Ductile-brittle transition temperature shift controlled by grain boundary decohesion and thermally activated energy in Ni-Cr steels

1 Introduction

Classical structural problems of temper embrittlement are evaluated in terms of the change in the ductile-brittle transition temperature (DBTT). The development of scanning Auger electron spectroscopy (scanning AES) enabled the detection of several types and amounts of metalloid elements (X_gb) at grain boundaries (GBs). Based on interfacial thermodynamic theory (Rice, 1976; Hirth & Rice, 1980; Rice & Wang, 1989), first-principles calculations provide an atomistic view of the effects of immobile solutes (Sb, Sn and P) on the GB decohesion. The fracture surface (FS) energy linearly deceases with the amount of embrittling solutes. The embrittling potency Δe_p (eV) is ranked as Δe_p for 1.36 for Sb, 0.99 for Sn and 0.38 for P (Wu et al., 1994; Yamaguchi, 2011; Yamaguchi & Kameda, 2014). The GB decohesion (2γ_int) is given by

where 2γint0=4.02 J/m2 at X_gb=0, and the 1.152 includes an area factor to convert from eV to J/m².

The relationship between the slope (α) of DBTT vs. X_gb, and Δe_p is a function of displacement rate (dδ/dt) and hardness. An Arrhenius plot of the dδ/dt and the reciprocal DBTT is analyzed to derive the activation energy (E_act). High hardness steel has a stronger dependence on GB decohesion than medium hardness steels.

This study reanalyzes the effect on temper embrittlement in 3.5Ni-1.7Cr steels doped individually with Sb, Sn and P undertaken by McMahon’s group of the University of Pennsylvania (Mulford et al., 1976a,b; Cianelli et al., 1977; Kameda & McMahon, 1980; Takayama et al., 1980). The temper embrittlement induced by solute segregation was investigated in light of the GB decohesion and E_act.

2 Materials and methods

These steels were thermally treated by austenitizing, oil-quenching and tempering. Samples were aged between 10 and 1000 h at about 753 K to achieve a wide range of GB segregation without softening. The solute compositions of the steels studied are listed in Table 1. GB FSs broken in an ultra-high vacuum chamber were analyzed by (scanning AES), the results of which were converted to the GB coverage X_gb of the segregated solute. The DBTT values of these differently embrittled samples were measured by Charpy dynamic and cantilever static notched tests under dynamic (5.25 m/s) and static (8.27×10⁻⁶ m/s) dδ/dt. The DBTT was defined by the midpoints between the upper and lower shelf energy or the ductile/brittle fracture mode. Some samples doped with weaker embrittling solutes in medium hardness steels with slow dδ/dt exhibited a mixture of GB and cleavage fracture. Cleavage DBTT of pure Ni-Cr steels is lower than Ni with less alloy steels.

3 Results and discussion

3.1 DBTT relevance to GB decohesion

The previously obtained experimental data were reanalyzed in terms of the GB decohesion and their relationships with the effects of dδ/dt and hardness on the DBTT in Ni-Cr steels. It was found that the DBTT has a linear relationship with X_gb. Figure 1 shows the effects of segregated Sb in high, medium and low hardness steels, under dynamic and static loading. The linear relationship between DBTT and X_gb is in Equation (1) where the values of DBTT_tg for cleavage fracture were identified from the baseline as indicated in Figure 1 for segregated Sb for X_gb=0.

Figure 1:

Linear dependence of DBTT on segregated Sb for dynamic and static displacement rates dδ/dt in high hardness steels together with low hardness steels tested under slow dδ/dt.

(2) DBTT = DBTT tg + α X gb

Figure 2 shows the slope in terms of increases in the order of the potency of segregated solutes, Sb, Sn and P. The value of α remains the same regardless of the dδ/dt in the high hardness steels. Sn- and P-doped medium hardness steels exhibited a similar order potency. However, the dynamic dδ/dt produces higher values of α than the static dδ/dt in medium hardness steels. Figure 3 depicts the linear relations between α and Δe_p for all three dopants at both dδ/dt. The medium hardness steels clearly are affected by the dδ/dt; this is not true for high hardness steels where there is no dependence on dδ/dt. The value of α for Sb-doped steel with lower hardness in slow dδ/dt was observed to be close to that of segregated Sn with the medium hardness.

Figure 2:

Relationship between slope (α) for dynamic and static dδ/dt and high and medium hardness steels.

Figure 3:

Relationship between slope (α) and Δe_p for all dδ/dt and high and medium hardness steels.

3.2 Relation of activated energy to GB decohesion

dδ/dt is related to the E_act. The mode change between ductile and GB fracture is characterized with the DBTT. The dδ/dt is an experimental parameter that is related to DBTT through Equation (3). dδ/dt drives dislocation motion, overcoming the energy barrier E_act. k_B is the Boltzmann constant (Magnusson & Baldwin, 1957; Giannattasio et al., 2007; Kameda & Nishiyama, 2011).

(3) d δ / d t = V  exp  [ − E act / ( k B  DBTT ) ]

The E_act is calculated from the slope of an Arrhenius plot of the natural log of dδ/dt vs. the reciprocal of DBTT. An example of such plots for Sb in high hardness steels is shown in Figure 4 for a range of X_gb. E_act was calculated for the three metalloids at varying X_gb using Equation (4).

Figure 4:

Reciprocal plot of DBTT on natural log (displacement rate) for various segregated Sb and high hardness.

(4) E act =   k B  ln[ ( d δ / d t ) s / ( d δ / d t ) d ] ( 1 DBTT d − 1 DBTT s )

3.3 Activation energy relevance to GB decohesion

Equation (4) was applied to selected values of X_gb for both the high and medium hardness steels (using Figure 1: for examples for segregated Sb with high hardness). In Figure 5, E_act exponentially increases with X_gb for all three solutes in high and medium hardness steels. E_act is much higher in the high hardness steels than in the medium hardness steels. As indicated clearly in Figure 6, E_act is correlated with 2γ_int regardless of the type of segregated solute. The E_act with high hardness depends strongly and approximately linearly on 2γ_int, but the dependence is weak for medium hardness steels.

Figure 5:

Relationship of activation energy (E_act) to segregated solute (X_gb) for all test conditions.

Figure 6:

Activation energy vs. 2γ_int for all test conditions. Red curve, high hardness; blue, medium hardness; black, A533B and Cr-Mo.

4 Summary

Temper embrittlement is affected not only by segregated metalloid solutes but also by dδ/dt and hardness. It is important to relate changes in the FS energy, and the energy barrier to dislocation motion, E_act, to the transition from ductile to brittle GB fracture. GB metalloid segregation leads to an increase in E_act, a decrease in FS energy, and leads to the transition from ductile to brittle GB fracture.

1. The slope of DBTT vs. X_gb, (α) is linearly related to Δe_p under dynamic and static dδ/dt states in high hardness steels, but it depends on dδ/dt in medium hardness steels.

2. An Arrhenius plot is plotted to the reciprocal DBTT to derive E_act.

3. The value of E_act increases exponentially with X_gb in both the high and medium hard steels, while it is more strongly related to 2γ_int in the hard steels than in the medium steels.

4. The dependence of E_act on 2γ_int is much stronger in high hardness steel than in medium hardness steels.