Strain-Rate Sensitivity (SRS) of Nickel by

Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation Application Note Jennifer Hay, Agilent Technologies, Nano-Scale Sciences Division Verena Maier, Dr. Karsten Durst, and Dr. Mathias Göken, University of Erlangen-Nuremberg, Department of Material Science and Engineering

Introduction In many materials, the plastic stress that can be sustained depends on strain rate through a power-law relationship: higher stresses are sustained with higher strain rates and vice versa. In a uniaxial tensile configuration, this relationship between plastic stress, , and strain rate, •u, is expressed as m,  = B*•u

Eq. 1

where B* is a constant and m is the strain-rate sensitivity (SRS), which is always greater than or equal to zero. For materials which manifest negligible strain-rate sensitivity, m is near zero, making  a constant. (Sapphire is an example of such a material.) Materials with greater strain-rate sensitivity have greater values of m. Provided that hardness (H) is directly related to plastic stress, then hardness also manifests this same phenomenon, giving the relation H = B• m .

Eq. 2

In Eq. 2, B is a constant (though different in value from B* in Eq. 1) and • is the indentation strain rate, 1.

defined as the loading rate divided • by the load (P /P)1. The strain-rate sensitivity, m, has the same meaning and value in Eq. 2 as it does in Eq. 1. Taking the logarithm of both sides of Eq. 2 and simplifying yields In(H) = m • In(• ) + In(B).

Eq. 3

Thus, for many materials, there is a linear relationship between the logarithm of hardness and the logarithm of strain rate, with the slope being the strain-rate sensitivity, m. Lucas and Oliver showed that the strain-rate sensitivity, m, could be evaluated by performing a series of indentations, with each indentation performed using a different strain rate [1]. However, the approach of Lucas and Oliver is problematic, because indentations at small strain rates take so long that the results can easily be dominated by thermal drift. Recently, Maier et al. showed that all strain rates of interest may be executed within a single indentation test by switching strain rates as the indenter continues to move into the material [2].

Strictly, the term ‘indentation strain rate’ refers to the displacement rate divided by the • displacement (h /h). However, beginning with the definition of hardness, it is easily shown that • • h /h ≈ 0.5(P/P). Eq. 2 holds true for either definition of strain rate, because the constant (0.5) difference between the two definitions is simply absorbed into the constant B. Because the Agilent • • G200 NanoIndenter is a force-controlled instrument, it is logistically easier to control P/P than h /h. • Thus, in this work, the term ‘strain rate’ refers to P/P, unless specifically stated otherwise.

The protocol proposed by Maier et al. has a number of practical advantages. First, the testing time and thermal drift are minimized by using fast strain rates when the applied force is small and slow strain rates when the applied force is large. To understand this benefi t, it is important to understand how a controlled-strainrate experiment works. The forceapplication rate required to maintain a given strain rate changes with applied force. For example, let us compare the force-application rate required to achieve a strain rate of 0.01/sec at 1mN and 100mN. Knowing the • definition of strain rate (• = P /P), we calculate the necessary force• application rate for each situation (P) as the product of the desired strain rate and the applied force. When the applied force is 1mN, we have •

P = 0.01/sec*1mN = 0.01mN/sec. When the applied force is 100mN, we have •

P = 0.01/sec*100mN = 1mN/sec, which is much faster. Though the same strain rate is achieved in both cases, the associated force rate is much higher in the second case, because the applied force is much higher. Thus, it may take a prohibitively long time to examine a small strain rate when the applied force is small, but that same small strain rate can be examined rather quickly when the applied force is large. The protocol suggested by Maier et al. takes advantage of this reality by examining the largest strain rate at the beginning of the test (when the applied force is small) and by examining progressively smaller strain rates as the applied force increases. In this way, both testing time and thermal drift are minimized.

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The protocol of Maier et al. has been implemented in a new NanoSuite test method; this application note reports the results obtained with this new method on a nickel standard reference material (SRM) produced by the U.S. National Institute of Standards and Technology (NIST). The protocol of Maier et al. has a second important benefi t: because all strain rates of interest are examined in every test, it is possible to map out the spatial distribution of strain-rate sensitivity. Although this capacity will not be demonstrated in this note, Maier et al. measured local strain-rate sensitivity in and around a bond layer in roll-bonded aluminum.

Sample The sample tested in this work was a NIST standard reference material (SRM) for Vickers hardness. The sample consists of a 1.35 cm square test block of electrodeposited bright nickel, approximately 750 microns thick, on an AISI 1010 steel substrate, mounted and highly polished in a thermosetting epoxy. A template certificate for this kind of sample can be found on the NIST website [3]. The qualities which make this sample ideal as a Vickers SRM also make it ideal for the present demonstration. It has a smooth surface, is resistant to tarnish and corrosion, and has a small grain size. These qualities are important, because ideally, changes in strain rate should be the only explanation for the observed changes in hardness. Changes in hardness due to other factors such as surface layers, indentation size effect, and constraint influence can all compromise the validity of the measured strain-rate sensitivity.

Equipment

Parameter

An Agilent G200 NanoIndenter with a Berkovich indenter was used for all testing. The Continuous Stiffness Measurement Option (CSM) was also used in order to achieve hardness and elastic modulus as a continuous function of penetration depth [4].

Surface Approach Velocity Surface Approach Distance

Value

Units

25

nm/s

1000

nm

5

nm

Frequency Target

45

Hz

Poissons Ratio

0.3

Harmonic Displacement Target

Displacement, Initial Strain Rates, How Many?

1100

nm

3

Test Method

Displacement per Rate

150

nm

Twelve indentation tests were performed using the test method “G-Series XP CSM Strain-Rate Sensitivity.” Table 1 summarizes testing inputs. This test method allows the user to prescribe a penetration that must be achieved prior to strain-rate cycling (Displacement, Initial). This initial penetration is used to achieve a penetration depth that is large enough so that no further changes in hardness are expected due to indentation size effect, surface inhomogeneities, tip anomalies, etc. Once this initial penetration has been achieved, the method prescribes cycling between a test strain rate and a base strain rate. The test strain rate is executed in the first part of the cycle, and the base strain rate is executed in the second part of the cycle. The return to the base strain rate after each test strain rate provides a means for confirming that hardness is not changing with increasing penetration for any reason other than the changing influence of strain rate. Figure 1 shows the strainrate history for each indentation test on the Ni SRM.

Strain Rate, Maximum

0.05

1/s

Strain Rate, Minimum

0.001

1/s

Table 1. Summary of inputs used to measure the strain-rate sensitivity of a Ni Vickers SRM by the method “G-Series XP CSM Strain-Rate Sensitivity.”

Figure 1. Strain-rate cycling imposed on the test sample. In the first part of the cycle, the test strain rate is imposed. In the second part of the cycle, the base strain rate is imposed.

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Results and Discussion

Test 1 2 3 4 5 6 7 8 9 10 11 12 Avg. Std. Dev.

Table 2 summarizes the most important results. The elastic modulus (E) of the Ni SRM was measured to be 229±3 GPa, and the strain-rate sensitivity (m) was measured to be 0.021±0.002. Table 3 is a survey of strain-rate-sensitivity values measured by others for finegrained Ni. Figure 2 shows the continuous elastic modulus during strainrate cycling for one typical test. As expected, the modulus did not change significantly during strainrate cycling. Modulus is reported for each cycle by averaging the continuous measurements which fall within 80-90% of the displacement range for the base-strain-rate segment of the cycle. In Figure 2, these measurements are plotted as green data points. The modulus value reported for each test in Table 2 is the average of the three cycle-level results for that test. The average over all tests, 229 GPa, is 15% higher than the nominal value of 200 GPa for pure nickel. One possible explanation for the discrepancy is that the Oliver-Pharr model for the contact area may overestimate the true contact area. Because the calculation of elastic modulus by indentation goes as the inverse of the square root of the contact area, an underestimation of the contact area leads to an overestimation of the modulus. Finite-element simulations of indentations into a material with nickel-like properties could be used to further investigate this explanation, because finiteelement simulations allow a comparison between contact area determined by the Oliver-Pharr model and contact are determined from the finite-element mesh.

E, GPa 226.8 225.5 228.8 230.5 228.3 234.5 228.4 235.5 229.9 224.6 229.8 228.9 229.3 3.2

m 0.0207 0.0207 0.0238 0.0207 0.0228 0.0212 0.0187 0.0228 0.0220 0.0179 0.0189 0.0210 0.0209 0.0018

Table 2. Summary of Results.

Source This work Maier et al. [2] Maier et al. [2] Shen et al. [5] Dalla Torre et al. [6, 7] Wang et al. [8]

Sample Ni Vickers SRM Nanocrystalline Ni Nanocrystalline Ni Nanocrystalline Ni Nanocrystalline Ni

Method m Indentation 0.021 Indentation 0.019 Uniaxial creep (compression) 0.016 Uniaxial creep (tension) 0.016–0.045 Uniaxial creep (tension) 0.010–0.030

Nanocrystalline Ni Uniaxial creep (tension)

0.019

Table 3. Survey of SRS (m) values measured by others on fine-grained Ni.

Figure 2. Modulus during strain-rate cycling for one typical test. As expected, modulus is not sensitive to strain rate.

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Figure 3. Hardness during strain-rate cycling. Sensitivity to strain rate is evident. Black symbols denote data used to calculate the hardness for each test strain rate. Green symbols denote data used to calculate the hardness for each base strain rate.

Figure 4. Plot of ln(H) vs. ln(• ) for each of twelve tests. Slope of ln(H) with respect to ln(• ) for each test gives the strain-rate sensitivity, m, for that test. Linearity of these data demonstrates that strain-rate sensitivity for this material is well modeled by Eq. 2.

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Figure 3 shows the continuous hardness measured during strain-rate cycling for a typical test. (These data are from the same test for which the modulus is plotted in Figure 2.) The influence of changing strain rate is obvious. At each change, there is a transient in the hardness response as the microstructure adjusts to the new rate. For each test strain rate, the hardness values within 80%-90% of the displacement range for the segment are averaged to report a single value of hardness; data within this range for each cycle are plotted as black symbols in Figure 3. Figure 4 shows Ln(H) vs. Ln(° ) for all 12 tests. The linearity of these results supports the hypothesis that this material is well described by Eq. 2. For each test, the strain-rate sensitivity, m, is calculated as the slope of Ln(H) vs. Ln(•) and reported in Table 2. The value for strain-rate sensitivity obtained by averaging over all 12 tests (m = 0.021±0.002) is well within the range of SRS values that have been measured by others for fine-grained Ni (Table 3).

A hardness value for each implementation of the base strain rate was also determined. For each base strain rate, the hardness values within 80%-90% of the displacement range for the segment are averaged to report a single value of hardness for that segment; in Figure 3, the included hardness values are plotted as green symbols. For all 12 tests, Figure 5 shows hardness associated with the base strain rate for each cycle. The lack of any trend in hardness with cycle number confirms that hardness is not changing with depth when the same strain rate is applied.

Conclusions An experimentally robust test method has been implemented in NanoSuite for measuring strain-rate sensitivity by instrumented indentation. The method overcomes problems associated with long testing times by imposing small strain rates only when the applied force is large. Using this method, the strain-rate sensitivity of a sample of nickel sold by NIST as a Vickers SRM was measured to be m = 0.021. This value is in good agreement with values obtained by others on similar materials using both instrumented indentation and uniaxial creep testing.

Figure 5. Hardness measured during the base-strain-rate segment of each cycle. Lack of any trend with cycle number demonstrates that the same hardness is measured when the same strain rate is applied, despite increasing penetration.

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References 1. Lucas, B.N. and Oliver, W.C., “Indentation Power-Law Creep of High-Purity Indium,” Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science 30(3), 601-610, 1999. 2. Maier, V., Durst, K., Mueller, J., Backes, B., Hoppel, H., and Göken, M., “Nanoindentation strain rate jump tests for determining the local strain rate sensitivity in nanocrystalline Ni and ultrafine-grained Al,” Journal of Materials Research 26(11), 1421-1430, 2011. 3. NIST Certificate Standard Reference Material 1896a Vickers Microhardness of Nickel. [cited 2011 October 10, 2011]; Available from: http:// ts.nist.gov/MeasurementServices/ ReferenceMaterials/upload/1896a.pdf. 4. Hay, J.L., Agee, P., and Herbert, E.G., “Continuous Stiffness Measurement during Instrumented Indentation Testing,” Experimental Techniques 34(3), 86-94, 2010. 5. Shen, X., Lian, J.S., Jiang, Z., and Jiang, Q., “High Strength and High Ductility of Electrodeposited Nanocrystalline Ni with Broad Grain Size Distribution,” Material Science and Engineering A 487, 410, 2008. 6. Dalla Torre, F., Van Swygenhoven, H., and Victoria, M., “Nanocrystalline Electrodeposited Ni: Microstructure and Tensile Properties,” Acta Materialia 50, 3957, 2002. 7. Dalla Torre, F., Spätig, P., Schäublin, R., and Victoria, M., “Deformation Behavior and Microstructure of Nanocrystalline Electrodeposited and High Pressure Torsioned Nickel,” Acta Materialia 53, 2337, 2005. 8. Wang, Y.M., Hamza, A.V., and Ma, E., “Temperature-Dependent Strain-Rate Sensitivity and Activation Volume in Nanocrystalline Ni,” Acta Materialia 54, 2715, 2006.

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