Microbeam analysis of hydrogen near a crack tip in titanium

NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 261 (2007) 477–482 www.elsevier.com/locate/nimb

Microbeam analysis of hydrogen near a crack tip in titanium B. Lovelace b

a,*

, H. Bakhru b, A.W. Haberl a, R.E. Benenson

b,1

a Ion Beam Laboratory, University at Albany, 1400 Washington Avenue, Albany, NY 12222, USA College of Nanoscale Science and Engineering, University at Albany, 1400 Washington Avenue, Albany, NY 12203, USA

Available online 30 March 2007

Abstract Microbeam transmission elastic recoil detection (ERD) was used to analyze microscopic hydrogen distributions near a crack tip in Ti foil loaded with an initial atomic hydrogen concentration of 3.0% relative to Ti. A 5.8 MeV He ion beam focused down to the order of 10 lm was scanned in a 500 lm line perpendicular to the crack and approximately 20 lm ahead of the crack tip. ERD line maps were made for a series of increasing stresses which were applied by uniaxial tension perpendicular to the crack. The crack opening displacement (COD) for each stress load was measured from an ion-beam-induced secondary electron emission (SEM) spectrograph of the crack opening. The technique was used to characterize the fracture mechanical properties of a-Ti hydride and demonstrates the use of microbeam analysis for the study of binary hydrogen metal systems. Ó 2007 Elsevier B.V. All rights reserved. PACS: 39.10.+j; 39.25.+k; 46.80.+j; 62.20; 81.40; 81.70.Bt; 81.70.Eq; 82.80.Yc; 83.60.a Keywords: Hydrogen in metals; Hydrogen cracking; Microbeam ERD; Microbeam fracture analysis; Titanium hydride; Binary metal hydrogen systems; Environmental cracking

1. Introduction Microbeam analysis [1] is an effective technique for the study of microscopic fracture mechanics of binary metal hydrogen systems. Microbeam elastic recoil detection (ERD) [2] and secondary electron emission (SEM) [3] are essential instruments for the characterization of the mechanical properties of metal foils as a function of the spatial hydrogen distribution. In this work, the dynamic hydrogen response to stress and strain near the crack tip was measured by scanning the microbeam over a region of interest and recording ERD positional data. The applied stress was uniaxial and perpendicular to the initial crack opening. For each discrete stress load, an ERD line scan mapped the hydrogen distribution along a line perpendicular to the crack and about * Corresponding author. Address: P.O. Box 1635, Latham, NY 12110, USA. Tel.: +1 518 221 0352; fax: +1 518 235 4492. E-mail address: [email protected] (B. Lovelace). 1 Professor Emeritus, Physics Department, University at Albany.

0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.03.035

20 lm ahead of the crack tip. The strain was measured using the SEM. The SEM can produce electron intensity images of the crack opening by scanning the ion beam over the crack opening. The crack opening displacement (COD), normalized by the initial crack width, is the approximate strain near the crack tip. The COD is the difference of the strained crack width from the unstrained width. Important fracture mechanical properties [4–6] such as the elastic limit, plastic limit, critical stress for fracture, work energy per unit volume to extend the crack, and energy release rate all can be inferred from a graph of stress versus strain (load–displacement curve). The elastic limit is the maximum stress before mechanical yielding occurs. The plastic limit is the maximum stress before crack extension, and the critical stress is the final stress applied before crack extension. The work energy per unit volume expended to extend a given crack is the area under the load–displacement curve. The energy release rate is the energy release per crack extension and can be calculated from the difference in work energy expended to extend two cracks of different initial lengths.

B. Lovelace et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 477–482

The following experiment demonstrates the microbeam technique to resolve a quantitative correlation between hydrogen behavior and fracture mechanical properties in a-Ti hydride. Microbeam ERD analysis was used to show that the hydrogen is displaced in the plastic region near the crack tip during yielding. In addition, the microbeam SEM was utilized to obtain load–displacement curves which were used to measure the energy release rate for crack extension and showed that the mechanism for fracture is ductile [4–6]. 2. Experiment In this experiment, the energy release rate was determined for crack propagation for a pair of a-Ti foils, 25 lm thick. Each foil was loaded with an initial atomic hydrogen concentration of 3.0% relative to Ti. The energy release rate was determined from the load–displacement curves acquired by measuring the strain for a sequence of increasing uniaxial stresses applied perpendicular to the crack axis. The load–displacement curves were determined from COD measurements taken for each stress. The stresses were applied using a calibrated spring tensioner, schematically shown in Fig. 1. The initial crack lengths were controlled by notching each foil on one edge. The ratios of crack length to sample width were 0.31 and 0.25. The COD for each stress was measured using a SEM spectrograph of the crack opening. Fig. 2(a) shows a two dimensional SEM spectrograph of a crack under tension near the plastic limit. The crack opening was measured along the cross sectional line marked B, and the cross section is shown in Fig. 2(b). The measurements were systematically repeated for both crack specimens over the entire strain range which corresponds to a stress domain from 0.0 to 26.0 lkg/lm2. Fig. 3 shows the SEM’s of a crack opening for a sequence of stresses over the entire strain range. The dynamic hydrogen distribution was observed for the entire strain range by taking an ERD line scan for each discrete stress load. A 5.8 MeV He2+ ion beam focused down to the order of 10 lm was scanned along a 440 lm line perpendicular to the crack axis and approximately 20 lm in front of the crack tip, as shown by line A of Fig. 2(a). Lateral hydrogen profiles were deduced from

crack width

GRIP

Ti FOIL

crack length

sample width

Tension

GRIP

sample length

Tension

notch (initial crack) Fig. 1. Schematic of notched Ti foil under uniaxial tensile stress with fixed grips.

Fig. 2(a). Secondary electron emission (SEM) spectrograph of crack opening in a-Ti foil. The view shown gives a three dimensional perspective. Line A is the microbeam line scan across the crack path for RBS and ERD analysis. Line B is the cross section of the crack opening where the COD is measured.

SECONDARY ELECTRON INTENSITY (ARBITRARY UNITS)

478

0

LINE DISPLACEMENT (MICRONS) 100 200 300 400

500

1000 SEM INTENSITY 10PT AVERAGE

800 600 400

CRACK OPENING 80 MICRONS

200 0

0

51

102 153 PIXEL NUMBER

204

255

Fig. 2(b). Cross section of the crack opening indicated by line B of (a). The crack opening is about 80 lm.

the ERD line graphs shown in Fig. 3, and the hydrogen depth profile along the scan line was determined from the ERD energy spectra similar to that shown in Fig. 4. Four line graphs were acquired for each line scan shown in Fig. 3. Each line graph corresponds to the counts in a specific energy window of the ERD or Rutherford backscattering spectrum (RBS). Each line graph represents the counts per pixel along the line scan in the specific energy window. The energy windows, shown in Fig. 4, include the entire ERD spectrum, the RBS signal of the Ti surface, the high energy ERD counts, and the low energy ERD counts. All of the line graphs were normalized against the average yield per pixel of the RBS line graph. The RBS line graph is a measure of the distribution of incident ions along the scan line, and it also indicates discontinuity of the Ti surface when the crack extends. The high energy ERD counts represent the hydrogen concentration near the surface to a depth of about 2.2 lm, and the low energy ERD counts represent the hydrogen concentration in the bulk from about 2.2 lm to the maximum probing depth for the ERD spectrum, which is approximately 5.7 lm. A 12.5 lm thick Ni stopping foil was placed over the detector to prevent incident He from entering the detector and distorting the ERD energy spectrum. Incident He can sometimes penetrate the sample under plastic strain

B. Lovelace et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 477–482

SEM

479

LINE SCAN 500 μm

15

a. unstrained

Pixel Number 108

2

/μm

ss

80

1.0

Kg 0μ

e str

240

crack axis RBS (Ti surface) ERD (Full Spect) ERD (Low energy) ERD (High energy)

. =0

7.4

H clusters for markers

5.6 0.0

b. elastic

0 80

2

es

str

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2

/μm

.3

= ess

15

g μK

str

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2

m

g/μ

K 9μ

2.

s res

=2

st

2

e. critical

m g/μ

.5

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24

f. extended

2

m g/μ

ess

=

0.0

0 80

1.0

12.8

11.7

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18.4 4.0 0.0

0

31.9 1.0

40

μK

str

.5 26

9.6 6.6 Absolute Yield (counts/pixel)

.2 μ

9 s=

1.0

Relative Yield (counts/average RBS counts/pixel)

/μm Kg

14.7

0.0

0

1.0

8

μK

str

0.0

0

30

Beam Displacement (μm)

470

Fig. 3. SEM’s (left) for sequential key stress points of a crack opening in Ti with an initial crack length to sample width ratio of 0.31. The load– displacement curve is shown in Fig. 5. Corresponding line scans (right) show the peak atomic hydrogen concentration in percent relative to Ti for the ERD peaks adjacent to the crack axis. The crack axis is the line which bisects the initial crack along its length.

through the crack extension, and occasionally, the beam can overlap the crack opening and scatter into the detector. The stopping foil protects the detector from being destroyed from potential irradiation by the direct beam. 3. Sample preparation Pre-notched samples were cut from 99.99% pure Ti rolled foil, 25 lm in thickness. The samples were notched by shearing one edge of the foil with a single cut such that the notch was perpendicular to the edge as shown in Fig. 1. Each sample was cleaned in 20% HNO3, rinsed with H2O, and dried with ethanol. To remove oxides, residual hydrogen and other contaminants, each sample was resistively outgassed in high vacuum (<104 Torr) in temperature

steps of 200 °C up to 800 °C. The time duration of each annealing step was 3 min. The final annealing was at 856 °C for 3 min to re-crystallize the crack tip and generate a uniform a-Ti texture. The foils were then cathodically loaded with hydrogen in 1.0 N HCl + 0.5 N NaCl at 250 mA and 3.67 VDC for 20 min, giving a net charge of approximately 100 C/cm2. The foils were then annealed in 20 min cycles from 280 °C to 350 °C for 24 h in high vacuum (<104 Torr) to diffuse hydrogen into the bulk and form a uniform aTi hydride solution. The initial atomic hydrogen concentration was approximately 3.0% relative to Ti. The hydrogenated samples were trimmed to the final dimensions of approximately 0.4 cm in width and 2.0 cm in length.

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B. Lovelace et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 477–482 Channel Number 100

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50 ERD Surface Window Absolute Yield (counts/channel)

Absolute Yield (counts/channel)

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Channel Number 350 400 450

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0.5 3.5 4.0 4.5 5.0 RBS Energy (MeV)

2.0

2.5

Normalized Yield (counts/nC)

0

0.0 3.0

ERD Energy (MeV)

Fig. 4. ERD and RBS energy spectra for the line scan in Fig. 3(c). The solid ERD line is a theoretical simulation spectrum for a uniform depth profile of 5.0% H. The depth profile used in simulation represents the average hydrogen concentration relative to Ti. The counts in each window correspond to the counts in each line graph shown in Fig. 3(c). The spectra were smoothed using the convoluted average over a 4 channel window. The incident beam was 5.8 MeV He2+, and the total incident charge was 32.4 nC. The misfit counts between 1.5 MeV and 2.0 MeV occurred because of reduced thickness in the Ti foil caused by plastic strain at the 190 pixel mark on the line scan.

4. Microbeam analysis The line graphs of Fig. 3 can be analyzed to obtain quantitative lateral hydrogen profiles. To improve counting statistics, the line graphs were smoothed by computing the convoluted average over a 20 pixel window. Since the beam size was of the order of 5 pixels (10 lm), the resulting lateral resolution of the line graph is 14.1 lm while the lateral sensitivity is increased by a factor of 20. The lower detection limit is 0.1% H/pixel/nC. The sacrifice of lateral resolution for higher count rates is justified because the separation of features observed in the plastic zone is typically greater than 14 lm, and the precision of the COD measurement depends on the pixel separation of the scan, which is 2.0 lm. It is imprudent to attempt to analyze an ERD spectrum for each pixel in the line scan in order to obtain a depth profile along the scan line; this would require up to 255 ERD spectra. Alternatively, the hydrogen concentration along the scan line can be determined from the ERD line data and the ERD energy spectrum. The ERD energy spectrum in Fig. 4 represents the sum of ERD energy spectra for each pixel in the line scan path of Fig. 3(c). The ERD simulation shown in Fig. 4 assumes an average uniform hydrogen profile. The average hydrogen concentration over an arbitrary line segment of the scan path is P 0 1 Y ðxÞ 0 Y C ¼ 1 Px 0 C; ð1Þ x Q ðxÞ Q where C is the overall average hydrogen concentration, Y is the total ERD yield in the line scan, Y 0 is the yield per pixel, Q is the total number of incident ions, Q 0 is the number of incident ions per pixel, and x is the pixel number. The sums include all pixels in the line segment of interest. A similar

analysis can be made for ERD line graphs of a specific energy window, provided that the hydrogen depth profile is known for that window. For example, for the 2 peaks adjacent to the crack axis in the line graph of Fig. 3(c), the maximum atomic hydrogen concentrations are 12.8% for the peak centered on pixel number 93 and 11.7% for the peak centered on pixel number 121. The background hydrogen concentration is 3.0%. The line graph corresponding to the entire ERD spectrum was used to compute the sums in Eq. (1), and C was 5.0%. C represents the average uniform hydrogen concentration computed from the ERD energy spectrum of Fig. 4. Q was determined from the RBS spectrum of the Ti surface. 5. ERD analysis An overall average hydrogen depth profile was determined by computing a simulated ERD spectrum using the computer program, ITSPECT [7]. The simulation program accepts a set of ion beam and composition parameters and generates a theoretical ERD spectrum for a hypothetical hydrogen profile [8]. The hydrogen profile is adjusted until the theoretical simulation fits the experimental spectrum. For example, a uniform depth profile of 5.0% H relative to Ti was used to generate the ERD simulation of Fig. 4. In Fig. 4, the misfit between the simulation and the experimental data in the energy range of 1.5–2.0 MeV is due to a reduced thickness in the Ti foil near the 190 pixel mark on the line scan. The non-uniform thickness is due to localized yielding of the metal during plastic strain. Nonuniform foil thickness complicates linear depth profiling. For accurate profiling, these regions should be analyzed discretely, but in this case the analysis error was minor. The number of incident He ions must be known to accurately determine the hydrogen concentration from the ERD spectrum. The number of incident He ions Q was determined by RBS analysis [9] of the Ti surface. If Yexp is the RBS yield from the Ti surface, then Q in Eq. (1) is given by Q¼

Y exp ; Y rbs

ð2Þ

where Yrbs is the theoretical RBS yield per incident ion. 6. Results The load–displacement curves for two different crack lengths are shown in Fig. 5. In general, the shape of each curve is characteristic of ductile fracture [5]. The average values for the elastic limit, plastic limit, critical stress and tensile stress,2 accurate to within about 1.0 lkg/lm2, are 2 The tensile stress is the applied stress where crack extension was observed.

B. Lovelace et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 477–482

25.0

1.50

20.0

10.0

0.31 0.25

0.50 0.00

15.0

Crack Length/Width (mm/mm)

1.00

0

1

2

3

(Kg/micron2 x10-6)

Stress (arbitrary units)

30.0 2.00

5.0 4

5

6

0.0

Strain (microns/micron)

Fig. 5. Load–displacement curves for two different relative crack lengths in Ti. The extension energy release rate, calculated from the area between the two curves, is 12.3 g lm/lm3/% extension.

15.3, 21.4, 23.8 and 25.8 lkg/lm2, respectively. Critical fracture3 was not observed at the tensile stress, although some samples exhibited delayed critical fracture. The ERD line scans of Fig. 3 show the correlation between the key stress points and the hydrogen distribution across the near crack tip region. The ratio of crack length to sample width for the specimen was 0.31. The crack axis intersects the line scan near pixel number 108. The two ERD peaks near pixel numbers 190 and 226 are fixed hydrogen clusters which conveniently serve as reference markers demonstrating the alignment of subsequent line scans.4 The sequence of line scans in Fig. 3 shows that most of the hydrogen activity occurred in the line segment between pixel numbers 50 and 150. In this region, Fig. 3(a) shows a random initial hydrogen distribution for the unstrained sample. When tension was applied, the hydrogen distribution was defined by a small build up on both sides of the crack axis as shown in Fig. 3(b). After the initial tension was applied, the hydrogen distribution remained virtually unchanged during elastic strain until the applied stress reached the elastic limit as shown in Fig. 3(c). Fig. 3(c) shows hydrogen accumulation in two plastic regions on each side of the crack axis. The peak hydrogen concentration in the plastic regions randomly varied from about 9% to 13% relative H during subsequent plastic strain. At the plastic limit, Fig. 3(d) shows that the hydrogen concentration on the extension side of the crack axis was reduced to 4.0%, and the hydrogen concentration in the plastic region of the non-extension side increased to about 18.4%. At critical stress, Fig. 3(e) shows that the hydrogen concentration in both plastic regions increased dramatically to 14.7% and 31.9% for the extension and non-extension sides, respectively.5 Fig. 3(f) shows the hydrogen on both edges of the 3 Critical fracture is unstable crack propagation across the entire width of the sample. 4 Hydrogen clusters of this type were identified with bundles of extruding slip bands. 5 Critical stress is an unstable condition and is the final stress before crack extension.

481

extended crack. The RBS line graph in Fig. 3(f) clearly shows the separation of the two edges. The line scan in Fig. 3(f) is cut off because the sample critically fractured while the line scan was in progress, and the subsequent data of the displaced edge was removed from the line scan. Data is shown only for the intact sample.6 The high energy ERD line graphs of Fig. 3 represent the lateral hydrogen distribution near the surface, and the low energy ERD line graphs represent the hydrogen in the bulk. The line graphs show the same relative hydrogen activity for both the bulk and the near surface regions indicating no net out-of-plane hydrogen displacement. The purely lateral hydrogen displacement is likely due to the low out-of-plane plastic strain of the foil. The SEM of Fig. 3(f) shows the crack extending to one side of the crack axis. The angle of extension was measured at 36° relative to the crack axis. A shear displacement is clearly shown in Fig. 3(d)–(f) by the dark line extending across the crack axis and in front of the crack tip. The line, indicated by arrows in Fig. 3(d)–(f), was caused by beam damage from the line scans. In Fig. 3(f), the line is displaced in a shear along the crack extension axis, and the non-extension side of the line is displaced toward the crack opening. The shear displacement in Fig. 3(f) is characteristically related to the angle of crack extension and the shear stress field near the crack tip [5,6]. The energy release rate for crack extension, calculated from the area between the two curves of Fig. 5, is 12.3 g lm/lm3/% extension. The preliminary results from previous trials suggest that the energy release rate approaches 2.0 g lm/lm3/% extension as the hydrogen concentration approaches 0%. The dynamic response of hydrogen to yielding suggests that part of the energy expended for fracture is used to activate hydrogen mobility. Therefore, one could hypothesize that the energy release rate should increase with an increase in initial hydrogen concentration, and the fracture mechanism should exhibit less ductile character. A more quantitative interpretation could be achieved by systematically varying the initial hydrogen concentration and analyzing the load–displacement curves. 7. Conclusion From this work, some general inferences can be made about the hydrogen dynamics near crack tips in a-Ti hydrogen systems. The hydrogen activity near the crack tip shown in Fig. 3 is clearly a response to plastic strain, and the fracture mechanism for crack extension in the aTi hydrogen system is ductile. The random hydrogen peaks near the crack tip of the unstrained sample in Fig. 3(a) are likely TiH complexes made of hydrogen trapped in residual defects. The initial elastic strain probably causes these 6

The absolute hydrogen concentration can not be determined for Fig. 3(f) because the ERD energy spectrum was corrupted when the sample parted.

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B. Lovelace et al. / Nucl. Instr. and Meth. in Phys. Res. B 261 (2007) 477–482

complexes to seek positions of lowest energy which defines the hydrogen distribution during subsequent elastic strain as shown in Fig. 3(b). There is relatively little hydrogen activity under elastic strain until the elastic limit is reached. This suggests that mobile hydrogen is in positional equilibrium while hydrogen trapped in TiH complexes remains fixed. The hydrogen accumulation in the plastic regions under plastic strain in Fig. 3(c) is likely due to mobile hydrogen bonding to Ti in new plastically formed defects to form TiH complexes. Hydrogen displaced on the extension side of the crack axis at the plastic limit in Fig. 3(d) is likely due to the ductile activity of Ti where the hydrogen migrates as a TiH complex. One could hypothesize that in ductile fracture, vacancies in the form of dislocations migrate toward the crack opening to extend the crack as they are displaced by Ti atoms and TiH complexes. At the critical stress in Fig. 3(e), the plastic region is unstable, and the surge of hydrogen in this region is likely due to the formation of TiH in a surge of newly created defects. The techniques for obtaining quantitative load–displacement curves and measuring the dynamic response of hydrogen to strain and stress were effective developments in the metrology of hydrogen in binary metal-hydrogen systems. The microbeam SEM is adequate for measuring strain as long as the COD ‘s can be resolved within the precision

of the pixel separation of the scan. The experimental data of Figs. 3 and 4 demonstrate the capabilities of microbeam ERD analysis as an essential instrument for quantitative hydrogen microscopy in metal foils. In conclusion, microbeam ERD is clearly an effective technique for microscopic fracture mechanical analysis of hydrogen behavior in metals. References [1] B.L. Doyle, Nucl. Inst. and Meth. B 15 (1986) 658. [2] J. Tirira, Y. Serruys, P. Trocellier, Forward Recoil Spectrometry: Applications to Hydrogen Determination in Solids, Plenum Press, 1996. [3] W.G. Morris, H. Bakhru, A.W. Haberl, Nucl. Instr. and Meth. B 15 (1986) 661. [4] P.C. Paris, G.C. Sih, Fracture Toughness Testing and its Applications, ASTM, 1964, p. 30. [5] I. Lemay, Principles of Mechanical Metallurgy, Elsevier, North Holland, 1981. [6] D. Broek, Elementary Engineering Fracture Mechanics, Martinus Nijhoff, 1986. [7] B. Lovelace, H. Bakhru, A.W. Haberl, R.E. Benenson, Nucl. Instr. and Meth. B, these Proceedings, doi:10.1016/j.nimb.2007.03.038. [8] R.E. Benenson, L.S. Wielunski, W.A. Lanford, Nucl. Instr. and Meth. B 15 (1986) 453. [9] B. Lovelace, H. Bakhru, A.W. Haberl, R.E. Benenson, Nucl. Instr. and Meth. B, these Proceedings, doi:10.1016/j.nimb.2007.03.036.