Characterization of the strain rate sensitivity of basal, prismatic and pyramidal slip in Zircaloy-4 using micropillar compression

The slip strength of individual slip systems at different strain rates will control the mechanical response and strongly influence the anisotropy of plastic deformation. In this work, the slip activity and strain rate sensitivity of the basal, prismatic, and pyramidal slip systems are explored by testing at variable strain rates (from 10−4 s−1 to 125 s−1) using single crystal micropillar compression tests. These systematic experiments enable the direct fitting of the strain rate sensitivities of the different slips using a simple analytical model and this model reveals that deformation in polycrystals will be accommodated using different slip systems depending on the strain rate of deformation in addition to the stress state (i.e. Schmid's law). It was found that the engineering yield stress increases with strain rate, and this varied by slip systems. Activation of the prismatic slip system results in a high density of parallel, clearly discrete slip planes, while the activation of the pyramidal slip leads to the plastic collapse of the pillar, leading .to a ‘mushroom’ morphology of the deformed pillar. This characterization and model provide insight that helps inform metal forming and understanding of the mechanical performance of these engineering alloys in the extremes of service conditions.</p

Indentation and compression apparent elastic moduli (GPa).

Indentation and compression apparent elastic moduli (GPa).</p

Load-displacement graph of indentation.

Load-displacement graph showing indentation in six different locations on the same sample. The bone was loaded to 10000 mN (10 N), there was a 60 second hold period and then it was unloaded to 5 N, followed by immediate reloading to 10 N, with another 60 second holding period at 10 N. There were 10 cycles of loading and unloading at each indent location, followed by complete unloading. The indenter then moved to a new location on a pre-defined grid and there were a further 10 cycles. With 10 cycles of indentation at 6 different locations, 60 indentations were performed in total for each sample.</p

Sample preparation.

<p>(<b>a</b>) The femoral neck cut from the femoral head using a water-cooled bandsaw. (<b>b</b>) Femoral neck after sectioning with the bandsaw, displaying the thicker cortical bone on the medial, calcar area of the femoral neck. (<b>c</b>) Custom-made clamp (sample grip) with the four screws gripping the cortical bone section, positioned for the 3 mm-apart parallel cuts. The sample was orientated so that the wafering blade cut the bone perpendicular to the arrow marked on the bone. Arrow corresponds to the direction of the osteons. (<b>d</b>) 6x3x3 mm rectangular parallelepiped cortical bone sample from the medial femoral neck cortex. The 6mm length surface is parallel to the direction of the osteons (marked with blue arrow).</p

Schematic of compression testing, compared to indentation testing.

<p>Left: Bone (B) undergoing compression testing between two stainless steel platens (P). The blue arrow indicates the load being applied. Centre: Bone undergoing indentation using the 1.5 mm diameter, ruby, spherical indenter tip (R) used in this study. Right: Bone undergoing indentation using a proposed larger diameter, spherical indenter tip (S).</p

Indentation modulus vs compression modulus scatter plot.

<p>Scatter plot of the compression apparent elastic modulus (GPa) compared to the indentation apparent modulus (GPa). The regression line plotted has an <i>r</i> value of 0.33, <i>p</i> = 0.17.</p

Repeatability of indentation measurements of bone elastic modulus.

<p>Distribution plot of the co-efficient of repeatability measurements. The co-efficient of repeatability values (GigaPascals) are on the x-axis. The y-axis displays the relative probability. Two graphs are plotted: In blue, the co-efficient of repeatability values for repeated indentations at the same locations are plotted. There were six different locations on each of the 19 patient bone samples so there are 114 data points for repeated, same location, indentation repeatability co-efficient values. In red, the co-efficient of repeatability values for indentations at different locations are plotted. There were 19 data points, corresponding to the 19 patient samples. The mean co-efficient of repeatability was 0.4 GigaPascals (GPa) (confidence interval (C.I): 0.33–0.42 GPa) for indentations at the same bone locations and 3.1 GPa (C.I: 2.2–3.90 GPa), at different locations on the bone samples.</p

Stress-strain curve.

<p>Stress-strain curve demonstrating the proposed “safe elastic range” of bone deformation during press-fit cementless joint replacement surgery. A “safe elastic range” is demonstrated. A comparison is shown between healthy bone (black curve) and more porous, osteoporotic bone (blue curve).</p

Compression testing stress-strain graph.

<p>Graph displaying strain on the x-axis and stress (in GigaPascals) on the y-axis from one of the cortical bone samples that underwent compression testing in the materials testing machine in this study. The elastic modulus was calculated from the slope of a best-fit line at the steepest part of the linear section of the stress-strain curve, over a 1% strain range, which is displayed on the graph.</p

Experimental setup.

<p>(<b>a</b>) Cortical bone sample mounted in the Micro Materials NanoTest indentation machine. A 1.5 mm diameter, spherical, ruby tip is being used to indent the bone in the direction of the osteons. (<b>b</b>) 6x3x3 mm rectangular parallelepiped sample being compressed between two stainless steel platens on a screw-driven Instron materials testing machine.</p