645

Scripta Materialia, Vol. 38, No. 4, PP. 645-651, 1998

Elsevier Science Ltd.

Copyright © 1998 Acta Metallurgica Inc.

INDENTATION-ENERGY-TO-FRACTURE (IEF) PARAMETER

FOR CHARACTERIZATION OF DBTT IN CARBON STEELS

USING NONDESTRUCTIVE AUTOMATED BALL

INDENTATION (ABI) TECHNIQUE

Fahmy M. Haggag1 ,Thak-Sang Byun2 , J. H. Hong2 , P. Q. Miraglia3 , and K. Linga Murty3

1Advanced Technology Corporation, 661 Emory Valley Road, Suite A, Oak Ridge TN 378302Korea Atomic Energy Research Institute, Yusong P. O. Box 105, Taejon 305-600, S. Korea

3North Carolina State University, Raleigh NC 27695-7909

(Received August 29, 1997)

(Accepted November 7, 1997)

Integrity of structures in various technologies depend on the fracture behaviors of materials, and ingeneral the fracture characteristics of structural materials are evaluated using destructive tests, such asCharpy, fracture toughness, and other such techniques. However, for evaluating the material condition in-service, it is often not feasible or practical to cut samples from operating structures and nondestructivetechniques are employed to determine the mechanical properties from which fracture behaviors areconjectured. Although many techniques, such as magnetic strength, Berkhausen noise, hardness, etc., wereused in correlating the respective properties with fracture energy measured from Charpy or fracturetoughness tests, these methodologies are essentially empirical with no real underlying technicaljustification. Recent advances using Automated Ball Indentation (ABI) technique clearly demonstrated thefeasibility of obtaining, with excellent accuracy, the true stress-strain behaviors of ferritic steels and theirweldments as well as heat-affected-zones (HAZs), stainless steels as well as electronic solders (SnSb,AgSn, etc.). We demonstrate here the application of the ABI technique in evaluating the energy to fracturein terms of a new parameter named Indentation Energy to Fracture (IEF). The new IEF parameter clearlydepicts the DBTT (ductile-to-brittle-transition-temperature).

ABI Technique

The Automated Ball Indentation (ABI) has been demonstrated to measure the stress-strain behaviorsof many structural metals such as ferritic steels, stainless steels, aluminum alloys, electronic solders, etc. (1)While the idea of ball indentation is not new, (2) the uniqueness of ABI lies in the fact that this techniquedoes not require post measurement of the diameter of indentation using elaborate profilometry, opticalinterferometry, etc., which render the traditional methodology unsuitable for on-line monitoring of themechanical properties of structures in-service. Based on this principle, a portable/in-situ Stress-StrainMicroprobe™ (SSM) system was developed by Advanced Technology Corporation (ATC) to test minimalmaterial and to determine several mechanical properties (e.g. yield strength, flow properties, strain-hardeningexponent, strength coefficient) of metallic structures including their welds and heat-affected zones.(3) TheSSM system and test methods are based on well demonstrated and accepted physical and mathematicalrelationships which govern metal behavior under multiaxial indentation loading. (4)

Vol. 38, No. 4 AUTOMATED BALL INDENTATION 646

Figure 1. SSM Machine (left) and Close-Up (right) Showing the Indenter and LVDT

Stress-Strain Microprobe™ (SSM)

The microprobe system currently utilizes an electro-mechanically-driven indenter, high resolutionpenetration transducer and load cell, a personal computer (PC), a 16-bit data acquisition/control unit, anda copyrighted ABI software. Automation of the test, where a PC and a test controller were used ininnovative ways to control the test including real-time graphics and digital display of load-depth test data)as well as to analyze test data (including tabulated summary and macro-generated plots), made it accurateand highly reproducible. Figure 1 shows the overall view of the SSM along with a close-up of the indenterand the LVDT. The technique involves indenting a specimen with a tungsten carbide sphere (of appropriatediameter varying from 0.254 mm to 1.575 mm) while monitoring the load versus depth of penetration usingan on-line load cell and an LVDT respectively. The ball indenter is electro-mechanically-driven at aconstant speed, and progressive multiple loadings/partial-unloadings were performed, at single test location,to measure incremental strain and stress values. Unique PC software was developed to evaluate the trueplastic stress and true plastic strain using elastic and plastic analyses. These innovative techniqueseliminated the cumbersome post indentation measurement of the indentation diameter at specific loads.Recent extensions include single cycle tests with no intermediate partial unloadings. Such tests are requiredfor high strain-rate testing and continuous stress-strain measurement. In addition, low and high temperaturetest facility was recently developed, and we report here the ABI tests performed on a ferritic steel (A533B)from 116 K (-157º C) to 561 K (288º C) from which fracture characteristics are derived.

ABI tests were performed on a nuclear pressure vessel steel (A533B Class 1) using a 1.57 mm (62 mils)diameter ball at a constant indentation velocity, 0.015 mm/s with several intermediate unloadings from whichthe plastic indentation diameters were derived. Figure 2 depicts the room-temperature ABI plot ofindentation load (N) versus depth (mm) curve which illustrates approximate linear relation which is a resultof the opposing curvatures of the ball profile and the true stress versus strain behavior. These data areanalyzed using the ABI software to obtain true stress (F) and true plastic strain (,p),

(1)

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Figure 2. Load Versus Depth in an ABI Test

where dp and D are the plastic indentation diameter and the diameter of the indenter respectively. Thecorresponding flow stress is calculated using, (3,4)

. (2)

In Equation 2, F is the true indentation stress, P is indentation load and * is a parameter which depends onthe plastic zone developed underneath the indenter (i.e. deformation state of the indented material) and hasa value between 1.12 and 2.87"m; "m is known as the constraint factor which depends on the strain ratesensitivity and triaxial hardening, with a value of unity for strain-rate insensitive materials.(4) The valueof * increases with increasing the indentation load and is determined from the current indentation load andassociated depth.(4) The plastic indentation diameter dp, is given by (4),

(3)

Here, Ei and Es are the elastic moduli of the indenter and the specimen respectively. As we note here, theparameter dp appears in both the left and right hand terms and thus an iterative solution is used in the ABIsoftware to solve Equation 3. This equation is derived from Hertz’s classical equations describing the elasticdeformation of spherical surfaces. (2,4)

Figure 3 shows the ABI-measured true stress-strain curve along with that obtained using theconventional tensile test; to minimize specimen to specimen scatter, ABI tests were performed on theshoulder portions of the dog-bone type tensile specimens. An excellent correlation is noted between theABI-measured stress-strain curve and that obtained from the tensile test. Similar correlations were shownfor many different materials including welds and HAZs.(1,4) In this work, several ABI tests were performedat various temperatures on a broken Charpy bar of A533B steel, and representative true stress versus straincurves are shown in Fig. 4.

Vol. 38, No. 4 AUTOMATED BALL INDENTATION 648

Figure 3. Comparison of F— , Curves (ABI vs Tensile)

Indentation Energy to Fracture (IEF)

We have developed a new ABI energy parameter call Indentation Energy to Fracture (IEF). This IEFallows the nondestructive determination of fracture energy from ABI-measured true stress-strain curves upto the controlling micro-mechanical fracture mechanism of the critical fracture stress or the critical fracturestrain (depending on the test temperature). The indentation load versus depth curves from ABI tests atvarious temperatures were used together with the critical fracture stress model(5) to evaluate the temperaturevariation of fracture energy. The development of the IEF parameter is based on the following premise:

Figure 4. ABI-Measured F-, Curves at Various Temperatures

Vol. 38, No. 4 AUTOMATED BALL INDENTATION 649

(a) Fracture toughness can be interpreted as the deformation capability of the material under a concentratedstress field.

(b) Indentation with a small ball indenter generates concentrated stress (and strain) fields near and aheadof the contact of the indenter and the test surface, similar to concentrated stress fields ahead of a crackalbeit the indentation stress fields are compressive.

(c) Monotonic tensile versus compressive stress-strain curves are similar; true for the pressure vessel (PV)steels.

(d) The cleavage fracture stress in ferritic PV steels is nearly temperature insensitive (the elastic modulusis relatively constant over the brittle and transition regions).

(e) The deformation energy due to the ball indentation up to a limit stress level is related to the Charpyenergy or fracture toughness; the limit stress in ABI tests is proportional to the critical fracture stressin tensile and fracture toughness tests.

The IEF is thus defined as,

, where, (4)

In the above equation, Pm is the mean indentation contact pressure, P is the indentation load, h is theindentation depth, hf is the indentation depth up to the cleavage fracture stress, and d is the chordal diameterof the indentation. As to be noted in Figure 2, the indentation load versus depth curves are essentially linearin which case, the slope (S) of the curves can be used to calculate IEF,

P = Sh, and (5)

where D is the indenter diameter, so that,

(6)

where ln is the natural logarithm.The ABI-measured true stress-strain curves at various temperatures are superimposed with a

representative true stress at fracture of 800 MPa (Figure 4). The stress index of 800 MPa is approximatelyhalf of the measured critical fracture stress.(5) This assumed smaller value is required to account for thedifferent tri-axial stress state underneath the ball indenter as compared to that near a sharp crack tip.Additional analytical and numerical work is in progress to refine and verify this assumption. However, itis clear from Figure 4 that the area under the stress-strain curves up to the intersection of therepresentative/index stress (at the hypothetical indentation fracture limit) decreases with lower testtemperatures, as expected from Charpy impact and fracture toughness tests. The indentation depth at fracture(hf), is determined by interpolation or extrapolation (depending on the test temperature) from the plot of truestress versus indentation depth as shown in Figure 5a for 116 K (-157º C). The Slope, S, of the indentationload versus depth curves (such as in Figure 2) decreases while IEF increases with increasing temperature.Figure 5b shows IEF versus indentation depth for an ABI test at -157º C.

From each ABI test results at a specific test temperature, the critical indentation depth (hf) is determinedusing the stress-index as shown in the example of Fig. 5a. The slope of the ABI-measured load-depth curve(S) is used with the corresponding hf and the indenter diameter to calculate the IEF for this test temperatureaccording to Equation 6 (Figure 5b is a graphical illustration of this second step). The temperature variationof the IEF (calculated using the two steps illustrated earlier for each ABI test temperature) is shown in Figure

Vol. 38, No. 4 AUTOMATED BALL INDENTATION 650

Figure 5a. True Stress vs Indentation Depth

Figure 5b. IEF (Eq. 6) versus Indentation Depth

6 which clearly illustrates that this newly developed ABI energy parameter delineates the brittle to ductiletransition. The data at and beyond room temperature are shown with dashed line to emphasize the fact thatin the upper shelf regime, the critical fracture stress model is not valid,(5) and one needs to incorporate acritical fracture strain criterion.(4,5) A correlation of the IEF results with the Charpy impact data(6),obtained on the same material at the same test temperatures, attests to the validity of utilizing the IEF indetermining the ductile-to-brittle transition temperature(DBTT) for carbon steels (BCC materials); inparticular the effects of cold-work, irradiation, etc.

The results are now being extended to other steels as well as weldments and heat-affected zones. Figure7 compiles the IEF versus temperature results recently obtained (7) on a HAZ of A533B steel but obtainedusing smaller diameter (0.76 mm/ 30 mils) ball and clearly illustrates the transition from brittle to ductilefracture. The absolute values for IEF here are relatively smaller due to the reduced indentation volume. Theunique localized capability of the ABI/IEF method is clearly demonstrated for gradients in welds and theirHAZs. The validity of application of the IEF concept to other BCC metallic materials needs to beinvestigated.

Figure 6. Temperature Variation of IEF for A533B Steel

Vol. 38, No. 4 AUTOMATED BALL INDENTATION 651

Figure 7. Temperature Variation of IEF for HAZ (ORNL 72W Weld)

Summary and Conclusion

The ABI technique is an excellent nondestructive tool for characterizing the key mechanical propertiesof metallic materials. In addition, this technique is shown to yield a fracture parameter, IEF, which can beused to monitor the DBTT of carbon steels (BCC materials). Further work is needed to incorporate thecritical fracture strain model for a quantitative description of the ductile upper shelf regime. In addition, weare developing an IEF-index to replace the commonly used 41-J Charpy impact energy index so that ABItechnique and its IEF-concept can stand alone and give information nondestructively on the fracturecharacteristics and the DBTT of carbon steels.

REFERENCES

1. F. M. Haggag and K. L. Murty, “A Novel Stress-Strain Microprobe for Nondestructive Evaluation ofMechanical Properties of Materials,” in Nondestructive Evaluation and Material Properties III, ed. P.K. Liaw et al, pp. 101-106, TMS, Warrendale, PA (1997).

2. D. Tabor, The Hardness of Metals, Oxford University Press, New York (1951).3. F. M. Haggag, Field Indentation Microprobe for Structural Integrity Evaluation, U.S. Patent No.

4,852,397, August 1, 1989.4. F. M. Haggag, in Small Specimen Test Techniques Applied to Nuclear Reactor Thermal Annealing and

Plant Life Extension, ASTM STP 1204, W. R. Corwin, F. M. Haggag, and W. L. Server, ed., pp. 27-44,American Society for Testing and Materials, Philadelphia (1993).

5. R. O. Ritchie, W. L. Server, and R. A. Wullaert, Met. Trans., Vol. 10A, pp. 1557-1570, (1979).6. W. L. Server and W. Oldfield, Nuclear Pressure Vessel Steel Data Base, EPRI Report NP-933 (1978).7. P. Q. Miraglia, MS Thesis, North Carolina State University (1997).