Viscoplastic behavior of zirconium alloys in the temperatures range 20°C-400°C : characterization and modeling of strain ageing phenomena
Résumé
The anomalous strain rate sensitivity of zirconium alloys over the temperatures range 20C–
600° has been widely reported in the literature. This unconventional behavior is related
to the existence of strain ageing phenomenon which results from the combined action of
thermally activated diffusion of foreign atoms to and along dislocation cores and the long
range of dislocations interactions. The important role of interstitial and substitutional atoms
in zirconium alloys, responsible for strain ageing and the lack of information about the domain
where strain ageing is active have not been yet adequately characterized because of the
multiplicity of alloying elements and chemical impurities.
The aim of this work is to characterize experimentally the range of temperatures and strain
rates where strain ageing is active on the macroscopic and mesoscopic scales. We propose
also a predictive approach of the strain ageing effects, using the macroscopic strain ageing
model suggested by McCormick (McCormick, 1988; Zhang et al., 2000).
Specific zirconium alloys were elaborated starting from a crystal bar of zirconium with 2.2 wt%
hafnium and very low oxygen content (80 wt ppm), called ZrHf. Another substitutional atom
was added to the solid solution under the form of 1 wt% niobium. Some zirconium alloys were
doped with oxygen, others were not. All of them were characterized by various mechanical
tests (standard tensile tests, tensile tests with strain rate changes, relaxation tests with
unloading). The experimental results were compared with those for the standard oxygen
doped zirconium alloy (1300 wt ppm) studied by Pujol (Pujol, 1994) and called Zr702. The
following experimental evidences of the age–hardening phenomena were collected and then
modeled:
• low and/or negative strain rate sensitivity around 200°C–300°C,
• creep arrest at 200°C,
• relaxation arrest at 200°C and 300°C,
• plastic strain heterogeneities observed in laser extensometry on the millimeter scale.
Relaxation experiments give information about deformation mechanisms. At lower plastic
strain rates, the macroscopic response is associated with the dragging mode (higher
temperatures) and at higher plastic strain rates, the macroscopic response is associated with
the friction mode (lower temperatures). Between these two limiting modes, the behavior
is unstable. For Zr702, the change in the deformation mechanism was observed between
200°C and 400°C. The apparent activation volumes associated with friction and dragging
modes are almost the same for Zr702, close to 0.7 nm3.atom−1. By reconstruction of the
entire relaxation curve at the temperature peak of 300C for strain ageing, an estimated
”drag stress” of about 250 MPa was determined for Zr702 (1300 wt ppm oxygen). For ZrHf,
the dragging mechanism was observed for lower temperatures close to 300°C. The apparent
activation volumes are close to 2 nm3.atom−1 for the friction mode and 1 nm3.atom−1 for
the dragging mode. For this alloy which contains only about 80 wt ppm of oxygen, the ”drag
stress” was estimated at about 130 MPa. These relaxation tests provided also evidence that
strong internal stresses develop in the tested specimens for both alloys.
The macroscopic strain ageing model was implemented in a finite element code. An internal
variable, characterizing a global ageing time of the material and associated with a non–
linearity of the constitutive equations allows to simulate plastic strain (rate) localization
under the form of bands extending across the width of the sample. The material parameters
were identified for Zr702. A reliable prediction of the strain ageing phenomena observed
experimentally can be ensured with this model. The development of strain heterogeneous
fields observed by laser scanning extensometry may be also predicted by the model.
600° has been widely reported in the literature. This unconventional behavior is related
to the existence of strain ageing phenomenon which results from the combined action of
thermally activated diffusion of foreign atoms to and along dislocation cores and the long
range of dislocations interactions. The important role of interstitial and substitutional atoms
in zirconium alloys, responsible for strain ageing and the lack of information about the domain
where strain ageing is active have not been yet adequately characterized because of the
multiplicity of alloying elements and chemical impurities.
The aim of this work is to characterize experimentally the range of temperatures and strain
rates where strain ageing is active on the macroscopic and mesoscopic scales. We propose
also a predictive approach of the strain ageing effects, using the macroscopic strain ageing
model suggested by McCormick (McCormick, 1988; Zhang et al., 2000).
Specific zirconium alloys were elaborated starting from a crystal bar of zirconium with 2.2 wt%
hafnium and very low oxygen content (80 wt ppm), called ZrHf. Another substitutional atom
was added to the solid solution under the form of 1 wt% niobium. Some zirconium alloys were
doped with oxygen, others were not. All of them were characterized by various mechanical
tests (standard tensile tests, tensile tests with strain rate changes, relaxation tests with
unloading). The experimental results were compared with those for the standard oxygen
doped zirconium alloy (1300 wt ppm) studied by Pujol (Pujol, 1994) and called Zr702. The
following experimental evidences of the age–hardening phenomena were collected and then
modeled:
• low and/or negative strain rate sensitivity around 200°C–300°C,
• creep arrest at 200°C,
• relaxation arrest at 200°C and 300°C,
• plastic strain heterogeneities observed in laser extensometry on the millimeter scale.
Relaxation experiments give information about deformation mechanisms. At lower plastic
strain rates, the macroscopic response is associated with the dragging mode (higher
temperatures) and at higher plastic strain rates, the macroscopic response is associated with
the friction mode (lower temperatures). Between these two limiting modes, the behavior
is unstable. For Zr702, the change in the deformation mechanism was observed between
200°C and 400°C. The apparent activation volumes associated with friction and dragging
modes are almost the same for Zr702, close to 0.7 nm3.atom−1. By reconstruction of the
entire relaxation curve at the temperature peak of 300C for strain ageing, an estimated
”drag stress” of about 250 MPa was determined for Zr702 (1300 wt ppm oxygen). For ZrHf,
the dragging mechanism was observed for lower temperatures close to 300°C. The apparent
activation volumes are close to 2 nm3.atom−1 for the friction mode and 1 nm3.atom−1 for
the dragging mode. For this alloy which contains only about 80 wt ppm of oxygen, the ”drag
stress” was estimated at about 130 MPa. These relaxation tests provided also evidence that
strong internal stresses develop in the tested specimens for both alloys.
The macroscopic strain ageing model was implemented in a finite element code. An internal
variable, characterizing a global ageing time of the material and associated with a non–
linearity of the constitutive equations allows to simulate plastic strain (rate) localization
under the form of bands extending across the width of the sample. The material parameters
were identified for Zr702. A reliable prediction of the strain ageing phenomena observed
experimentally can be ensured with this model. The development of strain heterogeneous
fields observed by laser scanning extensometry may be also predicted by the model.
De nombreuses manifestations macroscopiques de vieillissement dans les alliages dilués de zirconium et dans le domaine de température 20°C-600°C ont été reportés dans la littérature. Les phénomènes de vieillissement peuvent être associés à l'interaction dislocations-atomes de soluté. Toutefois, l'influence systématique des éléments d'addition et la caractérisation précise du domaine de vieillissement en termes de température et de vitesse de déformation restent toutefois mal appréhendées à ce jour .....