Synchrotron Radiography Studies of Shear-Induced Dilation in Semisolid Al Alloys and Steels
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An improved understanding of the response of solidifying microstructures to load is required to further minimize casting defects and optimize casting processes. This article overviews synchrotron radiography studies that directly measure the micromechanics of semisolid alloy deformation in a thin-sample direct-shear cell. It is shown that shear-induced dilation (also known as Reynolds’ dilatancy) occurs in semisolid alloys with morphologies ranging from equiaxed-dendritic to globular, at solid fractions from the dendrite coherency point to ~90% solid, and it occurs in both Al alloys and carbon steels. Discrete-element method simulations that treat solidifying microstructures as granular materials are then used to explore the origins of dilatancy in semisolid alloys.
KeywordsSolid Fraction Volumetric Strain Shear Cell Local Dilation High Solid Fraction
Many casting defects have their origin in the natural flow, shrinkage/contraction and gas evolution that occurs during solidification. Additionally, it is common for a casting process to deform the solidifying alloy, either intentionally such as the application of pressure in high-pressure die casting and squeeze casting, or unintentionally such as the bulging between rolls in continuous casting. Therefore, to minimize casting defects and optimize casting processes, we require a detailed understanding of how solidifying microstructures respond to load and how deformation leads to casting defects.
Despite this importance, the study of semisolid alloy deformation has received little attention compared with fully solid alloys, and our understanding is much less developed. The focus of a large proportion of past work has been on either low-solid-fraction suspension rheology relevant to semisolid processing routes such as rheocasting,1, 2, 3 or on tensile loading at high solid fraction (>~0.90) relevant to hot tearing4, 5, 6, and several combinations of semisolid microstructure and loading mode that remain largely unexplored.
A common mode of solidification in casting is the nucleation and growth of numerous equiaxed crystals. In the case that no other phase forms first, free crystals impinge on one another during growth, creating a crystal network.1 This point is commonly termed “dendrite coherency,”7, 8, 9 although this term is also used to describe other transitions in the mushy zone.10 Dendrite coherency marks the onset of measurable shear and compressive strength, but the alloy has negligible tensile strength at this stage as there is negligible cohesion between crystals.1,11 Recently, it has been found that shear/compressive deformation at solid fractions above dendrite coherency causes shear-induced dilation12 (also known as Reynolds’ dilatancy13). This is the phenomenon in granular materials whereby the volume occupied by the particles/grains increases during shear (i.e., the packing density of the particles decreases during shear). This occurs when the particles are sufficiently densely packed that they push or lever one another apart as they begin to rearrange under load. Shear-induced dilation is a fundamental mechanical property of granular materials such as dense particulate soils14 and powders but was not expected of partially solid alloys.
Subsequent studies have shown that dendrite coherency marks the onset of dilatancy (i.e., shear-induced dilation) in partially solid alloys,12,15,16 and it has been suggested that dilatancy may be important in semisolid processing,17 high-pressure die casting,18 and direct chill casting,19 for example, through dilatant shear banding. However, this remains a little explored area and the development of physically based models that include shear-induced dilation requires an improved understanding of the fundamentals. Therefore, the aims of this work have been: (I) to obtain direct proof of shear-induced dilation in semisolid alloys, (II) to understand the micromechanics of semisolid deformation at intermediate solid fractions and how this leads to shear-induced dilation, and (III) to explore modeling techniques that are well suited to capturing shear-induced dilation in semisolid alloys.
The rig was incorporated into beamline BL20B2 at the SPring-8 synchrotron in Hyogo, Japan.21 As depicted in Fig. 1, the pushing plate penetrates vertically upward and the displacement rate was set to du z/dt = 100 μm s−1, giving a global shear rate of ~1 × 10−2 s−1. Deformation was conducted to accumulated global shear strains of γ ~ 10–30%. Some experiments were conducted on Al-15Cu alloys, which have strong solid–liquid contrast in the transmitted x-ray images. Other experiments were conducted on Fe-2C alloys to develop the deformation/imaging technique toward industrially relevant steels. In carbon steels, the γ-Fe and liquid phases have only weak x-ray absorption contrast, and the imaging challenges have only recently been overcome as overviewed in Ref. 22. Full experimental details on imaging and deformation can be found in Ref. 23 for Al-Cu alloys and Ref. 24 for Fe-C alloys.
Results and Discussion
It might be thought that partially solid alloys containing a solid network would not deform in this way because the grains have a yield strength of only up to a few MPa at T/T m ~ 1,1,26,27 and grain–grain contacts can be cohesive due to the formation of solid–solid interfaces (grain boundaries) where the misorientation angle is favorable.28,29 However, direct in situ imaging has shown that semisolid alloys often deform by shear-induced dilation.23,24,30,31 As an example, Fig. 2c shows a local region of microstructure where the configuration of four grains and the loading direction are similar to the geometry in Fig. 2a. In Fig. 2c, it can be directly observed that, during loading, the grains push each other apart in a manner similar to Fig. 2a. It can also be seen that the expansion of interstitial spaces is compensated by the inflow of liquid (dark) from elsewhere in the sample. The absence of observed cohesion between grains suggests that the relationship of σ S–S > 2σ S–L is generally satisfied for most grain–grain misorientations (σ = interfacial energy) and that liquid films exist between grains.
There is rarely any discernible deformation of the individual grains (see the section, “Equiaxed-Dendritic Al-15Cu at ~30% Solid” for an exception to this statement).
Macroscopic deformation occurs predominantly by grain rearrangement coupled with interstitial liquid flow.
Most grains translate and rotate as discrete bodies under the action of contact forces.
After loading, there is an adjustment of grain positions that causes changes in the local grain-packing density (the local solid fraction) so that the overall response comes from a combination of local dilation and local compaction. For the combinations of solid fraction, morphology, and strain rate overviewed in this article, changes in solid fraction were accommodated by the inflow or outflow of the interstitial liquid from other regions of the samples. An analysis of the grains has confirmed that there was no measurable remelting or solidification during testing in the experiments in this article.
Macroscopic shear-induced dilation occurs causing the overall solid fraction to decrease during grain rearrangement.
Grain motion often becomes localized in certain areas, producing inhomogeneous deformation.
We next focus on the detailed grain-scale response to load in three data sets from microstructures containing numerous equiaxed grains in mechanical contact but that have markedly different semisolid microstructures: equiaxed-dendritic at ~30% solid, globular at ~70% solid, and globular-polygonal at ~88% solid.
Globular Al-15Cu at ~70% Solid
An example of local dilation is overviewed in Fig. 3, which is a region near the half-plane of the shear cell. Note that the pushing plate is located at the bottom right of the grain labeled A in Fig. 3a. As the plate moves upward, grain A pushes B and C up and to the left, and A, B, and C slide past D and E between Fig. 3a and b. Now A is in contact with both B and E and, as A is pushed further up and to the left, the position of the contacts between A–B and A–E causes grain A to push B and E apart (compare Fig. 3b and c). These grain movements are due to force transmission across contacts and cause the packing density of the grains to decrease and the volume of the liquid-filled intergrain spaces to increase. The projected grain perimeters and centroids corresponding to Fig. 3a and c are plotted in Fig. 3d and e, respectively. The centroid displacement field (Fig. 3f) contains diverging vectors because the grains are pushing each other apart. In Fig. 3g–i, the local dilatational volumetric strain is quantified by triangulation of the centroids in Fig. 3d and e. The values in each triangle show the volumetric strain in each triangle, and the overall dilation of this local assembly is 10.1% as shown in Fig. 3i.
Figure 4 is the same region as that in Fig. 3 but spans a longer period of deformation. In Fig. 4, it can be inferred from the motion of grain C that this grain is actually welded to (has a grain boundary with) the smaller grain to its right, making an effective structural unit (an agglomerate) shaped like a bowling pin. In Fig. 3, grain C only translates upward, but in Fig. 4 grain C undergoes significant rotation. This can be understood by considering the position of the two contacts marked with white dots in Fig. 4 and noting that the contact normal force is not collinear with the vector joining the centroids (the branch vector), causing the contact normal force to apply a significant moment. Between Fig. 4b and c, the major axis of the bowling pin agglomerate undergoes a 46° anticlockwise rotation, which creates significant interstitial space because the bowling pin shape sweeps out a much larger projected area than its true projected area. Therefore, the rotation of grain C with high aspect ratio causes strong local dilation.
Globular-Polygonal Fe-2C-1Mn-0.5Si at ~88% Solid
It can be seen in Fig. 5 that deformation at such high solid fraction leads to strong shear-induced dilation with large liquid-filled spaces opening up between grains during shear. As discussed in Ref. 31, this liquid was drawn in from the sides of this sample, and there was no measurable deformation of the individual grains at the resolution of the experiment.
Similar to the globular sample at ~70% solid in Figs. 3 and 4, shear-induced dilation in Fig. 5 is caused by the translation and rotation of quasi-rigid grains that were initially tightly packed. The rotation of a large grain with a relatively high aspect ratio is highlighted in Fig. 5. This grain rotates 14° clockwise between the two frames in Fig. 5, which levers neighboring grains apart and creates significant interstitial space.
Figure 6c and d quantify the inhomogeneous volumetric and shear strain fields. It can be seen that, in general, regions of high shear correspond to regions of high dilation. A region of high shear and simultaneous dilation has developed both in a vertical band and a horizontal band that start close to the large grain highlighted in Fig. 5. As shown in Ref. 31, the regions of high shear and dilatational volumetric strain in this sample correspond to regions of highest grain rotation, the greatest reduction in number of contacts per grain, and the greatest increase in distance between neighboring grains.
Equiaxed-Dendritic Al-15Cu at ~30% Solid
Comparing Fig. 7a and b, it can be seen that in most of the field of view, deformation was accommodated by grain rearrangement by discrete translations and rotations of the crystal envelopes. The exception to this occurred at the pushing-plate front where global deformation occurred by crystal deformation, and the crystal assembly deformed as a viscoplastic solid skeleton that squeezed out interstitial liquid as it was compressed. This shows that there is added complexity in equiaxed-dendritic structures caused by a competition between deformation of the individual grains and rearrangement of grains that was not measured for the globular and globular-polygonal structures in sections titled, “Globular Al-15Cu at ~70% Solid” and “Globular-Polygonal Fe-2C-1Mn-0.5Si at ~88% Solid.”
Comparing the deformation of the equiaxed-dendritic microstructure in Figs. 7 and 8 with the globular microstructure in Figs. 3 and 4 and the globular-polygonal microstructure in Figs. 5 and 6, there are a variety of differences in the details of the micromechanics. For example, the contacts across which force is transmitted in the equiaxed-dendritic and globular microstructures are relatively well approximated as point contacts similar to the circles in Fig. 2a and b. In contrast, a high proportion of each grain perimeter is involved in force transmission in the globular-polygonal microstructure in Figs. 5 and 6. Additionally, the magnitude of the shear-induced dilation is significantly different in each microstructure, which is mostly because of the different initial packing-densities of the crystal envelopes. Despite these differences, each microstructure deforms predominantly by grain rearrangement and undergoes shear-induced dilation, highlighting the ubiquity of this phenomenon in equiaxed semisolid microstructures containing a solid network.
Discrete-Element Method (DEM) Modeling
During experiments on semisolid alloys containing a solid network, the synchrotron radiography studies have shown that shape change predominantly occurs by the rearrangement of grains within an assembly of grains in mechanical contact and that shear-induced dilation is a fundamental part of the microstructural response to load. Other materials that exhibit these deformation phenomena such as soils,34 powders, and other compacted granular materials are often modeled using the particulate DEM. In DEM, the material is explicitly treated as an assembly of rigid particles that can move independently by translation and rotation caused by forces acting at particle–particle contacts,35 and shear-induced dilation emerges naturally with this approach.
A DEM model was developed within the commercial DEM package PFC2D (Itasca Consulting Group, Inc. based on Ref. 35) that takes simulated two-dimensional (2D) solidification microstructures as inputs and models the microstructural response to an imposed deformation.33 The study in Ref. 33 used equiaxed solidification microstructures modeled with the approach from Lee and co-workers.36 We showed that dendrite coherency can be considered to be the lowest solid fraction at which long-range interconnectivity in the force chain network develops during shear, and we confirmed that dendrite coherency marks the lowest solid fraction at which shear-induced dilation occurs. The study can also be used to gain insights on shear-induced dilation in a grain assembly created by equiaxed solidification.
Particulate numerical modeling including the DEM has been applied to semisolid alloy deformation by other groups,37, 38, 39 which are combining finite-element and discrete-element methods to account for the viscoplastic deformation of the solid. The in situ imaging results and these initial models suggest that DEM is likely to be an important component within future models of metallic alloy mush mechanics.
In situ studies of semisolid deformation have provided direct proof for shear-induced dilation in semisolid alloys with morphologies ranging from equiaxed-dendritic to globular and solid fractions ranging from dendrite coherency to ~90% solid. It has been shown that this behavior is the result of load transmission across grain–grain contacts and grains rearranging as largely cohesionless, quasi-rigid bodies within a network of grains in mechanical contact. It has been shown that these deformation characteristics can be captured by the DEM, which has significant potential as a component of mush mechanics models.
Experiments were conducted at the SPring-8 synchrotron on beamline BL20B2 under proposal numbers 2008A-1428 and 2011A-1209 and were supported by a Grant-in-Aid for Scientific Research (S), MEXT, Japan. The analysis was carried out under grant EP/K026763/1 (EPSRC) and with a Royal Society Daiwa Anglo-Japanese Foundation International Exchanges Award.
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