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<h3>Abstract</h3>
In this work<ref>Mulholland, M., Kharaishi, T., Shen, Y.L., Horstemeyer, M., "Void Growth and interaction experiments:  Implications to the optimal straining rate in superplastic forming," ''International Journal of Plasticity,'' No. 22, 2006, pp. 1728-1744.</ref>, a set of parametric experiments was conducted on a superplastic material (eutectic tin–lead alloy) with one or more pre-drilled holes in each specimen. The small-sized holes were for simulating microvoids that occur and grow during superplastic forming. All holes were axially aligned with the tensile axis. The results revealed an increase in ductility with the number of holes up to 10 holes and a decrease thereafter. The ductility enhancement was explained based on the m-curve as due to a rise in the strain rate sensitivity locally around the holes. The decrease was explained due to strong void interaction that resulted in shear failure. This was further verified by a separate set of experiments of only two interacting voids with various interspacing. Finally, the void size versus applied strain was fully characterized and the results supported the ductility observations.

Author(s): Mulholland, M., Khraishi, T., Shen, Y.L., Horstemeyer, M.
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<h3>Methodology</h3>

	Dog-bone specimens of a rolled 63Sn-37Pb alloy were subjected to material testing.  Scanning electron microscope (SEM) techniques were used to examine the material microstructure.  The major material phases were determined to be Pb-rich particles and Sn-rich matrix material via chemical spectrum analysis.  The microstructure was determined to be random with no discernable phase anisotropy.  Some of the specimens were drilled along the centerline of gauge section parallel to the loading axis in order to study void growth mechanisms.

	The specimens were tested under constant applied strain rates in Instron tensile testing machines.  The evolution of hole deformation in the specimens was recorded via digital camcorder and digital imaging software was used to calculate the evolution of void area with changing strain.  Plots were generated for the void area vs. strain and are shown in Figure 1.
 
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<h3>Material Model</h3>
The material constitutive model uses a simple power law relation that maps strain and strain rate to stress.  
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<h3>Results</h3>


	Engineering stress – strain curves were generated for specimens with varying numbers of holes, shown in Figure 1.  Generally, and perhaps counter-intuitively, increasing the number of holes up increased the strain to failure, except for the case of zero holes in the specimen.  However, Figure 2 demonstrates that the number of holes to increasing failure strain behavior seemed to saturate at 10 holes at which point, increasing the number of holes decreased the strain to failure.
{| border="1"|center|
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[[file:VGFigure1.png|center|thumb|300px|Figure 1.  Stress strain behavior for varying number of initial specimen holes.  In general, increasing the number of holes increased the strain to failure until reaching a saturation point of 10 initial holes.  The control specimen with zero holes exhibited greater strain to failure than specimens with up to 7 holes.]]
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[[file:VGFigure2.png|center|thumb|300px|Figure 2.  Strain to failure for specimens with 0-20 holes aligned in the tensile loading direction.]]
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[[file: VGFigure3.png|center|thumb|300px|Figure 3.  Strain to failure for various spacing distances between two holes and similar strain rates.  In general, increasing the diameter between holes increased the strain to failure. ]]
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	Failure characteristics were examined for varying the distance between the holes in the test specimen gauge areas.  Figure 3 shows that increasing the distance between the holes increased the strain to failure.  Specimens with relatively long initial hole spacing tended to fail in tensile tearing while specimens with short initial hole spacing underwent shear failure shown in Figure 4.

[[image: VGFigure4.png|center|thumb|300px|Figure 4.  Failure mechanisms for initial hole spacing of 5d (left) and 1d (right).  The specimen with greater initial hole spacing distance exhibited tensile tearing while the specimen with less initial hole spacing underwent shear failure.]]

	Void area evolution for increasing strain was examined for specimens with pre-existing holes.  Varying the strain rate for specimens with a single hole resulted in a decreasing strain to failure for increasing strain rate as shown in Figure 5.  Tests for specimens with various initial hole sizing resulted in little discrepancy between void growth for similar strains but specimens with larger initial holes tended to have lower strain to failure (Figure 6).  The last set parametric experiment involved comparing the effects of the number of holes in the test specimens.  The study in Figure 7 shows that a lower numbers of holes resulted in increased void growth rates and decreased strain to failure values.

{| border="1"
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[[image: VGFigure5.png|center|thumb|300px|Figure 5.  Normalized void area versus strain for one-hole specimens with varying strain rates of 0.0001, 0.0002, 0.0005, and 0.001s<sup>-1</sup>.  Strain to failure decreases with increasing strain rate.  Void growth rates generally increase with increasing strain rate.]]
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[[image: VGFigure6.png|center|thumb|300px|Figure 6.  Normalized area versus strain for one-hole specimens under 0.002s<sup>-1</sup> strain rate with varying hole diameters.  The hole size did not appear to have a significant effect on the rate of void growth, but larger hole size decreased the total strain to failure.]]
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[[image: VGFigure7.png|center|thumb|300px|Figure 7.  Normalized area versus strain for one-, two-, three-, and four-hole specimens under a 0.001s<sup>-1</sup> and constant initial hole diameter.  Increasing the number of holes decreased the void growth rate.  Specimens with multiple holes exhibited greater strain to failure than the single hole specimen. ]]
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<h3>Acknowledgments</h3>

This work was sponsored in part by a Sandia National Laboratories (SNL) SURP
Contract.
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<h3>References</h3>

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