Instytut Podstawowych Problemów Techniki

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This work presents a comprehensive examination of the physical mechanisms driving hardening in irradiated face-centered cubic FeNiCr alloys. The evolution of irradiation-induced defects during shear deformation is modeled by atomistic simulations through overlapping cascade simulations, where the nucleation and evolution of dislocation loops is validated by transmission electron microscopy images obtained from irradiated FeNiCr alloys using tandem accelerator. The effect of different shear rates on the microstructure of irradiated materials with a specific focus on the changes in the density of voids and dislocation loops induced by irradiation was analyzed. Additionally, the fundamental interaction processes between single irradiation-induced defects contributing to irradiation hardening, such as voids and dislocation loops in the alloy are explained. The analysis at atomic level indicates that both the dislocation loops and the voids exhibit strengthening effects. Furthermore, the nanometric voids are much stronger obstacles than dislocation loops of comparable size. The mechanism of cutting the voids leads to an increase of voids density and thus contributes to an increase in irradiation hardening. The mechanism of collapse of small voids into dislocation loops leads to decrease of voids density and at the same time increase of loops density. The coupling effect between the density of voids and dislocation loops is determined. Finally, the novel, physical mechanisms-based model of irradiation hardening and dislocation-radiation defect reaction kinetics are developed, which consider the mechanisms of void cutting, void shrink and void collapse to dislocation loop.

Słowa kluczowe:

Radiation-induced defects,Irradiation hardening,Collision cascades,MD simulations,Radiation defects evolution,Cr-rich alloys

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This study presents the novel peridynamic constitutive relations formulated in order to predict the plastic deformation and damage evolution in irradiated materials. The plastic behaviour of the material in which radiation induced defects contribute to the defined peridynamic porosity is described by the Gurson-Tvergaard-Needleman (GTN) yield criterion with irradiation hardening. The definition of peridynamic porosity is proposed as a volume of discontinuities created in the volume of peridynamic particles. The new constitutive relations for irradiation hardening based on the dilatational part of elastic strain energy are formulated. The physical relevance of coupling the porosity with the nonlinear irradiation hardening is discussed. The expressions for the yield function, kinetics of evolution of radiation induced porosity, irradiation hardening and plastic flow rule are derived in terms of the peridynamics variables. The peridynamic predictions are calibrated based on the experimental data obtained during the advanced experimental campaigns dedicated to irradiated materials to verify the validity of the proposed constitutive model. Ion irradiation campaigns were carried out to mimic the effects of neutron irradiation. A series of indentation experiments were conducted to elucidate the effects of material structure modification and assess the hardening effect originating from radiation defects.

Słowa kluczowe:

Peridynamics,Constitutive modeling,Radiation induced damage,Peridynamic porosity,Gurson yield function,Irradiation hardening,Ion irradiation,Nano-indentation test

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Fe-based alloys with high chromium and nickel concentrations are very attractive for efficient energy production in extreme operating conditions. We perform molecular dynamics (MD) simulations of nanoindentation on fcc FeNiCr multicomponent materials. Equiatomic FeNi, Fe55Ni19Cr26, and Fe74Ni8Cr18 are tested by using established interatomic potentials and similar conditions, for the elucidation of key dislocation nucleation mechanisms and interactions. Generally, we find that the presence of Cr in these alloys reduces the mobility of prismatic dislocation loops, and increases their area, regardless of crystallographic orientation. Dislocation nucleation and evolution is tracked during mechanical testing as a function of nanoindentation strain and Kocks–Mecking continuum modeling displays good agreement with MD findings. Furthermore, the analysis of geometrically necessary dislocations (GNDs) is consistent with the Ma–Clarke’s model at depths lower than 1.5 nm. The presence of Cr leads to a decrease of the GND density with respect to Cr-less FeNi samples, thus we find that Cr is critically responsible of increasing these alloys’ hardness. Post-indentation impression maps indicate that Ni–Fe–Cr compositions display strain localization and hardening due to high Cr concentration.

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The present work describes the physical mechanisms of low temperature creep in irradiated and unirradiated metals. The slow inelastic deformations of solids under stress below the yield stress of the material are considered. For the problem of creep at cryogenic temperatures, the classical creep models are not enough. The purpose of this paper is to formulate a physically-based constitutive model of creep for irradiated materials at cryogenic temperatures (liquid nitrogen 77 K, liquid helium, 4.2 K) based on the idea that a dislocation held up by a potential barrier can pass through it owing to the quantum-mechanical tunnelling effect. The problem is novel in the context of recognition of physical mechanisms taking place at cryogenic temperatures leading to the evolution of radiation induced defects under mechanical loads. Creep produced by the expansion of irradiation induced dislocation loops is considered. The kinetic law for evolution of a dislocation loop is proposed using the mechanism of development of a dislocation line over Peierls stress hills. Also, creep produced by the elastic interaction of a radiation induced point defects with existing dislocations in materials is regarded. Predicted creep rate behaviour as a function of stresses and dpa are presented which would need to be validated with data in irradiated materials. Moreover, the new constitutive model of low temperature creep in unirradiated materials is formulated. The Glen-Mott quantum mechanical dislocation tunnelling effect allows extending the theory to the liquid helium temperature range. For this case of unirradiated materials, the creep curves validated experimentally for copper and stainless steel in cryogenic temperature are shown.

Słowa kluczowe:

creep in the proximity of absolute zero,irradiation creep,quantum-mechanical tunneling effect,cryogenic temperatures,low thermal energy,Peierls stress hills

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The present work provides description of fatigue crack initiation in metals subjected to cyclic loading within the nominal elastic or initial elastic-plastic regimes next passing to elastic response during cyclic deformation and shake down process. It is assumed that damage growth proceeds due to action of local stress, specified as the sum of mean stress and its fluctuations induced by material inhomogeneities such as grain boundaries, inclusions, cavities, boundary asperities, also due to design notches or holes introduced into the element. The damage growth model is proposed, based on the critical plane concept. The macrocrack initiation then corresponds to a critical value of accumulated damage. The modelling of damage growth is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using the coherent laser light. The damage growth effect is analysed by microindentation tests. The fatigue tests are performed for high strength steel specimens with central hole.

Słowa kluczowe:

fatigue crack initiation, micro-plasticity, damage evolution, optical ESPI method, micro indentation

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The paper presents experimental and numerical characterization of damage evolution for ion-irradiated materials subjected to plastic deformation during nano-indentation. Ion irradiation technique belongs to the methods where creation of radiation-induced defects is controlled with a high accuracy (including both, concentration and depth distribution control), and allows to obtain materials having a wide range of damage level, usually expressed in terms of displacements per atom (dpa) scale. Ion affected layers are usually thin, typically less than 1 micrometer thick. Such a low thickness requires to use nano-indentation technique to measure the mechanical properties of the irradiated layers. The He or Ar ion penetration depth reaches approximately 150 nm, which is sufficient to perform several loading-partial-unloading cycles at increasing forces. Damage evolution is reflected by the force-displacement diagram, that is backed by the stress–strain relation including damage. In this work the following approach is applied: dpa is obtained from physics (irradiation mechanisms), afterwards, the radiation-induced damage is defined in the framework of continuum damage mechanics to solve the problem of further evolution of damage fields under mechanical loads. The nature of radiation-induced damage is close to porosity because of formation of clusters of vacancies. The new mathematical relation between radiation damage (dpa) and porosity parameter is proposed. Deformation process experienced by the ion irradiated materials during the nano-indentation test is then numerically simulated by using extended Gurson–Tvergaard– Needleman (GTN) model, that accounts for the damage effects. The corresponding numerical results are validated by means of the experimental measurements. It turns out, that the GTN model quite successfully reflects closure of voids, and increase of material density during the nano-indentation.

Słowa kluczowe:

radiation-induced damage, evolution of vacancy clusters, nano-indentation test, ion irradiation, radiation hardening

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Optimal shapes in the class of polynomial functions for rotating annular disks with respect to the mixed creep rupture time are found. Two effects leading to damage: diminishing of transversal dimensions and growth of micro-cracks are simultaneously taken into account. The first of them requires the finite strain analysis, the latter is described by Kachanov's evolution equation. Behaviour of the material is described by nonlinear Norton's law, generalized for true stresses and logarithmic strains, and the shape change law in form of similarity of true stresses and logarithmic strains deviators. For optimal shapes of the disk, changes of geometry and a continuity function are presented. The theoretical considerations based on the perception of the structural components as some highlighted objects with defined properties is presented

Słowa kluczowe:

annular disk, mixed creep rupture, optimal design

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The present work is devoted to simulation of fatigue crack initiation for cyclic loading within the nominal elastic regime. It is assumed that damage growth occurs due to action of meanstress and its fluctuations induced by crystalline grain inhomogeneity and the free boundary effect. The macrocrack initiation corresponds to a critical value of accumulated damage. The modelling of damage growth is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using coherent laser light.

Słowa kluczowe:

fatigue crack initiation, damage evolution, optical methods

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The present paper aims at predicting evolution of radiation induced damage in the solids subjected to mechanical loads beyond the yield stress. Moreover, the evolution of radiation induced damage is combined with the evolution of mechanically induced damage within the common framework of Continuum Damage Mechanics (CDM). An additive formulation with respect to damage parameters (tensors) has been postulated. Multiscale constitutive model containing strong physical background related to the mechanism of generation of clusters of voids in the irradiated solids has been built. The model is based on the experimental estimation of concentration of lattice defects (interstitials, di-interstitials, interstitial clusters, vacancies, di-vacancies, vacancy clusters) in Al as a function of dpa (displacement per atom), and comprises the relevant kinetics of evolution of radiation induced damage under mechanical loads. Two kinetic laws of damage evolution were taken into account: the Rice & Tracey model and – for comparison – the Gurson model. As an application, estimation of lifetime of a cylindrical shell (coaxial target embedded in a detector of particles) subjected to combination of irradiation and mechanical loads, has been carried out. It is demonstrated that the number of cycles to failure depends strongly on the accumulation of micro-damage due to irradiation. The lifetime of irradiated components has been expressed as a function of two parameters: maximum dpa and axial stress amplitude on cycle.

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A simulation model is presented for the creep process of the rotating disks under the radial pressure in the presence of body forces. The finite strain theory is applied. The material is described by the Norton-Bailey law generalized for true stresses and logarithmic strains. A mathematical model is formulated in the form of a set of four partial differential equations with respect to the radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, a numerical procedure is proposed. The given example shows the effectiveness of this procedure. The results show that the classical finite element method cannot be used here because both the geometry and the loading (body forces) change with the time in the creep process, and the finite elements need to be redefined at each time step.

Słowa kluczowe:

creep process, rotating disk, finite strain theory, simulation model

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The paper presents a simulation model for the creep process of rotating disks under radial tensional pressure subjected to of body force. The finite strain theory is applied. The material is described by the Norton - Bailey law generalized for true stresses and logarithmic strains. The mathematical model is formulated in form of set of four partial differential equations with respect to radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, the numerical procedure for solving this set is proposed. What is worth noticing the classical F EM is not applicable, because not only geometry, but also loading (body forces) change in time during the creep process. It would demand redefinition of finite elements at each time step. In uniaxial problem similar model was presented in [ 4 ], but now it is developed for complex stress state. Possible different formulations of initial and boundary conditions may be found in [ 5 ]. The procedure may be useful in problems of optimal design of full disks in [ 6 ]

Słowa kluczowe:

creep process, rotating disks, finite strain theory, simulation model

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We present a new design study of the neutrino Super Beam based on the Superconducting Proton Linac at CERN. This beam is aimed at megaton mass physics, a large water Cherenkov detector, proposed for the Laboratoire Souterrain de Modane in France, with a baseline of 130 km. The aim of this proposed facility is to study CP violation in the neutrino sector. In the study reported here, we have developed the conceptual design of the neutrino beam, especially the target and the magnetic focusing device. Indeed, this beam presents several unprecedented challenges, related to the high primary proton beam power (4 MW), the high repetition rate (50 Hz), and the low kinetic energy of the protons (4.5 GeV). The design is completed by a study of all the main components of the system, starting from the transport system to guide the beam to the target up to the beam dump. This is the first complete study of a neutrino beam based on a pebble-bed target capable of standing the large heat deposition of MW class proton beams

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The mixed creep rupture theory to the optimization problem for the complex stress state is used. The problem of optimal shape for the rotating full disk with respect to mixed rupture time is investigated. The mathematical model of mixed creep rupture is described by the system of five partial differential equations. Difficulty of the problem results from two types of nonlinearities: geometrical connected with the use of the finite strain theory and physical – the material is described by the Norton’s creep law, here generalized for true stresses and logarithmic strains. Additional time factor leads to subsequent complications. The parametric optimization describing the initial shape of the disk is applied. The obtained results are compared with the optimal disks with respect to ductile creep rupture time

Słowa kluczowe:

Mixed creep rupture, Structural optimization, Full disk

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This article deals with the influence of boundary conditions on the optimal shape of a rotating, axisymmetric annular disk of given volume that maximizes the ductile creep rupture time. The finite strain theory and physical law in form of Norton's law generalized for true stresses and logarithmic strains are applied. The optimal shape is found using parametric optimization. The initial shape of the disk is defined by class of polynomial function.

Słowa kluczowe:

Boundary conditions, Optimal design, Ductile creep rupture time, Annular disk

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The EUROnu project has studied three possible options for future, high intensity neutrino oscillation facilities in Europe. The first is a Super Beam, in which the neutrinos come from the decay of pions created by bombarding targets with a 4 MW proton beam from the CERN High Power Superconducting Proton Linac. The far detector for this facility is the 500 kt MEMPHYS water Cherenkov, located in the Fréjus tunnel. The second facility is the Neutrino Factory, in which the neutrinos come from the decay of μ+ and μ− beams in a storage ring. The far detector in this case is a 100 kt magnetized iron neutrino detector at a baseline of 2000 km. The third option is a Beta Beam, in which the neutrinos come from the decay of beta emitting isotopes, in particular He6 and Ne18, also stored in a ring. The far detector is also the MEMPHYS detector in the Fréjus tunnel. EUROnu has undertaken conceptual designs of these facilities and studied the performance of the detectors. Based on this, it has determined the physics reach of each facility, in particular for the measurement of CP violation in the lepton sector, and estimated the cost of construction. These have demonstrated that the best facility to build is the Neutrino Factory. However, if a powerful proton driver is constructed for another purpose or if the MEMPHYS detector is built for astroparticle physics, the Super Beam also becomes very attractive

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The first attempt of finding of optimal shape for bars in presence of body forces with respect to mixed creep rupture is made. For given volume of the bar, distribution of initial cross-section, ensuring the longest life-time to mixed rupture is sought. The finite strain theory and physical law in form of Norton's law generalized for true stresses and logarithmic strains are applied. Using the method of parametric optimization, the best of linear and quadratic functions describing the initial shape of the bar are found. The shape of initial strength is corrected in a way leading to longer life-time. Results of both approaches are compared

Słowa kluczowe:

Mixed rupture, Structural optimization, Nonhomogeneity

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Axisymmetric rotating disks optimal with respect to ductile creep rupture time are considered. Finite strain theory is applied. The material is describe d by the Norton-Bailey law generalized for true stresses and logarithmic strains. The set of four partial differential equations describes the creep conditions of parabolic disk. The optimal shape of the disk is found using parametric optimisation with two free parameters. The results are compared with disks of conical shape.

Słowa kluczowe:

finite strain theory, annular disk, ductile creep rupture time, biparametric optimization

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This paper presents the problem of optimal design with respect to ductile creep rupture time for rotating disk. The material is described by the Norton–Bailey nonlinear creep law, here generalized for true stresses and logarithmic strains. For complex stress states, the law of similarity of deviators, combined with the Huber–Mises–Hencky hypothesis is applied. The set of four partial differential equations describes the creep conditions of annular disk. The optimal shape of the disk is found using parametric optimisation with one free parameter. The results are compared with disks of uniform thickness.

Słowa kluczowe:

optimal design, annular disk, ductile creep rupture time

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This paper presents several attempts to use novel optical techniques for damage evaluation of materials subjected to either monotonic or cyclic loading and its monitoring on specimens made of the nickel super-alloy and power engineering steel. Effectiveness in damage analysis of Digital Image Correlation (DIC) and Electronic Speckle Pattern Interferometry (ESPI) is compared.

Słowa kluczowe:

fatigue, damage, optical full-field methods

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This paper presents an attempt to use the Electronic Speckle Pattern Interferometry (ESPI) and Digital Image Correlation (DIC) for damage evaluation and its monitoring on specimens made of the P91 steel and aluminide coated nickel super-alloys subjected to monotonic or cyclic loading.

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In most cases, fatigue damage has a local character and it is based on damage development leading to generation of cracks appearing around structural defects or geometrical notches. An identification of these areas and their subsequent monitoring requires a full-field displacement measurements performed on the objects surfaces. This paper presents an attempt to use the Electronic Speckle Pattern Interferometry (ESPI) method for fatigue damage evaluation and its monitoring on specimens made of the P91 steel and aluminide coated nickel super-alloys. In this work, also a development of fatigue damage was investigated using destructive and non-destructive methods in materials commonly applied in power engineering or automotive industry. The fatigue tests for a range of different materials were interrupted for selected number of cycles in order to assess a damage degree. As destructive methods the standard tensile tests were carried out after prestraining due to fatigue. Subsequently, an evolution of the selected tensile parameters was taken into account for damage identification. The ultrasonic or magnetic techniques were used as the non-destructive methods for damage evaluation. In the final step of the experimental programme microscopic observations were performed. The results show that ultrasonic and magnetic parameters can be correlated with those coming from destructive tests. It is shown that good correlation of mechanical and selected non-destructive parameters identifying damage can be achieved for the materials tested

Słowa kluczowe:

Fatigue, damage, optical methods, non-destructive techniques

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Słowa kluczowe:

Creep in the proximity of absolute zero, Irradiation creep, Quantum-mechanical tunneling effect, Cryogenic temperatures, Low thermal energy, Peierls stress hills

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Słowa kluczowe:

Fatigue Crack Initiation, Damage Evolution, Optical Methods, Indentation Method

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The aim of this work consists a development of the Gurson-Tvergaard-Needleman model (GNT) of damage evolution in elastic-plastic materials. This model is supported by optical method of stress and strain monitoring (ESPI) for early detection, localization and monitoring of damage in materials under fatigue loading.

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The problem investigated in the present work concerns the damage evolution in elastic-plastic materials subjected to cyclic loading. The modeling of damage mechanisms is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using coherent laser light. Such a study can help better understanding of the damage and failure mechanism of modern structural materials for practical engineering problems.

Słowa kluczowe:

damage mechanisms, void growth, optical methods

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Recent investigations reveal that interface bonding strength is dependent on the relative orientation of crystallites of the both phases [2]. The experimental, theoretical and computational investigations confirm this observation in the case of Cu/Al2O3 system, [3], [4]. It is shown that the statistical distribution of the values of interface strength for different relative orientations of bonded phases should be included in the phenomenological model of the damage initiation in nanocomposites. The novelty of the presented study is the combination of different experimental techniques: HRTEM, EBSD and molecular dynamics simulations with phenomenological theory of damage development in nanocomposites due to debonding at the interphase boundary [5], [6], [7]. A class of new models with the yield condition determined by one of quadric surfaces, in particular paraboloid or ellipsoid one is considered and the comparison with popular Gurson approach is discussed, [8].

Słowa kluczowe:

nanocompistes, strength, interface, bonding, HRTEM, EBSD, molecular dynamics

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Structural elements working under creep conditions belong to the relatively new branches of structural optimization. Among many new possibilities of optimization criteria, which offers optimization of structures in creep conditions, the most important seems to be time to rupture. Most papers on optimal structural design are based on the brittle creep rupture theory proposed by Kachanov (small strain theory). Application of the ductile rupture theory proposed by Hoff in optimization problems are rather scare as it requires finite strain theory. For the first time it was used by Szuwalski [ 1], [2] and Szuwalski, Ustrzycka [4]. The first attempt of application the mixed theory to shape optimization was made by Ustrzycka and Szuwalski [3] for bars under nonuniform tension. Here, for the first time, the optimization problem with respect mixed rupture time, is solved for the complex stress state. Application of mixed rupture theory proposed by Kachanov takes into account: geometrical changes - diminishing of transversal dimensions resulting from large strains (as in ductile rupture) and growth of microcracks (as in brittle rupture). In present paper the problem of optimal shape with respect to mixed creep rupture time for the rotating full disk is investigated. Difficulty of the problem results from two types of nonlinearities: geometrical connected with the use of the finite strain theory and physical - the material is described by the Norton’s creep law, here generalized for true stresses and logarithmic strains. The mathematical model of mixed creep rupture is described by the system of five partial differential equations in dimensionless form. The system must be integrated with respect to material coordinate (Runge – Kutta fourth order method) and to time with variable step (Euler’s method). The parametric optimization with one, or two free parameters describing the initial shape of the disk is applied. The obtained results are compared with the disks with respect to ductile creep rupture time [2]

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The problem of optimal design with respect to mixed creep rupture time is a new one. The first attempt of solution for rotation bar was made in 2010 by Szuwalski and Ustrzycka [5]. Difficulties of the problem result from physical an d geometrical nonlinearities, and were observed earlier in solution for ductile creep rupture [4], [6]. Some problems of optimal design for annular rotating disks were discussed by Farshi and Bidabadi [2]. Analytical solution for the elastic-plastic stress distribution in rotating annular disks were obtained by Ç ğ allio ğ lu et al. [1] and Gun [3]. Because of those difficulties the parametric optimization was adopted. In certain class of function describing the initial shape of the disk we are looking for optimal parameters leading to the longest time to mixed rupture under assumption of constant volume. The axially symmetric annular disk rotating with constant angular velocity is loaded by centrifugal forces resulting from the own mass of the disk and additional mass uniformly distributed at the outer edge (Figure 1). The mathematical model of mixed creep rupture is described by the system of five partial differential equations in dimensionless form. n the last equation the continuity function Ψ describing damage of material was introduced. The criterion of rupture is fulfilled when Ψ takes values 0. The optimal shape among linear functions (uniparametric optimization) and quadratic functions (biparametric optimization) was found by checking some disks in earlier predicted domain of admissible solutions. The better results were obtained using biparametric optimization. The obtained results are compared with the disks with respect to ductile creep rupture time [6].

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