue model if the defect size is computed from the maximum Feret diameter, which identiﬁes the circumference inscribing the serrated perimeter of the pore.

Author Contributions: V.F. contributed to the experimental investigation, writing and supervision, A.M. supervised the research and contributed to the discussion, W.P. followed all the production steps, M.M. carried out the Finite Element analysis, M.B. contributed to fatigue testing, formal analysis and writing. Funding: This research received no external funding. Acknowledgments: Pietro Valcozzena is kindly acknowledged for his helpful technical support. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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