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Interplay of stresses induced by phase transformation and plastic deformation during cyclic load of austenitic stainless steel
ARTICLE IN PRESS
Physica B 350 (2004) 98–101
Interplay of stresses induced by phase transformation and plastic deformation during cyclic load of austenitic stainless steel Yu.V. Tarana,*, M.R. Daymondb, J. Schreiberc a
Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Moscow region 141980, Russia b ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK c EADQ, Fraunhofer Institute for Nondestructive Testing, Dresden D-01326, Germany
Abstract Austenitic stainless steel AISI 321 samples subjected to low-cycle fatigue (LCF) were analysed using in situ neutron diffraction stress rig experiments on the ENGIN instrument at the ISIS pulsed neutron facility. The elastoplastic properties of the austenitic matrix and martensitic inclusions as well as the residual stresses of the both phases were studied. The martensite formation is connected with volume dilation. Since the specific volume of martensite is larger (about 2%) than that one of austenite, the martensite phase is generally expected to be in hydrostatic compression, whereas the austenite one is in tension. However, these phase transformation stresses can be superimposed on the deformation stresses caused by the plastic deformation during LCF. The resulting residual stresses have a nonhydrostatic nature. In this study, only deviatoric components of the residual stress tensor were obtained because of the lack of the strain free lattice parameters of both phases. We have established that in the axial direction (along cyclic load) the deviatoric phase stress and the microstress of the austenitic phase were compressive and tensile for the martensite phase, i.e. an overshot of the deformation stress is observed. r 2004 Elsevier B.V. All rights reserved. Keywords: Neutron; Diffraction; Stress; Steel; Austenite; Martensite
1. Introduction Austenitic stainless steels (ASS) are widely used in engineering applications because of their high corrosion resistance and toughness. A major concern in a number of applications including *Corresponding author. Tel.: +7-09621-65-945; fax: +7-0962165-882. E-mail address: [email protected] (Yu.V. Taran).
nuclear power plants, however, is fatigue damage of ASS components. During fatigue loading microstructural changes occur in ASS which affect both the mechanical and physical properties of the steel. The ferromagnetic martensitic phase formed in some ASS due to the plastic deformation occurring during mechanical fatigue presents a particularly interesting phenomenon. Many investigations have shown the influence of the martensitic transformation on the fatigue properties of
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.04.004
ARTICLE IN PRESS Yu.V. Taran et al. / Physica B 350 (2004) 98–101
The material was a low carbon Ti-alloyed austenitic stainless steel AISI 321 (17.74% Cr, 9.3% Ni). The steel was delivered as a cold formed bar with a diameter of 20 mm. The bars were annealed at 1050 C and quenched in water. Eight samples (A–H) were machined, with a central gauge diameter of 7.5 mm and a length of 16 mm. Seven samples (A–G) were cycled under uniaxial tensile-compressive loading under total-strain control with a triangular waveform and an amplitude of 1% (a strain ratio Re ¼ 1) at a frequency of 0.5 Hz. While sample A was cycled to failure (N ¼ Nf ¼ 1161), six of them (B–G) were each subjected to varying numbers N of fatigue cycles. Sample H, which was not cycled, was intended as a reference sample for the austenite phase. The samples were measured using the in situ servohydraulic stress rig under tensile stress control on the ENGIN instrument. The stress rig loading axis is horizontal at 45 to the incident
3. Results and discussion The direct result from diffraction data processing is the dependence of the phase lattice parameter aii on the applied stress sL for directions ‘ii’ equal to ‘11’ or ‘33’, corresponding to the axial or transverse direction, respectively. An example of the lattice parameter dependencies of austenite and martensite is shown for sample B in Fig. 1. Note that the axial and transverse lattice parameters for each phase do not intersect at zero applied stress, differing by an equivalent strain of around 150 me. This is most likely due to the
2.885
Austenite, axial 3.595
2.880 3.590 2.875 Austenite, trans 3.585
Martensite, axial 2.870 Martensite, trans
3.580 0
100
200
300
400
Martensite lattice parameter [Å]
2. Samples and experiment
neutron beam, thus providing simultaneous measurements of strains parallel (axial) and perpendicular (transverse) to the applied stress. A neutron gauge volume of E50 mm3 is formed inside the central part of the sample in a form of a thin rectangular parallelepiped, located at 45 to the sample axis, with thickness of 2 mm and the incident dimensions of 5 5 mm2, by using two multislit radial collimators in front of the 790 detectors and a primary slit in front of the sample, respectively. The lattice parameters of the austenitic and martensitic phases were determined using a spherical harmonic approach within the Rietveld refinement. Fitting was carried out in a d-spacing interval from 0.04 to 0.23 nm in which 38 austenite and 32 martensite reflections are observed.
Austenite lattice parameter [Å]
ASS (see, e.g., Ref. [1]). Whereas the mechanical properties of austenitic steel are well known [2], a transforming or partly transformed material is much more difficult to characterise due to the interaction between two phases. For instance, the elastic mismatch and the plastic misfit between the martensite and austenite, as well as the larger specific volume of martensite are likely to cause considerable stresses throughout the sample. Knowledge of the residual stress state of the phases and their relation to the fatigue process is very important, in order to develop a proper understanding of how the individual phases interact to produce the bulk mechanical response of the material. In Ref. [3] we have described the time-of-flight neutron diffraction measurements of the mechanical behaviour of the austenite matrix and martensite inclusions in ASS of type AISI 321 with varying martensite volume fractions produced by plastic deformation during low cycle fatigue (LCF). This paper presents the results of the residual stress determination from these measurements.
99
500
Applied stress [MPa]
Fig. 1. Lattice parameters of austenite and martensite vs. applied stress for sample B.
ARTICLE IN PRESS Yu.V. Taran et al. / Physica B 350 (2004) 98–101
100
presence of residual deviatoric stresses from technological treatment and fatigue. This origin of the effect, rather than some instrumental aberration, is reinforced by the fact that the cross over stress for axial and transverse lattice parameters is of opposite sign for the austenite and martensite phases. From the linear fit of the elastic part of the phase curves aii ðsL Þ in Fig. 1 one obtains the zero stress intercepts I11 and I33 ; the slopes S11 and S33 which depend on the phase elastic constants E and n, the stress-free value of the phase lattice parameter a0 and thus the total phase stress tensor. The initial intercept lattice parameters for each sample (i.e. after fatigue) in both austenite and martensite phases (Fig. 2) show a dependence on the level of fatigue, particularly clearly seen in the transverse strains, for which both austenite and martensite phases show an increase in lattice parameter with fatigue. The dependence in the axial direction is much weaker. To calculate the phase residual strain eii ¼ ðIii 2a0 Þ=a0 the parameter a0 has to be known. Usually in order to determine this parameter a sample is made with the same structure, but free from internal stresses. However, in our case such samples were not available. In Ref. [4] we have showed that the deviatoric components of the residual stress tensor may be determined without the knowledge of a0 using the experimental data about the intersection sL;int (stress at which axial
and transverse phase lattice parameters are equal; see Fig. 1): sL;int ¼ ðI11 I33 Þ=ðS11 S33 Þ ¼ ðs11;res s33;res Þ;
ð1Þ
where sii;res is the phase residual stress in iidirection. Separating the residual stress tensor into the hydrostatic and deviatoric residual stress tensors tH;res and tii;res ; respectively, and assuming transverse symmetry of the sample, we obtain the deviatoric phase residual stresses in both axial and transverse directions (Fig. 3): t11; res ¼ ð2=3ÞsL;
int
and t33;
res
¼ ð1=3ÞsL; int : ð2Þ
The austenite phase shows a compressive deviatoric stress in the axial direction, while the martensite shows a balancing tensile deviatoric stress in this direction. The magnitude of the austenite deviatoric compressive stress increases with fatigue, however the tensile deviatoric stress in the martensite decreases in magnitude, corresponding to the increasing volume fraction of martensite. From Eq. (2), the transverse deviatoric stress component is opposite in sign and half the magnitude of the axial component. The martensite formation is connected with volume dilation. Since the specific volume of martensite is larger (about 2%) than that one of austenite, the martensite phase is generally expected to be in hydrostatic compression, whereas the austenite one is in tension. However, the
Transverse
3.5895 3.5890
F
B D
E
A
C
H G
Axial
3.5885 3.5880
2.872 Axial 2.870 Transverse 2.868 0
20
40
60
80
100
Phase residual stress [MPa]
3.5900
Martensite Iii [Å]
Austenite Iii [Å]
100
Martensite
50
0
Austenite -50
0
20
40
60
80
N/Nf [%]
N/Nf [%]
Fig. 2. Zero applied stress intercepts Iii as a function of fatigue level: austenite—two upper curves, martensite—two lower curves.
Fig. 3. Phase deviatoric residual stresses in austenite and martensite in the axial direction as a function of the fatigue level.
ARTICLE IN PRESS Yu.V. Taran et al. / Physica B 350 (2004) 98–101
interplay of stresses induced by phase transformation and plastic deformation during LCF, respectively, creates the resulting residual stresses of a nonhydrostatic nature with the opposite signs, i.e. an overshot of the deformation stress is observed. While the axial stresses are mainly deformation stresses the phase transformation stresses dominate in the transverse direction.
101
References [1] Yu.V. Taran, et al., Mater. Sci. Forum 347–349 (2000) 322. [2] M.R. Daymond, et al., J. Appl. Phys. 82 (1997) 1554. [3] Yu.V. Taran, et al., Appl. Phys. A 74 (2002) S1391. [4] Yu.V. Taran, et al., Communication of JINR E14-2002-161, Dubna, 2002, 22pp.
Physica B 350 (2004) 98–101
Interplay of stresses induced by phase transformation and plastic deformation during cyclic load of austenitic stainless steel Yu.V. Tarana,*, M.R. Daymondb, J. Schreiberc a
Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Moscow region 141980, Russia b ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK c EADQ, Fraunhofer Institute for Nondestructive Testing, Dresden D-01326, Germany
Abstract Austenitic stainless steel AISI 321 samples subjected to low-cycle fatigue (LCF) were analysed using in situ neutron diffraction stress rig experiments on the ENGIN instrument at the ISIS pulsed neutron facility. The elastoplastic properties of the austenitic matrix and martensitic inclusions as well as the residual stresses of the both phases were studied. The martensite formation is connected with volume dilation. Since the specific volume of martensite is larger (about 2%) than that one of austenite, the martensite phase is generally expected to be in hydrostatic compression, whereas the austenite one is in tension. However, these phase transformation stresses can be superimposed on the deformation stresses caused by the plastic deformation during LCF. The resulting residual stresses have a nonhydrostatic nature. In this study, only deviatoric components of the residual stress tensor were obtained because of the lack of the strain free lattice parameters of both phases. We have established that in the axial direction (along cyclic load) the deviatoric phase stress and the microstress of the austenitic phase were compressive and tensile for the martensite phase, i.e. an overshot of the deformation stress is observed. r 2004 Elsevier B.V. All rights reserved. Keywords: Neutron; Diffraction; Stress; Steel; Austenite; Martensite
1. Introduction Austenitic stainless steels (ASS) are widely used in engineering applications because of their high corrosion resistance and toughness. A major concern in a number of applications including *Corresponding author. Tel.: +7-09621-65-945; fax: +7-0962165-882. E-mail address: [email protected] (Yu.V. Taran).
nuclear power plants, however, is fatigue damage of ASS components. During fatigue loading microstructural changes occur in ASS which affect both the mechanical and physical properties of the steel. The ferromagnetic martensitic phase formed in some ASS due to the plastic deformation occurring during mechanical fatigue presents a particularly interesting phenomenon. Many investigations have shown the influence of the martensitic transformation on the fatigue properties of
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.04.004
ARTICLE IN PRESS Yu.V. Taran et al. / Physica B 350 (2004) 98–101
The material was a low carbon Ti-alloyed austenitic stainless steel AISI 321 (17.74% Cr, 9.3% Ni). The steel was delivered as a cold formed bar with a diameter of 20 mm. The bars were annealed at 1050 C and quenched in water. Eight samples (A–H) were machined, with a central gauge diameter of 7.5 mm and a length of 16 mm. Seven samples (A–G) were cycled under uniaxial tensile-compressive loading under total-strain control with a triangular waveform and an amplitude of 1% (a strain ratio Re ¼ 1) at a frequency of 0.5 Hz. While sample A was cycled to failure (N ¼ Nf ¼ 1161), six of them (B–G) were each subjected to varying numbers N of fatigue cycles. Sample H, which was not cycled, was intended as a reference sample for the austenite phase. The samples were measured using the in situ servohydraulic stress rig under tensile stress control on the ENGIN instrument. The stress rig loading axis is horizontal at 45 to the incident
3. Results and discussion The direct result from diffraction data processing is the dependence of the phase lattice parameter aii on the applied stress sL for directions ‘ii’ equal to ‘11’ or ‘33’, corresponding to the axial or transverse direction, respectively. An example of the lattice parameter dependencies of austenite and martensite is shown for sample B in Fig. 1. Note that the axial and transverse lattice parameters for each phase do not intersect at zero applied stress, differing by an equivalent strain of around 150 me. This is most likely due to the
2.885
Austenite, axial 3.595
2.880 3.590 2.875 Austenite, trans 3.585
Martensite, axial 2.870 Martensite, trans
3.580 0
100
200
300
400
Martensite lattice parameter [Å]
2. Samples and experiment
neutron beam, thus providing simultaneous measurements of strains parallel (axial) and perpendicular (transverse) to the applied stress. A neutron gauge volume of E50 mm3 is formed inside the central part of the sample in a form of a thin rectangular parallelepiped, located at 45 to the sample axis, with thickness of 2 mm and the incident dimensions of 5 5 mm2, by using two multislit radial collimators in front of the 790 detectors and a primary slit in front of the sample, respectively. The lattice parameters of the austenitic and martensitic phases were determined using a spherical harmonic approach within the Rietveld refinement. Fitting was carried out in a d-spacing interval from 0.04 to 0.23 nm in which 38 austenite and 32 martensite reflections are observed.
Austenite lattice parameter [Å]
ASS (see, e.g., Ref. [1]). Whereas the mechanical properties of austenitic steel are well known [2], a transforming or partly transformed material is much more difficult to characterise due to the interaction between two phases. For instance, the elastic mismatch and the plastic misfit between the martensite and austenite, as well as the larger specific volume of martensite are likely to cause considerable stresses throughout the sample. Knowledge of the residual stress state of the phases and their relation to the fatigue process is very important, in order to develop a proper understanding of how the individual phases interact to produce the bulk mechanical response of the material. In Ref. [3] we have described the time-of-flight neutron diffraction measurements of the mechanical behaviour of the austenite matrix and martensite inclusions in ASS of type AISI 321 with varying martensite volume fractions produced by plastic deformation during low cycle fatigue (LCF). This paper presents the results of the residual stress determination from these measurements.
99
500
Applied stress [MPa]
Fig. 1. Lattice parameters of austenite and martensite vs. applied stress for sample B.
ARTICLE IN PRESS Yu.V. Taran et al. / Physica B 350 (2004) 98–101
100
presence of residual deviatoric stresses from technological treatment and fatigue. This origin of the effect, rather than some instrumental aberration, is reinforced by the fact that the cross over stress for axial and transverse lattice parameters is of opposite sign for the austenite and martensite phases. From the linear fit of the elastic part of the phase curves aii ðsL Þ in Fig. 1 one obtains the zero stress intercepts I11 and I33 ; the slopes S11 and S33 which depend on the phase elastic constants E and n, the stress-free value of the phase lattice parameter a0 and thus the total phase stress tensor. The initial intercept lattice parameters for each sample (i.e. after fatigue) in both austenite and martensite phases (Fig. 2) show a dependence on the level of fatigue, particularly clearly seen in the transverse strains, for which both austenite and martensite phases show an increase in lattice parameter with fatigue. The dependence in the axial direction is much weaker. To calculate the phase residual strain eii ¼ ðIii 2a0 Þ=a0 the parameter a0 has to be known. Usually in order to determine this parameter a sample is made with the same structure, but free from internal stresses. However, in our case such samples were not available. In Ref. [4] we have showed that the deviatoric components of the residual stress tensor may be determined without the knowledge of a0 using the experimental data about the intersection sL;int (stress at which axial
and transverse phase lattice parameters are equal; see Fig. 1): sL;int ¼ ðI11 I33 Þ=ðS11 S33 Þ ¼ ðs11;res s33;res Þ;
ð1Þ
where sii;res is the phase residual stress in iidirection. Separating the residual stress tensor into the hydrostatic and deviatoric residual stress tensors tH;res and tii;res ; respectively, and assuming transverse symmetry of the sample, we obtain the deviatoric phase residual stresses in both axial and transverse directions (Fig. 3): t11; res ¼ ð2=3ÞsL;
int
and t33;
res
¼ ð1=3ÞsL; int : ð2Þ
The austenite phase shows a compressive deviatoric stress in the axial direction, while the martensite shows a balancing tensile deviatoric stress in this direction. The magnitude of the austenite deviatoric compressive stress increases with fatigue, however the tensile deviatoric stress in the martensite decreases in magnitude, corresponding to the increasing volume fraction of martensite. From Eq. (2), the transverse deviatoric stress component is opposite in sign and half the magnitude of the axial component. The martensite formation is connected with volume dilation. Since the specific volume of martensite is larger (about 2%) than that one of austenite, the martensite phase is generally expected to be in hydrostatic compression, whereas the austenite one is in tension. However, the
Transverse
3.5895 3.5890
F
B D
E
A
C
H G
Axial
3.5885 3.5880
2.872 Axial 2.870 Transverse 2.868 0
20
40
60
80
100
Phase residual stress [MPa]
3.5900
Martensite Iii [Å]
Austenite Iii [Å]
100
Martensite
50
0
Austenite -50
0
20
40
60
80
N/Nf [%]
N/Nf [%]
Fig. 2. Zero applied stress intercepts Iii as a function of fatigue level: austenite—two upper curves, martensite—two lower curves.
Fig. 3. Phase deviatoric residual stresses in austenite and martensite in the axial direction as a function of the fatigue level.
ARTICLE IN PRESS Yu.V. Taran et al. / Physica B 350 (2004) 98–101
interplay of stresses induced by phase transformation and plastic deformation during LCF, respectively, creates the resulting residual stresses of a nonhydrostatic nature with the opposite signs, i.e. an overshot of the deformation stress is observed. While the axial stresses are mainly deformation stresses the phase transformation stresses dominate in the transverse direction.
101
References [1] Yu.V. Taran, et al., Mater. Sci. Forum 347–349 (2000) 322. [2] M.R. Daymond, et al., J. Appl. Phys. 82 (1997) 1554. [3] Yu.V. Taran, et al., Appl. Phys. A 74 (2002) S1391. [4] Yu.V. Taran, et al., Communication of JINR E14-2002-161, Dubna, 2002, 22pp.