The radiation swelling effect on fracture properties and fracture mechanisms of irradiated austenitic steels. Part I. Ductility and fracture toughness

Journal of the Mechanics and Physics of Solids

2017

Ductile fracture through void growth and coalescence depends significantly on the plastic anisotropy of the material and on void size, as shown by experiments and/or numerical simulations through several studies. Macroscopic (homogenized) yield criteria aiming at modeling nanoporous materials have been proposed only for the growth regime, i.e. non-interacting voids. The aim of this study is thus to provide a yield criterion for nanoporous materials relevant for the coalescence regime, i.e. when plastic flow is localized between voids. Through homogenization and limit analysis, and accounting for interface stresses at the void-matrix interface, analytical coalescence criterion is derived under the following conditions: axisymmetric loading, orthotropic material obeying Hill's plasticity, cylindrical voids in cylindrical unit-cell. Incidentally, an orthotropic extension of the existing isotropic modeling of interface stresses through limit analysis is described and used. The proposed coalescence criterion is then extended to account for combined tension and shear loading conditions. Numerical limit analyses have been performed under specific conditions / materials parameters to get supposedly exact (up to numerical errors) results of coalescence stress. A good agreement between the analytical coalescence criteria derived in this study and numerical results is found for elongated spheroidal voids, making them usable to predict the onset of void coalescence in ductile fracture modeling of nanoporous materials.

Section: Introductionmentioning

confidence: 97%

Anisotropic coalescence criterion for nanoporous materials

Journal of the Mechanics and Physics of Solids

2017

“…Physically-based models aiming at predicting fracture toughness of irradiated materials [27,14] assume some physical fracture mechanisms which need validation through dedicated experimental observations. In particular, irradiation of austenitic stainless steels and copper alloys leads to a change at the crystal scale of deformation mechanisms from an homogeneous to heterogeneous one: dislocations sweep away irradiation defects in narrow channels, making subsequent motion of dislocations easier.…”

Section: Introductionmentioning

confidence: 99%

Void growth and coalescence in irradiated copper under deformation

Barrioz

Journal of Nuclear Materials

Tanguy

2018

A decrease of fracture toughness of irradiated materials is usually observed, as reported for austenitic stainless steels in Light Water Reactors (LWRs) or copper alloys for fusion applications. For a wide range of applications (e.g. structural steels irradiated at low homologous temperature), void growth and coalescence fracture mechanism has been shown to be still predominant. As a consequence, a comprehensive study of the effects of irradiation-induced hardening mechanisms on void growth and coalescence in irradiated materials is required. The effects of irradiation on ductile fracture mechanisms -void growth to coalescence -are assessed in this study based on model experiments. Pure copper thin tensile samples have been irradiated with protons up to 0.01 dpa. Micron-scale holes drilled through the thickness of these samples subjected to uniaxial loading conditions allow a detailed description of void growth and coalescence. In this study, experimental data show that physical mechanisms of micron-scale void growth and coalescence are similar between the unirradiated and irradiated copper. However, an acceleration of void growth is observed in the later case, resulting in earlier coalescence, which is consistent with the decrease of fracture toughness reported in irradiated materials. These results are qualitatively reproduced with numerical simulations accounting for irradiation macroscopic hardening and decrease of strain-hardening capability.

“…The range of validity of the model comes from the assumptions used in the derivation of the yield criteria, namely continuum mechanics and isotropic plastic flow. For nanometric voids, the first assumption seems justified in situations where dislocations (sources) density is high and/or large applied strain, as can be inferred from some experimental results [47,48]. The second assumption makes the model relevant for high stress triaxialities, where crystallographic-induced anisotropy has been shown to affect only weakly void deformation.…”

Section: Discussionmentioning

confidence: 99%

“…All these yield criteria for porous materials were derived in the continuum mechanics framework, assuming that plastic flow occurs at a scale well below the void size, which might be questionable for very small voids. Recent experimental observations however show clear evidences of homogeneous deformation of nanometric voids [47,48], justifying the use of continuum models for porous materials down to the nanometric range, at least for applications involving large strain levels and/or large initial dislocations (sources) density. To the authors' knowledge, no size-dependent homogenized yield criterion for porous single crystals is available in the literature.…”

mentioning

confidence: 99%

A size-dependent ductile fracture model: Constitutive equations, numerical implementation and validation

Scherer

European Journal of Mechanics - A/Solids

2019

Size effects have been predicted at the micro-or nano-scale for porous ductile materials from Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Mechanics numerical simulations, as a consequence of Geometrically Necessary Dislocations or due to the presence of a void matrix interface. As voids size decreases, higher stresses are needed to deform the material, for a given porosity. However, the majority of the homogenized models for porous materials used in ductile fracture modeling are size-independent, even though micrometric or nanometric voids are commonly observed in structural materials. Based on yield criteria proposed in the literature for nanoporous materials, a size-dependent homogenized model for porous materials is proposed for axisymmetric loading conditions, including void growth and coalescence as well as void shape effects. Numerical implementation of the constitutive equations is detailed. The homogenized model is validated through comparisons to porous unit cells finite element simulations that consider interfacial stresses, consistently with the model used for the derivation of the yield criteria, aiming at modeling an additional hardening at the void matrix interface. Potential improvements of the model are finally discussed with respect to the theoretical derivation of refined yield criteria and evolution laws. cell simulations [16,17,18]. Homogenized yield criteria for porous single crystals have been developed to account for the effects of crystal orientation [19,20,21,22,23].Most of these homogenized models for porous materials are size-independent, assuming implicitly that only void volume fraction matters irrespectively of void size, although porous materials with voids ranging from micrometric [13] down to nanometric sizes [24,25] are encountered in industrial applications. Moreover, size effects have been predicted from theoretical and numerical studies. A first kind of size effect, occurring when voids size is lower than the dislocation mean free-path, has been revealed through Discrete Dislocation Dynamics (DDD) simulations [26]. In such situations, dislocations exhaustion can lead to the absence of void growth under mechanical loading. A second kind of size effect is related, in a broad sense, to an additional hardening at or close to the void matrix interface. Strain gradient (crystal-)plasticity models -accounting for the presence of Geometrically Necessary Dislocations [27] to extend conventional plasticity to lower scales -have been used in porous unit cells simulations (see [28,29,30,31] and reference therein), showing a strong effect of the void size on both void growth rate and strength of the porous material, consistently with DDD simulations [32]. Numerous Molecular Dynamics (MD) studies have also been performed to assess the strength of (nano-)porous materials, considering voids in an initially dislocation free matrix material ([33, 34, 35] and references therein). Plasticity occurs through dislocation emission from void matrix interface [36], and an influence...