Low-Cycle Fatigue Behavior of 10CrNi3MoV High Strength Steel and Its Undermatched Welds

The use of high strength steel allows the design of lighter, more slender and simpler structures due to high strength and favorable ductility. Nevertheless, the increase of yield strength does not guarantee the corresponding improvement of fatigue resistance, which becomes a major concern for engineering structure design, especially for the welded joints. The paper presents a comparison of the low cycle fatigue behaviors between 10CrNi3MoV high strength steel and its undermatched weldments. Uniaxial tension tests, Push-pull, strain-controlled fatigue tests were conducted on base metal and weldments in the strain range of 0.2–1.2%. The monotonic and cyclic stress-strain curves, stress-life, strain-life and energy-life in terms of these materials were analyzed for fatigue assessment of materials discrepancy. The stress-life results of base metal and undermatched weld metal exhibit cyclic softening behaviors. Furthermore, the shapes of 10CrNi3MoV steel hysteresis loops show a satisfactory Masing-type behavior, while the weld metal shows a non-Masing type behavior. Strain, plastic and total strain energy density amplitudes against the number of reversals to failure results demonstrate that the undermatched weld metal presents a higher resistance to fatigue crack initiation than 10CrNi3MoV high strength steel. Finally, fatigue fracture surfaces of specimens were compared by scanning electron microscopy to identify the differences of crack initiation and the propagation between them.


Introduction
Modern steel manufacturing techniques make it easier to produce high strength steel for various fields of engineering structure applications, such as shipbuilding, marine structures, engineering machinery, bridges, and so on [1,2]. Although it has a bright future for engineering applications due to high yield strength, favorable toughness, good weldability and cost efficiency, these properties improvement do not guarantee the corresponding enhancement of fatigue resistance. Especially for the welded joints, the toughness will be decreased unavoidably after welding when the strength of welded joints keep the same level with base metal. Usually, it needs to sacrifice weld metal strength to enhance the ductility of welded joints. 10CrNi3MoV high strength steel is one of the reliable materials for key components in shipbuilding due to its superior mechanical properties and good weld ability [3]. So far, the welding process of this steel has been widely investigated by some researchers. The influence of different welding conditions on varied heat affected zone (HAZ) by double-sided double gas tungsten arc welding (DSGTAW) was studied by microstructure observations by Peng et al. [4][5][6]. Its corrosion microscope. Figure 1 compares the microscopes difference of these materials. The micrographs illustrate the grain boundaries and the non-uniform distribution of precipitates. 10CrNi3MoV high strength low alloy steel, which is quenched and tempered, has a fine microstructure mainly composed of acicular ferrite and granular carbides. For the weld metal after high speed cooling, it is observed that smaller ferrite needles are embed into the martensite grains. Table 1. Comparison of the chemical composition between 10CrNi3MoV steel and under-matched welds. All the smooth fatigue test specimens were machined and processed from a 500 mm × 300 mm × 16 mm welding plate. Table 2 provides the plate multi-pass welding conditions using the GMAW process. The extracted locations of base metal and weld metal smooth specimens are depicted in Figure 2a. It should be noted that the extracted direction of weld metal specimens is vertical to welding bead direction. The width of weld bead is in the range from 5 mm to 10 mm, which does not exceed the limited range of extensometer. The location relationship between the butt weld joint and extracted specimens is shown in Figure 2b. It means that the fatigue failure may occur in HAZ or fusion zone. The judgement of failure location will be presented in the next section. The geometry of smooth LCF cylindrical specimens is also shown in Figure 2b. The gauge length of specimens was polished by an appropriate sequence of sandpapers. The LCF tests for base metal and welds were conducted as ASTM E606 standard [31] in INSTRON 8802 electromechanical fatigue testing machine in the air environment. The strain amplitude was controlled using a dynamic clip gauge of INSTRON. The specimens of these materials were instrumented with a reference gauge length of 12.5 mm for the fatigue tests. In order to investigate the effect of strain amplitude on fatigue mechanical response, these LCF tests were carried out at strain amplitudes varying from ±0.2 to ±1.2% under full reverse sinusoidal waveform with total axial strain control mode.
Optical and scanning electron microscopic investigation was conducted to understand the microstructural and fracture appearance difference after fatigue tests between the base metal and weldments. All the smooth fatigue test specimens were machined and processed from a 500 mm × 300 mm × 16 mm welding plate. Table 2 provides the plate multi-pass welding conditions using the GMAW process. The extracted locations of base metal and weld metal smooth specimens are depicted in Figure 2a. It should be noted that the extracted direction of weld metal specimens is vertical to welding bead direction. The width of weld bead is in the range from 5 mm to 10 mm, which does not exceed the limited range of extensometer. The location relationship between the butt weld joint and extracted specimens is shown in Figure 2b. It means that the fatigue failure may occur in HAZ or fusion zone. The judgement of failure location will be presented in the next section. The geometry of smooth LCF cylindrical specimens is also shown in Figure 2b. The gauge length of specimens was polished by an appropriate sequence of sandpapers. The LCF tests for base metal and welds were conducted as ASTM E606 standard [31] in INSTRON 8802 electromechanical fatigue testing machine in the air environment. The strain amplitude was controlled using a dynamic clip gauge of INSTRON. The specimens of these materials were instrumented with a reference gauge length of 12.5 mm for the fatigue tests. In order to investigate the effect of strain amplitude on fatigue mechanical response, these LCF tests were carried out at strain amplitudes varying from ±0.2 to ±1.2% under full reverse sinusoidal waveform with total axial strain control mode.
Optical and scanning electron microscopic investigation was conducted to understand the microstructural and fracture appearance difference after fatigue tests between the base metal and weldments.   As seen from the results, the ratio between the 0.2% proof yield strength (σYS) and the ultimate tensile strength (σUTS) is high for 10CrNi3MoV steel, which is 1.07. It means that the capability for hardening is limited. Compared with base metal, the undermatched welds have a higher T/Y ratio, which is 1.12. The mechanical properties of these materials under monotonic tension loading are summarized in Table 3.     Figure 3 shows the monotonic stress-strain curve under the strain rate of 2 × 10 −3 /s. As seen from the results, the ratio between the 0.2% proof yield strength (σ YS ) and the ultimate tensile strength (σ UTS ) is high for 10CrNi3MoV steel, which is 1.07. It means that the capability for hardening is limited. Compared with base metal, the undermatched welds have a higher T/Y ratio, which is 1.12. The mechanical properties of these materials under monotonic tension loading are summarized in Table 3.   As seen from the results, the ratio between the 0.2% proof yield strength (σYS) and the ultimate tensile strength (σUTS) is high for 10CrNi3MoV steel, which is 1.07. It means that the capability for hardening is limited. Compared with base metal, the undermatched welds have a higher T/Y ratio, which is 1.12. The mechanical properties of these materials under monotonic tension loading are summarized in Table 3.      distributed from 315 to 270 HV. According to the hardness distribution of welded joints, it shows that fusion region (weld metal) is the weakest zone of the whole joint.   Table 4 summarized the results of fatigue test carried out with smooth specimens for base metal and its undermatched welds under strain-controlled conditions. The table includes the controlled total strain amplitudes, elastic and plastic strain amplitudes, responding stress amplitudes, plastic strain energy density, total strain energy density and the resulting number of cycles to failure, Nf, for each specimen. The stabilized hysteresis loops were used to determine the plastic strain and corresponding energy density values directly.

Fatigue Tests Results
Given the size of the fatigue specimen (Φ7 mm), a great proportion of welding residual stress has been released in the cutting process of specimens. On the other hand, a considerable residual stress relaxation occurs during the beginning fatigue cycles under large loading in low cycle fatigue. Thus, the residual stress can be neglected in low cycle fatigue.
The influence of total strain amplitudes on cyclic stress response (Maximum stress and Minimum stress) against normalized life ratio of 10CrNi3MoV steel and its undermatched welds are depicted in Figure 5a,b, respectively. Regardless of the strain amplitude, the obvious cyclic strainsoftening behaviors can be observed from the base metal and undermatched weld metal plots. As can be seen from these figures, the cyclic stress variation composes a rapid initial softening at the beginning 5-15% cyclic stage. Then keeps stable stress responses until 90-95% of life ratio and experiences a rapid drop in stress culminating in fatigue failure finally. Therefore, the stable stress and strain magnitudes at half-life can be used to assess the fatigue behavior of materials. These results further illustrate the effectiveness of parameters from stabilized half-life cyclic stress-strain hysteresis loops. Since the lower cycle strength of undermatched welds than base metal, the cycle stress responses also exhibit the corresponding decreasing under the same strain amplitudes. The softening behaviors of these materials verified the empirical rule proposed in [32], in which metals with   Table 4 summarized the results of fatigue test carried out with smooth specimens for base metal and its undermatched welds under strain-controlled conditions. The table includes the controlled total strain amplitudes, elastic and plastic strain amplitudes, responding stress amplitudes, plastic strain energy density, total strain energy density and the resulting number of cycles to failure, N f , for each specimen. The stabilized hysteresis loops were used to determine the plastic strain and corresponding energy density values directly.

Fatigue Tests Results
Given the size of the fatigue specimen (Φ7 mm), a great proportion of welding residual stress has been released in the cutting process of specimens. On the other hand, a considerable residual stress relaxation occurs during the beginning fatigue cycles under large loading in low cycle fatigue. Thus, the residual stress can be neglected in low cycle fatigue.
The influence of total strain amplitudes on cyclic stress response (Maximum stress and Minimum stress) against normalized life ratio of 10CrNi3MoV steel and its undermatched welds are depicted in Figure 5a,b, respectively. Regardless of the strain amplitude, the obvious cyclic strain-softening behaviors can be observed from the base metal and undermatched weld metal plots. As can be seen from these figures, the cyclic stress variation composes a rapid initial softening at the beginning 5-15% cyclic stage. Then keeps stable stress responses until 90-95% of life ratio and experiences a rapid drop in stress culminating in fatigue failure finally. Therefore, the stable stress and strain magnitudes at half-life can be used to assess the fatigue behavior of materials. These results further illustrate the effectiveness of parameters from stabilized half-life cyclic stress-strain hysteresis loops. Since the lower cycle strength of undermatched welds than base metal, the cycle stress responses also exhibit the corresponding decreasing under the same strain amplitudes. The softening behaviors of these materials verified the empirical rule proposed in [32], in which metals with σ UTS /σ YS < 1.2 demonstrated cyclically soften (10CrNi3MoV steel σ UTS /σ YS = 1.07 and undermatched welds σ UTS /σ YS = 1.12). Additionally, the degree of softening is decreased with the increases of strain amplitudes.   Figure 6 presents the stabilized cyclic stress-strain hysteresis loops using a half-life criterion obtained from these materials fatigue results. It is clear that 10CrNi3MoV steel shows a great consistency with increases of strain amplitudes from Figure 6a. While the cyclic stress-strain hysteresis of weld metal in Figure 6b demonstrates some difference with the base metal, the peak cyclic stress response cannot be superimposed under different strain levels. Based on the combination of hysteresis curves under different strain amplitudes, the stabilized cycle Ramberg-Osgood relationships are determined by the fitting of each maximum cyclic stress. Generally, the Masing behaviors can be observed if the upper branches of the hysteresis loops are all coincident. For a material obeying the Masing-type behavior, the relationship between cyclic stress and plastic strain amplitudes, the plastic strain energy density variation may be illustrated by the cyclic curves of the material. Thus, the shape of the hysteresis loops of 10CrNi3MoV steel exhibits a satisfactory Masing-type behavior. Whereas the undermatched welds do not have the characteristics of Masing behavior, being a non-Masing material. strain energy. As for the calculation of ∆Wp, they can be conducted by a "master curve" for both non-Masing and ideal Masing material description [33]. The curve is different from the defined cyclic stress-strain curve. We can match the upper branches of half-life hysteresis loops under many strain amplitudes by translating the locations along its linear response portion. The relationship for the master curve with the origin at the tip of the smallest plastic strain hysteresis loop is proposed as follows: The hysteresis loops for 10CrNi3MoV steel, Figure 8a, show the good superposition of peak stress values under different strain amplitudes without translating the original coordination. Moreover, the corresponding master curve and the cyclic curve are superimposed for comparison.
Regardless of the hysteresis loops of weld metal, the upper branches of loops do not form a unique continuous curve as a non-Masing behavior. However, translating the original position of hysteresis loops under different strain amplitudes in coordination makes the upper branches superimposed alone a linear response, which is shown in Figure 8b. The original coordination 0 is moved to another position 0  by numeric conversion for superimposing. A new auxiliary with a new origin 0  was established. Therefore, the master curve of non-Masing material is obtained from these transitions. As stated above, the plastic strain energy density (∆Wp) due to the plastic deformation can be calculated by the area of hysteresis loop. For a Masing-type material, it can be expressed as [34]: is the plastic strain range and n is the cyclic hardening exponent. For a non-Masing material, the ∆Wp can be calculated from the equation as following [28]: where the n  is the hardening exponent of the master curve and Summaries of all parameters of cyclic stress-strain curves and master curves for 10CrNi3MoV steel and weld metal are given in Table 6. More discussion of on the results of hysteresis loops in provided in next section.   Figure 7a depicts the stress-strain comparison between monotonic tension and cyclic Ramberg-Osgood relationships for 10CrNi3MoV steel. The results show that stress in the plastic stage from cyclic curves is lower than the monotonic stress-strain curves due to the material cyclic softening behavior. Similarly, the weld metal cyclic stress-strain curves also indicate the stress declining tendency in Figure 7b. After that, the parameters of different cyclic stress-strain curves are computed according to Equation (1), which are summarized in Table 5.

Low Cycle Fatigue Life
The fatigue assessment of material and components generally classes into S-N, local and fracture mechanics-based approaches. As the global approach, S-N curves method for components and structures are a fundamental method and included in some standard recommendations, such as IIW, Eurocode 3. However, this approach does not account for the material life behaviors. The local approaches can illustrate the local fatigue behavior since it can recognize the localized nature of the fatigue damage. The most well-known relationships are the proposals by Basquin [35], Equation (5) Manson [36] and Coffin [37], Equation (6), and the Morrow [34], Equation (7):

The Analysis of Hysteresis Loops
Although the cyclic stress-strain curve describes the relationship between stable stress and strain amplitudes, it cannot acquire some analytical information about the shape of hysteresis loop branches. As mentioned above, 10CrNi3MoV steel exhibits a good Masing behavior, while weld metal shows a non-Masing behavior. Hence, the analysis of hysteresis loops may provide a way to understand the microstructural behavior of the material. Generally, the hysteresis loops can be extracted at half-life for materials fatigue results.
The plastic strain energy density per cycle, ∆W p , is the area of the hysteresis loop. The total damage under fatigue loading, ∆W T , are the plastic strain energy and the tension part of the elastic strain energy. As for the calculation of ∆W p , they can be conducted by a "master curve" for both non-Masing and ideal Masing material description [33]. The curve is different from the defined cyclic stress-strain curve. We can match the upper branches of half-life hysteresis loops under many strain amplitudes by translating the locations along its linear response portion. The relationship for the master curve with the origin at the tip of the smallest plastic strain hysteresis loop is proposed as follows: The hysteresis loops for 10CrNi3MoV steel, Figure 8a, show the good superposition of peak stress values under different strain amplitudes without translating the original coordination. Moreover, the corresponding master curve and the cyclic curve are superimposed for comparison.

Low Cycle Fatigue Life
The fatigue assessment of material and components generally classes into S-N, local and fracture mechanics-based approaches. As the global approach, S-N curves method for components and structures are a fundamental method and included in some standard recommendations, such as IIW, Eurocode 3. However, this approach does not account for the material life behaviors. The local approaches can illustrate the local fatigue behavior since it can recognize the localized nature of the fatigue damage. The most well-known relationships are the proposals by Basquin [35], Equation (5) Manson [36] and Coffin [37], Equation (6), and the Morrow [34], Equation (7):  Figure 8b. The original coordination 0 is moved to another position 0 * by numeric conversion for superimposing. A new auxiliary coordinate system (∆ε * , ∆σ * ) with a new origin 0 * was established. Therefore, the master curve of non-Masing material is obtained from these transitions.
As stated above, the plastic strain energy density (∆W p ) due to the plastic deformation can be calculated by the area of hysteresis loop. For a Masing-type material, it can be expressed as [34]: where the ∆σ is the stress range, ∆ε p is the plastic strain range and n is the cyclic hardening exponent. For a non-Masing material, the ∆W p can be calculated from the equation as following [28]: where the n * is the hardening exponent of the master curve and δ∆σ 0 = ∆σ − ∆σ * . Summaries of all parameters of cyclic stress-strain curves and master curves for 10CrNi3MoV steel and weld metal are given in Table 6. More discussion of on the results of hysteresis loops in provided in next section.

Low Cycle Fatigue Life
The fatigue assessment of material and components generally classes into S-N, local and fracture mechanics-based approaches. As the global approach, S-N curves method for components and structures are a fundamental method and included in some standard recommendations, such as IIW, Eurocode 3. However, this approach does not account for the material life behaviors. The local approaches can illustrate the local fatigue behavior since it can recognize the localized nature of the fatigue damage. The most well-known relationships are the proposals by Basquin [35], Equation (5) Manson [36] and Coffin [37], Equation (6), and the Morrow [34], Equation (7): where the σ f and b are the fatigue strength coefficient and exponent, respectively. ε f and c are the fatigue ductility coefficient and exponent, respectively. The 2N f is the number of reversals to failure. ∆ε t , ∆ε e and ∆ε p are the total, elastic and plastic strain range, respectively. ∆σ is the stress range. E is the Young's modulus. Figure 9 shows the low cycle fatigue life according to Manson-Coffin curves for 10CrNi3MoV steel and its undermatched welds. The analysis of the results shows that the number of transition reversals (2N f ) is very distinct between the two materials. The base metal has a small number of transition reversals about 1000 cycles in Figure 9a. It means that the fatigue life above 1000 cycles the fatigue behavior of the steel is governed by fatigue strength properties rather than the ductility properties. However, the undermatched welds have a larger number of transition reversals than base metal, which is about 3854 cycles, as shown in Figure 9b. Therefore, the plastic deformation leads to more fatigue damage for the base metal than for its undermatched weld metal. To compare the fatigue properties of these materials directly, the total strain amplitudes against life curves were fitted according to Equation (7). Figure 10 depicts a comparison of total strain amplitudes-life between base metal and undermatched welds. For the final results of strain-life curves, it can be seen that the low strength weld metal demonstrates a stronger fatigue behavior than the high strength base metal for all the range of total strain amplitudes. We also compare LCF results of similar material (10% Cr martensitic steel) and its Ni-based welds from [38] in Figure 10. According to the fatigue ductility and strength-life points of these materials, the BM and WM demonstrate the similar fatigue resistance behavior. However, the base metal (10CrNi3MoV steel) in our study has lower fatigue resistance than the 10% Cr martensitic steel and its Ni-based welds. The undermatched welds show the similar fatigue failure behaviors with 10% Cr martensitic steel. Finally, fatigue strength and fatigue ductility parameters of 10CrNi3MoV high strength steel and undermatched welds are summarized in Table 5.
where the is the stress range. E is the Young's modulus. Figure 9 shows the low cycle fatigue life according to Manson-Coffin curves for 10CrNi3MoV steel and its undermatched welds. The analysis of the results shows that the number of transition reversals ( 2 f N ) is very distinct between the two materials. The base metal has a small number of transition reversals about 1000 cycles in Figure 9a. It means that the fatigue life above 1000 cycles the fatigue behavior of the steel is governed by fatigue strength properties rather than the ductility properties. However, the undermatched welds have a larger number of transition reversals than base metal, which is about 3854 cycles, as shown in Figure 9b. Therefore, the plastic deformation leads to more fatigue damage for the base metal than for its undermatched weld metal. To compare the fatigue properties of these materials directly, the total strain amplitudes against life curves were fitted according to Equation (7). Figure 10 depicts a comparison of total strain amplitudes-life between base metal and undermatched welds. For the final results of strain-life curves, it can be seen that the low strength weld metal demonstrates a stronger fatigue behavior than the high strength base metal for all the range of total strain amplitudes. We also compare LCF results of similar material (10% Cr martensitic steel) and its Ni-based welds from [38] in Figure 10. According to the fatigue ductility and strength-life points of these materials, the BM and WM demonstrate the similar fatigue resistance behavior. However, the base metal (10CrNi3MoV steel) in our study has lower fatigue resistance than the 10% Cr martensitic steel and its Ni-based welds. The undermatched welds show the similar fatigue failure behaviors with 10% Cr martensitic steel. Finally, fatigue strength and fatigue ductility parameters of 10CrNi3MoV high strength steel and undermatched welds are summarized in Table 5.   Fitting. Exp. 10CrNi3MoV Undermatched welds 9-12% Cr steel [38] Related welds [38] Strain amplitude Reversal to failure, 2N f Figure 10. Comparison between Manson-Coffin curves of materials from test and reference [38].

Energy-Life Relationships
From experimental data of base metal and weld metal cyclic curves in Figure 7, the master curve hardening exponents fitted by the least square method are obtained. Thus, the evolution of P W  at the half-life reversals to failure life (2Nf) can be compared with a log-log scale, which is determined by the measuring area of hysteresis loops, Masing-type Equation (3), and non-masing type Equation (4). Table 6 Table 6, the results of different methods are quite close. It is worthy to note that these values can be fitted by a linear relationship. Further, the stable linear relationship realizes the quantity of fatigue life by a proper damage parameter. The evolution of P W  from experiments against fatigue life, which is shown as dashed line in Figure 11, can be fitted by a power law function from Equation (8). Figure 12 shows the comparison of plastic strain energy density ∆Wp between 10CrNi3MoV high strength steel and its undermatched welds. The fitting linear relationship agrees well the experimental data for base metal and weld metal. In this manner, the stable trends give to the quantity the attribute of a proper fatigue damage parameter for fatigue assessment. From the results in Figure 13, the fatigue life of weld metal is longer than the base metal under the same plastic strain energy density values. It further illustrates that undermatched welds show better fatigue behaviors than the base metal.
In general, the Masing-type Equation (3) for plastic strain energy density is more suitable for the perfect Masing material, such as the base metal 10CrNi3MoV steel. Whereas the predicted Equation (4) for non-Masing material appear to be much accurate than Masing-type Equation (3). A compared summary of experimental data and predicted equations is presented in Table 7. The results are also shown in Figure 13. As can be seen from Figure 13a, the results from predicted equations for 10CrNi3MoV steel are close to the experimental data for high plastic strain energy density. While some deviation appears compared with experimental data in the range of small plastic strain energy density amplitudes. Nevertheless, the results from Masing-assumption model and non-Masingassumption model are consistency for all the range of plastic strain energy density. Figure 13b shows the comparison of predicted models and experimental data for undermatched welds that reflects a typical non-Masing material behavior. From the results of comparison, the non-Masing material equation is more accurate than the Masing material equation for the weld metal, yet there are close to experimental data.
To reflect the integrity of strain energy under different strain amplitudes, the total strain energy density is computed by the sum of the plastic and the tension elastic strain energy densities of the half-life stress-strain hysteresis loop, from the following Equation (9):

Energy-Life Relationships
From experimental data of base metal and weld metal cyclic curves in Figure 7, the master curve hardening exponents fitted by the least square method are obtained. Thus, the evolution of ∆W P at the half-life reversals to failure life (2N f ) can be compared with a log-log scale, which is determined by the measuring area of hysteresis loops, Masing-type Equation (3), and non-masing type Equation (4). Table 6 exhibits the values of ∆W P with the corresponding strain amplitudes based on different equations. Seen from values in Table 6, the results of different methods are quite close. It is worthy to note that these values can be fitted by a linear relationship. Further, the stable linear relationship realizes the quantity of fatigue life by a proper damage parameter. The evolution of ∆W P from experiments against fatigue life, which is shown as dashed line in Figure 11, can be fitted by a power law function from Equation (8). Figure 12 shows the comparison of plastic strain energy density ∆W p between 10CrNi3MoV high strength steel and its undermatched welds. The fitting linear relationship agrees well the experimental data for base metal and weld metal. In this manner, the stable trends give to the quantity the attribute of a proper fatigue damage parameter for fatigue assessment. From the results in Figure 13, the fatigue life of weld metal is longer than the base metal under the same plastic strain energy density values. It further illustrates that undermatched welds show better fatigue behaviors than the base metal.          In general, the Masing-type Equation (3) for plastic strain energy density is more suitable for the perfect Masing material, such as the base metal 10CrNi3MoV steel. Whereas the predicted Equation (4) for non-Masing material appear to be much accurate than Masing-type Equation (3). A compared summary of experimental data and predicted equations is presented in Table 7. The results are also shown in Figure 14. As can be seen from Figure 14a, the results from predicted equations for 10CrNi3MoV steel are close to the experimental data for high plastic strain energy density. While some deviation appears compared with experimental data in the range of small plastic strain energy density amplitudes. Nevertheless, the results from Masing-assumption model and non-Masing-assumption model are consistency for all the range of plastic strain energy density. Figure 14b shows the comparison of predicted models and experimental data for undermatched welds that reflects a typical non-Masing material behavior. From the results of comparison, the non-Masing material equation is more accurate than the Masing material equation for the weld metal, yet there are close to experimental data.

The Failure Location of Welded Joints
Due to the discrepancy of the chemical composition and microstructures between the base metal and undermatched weld metal, it is necessary to confirm the fracture location of the undermatched welded joints under low cycle fatigue. It can be seen for all strain amplitudes from Figure 15, the fracture crack is initiated from the undermatched weld metal. During the LCF tests, the strain of the welded joints mainly concentrated on the weld metal (WM) region. Especially at the large strain amplitude (1.2%) from Figure 15a, obvious plastic deformation can be observed in WM region. Although it occurs secondary crack in the HAZ, the final fracture position appears in the weld metal. To further verify fatigue failure locations in low cycle fatigue tested specimens of weld joints, optical metallographic studies had been carried out on longitudinal cross section of the fatigue tested sample (∆ε/2 = 0.6%) in Figure 15b. It can be observed from this figure, the fatigue crack was initiated and propagated in the WM region. It demonstrates again that the weakest region is the weld metal zone.
Since displacement-controlled loading was used for fatigue tests, different peak tensile stresses were observed for weldments and base metal under the same strain amplitude. Due to the lower fatigue strength and fatigue ductility coefficient of the undermatched welds, it is more likely that plastic deformation occurs in these samples. Thus, the final fatigue damage of welds is larger than that of base metal. When the location of fatigue crack initiation is determined, the fatigue life is dependent on the material properties. To reflect the integrity of strain energy under different strain amplitudes, the total strain energy density is computed by the sum of the plastic and the tension elastic strain energy densities of the half-life stress-strain hysteresis loop, from the following Equation (9): where k T and α T are constants, and ∆W e+ 0 is the tension strain energy at the material fatigue limit estimated at 2N f = 10 7 . Finally, the corresponding parameters about plastic strain energy density and total strain energy density are summarized in Table 8. The total strain energy density against the number of reversals to failure for base metal and its undermatched welds are compared in Figure 14. The difference of fatigue behaviors under different total strain energy density amplitudes between the two materials is obvious. Similar with the fatigue assessment of plastic strain energy density, the undermatched weld metal demonstrates better fatigue properties than base metal, even though the cyclic strength of weld metal is lower than base metal. Figure 15 depicts the comparison of total strain energy density ∆W T based on Equations (8) and (9) for the two materials. The fitting function of Equation (9) has shown good agreement with the experimental observations. Moreover, it is not only suitable for low cycle fatigue but for high cycle fatigue, even can illustrate the mean stress effect. For some complicated components, such as notch components, it has more widely used to assess the fatigue behavior considering stress concentration phenomenon.

The Failure Location of Welded Joints
Due to the discrepancy of the chemical composition and microstructures between the base metal and undermatched weld metal, it is necessary to confirm the fracture location of the undermatched welded joints under low cycle fatigue. It can be seen for all strain amplitudes from Figure 15, the fracture crack is initiated from the undermatched weld metal. During the LCF tests, the strain of the welded joints mainly concentrated on the weld metal (WM) region. Especially at the large strain amplitude (1.2%) from Figure 15a, obvious plastic deformation can be observed in WM region. Although it occurs secondary crack in the HAZ, the final fracture position appears in the weld metal. To further verify fatigue failure locations in low cycle fatigue tested specimens of weld joints, optical metallographic studies had been carried out on longitudinal cross section of the fatigue tested sample (∆ε/2 = 0.6%) in Figure 15b. It can be observed from this figure, the fatigue crack was initiated and propagated in the WM region. It demonstrates again that the weakest region is the weld metal zone.
Since displacement-controlled loading was used for fatigue tests, different peak tensile stresses were observed for weldments and base metal under the same strain amplitude. Due to the lower fatigue strength and fatigue ductility coefficient of the undermatched welds, it is more likely that plastic deformation occurs in these samples. Thus, the final fatigue damage of welds is larger than that of base metal. When the location of fatigue crack initiation is determined, the fatigue life is dependent on the material properties.

The Fatigue Fracture Morphology
The fractographs of base metal after LCF fatigue tests under 0.4% and 0.8% strain amplitudes are exhibited in Figure 16. Figure 16a (∆ε/2 = 0.4%) shows a fracture surface caused by propagation of cracks nucleated at the specimen periphery. Thus, it leads to some steps in the fracture surface due to the junctions of different propagation planes. In the bottom of this fracture surface, it shows the cleavage steps for final fracture. Figure 16b (∆ε/2 = 0.8%) also gives the fracture surface by propagation of some small cracks, the fracture behaviors of crack nucleation and propagation under ∆ε/2 = 0.8% show the similar behavior with ∆ε/2 = 0.4%. Normally, the junction under different planes (b)

The Failure Location of Welded Joints
Due to the discrepancy of the chemical composition and microstructures between the base metal and undermatched weld metal, it is necessary to confirm the fracture location of the undermatched welded joints under low cycle fatigue. It can be seen for all strain amplitudes from Figure 15, the fracture crack is initiated from the undermatched weld metal. During the LCF tests, the strain of the welded joints mainly concentrated on the weld metal (WM) region. Especially at the large strain amplitude (1.2%) from Figure 15a, obvious plastic deformation can be observed in WM region. Although it occurs secondary crack in the HAZ, the final fracture position appears in the weld metal. To further verify fatigue failure locations in low cycle fatigue tested specimens of weld joints, optical metallographic studies had been carried out on longitudinal cross section of the fatigue tested sample (∆ε/2 = 0.6%) in Figure 15b. It can be observed from this figure, the fatigue crack was initiated and propagated in the WM region. It demonstrates again that the weakest region is the weld metal zone.
Since displacement-controlled loading was used for fatigue tests, different peak tensile stresses were observed for weldments and base metal under the same strain amplitude. Due to the lower fatigue strength and fatigue ductility coefficient of the undermatched welds, it is more likely that plastic deformation occurs in these samples. Thus, the final fatigue damage of welds is larger than that of base metal. When the location of fatigue crack initiation is determined, the fatigue life is dependent on the material properties.

The Fatigue Fracture Morphology
The fractographs of base metal after LCF fatigue tests under 0.4% and 0.8% strain amplitudes are exhibited in Figure 16. Figure 16a (∆ε/2 = 0.4%) shows a fracture surface caused by propagation of cracks nucleated at the specimen periphery. Thus, it leads to some steps in the fracture surface due to the junctions of different propagation planes. In the bottom of this fracture surface, it shows the cleavage steps for final fracture. Figure 16b (∆ε/2 = 0.8%) also gives the fracture surface by propagation of some small cracks, the fracture behaviors of crack nucleation and propagation under ∆ε/2 = 0.8% show the similar behavior with ∆ε/2 = 0.4%. Normally, the junction under different planes reflects a microscopically inclined fracture. The crack propagation near the nucleation area under ∆ε/2 = 0.4% is shown in Figure 16c. Along the direction of crack propagation, ridges appear in propagation regions. The propagation area contains some fatigue striations combined with secondary cracks between large slip bands. These fatigue striations denote essentially transgranular crack propagation. Figure 16d presents the fatigue initiation region under ∆ε/2 = 0.8%. The fatigue cracks mainly initiate from the edge of rounding bar. According to the source of cracks, cracks tip propagation pattern is radial. Obvious ridges can be observed from the radial crack.
Similarly, the fractographs of undermatched welds after LCF fatigue strain amplitudes 0.4% and 0.8% are shown in Figure 17. Fracture surfaces under ∆ε/2 = 0.4%, 0.8% initiate from the specimen periphery and propagate along the crack sources. Comparing Figure 17a with Figure 16a, the fracture surface of undermatched welds is smoother than base metal under the same strain loading. No remarkable fatigue striations can be observed by comparing crack propagation details between Figure 17c with Figure 16c. Moreover, it does not appear the second cracks between the flat fatigue bands in the stage of crack propagation. In the stage of crack origination under 0.8% strain amplitude, the same phenomenon shows that the fracture surface of undermatched welds is also more flat than base metal, as shown in Figure 17b. In addition, the microscope pores are found inside of the fractograch, which are formed in the process of melting. Due to the difference of material strength and microstructure, the larger acicular ferrite and granular carbides in base metal facilities the trapping of particles between intercellular spacing than the grain boundaries. Thus, slip bond occurs more steadily across the cells that lead to transgranular cracking. As the fracture path is shorter for transgranular cracking, fatigue resistance can be reduced for base metal. Therefore, the undermatched welds demonstrate better fatigue ductility longer fatigue life than base metal.

Conclusions
The low cycle fatigue behaviors of 10CrNi3MoV high strength steel and its corresponding undermatched welds were evaluated by means of experimental tests. A series of strain-controlled fully-reversed fatigue tests were conducted under strain amplitudes ranging from 2-1.2% by smooth specimens. The cyclic deformation response, fatigue strength, fatigue ductility properties and cyclic strain energy density were analyzed. The following conclusion can be drawn as follows:

Conclusions
The low cycle fatigue behaviors of 10CrNi3MoV high strength steel and its corresponding undermatched welds were evaluated by means of experimental tests. A series of strain-controlled fully-reversed fatigue tests were conducted under strain amplitudes ranging from 2-1.2% by smooth specimens. The cyclic deformation response, fatigue strength, fatigue ductility properties and cyclic strain energy density were analyzed. The following conclusion can be drawn as follows:

Conclusions
The low cycle fatigue behaviors of 10CrNi3MoV high strength steel and its corresponding undermatched welds were evaluated by means of experimental tests. A series of strain-controlled fully-reversed fatigue tests were conducted under strain amplitudes ranging from 2-1.2% by smooth specimens. The cyclic deformation response, fatigue strength, fatigue ductility properties and cyclic strain energy density were analyzed. The following conclusion can be drawn as follows: (1) The cyclic strength mismatch ratio showed some discrepancy with the mismatch ratio under monotonic loading for these materials. (2) A gradual cyclic softening behavior under different strain amplitudes was observed for the two materials. Moreover, the soften behavior mainly appeared in the beginning cyclic stage, which took nearly 5-15% of fatigue life ratio. (3) The fatigue results show low strength weld metal exhibit a higher fatigue resistance than 10CrNi3MoV steel for all the range of total strain amplitudes, it illustrates that the enhancement of material strength cannot guarantee the proper improvement of fatigue properties. (4) According to the hysteresis loops under different strain amplitudes, 10CrNi3MoV high strength steel demonstrated almost ideal Masing-type behavior, whereas the undermatched weld metal exhibited non-Masing-type behavior. (5) The relationship between plastic strain energy density at half-life cycle against the number of reversals to failure is fitted satisfactorily by the power-low equation. The total strain energy density is an adequate parameter for both high-and low-cycle fatigue regimes. (6) The fatigue assessment for these two materials based on the plastic and total strain energy density all shows that the undermatched weld metal has better fatigue resistance than base metal.