Crystal plasticity modeling of irradiation growth in Zircaloy-2

Abstract

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.     

Comparison of the deformation behaviour of commercially pure titanium and Ti–5Al–2.5Sn(wt.%) at 296 and 728 K

The tension and tensile-creep deformation behaviours of a fully-α phase commercially pure (CP) Ti and a near-α Ti–5Al–2.5Sn(wt.%) alloy deformed in situ inside a scanning electron microscope were compared. Tensile tests were performed at 296 and 728?K, while tensile-creep tests were performed at 728?K. The yield stress of CP Ti decreased dramatically with increasing temperature. In contrast, temperature had much smaller effect on the yield stress of Ti–5Al–2.5Sn(wt.%). Electron backscattered diffraction was performed both before and after the deformation, and slip trace analysis was used to determine the active slip and twinning systems, as well as the associated global stress state Schmid factors. In tension tests of CP Ti, prismatic slip was the most likely slip system to be activated when the Schmid factor exceeded 0.4. Prismatic slip was observed over the largest Schmid factor range, indicating that the local stress tensor varies significantly from the global stress state of uniaxial tension. The basal slip activity in Ti–5Al–2.5Sn(wt.%) was observed in a larger faction of grains than in CP Ti. Pyramidal ?c?+?a? slip was more prevalent in CP Ti. Although twinning was an active deformation mode in tension tests of the CP Ti, it was rare in Ti–5Al–2.5Sn(wt.%). During creep, dislocation slip was the primary apparent deformation mechanism in CP Ti, while evidence for dislocation slip was much less apparent in Ti–5Al–2.5Sn(wt.%), where grain boundary sliding was dominant. A robust statistical analysis was carried out to assess the significance of the comparative activity of the different slip systems under the variety of experimental conditions examined.     

Effect of thermomechanical processing on the creep behaviour of Udimet alloy 188

Udimet alloy 188 was subjected to grain-boundary engineering involving thermomechanical processing in an attempt to improve the creep performance and determine the effects on creep deformation processes. The as-received sheet was cold-rolled to either 10, 25 or 35% reduction per pass followed by a solution treatment at 1191°C for 1 h plus air cooling. This sequence was repeated four times and the resultant microstructure and grain-boundary character distribution were described using electron backscatter diffraction. The fraction of general high-angle grain boundaries tended to increase with increased cold rolling. The 10 and 25% cold-rolled materials exhibited lower creep rates than the 35% cold-rolled material. The measured creep stress exponents and activation energies suggested that dislocation creep with lattice self-diffusion was dominant at 760°C for stresses ranging between 100 and 220 MPa. A transition in the creep exponent below the applied stresses of 100 MPa indicated that a different secondary creep mechanism was rate-controlling at low stresses. A significant amount of grain-boundary cracking was observed both on the surface and subsurface of deformed samples, but surface cracks were greater in number and size than those within the bulk. The cracking behaviour was similar in both vacuum and air environments, indicating that grain-boundary cracking was not caused by environment. To assess the mechanisms of crack nucleation, in situ scanning electron microscopy was performed during elevated-temperature (T ≤ 760°C) tensile-creep deformation. Sequential secondary electron imaging and electron backscatter diffraction orientation mapping were performed in situ to allow the evolution of crack nucleation and linkage to be followed. Cracking occurred preferentially along general high-angle grain boundaries and less than 15% of the cracks were found on low-angle grain boundaries and coincident site lattice boundaries. A fracture initiation parameter analysis was performed to identify the role of slip system interactions at the boundaries and their impact on crack nucleation. The parameter was successful in separating the population of intact and cracked general high-angle boundaries at lower levels of strain, but not after crack coalescence dominated the fracture process. The findings of this work have significant implications regarding grain-boundary engineering of this alloy and potentially for other alloy systems.     

Physical property characterization of bulk MgB<Subscript>2</Subscript> superconductor

We report synthesis, structure/micro-structure, resistivity under magnetic field [ρ(T)H], Raman spectra, thermoelectric power S(T), thermal conductivity κ(T), and magnetization of ambient pressure argon annealed polycrystalline bulk samples of MgB₂, processed under identical conditions. The compound crystallizes in hexagonal structure with space group P6/mmm. Transmission electron microscopy (TEM) reveals electron micrographs showing various types of defect features along with the presence of 3–4 nm thick amorphous layers forming the grain boundaries of otherwise crystalline MgB₂. Raman spectra of the compound at room temperature exhibited characteristic phonon peak at 600 cm^-1. Superconductivity is observed at 37.2 K by magnetic susceptibility χ(T), resistivity ρ(T), thermoelectric power S(T), and thermal conductivity κ(T) measurements. The power law fitting of ρ(T) give rise to Debye temperature (Θ_D) at 1400 K which is found consistent with the theoretical fitting of S(T), exhibiting Θ _D of 1410 K and carrier density of 3.81 × 10²⁸/m³. Thermal conductivity κ(T) shows a jump at 38 K, i.e., at T_c, which was missing in some earlier reports. Critical current density (J_c) of up to 10⁵ A/cm² in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements. The irreversibility field, defined as the field related to merging of M(H) loops is found to be 78, 68 and 42 kOe at 4, 10 and 20 K respectively. The superconducting performance parameters viz. irreversibility field (H_irr) and critical current density J_c(H) of the studied MgB₂ are improved profoundly with addition of nano-SiC and nano-diamond. The physical property parameters measured for polycrystalline MgB₂ are compared with earlier reports and a consolidated insight of various physical properties is presented.     

Fabrication and microstructural characterization of functionally graded porous acrylonitrile butadiene styrene and the effect of cellular morphology on creep behavior

The ability to control material properties in space and time for functionally graded viscoelastic materials makes them an asset where they can be adapted to different design requirements. The continuous microstructure makes them advantageous over conventional composite materials. Functionally graded porous structures have the added advantage over conventional functionally graded materials of offering a significant weight reduction compared to a minor drop in strength. Functionally graded porous structures of acrylonitrile butadiene styrene (ABS) had been fabricated with a solid‐state constrained foaming process. Correlating the microstructure to material properties requires a deterministic analysis of the cellular structure. This is accomplished by analyzing the scanning electron microscopy images with a locally adaptive image threshold technique based on variational energy minimization. This characterization technique of the cellular morphology is analyst independent and works very well for porous structures. Inferences are drawn from the effect of processing on microstructure and then correlated to creep strain and creep compliance. Creep is strongly correlated to porosity and pore sizes but more associated to the size than to porosity. The results show the potential of controlling the cellular morphology and hence tailoring creep strain/compliance of ABS to some desired values. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 795–803     

High temperature creep behavior of phosphoric acid‐polybenzimidazole gel membranes

This work investigates the effects of polymer solids content and macromolecular structure on the high temperature creep behavior of polybenzimidazole (PBI) gel membranes imbibed with phosphoric acid (PA) after preparation via a polyphosphoric acid (PPA) mediated sol‐gel process Low‐solids, highly acid‐doped PBI membranes demonstrate outstanding fuel cell performance under anhydrous, ambient pressure, and high temperature (120–200 °C) operating conditions. However, PBI membranes are susceptible to creep under compressive loads at elevated temperatures, so their long‐term mechanical durability is a major concern. Here, we report results for the creep behavior of PBI membranes subject to compression at 180 °C. For para‐ and meta‐PBI homopolymers, increasing polymer solids content results in lower creep compliance and higher extensional viscosity, which may be rationalized by increasing chain density in the sol‐gel network. Comparing various homo‐ and copolymers at similar solids loading, differences in creep behavior may be rationalized in terms of chain–chain and chain‐solvent interactions that control macromolecular solubility and stiffness in the PA solvent. The results demonstrate the feasibility of improving the mechanical properties of PA‐doped PBI membranes by control of polymer solids content and rational design of PBI macromolecular structure. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1527–1538     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

Effects of crossed columnar defects on vortex pinning in Bi2Sr2CaCu2O8

To investigate the existence of a splay effect in Bi₂Sr₂CaCu₂O₈ (Bi-2212), vortex pinning has been studied in different configurations of strongly inclined columnar defects (75 from the c axis), installed by heavy-ion irradiation. It is shown that the symmetry of the track setting with respect to the field direction is a more influent parameter than the presence of a dispersion in the track directions. We claim that the enhanced pinning efficiency which is observed in some splayed configurations of columnar defects in Bi-2212 can be interpreted without invoking a splay effect. Received 27 December 1999     

The Labusch parameter of a driven flux line lattice in YBa Cu O superconducting films

We have investigated the influence of a driving force on the elastic coupling (Labusch parameter) of the field-cooled state of the flux line lattice (FLL) in 400 nm thick YBa₂Cu₃O₇ superconducting films. We found that the FLL of a field-cooled state without driving forces is not in an equilibrium state. Results obtained for magnetic fields applied at and 30 relative to CuO₂ planes, show an enhancement of the elastic coupling of the films at driving current densities several orders of magnitude smaller than the critical one. Our results indicate that the FLL appears to be in a relatively ordered, metastable state after field cooling without driving forces. Received 21 December 1999     

Perzyna粘塑性模型的参变量变分原理*

Perzyna模型是粘塑性本构关系的主要形式之一,本文给出该模型的参变量变分原理,该原理将原问题化为求解带约束条件的泛函极值,其约束条件就是由粘塑性本构关系推导出的系统状态方程,所讨论的问题其塑性流动不受Drucker假定的限制,文中给出原理的证明,并研究弹塑性蠕变问题.