Cyclic Yield Characterization for Low-Carbon Steel with HAZ Microstructures

Abstract

To characterize the relationship between the cyclic yield and monotonic tensile properties of HAZ microstructures, incremental step tests were carried out on a total of eight microstructures of low-carbon steel that had been subjected to several simulated HAZ heat treatments. The results showed that most of the cyclic stress-strain relationships evaluated using incremental step tests roughly agreed with those from constant-stress amplitude tests. Furthermore, the cyclic yield stresses of simulated HAZ microstructures were proportional to these tensile strengths, similar to ordinary carbon and low-alloy steels. Although cyclic yield coefficients were also proportional to these tensile strengths, the slope of the proportional line is steeper than that of ordinary steels. Approximation formulas using monotonic tensile stress to calculate cyclic hardening coefficients for simulated HAZ were therefore determined as the least-squares line compiled from the experimental data.

1. Introduction

The “Development of Materials Integration (MI) System,” a project within the “Cross-ministerial Strategic Innovation Promotion Program (SIP)” focuses on fatigue life prediction of weld joints. Due to stress concentration in weld toes, fatigue cracks in welding components are initiated around the heat-affected zones (HAZ) that have various microstructures derived from their welding thermal history. Therefore, to predict the fatigue life of a weld, it is important to understand the fatigue properties of its HAZ microstructures. To investigate the local mechanical properties of HAZ areas, a small specimen taken from the actual weld joint is often used.¹⁾ However, it is difficult to completely ignore the effects of microstructural gradients around the HAZ area that will possibly limit plastic deformation. Hence, several investigations have also been reported using specimens that have individual HAZ microstructures generated by heat treatments that are simulations of the thermal history of the HAZ area.^2–4) However, the fatigue behaviors of individual HAZ microstructures, particularly for cyclic yield behavior, have not yet been investigated. This study focuses on the cyclic yield behavior of HAZ microstructures.

In these microstructures, fatigue life is usually dominated by the applied stress-strain conditions. Since fatigue cracks are initiated at stress concentrations, local stress or strain values are usually calculated using elastic-plastic finite element analysis (FEA). However, because cyclic softening or hardening occurs during cyclic loading, monotonic stress-strain curves are not always useful for stress analysis under cyclic loading conditions. Cyclically stabilized stress-strain relationships, as expressed by cyclic stress-strain curves, are therefore often used as the stress-strain properties under cyclic loading conditions. Consequently, there is a great deal of research into the cyclic stress-strain behavior of structural materials.

A cyclic stress-strain curve is normally determined by applying strain-controlled cyclic loading tests. To quickly determine cyclic stress-strain curves, Landgraf et al.⁵⁾ proposed an incremental step test in which the specimen is subjected to blocks of gradually increasing, followed by gradually decreasing, strain amplitude. They demonstrated the applicability of their incremental step test to several metallic materials by showing that the cyclic stress-strain curves determined from such step tests are comparable to those obtained in constant strain amplitude tests.⁵⁾ Tanaka et al.⁶⁾ used this testing method to evaluate the cyclic yield properties of several heats of nine carbon and low-alloy steels, 37 materials in total. They noted the cyclic yield stress to have a good correlation with monotonic tensile properties such as tensile or yield strength.

Several researchers^7–13) have analyzed the correlation of numerous cyclic and monotonic data accumulated over many years and have proposed approximation formulas for cyclic stress-strain curve parameters, specifically for the cyclic yield coefficients C and n in the following Ramberg-Osgood type equation.   

\begin{equation} \varepsilon_{a} = \varepsilon_{\textit{el}} + \varepsilon_{\textit{pl}} = \frac{\sigma_{a}}{E} + \left(\frac{\sigma_{a}}{C}\right)^{1/n} \end{equation} (1)

Here, ε_a is strain amplitude, ε_el is elastic strain, ε_pl is plastic strain, E is Young’s modulus and σ_a is stress amplitude. Li et al.¹¹⁾ analyzed the data for more than 120 materials and proposed an approximation formula for cyclic yield coefficients, calculated from monotonic tensile strength and reduction of area. More recently, Zonfrillo¹²⁾ has investigated appropriate monotonic parameters to describe cyclic coefficients by using data from more than 300 materials and has proposed an approximation formula using the monotonic tensile and yield stress ratio as the exponent. However, since previous studies have covered only general structural materials, there is a possibility that the cyclic yield behavior of various HAZ microstructures might be different.

The purpose of this study is to characterize the relationship between the cyclic yield properties and monotonic tensile properties of HAZ microstructures. For this purpose, incremental step tests were carried out on low-carbon steel subjected to several simulated HAZ heat treatments. Several load-controlled constant-amplitude fatigue tests were also carried out to confirm the applicability of the incremental step test to simulated HAZ microstructures.

2. Experimental Procedure

2.1 Preparation of materials

The materials used in this study were two heats of low carbon steel that had undergone several simulated HAZ heat treatments. Table 1 shows their chemical compositions. Heat treatments were applied to a 12 × 13 × 85 mm shaped bar before machining the specimen. The maximum heat treatment temperatures were 1673 K for coarse-grain microstructure materials and 1273 K for relatively fine-grain microstructure materials. After holding at the maximum temperature for 5 seconds, the cooling rates were controlled as follows. When cooling from 1673 K, the cooling rate was 50 K/s at above 1273 K and 30, 3 and 1 K/s for below 1273 K. When cooling from 1273 K, the cooling rates were 30 K/s and 10 K/s. In this study, eight microstructures were prepared for cyclic tests. Figure 1 shows an example of simulated HAZ microstructure images for Heat A. The microstructure image of a) shows martensitic, b) and c) shows bainitic microstructure. In addition, grain boundary ferrite is appeared in the microstructure of c). Monotonic tensile properties for these microstructures are described in Table 2 of the following section.

Table 1 Chemical compositions (mass%).

Fig. 1

Simulated HAZ microstructure images (Heat A).

Table 2 Monotonic and cyclic properties of simulated HAZ specimens.

2.2 Testing procedures

Cyclic loading tests were carried out using servo hydraulic-type fatigue testing. Cyclic yield properties were investigated using strain-controlled incremental step tests. The incremental step test conditions are described as follows. The programmed loading block, shown in Fig. 2, was repeatedly applied to the specimen. After the specimen broke at the n_th applied block, the cyclic stress-strain was determined from the hysteresis loop at 0.5 × n_th applied block as a cyclically stabilized yield property. Figure 3 shows an example of a stabilized hysteresis loop and cyclic stress strain curve acquired in an incremental step test. As shown in the Figure, the cyclic stress-strain curve is determined from the line connecting the peaks of the hysteresis loops.

Fig. 2

Shape of the loading block for incremental step testing.

Fig. 3

Example of hysteresis loop and cyclic stress-strain curve for incremental step test.

In this test, an extensometer with a gauge length of 3 mm was used to prevent the effects of the microstructure gradient in the longitudinal direction of the specimen. The waveform of the block described in Fig. 2 has 25 loading cycles. The strain rate of the incremental step tests was 4 × 10⁻³/s. Load-controlled constant-amplitude fatigue tests were carried out under a loading frequency of 10–20 Hz. During the load-controlled constant-amplitude fatigue test, strain data were also collected by the same extensometer or strain gauge with a gauge length of 0.3 mm.

Figure 4 shows the specimens’ configurations. Although type B specimens have no straight elements, a stress-strain gradient of gauge length of 3 mm has an area that is sufficiently small to be negligible. As a result, the shape of the hysteresis loop measured by the extensometer and strain gauge were almost the same.

Fig. 4

Specimen configurations (in mm). Specimen a) is used for Heat A and b) is used for Heat B.

3. Results and Discussion

Figure 5 shows cyclic stress-strain curves for the simulated HAZ specimen of heat A. Solid symbols represents cyclic stress-strain plots, the peaks of the hysteresis loop shown in Fig. 3. The solid line is the fitting curve of cyclic stress-strain plots using eq. (1). The dotted line describes the elastic gradient of E = 206 GPa. Open symbols represent stress-strain data measured at half the fatigue fracture cycle of a constant-stress amplitude test. The cyclic yield stress level varies according to the heat treatment conditions. Most stress-strain data obtained from constant stress amplitude tests approximately agreed with that from the incremental step tests, indicating that the effects of strain history or strain rate of these microstructures are relatively small. We therefore conclude that incremental step testing is an appropriate method for determining the cyclic stress-strain curve of simulated HAZ microstructures.

Fig. 5

Cyclic stress-strain curves for simulated HAZ of Heat A.

Table 2 shows monotonic and cyclic yield properties of simulated HAZ microstructures. The coefficients C and n in the table are described in eq. (1). The cyclic 0.2% proof stress, σ_{0.2 cy}, was derived from the following eq. (2).   

\begin{equation} \sigma_{0.2\,cy} = C0.002^{n} \end{equation} (2)

All yield stress results from cyclic tests are lower than those from monotonic tests. It thus appears that cyclic softening is relatively dominant in these simulated HAZ microstructures.

Figure 6 shows the relationship between tensile strength and cyclic yield stress from incremental step tests. This Figure also represents other general structural materials data published by NIMS Fatigue Data Sheets (NIMS FDS). As shown in this Figure, cyclic yield stresses of simulated HAZ microstructures are comparable to those of quench-tempered or normalized carbon and low alloy steels. This trend does not depend on the maximum heat treatment temperature, which changes the prior austenite grain size.

Fig. 6

Cyclic yield stress versus tensile strength.

Figure 7 shows the relationship between tensile strength and cyclic yield coefficient C of eq. (1). Ordinary structural steels data from NIMS FDS are also plotted in this figure. The cyclic yield coefficients C of simulated HAZ show good correlation with monotonic tensile strength, similar to ordinary steels. However, the slope of the proportional line of simulated HAZ is relatively steeper than that of ordinary steels. In this Figure, the lines calculated using the following formulas proposed by Li et al.,¹¹⁾ eq. (3) and Zonfrillo’s¹²⁾ eq. (4) are also represented.   

\begin{equation} C = 3.63 \times 10^{-4}\sigma_{B}{}^{2} + 0.68\sigma_{B} + 570 \end{equation} (3)

  

\begin{align} C &= 0.363\sigma_{0.2}\exp\left(\frac{\sigma_{B}}{\sigma_{0.2}}\right) + 0.135\sigma_{B}\exp\left(\frac{\sigma_{B}}{\sigma_{0.2}}\right) \\ &\quad- 9.1678 \end{align} (4)

For the purpose of comparison, the line in this Figure, σ_0.2 of eq. (5) was decided from σ_B by assuming $\frac{\sigma _{B}}{\sigma _{0.2}} = 1.38$ which is the average value of the materials used in this study. Although each line is comparable to data for ordinary steels, these lines cannot describe the behavior of simulated HAZ. Most structural steels used in previous studies appear to have been subjected to tempering heat treatment. However, our simulated HAZ heat treatment is applied to as-quenched microstructures. It is therefore possible that the balance of yield behavior differs from that of ordinary steel data. The approximation line of the simulated HAZ, obtained using the least squares method, is described as follows.   

\begin{equation} C = 2.80\sigma_{B} - 877\quad(R^{2} = 0.94) \end{equation} (5)

Figure 8 also shows the relationship between cyclic hardening exponent n and coefficient C. Unlike with ordinary steels, C and n of simulated HAZ appear to have a positive correlation. The least squares line of this correlation is expressed as follows.   

\begin{align} n &= -8.43 \times 10^{-8}C^{2} + 2.75 \times 10^{-4}C - 4.65 \times 10^{-2}\\ &\quad(R^{2} = 0.82) \end{align} (6)

Like ordinally steel, as described following equations, hardening exponent n becomes constant when σ_{0.2 cy} and coefficient C are linearly proportional to tensile strength.   

\begin{equation} \sigma_{0.2\,cy} = C0.002^{n} = A\sigma_{B} \end{equation} (7)

  

\begin{equation} C = B\sigma_{B} \end{equation} (8)

  

\begin{equation} 0.002^{n} = A/B \end{equation} (9)

Where A and B are proportional constants. As shown in Fig. 6, since simulated HAZ has slight nonlinearity, it is considered that weak correlation of n and C of eq. (6) was appeared.

Fig. 7

Relationship between cyclic hardening coefficient C and tensile strength.

Fig. 8

Relationship between cyclic hardening exponent n and coefficient C.

As shown in above eqs. (5) and (6), the cyclic yield parameters of simulated HAZ can be calculated from tensile strength alone.

Here, to confirm the accuracy of these approximation formulas for simulated HAZ, 0.2% cyclic proof stress calculated from eqs. (2), (5) and (6) were compared to the experimental values. Figure 9 shows the comparison result. For comparison, this figure also described the stress calculated by average value of exponent n, 0.15, instead of eq. (6). The difference between all calculation and experimental values is less than 10%. It appears that these approximation formulas are useful for predicting the cyclic stress strain parameters of simulated HAZ microstructures. Here, the local tensile strength of actual HAZ of welding can possibly be predicted from local hardness. These formulas may also be applicable to actual weld joints of low carbon steel.

Fig. 9

Experimental and calculated cyclic yield stress.

4. Conclusion

To characterize the relationship between the cyclic yield and monotonic tensile properties of HAZ microstructures, incremental step tests were carried out on a total of eight microstructures comprising low-carbon steel that had been subjected to several simulated HAZ heat treatments. The results showed that:

1. (1)    Most of the cyclic stress strain relationships evaluated from incremental step tests roughly agreed with those obtained in constant-stress amplitude tests.
2. (2)    The cyclic yield stress of simulated HAZ microstructures was proportional to these tensile strengths. This behavior was similar to that of ordinary carbon and low-alloy steels.
3. (3)    Although the cyclic yield coefficients were also proportional to these tensile strengths, the slope of the proportional line is somewhat steeper than that of ordinary steels. Hence, approximation formulas to calculate the cyclic hardening coefficients from monotonic tensile strength were derived from the least-squares line compiled from the experimental data.

Acknowledgments

This work was supported by the Council for Science, Technology and Innovation (CSTI), the Cross-ministerial Strategic Innovation Promotion Program (SIP), and “Structural Materials for Innovation” (Funding agency: JST). Material preparation and heat treatment was supported by Professor Tadashi Kasuya of Tokyo University.

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