Factors Affecting Static Strain Aging under Stress at Room Temperature in a Fe–Mn–C Twinning-induced Plasticity Steel

Abstract

We investigated the factors affecting static strain aging under stress in a Fe–22Mn–0.6C twinning-induced plasticity steel at room temperature. The magnitude of strengthening by the static strain aging was estimated by tensile strain holding and subsequent re-loading. Strain holding time, pre-strain, strain rate, external stress, and diffusible hydrogen content were varied to clarify their effects on static strain aging, and the present static strain aging was found to be affected by all of these factors. In this paper, we show the phenomenological laws of the relationship among the factors and the stress increase due to the static strain aging.

1. Introduction

Strain aging is a notable phenomenon that strengthens Fe–Mn–C austenitic steels. Dastur et al. reported static and dynamic strain aging in a Hadfield steel at room temperature,¹⁾ and Owen et al. discussed its strain aging behavior.²⁾ They pointed out that strain aging of Fe–Mn–C austenitic steels have an exceptional effect on strengthening compared with other FCC materials, because of the formation of Mn–C couples. A recent report mentioned that an enhancement of static strain aging occurred in Fe–Mn–C twinning-induced plasticity (TWIP) steels when the specimen was under stress with a constant plastic strain.³⁾

Static strain aging is important since it causes hydrogen embrittlement and is also a strengthening method. Fe–Mn–C TWIP steels were recently reported to show hydrogen embrittlement^{4,5,6,7,8,9,10)} which causes a serious problem, since they are expected to be used for automobile parts with significant residual stress.⁴⁾ In our previous studies, the hydrogen embrittlement susceptibility of TWIP steels was found to decline when the static strain aging was suppressed.^11,12) However, the factors that affect the static strain aging in Fe–Mn–C TWIP steels have not been clarified yet.

Static strain aging behavior essentially depends on pre-strain, aging temperature, and aging time, since static strain aging is attributed to carbon diffusion and an increase in dislocation density. As mentioned above, dynamic strain aging occurs at room temperature in Fe–Mn–C austenitic steels, and its behavior depends on the strain rate.¹⁾ Since dynamic strain aging also stems from carbon-dislocation interactions, static strain aging must be affected by dynamic strain aging during the pre-strain. Therefore, static strain aging is considered to show a pre-strain rate dependence due to the dynamic strain aging behavior. The static strain aging of a pre-strained specimen in Fe–Mn–C austenitic steels at room temperature is also enhanced by an applied stress during aging.³⁾ This fact implies that an application of a stress during aging is also an important factor for the static strain aging.

For these reasons, we examined the magnitude of strengthening by static strain aging at various pre-strains, strain rates, strain holding times, and applied stresses. The influence of the hydrogen uptake on static strain aging was also investigated to correlate the static strain aging with the hydrogen embrittlement. In this paper, we clarify how the various factors affect the static strain aging behavior in a Fe–Mn–C TWIP steel.

2. Experimental

2.1. Material

A Fe–22.05Mn–0.61C–0.01P–0.004S (wt.%) steel was prepared by vacuum induction melting. The Fe–22Mn–0.6C steel is a typical TWIP steel, which was reported to show static strain aging under stress³⁾ and hydrogen embrittlement.^4,11) This steel shows a considerable amount of deformation twins without any deformation-induced martensite.¹³⁾ We showed that the hydrogen embrittlement of this steel was affected by strain aging behavior in a previous study.¹¹⁾ The thickness of the steel was reduced from 60 to 2.6 mm by hot rolling at 1273 K and subsequently reduced to 1.4 mm by cold rolling. Then, it was solution treated at 1073 K. All the specimens were cut with spark erosion. The microstructure had an average grain size of 3 μm that included some annealing twin boundaries as shown in Fig. 1. The initial microstructure was fully austenitic. Finally, the thickness was reduced further to 0.3 mm by mechanical grinding to remove the layer affected by the solution treatment. The tensile specimens that were produced had a gauge dimension of 4.0 mm in width × 0.3 mm in thickness × 10 mm in length with a grip section on both ends to be fixed in an Instron type machine.

Fig. 1.

Optical micrographs of the as-solution treated Fe–22Mn–0.6C steel.

2.2. Tensile Test with Strain Holding

Tensile tests with strain holding were carried out at different strain rates and pre-strains for various holding times at room temperature. The maximum stress increase and the aging temperature dependence of static strain aging have often been examined to obtain the activation energy in other studies. However, the tests were only carried out at room temperature (294 K) in this study, and we did not determine the maximum stress increase for the following reasons.

1) The time to reach the maximum stress due to the static strain aging at room temperature is unrealistically long in experimental studies using austenitic steels since the diffusivity of carbon is much lower than that of ferritic steels.

2) Although increasing the aging temperature promotes the static strain aging, heating at a fixed strain is experimentally difficult, since the stress at a fixed strain decreases due to the heat expansion of the tensile machine.

3) The static strain aging without stress is not observed even after aging at 473 K for 7 days.¹⁾

4) Heating to more than 573 K causes precipitation.¹⁾

Thus, tensile tests with strain holding were performed at room temperature under various conditions to estimate the magnitudes of strengthening by static strain aging. Figure 2(a) shows an example of the true stress-plastic strain curves that includes the process of strain holding. The serrations are reported to arise from dynamic strain aging.¹⁾ In this example, the initial strain rate was 1.7×10^–2 s^–1. Subsequently, the strain was held at a 0.40 true plastic strain for 1000 seconds. Then, the specimen was deformed again at a strain rate of 1.7×10^–2 s^–1. The strain rate in the present work was varied from 1.7×10^–5 to 1.7×10^–2 s^–1, and the strain rate after the strain holding treatment was determined to be the same as that of the pre-deformation state.

Fig. 2.

(a) An example of the true stress-strain curves measured in the present study. The left upper diagram schematically indicates straining process plotted against test time. (b) Portion of the stress-strain curve outlined by the dotted lines in Fig. 2(a).

Figure 2(b) shows the section of the true stress-strain (σ-ε) curve outlined by the square in Fig. 2(a). The stress drop during strain holding and the stress increase by the subsequent deformation are caused by relaxation³⁾ and static strain aging,^3,11,12) respectively. The magnitude of the stress increase due to the static strain aging is defined as   

$$\Delta \sigma ={\sigma }_1-{\sigma }_0$$(1)

where σ₀ is the stress just before relaxation, and σ₁ is the peak stress of the yield tooth as indicated in Fig. 2(b). Due to the limitation of the tensile machine, the maximum strain holding time is 10 hours.

2.3. Strain Holding Tests under Hydrogen Charging

To examine the effect of hydrogen uptake, tensile tests with strain holding were performed under hydrogen charging. Hydrogen was introduced into the specimens by electrochemical charging in a 3% NaCl aqueous solution containing 3 g/L of NH₄SCN at ambient temperature under tensile loading at a constant strain in a fixed cross head position. A platinum wire was used as the counter electrode. Tensile deformations at a strain rate of 1.7×10^–2 s^–1 were stopped once at the 0.52 true plastic strain, then hydrogen was introduced at current densities of 1, 3, and 7 Am^–2 under stress for 10 hours. After the strain holding, the specimens were deformed again to fracture at the same strain rate of 1.7×10^–2 s^–1 under hydrogen charging.

2.4. Measurement of Hydrogen Content

After making an estimation of strengthening by static strain aging under hydrogen charging, the hydrogen content was measured by thermal desorption analysis (TDA) from room temperature to 550 K. The TDA measurements started within 20 minutes after the specimen fractured. The heating rate was 200 K/h. The diffusible hydrogen content was determined by measuring the cumulative desorbed hydrogen content from room temperature to 523 K. The diffusible hydrogen is defined as the hydrogen that diffuses at room temperature, and it was reported to be potentially trapped at dislocations, in the matrix (here preferentially at vacancies), twin boundaries, and grain boundaries in a TWIP steel.¹⁴⁾

3. A Model Used for This Study

In Fe–Mn–C austenitic steels, two types of carbon motion act as the strain aging mechanism. The first one is segregation to dislocations and stacking faults due to a simple diffusion, which has been discussed for conventional static strain aging.¹⁵⁾ The second one is a single jump of carbon from tetrahedron to octahedron sites. Lee et al. proposed^16,17) that strain aging can be caused by an interaction between carbon and a single defect of a stacking fault via the following steps. The perfect dislocations in TWIP steels are dissociated into leading and trailing partial dislocations. For example,   

$$\frac{a}{2}[\overline{1}01]\to \frac{a}{6}[\overline{1}\overline{1}2]+\frac{a}{6}[\overline{2}11]$$(2)

where a is a lattice constant. The carbon position moves from an octahedron site to a tetrahedron site by the shear displacement for a leading partial, since the local atomic sequence transforms from FCC to HCP.¹⁸⁾ Then, the carbon atom moves back to the octahedron site spontaneously due to the low activation energy except when the trailing partial can pass the point where the carbon atom exists. The direction of reordering of C is determined by the atomic interaction. The reordering of C produces a Mn–C complex in the stacking fault, preventing the motion of dislocation,¹⁷⁾ since the Mn–C interaction is relatively-strong in Fe–Mn–C austenitic steels.^1,2)

The first type of carbon motion is controlled by diffusivity of carbon in matrix, implying that static strain aging by the first type of carbon motion requires long time at room temperature. In contrast, the second type of carbon motion is controlled by stacking fault energy and the activation energy for the single jump. The single jump can occur within several seconds, and a second jump does not occur by the same mechanism since the carbon is in the octahedron site already after the first single jump. Namely, the controlling factor and the time scale of the two types of carbon motion are completely different. Therefore, we must consider the two types of carbon motion separately.

First of all, we consider contribution of the first type of carbon motion to static strain aging. Harper reported¹⁵⁾ that the fraction of solute which segregated to dislocations, f, can be expressed as   

$$f=1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]$$(3)

where ρ is the dislocation density, D the diffusion coefficient of the solute, t the aging time, T the aging temperature, k the Boltzmann’s constant, and A and α as constants. In the present paper, we refer to the contribution of static strain aging expressed in Eq. (3) as a Cottrell component. Eq. (3) can be replaced by   

$$\frac{\Delta \sigma }{\Delta {\sigma }_{maxc}}=1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]$$(4)

where Δσ_maxc is the maximum stress increase due to the Cottrell component of static strain aging. When static strain aging under stress is considered, the effect of stress-induced reordering of the solute can be added simply to Eq. (4).^19,20) Namely,   

$$\Delta \sigma =(\Delta {\sigma }_{maxc})\left\{1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]\right\}+\Delta {\sigma }_{maxr}f(t,\mathrm{\hspace{0.17em} }T)$$(5)

where Δσ_maxr is the stress increase associated with the stress-induced re-ordering of the solute, and f (t, T) is the function of aging time and temperature. In fact, the stress increase due to the stress-induced re-ordering of the solute was proposed for the Snoek ordering that does not occur in FCC metals. Instead, the abovementioned reordering arising from the change in carbon position from octahedron to tetrahedron sites takes place in Fe–Mn–C TWIP steels.^16,17) The applied stress must affect the effect of carbon reordering on strengthening. Further details will be discussed in section 4.3.

The present static strain aging must also depend on the strain rate, since dynamic strain aging even occurs at room temperature as shown in Fig. 2(a). Various mechanisms for the dynamic strain aging have already been proposed,^{1,16,17,21,22,23,24)} and in all of the cases, the dynamic strain aging consumes mobile carbon, and depends on the strain rate. The consumption of mobile carbon due to the dynamic strain aging during pre-straining decreases the magnitude of strengthening by the static strain aging. Therefore, Δσ_maxc in Eq. (5) is dependent on the strain rate. Eq. (5) can be modified as   

$$\begin{array}{l}\Delta \sigma =\left(\Delta {\sigma }_{maxc}-\Delta {\sigma }_{dyn}(\epsilon ,\mathrm{\hspace{0.17em} }\dot{\epsilon },\mathrm{\hspace{0.17em} }T)\right)\left\{1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]\right\}\\ \hspace{1em}\mathrm{\hspace{0.17em} }\hspace{0.17em} +\Delta {\sigma }_{maxr}f(t,\mathrm{\hspace{0.17em} }T)\end{array}$$(6)

where Δσ_dyn is the contribution of the stress increase due to the dynamic strain aging, ε the pre-strain, and $\dot{\epsilon }$ the strain rate. In this study, we will discuss our results using Eq. (6).

4. Results and Discussion

4.1. Aging Time Effect

Figure 3(a) shows the changes in Δσ with strain holding time. The strain rates are 1.7×10^–2 and 1.7×10^–4 s^–1, and the strain is held at a 0.40 true plastic strain. Δσ is shown to increase monotonically with logarithmic aging time when the solute reordering is accomplished, and the aging time is much shorter than that for the saturation of the Cottrell component.²⁰⁾ In the case of Fe–Mn–C austenitic steels, the solute reordering is caused by a single jump of interstitial carbon from the unfavorable tetrahedron site to the favorable octahedron site, and is assisted by the attractive atomic force between carbon and manganese.¹⁷⁾ Therefore, the time for accomplishing the solute reordering cannot be a long time such as 10⁴ seconds. Figure 3(b) shows that Δσ increases linearly with increasing logarithmic holding time till 10⁴ seconds. The linear relationship is maintained, regardless of the strain rate and pre-strain as shown in Figs. 3(b) and 4. This fact indicates that 10³ seconds which are the minimum holding time used for the present study are long enough to accomplish the solute reordering, and f (t, T) in Eq. (6) can be regarded as a constant at the same temperature. Namely,   

$$\frac{\Delta \sigma -\beta \Delta {\sigma }_{maxr}}{\Delta {\sigma }_{maxc}-\Delta {\sigma }_{dyn}(\epsilon ,\mathrm{\hspace{0.17em} }\dot{\epsilon },\mathrm{\hspace{0.17em} }T)}=1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]$$(7)

where β is constant. When all the variables are constant except for holding time,   

$$ln\left(1-\frac{\Delta \sigma -\beta \Delta {\sigma }_{maxr}}{\Delta {\sigma }_{maxc}-\Delta {\sigma }_{dyn}}\right)\propto t^{2/3}$$(8)

The linear relationship described by Eq. (8) should be maintained, regardless of Δσ_maxr, Δσ_maxc, and Δσ_dyn. Thus, by assuming Δσ_maxr, Δσ_maxc, and Δσ_dyn to be constants at a given pre-strain and strain rate, the linear relationship can be confirmed experimentally. The experimental relationship between the left and right parts of Eq. (8) is shown in Fig. 5. The relationship can be approximated to be a linear one, and corresponds to Eq. (8). Since the slope depends on βΔσ_maxr and Δσ_maxc–Δσ_dyn, the quantitative values of slopes do not have any physical meaning. The law of t^2/3 is generally accepted in static strain aging without stress, which is attributed to the Cottrell component.²⁵⁾ Hence, the changing trend of Δσ against holding time is mainly attributed to the Cottrell component.

Fig. 3.

(a) True stress increase (Δσ) plotted against strain holding time. The specimens were deformed to 0.40 true plastic strain at pre-strain rates of 1.7×10^–2 and 1.7×10^–4 s^–1. (b) True stress increase re-plotted against logarithmic holding time.

Fig. 4.

Pre-strain dependence of the relationship between true stress increase and strain holding time. The pre-strain rate was 1.7×10^–2 s^–1.

Fig. 5.

Fitting of the law of t^2/3 using Eq. (8). The original data used for this plot are Figs. 3 and 4. As an example, βΔσ_maxr and Δσ_maxc–Δσ_dyn are assumed to be 20 and 150 MPa, respectively. The assumed values are shown to be adequate values since 20 MPa is lower than the lowest Lσ in Figs. 3 and 4, and 150 MPa is higher than the highest Δσ in Figs. 3 and 4.

4.2. Strain Rate Effect

The results of our previous work¹¹⁾ and the present work in Fig. 6 show that Δσ increases linearly with increasing logarithmic strain rate. According to Eq. (6), the strain rate dependence is explained by the influence of dynamic strain aging. Fe–Mn–C TWIP steels are known to show negative strain rate sensitivity due to the suppression of dynamic strain aging by increasing strain rate.^1,16,26) Therefore, the relationship between strain rate and Δσ_dyn in Eq. (7) can be clarified from the strain rate dependence of flow stress that is shown in Fig. 7. Flow stress decreases linearly with increasing logarithmic strain rate, although it is not clear at the 0.25 true plastic strain. The negative strain rate sensitivity is generally known to become clearer with increasing plastic strain.^24,27) The same tendency was reported at similar strain rates and strain ranges in the Fe–22Mn–0.6C steel.^27,28) Hence,   

$$\sigma \propto ln\dot{\mathit{\epsilon }}$$(9)

where σ is the true flow stress. By using Eq. (9), Eq. (7) at a constant pre-strain and temperature leads to   

$$\frac{\Delta \sigma -\beta \Delta {\sigma }_{maxr}}{\Delta {\sigma }_{maxc}-pln\dot{\mathit{\epsilon }}+q}=1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]$$(10)

where p and q are constants. Eq. (10) can be changed to   

$$\begin{array}{l}\Delta \sigma =ln\dot{\mathit{\epsilon }}\left\{pexp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]-p\right\}\\ \hspace{1em}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }+(\Delta {\sigma }_{maxc}+q)\left\{1-exp\left[-\alpha \rho {\left(\frac{ADt}{kT}\right)}^{\frac{2}{3}}\right]\right\}+\beta \Delta {\sigma }_{maxr}.\end{array}$$(10’)

Fig. 6.

Pre-strain dependence of the relationship between true stress increase and pre-strain rate. The holding time was 1000 seconds.

Fig. 7.

Negative strain rate sensitivity of flow stress at various true plastic strains.

The second and third terms of the right side are constants at a constant aging time, pre-strain and aging temperature. Hence, at a constant aging time, pre-strain and aging temperature, Eq. (10’) indicates   

$$\Delta \sigma \propto ln\dot{\mathit{\epsilon }}.$$(11)

Equation (11) explains the linear relationship between the logarithmic strain rate and Δσ shown in Fig. 6. Hence, the increase in Δσ with increasing strain rate arises from the suppression of dynamic strain aging.

4.3. Stress Effect

We also investigated the external stress dependence of Δσ. The external stress was controlled by adjusting the strain from a 0.40 true plastic strain after the pre-deformation to a strain rate of 1.7×10^–2 s^–1. Figure 8 shows an example of the true stress-strain curves with the process of decreasing stress. The strain was held when the stress reached the target value, e.g. 745 MPa. Figure 9 shows the relationship between the initial stress at a fixed strain, σ₀, and Δσ. When we consider the effect of external stress, the influence of solute reordering on strengthening is important. As mentioned in section 3, the formation of Mn–C complexes due to the reordering of carbon in stacking faults was reported to act as a strengthening mechanism.¹⁷⁾ Carbon fraction in stacking faults at a fixed strain can be assumed to have a linear relationship with Δσ_maxr. Since the carbon fraction in stacking faults under a constant dislocation density is proportional to the separation distance of the stacking faults,   

$$\Delta {\sigma }_{maxr}\propto d_{sf}$$(12)

where d_sf is the separation distance of the stacking faults. d_sf is often discussed as having external stress dependence.^29,30,31) According to Copley’s theory,²⁹⁾ the tensile stress dependence of d_sf is defined as   

$$\frac{1}{d_{sf}}=\frac{1}{c}\left(\gamma +\frac{(m_2-m_1)}{2}\sigma b\right)$$(13)

where γ is the stacking fault energy, m₁ and m₂ the absolute values of the Schmid factors of the leading and trailing partials, and b the absolute value of the Burgers vector for the partial dislocations. c is defined as   

$$c=\frac{\mu a^2}{48\pi (1-\nu )}[2-\nu (4{cos}^2\theta -1)]$$(14)

where μ is the shear modulus, ν the Poisson’s ratio, and θ the angle between the dislocation line and the resultant Burgers vector. The tensile external stress effect increases the separation distance when the orientation is close to <111> or <110>, and decreases when the orientation is close to <001>. The negative effect on the separation distance is not considered here, since the carbon fraction in stacking faults at a fixed strain is important for the solute reordering, namely, the extension of dislocations during decreasing stress is not effective for the present static strain aging. Therefore, the tensile external stress effect is always considered to increase the separation distance in the present discussion. Assuming that the dislocation lines are randomly oriented, c is constant. From Eqs. (12) and (13), we can obtain the following relationship.   

$$\Delta {\sigma }_{maxr}\propto \frac{1}{2\gamma +(m_2-m_1)\sigma b}$$(15)

where γ = 22 mJ/m^{2 32)} and b = 1.45×10^–10 m.³¹⁾ The major tensile orientations of the Fe–22Mn–0.6C steel are <111> and <001> when the true strain is above 0.40.³³⁾ Additionally, the volume fraction of the <111> fiber that shows a positive effect on the dislocation separation becomes larger than 50% at the 0.40 true strain.³³⁾ Thus, we assume that m₁ corresponds to the highest Schmid factor of a leading partial in the <111> tensile orientation, namely, m₁ = 0.31. Accordingly, the Schmid factor of the trailing partial (m₂) is assumed to be 0.16. The experimental results in Fig. 9 show a rough agreement with Eq. (15) as shown in Fig. 10.

Fig. 8.

An example of true stress-strain curves with the process of decreasing stress.

Fig. 9.

True stress increase plotted against holding stress, s₁. The strain holding times were chosen to be 1000 and 10000 seconds.

Fig. 10.

The re-plot of Fig. 9 expressed by Eq. (15). The notations and their values correspond to those in Eq. (15).

Figure 11 shows Δσ at various σ₀ plotted against holding time. The slope did not change with σ₀, and can be explained by Eqs. (6) and (15). When the effect of the solute reordering is saturated against holding time, the effect contributes as an intercept to Δσ, according to Eq. (6). Since Δσ_maxr increases with increasing external stress as explained by Eq. (15), Δσ against holding time shifts in a parallel direction with σ₀ as shown in Fig. 11.

Fig. 11.

Δσ plotted against holding time at various holding stresses, s₀. “As tensiled” means no process for decreasing external stress.

4.4. Pre-strain Effect

Figure 12 shows that Δσ increases with increasing pre-strain. The changing trend of Δσ against pre-strain is roughly exponential, but is more complicated. The complicated tendency cannot be discussed quantitatively here, since the pre-strain affects many parameters: ρ, p, q, and Δσ_maxr. From the view point of the stress effect mentioned in the previous section, the strain dependence of texture components must also affect the pre-strain effect. For example, the difference in the pre-strain changed the slopes shown in Figs. 4 and 6. The different slopes in Fig. 4 are attributed to the change in ρ, while the different slopes in Fig. 6 are attributed to the changes in p and q. These facts indicate that the contributions of ρ, p and q are significant for the pre-strain effect. First, we consider the effect of ρ that depends on the plastic strain. The plastic strain dependence of ρ in a Fe–Mn–C austenitic steel was reported to be³⁴⁾   

$$\rho =C\mathit{\epsilon }$$(16)

where ε is the true plastic strain and C is a constant. From the viewpoint of the pre-strain dependence of ρ under a constant condition, Eqs. (6) and (16) indicate   

$$\Delta \sigma \propto \left[1-exp(-C^{\prime }\mathit{\epsilon })\right]$$(17)

where C′ is a constant. Although the contribution of ε in Eq. (17) is significant, it does not explain the exponential increase in Δσ against pre-strain.

Fig. 12.

True stress increase plotted against true pre-strain at various strain holding time.

Next, we attempt to consider the effects of Δσ_maxr and texture components. Δσ_maxr affects Δσ as an intercept when the effect of reordering of the solute is accomplished; however, it does not explain the increase in the slope of Δσ against holding time with increasing pre-strain which is shown in Fig. 4. Thus, the contribution of Δσ_maxr cannot explain the pre-strain dependence of Δσ. Since there is no significant difference between the volume fractions of the <111> fiber at the 0.40 and 0.50 true strains in the Fe–22Mn–0.6C steel,³³⁾ the effect of texture components is also not useful for expressing the pre-strain dependence at a relatively-large strain. The remaining parameters affecting the effect of pre-strain are p and q, but we were also not able to clarify how those parameters affect the effect of pre-strain in this work. Therefore, further investigations must be made to consider the combined effect among ρ, p, q, Δσ_maxr, and texture components on the pre-strain dependence.

4.5. Hydrogen Effect

Figure 13 shows the stress-strain responses around the strain holding processes with hydrogen charging at current densities of 0, 1, 3, and 7 Am^–2. The diffusible hydrogen content increases with increasing current density as shown in Fig. 14. Figure 15 shows that Δσ decreases with increasing diffusible hydrogen content. Solute hydrogen has been reported to increase the macroscopic yield and flow stresses in austenitic stainless steels, e.g. type 310.^35,36,37) In contrast, there is no report showing a decrease in macroscopic yield and flow stresses in austenitic steels, although microscopic softening was confirmed by microstructure observations^38,39) and nano-indentation.⁴⁰⁾ Therefore, the decrease in Δσ is a more controversial result, compared to the conventional reports for austenitic steels.

Fig. 13.

Influence of hydrogen charging on static strain aging at a pre-strain rate of 1.7×10^–2 s^–1. The specimens were held at 0.52 true plastic strain. The current densities for the hydrogen charging were chosen to be 0, 1, 3, and 7 Am^–2.

Fig. 14.

Diffusible hydrogen content plotted against current density. The diffusible hydrogen contents were measured just after the tests of Fig. 13.

Fig. 15.

Stress increase plotted against diffusible hydrogen content. The original data used for this plot are Figs. 13 and 14.

Eastman et al. reported⁴¹⁾ that solute hydrogen decreases the interaction between dislocation and another solution element such as carbon, by softening a material such as the FCC Ni–C alloy. Since the present static strain aging is caused by the dislocation-carbon interaction, the solute hydrogen effect on the effectiveness of carbon would explain the decrease in Δσ. Additionally, an important difference between the austenitic stainless steel and the present Fe–Mn–C steel is their carbon concentration. Since the present steel includes a high carbon concentration of 0.6 wt.%, the hydrogen effect on carbon-dislocation interaction must be much greater than that of the austenitic stainless steels.

5. Summary

We investigated the factors affecting static strain aging under stress at room temperature in a Fe–22Mn–0.6C twinning-induced plasticity steel. The factors and the changing trends of stress increase by the static strain aging, Δσ, are as follows.

1) The changing trend of Δσ against strain holding time can be explained by the so called t^2/3 law, which is similar to the conventional law.

2) Δσ increases linearly with increasing logarithmic strain rate.

3) Tensile external stress dependence of Δσ was found, and was explained by the effect of reordering of carbon.

4) Δσ showed a roughly-exponential increase with increasing pre-strain.

5) Δσ decreased with increasing diffusible hydrogen content.

Some of these facts could be explained by considering three phenomena associated with carbon motion, namely, <I> carbon segregation to dislocation and stacking fault, <II> dynamic strain aging during pre-straining, and <III> re-ordering of carbon from tetrahedron to octahedron sites under external stress.

Acknowledgements

M. K. acknowledges the Japan Society for the Promotion of Science for Young Scientists. POSCO supported this work through the provision of the samples and funding.

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