Distribution Of Dislocation Loops Research Articles

Fluctuations in misfit volume by interstitial carbon atoms contribute to the unusual dislocation loop evolution in high-entropy alloys under irradiation

Dislocation loops play a pivotal role for the irradiation behavior and associated mechanical properties of materials. This study employs advanced transmission electron microscopy, nanoindentation and first-principles calculations to elucidate the impact of interstitial carbon atoms on the evolution of dislocation loops in an Fe49.5Mn30Co10Cr10C0.5 high-entropy alloy under ion irradiation at temperatures ranging from 420 °C to 540 °C with a peak dose of 50 DPA. Interstitial carbon atoms have been revealed to broaden the size distribution of dislocation loops, rendering their morphologies more jagged, and consequently inducing a more substantial pinning effect. These outcomes can be attributed to the enhancement of misfit volume fluctuations of the alloying elements, which drives more severe local lattice distortions and larger variation of local chemical environments. As a result, these fluctuations promote the local pinning of dislocation loops, lead to their rugged movement and contribute to the rise in hardening. Our findings bring previously unrecognized insights into the role of interstitial carbon atoms in influencing the nature of dislocation loops in high-entropy alloys, and provide important clues to the design of alloys for nuclear applications.

Displacement cascades database from molecular dynamics simulations in tungsten

In this work, we have carried out a series of displacement cascade simulations in tungsten (W), including seven different primary-knock-on atom (PKA) directions, and PKA energy covers 1 to 300 keV at 363 K; 10, 50, 100, and 200 keV cascades are considered at 600 K, and 10 and 50 keV cascades are simulated at 300 K. Then, a systematic database of W cascade simulations has been established, containing more than 2000 cascades. The number of Frenkel pairs, the type of defect, and its spatial distribution were all determined. The effects of PKA direction, PKA energy and temperature have been discussed in terms of defect generation, defect clustering, and dislocation loops. It is found that, the PKA direction may have an effect on the configuration of defects, such as the formation probability of 〈100〉 interstitial loops, C15 clusters and the sub-cascades, and also has an effect on the number of Frankel pairs when PKA energy larger than 50 keV. Furthermore, from 363 K to 600 K, the number of Frankel pairs is reduced by ∼10%, and high temperature can promote the clustering of interstitial. We further found that temperature may affect the distribution of dislocation loops, and the number of 〈100〉 interstitial dislocation loops is more at 363 K than at 600 K. These results can provide a database of key input parameters for the subsequent larger-scale simulations, and give an important reference for the prediction of defect behaviour, mechanical and thermal properties of W-based materials under fusion neutron irradiation.

Local chemical ordering and its impact on radiation damage behavior of multi-principal element alloys

• LCOs promotes the nucleation of dislocations but inhibits their growth in the CrFeNi MPEA under irradiation. • LCOs reduces the number of stair-rod dislocation associated with SFTs, which may help to suppress irradiation swelling. • LCOs is conducive to enhance radiation damage tolerance of MPEAs. Multi-principal element alloys (MPEAs) have attracted much attention as future nuclear materials due to their extraordinary radiation resistances. In this work, we have elucidated the development of local chemical orderings (LCOs) and their influences on radiation damage behavior in the typical CrFeNi MPEA by hybrid-molecular dynamics and Monte Carlo simulations. It was found that considerable LCOs consisting of the Cr-Cr and Ni-Fe short-range orders existed in the ordered configuration with optimized system energy. Through modeling the accumulation cascades up to 1000 recoils, we revealed that the size of defect clusters and dislocation loops is smaller in the ordered configuration than those in the random one, although the former formed more Frenkel pairs (i.e., self-interstitials and vacancies). In addition, the distribution of dislocation loops is relatively more dispersed in the ordered configuration, and the stair-rod dislocations related to irradiation swelling are also smaller, implying that the existence of LCOs is conducive to enhancing radiation damage tolerance. To understand the underlying mechanism, the effects of LCOs on the formation and evolution of defects and radiation resistance were discussed from the aspects of atomic bonding, migration path, and energy of defect diffusion, which provides theoretical guidance for the design of MPEAs with enhanced radiation resistance.

Analysis of dislocation characteristics and inside-outside contrasts in irradiated and annealed tungsten as a fusion reactor material

Tungsten is an important candidate of plasma-facing material for fusion reactors. Its irradiation response, especially the post-irradiation annealing (PIA) behavior needs further investigating. In addition, the practice of the “inside-outside” contrast method of determining the characteristics of irradiation induced dislocation loops has not been utilized frequently, and the present research serves as an example to present some practical considerations. In the present work, a tungsten thin-foil specimen is irradiated at 400 ℃ with 58 keV D<sup>+</sup> to a final fluence of 1× 10<sup>17</sup> cm<sup>–2</sup>, corresponding to a dose of about 0.1 dpa. The specimen is prepared through the electro-polishing method by using a NaOH based electrolyte. The ion irradiation is carried out directly on the electro-polished specimen. The irradiated specimen is followed by isothermal annealing at 900 ℃ for 1 h. The as-irradiated and post-irradiation annealing modified defects are investigated with a transmission electron microscope (TEM) operated at 200 kV. The irradiation defects are characterized by using TEM bright-field imaging for the same imaging field with different <i> <b>g</b> </i> vectors around the three major zone axes: the [001], [111], and [011] zone axis of the body-center cubic lattice of W. For each <i> <b>g</b> </i> vector, the ±<i> <b>g</b> </i> are characterized, and the corresponding contrast-extinctions and “inside-outside” contrasts of selected dislocation loops are identified. The indices of the <i> <b>g</b> </i> vectors around different zone axes are assigned consistently with the Kikuchi map. As a result, the D<sup>+</sup> irradiation increases a fine distribution of dislocation loops with an average size of (11.10±5.41) nm and a bulk density of 2.40×10<sup>22</sup> /m<sup>3</sup>. Voids are not observed obviously. The post-irradiation annealing causes the loop size to increase and the loop density to decrease, with numbers of (18.25±16.92) nm and 1.19×10<sup>22</sup> /m<sup>3</sup>, respectively. Through the contrast-extinction analysis, the dislocation loops in the irradiated and annealed specimen are identified to be <i> <b>a</b> </i>/2<inline-formula><tex-math id="Z-20230218170937">\begin{document}$\langle {111} \rangle$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20222124_Z-20230218170937.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20222124_Z-20230218170937.png"/></alternatives></inline-formula>-type dislocation loops. The post-irradiation annealing also causes the coalescence of large loops and forms large irregular-shaped dislocation loops. Voids with typical sizes of 1–2 nm are also observed in the annealed specimen. The PIA modified microstructure is consistent with the stage IV or stage V characterization of classical PIA induced microstructures. Through the “one-step” inside-outside contrast method, the dislocation loops are identified as an interstitial type. The influcing factors for the “one-step” method are discussed and the importance of consistent indexing is also noted.

TEM characterization of irradiation-induced dislocation loops and voids in ion-irradiated pure chromium

Chromium (Cr) based coatings have been proposed for Zircaloy fuel rods to enhance the accident tolerance in water-cooled reactors. However, the response of Cr to irradiation has received limited attention in prior studies. To get a better understanding of radiation damage in Cr for future nuclear applications, in the present study, the irradiation-induced microstructure evolution of dislocation loops and voids was studied in pure Cr subjected to 2.8 MeV iron ions irradiation at 550 °C (belonging to stage III, intermediate-temperature). TEM observation results show that the distribution of dislocation loops extends the SRIM simulated irradiation depth to 3.5 µm, while voids were only formed in the irradiated region up to a depth of 1.3 µm. A rigorous method with combined consideration of edge-on view and inside-outside analysis was proposed to determine the habit plane. With this method, what has normally considered as an unsafe zone becomes a favored zone for determining the nature of dislocation loops. The nature of dislocation loops was determined including both interstitial and vacancy types with ½<111> Burgers vector in all regions. Within the irradiation region, the loops are approaching half interstitial and half vacancy, while beyond the irradiated region interstitial loops became dominant. The irradiation-induced swelling was quantified by the void size and density. The swellings are mostly corresponding well with the irradiation dose distribution which is simulated by SRIM. The swelling rate close to the peak region is around 0.3%/dpa. Results demonstrate that Cr tends to experience some similarities in irradiation loop evolution to W-based, Mo-based materials, as they are in the same group in the periodic table, despite the discrepancy in the characteristic of loops such as the irradiation temperature-dependent dislocation loop formation was observed as well. The present study is significant not only for supplementing the fundamental knowledge of irradiation damage in Cr but also for the application of Cr coating to the accident tolerant fuel claddings or other nuclear structure materials.

In-situ TEM investigation of dislocation loop evolution in Al-forming austenitic stainless steels during Fe+ irradiation: Effects of irradiation dose and pre-existing dislocations

Alumina-forming austenitic (AFA) stainless steel with excellent properties has been regarded as a promising candidate of fuel claddings in Supercritical carbon dioxide (S-CO2) gas cooled nuclear reactor. In current work, in-situ irradiation with 400 keV Fe+ in transmission electron microscope were performed on AFA stainless steel to investigate the influences of irradiation dose and pre-existing dislocation lines on loop evolution at 773 K. The irradiation damage caused by irradiation-induced loops was also analyzed. In-situ TEM observation displayed the evolution and characteristics of dislocation loops, including initiation, migration, aggregation, growth, annihilation, and combination. Both Frank loops with b = 1/3<111> and perfect loops with b = 1/2<110> were formed, and at 0.54 dpa, 1/2<110> loops accounted for the majority and was up to 64.6%. Pre-existing dislocation lines obviously affected not only the evolution and distribution of dislocation loops, but also the degree of irradiation hardening. At the same irradiation dose, not only the size and number density of dislocation loops in the region with dislocation lines were smaller than those in the region without dislocation lines, but also the increment of yield strength and irradiation damage was lower before the formation of dislocation network. Increasing pre-existing dislocation density should be beneficial to improve the irradiation resistance of materials, but it needed to be comprehensively considered with the mechanical properties of the material. Al component played an important role in irradiation behavior of AFA steels and the corresponding mechanism was discussed subsequently.

Microstructure characterization of reactor pressure vessel steel A508-3 irradiated by heavy ion

As one of the key structures used in nuclear power plants, the study of irradiation effects of pressure vessel steel (RPV) is of great scientific value to nuclear safety. The RPV steel was irradiated by Fe ions up to three different irradiation damage levels (0.08 dpa, 0.15 dpa, and 0.6 dpa). The transmission electron microscope was utilized to measure the irradiated microstructure and it was found that after the irradiation of 0.08 dpa, the density and size of dislocation loops in Fe ions irradiated samples was small and the dislocation loops were distributed near the surface. When irradiation dose was up to 0.15 dpa, many black dots were distributed in the whole irradiation region and some large size dislocation loops appeared. In the case of 0.6 dpa, a large number of dislocation loops were produced and the distribution of dislocation loops extended to the whole irradiation region owing to the production and growth of defects such as vacancies and black dots.

Fracture mechanics approach to the problem of subsidence induced by resource extraction

A new area of application of Fracture Mechanics methods is proposed: the determination of surface deformation induced by internal volume change (e.g. due to underground hydrocarbon extraction). The finite layer-like zone of volume alteration is modelled as a crack, that is as a continuous distribution of dislocation loops. This approach allows the determination of surface deformation and can serve as the basis for monitoring of the volume alteration from surface measurements. In a limiting case of nearly uniform deformation of the reservoir boundaries the model consists of a single dislocation loop (an inserted cylindrical body of a constant height) in half-space and results in simple approximate expressions for the normal and tangential displacement components of the free surface. For the example of subsidence in the Groningen gas field the proposed method produces more realistic results describing reality better than the traditional models based on representing the reservoir as a collection of independent dilation centres. Also, analytical expressions are proposed for the nuclei – the basic Green’s function type expressions that allow representation of a planar horizontal reservoir layer of an arbitrary shape as a distribution of infinitesimal dislocation loops. For the case of a cylindrical reservoir, the nuclei integration recovers the exact distribution of the surface displacements.

3D reconstruction of the spatial distribution of dislocation loops using an automated stereo-imaging approach

We propose an automated stereoscopic imaging approach for reconstructing the 3D spatial distribution of small dislocation loops (DLs) from 2D TEM micrographs. This method is demonstrated for small DLs in tungsten, formed by low-dose ion-implantation, that appear as circular spots in diffraction contrast TEM images. To extract the 3D position of specific DLs, their 2D position in multiple weak-beam dark-field TEM micrographs, recorded at different tilt angles, is fitted. From this fit the geometric centre and size of each DL in each micrograph can be extracted. To identify each specific DL in all the 2D projections, an automated forward prediction approach is used. A system of linear equations can then be setup, linking the 3D position of each DL to its 2D position in each projection, and solved using least-squares fitting. This approach is initially tested on synthetic data. For low projected loop densities (<20 × 1015 m−2) only 3 projections are required for perfect recovery of the defect microstructure. More projections are required when the projected number density increases or realistic errors are included. 3D reconstruction of experimental data from the low-dose self-ion implanted tungsten sample reveals a damage microstructure in good agreement with the depth-dependent damage profile predicted by SRIM. A comparison with weighed back-projection shows that the stereo-imaging-approach requires fewer projections, is less sensitive to the angular range spanned, and is more resilient to spurious variations in local contrast. It also allows a more straightforward retrieval of quantitative information such as size and position of each loop.

Radiation-induced segregation on defect clusters in single-phase concentrated solid-solution alloys

A group of single-phase concentrated solid-solution alloys (SP-CSAs), including NiFe, NiCoFe, NiCoFeCr, as well as a high entropy alloy NiCoFeCrMn, was irradiated with 3 MeV Ni2+ ions at 773 K to a fluence of 5 × 1016 ions/cm2 for the study of radiation response with increasing compositional complexity. Advanced transmission electron microscopy (TEM) with electron energy loss spectroscopy (EELS) was used to characterize the dislocation loop distribution and radiation-induced segregation (RIS) on defect clusters in the SP-CSAs. The results show that a higher fraction of faulted loops exists in the more compositionally complex alloys, which indicate that increasing compositional complexity can extend the incubation period and delay loop growth. The RIS behaviors of each element in the SP-CSAs were observed as follows: Ni and Co tend to enrich, but Cr, Fe and Mn prefer to deplete near the defect clusters. RIS level can be significantly suppressed by increasing compositional complexity due to the sluggish atom diffusion. According to molecular static (MS) simulations, “disk” like segregations may form near the faulted dislocation loops in the SP-CSAs. Segregated elements tend to distribute around the whole faulted loop as a disk rather than only around the edge of the loop.

Transmission electron microscopy investigation of the microstructure of Fe–Cr alloys induced by neutron and ion irradiation at 300 °C

Four Fe–Cr binary alloys, with Cr content from 2.5 up to 12wt%, were neutron or ion irradiated up to a dose of 0.6 dpa at 300 °C. The microstructural response to irradiation has been characterised using Transmission Electron Microscopy (TEM). Both, neutrons and ions, gave rise to the formation of dislocation loops. The most striking difference between ion and neutron irradiation is the distribution of these loops in the sample. Except for the lowest Cr content, loops are distributed mainly along grain boundaries and dislocations in the neutron irradiated samples. The inhomogeneous distribution of dislocation loops could be related to the presence of α′ precipitates in the matrix. In contrast, a homogeneous distribution is observed in all ion irradiated samples. This important difference is attributed to the orders of magnitude difference in dose rate between these two irradiation conditions. Moreover, the density of loops depends non-monotonically on Cr content in case of neutron irradiation, while it seems to increase with Cr content for ion implantation. Differences are also observed in terms of cluster size, with larger sizes for neutron irradiation than for ion implantation, again pointing towards an effect of the dose rate.

Te implantation in Ge(001) for n-type doping applications

5×1015 Te+ ionscm−2 were implanted in an Ge(001) substrate using an industrial implanter with a Te+ beam energy of 180keV. In addition to usual implantation-mediated defects observed in Ge with usual dopants, Te implantations lead to the formation of amorphous surface GeO clusters exhibiting micrometer scale sizes, as well as deep extended defects. Implantation defects promote the formation of two distributions of dislocation loops and clusters located at two different depths in the Ge substrate during annealing. No interactions between Te atoms and dislocation loops were observed. However, the formation of non-equilibrium Te–Ge clusters, probably mediated by Ge self-interstitials, was found to prevent the Te solubility to exceed ~5×1019cm−3 in Ge. The regular implantation method is shown to be ineffective for the production of high level n-type Ge doping using Te, due to the important Ge damage caused by Te implantation.

Anisotropic dislocation loop distribution in alloy T91 during irradiation creep

Ferritic–martensitic (FM) steel T91 was subjected to irradiation with 3MeV protons while under load at stresses of 100MPa, 180MPa, and 200MPa. Transmission electron microscopy of crept T91 samples was conducted to determine the nature of the loops and to quantify the edge-on dislocation loop density as a function of their orientation to the tensile axis. Loops were determined to be interstitial in nature of the type ao〈100〉. The distribution of ao〈100〉 loops was found to be strongly anisotropic in which loops preferentially formed with their normal in the tensile direction. An empirical correlation was developed to describe the relationship between the orientation of the loop normal to the tensile axis and the local dislocation loop density. Loop anisotropy was found to increase as a function of the applied stress and their strain contributions relative to total creep strain were calculated at 4–11% of the total creep strain. Results from this study provide a means for quantifying empirically measured anisotropic microstructure and including it in irradiation creep mechanisms for FM steels.

Treating internal surfaces and interfaces in discrete dislocation dynamics

AbstractThe treatment of coherent interfaces and cracks is discussed in the framework of dislocation dynamics (DD). In the case of interfaces, we use DD to study dislocation interactions in nanoscale bimetallic laminates, and to predict their structure after relaxation and during loading. In agreement with experimental observations, our discrete dynamics simulations show that dislocation structure develops only at the interface between coherent layers leaving layers’ interior dislocation-free. The main dislocation mechanism at this length scale is Oworan bowing of threading dislocations confined to their respective layers by the sign-alternating coherency stress field in the layers. Slip transmission across the interfaces marks the end of the confined slip regime, hence, the breakdown of the interfaces and macroscopic yielding of these structures. In the case of crack, its long-range and singular stress field is determined by modeling the crack as continuous distribution of dislocation loops. The traction boundary condition to be satisfied at the crack surface, results into a singular integral equation of the first kind that is solved numerically. The model is integrated with the DD technique to investigate the behavior of a specimen containing cracks of different shapes under fatigue. The results are compared with the behavior of an uncracked specimen and conclusions are extracted. Extension of this crack treatment methodology to account for their presence at interfaces, all within the frame dislocations dynamics, opens the door for a more realistic approach to a wide range of interfaces-related problems.

X-ray diffraction study of silicon single crystals highly doped with boron

The section Lang method of X-ray diffraction topography in combination with X-ray diffractometry based on the Borrmann effect was previously shown to be effective for detection of cluster formation during the growth process of highly doped Si-Cz single crystals. In the present work, the same techniques have been used to choose the best condition of technological heat treatment of boron-doped silicon from the view-point of formation of microdefects. The concentration and average size of dislocation loops have been calculated for two conditions of standard heat treatment from the analysis of diffusion scattering. The distribution of dislocation loops along the growth axis and crystal diameter has been determined as well.

Grain-size dependent accommodation due to intragranular distributions of dislocation loops

A grain-size dependent accommodation law for polycrystals is deduced from an inclusion/matrix problem (i.e., each grain is seen as embedded in a homogeneous equivalent medium) where plastic strain inside the inclusion is given as a discrete distribution of circular coaxial glide dislocation loops. The loops are assumed constrained at spherical grain boundaries. From thermodynamic considerations specific to a process of identical plastification in all the loops (considered as “super-dislocations”), an average back-stress over the grain is derived. In order to compute the very early stages of plastic deformation in a face-centred cubic polycrystal, this back-stress is incorporated into a diluted model in terms of concentration of plastic grains. Contrary to conventional mean-field approaches, a grain-size effect is obtained for the initial overall strain-hardening behaviour. This size effect results from an intrinsic contribution of intragranular slip heterogeneities on the kinematical hardening.

Formation of dislocation loops in silicon by ion irradiation for silicon light emitting diodes

We have studied the influence of the ion species, ion energy, fluence, irradiation temperature and post-implantation annealing on the formation of shallow dislocation loops in silicon, for fabrication of silicon light emitting diodes. The substrates used were (100) Si, implanted with 20–80keV boron at room temperature and 75–175keV silicon at 100 and 200°C. The implanted fluences were from 5×1014 to 1×1015 ions/cm2. After irradiation the samples were processed for 15s to 20min at 950°C by rapid thermal annealing. Structural analysis of the samples was done by transmission electron microscopy and Rutherford backscattering spectrometry. In all irradiations the silicon substrates were not amorphized, and that resulted in the formation of extrinsic perfect and faulted dislocation loops with Burgers vectors a/2〈110〉 and a/3〈111〉, respectively, sitting in {111} habit planes. It was demonstrated that by varying the ion implantation parameters and post-irradiation annealing, it is possible to form various shapes, concentration and distribution of dislocation loops in silicon.

Structure-Phase State, Corrosion and Irradiation Properties of Zr-Nb-Fe-Sn System Alloys

Abstract In the search for more optimal core materials for a water cooled reactor at extended burnup, much attention is paid to alloys of the Zr-Nb and Zr-Nb-Fe-Sn systems. E110 and E635 alloys are two such. In the current VVER fuel cycle, the E110 alloy is used as fuel cladding and in SG components. The E635 alloy is under development as a fuel cladding and for fuel assembly structural elements for water cooled reactors of the VVER and RBMK types. E110, while having a unique corrosion resistance in pressurized water reactors, is subject to noticeable disadvantages in terms of corrosion resistance under conditions of boiling and higher coolant oxygen contents as well as in deformation stability under stresses and irradiation. Currently, the E635 alloy has passed the most important steps of qualification and is being introduced into cores as a material for guide thimbles, central tubes, and stiff frame angles in VVER-1000 FAA and FA-2. Properties of alloys are governed by their compositions and microstructure and even small changes in composition (Nb, Fe, Sn) and processing (heating in the α or the α+β regions) lead to substantial changes in properties as a result of changes in second phase precipitates and matrix composition. ATEM was used to study structure—phase states of a series of alloys Zr-(0.6–1.2) Nb-(0–0.6) Fe-(0–1.5) Sn (% weight), to determine the microstructural characteristics of recrystallized cladding tubes and the temperature stability regions of β-Nb, β-Zr, Zr(Nb,Fe)2, and (Zr,Nb)2Fe second phase precipitates. An increase in the relative content of iron R=Fe/(Fe+Nb) results in a larger volume fraction of (Zr,Nb)2 Fe precipitates. β-Nb and Zr(Nb,Fe)2 particles are completely dissolved at ⩽750°C, the (Zr,Nb)2Fe phase at ⩽800°C. Autoclave corrosion tests revealed that the corrosion resistance of the materials depends on alloy composition. The content of tin lowered down to 0.8 % reduces weight gains in water, water containing Li, and particularly in steam. The content of Nb reduced to 0.6 % results in lower weight gains in water and steam and higher weight gains in Li containing water. The optimal content of iron in Zr-Nb-Fe-Sn alloys for corrosion resistance depends on the R ratio and makes up 0.2–0.4 %. Tests of samples produced from tubes of the above alloys and irradiated in BOR-60 at 315–345°C show that alloying Zr-Nb alloys with iron and tin improves their resistance to irradiation growth and creep. Sn and a higher Fe content in solid solution effected by transfer of Fe from the Laves phase precipitates to the matrix under irradiation strengthens the alloys. The influence of irradiation on phase compositions was established using irradiated samples (gas filled and unstressed) of cladding tubes: β-Nb (85-90 % Nb) precipitates become depleted in niobium (or enriched in zirconium) to 50-60 % Nb and finely dispersed irradiation induced second particles (IIPs) enriched in niobium are formed. The Laves phase becomes depleted in iron and alters its crystal structure from hcp to bcc of the β-Nb type. The fcc (Zr,Nb)2Fe precipitates retain on the whole their composition and structure, but the peripheries of particles reveal structural features, possibly related to niobium redistribution. No amorphization of any of the precipitates was identified. Alloy composition and applied stress under irradiation influence density and distribution of dislocation loops and IIP precipitates. Proceeding from results of out-of-pile and from post-irradiation examinations of the structure and properties of E110 and E635 type cladding tubes, compositions of alloys having improved corrosion and irradiation resistances are proposed. E110 type (Zr-1Nb-0.1Fe-0.1O) alloy features enhanced strength characteristics as a result of iron transfer from Laves phase precipitates to the matrix under irradiation, lower irradiation induced growth strain, and irradiation-thermal creep. An E635 type alloy (tin and niobium content lowered down to &amp;lt;0.8 %) has a higher corrosion resistance and comparable creep and growth resistance as compared to the standard E635 alloy.

Analysis of Slant Surface Cracks with Step Notches Subject to Contact Loadings by a Variational Boundary Integral Method

Modes I and II stress intensity factors are analyzed by means of a variational boundary integral method (VBIM) for slant surface-breaking cracks in a half-plane with surface steps subject to contact loadings. This method represents the crack as a continuous distribution of dislocation loops. The crack opening displacements, which are related to the geometry of loops and their Burgers vectors, can be determined by minimizing the elastic potential energy, obtained from the known expressions of the interaction energy of a pair of dislocation loops, of the solid. In contrast to other methods, this approach finally reduces to a symmetric system of equations with milder singularities of the type 1/R, which facilitate the numerical treatments. By modeling the surface boundary of the half-plane as half part of an infinite crack breaking through an infinite solid, this paper demonstrates that the VBIM can be well extended to solve the fracture problems of inclined surface-breaking cracks in a half-plane with curve or step notches subject to combined contact loadings, and presents results of stress intensity factors for a variety of loadings, cracks and step surface configurations. Numerical results of test examples are in good agreement with the existing results in the literature.

Shielding and amplification of a penny-shape crack due to the presence of dislocations

The interaction between a penny-shape crack and a dislocation in crystalline materials is investigated within the framework of dislocation dynamics. The long-range and singular stress field resulting from the crack is determined by modeling the crack as continuous distribution of dislocation loops. This distribution is determined by satisfying the traction boundary condition at the crack face, resulting into a singular integral equation of the first kind that is solved numerically. This crack model is integrated with the dislocation dynamics simulation technique to yield the stress field of the combine system of crack and different types of dislocations situated at different positions in a three dimensional space. The integrated system is then used to investigate the dislocation behavior and its influence on the crack opening displacement and the characteristic of the stress field near the crack tip. It is shown that, depending on the relative position of the dislocation and its character, the dislocation may result in reduction in the stress amplitude at the crack tip and in some cases in closure of the crack tip. These analyses yield shielding and amplification zones near the crack providing an insight of the dislocation influence on the crack. The full dislocation dynamic analysis reveals the nature of the crack dislocation interaction and the manner in which the dislocation morphology changes as it is attracted to the crack surfaces, as well as the changes it causes to the crack profile.