The characteristics of load frequency of corrosion fatigue crack growth rate for Ti–6Al

Abstract

Ti–6Al–4V alloys have been developed not only as structural materials for aerospace field but also as biomaterials for orthopedic surgery. As a crack growth mechanism under corrosive condition for Ti–6Al–4V alloys, mechanisms of anodic dissolvent chemical reaction and hydrogen embrittlement (HE) caused by chemical corrosive reaction have been proposed, however, the latter has not yet been clarified. In this study, corrosion fatigue (CF) crack growth tests under ringer and 3.5% NaCl solution were conducted for various type of Ti–6Al–4V alloys such as forging and casting with different values of yield stress. The characteristics of load frequency of corrosion fatigue crack growth rate (CFCGR) were investigated for these materials. It was found that various characteristics of load frequency for CFCGR appear depending on yield stress and concentration of NaCl solution. In some cases, it was found to show different characteristics of load frequency of CFCGR from those dominated by usual time dependent mechanism. In this research, a map of load frequency of CFCGR for these materials were established in terms of concentration of NaCl and yield stress. Finally some considerations were conducted which concerns the mechanisms of CFCGR such as anodic corrosive reaction and hydrogen embrittlement.

Keywords

Ti–6Al–4V alloys load frequency corrosion fatigue crack growth rate hydrogen embrittlement

1. Introduction

Generally, FCGR is accelerated with decrease in f (load frequency) under corrosive condition [9–13], when time dependent mechanism is controlled factor for corrosion fatigue crack growth rate (CFCGR), however, CFCGR is sometimes decelerated with decrease in f due to the formation of impassive film [9,12].

In this study, corrosion fatigue crack growth tests under 3.5% NaCl solution and 0.9% NaCl ringer solution were conducted for various type of Ti–6Al–4V alloys such as forging and casting. The characteristics of load frequency of CFCGR were investigated and dominating factors of CFCGR was studied by making a map of characteristics of load frequency for CFCGR in the two dimensional representation between yield stress and concentration of NaCl solution.

Fig. 1.

Dimension of C(T) specimen (thicknesses of 0.8 and 1.0 mm).

2. Test method, materials and experimental conditions

Specimens used were cut out into C (T) specimens in the T–L direction with width and thickness of 16.6 mm and 1.0 mm respectively as shown in Fig. 1. Materials used are ( $α + β$ ) Ti–6Al–4V alloys of forging and casting. Forging was conducted by the following process: β forging at 1150°C, β rolling at 1150°C, $α + β$ rolling at 950°C, annealing at 700°C and furnace cooling for yield stress of 1431 MPa and annealing at 790°C and air cooling for yield stress of 1360 MPa respectively. Casting was conducted by the following process and prepared by Osaka Dental University: Vacuum pressurized casting machine was used. Heating was conducted up to 800°C for 3 hours and 30 minutes holding at the temperature and heating was conducted again up to 1050°C for 3 hours and 1 hour holding at the temperature. After that, cooling was conducted in the furnace up to room temperature. Values of yield stress are ranging from 931 to 1431 MPa. Mechanical properties and chemical composition were shown in Tables 1 and 2. Grain size is $4 \sim 5$ µm for forging materials and 100 µm for casting material.

Table 1
Mechanical properties of Ti–6Al–4V alloys

Material Tensile strength (MPa) Yield stress (MPa) Elongation (%)

Ti–6Al–4V forging 1509 1431 10

Ti–6Al–4V forging 1502 1360 9

Ti–6Al–4V casting 1068 931 4.2

Material	Tensile strength (MPa)	Yield stress (MPa)	Elongation (%)
Ti–6Al–4V forging	1509	1431	10
Ti–6Al–4V forging	1502	1360	9
Ti–6Al–4V casting	1068	931	4.2

Table 2

Chemical composition of Ti–6Al–4V alloys

Material	N	O	H	Fe	C	Al	V	Y	Ti
Ti–6Al–4V forging	0.003	0.157	0.062	0.187	<0.005	6.24	4.14	<0.001	bal.
Ti–6Al–4V forging	0.008	0.159	0.002	0.235	0.0195	6.31	4.17	<0.001	bal.
Ti–6Al–4V casting	0.005	0.152	0.0059	0.213	0.011	6.2	4.25	–	bal.

Fig. 2.

Experimental apparatus of corrosion fatigue crack growth.

A pre-fatigue crack was introduced in this specimen up to 0.4 mm. Fatigue crack growth tests were conducted under the load frequency ranging from $0.05 \sim 1.1$ Hz using our designed machine as shown in Fig. 2 and under the environmental condition of 37°C, ringer solution (0.9% NaCl, KCl and CaCl₂) and 25°C, 3.5% NaCl solution. Temperature in the water bath was kept at the specified temperature by combining heater and cooler controlled by temperature controller. Stress ratio was kept at $R = 0.1$ . Test conditions were shown in Table 3.

Table 3

Experimental conditions

Specimen	Environmental condition	Stress increasing time: decreasing time (s)	Temperature (°C)	Frequency (Hz)
Ti–6Al–4V forging (yield stress 1360 MPa)	Air	2 : 2	25	0.25
	Ringer	3 : 3	37	0.17
		3 : 1	37	0.25
		2 : 2	37	0.25
		1 : 3	37	0.25
		1 : 1	37	0.5
	3.5% NaCl	3 : 3	25	0.17
		2 : 2	25	0.25
		1 : 1	25	0.5
Ti–6Al–4V forging¹⁵⁾ (yield stress 1431 MPa)	3.5% NaCl	10 : 10	25	0.05
		5 : 5	25	0.1
		1.7 : 1.7	25	0.3
		0.71 : 0.71	25	0.7
		0.46 : 0.46	25	1.1
Ti–6Al–4V casting	Ringer	3 : 3	37	0.17
Ti–6Al–4V casting	Ringer	1 : 1	37	0.5

The amplitude of stress intensity factor is given by Eq. (1) [14]. $\begin{array}{l} Δ K = \frac{Δ P}{B \sqrt{W}} F (\frac{a}{W}) \\ F (\frac{a}{W}) = 4.55 - 40.32 (\frac{a}{W}) + 414.7 {(\frac{a}{W})}^{2} - 1698 {(\frac{a}{W})}^{3} \\ (1) & + 3781 {(\frac{a}{W})}^{4} - 4287 {(\frac{a}{W})}^{5} + 2017 {(\frac{a}{W})}^{6} \\ for 0.2 ⩽ (\frac{a}{W}) ⩽ 0.8 . \end{array}$

3. Results

3.1. The load frequency characteristics f of corrosion fatigue crack growth rate (CFCGR) under ringer solution

The characteristics of CFCGR for casting material (yield stress of 931 MPa) under ringer solution were shown in Fig. 3(a) and (b). Results of Fig. 3(a) showed that CFCGR was slightly accelerated rather than that under atmospheric condition through the whole $Δ K$ region for the case of 0.5 Hz. Furthermore, CFCGR was found to be slightly accelerated with increase in f as shown in Fig. 3(b) which is different from that dominated by time dependent mechanism. For the case of time dependent dominant mechanism being dominant, CGCGR is known to be accelerated with decrease in f.

Fig. 3.

(a) CFCGR for Ti–6Al–4V alloys (casting) under ringer solution. (b) Characteristics of load frequency of CFCGR under ringer solution.

Fig. 4.

(a) CFCGR for Ti–6Al–4V alloys (forging) under ringer solution. (b) Characteristics of load frequency of CFCGR under ringer solution.

The characteristics of CFCGR for forging (yield stress of 1360 MPa) under ringer solution were shown in Fig. 4(a) and (b). Results of Fig. 4(a) showed that CFCGR was also slightly accelerated rather than that under atmospheric condition through the major region of $Δ K$ in the load frequency range from 0.17 to 0.5 Hz. Furthermore, CFCGR was also found to be slightly accelerated with increase in f as shown in Fig. 4(b) which is different from that dominated by time dependent mechanism. This load frequency characteristics of CFCGR was found to become much more remarkable with increase in $Δ K$ .

3.2. The load frequency characteristics f of CFCGR under 3.5% NaCl solution

The characteristics of CFCGR for forging (yield stress of 1360 MPa) under 3.5% NaCl solution were shown in Fig. 5(a) and (b). Results of Fig. 5(a) showed that CFCGR was accelerated rather than that under atmospheric condition. It was more typical as compared with that under ringer solution which is lower concentration of NaCl (0.9%). Furthermore, CFCGR was found to be accelerated with decrease in f in the region of low $Δ K$ (20 MPa m^1/2) as shown in Fig. 5(b), which is the characteristics of time dependent mechanism related to the mechanism of corrosive anodic reaction. And it was different from that under ringer solution. On the other hand, in the region of higher $Δ K$ ( $> 30$ MPa m^1/2), this time dependent load frequency characteristic was found to diminish. This will be due to the fact that in the region of higher $Δ K$ , time dependent mechanism such as corrosive reaction is not feasible to involved in CFCGR.

Fig. 5.

(a) CFCGR for Ti–6Al–4V alloys (forging) under 3.5% NaCl solution. (b) Characteristics of load frequency of CFCGR under 3.5% NaCl solution.

3.3. Discussion of experimental results

The characteristics of load frequency, f of CFCGR for forging (yield stress of 1431 MPa) under 3.5% NaCl solution were shown in Fig. 6 [15]. For a material with higher yield stress, in the same frequency range, $0.1 \sim 1$ Hz, the eminent accelerated characteristics of CFCGR against f appeared and this characteristic is qualitatively similar one as shown in Figs 3(b) and 4(b) for large value of $Δ K$ . This characteristic becomes eminent for materials with higher yield stress as shown in Fig. 6. On the other hand, in the frequency range higher than 1 Hz, the load frequency characteristics of CFCGR is found to show the typical time dependent mechanism also as shown in Fig. 6, that is, CFCGR is accelerated with decrease in f [2].

Fig. 6.

CFCGR for Ti–6Al–4V alloys (1431 MPa of yield stress, forging) under 3.5% NaCl solution [2,15].

Fig. 7.

Distribution map of the load frequency of CFCGR in the two dimensional representation of yield stress and NaCl concentration. TD means time dependent mechanism.

On the basis of these results, the load frequency characteristics of CFCGR for Ti–6Al–4V alloys were found to be classified into two region in the two dimensional map as shown in Fig. 7. In the region of lower yield stress or higher concentration of NaCl (lower region divided by solid line in Fig. 7), CFCGR increases with decrease in f, that is, time dependent mechanism. Especially, for the case of yield stress of 1360 MPa and under 3.5% NaCl solution as shown in Fig. 5(b), except in the final region of CFCGR ( $Δ K = 40$ MPa m^1/2), major portion of CFCGR ( $Δ K = 20$ and 30 MPa m^1/2) increases with decrease in f, that is, time dependent mechanism is dominant. On the other hand, in the region of higher yield stress or lower concentration of NaCl (upper region divided by solid line in Fig. 7), CFCGR increases with increase in f. Previously, in the f characteristics of CFCGR, due to the formation of impassive film on the crack surface caused by corrosive reaction, CFCGR was found to sometimes increases with increase in f [9,12,13], that is, similar characteristics as shown in the upper region of Fig. 7. However, for the case of the formation of passive film, it is necessary for the corrosive reaction to overcome the formation of new surface due to dislocation slip [9,13]. Therefore, film formation will be typical in the region of lower yield stress and higher concentration of NaCl, that is, lower region of Fig. 7, which is the region of corrosive reaction being typical. However, in this research on the load frequency characteristics of CFCGR for T–6Al–4V alloys, this load frequency characteristics of CFCGR were found to be caused in the region of higher yield stress or lower concentration of NaCl, that is, upper region of Fig. 7, which is the region of corrosive reaction not being feasible to occur.

Therefore, this peculiar load frequency characteristics of CFCGR will be dominated by other mechanism. Under corrosive condition of NaCl, due to anodic corrosive reaction, hydrogen was found to be originated by the chemical reaction [16–18] and a hydride was also found to be originated [7,8].

However, a detailed mechanism of hydrogen embrittlement has not yet been clarified [1], hydrogen diffusion behavior around a notch tip also will be concerned with the CFCGR.

The following section, numerical analysis of hydrogen diffusion behavior around a notch tip was conducted using our proposed α multiplication method [19,20] coupled with FEM–FDM method [20,21].

4. Analysis of hydrogen diffusion around a notch under cyclic loading

4.1. Basic equation, model and method of analysis

The basic equation of local stress induced hydrogen diffusion has been proposed given by Eq. (2), that is, the α multiplication method [19,20,22], based on the classical equation [23,24], $\begin{matrix} (2) & \frac{\partial C}{\partial t} = α_{1} D \nabla^{2} C - α_{2} \frac{D Δ V}{R T} (\nabla C \cdot \nabla σ_{p}) - α_{3} \frac{D Δ V}{R T} C \nabla^{2} σ_{p}, \end{matrix}$ where, C is hydrogen concentration, D is the diffusion constant, R is gas constant (8.314 J/mol K), T is the absolute temperature, t is sequential time, $σ_{p}$ is the hydrostatic stress and $Δ V$ is the volume change when hydrogen enters into interstitial space ( $2 \times 10^{- 6}$ m³/mol) [25].

Values of $α_{i}$ are multiplication factors which cause the effect of each term on time sequential changing characteristics of particle concentration named α multiplication method [19–21]. The validity of introducing values of $α_{i}$ and its physical meaning were written in our previous researches [19,20,26]. This method has been applied to analyze the hydrogen concentration behavior around a notch tip under cyclic loading conditions [27] and it was linked with FEM–FDM method [20,21] as is discussed in the explanation of Figs 8 to 10. In this research, values of $α_{i}$ were determined as $α_{1} = 0.1$ , $α_{2} = 1.0$ , $α_{3} = 0.5$ .

Fig. 8.

(a) The analytical model of FEM. (b) The analytical model of FDM. (c) Boundary conditions of hydrogen diffusion by FDM analysis.

Fig. 9.

The schematic illustration of increment of load steps.

Fig. 10.

Flow chart of FEM–FDM combination analysis.

Models of analysis were shown in Fig. 8(a), (b) and (c). Hydrogen is considered to be originated by anodic dissolvent chemical reaction [16]–[18] and to enter into Ti–6Al–4V alloys from crack surface given by Eq. (3) and to diffuse toward to the site of maximum hydrostatic stress [19]. $\begin{matrix} (3) & C_{C} (t) = \{\begin{matrix} C_{0} + η {\dot{σ}}_{R} t & (t < t_{c}) \\ C_{0} + C_{C max} - η {\dot{σ}}_{D} (t - t_{c}) & (t ⩾ t_{c}), \end{matrix} \end{matrix}$ where $C_{C} (t)$ is the hydrogen concentration at a crack tip surface depending on the applied stress. $C_{0}$ and $C_{C max}$ is hydrogen concentration at the initial and maximum applied stress respectively during fatigue load cycle. ${\dot{σ}}_{R}$ is stress increasing rate and ${\dot{σ}}_{D}$ is stress decreasing rate. η is constant which adjusts the inflow of hydrogen from the crack tip.

In our analysis, on the basis of finite element analysis (FEM), analysis of elastic-plastic stress was conducted and hydrostatic stress were obtained. They were allocated into grids of finite difference analysis for the analysis of hydrogen diffusion using an interpolating method. Values of $\nabla σ_{p}$ and $\nabla^{2} σ_{p}$ were numerically calculated and they were substituted in the second and third terms of Eq. (2). Equation (2) was numerically solved using successive under relaxation method (SUR method) based on Crank Nicolson discretization (FDM) [19,20]. Since, Eq. (2) includes the first derivative of $\nabla σ_{p}$ , it was found that this term is not feasible to get stable convergence of numerical solution of Eq. (2). Therefore, in addition to adopt not SOR (Successive Over-Relaxation) method but SUR (Successive Under-Relaxation) method as is mentioned above, it was also found that a stable numerical solution can be obtained with high accuracy and short CPU time if $Δ t / Δ r^{2} < 0.4$ is satisfied [19]. This method is an original one to obtain accurate numerical solution of Eq. (2). We named α multiplication method coupled with FEM–FDM method [19,20].

Concerning the analysis under fatigue loading, increment of load steps were applied as shown in Fig. 9 and FEM–FDM analysis was conducted at each step. The number of increment of load steps in each load cycle was about 17,000 steps.

Flow chart of this analysis was shown in Fig. 10.

4.2. Results of analysis

Load cycle sequential change of the distribution of hydrostatic stress in the direction of notch tip and initial yielding and re-yielding region at the peak stress of 9 load cycles were shown in Fig. 11(a) and (b). These results showed that two peaks of hydrostatic stress were found at both of initial and re-yielding region. Correspondingly, hydrogen was found to concentrate at both of initial and re-yielding region as shown in Fig. 12, which is similar behavior given by previous paper [21]. Figure 12 showed the characteristics of load cycle sequential distribution of hydrogen concentration in the direction of the notch tip from 1 to 9 load cycles. Hydrogen concentration was found to increase with increase in load cycles and to saturate to a specified distribution. Two peaks of hydrogen concentration exist, that is, at the re-yielding region (near the notch tip) and at the initial yielding region (far from the notch tip) as shown in Fig. 12.

Fig. 11.

Distribution of hydrostatic stress around a notch tip. (a) Distribution in the direction of a notch tip. (b) Two dimensional distribution around a notch tip at 9 load cycles.

Fig. 12.

Characteristics of load cycle sequential distribution of hydrogen concentration in the direction of the notch tip from 1 to 9 load cycles. Hydrogen concentration increases with increase in load cycles and saturates to a specified distribution. Two peaks of hydrogen concentration exist, that is, at the re-yielding region (near the notch tip) and at the initial yielding region (far from the notch tip) [21].

In this study, further numerical analyses were conducted to investigate the effect of load frequency on the hydrogen concentration behaviors at both of initial and re-yielding region.

The load frequency characteristics of hydrogen concentration behaviors at 9 load cycles of both of initial and re-yielding region were shown in Fig. 13(a) and (b).

Fig. 13.

The load frequency characteristics of hydrogen concentration. (a) Hydrogen distribution in the direction of notch tip. (b) Maximum hydrogen concentration at both of initial and re-yielding region. $C_{r}$ : Maximum hydrogen concentration in the re-yielding region. $C_{i}$ : Maximum hydrogen concentration in the initial yielding region.

These results showed that the load frequency characteristic of maximum hydrogen concentration at the re-yielding region (near the notch tip) was found to increase with decrease in load frequency, that is, time dependent mechanism. It caused acceleration of fatigue crack growth rate, $d a / d N$ with decrease in load frequency if the hydrogen accumulated at the re-yielding region dominates $d a / d N$ . On the other hand, that at the initial yielding region was found to show a peculiar characteristic in the load frequency region ranging from 0.1 Hz to 1 Hz, that is, maximum hydrogen concentration increases with increase in load frequency. It is a similar characteristic to experimental load frequency characteristics of CFCGR ranging from 0.1 Hz to 1 Hz, such as shown in Figs 3(b) and 4(b). This peculiar characteristic of hydrogen concentration was considered to be caused by the following reason. As shown in Fig. 13(a), the distribution of hydrogen concentration in the initial yielding region takes maximum value at the right hand side of the initial yielding region at the 1 Hz, that is, far from the re-yielding region. With decrease in load frequency, the distribution of hydrogen concentration transits from the right hand side to left hand side of the initial yielding region and it takes maximum value at the left hand side of it at the 0.01 Hz. In the intermediate region, for example, in the region from 0.1 to 1 Hz, maximum hydrogen concentration in the initial yielding region decreases with decrease in load frequency, which results in the peculiar load frequency characteristics ranging from 0.1 Hz to 1 Hz. These load frequency characteristics of maximum hydrogen concentration in the initial yielding region were shown in Fig. 13(b).

5. Discussions

For Ti–6Al–4V alloys, due to the diffusive hydrogen, hydride was considered to be originated and the site of hydride origination will be localized not at the notch tip but around the notch tip [7,8]. Therefore, the hydrogen concentrated behavior at the initial yielding region apart from notch tip may play an important role for hydride origination. This peculiar load frequency characteristic of CFCGR for Ti–6Al–4V alloys, that is, CFCGR increase with increase in load frequency, was found to appear also for that for SUS 304 stainless steel under hydrogen condition in the region from 0.001 Hz to 0.1 Hz [28], and it was also found that film [9,12] formation did not occur [28].

In this research, as shown in Fig. 13(b), the load frequency characteristics of hydrogen concentration at the initial yielding region was found to decrease with decrease in load frequency in the frequency range from 0.1 Hz to 1.0 Hz, that is, the same frequency range of experimental CFCGR. Furthermore, as mentioned in the Section 3.3, this load frequency characteristic of CFCGR was found in Ti–6Al–4V alloys with higher yield stress or lower concentration of NaCl, that is, not feasible to occur anodic corrosive reaction.

From these results mentioned above, this peculiar characteristic is considered not to be caused by impassive film formation [9,12] but by hydrogen concentration behavior around a notch tip under hydrogen condition.

The sensitivity of corrosion and hydrogen embrittlement of Ti–6Al–4V alloys are not higher, however, with increase in yield stress, the sensitivity was found to become eminent as shown in Figs 5(b) and 6. Especially, for Ti–6Al–4V alloy with yield stress of 1431 MPa, CFCGR was found to be accelerated ten times as compared with that under atmospheric condition [15]. For such case, the effect of hydrogen concentration on CFCGR may be important.

6. Conclusions

The load frequency characteristics of corrosion fatigue crack growth rate under NaCl solution using a small C(T) specimen for Ti–6Al–4V alloys ( $σ_{y s} = 931, 1360$ , 1431 (MPa)) were investigated. It was found that, in the specified range of load frequency such as $0.1 \sim 1$ Hz for these alloys, there are some cases when crack growth rate increases with increase in load frequency distinguished from that dominated by time dependent mechanism. It was feasible to occur for those with higher yield stress or lower concentration of NaCl, that is, the case when corrosive reaction is not so feasible to occur. These phenomena were found to be well described by incorporating the effect of the hydrogen embrittlement sensitivity on the load frequency caused by hydrogen diffusion and concentration and they become typical with increase in yield stress.

These results showed that hydrogen embrittlement mechanism of Ti–6Al–4V alloys is caused by hydride formation apart from a notch tip dominated by hydrogen concentration behavior at the initial yielding region apart from the notch tip. It becomes typical with increase in yield stress. The analysis of stress induced hydrogen diffusion and concentration around a notch tip will be useful to understand such various behaviors of CFCGR caused by hydrogen diffusion.

Footnotes

Acknowledgements

This work was supported by Council for Science, Technology and Innovation (CSTI),

Cross-ministerial Strategic Innovation Promotion Program (SIP), “Structural Materials for Innovations” (Funding agency: JST).

Authors also express thanks to Kobe Steel Work for preparing materials and the Design and Manufacturing Center of the Department Mechanical Engineering of Tohoku University for manufacturing specimens. Authors also deeply appreciate Drs. Yoshiko Nagumo and Go Ozeki for valuable discussions about this research.

Conflict of interest

The authors have no conflict of interest to report.

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The characteristics of load frequency of corrosion fatigue crack growth rate for Ti–6Al–4V alloys

Abstract

Keywords

1. Introduction

Table 1 Mechanical properties of Ti–6Al–4V alloys Material Tensile strength (MPa) Yield stress (MPa) Elongation (%) Ti–6Al–4V forging 1509 1431 10 Ti–6Al–4V forging 1502 1360 9 Ti–6Al–4V casting 1068 931 4.2

3.1. The load frequency characteristics f of corrosion fatigue crack growth rate (CFCGR) under ringer solution

4.1. Basic equation, model and method of analysis

6. Conclusions

Footnotes

Acknowledgements

Conflict of interest

References

Table 1
Mechanical properties of Ti–6Al–4V alloys

Material Tensile strength (MPa) Yield stress (MPa) Elongation (%)

Ti–6Al–4V forging 1509 1431 10

Ti–6Al–4V forging 1502 1360 9

Ti–6Al–4V casting 1068 931 4.2