Resonant Ultrasound Spectroscopy to Measure Tensile Strength and Rockwell C Hardness

 

This month's NDT Solution describes a new use for resonant ultrasound spectroscopy (RUS). Currently, the standard test for Rockwell C hardness is the measured deformation of a part resulting from the application of a specified load by an indenter. This test, and the Brinnell test, correlate well with yield strength, because the indenter causes yield (deformation) at the surface. These deformations could be considered destructive, however, if they mar a bearing surface or cause stress risers in tensile areas. According to the author, with RUS it is now possible to measure tensile strength and hardness values for the entire sample, not just at the point of indentation, thus enabling 100 percent inspection of production. Rather than applying this test across the board, one should consider the part prints. One must take into account that in some parts it is desirable to have a tough core and a hard case in some areas, with no hardening in other areas, to prevent brittle fractures. The empirical four-point program listed at the end of this article must be rigorously followed to confirm that the RUS test can be applied to the part at hand. Emmanuel P. Papadakis Technical Editor

 

Figures 1-3
Figures 4-6

 

Introduction
A significant problem has plagued laboratories in their ability to perform 100 percent testing on metal samples when either the Rockwell C hardness or tensile strength measurements are needed. This is because many of the standard tests are destructive. It is desirable to perform these tests nondestructively, but heretofore most NDT techniques have been proven to be inadequate for these functions. Resonant ultrasound spectroscopy (RUS) has the potential to solve the problem since it has been well established that resonances result from three physical factors: density, geometry and elastic constants. In addition, the Q or quality factor of the resonance can be used as a sorting criterion. The Q value is obtained by dividing the line width, at 0.5 ´ maximum peak height, into the center frequency of a given resonance. The geometry and density of the samples is usually fixed, but the elastic constants vary when either the tensile strength or hardness deviate. This paper describes how simple tests for frequency and Q can provide absolute values for these measurements.

Although this technique is applicable to any RUS system, the best results will be obtained with those that are phase sensitive. When an accurate center frequency for the resonance is desired, the phase sensitive system will eliminate the problem of a coherent background and symmetrize the resonance shape in preparation for simple peak identifying algorithms (Rhodes, 1997). The resonance symmetry can be obtained and the most accurate frequency determination made by choosing the in-phase component of the resonance.

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Although this technique is applicable to any RUS system, the best results will be obtained with those that are phase sensitive.

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Experimental Results
Samples of fastener bolts 12.7 x 57.2 mm, 13 turns/25 mm (0.5 x 2.3 in., 13 turns/ in.) were obtained through NIST (Collaborative Testing Services, Inc., Herndon, Virginia) which had been part of lots previously characterized by standard tests for hardness and tensile strength. Several testing laboratories were instructed to employ the ASTM F606 method with a 254 mm (10 in.) wedge to determine the tensile strength of six fasteners (three each from two different lots). The average tensile strength value was found to be approximately 1227 ± 17 MPa (178 ± 2.5 klb/in.²) for the high strength fasteners, and approximately 1082 ± 17 MPa (157 ± 2.5 klb/in.²) for the lower strength pieces.

The sample sets were examined by RUS over the lowest 20 resonances. Several modes exhibited patterns that grouped the parts according to the known physical measurements. Figure 1 illustrates the use of the 173 kHz resonance to differentiate the low and high strength parts. The four parts grouped to the left of the vertical solid line 173.8 kHz are the high strength parts, while those to the right are the lower strength parts. These data show that each 6.89 MPa (1 klb/in.2) change results in a shift of 25 Hz. In addition to the absolute frequency dependence, another phenomenon was observed which provides a useful test. Figures 2 and 3 illustrate the effect of tensile strength, for a particular resonance, on line width (Q). Expressly, Figure 2 shows the line width, of the 93.4 kHz resonance, being 0.035 kHz or:

Q =	93,400	= 2688.
	35

Figure 3 shows the same measurement for a typical, low strength, sample having a line width of 0.018 kHz and a Q = 5189. A difference in 150 MPa (22 klb/in.²) resulted in a remarkable change in Q. Theoretically this may result from there being more dislocations present in the higher strength material, thus higher ultrasonic attenuation. Although not intuitively obvious, it is well documented that the yield strength of steels increases as the elastic constants decrease.

The comparative correlations of Rockwell C by RUS may have even more importance than those for tensile strength. The destructive test currently employed examines a surface region on a sample to a depth of a few millimeters only. Although the sample is usually sectioned, it is nonetheless a surface test only. The Vickers indent test is likewise a test of the surface only. Hardening of a fastener is never uniform. That is, when a part is quenched to increase the martensite content, the outer region may be 90 percent martensite. The inner region, due to thermal transfer, may range from 40 to 70 percent martensite. No surface impact hardness test can discern the difference between these two extremes. RUS is a test suitable not only for 100 percent inspection; it also tests the bulk elastic properties of the sample. Figure 4 illustrates the frequency differences for two test groups. The bolts to the left of the vertical line have Rockwell values averaging 39.8 ±1 while those to the right average 35.5 ±1. The average difference frequency between groups is 800 Hz. Since the Rockwell hardness differs about 4.3 points between sample sets, a 100 Hz shift corresponds to about 0.5 Rockwell points.

 

Application of the Technology
The proper use of RUS will combine the recognized techniques (Rockwell and Instron) to yield values for each property. For the ultimate in accuracy, the parts will be sectioned and the elastic properties measured using the RUS/RPR technique. The following paragraphs describe the steps that should be taken when setting up a new part for RUS evaluation.

We selected modes that are descriptive of the entire structure to perform our analysis. Since density, geometry, and elastic properties are the factors governing the resonance pattern, we care only about the latter when examining either hardness or tensile properties. The simplest modes do not create mechanical displacements on all surfaces, so we typically chose a mode between the 6th and the 20th to examine for comparative analysis. In addition, we selected a mode that is singularly degenerate so that doublets do not complicate the study. There are always several available for a cylinder.

Calibration is the critical step. This is an interesting problem in that Rockwell C and Instron tests are known to be somewhat inaccurate. We took resonance data on sample sets, as represented by the four parts in each set we plotted, and recorded specific mode data. We then sent the samples to accredited laboratories for corroborative Rockwell and tensile testing, and tabulated the results. For an industrial practice, we examine a series of parts (for instance, fasteners) and record numerous resonances complying with the requirements defined above. These parts will then be tested for either Rockwell or tensile strength. Once the pattern has been established, we can extrapolate the comparative resonance data in a reference table to yield a comparative hardness or tensile measurement. We believe that the RUS data yield unparalleled accuracy, obtained by taking a few baseline samples and preparing samples from which the elastic constants may be accurately determined, and whose form is a rectangular parallelepiped (a cubic shape with different dimensions for the three edges) (Rhodes and Willis, 1998). The comparison of specific resonance data with elastic constants will yield a measurement more accurate than any standard destructive technique. We believe that most industries will accept relative data more readily than those obtained by the more rigorous approach. The Rockwell C test sections the part and measures, optically, the depth to which a hard point is driven. Rather than limiting the measurement to a local region of the sample, RUS measures the average of the entire sample, thus yielding a more accurate value.

Only a single resonance will be required for a single part. Once the resonance pattern has been established, and assuming that the geometry and density are fixed, the variation in the designated frequency will be a direct comparative measurement of either the hardness or tensile strength. Thus the data will be processed to yield a pass/fail signal. For example, if the pass/fail algorithm (which has been defined to correspond to a Rockwell C of 57 to 59 points in a specific grade 8 bolt) has been set to pass parts that resonate between 85.2 and 85.8 kHz, any resonance outside this range will fail the test.

 

Material Properties
An analysis of two bolts was performed to ensure the observed shifts in frequency were due to actual differences in the hardnesses of the materials, and not due to possible dimensional variations resulting from the treatment. A
rectangular parallelepiped was prepared from the shank of a bolt taken from the high tensile strength group and a second sample was prepared from the shank of a bolt taken from the low tensile strength group. The parallelepipeds were prepared by surface grinding the shank of the bolt to the desired dimensions, while care was taken to avoid excessive heating of the material. The dimensions of the parallelepipeds were 8.448 x 8.747 x 10.256 mm; mass = 5.9 g (0.3325984 x 0.34437 x 0.4037795 in.; mass = 0.208 oz) and 8.439 x 8.729 x 10.28 mm; mass = 6.01 g (0.332244 x 0.3436614 x 0.4047244 in.; mass = 0.212 oz) respectively.

The first 40 resonant frequencies for each sample were measured and the elastic constants determined using the standard RPR (rectangular parallelepiped resonance) technique. The rms error on a fit of the first 40 resonances was less than 0.1 percent.

 

Materials
Many laboratories, including Los Alamos National Laboratory and NIST, perform this measurement using a DRS Modulus 1 Resonant Ultrasound Spectrometer, where the dimensions, weight, and resonance data are submitted to a code that yields all the elastic constants. Those possessing isotropic symmetry require two independent elastic constants. For convenience during the initial analysis, these independent elastic constants were taken to be C₁₁ and C₄₄. For comparison to hardness values, however, a better choice is Young's modulus. The values determined for the two bolts are shown in Table 1.

Table 1 shows that material from the higher tensile strength bolt has a lower Young's modulus (Migliori et al., 1997). This is the expected relationship, since Young's modulus is the fractional length change to an applied force. Stronger bolts would stretch a smaller amount than weaker bolts, resulting in a smaller Young's modulus for stronger bolts. Table 1 also shows that the frequency shifts shown earlier are indeed due to changes in the elasticity of the material and not due to other variables.

Table 1 Elastic Constants
	C11(GPa)	C44 (GPa)	Young's Modulus (GPa)
High Strength Bolt	271.87	80.71	208.04
Low Strength Bolt	278.03	82.72	213.12

 

 

Independent Hardness Results
We selected two groups of three bolts each from the tensile strength samples and two groups of four bolts each from the Rockwell C samples, for hardness testing. We analyzed these 14 samples first using RUS, and then sent them to an independent commercial testing facility for analysis (American Metallurgical Services, Salt Lake City, Utah).

The tensile strength for each of the first six bolts was measured individually and Rockwell C hardness was measured for each of the other eight bolts. These data are shown in Tables 2-3, along with the average frequency for the desired resonant mode shown earlier.

The measured tensile strengths and Rockwell hardness are plotted in Figures 5-6 as functions of measured frequencies. The solid circles are the actual data points. The vertical error bars are the reported uncertainty from many independent tests not reported herein. The straight line on each graph is a linear least squares fit to the data. The graphs show that there is an excellent correlation between the measured resonant frequencies and measured Rockwell C, or tensile strength, for each bolt.

In practice, graphs similar to Figures 5 or 6 would be constructed from measurements of resonant frequencies and hardness tests performed on a representative sampling of parts. The Rockwell C and tensile strength of an unknown part could then be determined by measuring the frequency of a resonant mode and finding the corresponding hardness value from the graph. The entire process could be easily incorporated into an RUS system.

 

Summary
Let us summarize the process of selecting a peak for analysis. This discussion will be confined to the measurement of tensile strength; the same approach, however, applies to the hardness determination. The process should begin with numerous samples; (ideally, a statistical set of 20 to 50). We scan each sample over a very broad range, say 40 to 400 kHz, and archive the data. The masses and dimensions of the parts are also recorded
to allow the variances to be analyzed later. These samples are then submitted to a testing laboratory to be measured for the appropriate physical characteristic, in this case tensile strength. We then select a
particular resonance and plot its frequency for each sample against that sample's determined tensile value, and note the correlation. A resonance that is suited for hardness testing will show a good correlation of frequency vs. hardness between many samples. The plotted points will fit well to some mathematical function, such as linear, quadratic, etc. We generally use singlets to provide accuracy and remove some ambiguity, but the use of doublets can provide additional sorting controls. We then select frequencies that are relatively insensitive to small length variations. In this case, we believe that the resonances that exhibit significant shifts are most likely due to compressional modes.

From these identified correlations, we can either employ a pass/fail test (in other words, is the resonance located at the proper frequency or not?) or establish a reference table that displays a value for the measurement; for example a mode at 174.15 kHz corresponds to a tensile value of 1085 MPa (157.5 klb/in.2) for this part, whose geometry and material are fixed. Once the set of values for the part has been established, a frequency measurement will yield the desired data. This is a real measurement, but can also be employed as a relative comparison if one observes patterns from different batches of parts and skips step 2.

The same process is used for hardness determinations. To restate the process:

• Collect and archive broadband RUS spectra.
• Perform tensile and hardness determinations on all samples.
• Correlate resonances with physical measurements.
• Establish pass/fail criteria or reference table.

The composition of the input materials and other variables must be held constant in order for Step 3 to maintain validity.

 

References
Rhodes, G.W. and F.A Willis, Method to Employ RUS to Measure Tensile Strength and Hardness, US Patent Application, February 11, 1998.

Rhodes, G.W. Dynamic Ultrasonic Resonant Testing, US Patent Application, June 23, 1997.

Migliori, A., et al., Report on the Measurement of Elastic Properties of 51XX Series Steels for the Heat Treatment Distortion Project, Los Alamos National Laboratory, LA-UR-97-1954 (1997).

American Metallurgical Services, 80 E. Claybourne Ave., Salt Lake City, UT 84115.

Collaborative Testing Services, Inc., 340 Herndon Parkway, Herndon, VA 20170.

 

* Dynamic Resonance Systems, Inc., 225 Lane 13, Powell, WY 82435; (505) 897-7147; fax (505) 898-3419; e-mail grhodes@NDTest.com.

Copyright © 1998  by the American Society for Nondestructive Testing, Inc. All rights reserved.

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