Dynamic shear deformation in high purity iron

E. Cerreta1, J. Bingert1, C. Trujillo1, M. Lopez1, C. Bronkhorst2, B. Hansen2

and G. Gray1

1 Los Alamos National Laboratory, MST-8/MS G755, Los Alamos, NM 87545, USA2 Los Alamos National Laboratory, T-3/MS B216, Los Alamos, NM 87545, USA

Abstract. The forced shear test specimen, first developed by Meyer et al. [1, 2], has been utilized ina number of studies. While the geometry of this specimen does not allow for the microstructureto exactly define the location of shear band formation and the overall mechanical responseof a specimen is highly sensitive to the geometry utilized, the forced shear specimen is usefulfor characterizing the influence of parameters such as strain rate, temperature, strain, and loadon the microstructural evolution within a shear band. Additionally, many studies have utilized thisgeometry to advance the understanding of shear band development. In this study, by varying thegeometry, specifically the ratio of the inner hole to the outer hat diameter, the dynamic shear locali-zation response of high purity Fe was examined. Post mortem characterization was performedto quantify the width of the localizations and examine the microstructural and textural evolutionof shear deformation in a bcc metal. Increased instability in mechanical response is strongly linkedwith development of enhanced intergranular misorientations, high angle boundaries, and classicalshear textures characterized through orientation distribution functions.

1. INTRODUCTION

Shear deformation and failure is significant to multiple engineering applications and serviceenvironments involving high rates of deformation ranging from metal cutting operations todynamic loading situations such as civilian crash-worthiness, aerospace foreign-object damage,and ballistic impact scenarios [3, 4]. In many shear loading environments, failure is preceded byshear localization or banding. Shear band formation is typically enhanced at high strain ratesbecause lack of time for thermal diffusion leads to non-uniform strain [4]. At its extreme, adiabaticshear banding is one of the best known examples of plastic flow localization due to thermalsoftening. This phenomenon, first observed by Zener and Holloman [5], is termed adiabaticbecause insufficient time scales and low thermal diffusivity produce large local temperatureincreases within a material driving localization [6].

Research on shear banding has typically concentrated on two specific areas of study: (1) themodeling of plastic flow instability and (2) the relationship of shear banding to initialmicrostructure. In shear deformed metals, many microstructural alterations have been observed.These include: dynamic recovery, dynamic recrystallization, phase transformations, melting, andamorphization [7, 8]. Recent studies have focused on correlating evolving microstructure andmechanical response during shear localization. Mechanisms that control substructures withinshear bands appear to be strongly related to initial microstructure, its evolution, and therefore itswork hardening capability [9–11]. Additionally, while the current understanding of the influenceof texture on shear banding is limited, it has been shown that some grain orientations with respectto the shear direction might be favorable for the propagation of shear bands [12].

A sample geometry that has been utilized to probe the influence of microstructure, strain rate,and temperature on the evolution of a shear localization is the forced shear or ‘tophat’ specimen.It is an axi-symmetric sample with an upper hat portion, a lower brim portion, and a shear section

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between the hat and brim sections. The geometry, originally designed by Meyer et al. [1, 2], hasbeen modified several times within the literature. This general geometry defines the location oflocalization and shear band formation making it inappropriate for studying shear band initiation.However, it is ideal for systematically quantifying evolution and growth because the difficultproblem of identifying shear band initiation sites within a specimen exposed to general loading isalleviated [13].

In this study, the geometry of the forced shear specimen was altered systematically as shown inFigure 1, to examine the influence of the combined shear-compression loading geometry of theforced shear specimen on microstuctural evolution during dynamic loading. Post mortemcharacterization, optical and electron microscopy techniques, was performed to quantify damageand examine the textural evolution from shear deformation. Increased instability in mechanicalresponse observed as the geometry approaches a simple shear loading configuration is linked withdevelopment of enhanced intergranular misorientations, high angle boundaries, and classicalshear textures.

2. EXPERIMENTAL

The polycrystalline Fe used in this study was electrical grade, hot finish, high-purity iron suppliedas a 12 cmr12 cm billet. The chemistry is given in Table 1 and the average equiaxed grain size is60 mm. The crystallographic texture of the high purity Fe in this study was characterized usingX-ray diffraction. The texture strength calculated from the orientation distribution function(ODF) for the high purity wrought iron was measured to be 1.25, indicative of a nearly randompolycrystalline solid [14]. Tophat specimens in the geometries shown in Figure 1 were machinedfrom the as-received metal. From this figure, it can be seen that the state of shear changes fromone that is a combined loading state of shear and compression in A and B geometries, becausethe inner hole diameter of the brim is smaller than the outer hat diameter, simple shear loadinggeometry in ‘C’, where the inner hole diameter of the brim is equal to the outer hat diameter. Thisevolution of specimen geometry is expected to cause a significant difference in the evolved shearlocalization structure and to understand the extent of this difference; the Fe specimens weredynamically loaded on a Split Hopkinson Pressure Bar. Post mortem specimens were characterizedboth optically and with electron back scattered diffraction (EBSD) to quantify differences in shearlocalization evolution based on specimen geometry. Specimens in each of the geometries shown inFigure 1 were loaded at 3100 /s and 298 K to total displacements between 0.27 and 0.35 mm.

Figure 1. The general tophat geometry and modification of this geometry for A, B, C, and D geometriesin mm.

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Each of these specimens was then cross-sectioned parallel to the loading axis, mounted, andpolished for post mortem characterization. Specimens were ground to 1 mm Alumina and thenetched with Nital. The cross sectioned specimens resemble the schematic in Figure 1 and thereforetwo shear affected zones (SAZ’s) can be viewed in each specimen.

3. RESULTS

The mechanical test data for the tophat tests is plotted as engineering shear stress vs. displacementin Figure 2. The flow stresses and rates of work hardening can be seen to have decreased asthe inner-hole diameter (dimension ID in Figure 1) increased. For the largest diameters (C and D),the work hardening rate is decreasing and this is indicative of significant shear localization. Therelatively higher rates of work hardening in specimens A and B are indicative of more stabledeformation and the combined shear and compression loading state in the gauge section of thesespecimens. This multi-component stress is due to forcing a larger diameter hat through a smallerdiameter inner hole. A stress is exerted by the brim on the gauge section creating a compressivestress component to the test.

Post mortem analysis of the shear deformed zones revealed that in all cases a pronouncedregion of localized plastic deformation developed in which grains in the gauge section of the testedtophat specimens had elongated in the shear direction, shown in Figure 3, by image quality maps.To quantify the extent of these regions, intragranular misorientation deviation (IMD) maps ofthe plastically deformed regions were calculated. The IMD is a measure of the average of alldeviations between each point in a grain and the grain’s average orientation. From these maps,Figure 4, the widths of the shear localized regions can be measured. This measurement is theaverage of five measurements of the width of the shear localized zone, determined by the boundarycreated by the light gray grains (IMD <2) in each map. These calculated widths are given inTable 2. The width of the shear localized regions decreases from A to B to C geometries and thenslightly increases with D geometry. This correlates with the high degree of microstructurallocalization expected in the geometry closest to single component simple shear loading stress stateconfiguration, geometry C.

Table 1. Chemical Analysis of Fe (in ppm wt%).

C Mn Si P S Cr Ni Fe

0.013 0.10 0.14 0.005 0.010 0.16 0.13 Bal.

0

200

400

600

0 0.1 0.2 0.3 0.4

ABCD

Displacement (mm)

Figure 2. Engineering Shear Stress vs. Displacement data for each of the geometries tested.

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The low angle (2–10x) boundary (LAB) and high angle (10–62.5x) boundary (HAB)distributions and the texture development within the shear localized zones have also beenexamined. Figure 5 gives the LAB and HAB percentages for the shear localized regions of each

Figure 3. Image quality maps of the shear deformed regions in the specimens with A through D geometries.

Figure 4. IMD maps of the shear deformed regions in the specimens with A through D geometries.

Table 2. Widths of the Shear Localized Region (mm).

Geometry A B C D

Width 228 203 192 207

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tested geometry. It can be seen from this data that the HAB percentage steadily increases as thegeometry approaches a simple shear loading configuration (A to C) and then decreases slightlywith the D geometry. Deformation texture development was also examined in the Fe tophatsamples as a function of specimen geometry, Figure 6. For each EBSD data set, the central shearzone was cropped so as to eliminate regions that may have experienced only modest shear strains.Within this heavily strained region, orientations with confidence indices <0.01 were notconsidered. This led to a reduction of no more than 10% of orientations within the croppedregion. Orientation data were rotated so as to align the shear direction (SD) with the horizontalaxis and the shear plane normal (SPN) with the vertical axis. While shear texture evolution in bccmetals has received significantly less attention than for fcc metals and alloys, shear textures can

Figure 5. LAB and HAB fractions as a function of geometry.

Figure 6. Deformation texture development as a function of geometry.

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be defined by {hkl}<uvw> associated with the {SP}<SD> sample reference frame [15]. Theprimary bcc fibers are {110}//SP and <111>//SD. 110 and 111 pole figures (PF’s) recalculatedfrom the ODF are shown in Figure 6. The PF’s qualitatively appeared to contain features expectedfor bcc shear textures, but did not represent ideal shear textures.

4. DISCUSSION AND CONCLUSIONS

The mechanical response of Fe, Figure 2, was found to be highly dependent upon specimengeometry. Both the flow stresses and rates of work hardening were observed to be higher for theA and B geometries as compared to the C and D geometries. This is attributed to differences inthe loading configuration (shear-compression) as a function of geometry, Figure 1. Clearly, as asimple shear loading configuration is approached instability in mechanical response is promoted.Considere’s criterion, originally developed to predict necking during tensile tests, statesthat mechanical instability is linked to diminished work hardening [16, 17]. The microstructuralevolution in the current study was found to reflect this effect. The narrowest region of shearlocalization, highest fractions of HABs, and most well developed shear textures, all associatedwith greater instability, were observed for the C-geometry.

Based on the observed microstructures in this study and the mechanical response, Figures 2–4,as well as the observations of shear deformation in Ta and Cu, it is clear that the specimengeometry influences the dislocation generation, glide and storage phenomena that control sheardeformation in Fe [11, 18]. Additionally the development of an increasing density of high angleboundaries, Figure 5, is important to accommodation of increasing degrees of shear deformation.

A subgrain rotation model called PriSM (progressive subgrain misorientation) was proposedto account for high angle dynamically recrystallized structures observed during dynamicmechanical deformation [19]. While in this study, not enough high resolution microstructuralanalysis has been performed to determine the true nature of the subgrain development in the shearlocalized regions – recrystallized or not – the development of the HAB fraction as a function ofgeometry is consistent with the substructural evolution model described in the PriSM model.

In summary, varying the inner diameter of the tophat specimen changes the shear-compressionloading stress state that in turn influences the mechanical response and microstructural evolutionduring deformation. More localized shear deformation, higher high angle boundaries fractions,and well-developed shear textures are all observed as the loading state approaches simple shear.This correlates well with decreasing work hardening rates observed as a function of geometry,A-D, and indicates that mechanical subgrain rotation is likely accommodating shear deformation.

Acknowledgments

This work was performed under the auspices of the US Department of Energy and was supported by theJoint DoD/DOE Munitions Technology Development Program.

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