Study on the Overload and Dwell-Fatigue Property of Titanium Alloy in Manned Deep Submersible

With the rapid development of ocean technology, the deep-sea manned submersible is regarded as a high-tech equipment for the exploration and exploitation of ocean resources. The safety of manned cabin has a decisive effect on the whole system. Ti-6Al-4V with the superior strength-to-weight ratio and corrosion resistance has been used for the manned cabin. The manned cabin experiences loading spectrum with different maximum stresses and different dwell time during their service life. The load sequence effects on dwell fatigue crack growth behavior of Ti-6Al-4V under different dwell time are investigated experimentally in this paper. The experimental results show that the crack tip plastic zone is enlarged by the dwell time and the overload retardation zone increases with dwell time under the same overload rate. A dwell fatigue crack growth model is proposed by modifying the crack tip plastic zone under the loading history with combinations of the single overload and dwell time factors are included in the modified model. Based on the experimental data, the overload retardation zone and the crack growth rates of Ti-6Al-4V are predicted by the modified model. A reasonable model for the load sequence effect on the dwell fatigue crack growth rates of Ti-6Al-4V is verified.


Introduction
During the service life, the manned deep submersible will inevitably go through the process of diving, working and floating. In this process, the pressure shell of the deep submersible will experience the dwell load in each cycle except for the normal cyclic loading (Lei et al., 2010). Then the fatigue problem of the pressure hull is actually a dwellfatigue problem. Owing to the complexity of severe marine environment and the uncertainty of the operating process of the deep submersible, the influence of random loads such as overload on the dwell fatigue growth rates should be studied to ensure the safety of the pressure hull of the deep submersible.
The crack growth rate of metal materials under an overload condition can be divided into three stages: instantaneous acceleration, retardation, and recovery (Wang et al., 2017;Li, 2015). The fatigue crack growth rate of metal material will be obviously reduced after an overload load, which is called load sequence effect. On the other hand, the fatigue life will be extended under multiple overload waveforms condition. Therefore, many experiments and predicted methods of the load sequence effect on the fatigue crack growth rates were investigated to obtain the accurate fatigue life under complexed load spectrum.
In the past 30 years, many experts and researchers have carried out experimental studies on single peak overload (Silva, 2007;Jono et al., 1999). Schijve and Broek (1962) studied the load sequence effect on the crack growth rate of aluminum alloy 2024-T3 by experimental method. It was found that the fatigue crack growth rate of aluminum alloy 2024-T3 decreased when the single peak overload waveform was applied to the constant amplitude load. And the crack growth rate recovered to the fatigue crack growth rate under the constant amplitude load condition. The fatigue life of the specimen was almost four times longer when three single peak overload was used in the constant amplitude load (Chen, 2002).
Different materials of load sequence effect on the fa-tigue crack growth rates were carried out by Chen et al. (2011). They found that with the increase of overload ratio OLR (Overload Ratio), the load sequence effects on the fatigue crack growth rates were more obvious. Based on the multiple overload test, more overloads in the load cycles, more retardation effect on the fatigue crack growth rates will be showed. The load sequence effects on the fatigue crack growth rate of three different metal materials under load ratio R<0 were studied by experiments. The experimental results showed that the crack growth rate of pure aluminum material AL7175 was accelerated after an overload. But Li (2015) found through the experimental methods that the low carbon steel and Titanium alloy Ti-6Al-4V had no obvious load sequence effect. The overload mode effect on the crack growth behavior was studied by Sunder et al. (2016). They found that an underload following an overload had a deleterious effect on the fatigue crack growth rates, and the retardation level was determined by the extent of the underload. The fatigue crack growth behavior under the constant amplitude and a single overload had also been discussed. The results showed that the strains near the crack tip became larger and the crack opening load increased under the introduction of the overload (Wu and Bao, 2018). Yumak and Aslantas (2019) studied a single overload effect on the fatigue crack growth behavior of Ti-6Al-4V alloy. The results showed that the crack growth rates of all specimens decreased with the introduction of a single overload, and the load sequence effect increased with the increase of notch angles. Rege et al. (2019) investigated the fatigue crack growth behavior of 316L austenitic stainless steel under two overloads in the cyclic load, finding that the two overloads in the cyclic load lead to the retardation of fatigue crack growth.
The fatigue crack propagation behavior of the aluminum alloy material 7 075-T651 was studied by Zhao et al. (2008). A modified Wheeler's model based on the evolution of the remaining affected plastic zone was introduced. And it was found to predict well the influence of the overload and sequence loading on the crack growth. Based on Zhao et al.'s (2008) model, a modified model was proposed by Wang (2015) to predict the single overload, underload, multiple overload and the combinations of a single overload and dwell time. The modified model was used to predict the fatigue crack growth rates of different metal materials. The predicted results agreed with the experimental data. However, the modified model could not be used to predict the load sequence effect on the dwell fatigue crack growth behaviors.
In general, most articles focused on the load sequence effect on the fatigue crack growth behavior for different metal materials. However, the load sequence effect on the fatigue problem of the pressure hull is actually a dwell-fatigue problem under complex loading. In this paper, the fatigue and dwell fatigue crack growth rates of Ti-6Al-4V un-der constant amplitude and variable-amplitude loadings are investigated experimentally. A modified model is thereby proposed based on the experimental data to predict the dwell fatigue crack growth behaviors under different loading spectra. In this modified model, the crack tip plasticity zone induced by the dwell time in the loading cycles is introduced. The dwell fatigue and fatigue crack tip plasticity zones of Ti-6Al-4V under single overload are predicted by the modified model. The single overload retardation of fatigue and dwell fatigue crack under different dwell time are predicted successfully by the modified model. The modified model gives a new way to study the dwell fatigue life of manned deep submersibles.

Material
Ti-6Al-4V is widely used in the pressure shell material of manned submersible. In this study, the fatigue and dwell fatigue crack growth rates of Ti-6Al-4V under constant amplitude and variable amplitude loading are investigated through experiments. Table 1 gives the composition of the Ti-6Al-4V as determined by the manufacturer.

Tensile mechanical property
Before presenting the results of the fatigue and dwell fatigue crack growth experiments, it is necessary to discuss the basic mechanical properties of Ti-6Al-4V at the room temperature. The tensile properties of three smooth specimens were measured on Universal testing machine. Tensile experiments were performed at room temperature. The experiments were carried out in accordance with GB/T228.1-2010. The tensile test specimen geometry is shown in Fig. 1. The original gauge length is 50 mm. The mechanical property parameters are listed in Table 2. 2.3 Fracture toughness The fracture toughness experiments of Ti-6Al-4V were performed under center tensile loading conditions. The tests were conducted at room temperature using the Instron servo-hydraulic testing machine. The three specimens, 12.5 mm thick (B) and 50 mm wide (W), were pre-cracked until the pre-crack reached the length of (0.45−0.7)W, 24.5 mm, according to GB/T 21143-2007. After fatigue precracking, the specimens were loaded monotonically to failure under center tensile loading. The results obtained from the fracture toughness experiments are summarized in Table 3. The average fracture toughness of Ti-6Al-4V is used in this study 62.278 MPa.

Experimental procedure
Constant amplitude loading testing of Ti-6Al-4V was firstly performed for fatigue and dwell fatigue crack growth analysis and served as the baseline data. Following this, several single overload testing of Ti-6Al-4V with different overload ratios were performed to serve as the preliminary testing data for the single overload retardation effect on Ti-6Al-4V. The overload ratio is defined as the ratio of the maximum loading level of the overload cycle to the maximum value of the constant load cycle.
The fatigue and dwell fatigue crack growth rate experiments of Ti-6Al-4V were performed on IST8802 high and low temperature fatigue testing machine. All the experiments were conducted at the room temperature. The maximum tensile force P max = 8 000 N and P min = 240 N (stress ratio R=0.03). CT specimens, 12.5 mm thick (B) and 50 mm wide (W), were pre-cracked until a crack length about 25 mm was achieved under triangular loading at 10 Hz. The specific dimensions are shown in Fig. 2. The fatigue crack growth rate experiments of Ti-6Al-4V were conducted under triangular cyclic loading with a 2 s rise and a 2 s fall. The dwell fatigue loading was consisted of a 2 s rise, a 10 s or 60 s dwell period at the maximum load level and a 2 s fall. The constant amplitude loading spectrums of fatigue and dwell fatigue are shown in Fig. 3.
The single overload tests are considered as a preliminary deterministic observation of the fatigue and dwell fatigue crack growth retardation behavior. Single overload specimen at two different overload ratios is used for this purpose. The P max and P min of regular load were set as the same as the constant amplitude loading. In this study, the maximum load value of the overload P max,ol were set as 9 600 N and 12 000 N (i.e., overload ratios were 1.2 and 1.5), respectively. The single overload was inserted into the constant loading spectrum when the crack was about 30 mm. The single overload spectra are shown in Fig. 4. The experimental setup is shown in Fig. 5. Fig. 6 shows that the crack growth results of Ti-6Al-4V under constant amplitude loading in the traditional form of crack length versus the fatigue cycle with and without dwell time at R=0.03. The material of Ti-6Al-4V displays a significant dwell time effect. With the increase of dwell time, the fatigue life of Ti-6Al-4V decreases. The fatigue life of Ti-6Al-4V with dwell time 10 s is about 1.6 times shorter than that without dwell time. The fatigue life in the case of dwell time 60 s is about 3.6 times shorter than that without dwell time. The dwell time effects on the fatigue crack growth behavior are potentially induced by the crack growth during the dwell time.

Constant amplitude loading
The crack growth rate data of Ti-6Al-4V obtained for cyclic loading with and without dwell periods at R=0.03 and at the room temperature are shown in Fig. 7. The experimental results clearly show that Ti-6Al-4V has a smaller  resistance against crack growth under dwell loading as compared with cyclic fatigue loading, even if the dwell time is 10 s. With an identical stress intensity factor range, a longer dwell time results in a faster crack growth rates. The crack growth rates of Ti-6Al-4V are about 1−2 times faster in the case with dwell time 10 s and 2−6 times faster in the case ∆K with dwell time 60 s across all the range of than the fatigue crack growth rates. The dwell time effect on the crack growth rate is more obvious in the range of larger stress intensity factor.

Single overload effects
The fatigue and dwell fatigue crack growth rates of Ti-6Al-4V with a single overload were tested and the experimental results are shown in Fig. 8. It can be clearly seen the retardation effect after the overload loading. After overloading, the fatigue crack growth rates of Ti-6Al-4V with and without dwell time decrease drastically to the minimum value. With the dwell time unchanged, the retardation effect increases with the increase of the overload ratio. With the same overload ratio, the retardation effect on the crack growth rates of Ti-6Al-4V increases as the dwell time increases. The crack growth rates of Ti-6Al-4V recover rapidly and gradually approach the crack growth rate of the constant amplitude loading. The transient zone size is influenced by the overload ratio and the dwell time. The experimental results of the transient zone sizes of Ti-6Al-4V are listed in Table 4. The transient zone sizes are 0.325 mm and 0.795 mm under cyclic loading without dwell time for the overload ratios of 1.2 and 1.5 respectively; 0.617 mm and 0.945 mm with dwell time 10 s; and 0.752 mm and 1.238 mm with dwell time 60 s. It is apparent that the transient zone sizes of Ti-6Al-4V increase as the overload ratio and the dwell time increase. It is obvious that the transient zone size is determined by the crack tip plastic zone induced by the overload. It means that the introduction of dwell time in the cyclic loading enlarges the crack tip plastic zone size. To explain this phenomenon, a modified model is then proposed to predict the crack tip plastic zone in consideration of the cyclic loading and dwell time.

Dwell fatigue crack growth model
Based on the constitutive relation of fatigue crack growth proposed by Cui et al. (2011), a dwell fatigue crack growth rate model is proposed by Wang (2015). The dwell fatigue crack growth rate model is a linear summation of fatigue and dwell fatigue. The model is found to be able to predict long and small fatigue crack growth behavior from the threshold to unstable fracture. The dwell fatigue crack growth behavior linearly increases as the dwell time under the maximum loading increases. The dwell fatigue crack growth rate model is given as follows:    where, where , , , , and are the material and environmental parameters; is the load stress ratio; is the maximum stress intensity factor; is the range of the stress intensity factor; is the fracture toughness of the material; is crack growth threshold value for small crack growth under stress ratio ; is crack growth threshold value for long crack growth under stress ratio ; is the level of the crack closure; is the intrinsic crack length; is the load holding time under the maximum stress; is the crack length; and are the width and thickness of specimens; is the geometrical correction functions.

A modified model for single overload effects
Φ RC For many materials under constant amplitude loading, Eq. (1) can be used to predict the fatigue and dwell fatigue crack growth behavior. However, Eq. (1) cannot be directly used to estimate the effects of overloading, underloading, and sequence loading on crack growth rates. To meet the practical requirements, based on Zhao et al. (2008) and Wang et al. (2014b), a modified model is proposed to consider the combination of overload and dwell time under the maximum stress. In this model, a load sequence correction factor is introduced to the right side of Eq. (1),

It is obvious that
is for the constant amplitude loading condition.
is defined as: represents the effective residual plastic region under combination of single peak overload and dwell time, it can be expressed as: The plastic zone size under cyclic loading in Eq. (8) is often calculated by using Irwin's method (Irwin, 1960). The plastic zone size under cyclic loading is estimated as: (9) r pi−hold In this paper, the plastic zone size in Eq. (8) under dwell time loading is estimated by the formulas proposed by Riedel and Rice (1980). The plastic zone size induced by the dwell time can be written as: where and are the stress exponent and coefficient in Norton creep Law; is angle; is time; is elastic modulus. and can be obtained by linear interpolation (Potirniche, 2019).
According to Wang et al. (2014a), the monotonic over-  (7) is modified to consider the dwell time under overload condition. The modified monotonic overload plastic zone size can be expressed as: r pR a R r pR is the crack tip plastic zone size when the crack length is .
can be expressed as follows: where is the material parameters, =1 and 3 for plane stress and plane strain conditions, respectively; is the current crack length at the i-th loading cycle; is the crack length at which the overload was applied; is the Wheeler's empirically adjustable shaping exponent which can be simply taken as the value that best fits the data. is the material yield strength; is the stress intensity factor corresponding to the overload.
is the range of the stress intensity factor when the crack length is .
can be determined as:

Constant amplitude loading
In this section, the experimental results of Ti-6Al-4V shown in Fig. 7 are applied to validate Eq. (1) in prediction of fatigue crack growth rates without and with dwell time under constant amplitude. The fatigue crack growth rates without and with dwell time are predicted under the same stress ratio and dwell time with the experiments. The model parameters for Ti-6Al-4V are listed in Table 5. Fig. 9 presents the comparison of the predicted results with the experimental results for fatigue crack growth rates of Ti-6Al-4V without and with dwell time under constant amplitude. Two dwell periods of 10 s and 60 s are considered. The crack growth rates increase with the increase of dwell time at the maximum stress. The experimental results and predicted results show that the Ti-6Al-4V alloy is very sensitive to the dwell time. The comparison displays that the prediction results of Eq. (1) agree well with the experimental results in all the stress intensity factor range with different dwell time. Eq. (1) can be used to predict the fatigue crack growth rates of Ti-6Al-4V under different dwell time.

Single overload effects
The modified model proposed in this paper will be used to explain the effects of a single overload with dwell time on the fatigue crack growth rate of Ti-6Al-4V. The main modification is directed to the crack tip plastic zone. The crack tip plastic zone is composed of the cyclic loading and dwell time at the maximum stress. To validate the modified model, the experimental results of the overload transient zone size will be compared with the prediction results. The comparison is listed in Table 6. From the experimental results, it is obtained that the transient zone size of Ti-6Al-4V with dwell period is larger than that without dwell period under the same overload ratio. The introduction of the dwell period enlarges the transient zone size. The predicted results of transient zone size coincide well with the experimental results. Fig. 10 and Fig. 11 present the comparison of predicted WANG Ke et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 738-745 743 results with the experimental data under overload ratios of 1.2 and 1.5, respectively. The predicted results and experimental data of Ti-6Al-4V display that the minimum value of the crack growth rates increases with the increase of the overload ratio and dwell period. The transient zone size of Ti-6Al-4V is large when the overload ratio and dwell period are introduced into the cyclic loading. It is apparent that the transient zone size is determined by the crack tip plastic zone caused by the overload ratio and dwell period at the maximum cyclic loading. The modified model is successful to explain the phenomenon. The predicted results agree well with the experimental results. The modified model will be discussed to predict the underload effect and high−low loading sequence effect of Ti-6Al-4V.

Conclusions
In the current investigation, the fatigue crack growth rates of Ti-6Al-4V with and without dwell time at the maximum cyclic loading are investigated by the experimental methods under constant amplitude and single overloading. Based on the experimental results, a modified model is proposed to predict the fatigue and dwell crack growth behavior of Ti-6Al-4V. To verify the modified model, the modified model is used to predict the dwell fatigue crack growth rates under different overload ratios and dwell periods. The following conclusions can be drawn from the current study.
(1) The fatigue and dwell fatigue crack growth rates experiments are conducted on Ti-6Al-4V under constant amplitude and single overload. Ti-6Al-4V is very sensitive to the dwell time at the maximum stress under constant amplitude and single overloading. The dwell fatigue crack growth rates increase with the increase of the dwell periods. The influences of overload and dwell time on the transient zone size of Ti-6Al-4V are experimentally investigated.
(2) A dwell fatigue crack growth model is introduced to predict the fatigue crack growth rates of Ti-6Al-4V under constant amplitude. The model can be used to explain the effects of dwell time on the crack growth rates. The pre- dicted results of Ti-6Al-4V agree well with experimental data. Based on the dwell fatigue crack growth model, a modified model is proposed to explain the overload effects. In the modified model, the crack tip plastic zone is composed of the cyclic loading and dwell time at the maximum stress. The crack tip plastic zone size is predicted by the modified model and compared with the experimental data.
(3) The modified model is applicable to Ti-6Al-4V under single overload. The modified model can bring satisfactory predicted results for crack growth rates of Ti-6Al-4V under different overload ratios and dwell time. The validation on the applicability of the modified model will provide a basis for its future application to the crack growth rates prediction of Ti-6Al-4V under different loading sequences.