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Initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires
Accepted Manuscript Initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires Jesús Toribio, Beatriz González, Juan-Carlos Matos PII: DOI: Reference:
S0167-8442(17)30184-2 http://dx.doi.org/10.1016/j.tafmec.2017.08.007 TAFMEC 1939
To appear in:
Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
9 April 2017 28 August 2017 28 August 2017
Please cite this article as: J. Toribio, B. González, J-C. Matos, Initiation and propagation of fatigue cracks in colddrawn pearlitic steel wires, Theoretical and Applied Fracture Mechanics (2017), doi: http://dx.doi.org/10.1016/ j.tafmec.2017.08.007
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Initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires Jesús Toribio, Beatriz González, Juan-Carlos Matos Fracture & Structural Integrity Research Group (FSIRG), University of Salamanca (USAL), E.P.S., Campus Viriato, Avda. Requejo 33, 49022 Zamora, Spain Abstract In this paper the important role of manufacturing by progressive cold drawing on initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires is addressed by analyzing the initiation (from surface defects) and propagation of fatigue cracks in two pearlitic steels with very different cold drawing degree or cumulative plastic strain (and the subsequent very distinct microstructural arrangement): a hot rolled pearlitic steel bar and a commercial highstrength cold-drawn prestressing steel wire to be used as a component of prestressed concrete in structural engineering. Experimental results show that the initiation of fatigue cracks in pearlitic steels takes place at the location of small surface defects, many of them in the form of localized damage in the area of material surface (in the case of hot rolled bar) or voids created by tearing during drawing due to the existence of particles near the wire surface (in the case of the cold drawn wire). In both materials, fatigue cracks are mostly transcollonial and tend to fracture pearlite (ferrite/cementite) lamellae, so that different micro-mechanisms of fatigue damage appear in the material such as non-uniform crack opening displacement, micro-discontinuities, branchings, bifurcations and frequent local deflections, all creating a sort of microstructural roughness in the fatigue crack path that is different in the hot rolled bar and in the cold drawn wire, thereby determining their distinct fatigue performance. Keywords: pearlitic steel; hot rolled bar; cold drawn wire; cold drawing; fatigue crack initiation; fatigue crack propagation; surface defects; fatigue crack path; micro-roughness. 1. Introduction The initiation of fatigue cracks in pearlitic microstructures [1] is strongly dependent on whether or not surface defects (scratches, voids, hard particles, inclusions, microcracks, localized damage regions…) are present in the considered material. In high-strength colddrawn pearlitic steel wires, the fatigue damage initiation process takes place in the vicinity of surface defects [2-4], broken martensite layers (due to an overheating during cold drawing), longitudinal grooves and holes mainly caused by surface inclusions [2]. In the case of drawing-based manufacturing techniques, very often surface defects are caused by the cold drawing process itself [5]. Although surface defects (e.g. scratches) might be removed by repeated cold drawing, when a flaw appears inside the wire it remains present in the steel because of the development of an overlap of two regions of the material with a discontinuity between them, and it is thus difficult to fully remove such a flaw [6]. In the case of fatigue crack growth in aggressive environments (corrosion-fatigue) the harsh atmosphere surrounding any surface defect is able to blunt it due a phenomenon of damage known as material dissolution, thereby increasing the number of cycles required to initiate cracking from the afore-said blunted surface defect and increasing the corrosion-fatigue life [7]. In this framework, the beneficial effect of crack tip blunting by localized anodic dissolution (LAD) in stress corrosion cracking (SCC) of highstrength cold-drawn pearlitic steel wires has been reported elsewhere [8]. As described in the scientific literature [9], one of the main causes of engineering failure in steel wires is the presence of non-metallic inclusions in the material, because they can promote the development of surface localized damage during wire drawing or they can affect
the fatigue performance of the material in service. The existence of non-metallic inclusions in cold-drawn pearlitic steel wires influences their fatigue behaviour [10] by modifying the local stress state surrounding the inclusions, depending on the size, localization, composition and geometry of the inclusion [11]. With regard to propagation of fatigue cracks [12], in the case of ferritic-pearlitic steels in which the local areas of pearlitic microstructure are uniformly distributed in the global ferrite, the fatigue crack path is more tortuous than in those with isolated pearlitic areas surrounded by ferrite, with larger angle deflections appearing during the crack advance [13]. In eutectoid steel with fully pearlitic microstructure, the crack during its advance tends to break the ferrite/cementite lamellae [14]. In this case the kind of fatigue fracture surface can be classified as transcollonial, cf. [14]. In banded ferritic-pearlitic steels the bands of pearlite (oriented in preferential directions) provoke a decrease of the fatigue crack growth rate, since they produce a more tortuous crack path, with more frequent and more angled deflections and branchings [15]. Such a tortuous propagation path frequently produces crack interlocking and the crack branching reduces the local crack tip driving forces for fatigue propagation. In fully pearlitic steels with oriented pearlite microstructure as a consequence of heavy cold drawing [14] or large shear deformation [16], the orientation of ferrite/cementite lamellae slows down the fatigue crack growth rate [14,16]. The reason for this particular behaviour is the fact that cementite lamellae behave as serious obstacles for dislocation movement and therefore for crack advance. In the framework of the fracture mechanics approach to fatigue crack growth, the nonlinear crack configuration should be taken into account in the analysis [17]. In addition, it is now well known that variations in crack deflection features influence considerably the fatigue crack propagation rates and the threshold stress intensity factor (SIF) range ΔKth, as described elsewhere [18]. This paper deals with the initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires. It goes further in the research performed in [12,19] dealing only with fatigue crack propagation, studying fatigue crack paths [12] in the Paris regime of crack growth and proposing a modification of the Paris law [19] considering the real fatigue crack accounting for micro-crack deflections and local mixed-mode propagation. In the present paper, in addition to the analysis of the initiation phase from surface defects, a materials science relationship is proposed between microstructural arrangement (specially lamellar orientation) in cold drawn pearlitic steel after cold drawing, tortuosity of the fatigue crack path, real fatigue crack increment and macroscopic cyclic crack growth rate on the basis of a Paris law approach to fatigue crack growth. 2. Materials The material used in the present research work was pearlitic steel with eutectoid chemical composition shown in Table 1.
%C 0.789
% Mn 0.681
Table 1. Chemical composition. % Si %P %S % Al 0.210 0.010 0.008 0.003
% Cr 0.218
%V 0.061
It was studied in two forms: firstly, as a hot rolled bar (non cold drawn at all) and, secondly, as a commercial prestressing steel wire which has undergone seven cold drawing steps up to reaching a cumulative plastic strain εP=1.57 and a posterior stress-relieving treatment to eliminate, or at least diminish, residual stresses. Steel was supplied in form of wires with
circular section, the diameter respectively 11.0 and 5.1 mm for the hot rolled bar and the prestressing steel wire. 2.1. Microstructure Fig. 1 shows a scheme of the cuts associated with the metallographic analysis. The horizontal axis of the micrographs corresponds to the radial direction in the wire, while the vertical axis of the micrographs is linked with the hoop cylindrical coordinate in the transverse section of the wire and associated with the axial cylindrical coordinate in the longitudinal section of the wire. Fig. 1. Scheme of the transverse (left) and longitudinal (right) sections used in the metallographic analysis. The microstructure of both materials (hot rolled bar and cold drawn wire) appears in Figs. 2 and 3 for their respective transverse and longitudinal sections. Cold drawing induces important microstructural changes in the steel at the two basic microstructural levels. The colonies become progressively enlarged and oriented in axial direction with cold drawing [20,21]. With regard to the lamellae, the interlamellar spacing decreases with cold drawing and at the same time the axial orientation increases [22,23]. Fig. 2. Microstructure of steel in transverse section [24]: (a) hot rolled bar; (b) cold drawn wire. Fig. 3. Microstructure of steel in longitudinal section [24]: (a) hot rolled bar; (b) cold drawn wire. A quantitative metallographic evaluation of the microstructural evolution in pearlitic steel during cold drawing was performed. To this end, Fig. 4 shows the microstructural angles θlam and βlam that form the ferrite/cementite (pearlite) lamellae respectively with the radial (r) and axial (z) axes. Fig. 5 plots the micro-angle βlam (in relation to the wire axis or cold-drawing direction) of the lamellae as a function of the cold-drawing degree expressed in terms of cumulative plastic strain εp during the manufacture process, showing the progressive microstructural orientation, so that the heavily cold drawn pearlitic steel wire acquires a microstructure with its lamellae oriented quasi-parallel to the drawing axis.
Fig. 4. Definition of microstructural orientation angles (ferrite/cementite lamellae).
Fig. 5. Relationship between the microstructural orientation angle of pearlitic (Fe/Fe3C) lamellae (angle βlam in relation to the wire axis or cold drawing direction, cf. Fig. 4) and the degree of cold drawing (evaluated by means of the cumulative plastic strain εp after drawing). In addition to these general features of microstructural evolution of cold drawing, some particular phenomena appear in the steel microstructure. One of the most remarkable ones is the appearance of a new (non-conventional) microscrostructural unit: the pearlitic pseudocolony [25], shown in Fig. 6. It is a special pearlitic colony in which the lamellae are not oriented along the wire axis or cold drawing direction, thereby producing an anomalous (extremely high) pearlitic interlamellar spacing. These characteristics make them weakest areas or potential fracture initiation units, i.e., places able to produce fracture path deflection.
Fig. 6. Pearlitic pseudocolony in heavily cold drawn pearlitic steel. 2.2. Mechanical properties The cold drawing process activates in the material a strain hardening mechanism, so that it produces a clear improvement of conventional mechanical properties (Table 2) obtained from a standard tension test: both the yield strength (σY) and the ultimate tensile strength (UTS, σR) increase with cold drawing, while the Young’s modulus (E) remains constant and the strain at UTS (εR) decreases with it. Table 2. Mechanical properties of the material in both conditions, i.e., as a hot rolled bar and as a cold drawn (prestressing steel) wire. Steel E (GPa) σY (MPa) σR (MPa) εR Hot rolled bar 202 700 1220 0.078 Cold drawn wire 209 1480 1820 0.060 3. Experimental programme 3.1. Fatigue crack initiation Wöhler fatigue tests were performed under tensile load control with constant Δσ, sinusoidal wave shape, frequency of 10 Hz, R-ratio equal to 0 and a maximum stress lower than the yield strength σY. The specimens were in the form of 30 cm long bars of circular cross section and the same diameter as the supplied wires (as received, 11.0 mm for the hot rolled bar and 5.1 mm for the cold drawn wire). A total number of 20 tests were performed. Fracture surfaces were analyzed by scanning electron microscopy (SEM). The surface quality (evaluated in terms of roughness) of both products, hot rolled bar and the cold drawn wire (commercial prestressing steel wire), is very different (Fig. 7). While in the first (which comes from a hot rolling process), some small surface defects can be detected, many of them in the form of localized damage in the area of material surface, in the second (heavily cold drawn pearlitic steel wire) voids created by tearing or longitudinal grooves (surface linear scratches oriented in the cold drawing direction) appear during drawing due to the existence of particles near the wire surface [2]. As a consequence of the afore-said phenomena, the surface roughness is higher in the hot rolled bar than in the prestressing steel wire. The surface defects (pre-existent in the hot rolled bar) change the geometry with the heavy cold drawing process, their depth decreasing up to the total disappearing in some cases [6]. Fig. 7. Surface appearance [1] for: (a) hot rolled bar; (b) cold drawn wire.
Another remarkable microstructural fact is the presence of inclusions that frequently appear in both materials (hot rolled bar and prestressing steel wire). Such inclusions are of different types: sulphides, oxides, silicates, etc, many times located in the vicinity of the wire surface, thus promoting the appearance of voids in the steel. The initiation of fatigue cracks in pearlitic steels usually takes place at the wire surface, specifically in the areas surrounding some of the described defects, as shown in Figs. 8 and 9. The defect size decreases with cold drawing, as the cross sectional of the wire does. In the hot rolled bar the fatigue initiators are mainly the surface defects with small aspect ratio (material losses at the peripheral zones during hot rolling) while in the heavily cold drawn prestressing steel wire such initiators are principally the voids in the form of longitudinal groves created by, probably, the existence of particles near the wire surface that scratch the surface during cold drawing of the prestressing steel wires, thereby creating the afore-said longitudinal defects (grooves). Initiation of fatigue cracks from surface defects is due to the fact that the latter acts as stress concentrators. Fig. 8. Initiation locus for fatigue cracks in the form of surface defects (flaws) in hot rolled bar: (a) specimen 1; (b) specimen 2 [1]. Fig. 9. Initiation locus for fatigue cracks in the form of surface defects (flaws) in cold drawn wire [1]: (a) transverse section; (b) longitudinal section. 3.2. Fatigue crack propagation The fatigue tests consisted of applying a cyclic tensile load on cylindrical samples taken from the bar and the wire. A sinusoidal wave was used with a frequency of 10 Hz and R-ratio equal to 0. The maximum stress applied during the tests was always lower than the yield strength of the material. The crack length was monitored through the compliance of the sample (after calibrating the cracked cylindrical specimens and obtaining the curves compliance vs. crack length for both the hot rolled bar and cold drawn wire) [14]. The fatigue fracture surfaces were examined by SEM after the fatigue crack growth tests (fractographic analysis). In addition, the fatigue crack paths were observed after longitudinal cuts on the fatigued specimens, metallographic preparation and SEM observation, thereby covering both fractographic and metallographic aspects (fracto-materialographic analysis). Fig. 10 shows a scheme of the micrograph on the fatigue fracture surface. The horizontal axis of the micrograph corresponds to the radial direction, while the vertical axis is linked with the hoop cylindrical coordinate. The fatigue surface exhibits ductile micro-tearing patterns (Figs. 11 and 12) corresponding to highly-localized plastic strains, which can be classified as tearing topography surface or TTS [26,27]. Such microtearings are less rough in the initiation period than in the propagation phase. In the drawn steel the ductile micro-tears are smaller and with curvier geometry than in the hot rolled bar, due to the microstructural changes (mostly in the cross sectional area of the wire) produced by the high plastic strain undergone by the heavily drawn, and a sort of materials science relationship appears between microstructural unit size and fatigue microfracture event. An increase of the SIF range ΔK also promotes this phenomenon (higher roughness for increasing stress intensity) in both steels. The afore-said TTS microfracture mode has been associated with hydrogen embrittlement in pearlitic steel [28,29] and it can be considered a slow propagation mode in hydrogen-assisted fracture processes linked with subcritical cracking at one micrometer per second or less, cf. [28]. The micro-tearing events with TTS appearance shown in Figs. 11 and 12 are consistent with plastic crack advance during fatigue [30], a mechanism that is not based on microfracture events but on transferring material from the vicinity of the crack tip to the crack
flanks, without any necessity of plasticity-induced fatigue crack closure, a really controversial phenomenon, as discussed elsewhere [31-37].
Fig. 10. Location of the picture used in the fractographic analysis. Fig. 11. Fractographic analysis for low regime of ΔK: (a) hot rolled bar; (b) cold drawn wire.
Fig. 12. Fractographic analysis for high regime of ΔK: (a) hot rolled bar; (b) cold drawn wire. Fig. 13 shows a scheme of the cut associated with the fracto-materialographic analysis. The horizontal axis of the micrograph corresponds to the radial direction in the wire, while the vertical axis of the micrograph is linked with the axial cylindrical coordinate in the longitudinal section of the wire. Fig. 14 includes various longitudinal cuts of the crack path caused by fatigue in the steels studied.
Fig. 13. Location of the picture used in the fracto-materialographic analysis. Fig. 14. Fracto-materialographic analysis for intermediate level of SIF range ΔK: (a) hot rolled bar; (b) cold drawn wire. Fatigue fracture in both steels essentially develops by breaking the lamellae inside the colonies, i.e., it can be classified as translamellar and transcollonial (breaking the ferrite/cementite lamellae and crossing the colonies), showing very localized plastic damage, which is consistent with previous numerical approaches to the fatigue phenomenon in highstrength steels [30,36,37]. Fatigue cracking takes place in a very tortuous manner, with frequent deflections (many micro-deviations from the main direction of macro-crack advance in mode I) and certain evidence of branches and bifurcations. The afore-said collection of events determines the existence of a local propagation regime with a very marked mode mixity that promotes locally multiaxial fatigue crack propagation. The described phenomenon, consisting of recurrent deviations from the main crack propagation path, provokes an increase of surface micro-roughness and, therefore, a decrease of the driving force for fatigue, thus slowing down the fatigue crack advance [11,14]. The fatigue cracks exhibit continuous changes in the matter of crack opening displacement (COD), although its magnitude usually drops from the crack mouth to the crack tip. Furthermore, in some zones the crack presents local micro-discontinuities during its growth. An analysis of the mixed mode crack advance (mode I + mode II) at the finest microscopic level shows some sections in which interlocking can be observed [38]. The common result of this phenomenon is a very small COD that can even end up with the contact of both fatigue fracture surfaces in some specific localized areas.
4. Discussion 4.1. Fatigue crack initiation Fig. 15 shows the aspect ratio of the initiation locus in hot rolled bar (Fig. 15a) and cold drawn wire (Fig. 15b), exhibiting very different aspect ratio as a consequence of the fact that the surface defect is different in both cases. Whereas in the hot rolled bar such a flaw is due to a clear loss of material during hot rolling (thereby producing a very shallow surface initiation crack, cf. Fig. 15a), in the cold drawn wire the initiation defect is caused by very aggressive fretting during heavy cold drawing (thus creating a scratching effect and producing a sort of micro-groove with smaller aspect ratio, cf. Fig. 15b). Fig. 15. Initiation locus for fatigue cracks in the form of surface defects (flaws) in: (a) hot rolled bar; (b) cold drawn wire. Apparently, there is no single initiation point over the defect boundary, but a set of points defining the emerging fatigue crack front at the early stages of cracking and diverging fatigue propagation lines emanating from the defect: lack of material previously lost during the manufacture process in the case of the hot rolled bar and longitudinal voids (grooves) created by a surface inclusion that scratches the material during cold-drawing for manufacturing commercial prestressing steel wires. It is seen that the surface defect (fatigue initiator) appearance is different in the two pearlitic steels (hot rolled bar and cold drawn wire). In the hot rolled bar the surface defect looks like an extremely shallow flaw with an approximate aspect ratio of 0.2÷0.5 whereas in the cold drawn wire such a defect looks like a relatively small circumferential flaw with an approximate aspect ratio equal to the unity (Fig. 16).
Fig. 16. Geometry of superficial defects (flaws) initiators of fatigue. In the matter of crack initiation (but with regard to crack propagation) one should analyze the intermediate phase of fatigue crack advance (middle stage of initiation/propagation). To this end, Fig. 17 shows two pictures of such a phase in a steel E5 that has undergone five steps of cold drawing. The cracks generated by fatigue tend to produce a circular crack front for small cracks (Fig. 17a), the aspect ratio tending to diminish during the propagation. Another possible phenomenon is the initiation of several cracks (even at the same transversal section of the bar or the wire) that can progress up to coalescence, thereby producing a unique (single) crack front, as shown in Fig. 17b. Fig. 17. Fatigue fracture surface: (a) microcrack; (b) four initiators and coalescence of cracks. 4.2. Fatigue crack propagation After applying several regimes of SIFs during fatigue crack growth, an analysis can be performed of the profiles developed by the fatigue crack in the longitudinal sections of the specimen. The fatigue crack paths at the micro-level can be characterized by means of two parameters: the average micro-deflection length lfat (or average length between deflections, deviations or kinks) and the average micro-deflection angle θfat, measured in relation to the main macroscopic crack advance direction (in global mode I), as shown in Fig. 18. The variables lfat and θfat described above are a measure of the roughness (asperity) of the fatigue fracture path. In the matter of the two parameters governing the fatigue crack growth, both the SIF range ΔK and the R-ratio influence the aspect of the fatigue fracture surface. The
rise of any of these (SIF range ΔK or R-ratio) produces the typical micro-tearing features and creates a more tortuous fractographic mode [13]. Fig. 18. Scheme of the fatigue crack: (a) hot rolled bar; (b) cold drawn wire. A quantitative estimation of both parameters lfat and θfat describing the fatigue microcracking path was made from the longitudinal cuts perpendicular to the crack front and parallel to the crack advance (fracto-materialographic analysis, see Fig. 14). It is observed that the average micro-deflection length lfat between two consecutive kinks (Fig. 19) diminishes with the cold drawing degree (with the drawing-induced cumulative plastic strain) and with the intensity of fatigue (i.e., with the level of the SIF range ΔK), whereas the average micro-deflection angle θfat (Fig. 20) increases its value with both the degree of cold drawing (measured through the cumulative plastic strain) and with the fatigue cracking level (evaluated by means of the SIF range ΔK). The phenomenological features described in the previous paragraphs are consistent with the appearance of the fatigue fracture topographies shown in Fig. 11 (fractographic analysis for low regime of ΔK) and in Fig. 12 (fractographic analysis for high regime of ΔK). In this set of pictures it is shown that the increase of the drawing degree and the level of fatigue intensity produces shorter micro-tearing events and a higher level of tortuosity in the fatigue crack path, cf. Figs. 11 and 12. Fig. 19. Average micro-deflection length (lfat) vs. SIF range (ΔK) for the hot rolled bar and the cold drawn wire.
Fig. 20. Average micro-deflection angle (θfat) vs. SIF range (ΔK) for the hot rolled bar and the cold drawn wire. An innovative procedure for estimating the real crack propagation rate (in the form of Paris law of fatigue crack growth) was proposed in reference [19] where the non-linear crack configuration (crack morphology at the micro-level) was taken into account on the basis of the variations in crack morphology (degree and periodicity of micro-crack kinks, deviations or deflections), so that a correction was made in the matter of the cyclic crack growth rate by considering the actual physical crack growth rate (the real length of propagation is different from the projected one in the global mode I direction of crack advance). The procedure (described in [19]) leads to the two different fatigue propagation laws (represented in Fig. 21). On one hand, the Conventional Paris Law (CPL) evaluated on the basis of the virtual crack advance in global mode I, i.e., without considering the microdeflections. Therefore, the crack length a is measured in the transverse direction of the bar or the wire and represents the projection of the real fatigue crack path in the direction of virtual (theoretical) crack advance in global mode I. This CPL takes the form: da C K m (1) dN where C and m are the conventional Paris coefficients of the material given in Table 3. On the other hand, the Actual Paris Law (APL) evaluated on the basis of the actual crack advance in local mixed mode I+II, i.e., considering the micro-deflections. Therefore, the actual crack length a* is measured in the real deflected direction of advance, i.e., following the real or physical fatigue crack path in the actual direction of micro-crack advance and taking into account the micro-deflections and the tortuosity of the fatigue crack path (with zigzag shape). This APL takes the form:
* da* C *K m dN where C* and m* are the actual Paris coefficients of the material given in Table 3.
(2)
Table 3. Conventional and actual Paris coefficients of the materials (units for da/dN in m/cycle and ΔK in MPam1/2). Steel C m C* m* -12 -12 Hot rolled bar 5.3·10 3.0 3.3·10 3.2 -12 -12 Cold drawn wire 4.1·10 3.0 3.2·10 3.2 Fig. 21. Conventional Paris Laws (CPLs) da/dN and Actual Paris Laws (APLs) da*/dN for the hot rolled bar and the cold drawn wire. Fig. 21 shows how the manufacturing process by cold drawing is beneficial from the fracture mechanics point of view, so that the improvement of fatigue performance can be attributed to the increase of the actual, physical or real fatigue propagation length in the cold drawn steel (associated with the corresponding increase of micro-roughness after cold drawing, with shorter and more angled micro-deflections). It is seen that the APLs in both materials become closer when considering the real fatigue crack advance, and are plotted more separated (in both materials) when represent CPLs.
In Fig. 22 a material science approach is shown in a plot representing the microstructural orientation angle θlam of pearlitic (Fe/Fe3C) lamellae (cf. Fig. 5, θlam=90º-βlam) and the microdeflection angles of fatigue crack propagation for different levels of fatigue (ΔK) and distinct cold drawing degree (HR: hot rolled bar; CD: cold drawn wire). It is seen that all angles evolve in similar manner, thereby showing the influence of the markedly oriented microstructure of the cold drawn pearlitic steel wire on the tortuosity of the fatigue crack path (angle of micro-deflections) and thus on the better fatigue performance of the commercial prestressing steel. An additional reason for the improvement of fatigue performance with cold drawing is the blocking of dislocational movement (a basis for plastic crack advance) produced by the cementite lamellae, they being oriented with a higher angle in the cold drawn material and thus increasing the blocking effect and retarding the crack growth rate, because the cementite lamellae act as barriers or obstacles for dislocation movements, thereby retarding plastic crack advance by fatigue in the steel. Fig. 22. Plot representing the microstructural orientation angle θlam of pearlitic (Fe/Fe3C) lamellae (cf. Fig. 5) and the micro-deflection angles θfat of fatigue crack propagation for different levels of fatigue ΔK and distinct degree of cold drawing (HR: hot rolled bar; CD: cold drawn wire; ΔK1: low stress intensity;ΔK2: high stress intensity).
5. Conclusions On the basis of the analysis of initiation and propagation of fatigue cracks in cold drawn pearlitic steel, the following conclusions can be drawn: (i) The initiation of fatigue cracks in pearlitic steel takes place near the wire surface and the initiators are small defects with different features. Whereas in the hot rolled bar such a flaw is due to a clear loss of material during hot rolling, in the cold drawn wire the initiation defect is caused by very aggressive fretting during heavy cold drawing. (ii) Fatigue crack propagation in pearlitic steel takes place as a consequence of microplastic tearing. The cold drawn wire exhibits a pattern resembling micro-tearing, these events being of lower size and more curved aspect than those associated with the hot rolled bar. (iii) Fatigue cracks are trans-colonial and trans-lamellar in both steels. As a matter of fact, fatigue crack propagation can be classified as tortuous, with certain quantity of microdiscontinuities, branchings (frequently bifurcations also appear) as well as local deflections. (iv) Fatigue fracture in the cold drawn pearlitic wire exhibits an appearance consisting of micro-roughness. The total fractured surface is greater than in the hot rolled bar (base material). The increase of the stress intensity factor (SIF) range, ∆K, also produces higher micro-roughness in the fracture surface. (v) The micro-roughness can be characterized by means of the parameters describing the micro-crack path: the average deflection length l (or average length between deviations or kinks) and the average deflection angle θ. The length l diminishes with the SIF range ΔK and with the degree of cold drawing in the material, whereas the angle θ increases with both variables (cold drawing degree and stress intensity). (vi) Two laws of fatigue crack growth can be evaluated in the materials: the Conventional Paris Law (CPL) for transverse crack advance in global mode I and the Actual Paris Law (APL) for inclined crack advance in local mixed-mode (considering micro-crack deflections and the tortuosity of the fatigue crack path with locally multiaxial fatigue crack growth).
(vii) A material science link was found between the markedly oriented microstructure of pearlitic steel after cold drawing (ferrite/cementite lamellae oriented quasi-parallel to the wire axis or cold drawing direction in the heavily drawn steel) and the tortuosity of the fatigue crack path enhancing a better fatigue performance in the cold drawn wire. Acknowledgements The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MICYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA2005-08965), Ministry for Science and Innovation (MICINN; Grant BIA2008-06810), Ministry for Economy and Competitiveness (MINECO; Grant BIA2011-27870), Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07 and SA039A08) and the Spanish University Foundation “Memoria de D. Samuel Solórzano Barruso” (Grant 2016/00017/001).
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S0167-8442(17)30184-2 http://dx.doi.org/10.1016/j.tafmec.2017.08.007 TAFMEC 1939
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Theoretical and Applied Fracture Mechanics
Received Date: Revised Date: Accepted Date:
9 April 2017 28 August 2017 28 August 2017
Please cite this article as: J. Toribio, B. González, J-C. Matos, Initiation and propagation of fatigue cracks in colddrawn pearlitic steel wires, Theoretical and Applied Fracture Mechanics (2017), doi: http://dx.doi.org/10.1016/ j.tafmec.2017.08.007
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Initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires Jesús Toribio, Beatriz González, Juan-Carlos Matos Fracture & Structural Integrity Research Group (FSIRG), University of Salamanca (USAL), E.P.S., Campus Viriato, Avda. Requejo 33, 49022 Zamora, Spain Abstract In this paper the important role of manufacturing by progressive cold drawing on initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires is addressed by analyzing the initiation (from surface defects) and propagation of fatigue cracks in two pearlitic steels with very different cold drawing degree or cumulative plastic strain (and the subsequent very distinct microstructural arrangement): a hot rolled pearlitic steel bar and a commercial highstrength cold-drawn prestressing steel wire to be used as a component of prestressed concrete in structural engineering. Experimental results show that the initiation of fatigue cracks in pearlitic steels takes place at the location of small surface defects, many of them in the form of localized damage in the area of material surface (in the case of hot rolled bar) or voids created by tearing during drawing due to the existence of particles near the wire surface (in the case of the cold drawn wire). In both materials, fatigue cracks are mostly transcollonial and tend to fracture pearlite (ferrite/cementite) lamellae, so that different micro-mechanisms of fatigue damage appear in the material such as non-uniform crack opening displacement, micro-discontinuities, branchings, bifurcations and frequent local deflections, all creating a sort of microstructural roughness in the fatigue crack path that is different in the hot rolled bar and in the cold drawn wire, thereby determining their distinct fatigue performance. Keywords: pearlitic steel; hot rolled bar; cold drawn wire; cold drawing; fatigue crack initiation; fatigue crack propagation; surface defects; fatigue crack path; micro-roughness. 1. Introduction The initiation of fatigue cracks in pearlitic microstructures [1] is strongly dependent on whether or not surface defects (scratches, voids, hard particles, inclusions, microcracks, localized damage regions…) are present in the considered material. In high-strength colddrawn pearlitic steel wires, the fatigue damage initiation process takes place in the vicinity of surface defects [2-4], broken martensite layers (due to an overheating during cold drawing), longitudinal grooves and holes mainly caused by surface inclusions [2]. In the case of drawing-based manufacturing techniques, very often surface defects are caused by the cold drawing process itself [5]. Although surface defects (e.g. scratches) might be removed by repeated cold drawing, when a flaw appears inside the wire it remains present in the steel because of the development of an overlap of two regions of the material with a discontinuity between them, and it is thus difficult to fully remove such a flaw [6]. In the case of fatigue crack growth in aggressive environments (corrosion-fatigue) the harsh atmosphere surrounding any surface defect is able to blunt it due a phenomenon of damage known as material dissolution, thereby increasing the number of cycles required to initiate cracking from the afore-said blunted surface defect and increasing the corrosion-fatigue life [7]. In this framework, the beneficial effect of crack tip blunting by localized anodic dissolution (LAD) in stress corrosion cracking (SCC) of highstrength cold-drawn pearlitic steel wires has been reported elsewhere [8]. As described in the scientific literature [9], one of the main causes of engineering failure in steel wires is the presence of non-metallic inclusions in the material, because they can promote the development of surface localized damage during wire drawing or they can affect
the fatigue performance of the material in service. The existence of non-metallic inclusions in cold-drawn pearlitic steel wires influences their fatigue behaviour [10] by modifying the local stress state surrounding the inclusions, depending on the size, localization, composition and geometry of the inclusion [11]. With regard to propagation of fatigue cracks [12], in the case of ferritic-pearlitic steels in which the local areas of pearlitic microstructure are uniformly distributed in the global ferrite, the fatigue crack path is more tortuous than in those with isolated pearlitic areas surrounded by ferrite, with larger angle deflections appearing during the crack advance [13]. In eutectoid steel with fully pearlitic microstructure, the crack during its advance tends to break the ferrite/cementite lamellae [14]. In this case the kind of fatigue fracture surface can be classified as transcollonial, cf. [14]. In banded ferritic-pearlitic steels the bands of pearlite (oriented in preferential directions) provoke a decrease of the fatigue crack growth rate, since they produce a more tortuous crack path, with more frequent and more angled deflections and branchings [15]. Such a tortuous propagation path frequently produces crack interlocking and the crack branching reduces the local crack tip driving forces for fatigue propagation. In fully pearlitic steels with oriented pearlite microstructure as a consequence of heavy cold drawing [14] or large shear deformation [16], the orientation of ferrite/cementite lamellae slows down the fatigue crack growth rate [14,16]. The reason for this particular behaviour is the fact that cementite lamellae behave as serious obstacles for dislocation movement and therefore for crack advance. In the framework of the fracture mechanics approach to fatigue crack growth, the nonlinear crack configuration should be taken into account in the analysis [17]. In addition, it is now well known that variations in crack deflection features influence considerably the fatigue crack propagation rates and the threshold stress intensity factor (SIF) range ΔKth, as described elsewhere [18]. This paper deals with the initiation and propagation of fatigue cracks in cold-drawn pearlitic steel wires. It goes further in the research performed in [12,19] dealing only with fatigue crack propagation, studying fatigue crack paths [12] in the Paris regime of crack growth and proposing a modification of the Paris law [19] considering the real fatigue crack accounting for micro-crack deflections and local mixed-mode propagation. In the present paper, in addition to the analysis of the initiation phase from surface defects, a materials science relationship is proposed between microstructural arrangement (specially lamellar orientation) in cold drawn pearlitic steel after cold drawing, tortuosity of the fatigue crack path, real fatigue crack increment and macroscopic cyclic crack growth rate on the basis of a Paris law approach to fatigue crack growth. 2. Materials The material used in the present research work was pearlitic steel with eutectoid chemical composition shown in Table 1.
%C 0.789
% Mn 0.681
Table 1. Chemical composition. % Si %P %S % Al 0.210 0.010 0.008 0.003
% Cr 0.218
%V 0.061
It was studied in two forms: firstly, as a hot rolled bar (non cold drawn at all) and, secondly, as a commercial prestressing steel wire which has undergone seven cold drawing steps up to reaching a cumulative plastic strain εP=1.57 and a posterior stress-relieving treatment to eliminate, or at least diminish, residual stresses. Steel was supplied in form of wires with
circular section, the diameter respectively 11.0 and 5.1 mm for the hot rolled bar and the prestressing steel wire. 2.1. Microstructure Fig. 1 shows a scheme of the cuts associated with the metallographic analysis. The horizontal axis of the micrographs corresponds to the radial direction in the wire, while the vertical axis of the micrographs is linked with the hoop cylindrical coordinate in the transverse section of the wire and associated with the axial cylindrical coordinate in the longitudinal section of the wire. Fig. 1. Scheme of the transverse (left) and longitudinal (right) sections used in the metallographic analysis. The microstructure of both materials (hot rolled bar and cold drawn wire) appears in Figs. 2 and 3 for their respective transverse and longitudinal sections. Cold drawing induces important microstructural changes in the steel at the two basic microstructural levels. The colonies become progressively enlarged and oriented in axial direction with cold drawing [20,21]. With regard to the lamellae, the interlamellar spacing decreases with cold drawing and at the same time the axial orientation increases [22,23]. Fig. 2. Microstructure of steel in transverse section [24]: (a) hot rolled bar; (b) cold drawn wire. Fig. 3. Microstructure of steel in longitudinal section [24]: (a) hot rolled bar; (b) cold drawn wire. A quantitative metallographic evaluation of the microstructural evolution in pearlitic steel during cold drawing was performed. To this end, Fig. 4 shows the microstructural angles θlam and βlam that form the ferrite/cementite (pearlite) lamellae respectively with the radial (r) and axial (z) axes. Fig. 5 plots the micro-angle βlam (in relation to the wire axis or cold-drawing direction) of the lamellae as a function of the cold-drawing degree expressed in terms of cumulative plastic strain εp during the manufacture process, showing the progressive microstructural orientation, so that the heavily cold drawn pearlitic steel wire acquires a microstructure with its lamellae oriented quasi-parallel to the drawing axis.
Fig. 4. Definition of microstructural orientation angles (ferrite/cementite lamellae).
Fig. 5. Relationship between the microstructural orientation angle of pearlitic (Fe/Fe3C) lamellae (angle βlam in relation to the wire axis or cold drawing direction, cf. Fig. 4) and the degree of cold drawing (evaluated by means of the cumulative plastic strain εp after drawing). In addition to these general features of microstructural evolution of cold drawing, some particular phenomena appear in the steel microstructure. One of the most remarkable ones is the appearance of a new (non-conventional) microscrostructural unit: the pearlitic pseudocolony [25], shown in Fig. 6. It is a special pearlitic colony in which the lamellae are not oriented along the wire axis or cold drawing direction, thereby producing an anomalous (extremely high) pearlitic interlamellar spacing. These characteristics make them weakest areas or potential fracture initiation units, i.e., places able to produce fracture path deflection.
Fig. 6. Pearlitic pseudocolony in heavily cold drawn pearlitic steel. 2.2. Mechanical properties The cold drawing process activates in the material a strain hardening mechanism, so that it produces a clear improvement of conventional mechanical properties (Table 2) obtained from a standard tension test: both the yield strength (σY) and the ultimate tensile strength (UTS, σR) increase with cold drawing, while the Young’s modulus (E) remains constant and the strain at UTS (εR) decreases with it. Table 2. Mechanical properties of the material in both conditions, i.e., as a hot rolled bar and as a cold drawn (prestressing steel) wire. Steel E (GPa) σY (MPa) σR (MPa) εR Hot rolled bar 202 700 1220 0.078 Cold drawn wire 209 1480 1820 0.060 3. Experimental programme 3.1. Fatigue crack initiation Wöhler fatigue tests were performed under tensile load control with constant Δσ, sinusoidal wave shape, frequency of 10 Hz, R-ratio equal to 0 and a maximum stress lower than the yield strength σY. The specimens were in the form of 30 cm long bars of circular cross section and the same diameter as the supplied wires (as received, 11.0 mm for the hot rolled bar and 5.1 mm for the cold drawn wire). A total number of 20 tests were performed. Fracture surfaces were analyzed by scanning electron microscopy (SEM). The surface quality (evaluated in terms of roughness) of both products, hot rolled bar and the cold drawn wire (commercial prestressing steel wire), is very different (Fig. 7). While in the first (which comes from a hot rolling process), some small surface defects can be detected, many of them in the form of localized damage in the area of material surface, in the second (heavily cold drawn pearlitic steel wire) voids created by tearing or longitudinal grooves (surface linear scratches oriented in the cold drawing direction) appear during drawing due to the existence of particles near the wire surface [2]. As a consequence of the afore-said phenomena, the surface roughness is higher in the hot rolled bar than in the prestressing steel wire. The surface defects (pre-existent in the hot rolled bar) change the geometry with the heavy cold drawing process, their depth decreasing up to the total disappearing in some cases [6]. Fig. 7. Surface appearance [1] for: (a) hot rolled bar; (b) cold drawn wire.
Another remarkable microstructural fact is the presence of inclusions that frequently appear in both materials (hot rolled bar and prestressing steel wire). Such inclusions are of different types: sulphides, oxides, silicates, etc, many times located in the vicinity of the wire surface, thus promoting the appearance of voids in the steel. The initiation of fatigue cracks in pearlitic steels usually takes place at the wire surface, specifically in the areas surrounding some of the described defects, as shown in Figs. 8 and 9. The defect size decreases with cold drawing, as the cross sectional of the wire does. In the hot rolled bar the fatigue initiators are mainly the surface defects with small aspect ratio (material losses at the peripheral zones during hot rolling) while in the heavily cold drawn prestressing steel wire such initiators are principally the voids in the form of longitudinal groves created by, probably, the existence of particles near the wire surface that scratch the surface during cold drawing of the prestressing steel wires, thereby creating the afore-said longitudinal defects (grooves). Initiation of fatigue cracks from surface defects is due to the fact that the latter acts as stress concentrators. Fig. 8. Initiation locus for fatigue cracks in the form of surface defects (flaws) in hot rolled bar: (a) specimen 1; (b) specimen 2 [1]. Fig. 9. Initiation locus for fatigue cracks in the form of surface defects (flaws) in cold drawn wire [1]: (a) transverse section; (b) longitudinal section. 3.2. Fatigue crack propagation The fatigue tests consisted of applying a cyclic tensile load on cylindrical samples taken from the bar and the wire. A sinusoidal wave was used with a frequency of 10 Hz and R-ratio equal to 0. The maximum stress applied during the tests was always lower than the yield strength of the material. The crack length was monitored through the compliance of the sample (after calibrating the cracked cylindrical specimens and obtaining the curves compliance vs. crack length for both the hot rolled bar and cold drawn wire) [14]. The fatigue fracture surfaces were examined by SEM after the fatigue crack growth tests (fractographic analysis). In addition, the fatigue crack paths were observed after longitudinal cuts on the fatigued specimens, metallographic preparation and SEM observation, thereby covering both fractographic and metallographic aspects (fracto-materialographic analysis). Fig. 10 shows a scheme of the micrograph on the fatigue fracture surface. The horizontal axis of the micrograph corresponds to the radial direction, while the vertical axis is linked with the hoop cylindrical coordinate. The fatigue surface exhibits ductile micro-tearing patterns (Figs. 11 and 12) corresponding to highly-localized plastic strains, which can be classified as tearing topography surface or TTS [26,27]. Such microtearings are less rough in the initiation period than in the propagation phase. In the drawn steel the ductile micro-tears are smaller and with curvier geometry than in the hot rolled bar, due to the microstructural changes (mostly in the cross sectional area of the wire) produced by the high plastic strain undergone by the heavily drawn, and a sort of materials science relationship appears between microstructural unit size and fatigue microfracture event. An increase of the SIF range ΔK also promotes this phenomenon (higher roughness for increasing stress intensity) in both steels. The afore-said TTS microfracture mode has been associated with hydrogen embrittlement in pearlitic steel [28,29] and it can be considered a slow propagation mode in hydrogen-assisted fracture processes linked with subcritical cracking at one micrometer per second or less, cf. [28]. The micro-tearing events with TTS appearance shown in Figs. 11 and 12 are consistent with plastic crack advance during fatigue [30], a mechanism that is not based on microfracture events but on transferring material from the vicinity of the crack tip to the crack
flanks, without any necessity of plasticity-induced fatigue crack closure, a really controversial phenomenon, as discussed elsewhere [31-37].
Fig. 10. Location of the picture used in the fractographic analysis. Fig. 11. Fractographic analysis for low regime of ΔK: (a) hot rolled bar; (b) cold drawn wire.
Fig. 12. Fractographic analysis for high regime of ΔK: (a) hot rolled bar; (b) cold drawn wire. Fig. 13 shows a scheme of the cut associated with the fracto-materialographic analysis. The horizontal axis of the micrograph corresponds to the radial direction in the wire, while the vertical axis of the micrograph is linked with the axial cylindrical coordinate in the longitudinal section of the wire. Fig. 14 includes various longitudinal cuts of the crack path caused by fatigue in the steels studied.
Fig. 13. Location of the picture used in the fracto-materialographic analysis. Fig. 14. Fracto-materialographic analysis for intermediate level of SIF range ΔK: (a) hot rolled bar; (b) cold drawn wire. Fatigue fracture in both steels essentially develops by breaking the lamellae inside the colonies, i.e., it can be classified as translamellar and transcollonial (breaking the ferrite/cementite lamellae and crossing the colonies), showing very localized plastic damage, which is consistent with previous numerical approaches to the fatigue phenomenon in highstrength steels [30,36,37]. Fatigue cracking takes place in a very tortuous manner, with frequent deflections (many micro-deviations from the main direction of macro-crack advance in mode I) and certain evidence of branches and bifurcations. The afore-said collection of events determines the existence of a local propagation regime with a very marked mode mixity that promotes locally multiaxial fatigue crack propagation. The described phenomenon, consisting of recurrent deviations from the main crack propagation path, provokes an increase of surface micro-roughness and, therefore, a decrease of the driving force for fatigue, thus slowing down the fatigue crack advance [11,14]. The fatigue cracks exhibit continuous changes in the matter of crack opening displacement (COD), although its magnitude usually drops from the crack mouth to the crack tip. Furthermore, in some zones the crack presents local micro-discontinuities during its growth. An analysis of the mixed mode crack advance (mode I + mode II) at the finest microscopic level shows some sections in which interlocking can be observed [38]. The common result of this phenomenon is a very small COD that can even end up with the contact of both fatigue fracture surfaces in some specific localized areas.
4. Discussion 4.1. Fatigue crack initiation Fig. 15 shows the aspect ratio of the initiation locus in hot rolled bar (Fig. 15a) and cold drawn wire (Fig. 15b), exhibiting very different aspect ratio as a consequence of the fact that the surface defect is different in both cases. Whereas in the hot rolled bar such a flaw is due to a clear loss of material during hot rolling (thereby producing a very shallow surface initiation crack, cf. Fig. 15a), in the cold drawn wire the initiation defect is caused by very aggressive fretting during heavy cold drawing (thus creating a scratching effect and producing a sort of micro-groove with smaller aspect ratio, cf. Fig. 15b). Fig. 15. Initiation locus for fatigue cracks in the form of surface defects (flaws) in: (a) hot rolled bar; (b) cold drawn wire. Apparently, there is no single initiation point over the defect boundary, but a set of points defining the emerging fatigue crack front at the early stages of cracking and diverging fatigue propagation lines emanating from the defect: lack of material previously lost during the manufacture process in the case of the hot rolled bar and longitudinal voids (grooves) created by a surface inclusion that scratches the material during cold-drawing for manufacturing commercial prestressing steel wires. It is seen that the surface defect (fatigue initiator) appearance is different in the two pearlitic steels (hot rolled bar and cold drawn wire). In the hot rolled bar the surface defect looks like an extremely shallow flaw with an approximate aspect ratio of 0.2÷0.5 whereas in the cold drawn wire such a defect looks like a relatively small circumferential flaw with an approximate aspect ratio equal to the unity (Fig. 16).
Fig. 16. Geometry of superficial defects (flaws) initiators of fatigue. In the matter of crack initiation (but with regard to crack propagation) one should analyze the intermediate phase of fatigue crack advance (middle stage of initiation/propagation). To this end, Fig. 17 shows two pictures of such a phase in a steel E5 that has undergone five steps of cold drawing. The cracks generated by fatigue tend to produce a circular crack front for small cracks (Fig. 17a), the aspect ratio tending to diminish during the propagation. Another possible phenomenon is the initiation of several cracks (even at the same transversal section of the bar or the wire) that can progress up to coalescence, thereby producing a unique (single) crack front, as shown in Fig. 17b. Fig. 17. Fatigue fracture surface: (a) microcrack; (b) four initiators and coalescence of cracks. 4.2. Fatigue crack propagation After applying several regimes of SIFs during fatigue crack growth, an analysis can be performed of the profiles developed by the fatigue crack in the longitudinal sections of the specimen. The fatigue crack paths at the micro-level can be characterized by means of two parameters: the average micro-deflection length lfat (or average length between deflections, deviations or kinks) and the average micro-deflection angle θfat, measured in relation to the main macroscopic crack advance direction (in global mode I), as shown in Fig. 18. The variables lfat and θfat described above are a measure of the roughness (asperity) of the fatigue fracture path. In the matter of the two parameters governing the fatigue crack growth, both the SIF range ΔK and the R-ratio influence the aspect of the fatigue fracture surface. The
rise of any of these (SIF range ΔK or R-ratio) produces the typical micro-tearing features and creates a more tortuous fractographic mode [13]. Fig. 18. Scheme of the fatigue crack: (a) hot rolled bar; (b) cold drawn wire. A quantitative estimation of both parameters lfat and θfat describing the fatigue microcracking path was made from the longitudinal cuts perpendicular to the crack front and parallel to the crack advance (fracto-materialographic analysis, see Fig. 14). It is observed that the average micro-deflection length lfat between two consecutive kinks (Fig. 19) diminishes with the cold drawing degree (with the drawing-induced cumulative plastic strain) and with the intensity of fatigue (i.e., with the level of the SIF range ΔK), whereas the average micro-deflection angle θfat (Fig. 20) increases its value with both the degree of cold drawing (measured through the cumulative plastic strain) and with the fatigue cracking level (evaluated by means of the SIF range ΔK). The phenomenological features described in the previous paragraphs are consistent with the appearance of the fatigue fracture topographies shown in Fig. 11 (fractographic analysis for low regime of ΔK) and in Fig. 12 (fractographic analysis for high regime of ΔK). In this set of pictures it is shown that the increase of the drawing degree and the level of fatigue intensity produces shorter micro-tearing events and a higher level of tortuosity in the fatigue crack path, cf. Figs. 11 and 12. Fig. 19. Average micro-deflection length (lfat) vs. SIF range (ΔK) for the hot rolled bar and the cold drawn wire.
Fig. 20. Average micro-deflection angle (θfat) vs. SIF range (ΔK) for the hot rolled bar and the cold drawn wire. An innovative procedure for estimating the real crack propagation rate (in the form of Paris law of fatigue crack growth) was proposed in reference [19] where the non-linear crack configuration (crack morphology at the micro-level) was taken into account on the basis of the variations in crack morphology (degree and periodicity of micro-crack kinks, deviations or deflections), so that a correction was made in the matter of the cyclic crack growth rate by considering the actual physical crack growth rate (the real length of propagation is different from the projected one in the global mode I direction of crack advance). The procedure (described in [19]) leads to the two different fatigue propagation laws (represented in Fig. 21). On one hand, the Conventional Paris Law (CPL) evaluated on the basis of the virtual crack advance in global mode I, i.e., without considering the microdeflections. Therefore, the crack length a is measured in the transverse direction of the bar or the wire and represents the projection of the real fatigue crack path in the direction of virtual (theoretical) crack advance in global mode I. This CPL takes the form: da C K m (1) dN where C and m are the conventional Paris coefficients of the material given in Table 3. On the other hand, the Actual Paris Law (APL) evaluated on the basis of the actual crack advance in local mixed mode I+II, i.e., considering the micro-deflections. Therefore, the actual crack length a* is measured in the real deflected direction of advance, i.e., following the real or physical fatigue crack path in the actual direction of micro-crack advance and taking into account the micro-deflections and the tortuosity of the fatigue crack path (with zigzag shape). This APL takes the form:
* da* C *K m dN where C* and m* are the actual Paris coefficients of the material given in Table 3.
(2)
Table 3. Conventional and actual Paris coefficients of the materials (units for da/dN in m/cycle and ΔK in MPam1/2). Steel C m C* m* -12 -12 Hot rolled bar 5.3·10 3.0 3.3·10 3.2 -12 -12 Cold drawn wire 4.1·10 3.0 3.2·10 3.2 Fig. 21. Conventional Paris Laws (CPLs) da/dN and Actual Paris Laws (APLs) da*/dN for the hot rolled bar and the cold drawn wire. Fig. 21 shows how the manufacturing process by cold drawing is beneficial from the fracture mechanics point of view, so that the improvement of fatigue performance can be attributed to the increase of the actual, physical or real fatigue propagation length in the cold drawn steel (associated with the corresponding increase of micro-roughness after cold drawing, with shorter and more angled micro-deflections). It is seen that the APLs in both materials become closer when considering the real fatigue crack advance, and are plotted more separated (in both materials) when represent CPLs.
In Fig. 22 a material science approach is shown in a plot representing the microstructural orientation angle θlam of pearlitic (Fe/Fe3C) lamellae (cf. Fig. 5, θlam=90º-βlam) and the microdeflection angles of fatigue crack propagation for different levels of fatigue (ΔK) and distinct cold drawing degree (HR: hot rolled bar; CD: cold drawn wire). It is seen that all angles evolve in similar manner, thereby showing the influence of the markedly oriented microstructure of the cold drawn pearlitic steel wire on the tortuosity of the fatigue crack path (angle of micro-deflections) and thus on the better fatigue performance of the commercial prestressing steel. An additional reason for the improvement of fatigue performance with cold drawing is the blocking of dislocational movement (a basis for plastic crack advance) produced by the cementite lamellae, they being oriented with a higher angle in the cold drawn material and thus increasing the blocking effect and retarding the crack growth rate, because the cementite lamellae act as barriers or obstacles for dislocation movements, thereby retarding plastic crack advance by fatigue in the steel. Fig. 22. Plot representing the microstructural orientation angle θlam of pearlitic (Fe/Fe3C) lamellae (cf. Fig. 5) and the micro-deflection angles θfat of fatigue crack propagation for different levels of fatigue ΔK and distinct degree of cold drawing (HR: hot rolled bar; CD: cold drawn wire; ΔK1: low stress intensity;ΔK2: high stress intensity).
5. Conclusions On the basis of the analysis of initiation and propagation of fatigue cracks in cold drawn pearlitic steel, the following conclusions can be drawn: (i) The initiation of fatigue cracks in pearlitic steel takes place near the wire surface and the initiators are small defects with different features. Whereas in the hot rolled bar such a flaw is due to a clear loss of material during hot rolling, in the cold drawn wire the initiation defect is caused by very aggressive fretting during heavy cold drawing. (ii) Fatigue crack propagation in pearlitic steel takes place as a consequence of microplastic tearing. The cold drawn wire exhibits a pattern resembling micro-tearing, these events being of lower size and more curved aspect than those associated with the hot rolled bar. (iii) Fatigue cracks are trans-colonial and trans-lamellar in both steels. As a matter of fact, fatigue crack propagation can be classified as tortuous, with certain quantity of microdiscontinuities, branchings (frequently bifurcations also appear) as well as local deflections. (iv) Fatigue fracture in the cold drawn pearlitic wire exhibits an appearance consisting of micro-roughness. The total fractured surface is greater than in the hot rolled bar (base material). The increase of the stress intensity factor (SIF) range, ∆K, also produces higher micro-roughness in the fracture surface. (v) The micro-roughness can be characterized by means of the parameters describing the micro-crack path: the average deflection length l (or average length between deviations or kinks) and the average deflection angle θ. The length l diminishes with the SIF range ΔK and with the degree of cold drawing in the material, whereas the angle θ increases with both variables (cold drawing degree and stress intensity). (vi) Two laws of fatigue crack growth can be evaluated in the materials: the Conventional Paris Law (CPL) for transverse crack advance in global mode I and the Actual Paris Law (APL) for inclined crack advance in local mixed-mode (considering micro-crack deflections and the tortuosity of the fatigue crack path with locally multiaxial fatigue crack growth).
(vii) A material science link was found between the markedly oriented microstructure of pearlitic steel after cold drawing (ferrite/cementite lamellae oriented quasi-parallel to the wire axis or cold drawing direction in the heavily drawn steel) and the tortuosity of the fatigue crack path enhancing a better fatigue performance in the cold drawn wire. Acknowledgements The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MICYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA2005-08965), Ministry for Science and Innovation (MICINN; Grant BIA2008-06810), Ministry for Economy and Competitiveness (MINECO; Grant BIA2011-27870), Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07 and SA039A08) and the Spanish University Foundation “Memoria de D. Samuel Solórzano Barruso” (Grant 2016/00017/001).
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