Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1993-02

AUTHORS

Ch. -A. Gandin, M. Rappaz, R. Tintillier

ABSTRACT

A two-dimensional (2-D) probabilistic model, previously developed for the prediction of microstructure formation in solidification processes, is applied to thin section superalloy precision castings. Based upon an assumption of uniform temperature across the section of the plate, the model takes into account the heterogeneous nucleation which might occur at the mold wall and in the bulk of the liquid. The location and crystallographic orientation of newly nucleated grains are chosen randomly among a large number of sites and equiprobable orientation classes, respectively. The growth of the dendritic grains is modeled by using a cellular automaton technique and by considering the growth kinetics of the dendrite tips. The computed 2-D grain structures are compared with micrographie cross sections of specimens of various thicknesses. It is shown that the 2-D approach is able to predict the transition from columnar to equiaxed grains. However, in a transverse section, the grain morphology within the columnar zone differs from that of the experimental micrographs. For this reason, a three-dimensional (3-D) extension of this model is proposed, in which the modeling of the grain growth is simplified. It assumes that each dendritic grain is an octaedron whose half-diagonals, corresponding to the <100> crystallographic orientations of the grain, are simply given by the integral, from the time of nucleation to that of observation, of the velocity of the dendrite tips. All the liquid cells falling within a given octaedron solidify with the same crystallographic orientation of the parent nucleus. It is shown that the grain structures computed with this 3-D model are much closer to the experimental micrographie cross sections. More... »

PAGES

467-479

References to SciGraph publications

  • 1989-02. Modeling of equiaxed microstructure formation in casting in METALLURGICAL AND MATERIALS TRANSACTIONS A
  • 1990-06. Analysis of solidification microstructures in Fe-Ni-Cr single-crystal welds in METALLURGICAL AND MATERIALS TRANSACTIONS A
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02657334

    DOI

    http://dx.doi.org/10.1007/bf02657334

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1035268094


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Engineering", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0912", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Materials Engineering", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "D\u00e9partement des Mat\u00e9riaux, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, MX-G Ecublens, Lausanne, Switzerland", 
              "id": "http://www.grid.ac/institutes/grid.5333.6", 
              "name": [
                "D\u00e9partement des Mat\u00e9riaux, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, MX-G Ecublens, Lausanne, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Gandin", 
            "givenName": "Ch. -A.", 
            "id": "sg:person.010332710054.26", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010332710054.26"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "D\u00e9partement des Mat\u00e9riaux, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, MX-G Ecublens, Lausanne, Switzerland", 
              "id": "http://www.grid.ac/institutes/grid.5333.6", 
              "name": [
                "D\u00e9partement des Mat\u00e9riaux, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, MX-G Ecublens, Lausanne, Switzerland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rappaz", 
            "givenName": "M.", 
            "id": "sg:person.013657516157.10", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013657516157.10"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "D\u00e9partment Mat\u00e9riaux et Proc\u00e9d\u00e9s-Direction Technique, Soci\u00e9t\u00e9 Nationale d\u2019Etude et de Construction de Moteurs d\u2019Aviation, 92230, Gennevilliers, France", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "D\u00e9partment Mat\u00e9riaux et Proc\u00e9d\u00e9s-Direction Technique, Soci\u00e9t\u00e9 Nationale d\u2019Etude et de Construction de Moteurs d\u2019Aviation, 92230, Gennevilliers, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Tintillier", 
            "givenName": "R.", 
            "id": "sg:person.014341202207.47", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014341202207.47"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf02672593", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041382735", 
              "https://doi.org/10.1007/bf02672593"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02670257", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040303849", 
              "https://doi.org/10.1007/bf02670257"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1993-02", 
        "datePublishedReg": "1993-02-01", 
        "description": "A two-dimensional (2-D) probabilistic model, previously developed for the prediction of microstructure formation in solidification processes, is applied to thin section superalloy precision castings. Based upon an assumption of uniform temperature across the section of the plate, the model takes into account the heterogeneous nucleation which might occur at the mold wall and in the bulk of the liquid. The location and crystallographic orientation of newly nucleated grains are chosen randomly among a large number of sites and equiprobable orientation classes, respectively. The growth of the dendritic grains is modeled by using a cellular automaton technique and by considering the growth kinetics of the dendrite tips. The computed 2-D grain structures are compared with micrographie cross sections of specimens of various thicknesses. It is shown that the 2-D approach is able to predict the transition from columnar to equiaxed grains. However, in a transverse section, the grain morphology within the columnar zone differs from that of the experimental micrographs. For this reason, a three-dimensional (3-D) extension of this model is proposed, in which the modeling of the grain growth is simplified. It assumes that each dendritic grain is an octaedron whose half-diagonals, corresponding to the <100> crystallographic orientations of the grain, are simply given by the integral, from the time of nucleation to that of observation, of the velocity of the dendrite tips. All the liquid cells falling within a given octaedron solidify with the same crystallographic orientation of the parent nucleus. It is shown that the grain structures computed with this 3-D model are much closer to the experimental micrographie cross sections.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf02657334", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136292", 
            "issn": [
              "1073-5623", 
              "1543-1940"
            ], 
            "name": "Metallurgical and Materials Transactions A", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "24"
          }
        ], 
        "keywords": [
          "grain structure", 
          "precision casting", 
          "dendritic grains", 
          "crystallographic orientation", 
          "solidification grain structures", 
          "dendrite tip", 
          "equiaxed grains", 
          "mold wall", 
          "same crystallographic orientation", 
          "solidification process", 
          "microstructure formation", 
          "grain growth", 
          "uniform temperature", 
          "grain morphology", 
          "cellular automata technique", 
          "columnar zone", 
          "experimental micrographs", 
          "time of nucleation", 
          "heterogeneous nucleation", 
          "liquid cell", 
          "casting", 
          "three-dimensional extension", 
          "grains", 
          "growth kinetics", 
          "probabilistic simulation", 
          "nucleation", 
          "automata technique", 
          "solidifies", 
          "cross sections", 
          "tip", 
          "structure", 
          "thickness", 
          "orientation", 
          "velocity", 
          "simulations", 
          "plate", 
          "temperature", 
          "liquid", 
          "micrographs", 
          "model", 
          "modeling", 
          "columnar", 
          "probabilistic model", 
          "bulk", 
          "wall", 
          "morphology", 
          "applications", 
          "kinetics", 
          "sections", 
          "specimens", 
          "zone", 
          "prediction", 
          "two-dimensional probabilistic model", 
          "transverse sections", 
          "process", 
          "technique", 
          "large number", 
          "location", 
          "formation", 
          "account", 
          "growth", 
          "transition", 
          "approach", 
          "time", 
          "integrals", 
          "assumption", 
          "observations", 
          "extension", 
          "number", 
          "reasons", 
          "orientation classes", 
          "sites", 
          "class", 
          "cells", 
          "parent nucleus", 
          "nucleus"
        ], 
        "name": "Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings", 
        "pagination": "467-479", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1035268094"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf02657334"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf02657334", 
          "https://app.dimensions.ai/details/publication/pub.1035268094"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-09-02T15:47", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_252.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf02657334"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02657334'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02657334'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02657334'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02657334'


     

    This table displays all metadata directly associated to this object as RDF triples.

    158 TRIPLES      21 PREDICATES      103 URIs      93 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf02657334 schema:about anzsrc-for:09
    2 anzsrc-for:0912
    3 schema:author Ndb8a7280d0f348919f3bef1899d178e0
    4 schema:citation sg:pub.10.1007/bf02670257
    5 sg:pub.10.1007/bf02672593
    6 schema:datePublished 1993-02
    7 schema:datePublishedReg 1993-02-01
    8 schema:description A two-dimensional (2-D) probabilistic model, previously developed for the prediction of microstructure formation in solidification processes, is applied to thin section superalloy precision castings. Based upon an assumption of uniform temperature across the section of the plate, the model takes into account the heterogeneous nucleation which might occur at the mold wall and in the bulk of the liquid. The location and crystallographic orientation of newly nucleated grains are chosen randomly among a large number of sites and equiprobable orientation classes, respectively. The growth of the dendritic grains is modeled by using a cellular automaton technique and by considering the growth kinetics of the dendrite tips. The computed 2-D grain structures are compared with micrographie cross sections of specimens of various thicknesses. It is shown that the 2-D approach is able to predict the transition from columnar to equiaxed grains. However, in a transverse section, the grain morphology within the columnar zone differs from that of the experimental micrographs. For this reason, a three-dimensional (3-D) extension of this model is proposed, in which the modeling of the grain growth is simplified. It assumes that each dendritic grain is an octaedron whose half-diagonals, corresponding to the <100> crystallographic orientations of the grain, are simply given by the integral, from the time of nucleation to that of observation, of the velocity of the dendrite tips. All the liquid cells falling within a given octaedron solidify with the same crystallographic orientation of the parent nucleus. It is shown that the grain structures computed with this 3-D model are much closer to the experimental micrographie cross sections.
    9 schema:genre article
    10 schema:isAccessibleForFree false
    11 schema:isPartOf N57e021afcac247508a442ddeee376771
    12 Nefea9cadc1c24bcc853210a93e110197
    13 sg:journal.1136292
    14 schema:keywords account
    15 applications
    16 approach
    17 assumption
    18 automata technique
    19 bulk
    20 casting
    21 cells
    22 cellular automata technique
    23 class
    24 columnar
    25 columnar zone
    26 cross sections
    27 crystallographic orientation
    28 dendrite tip
    29 dendritic grains
    30 equiaxed grains
    31 experimental micrographs
    32 extension
    33 formation
    34 grain growth
    35 grain morphology
    36 grain structure
    37 grains
    38 growth
    39 growth kinetics
    40 heterogeneous nucleation
    41 integrals
    42 kinetics
    43 large number
    44 liquid
    45 liquid cell
    46 location
    47 micrographs
    48 microstructure formation
    49 model
    50 modeling
    51 mold wall
    52 morphology
    53 nucleation
    54 nucleus
    55 number
    56 observations
    57 orientation
    58 orientation classes
    59 parent nucleus
    60 plate
    61 precision casting
    62 prediction
    63 probabilistic model
    64 probabilistic simulation
    65 process
    66 reasons
    67 same crystallographic orientation
    68 sections
    69 simulations
    70 sites
    71 solidification grain structures
    72 solidification process
    73 solidifies
    74 specimens
    75 structure
    76 technique
    77 temperature
    78 thickness
    79 three-dimensional extension
    80 time
    81 time of nucleation
    82 tip
    83 transition
    84 transverse sections
    85 two-dimensional probabilistic model
    86 uniform temperature
    87 velocity
    88 wall
    89 zone
    90 schema:name Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings
    91 schema:pagination 467-479
    92 schema:productId N0b32f2aac03d4ff2888cb086023d777e
    93 Nf593edca000a44e4ba81e27f274bb713
    94 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035268094
    95 https://doi.org/10.1007/bf02657334
    96 schema:sdDatePublished 2022-09-02T15:47
    97 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    98 schema:sdPublisher N3d522e26a5724bfe903a7619cb98066d
    99 schema:url https://doi.org/10.1007/bf02657334
    100 sgo:license sg:explorer/license/
    101 sgo:sdDataset articles
    102 rdf:type schema:ScholarlyArticle
    103 N0b32f2aac03d4ff2888cb086023d777e schema:name dimensions_id
    104 schema:value pub.1035268094
    105 rdf:type schema:PropertyValue
    106 N3d522e26a5724bfe903a7619cb98066d schema:name Springer Nature - SN SciGraph project
    107 rdf:type schema:Organization
    108 N57e021afcac247508a442ddeee376771 schema:volumeNumber 24
    109 rdf:type schema:PublicationVolume
    110 Ncebbd77fd1434fcdbcee673509ff4653 rdf:first sg:person.013657516157.10
    111 rdf:rest Ndddf70f45aa849528df01579417bbc4b
    112 Ndb8a7280d0f348919f3bef1899d178e0 rdf:first sg:person.010332710054.26
    113 rdf:rest Ncebbd77fd1434fcdbcee673509ff4653
    114 Ndddf70f45aa849528df01579417bbc4b rdf:first sg:person.014341202207.47
    115 rdf:rest rdf:nil
    116 Nefea9cadc1c24bcc853210a93e110197 schema:issueNumber 2
    117 rdf:type schema:PublicationIssue
    118 Nf593edca000a44e4ba81e27f274bb713 schema:name doi
    119 schema:value 10.1007/bf02657334
    120 rdf:type schema:PropertyValue
    121 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
    122 schema:name Engineering
    123 rdf:type schema:DefinedTerm
    124 anzsrc-for:0912 schema:inDefinedTermSet anzsrc-for:
    125 schema:name Materials Engineering
    126 rdf:type schema:DefinedTerm
    127 sg:journal.1136292 schema:issn 1073-5623
    128 1543-1940
    129 schema:name Metallurgical and Materials Transactions A
    130 schema:publisher Springer Nature
    131 rdf:type schema:Periodical
    132 sg:person.010332710054.26 schema:affiliation grid-institutes:grid.5333.6
    133 schema:familyName Gandin
    134 schema:givenName Ch. -A.
    135 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010332710054.26
    136 rdf:type schema:Person
    137 sg:person.013657516157.10 schema:affiliation grid-institutes:grid.5333.6
    138 schema:familyName Rappaz
    139 schema:givenName M.
    140 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013657516157.10
    141 rdf:type schema:Person
    142 sg:person.014341202207.47 schema:affiliation grid-institutes:None
    143 schema:familyName Tintillier
    144 schema:givenName R.
    145 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014341202207.47
    146 rdf:type schema:Person
    147 sg:pub.10.1007/bf02670257 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040303849
    148 https://doi.org/10.1007/bf02670257
    149 rdf:type schema:CreativeWork
    150 sg:pub.10.1007/bf02672593 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041382735
    151 https://doi.org/10.1007/bf02672593
    152 rdf:type schema:CreativeWork
    153 grid-institutes:None schema:alternateName Départment Matériaux et Procédés-Direction Technique, Société Nationale d’Etude et de Construction de Moteurs d’Aviation, 92230, Gennevilliers, France
    154 schema:name Départment Matériaux et Procédés-Direction Technique, Société Nationale d’Etude et de Construction de Moteurs d’Aviation, 92230, Gennevilliers, France
    155 rdf:type schema:Organization
    156 grid-institutes:grid.5333.6 schema:alternateName Département des Matériaux, Ecole Polytechnique Fédérale de Lausanne, 1015, MX-G Ecublens, Lausanne, Switzerland
    157 schema:name Département des Matériaux, Ecole Polytechnique Fédérale de Lausanne, 1015, MX-G Ecublens, Lausanne, Switzerland
    158 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...