Review of Positron Lifetime Studies of Lattice Defects Formed during Tensile Deformation in a Hydrogen Environment

Abstract

The lattice defects, especially vacancies, formed during tensile deformation in a hydrogen environment have been evaluated by positron annihilation lifetime spectroscopy (PALS). The results from several such evaluations in previous studies in hydrogen-charged iron, steels, and Ni-based alloys are reviewed in this study with reference to hydrogen embrittlement models. A strong tendency to increase the positron lifetime for the vacancy cluster component, that is, the larger the vacancy cluster size, the lower the fracture strains, was found in many PALS studies on tensile-deformed metals. This suggests that plastic strain localization, a characteristic feature of hydrogen embrittlement, is consistent with hydrogen-enhanced vacancy clustering during plastic deformation. Early studies suggested that hydrogen precharging would result in a significant increase in the vacancy density, as inferred from the hydrogen content obtained from thermal desorption analysis (TDA). However, recent PALS studies have been negative, as no significant increase in vacancy density were observed.

1. Introduction

The degradation of mechanical properties, which include reduced ductility and fracture toughness, is caused by hydrogen dissolved in metals, as is typical for high-strength steels. Elucidation of the mechanism of degradation is required to ensure the safe use of various metals in a hydrogen environment. The hydrogen enhanced decohesion model (HEDE)^1,2,3,4,5) and hydrogen enhanced localized plasticity model (HELP)^6,7,8,9,10) are two of the most established hydrogen-assisted fracture models. The HEDE model focuses on the interstitial hydrogen and lowers the cohesive strength by dilatation of the atomic lattice, thus lowering the fracture energy. By contrast, the HELP model focuses on enhancing the mobility of the dislocations through an elastic shielding effect in preferred crystallographic planes at the crack tip, causing locally reduced shear strength. More recently, the hydrogen-enhanced strain induced vacancy (HESIV) theory^11,12) has been proposed. This focuses on promoting the formation of vacancies by hydrogen.

Fukai et al. reported the formation of superabundant vacancies under high-pressure hydrogen in nikel,^13,14) palladium^13,15,16) and iron.¹⁷⁾ They also investigated the vacancy densities by in situ X-ray diffraction of palladium hydride at a hydrogen pressure of 5 GPa. The vacancy density in the palladium metal was estimated to be 18 ± 3 at%.¹⁵⁾ They concluded that the vacancy formation energy decreased, while the vacancy density significantly increased under a hydrogen environment.

In their statistical mechanics study of vacancy-lattice interactions, McClellan et al.^18,19,20) suggested that the presence of interstitials can result in the formation of higher metal vacancy densities. Gavriljuk et al.²¹⁾ performed transmission electron microscopy (TEM) observations on austenitic steel samples that were quenched from 1423 K, hydrogen-charged, and stored at room temperature. They observed high-density dislocation loops, presumably formed by the effects of “excessive” vacancy formation caused by hydrogen.

Previous thermal desorption analysis (TDA) studies have indicated that the formation behavior of the lattice defects, especially vacancies, during plastic deformation is affected by hydrogen. During the TDA, the hydrogen desorption rate is measured by heating a sample containing hydrogen at a constant rate to obtain a thermal desorption curve, that is, the relationship between the hydrogen desorption rate and sample temperature. From the hydrogen thermal desorption curve, the existing states of hydrogen in the sample (i.e., the type of defects that trap hydrogen and amount of hydrogen trapped in the defect) could be estimated.

The thermal desorption curve obtained from the TDA of tritium in tensile-strained ferritic steels performed by Nagumo et al.²²⁾ has a peak desorption rate around 423 K, with the desorption complete at 473 K. Since the recovery temperature of the vacancy clusters in iron determined using the positron annihilation lifetime spectroscopy (PALS) is 473 K,²³⁾ it was concluded that the tritium was trapped in the vacancies. The good correlation of the constraint factor for slip extension with the amount of tritium desorbed indicates the important effect of vacancies on the fracture toughness of steel in the ductile-to-brittle transition region. Takai et al. performed a TDA of hydrogen on deformed austenitic and pearlite steels after hydrogen charging.²⁴⁾ Their hydrogen desorption contents were higher than those in non-precharged samples and were reduced by annealing at 473 K, suggesting that hydrogen was trapped in the vacancies. These results suggest that superabundant vacancy formation occurs during the plastic deformation process in a hydrogen environment. These TDA results suggest that the main trapping sites of hydrogen are vacancies, which are significantly related to hydrogen embrittlement failures. However, it is currently difficult to accurately quantify the vacancy density and vacancy cluster size using TDA owing to the lack of sufficient information on the hydrogen trapping capacity of vacancies.

As described above, the superabundant vacancy formation in presence of hydrogen is theoretically suggested and had been investigated by in situ X-ray diffraction and TDA. This needs to be confirmed using a method that can directly detect and quantify vacancies in metals.

PALS is the most effective method that can detect open-volume defects, such as dislocations and vacancies and is the only method that exhibits sub-ppm sensitivity for vacancy defects. This method can identify the defect type and determine the defect density.²⁵⁾ PALS has been used to investigate the interaction between hydrogen and lattice defects in the study of hydrogen embrittlement in metals, and understanding the mechanism of hydrogen embrittlement failure.

This paper presents an overview of the PALS results from various evaluations of lattice defects, especially vacancy defects, in hydrogen-charged iron, steels, and Ni-based alloys. The discussion focuses on the effect of hydrogen precharging on the vacancy cluster size and vacancy density. The prospects of these evaluations in hydrogen embrittlement research studies are also discussed.

2. Evaluation of Lattice Defects Using PALS

The positron annihilation lifetime is the time difference between the time of positron injection into a sample and the time of pair annihilation with an electron. Since a positron is an antiparticle of an electron, its lifetime in matter is finite and dependent on the electron density at its annihilation site. The higher the electron density, the shorter is the positron lifetime. In a perfect metal crystal, the positrons are repelled to the interstitial positions away from the ion core owing to their positive charge. Subsequently, they are annihilated over a bulk positron lifetime specific to the metal (100–160 picoseconds (ps). When the open-volume defects are present, the positrons are trapped there and annihilated over longer lifetimes compared that in a perfect crystal. These lifetimes are specific to the defect type. The positrons are not trapped by substitutional and interstitial atoms, except in special cases; therefore, PALS is selectively sensitive to open-volume defects.

In conventional positron annihilation experiments, positrons, with a maximum energy of 540 keV emitted from β+ decay nuclides ²²Na, are employed. The maximum implantation depth of these positrons is estimated to be 100–200 μm in iron, steels, and nickel alloys.²⁶⁾

The experimental positron lifetime spectrum, T(t) of samples containing open-volume defects includes the lifetime components of the bulk, lattice defects, and positron source. In positron lifetime spectrum analysis, the experimental positron lifetime spectrum is reconstructed as a sum of exponentially decaying components (Eq. (1)) convoluted with a Gaussian resolution function of the measurement system.   

$$T(t)={\sum }_{i=1}^n\frac{I_i}{{\tau }_i}\text{exp}\left(-\frac{t}{{\tau }_i}\right)$$(1)

where τ_I and I_i are the positron lifetime and relative intensity of component i, respectively and t is the measured time difference. The positron lifetime of the defect components can be used to identify the defect types or the vacancy-cluster size in the case of vacancy clusters. Further, the positron lifetime of defects increases with increasing open volume of defects. For example, the positron lifetimes of perfect crystal, edge dislocation line, jog on the edge dislocation line, vacancy on the edge dislocation line, and monovacancy are 110 ps, 117 ps, 117 ps, 140 ps, and 181 ps, respectively.²⁷⁾ The positron lifetimes of vacancy clusters in iron were determined by theoretical calculations,^28,29) as shown in Fig. 1.

Fig. 1.

Theoretical positron lifetimes for the vacancy clusters in Fe.

The defect densities can be evaluated by substituting τ and I obtained from the multicomponent analysis of the positron lifetime spectra. For example, in the case of plastically deformed materials with two types of vacancy-type defects, such as dislocations and vacancies, the defect densities can be evaluated from Eqs. (2) and (3) using the results of the three-component analysis.   

$$C_d=\frac{1/{\tau }_f-1/{\tau }_d+I_v(1/{\tau }_d-1/{\tau }_v)}{1-I_d-I_v}\frac{I_d}{{\mu }_d}$$(2)

  

$$C_v=\frac{1/{\tau }_f-1/{\tau }_v+I_d(1/{\tau }_v-1/{\tau }_d)}{1-I_v-I_d}\frac{I_v}{{\mu }_v}$$(3)

where C is the defect density and μ is the specific positron trapping rate. The indices f, d, and v represent the positron lifetime components for the free positron (i.e., bulk, defect-free) state, dislocations, and monovacancies or vacancy clusters. The μ value is specific to the defect types. For example, the μ of pure iron dislocations has been reported as μ_d = 5.1 × 10⁻⁵ m²s⁻¹.³⁰⁾ In the present paper, the density of vacancy clusters C_v is expressed as a monovacancy-equivalent density, which is calculated using the μ of the monovacancies μ_1v (1.1 × 10¹⁵ s^{−1 23)}). The specific positron trapping rate of vacancy clusters consisting of n-vacancies can be estimated as μ_v = n·μ_1V for small vacancy cluster sizes.³¹⁾ Consequently, the obtained C_v indicates the proportion of the vacant lattice. However, Eqs. (2) and (3) cannot be used to evaluate the defect densities when the positron trapping is in saturation, that is, all positrons are trapped in the defects (I_d + I_v = 1). In that case only the relative ratio between the densities can be obtained.

3. PALS Studies on the Formation Behavior of Vacancies during Tensile Deformation

Studies on the formation behavior of vacancies during tensile deformation at room temperature in iron, steels, and Ni-based alloys and its effects on hydrogen embrittlement are summarized in Tables 1–2 and described separately in the following subsections.

Table 1. List of studies on the formation behavior of vacancies during tensile deformation in iron and ferritic steels. The strains marked with an asterisk denote fractured samples and the values in bold are those of the hydrogen-charged samples.

Metal	Deformation process	Strain (%)	Hydrogen charging	τv (ps)	Cv (at.ppm)	References
Pure iron (4 N)	Tensile test (1 × 10−3 s−1)	10	n	—	Not detected	Sakaki et al.32)
		20	n	480 ± 70	0.17
		10	y	—	0.17
		20	y	405 ± 15	0.82
AISI410	SSRT (8.7 × 10−5 s−1)	6	n	249 ± 14	13 ± 4	Sugita et al.33)
		11	n	271 ± 14	23 ± 4
		17	n	226 ± 9	63 ± 12
		32*	n	209 ± 9	74 ± 15
		9	y	388 ± 6	18 ± 2
		17*	y	363 ± 7	27 ± 4
AISI410	Tensile tests with strain rates of 3.2 × 10−7 to 4.0 s−1
	1.6 × 10−6s−1	31*	n	214 ± 11		Sugita et al.34)
	8.1 × 10−6 s−1	32*	n	209 ± 9
	8.1 × 10−5 s−1	32*	n	225 ± 8
	8.1 × 10−3 s−1	33*	n	233 ± 7
	4.0 s−1	31*	n	236 ± 7
	3.2 × 10−7 s−1	10*	y	358 ± 6
	1.6 × 10−6 s−1	13*	y	351 ± 13
	8.1 × 10−6 s−1	17*	y	363 ± 7
	8.1 × 10−5 s−1	27*	y	313 ± 6
	8.1 × 10−3 s−1	32*	y	284 ± 7
	4.0 s−1	31*	y	266 ± 8
Tempered martensitic steel	CLT at 0.7 times the maximum tensile stress	*	y	Not evaluated		Doshida et al.35)
JIS-SCM435 (Tensile strength 1488 MPa)	SSRT (4.2 × 10−6 s−1)	2	n	202 ± 26	1.6 ± 0.2	Omura et al.36)
		10*	n	337 ± 15	0.5± 0.1
		2*	y	500	0.2
		2*	y	465 ± 21	0.5
	CLT (900 MPa)	*	y	—	Not detected
JIS-SCM435 (Tensile strength 1060 MPa)	SSRT (4.2 × 10−6 s−1)	3	n	195 ± 9	4.8 ± 1.7
		15*	n	268 ± 9	2.9 ± 0.8
		11*	y	337 ± 6	2.2 ± 1.0
		3	y	500	0.4
		8*	y	350± 6	1.9 ± 0.4
Tempered martensitic steel	SSRT (3.2 × 10−6 s−1)	3.3	n	571	Not evaluated	Saito et al.37)
		3.3*	y	349–404	33.6–67.2 (speculated from TDA)

Table 2. List of studies on the formation behavior of vacancies during tensile deformation in austenitic stainless steels, pure nickel, and nickel alloys. The strains marked with an asterisk denote fractured samples and the values in bold are those of the hydrogen-charged samples.

Metal	Deformation process	Strain (%)	Hydrogen charging	τv (ps)	Cv (at.ppm)	References
JIS-SUS304	Tensile test (8.3×10−4 s−1)	30	n	191		Hatano et al.38)
		68*	n	179
		23*	y	285
JIS-SUS316L	Tensile test (8.3×10−4 s−1)	58*	n	179
		30	y	227
		61*	y	238
Polycrystalline Ni-201 (1 mm-grain size)	Tensile test (6.3×10−4 s−1)	10	n	303 ± 6		Lawrence et al.39)
		10	y	308 ± 10
Polycrystalline Ni-201 (35 μm -grain size)		10	n	298 ± 8
		10	y	314 ± 6
Nickel single crystal (4 N)		10	n	221 ± 6
		10	y	280 ± 4
JIS-SUS304	SSRT (3 × 10−6 s−1)	30	n	179 ± 4		Sugita et al.40)
		101*	n	175 ± 6
		30	y	240 ± 4
		75*	y	244 ± 3
JIS-SUS316		30	n	193 ± 4
		79*	n	184 ± 4
		30	y	230 ± 3
		71*	y	238 ± 3
Type 205		28	n	202 ± 4
		57*	n	186 ± 4
		28	y	304 ± 2
		37*	y	316 ± 2
Ni–Cr alloy (57 wt.% Ni–Cr)		30	n	200 ± 5
		60*	n	189 ± 5
		30	y	305 ± 2
		56*	y	310 ± 2
Ni–Cr alloy (80 wt.% Ni–Cr)		8	n	209 ± 6	4 ± 1
		48*	n	187 ± 4	27 ± 16
		8	y	327 ± 3	5 ± 2
		15*	y	312 ± 3	9 ± 3

3.1. Vacancy Formation in Iron and Ferritic Steels

Sakaki et al. investigated vacancies in 10%- and 20%-tensile deformed pure iron samples after hydrogen charging³²⁾ and observed that the average positron lifetime due to tensile deformation was enhanced by hydrogen charging. The vacancy densities from the three-component analysis of the positron lifetime spectra were 0.17 at.ppm and 0.82 at.ppm for the hydrogen-free and hydrogen-charged 20%-tensile deformed samples, respectively. The hydrogen charging increased the hydrogen content as determined using the TDA. Therefore, according to literature, hydrogen charging increases the vacancy density formed during the tensile process. The positron lifetime of the vacancy clusters was over 400 ps for both hydrogen-free and hydrogen-charged samples. This suggests that large-size vacancy clusters were formed and that the change in the vacancy cluster size due to hydrogen precharging was insignificant. This contrasts with other PALS studies^{33,34,35,36,37,38,39,40)} in which hydrogen precharging increased the vacancy cluster sizes. In high-purity iron, the vacancy diffusion is reported to start around 220 K.²³⁾ This suggests that vacancy clustering may be enhanced in pure iron by vacancy diffusion during deformation. Unfortunately, the effect of strain rate on the vacancy formation behavior has not been reported for pure iron.

The vacancy formation behavior in martensitic stainless steel AISI410 samples subjected to slow strain rate tensile testing (SSRT) at a strain rate of 8.7 × 10⁻⁵ s⁻¹ after hydrogen charging³³⁾ was investigated. The elongations at break were significantly reduced by hydrogen charging to 32% and 17% for hydrogen-free and hydrogen-precharged samples, respectively. The average positron lifetime of samples tensile deformed after hydrogen charging was up to 5 ps longer than that of the hydrogen-free samples at the same strain. From the three-component analysis of the positron lifetime spectra, the positron lifetimes of vacancy cluster components for hydrogen-free and hydrogen-precharged samples were 209–271 ps and 363–388 ps, respectively. Based on the relationship between the positron lifetime and vacancy cluster size,^28,29) the estimated number of vacancies in the vacancy clusters in the hydrogen-free and hydrogen-precharged samples were 3–5 and 15, respectively. The dependence of the positron lifetime of the vacancy clusters on tensile strain was minimal, indicating that the change in size of the vacancy clusters formed during the tensile deformation process was small.

The dislocation and vacancy densities were evaluated using Eqs. (2) and (3) from the three-component analysis results. The dislocation density in the as-tempered sample was relatively higher owing to its tempered martensitic microstructure. In the highly tensile-strained samples, the positron trapping was saturated owing to the high defect densities. Therefore, only the relative ratios between the dislocation and vacancy densities were evaluated as described above. In this case, the dislocation density was determined from the results of the samples annealed at 473 K to reduce the contribution of the vacancy cluster component. Assuming that the annealing did not change the dislocation density at 473 K, the vacancy densities of the highly tensile-strained samples were successfully determined. Despite the vacancy densities increasing with increase in the strain, no obvious changes in the vacancy densities were observed when the hydrogen-free and hydrogen precharged samples were compared at the same strain rates. Vacancy densities in the fractured samples were 74 at.ppm and 27 at.ppm for hydrogen-free and hydrogen precharged samples, respectively. Hydrogen precharging did not increase the vacancy densities. However, the vacancy densities decreased with decreasing fracture strains, contrary to the behavior of pure iron.³²⁾

The degradation of mechanical properties due to hydrogen embrittlement, such as the decrease in the fracture strain, is strongly affected by the strain rate. The lattice defects in the AISI410 samples tensile-fractured over a wide range of strain rates from 3.2 × 10⁻⁷ to 4.0 s⁻¹ were investigated.³⁴⁾ The fracture strains of the hydrogen-free samples were not significantly changed by the strain rate, and ranged from 0.31 to 0.33. The change in the average positron lifetime was also small, and the positron lifetime of the vacancy cluster component was approximately 209–236 ps. On the other hand, in the hydrogen precharged samples, the fracture strain decreased significantly with decreasing strain rate. The fracture strain decreased from 31% at a strain rate of 4.0 s⁻¹ to 10% at 3.2 × 10⁻⁷ s⁻¹. The average positron lifetime of the tensile-fractured samples after hydrogen charging increased with decreasing strain rate. The positron lifetime of the vacancy cluster component, that is, the vacancy cluster size, which was determined from the results of the two-component analysis, increased with decreasing strain rate. There was a good correlation between the positron lifetime of the vacancy cluster component and the fracture strain in the hydrogen-precharged samples. These results indicate that the vacancy cluster size formed during tensile deformation has a significant effect on the fracture strain.

Doshida et al. investigated the lattice defect formation of tempered martensitic steel under elastic stress using TDA and a positron probe microanalyzer (PPMA).³⁵⁾ The average positron lifetime of the fractured sample was more than 20 ps longer than that of the as-tempered samples. The average positron lifetime increased especially near the fracture areas, indicating that high-density vacancy clusters were formed. The hydrogen content, which was determined using TDA, also increased near the fracture area compared to other regions. Based on these results, Doshida et al. concluded that localized plastic deformation occurred under elastic stress in the near-fracture area. In addition to the presence of hydrogen, the local hydrogen-enhanced vacancies that were formed from the interaction between dislocations and hydrogen under elastic stress caused a loss in ductility.

The lattice defect formation in the Japanese Industrial Standards (JIS)-SCM435 low-alloy martensitic steel subjected to SSRT and constant load testing (CLT) under elastic loading stress was investigated.³⁶⁾ The vacancy clustering was enhanced by hydrogen precharging in the SSRT samples, and was more pronounced at higher hydrogen content. On the other hand, the dislocation and vacancy densities increased with strain; however, the effect of hydrogen precharging on the defect densities was small. The decrease in the fracture elongation because of the hydrogen precharging coincided with the vacancy clustering, suggesting that vacancy clustering is closely related to hydrogen embrittlement. The average positron lifetime of the brittle fractured CLT samples increase a little (~1 ps); however, vacancy formation was not evident. This was not consistent with the report on tempered martensite samples by Doshida et al.³⁵⁾ They reported that high-density vacancy clusters are formed in the CLT specimens after hydrogen charging. When vacancy clusters are formed in the tempered martensite with high-density dislocations, positrons are trapped in the vacancies and dislocations. The average positron lifetime does not increase significantly with increasing vacancy cluster density. The average positron lifetime increase due to hydrogen precharging was only 5 ps in the tensile-fractured AISI410³³⁾ and JIS-SCM435.³⁶⁾ The high-density dislocations in the tempered martensitic structure distinctly suppress the increase in the mean positron lifetime due to the introduction of new lattice defects during tensile deformation. Therefore, it is difficult to explain the increase in the average positron lifetime of 70 ps near the fracture area by defect formation alone, as reported by Doshida et al.³⁵⁾ These results suggest that other factors besides vacancies may have been responsible for the remarkable increase in the average positron lifetime. The major difference between the PPMA and our conventional PALS is the depth of distribution of the incident positrons. In the PPMA, the positrons penetrate to a depth of approximately 1 μm because of their low incident energy of 30 keV. The specimen is also sensitive to the surface conditions. The possibility of the formation of a corrosion layer owing to the immersion in the International Federation of Prestressed Concrete (FIP) solution is matter of concern.

Saito et al. evaluated the lattice defects in a tempered martensitic steel tensile deformed after hydrogen precharging.³⁷⁾ After a 3% tensile deformation, the average positron lifetime increased by 20 ps and 25–29 ps for hydrogen-free and hydrogen-precharged samples, respectively. The positron lifetimes of the vacancy cluster component were 304 ps and 349–404 ps for the hydrogen-free and hydrogen-precharged samples, respectively. Assuming a monovacancy traps 1 or 2 hydrogen atoms, the vacancy densities from the TDA results would be 33.6–67.2 at.ppm.

3.2. Vacancy Formation in Austenitic Stainless Steels, Nickel, and Nickel-based Alloys

Hatano et al. investigated the lattice defects formed during tensile deformation after hydrogen gas charging in two austenitic stainless steels, JIS-SUS304 and JIS-SUS316L.³⁸⁾ The two-component analysis of the positron lifetime spectra of the tensile-deformed samples showed that the hydrogen precharging increased the positron lifetime of the vacancy cluster component. The formation of the large-size vacancy clusters is attributable to the high-density monovacancies formed by the hydrogen-induced superabundant vacancies. The degradation process leading to the fracture is consistent with the HESIV mechanism during hydrogen embrittlement.^11,12) The finding that prestraining in the presence of hydrogen promotes the final fracture even without hydrogen in the final fracture stage demonstrates the essential role of damage accumulation in hydrogen embrittlement and strongly supports the preferential role of vacancies.

Lawrence et al. investigated the role of hydrogen in vacancy or vacancy cluster formation in pure nickel single crystal and polycrystalline samples using PALS and TDA.³⁹⁾ The changes in the positron lifetime and relative intensity suggest that hydrogen enhances and stabilizes the vacancies and vacancy clusters. The grain boundaries and adjacent regions were preferential sites for the vacancy and cluster formation. However, hydrogen-altered vacancies and vacancy clusters manifested in yield behavior differences i.e., uniform vacancy distributions increase the strength after hydrogen charging.

Further, the formation behavior of vacancies in hydrogen-precharged SSRT samples of austenitic steels and nickel-chromium alloys was studied using PALS.⁴⁰⁾ Hydrogen charging enhanced the vacancy clustering and the positron lifetime of the vacancy cluster component correlated well with the fracture strain. In 80 wt.% Ni–Cr alloy samples, the dislocation and vacancy density increased with strain, and little effect of hydrogen precharging was observed. This trend was similar to that observed in our previous studies on AISI410 and JIS-SCM435.^33,36) The relationship between the fracture strain and positron lifetime of the vacancy cluster component for the austenitic steels and nickel-chromium alloys was compared in our previous reports on ferritic steels.^33,34) In both the hydrogen-free and hydrogen-precharged samples of all alloys, the positron lifetime of the vacancy cluster component corresponded to the fracture strain. In the case of AISI410 and JIS-SCM435, which had longer positron lifetimes of the vacancy cluster component, the vacancy clustering could have been promoted by the high-density vacancy formation due to frequent dislocation intersections during the tensile deformation. The positron lifetime of the vacancy cluster component in the hydrogen-precharged samples was longer than that in the hydrogen-free samples at the same rupture strain. These results suggest that the clustering of vacancies is affected by the microstructure and that the vacancy clustering during the tensile deformation is enhanced by hydrogen precharging.

4. Discussion

4.1. Vacancy Clustering Behavior

The results from the positron lifetime studies discussed in this paper show that the size of the vacancy formed during the tensile deformation process in hydrogen charged samples was significantly larger than that in the hydrogen-free samples in most cases, except for pure iron. In pure iron, the vacancy clustering can occur at room temperature, since the temperature required for vacancy migration is 220 K.²³⁾ This could be the reason for the formation of large-size vacancy clusters even in hydrogen-free pure iron. In contrast, the temperature required for vacancy migration is 350 K for iron containing 50, 750 at.ppm carbon,²³⁾ indicating that vacancy clustering can be suppressed by the formation of vacancy-carbon pairs.

In hydrogen-precharged tempered martensitic and austenitic steels, a mechanism in support of HESIV has been proposed, wherein a significant increase in the vacancy densities formed during plastic deformation results in the formation of large-size vacancy clusters.^35,38) Doshida et al. reported an increase in the mean positron lifetime of approximately 20 ps on the gauge area and 70 ps near the fracture area in tempered martensitic steels. These were measured using a PPMA on CLT specimens.³⁵⁾ It is speculated that hydrogen embrittlement-related rupture is caused by local plastic deformation even under macroscopic elastic stress.

Hatano et al. reported the positron lifetimes of vacancy cluster components for tensile-deformed austenitic stainless steels.³⁸⁾ In JIS-SUS304 steel, they reported positron lifetimes of 179 ps, 191 ps, and 285 ps for 30% tensile interrupted, 68% tensile ruptured hydrogen-free, and 23% tensile ruptured hydrogen-precharged samples, respectively. In JIS-SUS316L steel, the positron lifetimes were 179 ps, 227 ps, and 238 ps for 58% tensile ruptures hydrogen-free sample, 30% tensile interrupted, and 61% tensile ruptured hydrogen-precharged samples, respectively. The increase in the vacancy cluster size was enhanced in the JIS-SUS304, showing a significant decrease in the elongation at break. This can be attributed to the formation of a large number of vacancies from the local plastic deformation during the tensile process, which leads to the formation of a large number of vacancy clusters and, thus, fracture.

Lawrence et al. also reported an increase in the vacancy cluster size due to hydrogen precharging in nickel-based alloys. The grain size dependence suggests that the grain boundaries and adjacent regions were suitable for the formation of vacancies and clusters. When the density of sites forming vacancy clusters increases, the vacancy cluster size and vacancy density could increase.³⁹⁾

Our measurements on the AISI410, JIS-SCM435, austenitic steels, and nickel-chromium alloys^33,34,36,40) also showed an increase in the positron lifetime of the vacancy cluster component in the tensile deformed samples because of hydrogen precharging. The strain rate dependence was investigated in AISI410. The positron lifetime and rupture strains did not change in the hydrogen-free samples. Meanwhile, in the hydrogen-precharged samples, the positron lifetime of the vacancy clusters increased and the rupture strains decreased with decreasing strain rates.

As mentioned above, many reports on the increase in the vacancy cluster size in steels and Ni–Cr alloys have been reported. From these reports, it can be concluded that vacancy formation is strongly influenced by dislocation shearing during plastic deformation, and vacancy clustering is enhanced by the stabilization due to the formation of vacancy-hydrogen complexes.

The relationship between the positron lifetime of the vacancy cluster components and the fracture strains of the tensile plastic deformation samples reported above is summarized in Fig. 2. Despite the presence of different metal and crystal structures in the matrix, the correlation between the positron lifetime of the vacancy component and the fracture strain was good in the hydrogen-precharged samples. The positron lifetime of the vacancy component increased as the fracture strain decreased. This indicates that the vacancy cluster size formed during plastic deformation is less affected by the vacancy diffusivity. Furthermore, it shows that the vacancy clustering is closely related to the reduction in the homogeneous deformability owing to hydrogen embrittlement. The results from our hydrogen-free samples are also shown in the figure. Surprisingly, the fracture strain decreased as the positron lifetime of the vacancy component increased, even for the hydrogen-free samples. This implies that the vacancy clustering is also related to the homogeneous deformability even in the absence of hydrogen precharging. The positron lifetime of the vacancy cluster component in the hydrogen-precharged samples is longer than that in the hydrogen-free samples at the same rupture strains, suggesting that the vacancy cluster size in the hydrogen-free samples is larger than that in the hydrogen-precharged samples. These results suggest that the formation behavior of the vacancy clusters during tensile deformation is strongly related to the localization of straining, reflecting the heterogeneity in the micro region, and that it is significantly affected by the presence of solute hydrogen.

Fig. 2.

Relationship between the positron lifetimes of vacancy cluster components and fracture strains of hydrogen-free and hydrogen precharged various metals.

4.2. Vacancy Cluster Density

Based on the TDA results, which show an increase in the hydrogen content due to the hydrogen precharging, it has been concluded elsewhere^{11,12,24,35,37,38,41)} that the vacancy densities are significantly increased by hydrogen precharging. However, extremely high vacancy densities have not been reported in PALS studies. The vacancy densities in AISI410,³³⁾ JIS-SCM435 steel,³⁶⁾ and nickel-based alloys⁴⁰⁾ were investigated using PALS, and it was revealed that the vacancy density is not increased by hydrogen precharging. The vacancy density in the hydrogen precharged sample was 27 at.ppm at maximum, which is sufficiently low not to be considered a direct cause of fracture. The only exception to this trend is the case of pure iron reported in ref.32. The vacancy densities after 20% tensile deformation were evaluated as 0.17 and 0.82 at.ppm for the hydrogen-free and hydrogen precharged conditions, respectively, which suggests that the vacancy density is increased by a factor of 4 due to hydrogen precharging. Unfortunately, it is difficult to discuss the vacancy density change due to hydrogen precharging because they are of the same or lower order of magnitude compared to the detection limit of vacancies by PALS (1 at.ppm order.⁴²⁾

Doshida et al. reported an increase in the hydrogen desorption content of 1.5 wt.ppm (83 ppm) in the region close to the fracture area in CLT samples.³⁵⁾ If the vacancy density in the area was high to allow for full positron trapping into the vacancies, the number of hydrogen atoms trapped per vacancy would have been small. According to Takai et al.,²⁴⁾ this increase in the hydrogen desorption content corresponds to a plastic deformation of approximately only 8% and cannot explain the increase in the average positron lifetime of 70 ps.

4.3. Mechanisms of Hydrogen Embrittlement and Future Issues

It is clear from the discussion herein that vacancies play an important role in hydrogen embrittlement and fracture. Although hydrogen-related failure is believed to be accompanied by superabundant vacancy formation due to hydrogen charging in the HESIV model, the PALS results show a different trend: the increase in vacancy density during tensile deformation is not enhanced by hydrogen precharging. This suggests that the HESIV model needs to be modified. The PALS results are partially consistent with the concept of “hydrogen-enhanced localized plasticity” proposed by the HELP mechanism. The positron lifetime of the vacancy cluster components had a good correlation with the fracture strain in various metals in the presence or absence of hydrogen precharging. The vacancy clustering is apparently related to a more general phenomenon of localized plasticity, including hydrogen embrittlement. It is suggested that vacancy clustering may be correlated with localized plasticity because the clustering proceeds owing to the repeated dislocation movements on a slip plane in the persistent slip band. The effect of dislocation migration on the vacancy clustering is not well understood and needs to be investigated in more detail in the future.

Although attempts have been made to use TDA to quantify vacancies, it is currently difficult to quantify vacancy densities using TDA. The quantitative relationship between the hydrogen desorption and vacancy density as well as the dependence on cluster size, is not fully understood and should be clarified in future studies. Since it is difficult to apply PALS to evaluate vacancy densities in practical materials, few reports compare the relationship between the hydrogen desorption contents and vacancy density. In our example of tensile-deformed AISI410 samples, if the contribution of dislocation density is ignored, the hydrogen desorption content is calculated as ~30 hydrogen atoms per vacancy. This could be explained by the hydrogen trapping around the vacancy clusters and contribution of dislocations. Another possible cause is the contribution of macroscopic voids, which are larger than the vacancy clusters detected by PALS. Microvoids (approximately 10–100 nm in diameter) with a density of approximately 10 μm⁻² were observed by TEM and SEM in the diffuse necks of copper specimens subjected to tensile deformation.⁴³⁾ It is assumed that a small fraction of the void nuclei grows in the 10–1000 nm range, leading to subsequent destruction. The vacancy clusters detected by the positron lifetime method are less than a few tens of atoms in size, which is small when compared to the microvoid reported in literature. The vacancy density detected by PALS and number density of vacancy clusters are in the order of 10 at.ppm and 1 at.ppm, respectively. As an example, if 1 at.ppm vacancy clusters are uniformly distributed in the bcc iron, the number density is calculated as 2300 μm⁻², which is more than two orders of magnitude higher than that in the copper samples. This suggests that a small number of microvoids are contained in the vacancy clusters. The positron trapping rate into the vacancy clusters is proportional to the number of vacancies when the number of vacancies is small. However, the increase in the trapping rate with increasing number of vacancies slows down as the number of vacancies increases.³¹⁾ This indicates that the experimentally determined positron lifetime of the clusters corresponds to the typical size of the vacancy clusters, even when large-size vacancy clusters (i.e., microvoids observed by the TEM and SEM) are included in low ratios. Considering the good correlation between the positron lifetime of the vacancy cluster components and the fracture strain, it is expected that the larger the typical size of the vacancy clusters obtained by PALS, the more likely the formation of macroscopic voids could lead to fracture.

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