Apparent fracture toughness of dental porcelain with a metal substructure

Acta Materialia 55 (2007) 691–704 www.actamat-journals.com

Microstructural characteristics of post-shear localization in cold-rolled 316L stainless steel Q. Xue *, E.K. Cerreta, G.T. Gray III Materials Science and Technology Division, Los Alamos National Laboratory, NM 87545, USA Received 20 July 2006; received in revised form 31 August 2006; accepted 1 September 2006 Available online 28 November 2006

Abstract The microstructural evolution in a cold-rolled 316L stainless steel during shear localization was comprehensively studied using transmission electron microscopy (TEM). The TEM results indicate that the main substructure inside a shear band consists of elongated lath, fine rectangular and equiaxed subgrains. The substructure at an early stage of shear banding was found to strongly depend upon existing defects, especially deformation twin patterns. These twin structures determine the initial dimensions of the elongated subgrains inside the shear bands. The coexistence of both rectangular and equiaxed subgrains suggests that no melting occurred though the predicted temperature was much higher than the bulk melting temperature. Dynamic/static recovery and continuous dynamic recrystallization are thought to be the main mechanisms by which these substructures form inside the shear bands. A new mechanism for nanostructure deformation of subgrains within shear bands is proposed to explain the temperature divergence between the experimental and calculated results.  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Adiabatic shear bands; TEM; Stainless steel; Pre-straining; Recrystallization

1. Introduction Narrow, band-like, localized deformation frequently appears in metallic materials subjected to a dynamic loading event, such as ballistic impact or shock loading. These features are generally termed adiabatic shear localizations or adiabatic shear bands. This phenomenon is an important failure mode and has therefore been extensively studied for more than 50 years [1,2]. Thermal accumulation in a local area subjected to high strain rate deformation is considered the dominant mechanism leading to a rapid development of localized deformation [3]. The residual products observed inside shear bands provide ample information about the occurrence of the localized catastrophic failure and the mechanisms that control the unstable deformation. However, the material inside a shear band experiences a complicated deformation and temperature history. *

Corresponding author. Tel.: +1 480 552 1138. E-mail address: [email protected] (Q. Xue).

The post-mortem microstructure within a shear band may also be a product of the rapid cooling from a state near melting. The analysis and decoding of the combined substructure is therefore a rather difficult task but is critical to understanding the process and mechanisms controlling shear localization. Although a great deal of research has been performed on the microstructural characteristics of shear bands, little is known about the evolution of microstructure during the formation of shear localization. The residual substructure within shear bands has often been studied, as this substructure is considered to be a characteristic of the shear band phenomenon. For example, the white etching of a shear band in steels was thought once to be a symbol of shear banding in metals [4,5]. Long before the concept of an adiabatic shear band had received widespread acceptance in academic circles, this phenomenon was termed as ‘‘white band’’ or ‘‘white line’’ until Zener and Hollomon [3] gave it a complete physical explanation. Backman and Finnegan [6] classified shear bands into two groups: deformed bands and phase-transformed

1359-6454/$30.00  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.09.001

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bands. A amount of early research attributed the white etching inside shear bands in steels to a phase-transformed product. High temperatures generated by plastic work inside shear bands were postulated to cause the steels to austenize, with subsequent quenching transforming the austenite to martensite (c ! a 0 ) [6]. Some recent results have argued that the white etching may not come from a phase transformation but from recrystallization [7,8]. In fact, the residual products within shear bands may be formed via different mechanisms depending on the material and the temperature and shear stress histories. The potential mechanisms controlling the residual substructures within shear bands may include dynamic and/or static recovery, dynamic and/or static recrystallization, and phase transformation. The substructures within shear bands in different materials have been extensively studied using transmission electron microscopy (TEM) [9–17]. Fine substructures have been reported within shear bands subjected to different loading conditions. These TEM examinations have yielded extensive information about the processes of adiabatic localization. However, the residual substructures within shear bands in these studies were principally explored at random loading stages due to the fact that it is difficult to capture a shear band at a pre-assigned stage during high strain rate deformation. The morphology of the residual substructures inside shear bands has been reported in the literature. Many of these studies lack a well-controlled shear condition to examine shear banding at pre-assigned stages of evolution. Some pioneering work on the in situ observation of shear localization has been performed using grid patterns. These studies correlated the mesoscopic evolution of localized deformation to the transient mechanical responses [18,19]. However, the in situ work has not been able to reveal the evolution of the microstructure. Very little information has been obtained about the microstructural evolution of the substructure inside shear bands. In addition, prestraining of materials has been verified to exert a significant influence on shear-localized deformation [20]. How the shear localization initiates and develops in a material with a high density of defects due to prestraining is of importance to understanding the dominant mechanisms controlling shear localization. In the present study, the evolution of microstructure during shear localization in a cold-rolled AISI 316L stainless steel (SS 316L) has been extensively investigated. A series of forced shear tests were conducted on a compressive split Hopkinson pressure bar (SHPB) using hat-shaped specimens. The well-controlled experiments, interrupted at different loading stages, ensured that the post-mortem observation of the shear band microstructure can be directly correlated to the mechanical response. A comprehensive microstructural examination of these shear bands was carried out using TEM. At the main stages of deformation, the microstructure within the shear sections, especially the substructure inside shear bands, was extensively studied. The characteristics and the transitions in the sub-

structures were analyzed and compared. The temperature increase and the thermal softening effect on shear localization are discussed. Potential mechanisms that control the resultant substructures within shear bands are proposed and discussed in terms of the observed results. 2. Materials and methods Cold-rolled SS 316L processed through multiple passes of cold cross-rolling of an as-received SS 316L plate was used in this study. The total rolling strain applied is roughly 32%. The as-received steel was previously hotrolled and then cooled in air as reported by the manufacturer. The chemical composition of this as-received SS 316L in weight percentages is: 0.015 C, 17 Cr, 1 Mn, 2.5 Mo, 12 Ni, 0.023 P, 0.015 S, 0.5 Si, 67 Fe. The alloying in SS 316L combined with its high work-hardening behavior make it an ideal material with which to study largestrain deformation and substructure evolution in shock recovery. Additionally, the alloying in SS 316L helps promote thermal stability in the evolved microstructures following large-strain shear deformation, unlike in pure copper or aluminum which experience extensive localized recovery and/or even recrystallization following extensive localized shear deformation. Finally, extensive cold-working can be utilized to locally evolve a substructure that is susceptible to strain localization. The microstructure of the cold-rolled SS 316L is shown in Fig. 1. The initial hot-rolling traces are identified in the image along the rolling striations. Some MnS inclusions were also found along these traces (not shown in Fig. 1). The grains are seen to be elongated slightly along the hot-rolling direction (left to right) and have an average grain size of 40 lm. A high density of deformation twins is observed in almost all grains in the cold-rolled SS

Fig. 1. Microstructure of the cold-rolled 316L stainless steel. Note that a high density of deformation twins exists in all grains and the rolling direction is horizontal.

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316L. Extensively intersected twin boundaries construct a network pattern in the heavily deformed grains. Forced shear experiments were carried out on a SHPB using hat-shaped specimens. This technique was introduced by Hartman et al. [21] and subsequently further developed by several investigators [22,23]. The previous studies [7,24] used stop rings with different thicknesses to achieve a group of pre-assigned loading stages. While effective for interrupting tests at prescribed stages, the use of stop rings significantly disrupts the signal of the corresponding mechanical responses. In the present experiments, a wellcontrolled loading condition was used to interrupt each individual test at a pre-assigned stage, based on an accurate calculation of the deformation speed (equivalent to strain rate) and the loading duration. Thus, no stop rings were required. A group of interrupted tests were conducted using identical loading wave amplitudes. Four loading durations, 25.1, 31.0, 36.1 and 41.2 ls, were selected, afforded by the use of different striker lengths. Fig. 2 illustrates a hat-shaped specimen and its loading configuration sandwiched on a SHPB system. Both shear and compressive stresses would be simultaneously exerted on the shear section identified in the schematic of the sample. The shear stress was calculated by including detailed consideration of the possible radial expansion effect of the sample as detailed previously in Ref. [20]. The post-mortem observations show the microstructural evolution of shear localization, which has been correlated to the transient constitutive responses. The microstructure of each specimen loaded to a certain displacement was examined using optical and transmission electron microscopy. The metallographic samples were sectioned, ground and polished. Electro-etching was performed with an electroetchant solution of 10% oxalic acid and 90% water at 6 V. The TEM samples were taken from both the untested cold-rolled SS 316L plate and the tested hat-shaped specimens. Thin sheets were cut parallel to the surface of the bisected hat-shaped specimens using a fine diamond saw. The samples displaying localized deformation have small residual sections which are marked between the notch tips in Fig. 2. The retained length is typically 0.2–0.5 mm. These samples were thinned and polished to a thin foil

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and were cut into 3 mm disks. A Gatan dimpler was used to locate the regions to be thinned on the paths of shear bands. Ion milling was completed on a Gatan Precision Ion Polishing system (PIPs) to ensure perforation exactly on the shear bands. A Philips CM30 TEM at 300 kV was utilized to examine the microstructure in both the asreceived and localized 316L steels. 3. Results The cold-rolled SS 316L was subjected to 32% rolling reduction and possessed a rather high initial density of defects. The majority of the defects included dislocations, deformation twins, and microbands. As a face-centered cubic (fcc) material with low stacking fault energy, SS 316L has its major slip systems lying on {1 1 1} planes along Æ1 1 0æ directions. This material exhibits a higher susceptibility to form deformation twins with twin boundaries along Æ1 1 2æ directions. Fine deformation twins in a grain are displayed in Fig. 3a. TEM was utilized to quantify and thereafter analyze the substructure. Tilting along various different g vectors shows that a relatively low density of dislocations was seen within the twin band channels. Many of the deformed grains also exhibit two or more activated slip systems and extensive interactions of twins. Fig. 3b shows multi-twin variants that intersected each other at approximately 60. Both fine twins and networks of intersecting twins constrained the generation and mobility of dislocations so that they comprehensively restrained the subsequent plastic deformation. Therefore, the accumulation and interaction of these defects in the cold-rolled steel is an important preliminary condition for the formation of shear localization. Microbands were also observed in the heavily deformed grains where a high density of twins existed before micro-bands formed. A microband intersecting deformation twins is shown in Fig. 3c, creating a visible offset of the twin boundaries. The width of the microband is about 100 nm. In fact, the microband in the heavily twinned grains is also a mode of localized deformation under quasi-static deformation. It implies that the high density of deformation twins may be one of the initial sources triggering localized deformation.

u1

u2

Shear bands

εi

Transmitted Bar

Incident Bar ls ln

Fig. 2. (a) Configuration of the forced shear test with the hat shaped specimen and (b) the schematic loading condition by which the hat shaped specimen was sandwiched between the incident and transmission bars in a compressive Hopkinson bar system.

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Fig. 3. Initial defects in the cold-rolled SS 316L: (a) dense twin bands; (b) intersected twins; (c) microbands cut through the twin structure.

The forced shear experiments were interrupted at different stages of shear deformation, and Fig. 4 displays the shear stress responses in the forced shear tests. All these true shear stress–displacement curves reflect nearly identical deformation characteristics. The cold-rolled steel displays a high yield stress, after which the shear stress rapidly reaches a strength peak. The subsequent deformation leads to a significant drop of stress that represents the start of unstable deformation, e.g. shear localization. The continuous deformation under the loading pulses from 25.1 to 41.5 ls localized into the band-like region. Since the shear section slightly changed direction during the shear deformation, the shear stress finally resulted in a saturation stage. The microstructures of the shear localization developed at the shortest (25.1 ls) and the longest (41.5 ls) loading durations are shown in Fig. 5. For the 25.1 ls sample, the shear band region was separated from the matrix by a pair of sharp boundaries. The heavily deformed area outside the shear band contains a high density of deformation

twins that were bent toward the shear direction in a curled shape and merged into the shear band (Fig. 5a). The band width is about 10.4 lm. The shear band in the 41.2 ls

1200

True Shear Stress (MPa)

Cold Rolled 316 SS 1000 800

t = 41.2 t = 36.1 t = 31.0 t = 25.1

600

μs μs μs μs

400 200 0

0

0.05

0.1 0.15 0.2 0.25 0.3 Displacement (mm)

0.35

0.4

Fig. 4. The forced shear responses of the cold rolled SS 316L. A wellcontrolled loading condition was applied to facilitate the interruption of the tests at different stages of the localized deformation.

Fig. 5. Microstructure of shear localization developed under different loading durations: (a) 25.1 ls and (b) 41.5 ls. Note that the width of shear band increases slightly with an increase of the displacement.

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sample increased its width slightly to 16.4 lm as indicated in Fig. 5b. A comparison between the shear bands in these two conditions indicates that the major difference is the band width. The areas outside the shear bands essentially retained similar deformation patterns. This finding provides supporting evidence for the conclusion that most of the subsequent deformation localized into the shear band region once it initiated. The deformed microstructure before the onset of shear banding should be similar to that in the matrix adjacent to the shear band because the rapid unloading from the shear band preserves the adjacent area in the state just before the onset of shear localization. Fig. 6 shows such

Fig. 6. Microbands intersecting the twin bands near a shear band. This complicated pattern represents substructures generated just before the formation of a shear band because the unloading from the shear band preserved the pre-shear band substructure in the adjacent matrix once the shear band started. The short arrows mark the microbands.

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an area near a shear band. A high density of deformation twins with a spacing ranging from about 100 to 200 nm filled the grain. Multiple microbands are seen to have intersected with these twin bands. The shear direction was verified to be consistent with the direction of the twin boundaries. This suggests that one of the 24 predominant twin systems in this fcc alloy was rotated toward and activated along the shear direction. At least two sets of microbands are observed across the twin bands. The angles between the microbands and the twins are 45 and 100, respectively. It is evident that both sets of microbands were developed after the formation of the deformation twins, according to the relative shifts. Such a strongly intersecting network of twins and microbands has not been observed in samples before the onset of dynamic shear deformation. The reason for generating such a structure was assumed to be associated with the occurrence of unstable shear deformation. These microbands accommodate pronounced localized deformation and may be one of the main sources responsible for triggering an adiabatic shear band. The distribution of the substructures within shear bands depends on the deformation and temperature history as well as the initial pre-existing microstructure. Fig. 7 displays a montage of an entire shear band developed under the 25.1 ls pulse, which represents an overview of the band structure between its two boundaries. The substructure is seen to gradually change dimensions from ultra-fine subgrains in the center to an elongated lath substructure near the boundaries. Although the substructure inside the shear band varies from the center to the boundaries, a characteristic throughout the band is that the substructure was aligned along the shear direction, while the heavily deformed area outside the band has a bent substructure formed at a higher angle to the shear band direction. The boundary between a shear band and its outside area provides valuable information about the formation and development of the substructures within a shear band. Fig. 8 shows a shear band boundary separating the shear localized region inside the shear band from the heavily deformed region outside the shear band. The arrows mark

Fig. 7. Montage of a shear band developed under a loading duration of 25.1 ls. The dashed lines mark the shear band boundaries and the solid lines mark the direction of the substructure boundaries outside the shear band.

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Fig. 8. A shear band boundary separates the heavily deformed area outside a shear band from the fine substructure area inside the shear band. The deformation twins close to the band are seen to be bent toward the shear direction and the diffraction pattern still shows a crystalline structure, while the substructure inside the shear band shows that the grains have been fragmented into fine subgrains.

a

b

Shear Band Direction

022

Selected Area

200

1 11

111

111

200 11 1

022

Primary Twin bands

B = 011]

]

Primary twins’ spots Secondary twins’ spots Original matrix spots

Secondary Twins

Fig. 9. Analysis of the diffraction pattern and the mechanism of the substructure subdivision. (a) Diffraction pattern in the selected area, showing twin spots; (b) the primary and secondary twins.

the location of the shear band boundary. Inside the shear band, the substructures are substantially finer than in the area outside. The selected area diffraction (SAD) pattern, for a selected area of about 800 nm in diameter inside the band, exhibits a complex multi-spot pattern. The SAD pattern indicates that multiple subgrains with different orientations were located in the selected area in Fig. 8. Outside the shear band, the SAD pattern clearly displays a [1 1 0] tilt axis. The spots were stretched because of the lattice misorientation within the heavily deformed grain. In Fig. 9a, the detailed analysis of the diffraction pattern in the region outside the shear band in Fig. 8 indicates that the extra spots exactly correspond to two sets of twins in this region. One set of deformation twins was gradually deformed to merge into the shear band with an average spacing of about 500 nm. These twins are referred to here

as primary twins because they were generated either during the cold-rolling or during the forced shear deformation prior to shear localization. A second set of diffraction spots index as secondary fine twins that are aligned along the shear (band) direction with a spacing of around 50– 100 nm. Additional extra spots imply the existence of higher-order twins. Fig. 9b shows the relative orientation of the two sets of twins, in which the secondary twins show they have been aligned along the shear band direction. The multiplication of the secondary twins led to the curvature of the primary twins. It has been observed that an intrinsic relationship between the twin patterns outside the shear band and the elongated subgrains inside the shear band exists. Both of them exhibit a similar width, e.g. the fine spacing of the secondary twins was equal to the width of the elongated

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a

697

b

Shear Band Direction

Shear Band Boundary

Densification and Sliding Initial spacing of elongated subgrains

Fig. 10. (a) Schematic illustration of the formation process of elongated subgrains within a shear band; (b) Fine secondary twins appear inside the primary twins. The solid line marks the shear band direction.

subgrains. The schematic plot in Fig. 10a illustrates the formation of the substructure. The density of the secondary twins determines the spacing of the elongated subgrains within the shear bands. Fig. 10b exhibits a close-up view, showing that the primary twin bands also generated secondary twins inside when they were bent toward the shear direction. The substructure inside the shear band is seen to gradually change from the shear band boundary to the center of the shear band. Fig. 11 exhibits the details of the shear localized region developed in the 31.0 ls pulse sample. Two distinct regions were distinguished by different features: the elongated lath subgrains and the fine rectangular/equiaxed subgrains. Elongated lath subgrains appear close to the shear band boundary while fine equiaxed subgrains are seen

to be located near the center of the shear band. In the elongated subgrain region, the width of the elongated subgrains varies from 100 to 400 nm and the aspect ratio (width/ length) is often more than 10. Higher-magnification TEM observations (not included here) indicate that the lath substructures include many tangled dislocations. These regions of tangles were high-contrast areas due to the strain fields associated with the dislocations, and the few dislocations that could be imaged clearly appeared to have multiple pinning points along their lengths. Tilting experiments revealed the complexity of the substructure, as dislocations on multiple {1 1 1} planes had been activated. The boundary between the elongated subgrain region and the fine rectangular subgrain region is distinct and abrupt. In the fine subgrain region, the elongated subgrains were subdivided into

0.5 μm

Toward the center of shear band

Fine subgrains

Fine equiaxed subgrains

Elongated lath subgrains Fine rectangular subgrains

Fig. 11. Substructures inside a shear band are divided into two typical regions: elongated lath subgrains and fine rectangular and equiaxed subgrains. The elongated lath subgrains appear close to the shear band boundary while the fine equiaxed subgrains are near the center of the shear band.

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rectangular subgrains. The average width of the rectangular subgrains is roughly 100 nm and the aspect ratio is about 6. The dimensions of the rectangular subgrains close to the shear band center are evidently smaller than those close to the elongated subgrain region. There the aspect ratio decreases to 3–4. At the shear band center, the number of rectangular subgrains diminishes and fine equiaxed subgrains dominate the substructure. Most of the equiaxed subgrains were 50–80 nm in diameter. Some rectangular subgrains are still visible and appear to be distributed in the shear band center and delineate the shear direction. These subgrains are seen to have blurred boundaries and to be surrounded by equiaxed subgrains. This phenomenon suggests that most of these equiaxed subgrains were evolved from the rectangular subgrains instead of the nucleation of recrystallization regions. The TEM images in Fig. 12 demonstrate the variation in substructures across a shear band from a region near the shear band boundary to the shear band center. Fig. 12a illustrates the elongated subgrains within a shear band but close to its boundary. The characteristics of the elon-

gated subgrains were seen also to vary from grain to grain. The elongated subgrains are seen to have a narrow width (50–100 nm) and a much higher aspect ratio (>16). The elongated lath subgrains appear to have been initially generated from the deformation twins parallel to the shear band direction as shown in Fig. 9. Once they evolved into a shear band, their widths thereafter depended on the density of the secondary twins and their initial length related to the spacing of the primary twin groups as shown in Fig. 9. The further evolution of these elongated subgrains is thought to come mainly from two contributions. One is further microtwin development along the shear band direction if they have not already saturated. The other is the breakdown of the elongated subgrains, which leads to further subgrain fragmentation into rectangular subgrains. The alternating black and white regions with high contrast in these elongated subgrains in Fig. 12a indicate that the misorientation along the laths and the density of defects are rather high. The boundaries of these misoriented regions determined the locations of this breakdown. The conjugated shear stress becomes the driving force to cause

Fig. 12. Characteristics of shear band substructures and corresponding diffraction patterns near the boundary (a), at the center (c), and in the intermediate area (b).

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the breakdown perpendicular to the elongated subgrains. The SAD in Fig. 12a demonstrates that the elongated lath subgrains still retained some crystalline characteristics. The SAD pattern corresponding to the dark area in Fig. 12a is close to a ½ 1 1 2 zone axis with distinct extra twin spots. The elongated spots reflect the extensive local lattice distortion and misorientation. Fig. 12b illustrates a region a little closer to the center of a shear band. The rectangular subgrains are seen to have roughly maintained a width similar to that of the elongated subgrains but their lengths were significantly reduced, leading to a lower aspect ratio of 4–5. The boundaries of these rectangular subgrains have become blurred and wavy. The applied shear stress helps to further fragment rectangular subgrains into the equiaxed subgrains as shown at the upper portion in Fig. 12b. The corresponding diffraction pattern displays scattered spots with partial rings that indicate the existence of fine substructures. Approaching the shear band center, rectangular subgrains were found

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to be gradually replaced by equiaxed subgrains (see Fig. 12c). Most of the substructure in the shear band center appeared finer than the substructure in the other parts of the shear band. The size of the equiaxed subgrains varies from less than 50 nm to 100 nm and the average size is about 80 nm. Although some of the equiaxed subgrains do not show a clear relationship to the shear direction, most of them can still be identified from the linkage to their parent rectangular subgrains. The existence of the rectangular subgrains at the shear band center indicates that the fragmentation of the subgrains was controlled by a breakdown mechanism. No evidence of melting was found. If melting had occurred, the residual substructure would be wiped out and the substructures would be replaced by new, isotropic, recrystallized fine grains. In our tests, no indication of this phenomenon was observed. The disordered multi-spots in the diffraction pattern demonstrate that multiple fine subgrains with different orientations continued to exist instead.

Fig. 13. Evolution of the shear band substructure with continuously localized deformation; A microstructural comparison shows the evolving substructures at the centers of shear bands developed at the loading durations of (a) 25.1 ls; (b) 30.0 ls, and (c) 36.1 ls, respectively. Note that the areas circled by the dashed lines are the conglomeration of the nano-subgrain clusters.

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The development of shear localization was also embodied through the evolving microstructure at the center of the shear bands. Fig. 13a–c shows the subgrain variation at the centers of shear bands developed to different loading stages. In the specimen subjected to a loading pulse of 25.1 ls, the substructure at the band center displayed a mixture of the rectangular and equiaxed subgrains (Fig. 13a). The rectangular subgrains were seen to maintain relatively straight boundaries along the shear direction. The equiaxed subgrains were seen to be subdivided from the elongated subgrains because their segments can be assembled into their parent, initially elongated subgrains. The diffraction pattern displays scattered spots that reflect the existence of polycrystalline structures in the selected area. The increase of loading duration in the 31.0 ls sample was found to result in further localized deformation within the shear band as shown in Fig. 13b. The fraction of equiaxed subgrains increased and the boundaries of the rectangular subgrains became wavy and embedded in each other. Some elongated subgrains were broken into several prismlike subgrains that were sheared off and extruded laterally. Although equiaxed subgrains formed in some parent rectangular subgrains, the shear direction was easily recognized from the orientation of the rectangular or prism subgrains that assembled from those parent subgrains. Fig. 13c demonstrates the shear band substructure that evolved due to a 36.1 ls loading. The subgrains were seen to be significantly smaller than those that developed in the shorter loading pulses mentioned above. Some tiny pieces of equiaxed subgrains with diameters less than 20 nm are scattered at the boundaries of the bigger subgrains and are shown in Fig. 13c. These smaller subgrains may be fine recrystallized products. Some adjacent equiaxed subgrains agglomerated into clusters (two clusters are circled by dashed lines in Fig. 13c). These equiaxed clusters possess a close crystalline orientation and a similar defect density, and therefore display a similar contrast in the image. The dimensions of such clusters are much larger than the width of the parent rectangular or elongated subgrains. This suggests a rotation of these equiaxed clusters within the shear band. The formation of such clusters completely conceals the traces of their parent rectangular subgrains and hence removes the indication of shear direction. In the elongated or rectangular subgrains, the breakdown and extrusion of the subgrains perpendicular to the shear direction is the dominant mechanism control-

ling the shear deformation. Once these subgrains break the constraint of the boundaries of their parent elongated subgrains, they can be rotated in a self-organized manner to form clusters. The localized shear strain within a shear band can be approximately estimated from the displacement and the corresponding width of the shear band. The measured values for the shear band widths and the displacements interrupted at different loading durations are listed in Table 1. The observations of the microstructures obtained using optical microscopy have verified that little deformation occurred outside the shear bands. Most of the deformation was contained within the shear band zone once the localization started. Assuming that the unstable deformation started at the critical displacement related to the peak shear stress, which corresponds to about 0.02 mm in Fig. 4, the localized displacements are obtained by subtracting this critical displacement from the interrupted displacement. Attributing the complete deformation after the stress peak to the shear band region seems to overestimate the shear strain within the bands but it nevertheless gives an upper bound of the shear strain. Using this method, the relative shear strains within shear bands developed to certain deformation stages are summarized in Table 1. The shear strain within the shear bands evolved from 13.1 to 23.2 for loading durations from 25.1 to 41.2 ls, respectively. Thermal softening plays an important role during adiabatic shear localization. The heat converted from plastic work continuously increases the local temperature and thus leads to continued softening in most materials. The calculation of temperature in a shear band depends on correct measurements of the plastic work. It requires an accurate description of the material’s constitutive response. In this study, the plastic work, which induced a temperature increase, was estimated from the area under the stress– strain curve. The temperature increase within a shear band is Z c bs DT ¼ dc; c0 cq where heat capacity c and the mass density q for SS 316L are 500 J/kg K and 7.9 g/cm3, respectively, and c0 is the shear strain for shear band initiation. However, the stress–strain curve cannot be obtained directly from the current tests due to the overlapping design of the stress zone in the hatshaped specimens. An alternative measure is to assume the

Table 1 The calculated shear strains and temperature increases within shear bands developed at different loading stages Loading duration (ls)

Interrupted displacement (mm)

Localized displacement (mm)

Shear band width (lm)

Shear strain within shear bands

Temperature increase (K)

25.1 31.0 36.1 41.5

0.203 0.222 0.321 0.401

0.183 0.202 0.301 0.381

10.4 10.7 14.7 16.4

17.6 18.9 20.5 23.2

2907.3 3014.4 3152.8 3398.9

Note. The energy converting factor b = 0.9.

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stress–strain curve has a similar shape to the stress–displacement curves. Assuming that all the displacement accumulated after the peak stress point was completely localized into the shear band, shear band widths and the correlating displacements can be measured at each loading stage to obtain the correlating shear strain. The value of the shear strains at the interrupted points can be measured directly from the specimens. Thus, the stress–displacement curve is converted to the stress–strain curve without significant changes to the profile of the curve. The plastic work, therefore, was calculated from the approximate area under that curve, starting from the stress peak to the terminal points. If the thermal conversion factor b is taken as 0.9, the calculated temperature increase within a shear band varies from 2907.3 to 3398.9 K, corresponding to the extremely high local strains. The calculated results are shown in Table 1. The temperature estimation based on the energy conversion indicates that the temperature increase inside a shear band in the cold-rolled steel is higher than the melting point of the material. However, the TEM results do not support this finding. In Fig. 13, the evolution of the substructure at the shear band center exhibits a variation from rectangular subgrains to equiaxed subgrains. The breakdown and splitting of the elongated substructure led to the concurrence of both the rectangular and equiaxed subgrains in late stages of the evolving shear band. This suggests that no melting occurred, otherwise a recrystallized region should dominate a significant portion of the shear localized area. The breakdown of rectangular subgrains provides pronounced evidence that they evolved from the parent elongated subgrains rather than from the nucleation and growth of new recrystallized subgrains. These subgrains maintained a solid linkage to the original substructure formed just before or just after the formation of shear localization. Dynamic recovery helps the formation of subgrains with low-angle boundaries at early stages of shear banding. The subsequent continuous dynamic recrystallization leads to the breakdown and splitting of subgrains. Therefore, dynamic recovery and subsequent continuous dynamic recrystallization are considered to be the dominant mechanisms controlling the development of substructures within shear bands in SS 316L. 4. Discussion Thermally assisted deformation is considered to be the dominant mechanism during shear localization [3]. The extremely high temperatures within a shear band may result in multiple metallurgical effects in the tested material. The white etching characteristic of the shear band region found in ferrous alloys was often attributed in early studies to phase transformation from austenite to martensite. However, studies in recent years indicate that some so-called transformed bands might not experience a true phase transformation. The fine substructures found within shear bands may be the products of dynamic recrystalllization or dynamic recovery [17,24,25]. The residual microstructure inside a shear

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band significantly depends on the temperature history that the band material undergoes, specifically in the heating and the cooling processes. In the present study, no white etching bands, indicative of a phase transformation, were observed in the shear band region in the cold-rolled SS 316L. Previous studies regarding the substructure inside shear bands have reported most of the substructures observed in the present TEM examinations of SS 316L. Elongated subgrains and equiaxed subgrains have been found within shear bands in various materials. Meyers et al. [22] studied shear localization in a preshocked copper using hat-shaped specimens. Fine equiaxed subgrains with an average size of 50 nm were observed inside the Cu shear bands. Beatty et al. [23] applied a similar experimental method to examine shear localization in AISI 4340 steel and declared that the white-etching band formed. Their TEM examination showed extremely fine equiaxed subgrains in the size range of 8–20 nm within the shear band. The authors of that study concluded that the extremely fine subgrains were comprised of heavily deformed martensite with no phase transformation products. Similar results were reported in other studies [26,27]. Mgbokwere et al. [28] and Cho et al. [13] demonstrated that both the highly elongated subgrains (laths) and fine equiaxed subgrains were present within shear bands in 4340 steel and in HY-100 steel, respectively. The equiaxed cells interspersed in the elongated subgrain regions were seen to vary from sample to sample. All the phenomena mentioned above have been found to be present in the current study. Most previous investigations only examined microstructural characteristics of shear bands following a non-specific loading stage. No sequential evolution of these microstructures was recorded such that no information is available concerning the details of the initiation and development of these substructures. The present research aimed to attain a well-controlled mechanical condition in order to examine substructural evolution in shear bands. The systematic TEM investigations of the stages of shear localization provide insight into the characteristics of shear band evolution. The variation in microstructure across the shear band in Fig. 12 reflects the synergistic effects of the localized deformation gradient and the thermal diffusion in a shear band. The fine equiaxed subgrains at the center of a shear band are seen to have retained a characteristic size similar to the width of the elongated substructure near the shear band boundaries. This observation suggests that the subdivision of the substructures within a band is strongly influenced by the transverse decomposition of the elongated or rectangular subgrains present. The observation that the evolution of the substructure at the centers of the shear bands developed to different stages (Fig. 13) demonstrates that the fragmentation of the substructure experiences two processes: the grain subdivision and the conglomeration of clusters. This phenomenon has not been reported previously to our knowledge but it characterizes a mechanism of deformation at the nanoscale level. The rotation of the nanoscopic clusters represents an important

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mechanism that may control the further deformation evolution within a well-developed shear band. In high strain rate deformation, extensive interactions among microbands, twin bands and dislocation networks are indicative of the formation of complicated deformation patterns. The formation of microbands characterizes a common deformation mode during severe plastic deformation and in many fcc and body-centered cubic metals and alloys subjected to high-rate shock loadings. Microbands are described as double dense dislocation wall (DDW) structures with localized deformation within the band and their directions are approximately parallel to the main slip systems. While some of the details of microband formation remain unclear, Huang and Gray [31] proposed a model for microband formation that ascribes the formation of a stable microband to the interaction between primary and secondary dislocations. Secondary generation of microbands has been observed to occur in severely deformed material. These defects often intersect with other features within the substructure and are closer in character to micro-shear-bands as shown near the shear bands in Fig. 6. The calculated temperature increments for the shear bands at different loading stages are not consistent with the TEM results. The estimation of temperature in a shear band, based on the converted strain energy obtained from the shear stress curves and corresponding local shear strain, predicts the possibility of local melting. However, TEM observations of the center of the shear band in all of the samples studied did not show any evidence of melting. Three pronounced reasons for this absence of melting are postulated. First, although some local areas are covered with fine equiaxed subgrains, some elongated and/or rectangular subgrains are always found scattered at the center of the shear bands, delineating the shear band direction. Second, even for the fine equiaxed subgrains themselves, the original parent pieces of elongated subgrains can still be traced. Third, most subgrains, either the broken-down rectangular subgrains or the equiaxed fine subgrains, have blurred subgrain boundaries that display significant differences from the nucleation/growth type of recrystallized grains. The observations suggest that the nucleation/ growth type of recrystallization did not prevail even though the predicted temperature was much higher than the ‘‘recrystallization’’ temperature. This significant anomaly suggests that there is some other mechanism controlling the localized deformation and resulting in a lower than predicted rate of plastic work that can be converted into heat. A substantial difference between the experimental results and the temperature calculation has previously been seen to exist in other studies. Many previous in situ measurements of temperature within shear bands have indicated that the temperatures measured experimentally are much lower than the temperature calculated via conversion of the strain energy [29,18,30]. Some researchers have argued that the limitations of the technique result in the lower values of measured temperatures inside shear bands; however,

the use of finer thermal elements [30] should compensate for this shortcoming. These significantly lower values of measured temperatures provide additional support for our TEM results. The post-localization behavior of the material within a shear band appears to be dominated by a nanoscopic mechanism, different from the traditional deformation of coarse-grained materials. Once the substructure has subdivided into fine nanograins inside a shear band, further shear deformation is proposed to be mainly accommodated via boundary sliding and rotation of the fine equiaxed subgrains. In the initial stage of shear localization, the sliding of elongated subgrains seems to play an important role. No distinctive reduction of the width of these elongated subgrains was observed during localized shear deformation. The main variation of these substructures is grain refinement through a subdivision (breakdown) process. If the deformation can be completely accounted for by these elongated subgrains, the pronounced change of shear strain within the band should lead to their rapid narrowing in width. The fact is that the continuously decomposed subgrains maintained a constant width until they were subdivided into equiaxed subgrains at a very late stage of shear band evolution (see Figs. 12 and 13). The rotation of the nanosized equiaxed subgrains controls the shear deformation within a shear band in the late stages. Such rotation includes two steps: the rotation of each equiaxed subgrain and the rotation of the subgrain clusters. The self-rotation of the equiaxed subgrains represents a local deformation of the subgrains, while the cluster rotation leads to agglomeration and reflects a self-organized deformation mode. When rotation dominates the main shear deformation within a shear band, equiaxed subgrains are seen to display reduced deformation in their interiors. Accordingly, their location shift due to cluster rotation and the self-rotation of a partial rigid body do not provide significant plastic work. Actually, both boundary sliding and grain rotation generate less plastic work and therefore can convert less plastic work to heat. The local temperature would therefore not increase as drastically as in previous estimations. It may, therefore, remain far lower than the melting temperature. Regarding recrystallization, the temperature within a shear band is obviously higher than the nucleation temperature of recrystallization in the stainless steel. The main reason thought to account for a lack of extensive nucleation/growth of new grains is the shortage of recrystallization time and appropriate nucleation conditions. The nanoscaled subgrains are postulated to constrain the nucleation of new grains as well as the growth via boundary migrations. Even if the nucleation starts, there is still insufficient time for significant growth of the recrystallized grains and the nanograins would also probably restrict the boundary migration of these recrystallized nuclei. Static recrystallization that may occur following the shear deformation is also significantly restrained due to the suppressing action of the nanoscale grains. Continuous dynamic recrystallization is characterized as the

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process of breakdown and splitting of substructure, consistent with the rotation and deformation-induced mechanisms. The mechanism proposed here for the deformation of nanograins within shear bands provides a plausible explanation for the dilemma of the temperature increase and the lack of new grains. The TEM results of the substructure evolution within the shear bands also support this mechanism. The temperature estimation obviously overpredicts the generated plastic work and leads to the higher temperatures that were not achieved in the shear bands experimentally observed in this study. The cold-rolled 316L shear localization microstructure reflects a deformation evolution that differs substantially from that reported recently by Xue and Gray [32,33] in the as-received SS 316L. In the as-received metal, shear localization occurred after a long hardening stage. Sufficient accumulation of strain is necessary to initiate the localized deformation. The boundaries of shear bands were seen to have a gradient of deformation in the as-received steel, while the cold-rolled steel shows a steep jump in the deformation at the shear band boundaries. In the asreceived steel, a shear band core structure was found, but this core region was not observed in the cold-rolled steel. The microstructure inside the shear bands in the asreceived steel shows many deformation-induced characteristics, such as an avalanched dislocation cell structure, which were not observed in the cold-rolled steel. For well-developed cold-rolled shear bands, the microstructures within the bands are similar in both steels except that a much finer equiaxed subgrain structure is seen in the cold-rolled steel. 5. Conclusions The microstructural evolution occurring during shear localization in cold-rolled SS 316L was systematically investigated using TEM. The shear bands were formed using a forced shear configuration at high strain rates. Well-controlled interrupted tests on a compressive split Hopkinson bar provided a series of comparable hatshaped samples tested to different stages of localization. The TEM observations exhibit a complete substructural spectrum from shear band boundaries to their centers and thus illustrate the detailed evolution processes during shear localization. The subdivision mechanisms were analyzed and compared with previous experimental results. A new mechanism based on nanoscopic shear deformation is proposed to explain the pronounced divergence of temperature increase between experimental measurements and calculated results. The main results are summarized below: (1) The substructures in the initiated shear bands consist of elongated lath subgrain and fine subgrain regions. The variation of substructure from the shear band boundaries to their centers represents a transition from elongated subgrains, to rectangular subgrains,

(2)

(3)

(4)

(5)

(6)

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and then finally to equiaxed subgrains. The fine subgrains at the shear band centers have an average size of 80 nm. Rectangular subgrains, which are seen to always mark the shear direction, were found to appear within the shear bands developed to different stages. The coexistence of both the equiaxed and rectangular subgrains at the shear band center suggests that no melting occurred there, where the local temperature is assumed to be the highest. The fine equiaxed subgrains were seen to be associated with their parent elongated subgrains. The breakdown and splitting of the elongated or rectangular subgrains is thought to be the main mechanism of grain subdivision. The nucleation/growth of recrystallized grains was not well developed due to the limited deformation time. Deformation-induced and/or rotation refinement substructure evolution is dominant within the shear bands. The process of grain refinement is considered to be controlled by dynamic recovery at early stages of shear banding and by continuous dynamic recrystallization at late stages of shear band formation. Substructure evolution at the centers of shear bands was characterized as continuous fragmentation. Fine equiaxed subgrains agglomerated during the continuous localized deformation. They tended to rotate and reassemble into new clusters with diameters a few times that of the equiaxed subgrains. Boundary sliding and rotation of these clusters appears to be the main mechanism for shear deformation within welldeveloped shear bands. Deformation twins, caused by prestraining, were seen to have a significant influence on shear banding. The activation of secondary twin groups aligned along the shear direction led to the curvature of the primary twins near shear band boundaries. Saturation of the secondary twin density determined the final spacing that correlates to the initial width of the elongated subgrains once the area evolved into a shear band. The spacing of the primary twins determined the length of the elongated subgrains within shear bands. A nanoscale mechanism for shear band deformation is proposed to explain the deformation process of fine nanoscale subgrains, based on the sliding and rotation of equiaxed subgrain clusters. This observation suggests that the high shear deformation within the bands does not generate sufficient plastic work to achieve the high temperatures predicted by calculations. TEM results verify that no evidence of melting was seen to exist within the shear bands even though the predicted local temperature is higher than the bulk melting point of this material. The conflicting results are discussed using the proposed nanodeformation mechanism and previous results in the literature.

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Acknowledgements This work was supported partly by the Joint Department of Defense (DoD) and Department of Energy (DOE) Munitions Technology Development Program. The authors sincerely acknowledge the thoughtful comments and discussions with Professors Guruswami Ravichandran and Ares Rosakis at Caltech, and Professor Naresh Thadani at Georgia Tech. The assistance of C.M. Cady and M.F. Lopez with the dynamic experiments and the metallographic sample preparation are graciously acknowledged. References [1] Rogers HC. Ann Rev Mater Sci 1979;9:283. [2] Bai YL, Dodd B. Adiabatic shear localization, occurrence, theories and applications. Oxford: Pergamon Press; 1992. p. 24. [3] Zener C, Hollomon JH. J Appl Mech 1944;15:22. [4] Hatherly M, Malin AS. Scripta Metall 1984;18:449. [5] Rogers HC. In: Mescall J, Weiss V, editors. Materials behavior under high stress and ultra-high loading rates. New York: Plenum Press; 1983. p. 101. [6] Backman ME, Finnegan SA. In: Rohde RW, Butcher BM, Holland JR, Karnes CH, editors. Metallurgical effects at high strain rates. New York: Plenum Press; 1973. p. 531. [7] Meyers MA, Subhash G, Kad BK, Prasad L. Mech Mater 1994;17:175. [8] Stelly M, Dormeval R. In: Murr LE, Staudhammer KP, Meyers MA, editors. Metallurgical applications of shock-wave and high-strain-rate phenomena. New York: Marcel Dekker; 1986. p. 607. [9] Craig JV, Stock TAC. J Aust Inst Metals 1970;15:1. [10] Stock TAC, Thompson KRL. Metall Trans 1970;1: 219. [11] Wingrove AL. J Aust Inst Metals 1971;16:67. [12] Glenn RC, Leslie WC. Metall Trans 1971;2:2945.

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