September 5, 2008
On the Micromechanism of Fatigue Damage in an Interstitial-Free Steel Sheet
By Majumdar, Shrabani Bhattacharjee, D; Ray, K K
The micromechanism of fatigue damage in an interstitial-free (IF) steel sheet has been studied using fully reversed stress amplitudes (Deltasigma/2). The stress-life (S-N) curve of the steel sheet has been generated, together with a series of interrupted fatigue tests at each of the chosen Deltasigma/2, to study the progress of fatigue damage in terms of the initiation, growth, and coalescence of the fatigue cracks on the surfaces of the sheet specimens using scanning electron microscopy. The steel sheet possesses a higher endurance limit (0.98 times its yield strength (YS)), as compared to conventional low-carbon steel sheets. This is attributed to (1) the occurrence of nonpropagating microcracks initiating primarily at the inclusions below the endurance limit and (2) a significant delay in the spread of plastic deformation, until Deltasigma/2 is close to YS. Above the endurance limit, widespread plastic deformation through slip bands promotes the formation of fatigue cracks at the ferrite grain boundaries and occasionally within a ferrite grain body, as well as at inclusions. Fatigue failure is preceded by the significant growth of grain-boundary cracks over and above those at inclusions and the ferrite grain body. A series of grain-boundary cracks link up to form mesocracks, one of which grows to cause the final failure. The predominance of grain-boundary cracks in the process of fatigue failure is attributed to the lesser cohesive strength of the grain boundaries caused by the depletion of interstitials. DOI: 10.1007/s11661-008-9537-y(c) The Minerals, Metals & Materials Society and ASM International 2008
(ProQuest: ... denotes formulae omitted.)
INTERSTITIAL-FREE (IF) steel sheets are extensively used to meet the severe cold-forming requirements of automotive industries. Detailed reports[1,2] exist that are related to the processing routes and properties, especially formability, etc., on these steel sheets. These sheets are primarily used in automobile structural components, which experience cyclic loading in service; hence, knowledge related to the fatigue properties of these materials is important. The number of research reports on the fatigue behavior of IF steel sheets, however, is limited. Earlier works indicate that efforts are primarily aimed at the estimation of fatigue life, with insignificant emphasis on the understanding of the micromechanism of fatigue damage, in terms of the initiation and growth of fatigue cracks at various microstructural locations. Microstructures play a decisive role in the process of fatigue damage, as the latter is primarily governed by the local stress conditions at and around its various features. Hence, an understanding of the micromechanism of fatigue in an extremely clean ultra-low-carbon ferritic microstructure, in which grain boundaries are depleted of interstitials (such as C, N, etc.), presents an interesting problem from the viewpoint of material science. Studies of this nature can sequentially elucidate the preferred location for the initiation of microcracks, the nature of the growth of these microcracks, and, thus, the weak links in the microstructure that provide the low-energy path in which the cracks prefer to grow. The IF steels are important commercial materials and a systematic study of the micromechanism can provide greater insight into both the alloy design and the consequent engineering applications in steels with a similar microstructure. This report is centered on addressing this issue.
The micromechanism of fatigue damage in structural components involves several sequential stages, e.g., (1) the initiation of microcracks, (2) the growth and coalescence of microcracks to form a dominant macrocrack, and (3) the propagation of the macrocrack to cause complete failure. In addition, fatigue damage is commonly associated with the formation of slip bands on the specimen surface, which are known to govern the mechanism of crack initiation and growth. In a flawfree, homogeneous material, a significant fraction of the total lifetime is spent before the first detectable microcrack appears.[5,6] The latter is defined as a discontinuity, all the dimensions of which are small in comparison to the characteristic microstructural dimensions, e.g., grain size, etc. Earlier experimental observations using optical and electron microscopy suggest that, in homogeneous materials, such cracks generally initiate at free surfaces. Therefore, the preferred and most widely used technique for studying fatigue crack initiation is the promotion of the natural initiation of microstructurally small surface cracks in smooth specimens. This method ensures the unrestrained initiation of the microcrack at a location determined entirely by the crack itself. Following initiation, the cracks do not grow equally; thus, it is important to know which of the initiated cracks grow faster than the others and can be considered to dominate the process of fatigue failure.
The design of automotive components fabricated from IF steel sheets (e.g., roof panels, door panels, etc.) is commonly stress based. Hence, from the point of view of the application, it is useful to study the process of fatigue damage with respect to applied stress. During some preliminary studies, it emerged that the nature of microcrack initiation in steel sheets is predominantly governed by the imposed stress amplitude and that its location is significantly different for stress levels above and below the endurance limit. Hence, the primary interest in the present investigation is to reveal the micromechanism of fatigue damage on the surfaces of an IF steel sheet, both above and below the endurance limit. In this study, first, stress-controlled fatigue tests have been carried out using smooth specimens, to estimate the fatigue life at various stress amplitudes. Next, a series of tests were carried out that were interrupted at various stages of fatigue life for a given stress amplitude. The surfaces of these specimens have been studied using scanning electron microscopy, in order to detect the initiation of the microcracks, examine their growth, and study their coalescence behavior as it applies to the formation of macrocracks. The results generated by the study illustrate the progression of fatigue damage at various levels of applied stress and with an increasing number of loading cycles. The prevailing mechanism of the initiation and growth of fatigue cracks and the effect of these cracks on fatigue life are discussed.
II. EXPERIMENTAL DETAILS
The experiments carried out to achieve the goals of this investigation are the following: (1) characterization of the investigated steel sheet in terms of cleanliness, microstructure, and tensile properties; (2) fatigue testing of the sheet specimens; and (3) examination of specimen surfaces after a controlled amount of fatigue damage. The relevant details of the experimental procedures are presented in this section.
A. Characterization of the Investigated Steel
The material selected for this investigation is a 1.25-mm-thick industrially processed Ti-stabilized IF steel sheet. The as- received steel sheet is known to be cold rolled from an initial thickness of 3.2 mm, batch annealed at 680 [degrees]C to 700 [degrees]C, and temper rolled. The sample was obtained as rectangular pieces approximately 960 x 600 mm in dimension, marked with rolling directions, supplied courtesy of Tata Steel, Ltd. (Jamshedpur, India). The composition of the investigated steel is shown in Table I. The standard metallographic technique of grinding and polishing (up to a 0.25-[mu]m diamond finish) was employed, to obtain specimens for the characterization of nonmetallic inclusions in terms of their volume fraction, average size, and chemical nature. The volume fraction of the nonmetallic inclusions in the investigated steel was determined using the Japanese standard JIS G0555. The inclusion size was estimated using a field-emission gun-scanning electron microscope (FEG-SEM) and the annotation toolbar available in the software associated with the microscope. Energy-dispersive X-ray (EDX) analyses were done at the center of the observed inclusions, using the SEM to ascertain their chemical nature. Specimens for examining the microstructure on the surface and at the transverse sections of the sheet were polished and chemically etched using Marshall's reagent.191 The average grain size was determined using the lineal intercept method, as suggested in the ASTM Standard E-1 1296, using an image analyzer that considered 100 fields at a magnification of 200 times. The microhardness of the steel was estimated using a Vickers indenter at a 245.2-mN load for an indentation duration of 30 seconds. The tensile properties of the investigated steel sheet were determined using 6-mm-wide specimens that had a 25-mm gage length and that were fabricated in line with the ASTM Standard E8M-04.[1,] The longitudinal axes of the specimens corresponded to the rolling direction of the sheet. Tensile tests were carried out with the help of a 100-kN-capacity screw-driven tensile-testing machine at a crosshead speed of 5 mm/min, which corresponds to a nominal strain rate of 3.33 x 10^sup -3^ s^sup -1^. B. Fatigue Test
The specimens for fatigue tests were fabricated from the selected steel sheet; the longitudinal axes were kept parallel to the rolling direction of the sheet. A configuration typical of a specimen is shown in Figure 1. The fatigue tests were carried out in laboratory air at room temperature ([asymptotically =]300 K), using a 100-kN servohydraulic fatigue testing machine at R = -1, at a frequency of 10 Hz, using sinusoidal waveform. During these tests, care was taken to ensure that (1) the specimen was properly aligned in the grips and (2) there was no bending or buckling of the sheet specimen during specimen fixing and its testing; a commercial antibuckling fixture was used. Two different types of stresscontrolled fatigue tests were carried out to (1) generate the stress-life (S-N) curve and (2) study the initiation and growth of fatigue cracks on the surfaces of the sheet specimens intermittently at various stages of fatigue life, at each of the selected stress amplitudes. The applied stress amplitude for the tests was selected between 0.5 and 1.3 times the yield strength (YS) of the steel. The rationale for carrying out stress-controlled fatigue tests above the YS is that, in the case of IF steel sheets, it is neither possible to initiate a sufficient amount of fatigue damage nor to achieve a systematic understanding of the progression of fatigue damage below the YS in an optimum time span.
The surfaces of the specimens were polished, using a standard metallographic technique with up to a 0.25micron diamond paste, prior to their testing, for the generation of the S-N curve. The stress-controlled fatigue tests were carried out to record the number of cycles to failure (N^sub f^) at a particular value of the applied stress amplitude. The S-N curve was constructed by plotting the applied stress amplitude (...) against the corresponding number of cycles to failure (N^sub f^) at that Deltasigma/2. In this investigation, failure is defined as the complete fracture of the specimens. For the interrupted fatigue tests, the surfaces of the specimens were polished and etched with Marshall's reagent, to reveal the ferrite grain boundaries prior to fatigue testing. In these experiments, tests were interrupted at various stages of fatigue life, e.g., at 1, 2, 5, 10, 20, 50, 70, 90, and 95 pet of the average N^sub f^ for each of the chosen Deltasigma/2. The surface of a specimen at the varied interruptions was examined using an SEM.
C. Scanning Electron Microscopy Study
The primary aim of the scanning electron microscopy study was to detect the microcracks and examine the nature of their growth (both in number and in size) and their coalescence behavior at various stages of fatigue ufe, for all the selected stress amplitudes (Deltasigma/2). Accordingly, the surfaces of the specimens, after the interrupted fatigue tests, were studied using an SEM, to characterize the fatigue cracks in terms of their (1) location in the microstructure, (2) number density, and (3) size. For estimating the number density of microcracks in a particular specimen, a surface area approximately 30 x 40 mm^sup 2^ in the center of the specimen was studied, using the FEG-SEM at a constant magnification of 2000 times. The total number of fields examined (including those that both did and did not exhibit cracks), the field size (in [mu]m^sup 2^), and the number and locations of microcracks were recorded. The number density was then calculated as the average number of microcracks per unit area (mm^sup 2^) recorded at different microstructural locations. For estimating the average crack size, at least 30 representative microcracks initiating at different microstructural locations in each specimen were taken into consideration. The maximum dimensions of the observed cracks were measured using the measurement toolbar available with the FEG-SEM software. The data generated on the number density and average size of the fatigue cracks were plotted against the number of imposed loading cycles for a particular value of Deltasigma/2. This was done to examine the nature of the initiation and growth of cracks at various microstructural locations. Representative photographs were recorded during the scanning electron microscopy examinations, in order to understand the mechanisms of the initiation, subsequent growth, and coalescence of the microcracks. In addition to these studies, fractographic examinations were also carried out on the failed specimens; in these examinations, a SEM was used to determine the predominant mode of fatigue fracture in the steel sheet.
A. Investigated Material
The chemical composition of the investigated IF steel sheet is shown in Table I. The volume fraction of inclusions in the sheet is 0.04 pct. A histogram showing the size distribution of the inclusions is shown in Figure 2. The mean and the maximum sizes of the observed inclusions estimated from 100 readings are 2.5 and 7.0 [mu]m, respectively; the majority (> 80 pct) of the inclusions, however, are found to be below 3.3 [mu]m in size. A few typical inclusions and their microanalyses are shown in Figure 3. The microanalyses indicate that the inclusions are rich in Fe, Ti, Al, Mg, S, N, and oxygen. The most frequently occurring inclusions are titanium nitride that is 1 to 3 [mu]m in size and shaped like a rhomboid (Figure 3(a)). In addition to TiN, mixed nitrides (Figure 3(b)), globular oxides (Figure 3(c)), a mixture of oxides and sulfides (Figure 3(d)), silicates (Figure 3(e)), and sulfides (Figure 3(0) are also found. A representative microstructure of the steel is shown in Figure 4. The microstructure exhibits equiaxed ferrite on the surface as well as at the cross sections; at both locations, the equiaxed ferrite displays similar values of grain size (12.5 and 13.5 [mu]m, respectively) but marginally varying values of microhardness (110 and 86.7 HV, respectively). The estimated values of the tensile properties are shown in Table II. The steel sheet does not exhibit yield point phenomenon.
B. S-N Curve
The estimated S-N curve (for the investigated IF steel sheet) is shown in Figure 5. It is observed that, as the applied stress amplitude is increased (from 0.5 to 1.3 YS), the number of loading cycles required to cause failure decreases continuously. The curve exhibits a knee at 0.98 YS (-140 MPa), below which there is no failure until 7 x 10^sup 6^ cycles. The endurance limit has been defined here as the maximum stress at which no failure occurs until 7 x 10^sup 6^ cycles. The estimated fatigue life of each specimen, the average value at each stress level, and their associated coefficient of variation (CEV) are presented in Table III, for easy reference. Although a smooth curve could be drawn through the data points in Figure 5, the results in Table III indicate that there is considerable scatter associated with the data on the number of cycles to failure (N^sub f^), for specimens tested at identical stress amplitudes. The magnitude of scatter (i.e., the CEV) tends to decrease with an increase in the stress amplitude.
C. Fatigue-Crack Initiation
The interrupted fatigue tests were conducted at each of the selected stress amplitudes, to study the progression of fatigue damage on the surface of the sheet specimens. The initiation of microcracks is considered to be the first stage in the process of fatigue damage. Representative specimens were subjected to interrupted tests for examinations under a SEM (1) to detect the formation of the microcracks and (2) to determine the number of cycles required for their initiation at a given stress amplitude. There are three preferential locations for the initiation of microcracks in IF steel sheets, depending upon the applied stress amplitudes and the number of loading cycles. These locations are (1) nonmetallic inclusions, (2) the grain boundary, and (3) the grain body. Some typical microcracks initiated at these locations are shown in Figures 6 through 8. The number of cycles after which the first microcrack appears (N^sub i^) at any of these locations was recorded for each of the selected stress amplitudes (varied between 0.5 to 1.3 YS). The values of N^sub i^ are then plotted against the corresponding Deltasigma/2, to obtain the fatigue-crack-initiation life curves for the investigated IF steel sheet, as shown in Figure 9. As the applied stress amplitude is increased, fewer loading cycles are required for microcrack initiation. It must be borne in mind that the N^sub i^ in Figure 9 denotes the initiation and marginal growth of the fatigue cracks to a size sufficient to be resolved by a SEM. The recorded number of cycles required to initiate microcrack (N^sub i^) at any specific location is also summarized in Table III. The obtained results indicate that the locations of fatigue-crack initiation are distinctly different for stress amplitudes above and below the endurance limit (0.98 x YS). For example, below the endurance limit, microcracks initiate only at the nonmetallic inclusions; above the endurance limit, however, microcracks initiate primarily at ferrite grain boundaries and occasionally at a ferrite grain body, in addition to at inclusions. Microcracks, therefore, do get generated even below the endurance limit in these steel sheets; at this stress level, however, these take a significantly larger number of loading cycles to form than is the case above the endurance limit. Below the endurance limit of these steel sheets, the amount of plastic deformation through the formation of slip bands is small and is limited to a few isolated surface grains, as shown in Figure 10(a). On the other hand, when the applied stress amplitude is above the endurance limit, the number of surface grains undergoing plastic deformation is significantly large in number. The plasticity is found to spread across the barriers of grain boundaries to a cluster of neighboring grains, leading to heavily deformed regions on the surface, as shown in Figure 10(b). The spread of plasticity on the sheet surface determines the mode of fatigue crack initiation at a specific location. The microcracks first initiate at the nonmetallic inclusions, at all levels of applied ?s/2 in IF steel sheets. The size of these cracks generally varies between 0.6 and 7 [mu]m, depending on the size of the inclusion. These cracks are mostly equiaxed or round in shape and are formed most predominantly through the decohesion of the inclusion matrix interface, as shown in Figures 6(a) through (c). Occasionally, these cracks are associated with a series of closely spaced inclusions and are elongated parallel to the principal loading direction (LD), as shown in Figures 6(d) and (e). The mechanism for crack initiation here is the separation of closely spaced inclusions. Below the endurance limit, fatigue cracks initiate only at inclusions. The average size of these cracks at this Deltasigma/2 level is 2 to 3 microns; microcracks of this size are generally not associated with any slip bands. On the other hand, above the endurance limit, cracks form at the inclusions apart from the other two locations. Microcracks at inclusions at such high Deltasigma/2 levels are generally associated with slip bands; these are larger in size, with an average size of 4 to 5 microns. Two additional mechanisms for crack initiation come in to play above the endurance limit. These are the fragmentation (Figures 6(0 through (h)) and uprooting of inclusions (Figure 6(i)).
In the investigated IF steel sheet, the initiation of fatigue cracks at the grain boundary occurs abundantly when Deltasigma/2 is close to or above the endurance limit and, in the same instance, the spread of plasticity through slip bands on the sheet surface becomes significant. These cracks initiate at grain-boundary triple points as well as along the grain boundaries, as shown in Figure 7. Grain- boundary cracks are generally associated with slip bands, with the exception of a few cases in which no slip bands could be detected in the adjoining grains. The mechanism of crack initiation is likely to be different in these two cases. It is evident from the scanning electron microscopy study that the associated slip bands impinge upon the grain boundaries, to initiate small, split-type fatigue cracks. Evidence of the impingement of slip bands could be gathered to a large extent. Representative photographs of the formation of slip bands and their impingement on the grain boundaries are shown in Figure 11. The mechanisms of fatigue-crack initiation at grain boundaries have been suggested by a number of investigators.[12-16] For example, based on the idea that grain boundaries act as obstacles to slip bands, Christ et al. proposed a slip band- grain boundary crack model. According to this model, an intergranular fatigue crack can be caused by the stress concentration, due to dislocation pileups against a grain boundary. Zhang et al. have reported that the most favorable site for fatigue-crack initiation (under low-cycle impact loading) in low- carbon steel is at the grain boundaries. They found that, at favorably oriented grain boundaries, crack initiation occurs through the mechanism of the impingement of slip bands at the grain boundaries to produce microsplits. These microsplits then link up to form small cracks. An alternative proposition for the initiation of the grain-boundary cracks has been provided by Hu et al., who contended that elastic and plastic deformation are incompatible in the vicinity of a grain boundary separating two grains that have a high angle of misorientation between them. This is due to the difference in the elastic constants and slip geometry on either side of the grain boundaries. As a consequence, additional internal stresses are induced, in order to fulfill the continuity requirements. This internal stress super-imposes on the applied stress and affects the deformation near the grain boundaries. Studies on bcc bicrystals[15,16] have shown that slip-deformation features near a grain boundary are quite different from those far away from it. Additional slip is usually activated near the grain boundaries to accommodate the elastic-plastic incompatibility at the interface. It is found that the elastic incompatibility plays the most important role in the deformation of the bicrystals, especially at low stress amplitudes. Based on the earlier reports[12- 17] and the scanning electron microscopy studies in this investigation, it can be concluded that the initiation of fatigue cracks at the grain boundaries in the IF steel sheet is a synergistic effect of both the impingements of slip bands at the grain boundaries and the stress-strain incompatibility between the grain boundaries and grain body. A similar contention has been made by one of the earlier investigators.
Fatigue cracks within the ferrite grain body can be observed above the endurance limit (Deltasigma/2 - 1.1 YS), but only to a very limited extent. The number density of microcracks initiating at the ferrite grain body in the steel sheet is considerably less than that at the grain boundaries or the inclusions. It emerges from the scanning electron microscopy study that the formation of small cracks with low aspect ratios occurs within the ferrite grains through the initiation of irregular voids within the slip bands; this is followed by their growth in number and final coalescence. The proposed process is illustrated in Figure 8, using a set of photographs. The formation of irregular steplike slip bands within the ferrite grains and the formation of a small voidlike structure within these bands are shown in Figures 8(a) and (b), respectively. Gradually, the number of voids increases (Figure 8(c)); these coalesce to form microcracks within the ferrite grain body (Figure 8(d)). These cracks are not sharp and do not grow considerably.
The initiation of cracks inside the grain body is commonly considered to occur within the slip bands in single-phase material. Essmann et al. proposed that crack initiation in the grain of single-phase fcc metals occurs inside the slip bands. In their proposed micromechanism for crack initiation inside a grain body, these investigators first considered that persistent slip bands lead to protrusions (intrusions and extrusions) on the specimen surface during cyclic loading. The interface between the persistent slip bands and the matrix of a material is a plane of discontinuity across which there are abrupt gradients in the density and distribution of dislocations. These interfaces are considered to serve as preferential sites for fatigue-crack initiation. Subsequently, the experimental evidence for crack initiation at the interface between the persistent slip bands and matrix in the case of copper has been reported by Hunsche et al. Hunche et al. studied the process of crack initiation in copper by slip localization in persistent slip bands. These investigators have confirmed that crack initiation takes place preferentially along the interface between persistent slip bands and the matrix. Long et al. have also reported crack initiation at slip bands in single- phase bcc alloys (beta titanium alloys), and have specifically emphasized that the initiation of fatigue cracks occurs at intersecting planar slip bands at or near the surface.
D. Growth of Fatigue Cracks with Number of Loading Cycles
The extent of fatigue damage on the surfaces of the sheet specimens increases with the increase in the number of loading cycles at a particular value of the applied stress amplitude. The surfaces of the specimens subjected to interrupted fatigue tests have been studied using an SEM, to examine the progression of fatigue damage in terms of the growth in the number density and the average size of initiated fatigue cracks at various microstructural locations. It is mentioned in Section C that the nature of the fatigue cracks initiating on the surface of the sheets is distinctly different for applied stress amplitudes above and below the endurance limit. Accordingly, three representative Deltasigma/2 levels are selected here, to examine and discuss the growth of fatigue cracks on the surface. The three values of the applied Deltasigma/2 are selected in such a way that these represent the mode of fatigue damage below the endurance limit, close to the endurance limit, and significantly above the endurance limit. Accordingly, the variation in the number density and average size of the fatigue cracks generated at different microstructural locations with the number of loading cycles for three different Deltasigma/2, e.g., (1) 0.7 YS (Figures 12(a) and (b)), (2) 1 YS (Figures 12(c) and (d)), and (3) 1.1 YS (Figures 12(e) and (0), are presented in this section. It has been mentioned in Section B that, below the endurance limit, microcracks initiate only at the inclusions; it emerges from Figure 12(a) that the number density of these increases steadily up to N- 3.5 x 10^sup 6^ cycles and then reaches a plateau. This implies that, with an increase in the number of loading cycles, more and more microcracks are generated around the inclusions (up to a critical number of loading cycles), governed by the local conditions of stress and strain around the inclusions. On the other hand, the average size of these cracks increases only marginally from 3 to 4 [mu]m with an increase in the loading cycles, as shown in Figure 12(b). The fact that the average size of the microcracks does not increase considerably indicates that the generated cracks are not propagating to a large extent with an increase in loading cycles. This is an interesting observation: although microcracks at the inclusions are forming on the surfaces of sheet specimens below the endurance limit, these cracks are largely nonpropagating in nature. It is mentioned in Section C that, close to and above the endurance limit, microcracks start initiating at the grain boundaries as well as at the inclusions. The variation in the number density and average size of these two types of cracks at Deltasigma/2 ~ 1 YS is shown in Figures 12(c) and (d), respectively. The number density of microcracks at inclusions (Figure 12(c)) increases continuously until N ~ 1.25 x 10^sup 6^ cycles is reached, after which it reaches a plateau. Similarly, the average size of the microcracks at the inclusions increases only marginally up to N ~ 3.5 x 10^sup 5^ cycles (Figure 12(d)). These observations are similar to the results obtained for fatigue cracking at Deltasigma/2 ~ 0.7 YS. The number density (Figure 12(c)) and size (Figure 12(d)) of the fatigue cracks at the grain boundary, on the other hand, increase continuously, even though the rate of increase of both decreases at the later part of the fatigue life. The most important observation is that the number density and average size of grain-boundary cracks far exceed those of the microcracks at the inclusions, beyond N ~ 8.9 10^sup 5^ and N ~ 8.9 x 10^sup 4^ cycles, respectively. It can, therefore, be inferred that grain-boundary cracks play a major role in spreading the fatigue damage on the surface of the sheet specimens close to or slightly above the endurance limit.
As mentioned in Section C, slip-band crack initiation within the ferrite grains is noticed to a limited extent above the endurance limit (Deltasigma/2~ -1.1 YS), upon exceeding N ~ 4.5 x 10^sup 5^ cycles. The variation in the number density and average size of all three types of cracks (e.g., those at inclusions, at grain boundaries, and at the grain body) with an increase in N at Deltasigma/2 ~ 1.1 YS are shown in Figures 12(e) and (0, respectively. It is observed that the number density of grain- boundary cracks is higher than that at the inclusions; the number density (Figure 12(e)) of both types of cracks increases steadily during the fatigue life. The number density of the cracks at the ferrite grain body, on the other hand, increases marginally with an increase in Nf. As far as the average size of the cracks is concerned (Figure 12(f)), it is observed that the average size of grain-boundary cracks is significantly higher than that of the other two types of cracks and that the crack size at the grain boundaries increases continuously during the entire fatigue life. The average size of the cracks at the inclusions and at the ferrite grain body increases marginally; the rate of increase is much slower than that of the grain-boundary cracks. It can, therefore, be inferred that, above the endurance limit, fatigue damage in these steel sheets is, again, largely because of the increase in the number density and average size of the cracks at the grain boundaries, which far exceed those at the inclusions or at the ferrite grain body.
In order to understand the coalescence behavior of fatigue cracks, the surfaces of a failed specimen were scanned using an SEM. Each surface was etched prior to fatigue testing, to reveal the ferrite grain boundaries. The initiation and growth of microcracks to cause failure are illustrated in Figure 13, using a set of photographs captured (on the specimen surface) at various distances away from the fractured end of the sheet specimens. The failed specimen exhibits the initiation of cracks at grain boundaries and at inclusions, as shown in Figure 13(a). While the cracks initiated at the inclusions do not grow considerably in size or number, the grain-boundary cracks in the fractured specimen are found to grow in size and number as the distance from the fractured surface decreases (Figures 13(b) through (e)). The deformation before final fracture is associated with a significant growth in the number density and size of grain-boundary cracks; also, a series of grain-boundary cracks join together to form a mesocrack a few hundred microns long, normal to the principal direction of loading on the surface prior to failure (Figure 13(f)). One of these cracks grows to cause final failure.
The macroscopic fatigue crack initiates at the sheet surface and propagates through the section, causing a significant amount of localized necking prior to fracture. The examination of the fatigue- fracture surface at higher magnification reveals that the origin of the fracture is not associated with any particle or inclusion. Both the origin and early propagation of the macroscopic fatigue crack are intergranular in nature.
The major results obtained in this investigation are presented in Section III, with the aim of bringing forth the prevailing micromechanism of fatigue damage in an IF steel sheet. In this section, an attempt has been made to discuss some of the important observations, e.g., (1) the presence of a definite endurance limit, (2) scatter in the estimated fatigue-life data, and (3) the prevalence of grain-boundary cracks in the fatigue failure of thin sheets, in the light of the suggested micromechanism.
A. On the Endurance Limit
It has been mentioned in Section HI-B that the selected steel sheet possesses a definite endurance limit close to its monotonie YS (0.98 YS). In general, lowcarbon steel sheets exhibit endurance limits of the order of 0.5 to 0.6 times the YS.t21] In comparison to these reported values, an IF steel sheet is found to exhibit a significantly higher endurance limit. The occurrence of an endurance limit in different metallic materials is attributed to several phenomena;[22-25] also, it is generally considered that fatigue failure does not takes place below the endurance limit, because (1) strengthening due to strain aging in a material exactly balances the fatigue damage during cyclic loading, (2) initiated fatigue cracks do not propagate on the surface of the specimen,[23,24] and (3) the initial locking of dislocations does not allow plastic deformation on the surface of a specimen sufficient to cause fatigue failure. An attempt is made here to examine the available propositions, in order to comment on the most prevalent mechanism governing the occurrence of a definite endurance limit and the reasons for its high value in IF steel sheets.
The accumulation of fatigue damage through cyclic loading and the progressive strengthening due to the relocking of the dislocations by interstitial solutes (strain aging) are perceived to be competitive processes. Below the endurance limit, strengthening predominates over fatigue damage and, hence, no fatigue failure takes place. Stresses above the endurance limit suffice to develop fatigue damage rapidly enough to outpace the strengthening due to strain aging. The selected IF steel sheets are temper rolled, however, in order to suppress the yield point elongation in service. Hence, it is not appropriate to consider strain aging as an assignable reason for the endurance limit of this steel. The fatigue limit is also understood as a set of conditions above which the already initiated microcracks can propagate to form macrocracks. In general, for polycrystalline materials, the amount of cyclic stress required to form a microcrack is much less than that required to propagate it; under these conditions, it is the stress required for propagation of the microcrack that determines the fatigue strength. Below the endurance limit, fatigue damage in the IF steel sheets is mainly manifested in nonpropagating microcracks at the inclusions. The fatigue cracks start initiating at the grain boundaries close to the endurance limit; it is only above the endurance-limit, however, that these cracks actually propagate, ultimately leading to failure. Hence, the endurance limit in IF steel sheets can be visualized as that limiting value of stress at which tiny microcracks form at the grain boundaries; these microcracks, however, do not propagate significantly.
Oates and Wilson showed through their pioneering work that, in certain metallic materials, fatigue failure does not occur until most of the dislocations remain locked. Cyclic stresses above the endurance limit are required for the widespread development of unlocked dislocations to cause failure. Under these circumstances, the value of the endurance limit is decided by the value of the stress above which the spread of plastic deformation on the surface of the specimen is significant. The spread of plastic deformation is perceived as a timedependent phenomenon by Oates and Wilson. These investigators explained that the relaxation of stress within the plastic regions increases the average stress acting on the surrounding elastic matrix. At the beginning of a test close to the endurance limit, the plastic regions are isolated in a relatively undeformed matrix. But with the growing spread of plasticity on the surface, a considerable number of localized stress concentrations are built up at the ends of the blocked slip bands. The number of these stress concentrations increases with an increase in plasticity. Thus, it is the spread of plasticity, rather than its initiation, that is expected to determine the critical stress above which fatigue failure would take place. Fatigue failure in an IF steel sheet is preceded by the growth and coalescence of grainboundary microcracks. Fatigue cracks at the grain boundaries, however, form mostly through the impingement of slip bands. Hence, a significant amount of plastic deformation through slip bands is a necessary condition for the fatigue failure to occur; the exact value of the endurance limit is determined by the stress level at which plastic deformation not only initiates at isolated grains but also spreads widely on the surface, engulfing a set of neighboring grains and causing a series of grainboundary cracks to link up. The stress at which the plastic deformation spreads during cyclic loading is governed by the chemistry and the processing history.[25,28] It can, therefore, be inferred from the present observations, with reference to the reports by Oates and Wilson and Suit and Chalmer, that, in the case of an IF steel sheet, the onset of plastic deformation on the surface is delayed until a very high value of Deltasigma/2 close to yield stress is reached, and that this phenomenon imparts the high endurance limit to these steel sheets. B. Scatter in Fatigue-Life Data
It is mentioned in Section III-A that the data pertaining to the number of cycles to failure (N^sub f^) at a chosen Deltasigma/2 exhibit some amount of scatter, and that the associated CEV generally decreases with an increase in the values of Deltasigma/2. The smaller magnitude of scatter at high stress levels is known to result, due to the shorter time required for macroscopic crack initiation prior to its propagation; this is well corroborated by the findings of this investigation. For example, it is evident from Table III that the time required to initiate fatigue cracks at various microstructural locations decreases considerably with an increase in the values of the applied Deltasigma/2. Hence, the formation of a mesocrack on the surface, primarily through the coalescence of grain-boundary cracks, also takes a progressively decreasing amount of time as the Deltasigma/2 is increased. One of the mesocracks results in a through-section macroscopic crack, upon reaching a surface inhomogeneity. The variation in N^sub f^ from one specimen to another tested at the same Deltasigma/2 is generally attributed to the variation in the locations, size, shape, and nature of surface inhomogeneities. The polished specimens considered in this investigation are associated only with the reduced magnitude of the surface asperity, but the presence of inhomogeneity in the surface topography remains the same. The probability of macroscopic crack initiation, therefore, increases significantly with an increase in ?s/2, thus reducing the scatter in the estimated fatigue life data.
C. Fatigue Cracks at Grain Boundaries
Microcrack initiation at the grain boundaries occurs very close to and above the endurance limit in the steel sheet, when the plastic deformation spreads widely in the matrix through slip bands. Crack initiation occurs primarily through the mechanism of impingement of slip bands, as elaborated in Section III. Furthermore, it is evident from the experimental results presented in Section III that fatigue failure in an IF steel sheet is caused by the significant growth (and subsequent coalescence) of grain- boundary cracks over the other two types of microcracks, e.g., those at inclusions and those at the ferrite grain body. The amount of plastic flow of the matrix around these two types of microcracks is considerable; it is this phenomenon that results in the blunting of crack tips which, in turn, results in a restriction of their growth. On the other hand, it is apparent that the grain boundaries offer a low-energy path for crack growth. The initiation and early propagation of the through-section macrocrack is also intergranular in these steel sheets. The occurrence of intergranular fracture in IF steel sheets during cyclic loading has also been reported by Yan et al. in an earlier investigation. This phenomenon was attributed to the low cohesive strength of the grain boundary in these steels, caused by the depletion of interstitial solutes such as carbon and nitrogen in the grain boundaries. ' It is well known that the concentration of solutes at the grain boundaries gives rise to frictional drag on the moving boundary, thus restricting the migration of the grain boundaries.[31,32]
The probability of the occurrence of fatigue cracks at the grain boundaries in a ductile material is enhanced by either an aggressive environment or an elevated temperature, although there have been some documentations of purely mechanical fatigue failure along grain boundaries in copper and pure iron.[33-37] For example, Kim and Laird and, later, Figueroa and Laird reported that the fatigue cracks initiate preferentially at the grain boundaries of polycrystalline copper and that the process is basically guided by the detailed crystallographic aspects of slip in adjoining grains. Crack initiation is preceded by the formation of a small step at a sensitive grain boundary in the early stages of the fatigue life; this small step continues to grow with an increasing number of loading cycles, until a microcrack develops. Those grain boundaries that are preferred for crack initiation are also preferred for the subsequent growth of the crack. In bcc metals such as commercially pure iron, intergranular crack initiation has been observed by Guiu et al. under reversed bending and push- pull axial loading over the cyclic frequency range 0.01 to 1000 Hz. The asymmetry of slip associated with the glide of screw dislocation in tension and compression can induce shape changes in bcc single crystals. The surface roughness created by shape changes in the near- surface grains of polycrystalline bcc metals such as a-iron can cause intergranular crack nucleation, as reported by Mughrabi et al. Finally, Tanaka et al. concluded that the preferential site of crack initiation in pure iron is basically dependent on the stress ratio (R). These investigators observed that, under reversed bending and axial stresses (R = -1), fatigue cracks always initiate at grain boundaries; under alternating tension (R = 0), however, cracks nucleate along slip bands inside the grains of pure iron.
In generalizing the current results, it may be unambiguously inferred that simple mechanical forces can cause intergranular cracking in IF steel, such as occurs in pure iron, as reported by Mughrabi et al. and Tanaka et al.; it is interesting that the microstructure of IF steel is close to that of polycrystalline pure iron. But the intergranular cracking originates at stress levels >0.95 YS. The initiation of intergranular cracks is enhanced by higher amplitudes of stress. As a consequence, one finds the initiation of intergranular cracks only after 1500 cycles for stress amplitudes of 1.3 YS; it is found after 10(6) cycles, however, for stress amplitudes of 0.98 YS (Table III). The results of the present investigation show the governing role played by grain boundaries in the process of fatigue failure in IF steel sheets and, hence, provide a guideline for enhancing the fatigue life of this material through suitable grainboundary engineering, etc.
The micromechanism of fatigue damage in an IF steel sheet has been studied using fully reversed Deltasigma/2, in terms of the initiation, growth, and coalescence of fatigue cracks on the surfaces of the sheet specimens. The major conclusions derived are as follows.
1. The investigated IF steel sheet is found to possess a high endurance limit 0.98 times its YS, as compared to conventional low- carbon steel sheets. The high endurance limit in these steel sheets is mainly attributed to (a) the occurrence of nonpropagating microcracks (initiating at the inclusions) below the endurance limit and (b) the significant delay in the spread of plastic deformation until a very high value of stress amplitude close to YS is reached.
2. It is found that microcracks can generate below the endurance limit in IF steel sheets; at this stress level, however, it takes a significantly larger number of cycles for its formation than is required above the endurance limit.
3. Above the endurance limit, microcrack initiation also takes place at ferrite grain boundaries and within the ferrite grains, in addition to at inclusions, assisted by widespread plasticity through slip bands on the surface grains.
4. The impingement of slip bands initiates most of the fatigue cracks at the grain boundaries, while the formation of voids inside the slip bands initiates microcracks within the ferrite grain body.
5. The common phenomena associated with the formation of microcracks at the inclusions are (a) the decohesion of inclusion- matrix interface and (b) the separation between closely spaced inclusions. Above the endurance limit, two additional mechanisms come into play; these are the fragmentation and uprooting of inclusions.
6. The final failure is preceded by the formation of a set of mesocracks, through the significant growth (in number density and size) of grain-boundary cracks and through the merger of these cracks, with negligible participation by the grain body or by the inclusion-associated microcracks. One of the mesocracks grows to cause through-section fatigue failure.
7. Fractography shows that through-section failure proceeds primarily in an intergranular fashion, assisted by grain-boundary microcracks.
One of the authors (SM) gratefully acknowledges the sponsorship rendered by Tata Steel, Ltd., for pursuing her doctoral studies program. The authors are grateful to Dr. N. Gope (Head, Product Research Group, R&D Division, Tata Steel, Ltd.), for making the experimental facilities available, and to Mr. Vikram Sharma of the R&D Division, Tata Steel, Ltd., for his help in carrying out the scanning electron microscopy work.
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SHRABANI MAJUMDAR, Researcher, R&D Division, and D. BHATTACHARJEE, Chief, R&D Division and Scientific Services Division, are with the Tata Steel, Ltd., Jamshedpur, 831 007, India. Contact e- mail: firstname.lastname@example.org K.K. RAY, Professor, is with the Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur. 721302, India.
Manuscript submitted August 21, 2007.
Article published online April 22, 2008
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