A three-dimensional model is proposed to simulate the grain structure in directionally solidified silicon. This includes the nucleation and growth of grains in twin relationship whose formation is very frequent during silicon solidification. Based on analyses of in-situ and real-time observations of the crystallization front, a three-dimensional cellular automaton method is developed to model the dynamic of {111} facets, groove formation at grain boundaries, nucleation and growth of grains in twin relationship. The model is applied to well-characterized experiments assuming the frozen temperature approximation. A comparison of solidification sequences, crystallographic orientation maps, and coincidence site lattice maps in both experiment and simulation results is achieved. Results demonstrate that the model could be applied to optimize crystallization processes for both polycrystalline and cast-mono silicon fabrication processes.

Production of silicon for solar cells in photovoltaic systems is mainly based on directional casting processes. Twin nucleation is favoured during silicon growth due to the low-level twin energy of formation. As a consequence, in all solidification process, a large amount of grain boundaries (GB) are in twin relationship. A 3D cellular automaton (CA) model has been recently developed for the growth of multi-crystalline silicon including facet formation and nucleation of new grains in twin relationship. Activation of facets is based on an undercooling parameter assigned to each grain and for each of the <111> crystal directions. The model also considers nucleation and growth of grains on <111> facets corresponding to Σ3 twin relationships between twin grains. This model is first applied to comparison with experimental observations. It is found that impingement of growing grains that nucleated in Σ3 twin relationships meet during growth and form Σ3, Σ9 and Σ27 GB, in good agreement with experimental observations. Finally, the model is applied at a larger scale to generate grain structures representative of industrial practice. While quantitative experimental data is missing for comparison at such scale, the model is promising and its implementation in heat and mass transfer models should be considered for assistance to production of silicon for solar cells dedicated to photovoltaic systems.

Cellular Automaton (CA) simulations of two-dimensional growth competition among columnar dendritic grains are carried out for a succinonitrile - 0.4 wt% acetone alloy. This is achieved by computing the Grain Boundary (GB) orientation during directional solidification of a bi-crystal in a frozen temperature gradient approximation, each crystal being defined by its own orientation. Comparisons are subsequently conducted with recent Phase Field (PF) results derived under the same conditions as well as with the Geometrical Limit (GL) criterion and the Favorably Orientated Grain (FOG) criterion. The GL criterion is defined mathematically considering infinitely small branching within each grain in directions perpendicular to the main dendrite arms growth directions. The FOG criterion states survival of the grain having the growth direction best aligned with the temperature gradient. The GB orientation is investigated by CA simulations as a function of the cell size, the cell neighborhood and the position used to compute the growth velocity. Results reveal that sufficiently small cells lead to the convergence of the GB orientation towards the GL criterion, while sufficiently large cells lead to the FOG criterion. Within a range of intermediate cell size, excellent agreement is found with a revised version of the FOG criterion (rev-FOG) extracted from PF simulations over a wide range of grain orientations. The cell size needs to be of the order of the maximum step between primary stationary dendrite tips of the two competing grains. The Moore neighborhood provides better results than the von Neumann neighborhood. Noticeable improvement is also observed when computing the growth velocity at the leading dendrite tip positions compared to using the cell center approximation. With computational times several orders of magnitudes lower than PF, the CA method offers a realistic and useful alternative for direct simulations of solidification grain structures in casting processes. This work is also an example of upscaling between models, showing how PF dedicated to model phenomena at the scale of the solid-liquid interface and sidebranching competition can be used to evaluate and calibrate CA developed for large scale simulations. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The very high cycle fatigue of high-strength steels and many other alloys is controlled by the initiation and the propagation of cracks initiated at nonmetallic inclusions. Tiny cracks are early initiated from these inclusions. They propagate very slowly in a specific zone located close to the inclusion and called the fine-grained area (FGA) or optical dark area. This area has a size of the order of that of the inclusion. The FGA is followed by the formation of conventional crack propagation area with the presence of striations in many cases. The details of initiation of these very high cycle fatigue cracks depend on the relative elastic and thermal properties of inclusions and matrix. The specificities of the FGA zone are dependent on the hydrogen segregated at the interface of the inclusions. An elasto-plastic finite element calculation is performed to determine the residual stresses in the vicinity of the inclusions and to evaluate the effect of residual stresses.

The crystallographic character of fine granular area (FGA) formation from internal particles in martensitic high strength steel has been revealed by an assessment of the plastic zone size at the FGA border. This plastic zone size corresponded to about 3 times the martensite lath width. Tests at different temperatures (20°C, 200°C and 400°C) revealed a decreasing FGA size with increasing temperature at constant applied stress amplitude. As a consequence, the critical stress intensity factor varied as the FGA decreased with temperature. In contrast, the critical plastic zone size remained constant and equal to the sizes of microstructural features. This represents a strong similarity between crystallographic, stage I-like, crack propagation and FGA formation in a vacuum.

This study deals with the experimental quantification and the numerical prediction of the intergranular damage which developed during residual stress relaxation in the notch root region of AISI 316L-type CT-like specimens tested at 550, 575 and 600 degrees C. Here, local damage, consisting of cracked grain boundaries, was quantified from synchrotron X-ray tomography data. The residual strain and stress field evolutions in the damaged regions were predicted by finite element calculations. A continuum damage model formulated in terms of a scalar damage variable was calibrated to reproduce the experimental damage distributions in the specimens. The numerical predictions were found to be consistent with the measured damage distributions. It is also shown that the damage model can provide a useful estimate of the propensity to stress relaxation cracking in highly pre-strained AISI 316L-type steels as a function of temperature and magnitude of the initial maximum principal residual stress. (C) 2017 Elsevier Ltd. All rights reserved.

Existing methods for computing the life of critical components in jet engines, such as discs, are based on determining the design allowable forcing function (e.g. stress, strain). This is done by subtracting six standard deviations from the mean of the property in question. For example, if a stress amplitude-based criterion is used, then the design allowable life is given by:Nadesign=Namean-nσastddevwhere:Nadesign=the safe operating design life at a given nominal stress amplitude, σanom.Namean=the mean life at the nominal stress amplitude.σastddev=the experimentally measured standard deviation in life from the mean at the nominal stress amplitude.n=the number of standard deviations or “knock down” from the mean life that will produce an acceptable safe operating life. In the aerospace industry, this value traditionally was 3 but now “6σ” has become common and even the norm.This means that those factors which affect the dispersion of results in the High Cycle Fatigue (HCF) and Very High Cycle Fatigue (VHCF) regimes must be well understood and controlled in order to allow higher operating stresses or, conversely, longer lives at a given operating stress.The fatigue resistance of metallic materials suffers from a number of uncertainties, in particular the dispersion associated with variance in microstructure and a component size effect (i.e. scale effect). At low stresses and longer lives, such dispersions are particularly troublesome since small variations in microstructure, for example, can produce large dispersions or uncertainties in life. An understanding of the life-limiting tail of the defect distribution is crucial for modelling and predicting minimum safe operating fatigue lives.This paper concentrates on the two problems of microstructural variance and on the effect of component or specimen size in introducing uncertainty. In the first part, an attempt is made to summarize the micromechanisms of crack initiation by the formation of intrusions/extrusions along the slip bands in pure metals. This is an attempt to develop microstructural elements which are necessary to model the dispersion in fatigue life. While these features are, for the most part, illustrated by using recent results published on Ni-based and Fe-Ni based superalloys, the procedures are applicable to a wide range of other classes of alloys.In the second part an attempt is made to account for the dispersion associated with specimen or component size in terms of the interaction between the defect distribution and size when fatigue cracks are initiated from inclusions. The case of a Nickel-based alloy, IN 718, in which inclusions are mainly formed by niobium carbides (NbC) is examined in more detail. It is shown how the fatigue resistance of smooth and notched specimens of this material can be simply modelled, knowing the size and the distribution of NbC particles which act as fatigue initiation sites. The approach is further developed to model the fatigue life of notched specimens. The results obtained with this microstructure-sensitive model are compared with those obtained empirically and used in the design of discs in aircraft engines.

In this interpretive review, fatigue in metallic systems is considered primarily from the perspective of interactions between the microstructure, the deformation mode and the mechanical state at both low and high temperatures. In Part 1 the development and early propagation of cracks is considered in terms of the basic damage mechanisms and the relative size of the crack with respect to applicable microstructural feature(s). In this section, a multistage grain scale approach to microstructure-sensitive fatigue crack formation and growth is presented which uses Fatigue Indicator Parameters (FIPs) to correlate these processes. Various FIPs parameters are discussed in terms of their indication of the state of fatigue. The development and early crack propagation is considered in the context of microstructure and notches, and probabilistic aspects of the notch fatigue problem are discussed. These features are integrated into a systematic approach for the selection of fatigue resistant microstructures for given applications. In Part 2, attention is focused on Ni-base superalloys and the interaction between oxidation, creep and microstructure (including coatings) in the formation and propagation of cracks. This part of the overview addresses both experimental and modelling aspects. Methodologies based upon fundamental physical processes are presented for understanding and predicting the development and propagation of fatigue cracks, including effects of sequential oxide type formation and of creep on either restraining or accelerating damage by oxidation. The variable fatigue resistance of discs in jet engines is seen to depend upon the variability of microstructure and its influence on the severity of creep/oxidation interactions. All of these factors are considered in the practical case where both temperature and loading parameters vary simultaneously (thermomechanical fatigue). A physics-based life prediction model considering the interactions of deformation and environmental damage is reviewed in terms of its applicability to life prediction of components.

This is the first of three overviews on failure of metals. Here, brittle and ductile failure under monotonic loadings are addressed within the context of the local approach to fracture. In this approach, focus is on linking microstructure, physical mechanisms and overall fracture properties. The part on brittle fracture focuses on cleavage and also covers intergranular fracture of ferritic steels. The analysis of cleavage concerns both BCC metals and HCP metals with emphasis laid on the former. After a recollection of the Beremin model, particular attention is given to multiple barrier extensions and the crossing of grain boundaries. The part on ductile fracture encompasses the two modes of failure by void coalescence or plastic instability. Although a universal theory of ductile fracture is still lacking, this part contains a comprehensive coverage of the topic balancing phenomenology and mechanisms on one hand and microstructure-based modeling and simulation on the other hand, with application examples provided.

This work concerns a study of the mechanisms responsible for intergranular cracking during high temperature stress relaxation in AISI 316L-type austenitic stainless steels. This phenomenon, also known as reheat cracking, is typically present in heat affected zones of massive welded parts used in the energy industry. Here, five steel grades with different C, N and P contents were considered to assess the effects of chemical composition on the three main mechanisms potentially responsible for reheat cracking, namely intergranular M23C6 carbide precipitation, stress relaxation phenomena, and intergranular P segregation. After testing the five AISI 316L-type grades under reheat cracking conditions by a pre-compressed CT-like specimen technique, different degrees of intergranular damage were observed in the specimens by optical microscopy and synchrotron X-ray tomography. Detailed grain boundary analyses by SEM and TEM in the five different steel grades showed the main mechanism responsible for reheat cracking to be the nucleation of microcavities at intergranular M23C6 carbides in high residual stress regions. The addition of P was found to increase the number of cavitated GBs but not to be the dominant mechanism responsible for intergranular damage. A comparison between elasto-plastic finite element predictions of the residual stresses in the CT-specimens and the results of microstructural investigations revealed no intergranular damage in regions where the initial maximum principal stresses in the specimens were below 740 +/- 30 MPa. (c) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Temper embrittlement in a thick plate of a Mn-Ni-Mo pressure vessel steel was investigated using fracture toughness tests on Charpy and CT type specimens. A shift of the ductile-to-brittle transition temperature (~30–40 °C) was measured when the material was aged at 450 °C for 5000 h. Moreover an unusual scatter in fracture toughness tests was determined on aged material, such as \(K_{IC} (P_{R} = 90\,\% )/K_{IC} (P_{R} = 10\,\% ) \sim 5\), where P R is the probability of failure. Scanning electron micrographs (SEM) indicated that the fracture surface was partly intergranular along micro-segregated zones (MSZ). This observation was made both on the initial and the aged conditions. Intergranular facets were largely covered by phosphorus segregation. A fully predictive model involving a combination of a local approach to fracture based on Beremin theory and accounting for MSZ distribution, and on the modelling of segregation kinetics in ternary (Fe-C-P) systems is developed to analyze these results. This model predicts the scatter in fracture toughness measurements and the shift in DBT. Moreover the statistical distribution of MSZ leads to a size effect in fracture toughness measurements which is different from the \(K^{4} B\) law inferred from the Beremin model applied to a homogeneous material.

The goals of this paper are: (i) to review the mechanisms of cyclic deformation, damage accumulation and crack propagation in three types of materials widely used in power generation industries, i.e. Cr-Mo steels, austenitic stainless steels and superalloys used in jet engine turbines (both Ni base and Fe-Ni base) when they are tested at elevated temperature; (ii) to relate these mechanisms to engineering applications; (iii) to review life prediction methodologies including thermomechanical fatigue (TMF); and (iv) to point out current and likely future trends in the development of more fatigue resistant materials and life prediction methods. The emphasis is laid on the creep-fatigue-oxidation behaviour of the two first classes of materials, i.e. 9-12% martensitic Cr steels and austenitic stainless steels. As the major issue for the design of components used in power generation industries is the extrapolation of short term laboratory data to much longer times, only physically based models for life prediction are examined. In Ni base superalloys, the emphasis is laid on the effect of oxidation on fatigue crack growth rate at elevated temperature and on their behaviour in TMF

Pushing the internal or external dimensions of metallic alloys down to the nanometer scale gives rise to strong materials, though most often at the expense of a low ductility and a low resistance to cracking, with negative impact on the transfer to engineering applications. These characteristics are observed, with some exceptions, in bulk ultra-fine grained and nanocrystalline metals, nano-twinned metals, thin metallic coatings on substrates and freestanding thin metallic films and nanowires. This overview encompasses all these systems to reveal commonalities in the origins of the lack of ductility and fracture resistance, in factors governing fatigue resistance, and in ways to improve properties. After surveying the various processing methods and key deformation mechanisms, we systematically address the current state of the art in terms of plastic localization, damage, static and fatigue cracking, for three classes of systems: (1) bulk ultra-fine grained and nanocrystalline metals, (2) thin metallic films on substrates, and (3) 1D and 2D freestanding micro and nanoscale systems. In doing so, we aim to favour cross-fertilization between progress made in the fields of mechanics of thin films, nanomechanics, fundamental researches in bulk nanocrystalline metals and metallurgy to impart enhanced resistance to fracture and fatigue in high-strength nanostructured systems. This involves exploiting intrinsic mechanisms, e.g. to enhance hardening and rate-sensitivity so as to delay necking, or improve grain-boundary cohesion to resist intergranular cracks or voids. Extrinsic methods can also be utilized such as by hybridizing the metal with another material to delocalize the deformation - as practiced in stretchable electronics. Fatigue crack initiation is in principle improved by a fine structure, but at the expense of larger fatigue crack growth rates. Extrinsic toughening through hybridization allows arresting or bridging cracks. The content and discussions are based on experimental, theoretical and simulation results from the recent literature, and focus is laid on linking microstructure and physical mechanisms to the overall mechanical behavior.

The size and the character (low and large angle, special boundaries, tilt and twist boundaries, twins) of the grain boundaries (GBs) in polycrystalline materials influence their strength and their fracture toughness. Recent studies devoted to nanocrystalline (NC) materials have shown a deviation from the Hall–Petch law. Special GBs formed by Σ3 twins in face-centred cubic metals are also known to have a strong effect on the mechanical behaviour of these metals, in particular their work-hardening rate. Grain orientation influences also crack path, the fracture toughness of body-centred cubic (BCC) metals and the fatigue crack growth rate of microstructurally short cracks. This paper deals both with slip transfer at GBs and with the interactions between propagating cracks with GBs. In the analysis of slip transfer, the emphasis is placed on twin boundaries (TBs) for which the dislocation reactions during slip transfer are analysed theoretically, experimentally and using the results of atomic molecular simulations published in the literature. It is shown that in a number of situations this transfer leads to a normal motion of the TB owing to the displacement of partial dislocations along the TB. This motion can generate a de-twinning effect observed in particular in NC metals. Crack propagation across GBs is also considered. It is shown that cleavage crack path behaviour in BCC metals is largely dependent on the twist component of the GBs. A mechanism for the propagation of these twisted cracks involving a segmentation of the crack front and the existence of intergranular parts is discussed and verified for a pressure vessel steel. A similar segmentation seems to occur for short fatigue cracks although, quite surprisingly, this crossing mechanism for fatigue cracks does not seem to have been examined in very much detail in the literature. Metallurgical methods used to improve the strength of the materials, via grain boundaries, are briefly discussed.

Mechanical tests on Charpy and CT specimens of a low alloy MnNiMo steel under two conditions, as received and thermally aged, revealed a shift of the ductile to brittle transition temperature. In this paper, an approach based on the combination of local fracture mechanics and segregation kinetics is proposed in order to describe this shift.

The understanding o f hold time effects on the fatigue crack growth rate (FCGR) behavior above 500°C in Inco718 DA is a great challenge to develop an efficient model for predicting crack propagation life. Trapezoidal wave shape signal fatigue tests from 500°C to 650°C with hold times up to 3600 s were carried out on a small grain size (5-15 |im) alloy. FCGRs were measured using potential drop technique. SEM observations were carried out to correlate the measured FCGRs with the trans-or inter-granular aspect of the fatigue fracture surfaces. Using equations developed in the frame of the Local Approach of Fracture (LAF) theory, predicted life and crack growth rates are compared to experimental results. The emphasis is laid on time dependent effects, in particular those associated with oxidation.

The effects of the thermal ageing at 400 °C, 500 °C and 600 °C during 5000 h on the mechanical properties of a 18%Cr ODS ferritic steel are investigated. A hardening effect is observed after ageing at 400 °C and 500 °C, probably due to the presence of chromium rich α′ particles as suggested by the literature. The impact resistance and the ductility of the material are strongly lowered by the ageing at 600 °C. This embrittlement is characterized on the fracture surfaces by the presence of cleavage facets on the whole range of testing temperatures. The intermetallic σ phase is found to be responsible for the occurrence of cleavage fracture on the material aged at 600 °C, and thus for the significant embrittlement of this material. M23C6 carbides are also observed before and after thermal ageing. The lattice parameters of the σ phase and the M23C6 carbides observed in this 18%Cr ODS steel aged at 600 °C during 5000 h are measured.

The damage and rupture mechanisms of a 2024 aluminum thin sheet are investigated.Mechanical tests are carried out on flat specimens including smooth tensile panels,U-notched samples with various notch radii and V-notched samples. Cracked samples werealso tested which include Kahn samples and large MT panels; stable crack growth is obtainedin both cases. The microstructure of the material is characterized to obtain the second phasevolume content. The largest particles consist of intermetallics. The macroscopic fracture surfaceof the different specimens is observed using scanning electron microscopy. Smooth andmoderately notched samples exhibit a slanted fracture surface, which has an angle of about45 with the loading direction. With increasing notch severity, the fracture mode changessignificantly. Failure initiates at the notch root in a small triangular region whose normal isparallel to the loading direction. Outside this zone, slant fracture is observed. Microscopicobservations show two failure mechanisms. Voids are first initiated at intermetallics in bothcases. At low stress triaxiality ratio (smooth or moderately notched samples), these voids tendto coalesce rapidly according to a “void sheet mechanism” which creates smaller dimples inthe inter-void ligaments. At higher triaxiality, void growth is promoted and final rupture iscaused by “internal necking” between the large cavities.

This chapter contains sections titled: Introduction Composition, elaboration, microstructure, and mechanical properties Thermal embrittlement of the ferrite phase in DSS Materials investigated and embrittlement heat treatments Damage and rupture Scale effect and scatter Modeling of rupture Conclusion References

In the framework of the development of Generation IV nuclear reactors and fusion nuclear reactors, materials with an improved high temperature (congruent to 650 degrees C) mechanical strength are required for specific components. The 9-12% Cr martensitic steels are candidate for these applications.Previous works showed that the application of a thermomechanical treatment, including warm-rolling in metastable austenitic phase, to the commercial Grade 91 martensitic steel, allowed refining its microstructure, improving its precipitation state and its mechanical properties (hardness, tensile and creep properties).In the present paper, experimental steel called NPM, designed for good high-temperature creep resistance, is evaluated in terms of microstructure and mechanical properties, and compared to the G91 steel. Then the developed thermomechanical treatment is applied to this steel. Its microstructure is refined and its hardness and tensile properties are much better than the as-received NPM and therefore than the G91 steel. The cyclic softening effect still occurs for the optimized NPM, but this material once softened by cyclic loadings, still presents better creep properties than the as-received NPM steel, and even more than the commercial G91 steel. (C) 2013 Elsevier B.V. All rights reserved.