CINXE.COM
Document Zbl 1272.74088 - zbMATH Open
<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1272.74088 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1272.74088?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1272.74088" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span> </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span> </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span> </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span> </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span> </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span> </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span> </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span> </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span> </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span> </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span> </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span> </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span> </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span> </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span> </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span> </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span> </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/fornell.j" title="Author Profile">Fornell, J.</a>; <a href="/authors/concustell.a" title="Author Profile">Concustell, A.</a>; <a href="/authors/surinach.s" title="Author Profile">Suriñach, S.</a>; <a href="/authors/?q=ai%3Ali.wenhe%7Cli.wanghong%7Cli.wen-huang%7Cli.wen-hsuan%7Cli.wen-hsiung%7Cli.wen-hwa%7Cli.wei-hsi%7Cli.wan-he%7Cli.wanghui%7Cli.weihao%7Cli.wenhao%7Cli.wenhui%7Cli.wenhua%7Cli.wenhang%7Cli.weihan%7Cli.wenhan%7Cli.weihai%7Cli.wenhu%7Cli.wenhong%7Cli.weihong%7Cli.weiheng%7Cli.weihua%7Cli.wenhai" title="Author Profile">Li, W. H.</a>; <a href="/authors/cuadrado.n" title="Author Profile">Cuadrado, N.</a>; <a href="/authors/gebert.a" title="Author Profile">Gebert, A.</a>; <a href="/authors/baro.m-d" title="Author Profile">Baró, M. D.</a>; <a href="/authors/sort.j" title="Author Profile">Sort, J.</a></div> <h2 class="title"> <strong>Yielding and intrinsic plasticity of Ti-Zr-Ni-Cu-Be bulk metallic glass.</strong> <i>(English)</i> <a class="label nowrap" href="/1272.74088">Zbl 1272.74088</a> </h2> <div class="source"> <a href="/serials/106" title="Journal Profile">Int. J. Plast.</a> <a href="/?q=in%3A250484" title="Articles in this Issue">25, No. 8, 1540-1559 (2009)</a>. </div> <div class="abstract">Summary: Bulk metallic glass with composition Ti\(_{40}\)Zr\(_{25}\)Ni\(_{8}\)Cu\(_{9}\)Be\(_{18}\) exhibits considerably high compressive yield stress, significant plasticity (with a concomitant vein-like fracture morphology) and relatively low density. Yielding and intrinsic plasticity of this alloy are discussed in terms of its thermal and elastic properties. An influence of normal stresses acting on the shear plane is evidenced by: (i) the fracture angle (\(<45^\circ \)) and (ii) finite-element simulations of nanoindentation curves, which require the use of a specific yield criterion, sensitive to local normal stresses acting on the shear plane, to properly match the experimental data. The ratio between hardness and compressive yield strength (constraint factor) is analyzed in terms of several models and is best adjusted using a modified expanding cavity model incorporating a pressure-sensitivity index defined by the Drucker-Prager yield criterion. Furthermore, comparative results from compression tests and nanoindentation reveal that deformation also causes strain softening, a phenomenon which is accompanied with the occurrence of serrated plastic flow and results in a so-called indentation size effect (ISE). A new approach to model the ISE of this metallic glass using the free volume concept is presented.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5572020">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74C99" title="MSC2020">74C99</a> </td> <td class="space"> Plastic materials, materials of stress-rate and internal-variable type </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74M25" title="MSC2020">74M25</a> </td> <td class="space"> Micromechanics of solids </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ayield+condition">yield condition</a>; <a href="/?q=ut%3Aelastic-plastic+material">elastic-plastic material</a>; <a href="/?q=ut%3Ametallic+glass+material">metallic glass material</a>; <a href="/?q=ut%3Amechanical+testing">mechanical testing</a>; <a href="/?q=ut%3Ananoindentation">nanoindentation</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1272.74088" data-ciurl="/ci/05572020" data-biburl="/bibtex/05572020.bib" data-amsurl="/amsrefs/05572020.bib" data-xmlurl="/xml/05572020.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05572020.pdf" title="Zbl 1272.74088 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.ijplas.2008.11.002" aria-label="DOI for “Yielding and intrinsic plasticity of Ti-Zr-Ni-Cu-Be bulk metallic glass”" title="10.1016/j.ijplas.2008.11.002">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ai, K.; Dai, L. H.: A new modified expanding cavity model for characterizing the spherical indentation behaviour of bulk metallic Glass with pile-up, Scripta mater. 56, 761-764 (2007)</td> </tr><tr> <td>[2]</td> <td class="space">Al-Rub, R. K. A.; Voyiadjis, G. Z.: Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro-and nano-indentation experiments, Int. J. Plasticity 20, 1139-1182 (2004)</td> </tr><tr> <td>[3]</td> <td class="space">Anand, L.; Su, C.: A theory for amorphous viscoplastic materials undergoing finite deformations, with application to metallic glasses, J. mech. Phys. solids 53, 1362-1396 (2005) · <a href="/1120.74361" class="nowrap">Zbl 1120.74361</a> · <a href="https://doi.org/10.1016/j.jmps.2004.12.006" class="nowrap">doi:10.1016/j.jmps.2004.12.006</a></td> </tr><tr> <td>[4]</td> <td class="space">Argon, A. S.: Plastic deformation in metallic glasses, Acta metall. 27, 47-58 (1979)</td> </tr><tr> <td>[5]</td> <td class="space">Ashby, M. F.; Greer, A. L.: Metallic glasses as structural materials, Scripta mater. 54, 321-326 (2006)</td> </tr><tr> <td>[6]</td> <td class="space">Concustell, A.; Sort, J.; Alcalá, G.; Mato, S.; Gebert, A.; Eckert, J.; Baró, M. D.: Plastic deformation and mechanical softening of pd40 cu30 ni10 P20 bulk metallic Glass during nanoindentation, J. mater. Res. 20, 2719-2725 (2005)</td> </tr><tr> <td>[7]</td> <td class="space">Daniel, B. S. S.; Reger-Leonhard, A.; Heilmaier, M.; Eckert, J.; Schultz, L.: Thermal relaxation and high temperature creep of zr55 cu30 al10 ni5 bulk metallic Glass, Mech. time-depend. Mat. 6, 193-206 (2002)</td> </tr><tr> <td>[8]</td> <td class="space">Dao, M.; Chollacoop, N.; Van Vliet, K. J.; Venkatesh, T. A.; Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation, Acta mater. 49, 3899-3918 (2001)</td> </tr><tr> <td>[9]</td> <td class="space">De Hey, P.; Sietsma, J.; Den Beukel, A. Van: Structural disordering in amorphous pd40 ni40 P20 induced by high temperature deformation, Acta mater. 46, 5873-5882 (1998)</td> </tr><tr> <td>[10]</td> <td class="space">Duan, G.; Wiest, A.; Lind, M. L.; Kahl, A.; Johnson, W. L.: Lightweight ti-based bulk metallic glasses excluding late transition metals, Scripta mater. 58, 465-468 (2008)</td> </tr><tr> <td>[11]</td> <td class="space">Fischer-Cripps, A. C.: Nanoindentation, (2002)</td> </tr><tr> <td>[12]</td> <td class="space">Fischer-Cripps, A. C.: Significance of a local temperature rise in nanoindentation testing, J. mater. Sci. 39, 5849-5851 (2004)</td> </tr><tr> <td>[13]</td> <td class="space">Flores, K. M.; Dauskardt, R. H.: Mean stress effects on flow localization and failure in a bulk metallic Glass, Acta mater. 49, 2527-2537 (2001)</td> </tr><tr> <td>[14]</td> <td class="space">Gao, Y. F.; Yang, B.; Nieh, T. G.: Thermomechanical instability analysis of inhomogeneous deformation in amorphous alloys, Acta mater. 55, 2319-2327 (2007)</td> </tr><tr> <td>[15]</td> <td class="space">Gerberich, W. W.; Tymiak, N. I.; Grunlan, J. C.; Horstemeyer, M. F.; Baskes, M. I.: Interpretations of indentation size effects, J. appl. Mech. 69, 433-442 (2002) · <a href="/1110.74454" class="nowrap">Zbl 1110.74454</a> · <a href="https://doi.org/10.1115/1.1469004" class="nowrap">doi:10.1115/1.1469004</a></td> </tr><tr> <td>[16]</td> <td class="space">Guo, F.; Wang, H. -J.; Poon, S. J.; Shiflet, G. J.: Ductile titanium-based glassy alloy ingots, Appl. phys. Lett. 86, 091907 (2005)</td> </tr><tr> <td>[17]</td> <td class="space">Heggen, M.; Spaepen, F.; Feuerbacher, M. J.: Creation and annihilation of free volume during homogeneous flow of a metallic Glass, J. appl. Phys. 97, 033506 (2005)</td> </tr><tr> <td>[18]</td> <td class="space">Huang, Y.; Qu, S.; Hwang, K. C.; Li, M.; Gao, H.: A conventional theory of mechanism-based strain gradient plasticity, Int. J. Plasticity 20, 753-782 (2004) · <a href="/1254.74019" class="nowrap">Zbl 1254.74019</a></td> </tr><tr> <td>[19]</td> <td class="space">Huang, Y.; Zhang, F.; Hwang, K. C.; Nix, W. D.; Pharr, G. M.; Feng, G.: A model of size effects in nano-indentation, J. mech. Phys. solids 54, 1668-1686 (2006) · <a href="/1120.74658" class="nowrap">Zbl 1120.74658</a> · <a href="https://doi.org/10.1016/j.jmps.2006.02.002" class="nowrap">doi:10.1016/j.jmps.2006.02.002</a></td> </tr><tr> <td>[20]</td> <td class="space">Jana, S.; Ramamurty, U.; Chattopadhyay, K.; Kawamura, Y.: Subsurface deformation during vickers indentation of bulk metallic glasses, Mater. sci. Eng. A 375 – 377, 1191-1195 (2004)</td> </tr><tr> <td>[21]</td> <td class="space">Jiang, W. H.; Fan, G. J.; Liu, F. X.; Wang, G. Y.; Choo, H.; Liaw, P. K.: Spaciotemporally inhomogeneous plastic flow of a bulk-metallic Glass, Int. J. Plasticity 24, 1-16 (2008) · <a href="/1290.74006" class="nowrap">Zbl 1290.74006</a></td> </tr><tr> <td>[22]</td> <td class="space">Johnson, K. L.: Correlation of indentation experiments, J. mech. Phys. solids 18, 115-126 (1970)</td> </tr><tr> <td>[23]</td> <td class="space">Johnson, W. L.; Samwer, K.: A universal criterion for plastic yielding of metallic glasses with a (T/tg)2/3 temperature dependence, Phys. rev. Lett. 95, 195501 (2005)</td> </tr><tr> <td>[24]</td> <td class="space">Kanungo, B. P.; Glade, S. C.; Asoka-Kumar, P.; Flores, K. M.: Characterization of free volume changes associated with shear band formation in zr- and cu-based bulk metallic glasses, Intermetallics 12, 1073-1080 (2004)</td> </tr><tr> <td>[25]</td> <td class="space">Keryvin, V.: Indentation of bulk metallic glasses: relationships between shear bands observed around the prints and hardness, Acta mater. 55, 2565-2578 (2007)</td> </tr><tr> <td>[26]</td> <td class="space">Kim, Y. C.; Kim, W. T.; Kim, D. H.: A development of ti-based bulk metallic Glass, Mater. sci. Eng. A 375 – 377, 127-135 (2004)</td> </tr><tr> <td>[27]</td> <td class="space">Kim, K. B.; Zhang, X. F.; Yi, S.; Lee, M. H.; Das, J.; Eckert, J.: Effect of local chemistry, structure and length scale of heterogeneities on the mechanical properties of a ti45cu40ni7.5zr5sn2.5 bulk metallic Glass, Philos. mag. Lett. 88, 75-81 (2008)</td> </tr><tr> <td>[28]</td> <td class="space">Kusy, M.; Kühn, U.; Concustell, A.; Gebert, A.; Das, J.; Eckert, J.; Schultz, L.; Baró, M. D.: Fracture surface morphology of compressed bulk metallic Glass-matrix-composites and bulk metallic Glass, Intermetallics 14, 982-986 (2006)</td> </tr><tr> <td>[29]</td> <td class="space">Lam, D. C. C.; Chong, A. C. M.: Model and experiments on strain gradient hardening in metallic Glass, Mater. sci. Eng. A 318, 313-319 (2001)</td> </tr><tr> <td>[30]</td> <td class="space">Lele, S.P., Anand, L., 2008. A large-deformation strain-gradient theory for isotropic viscoplastic materials. Int. J. Plasticity, doi:10.1016/j.ijplas.2008.04.003. · <a href="/1277.74009" class="nowrap">Zbl 1277.74009</a></td> </tr><tr> <td>[31]</td> <td class="space">Lewandowski, J. J.; Greer, A. L.: Temperature rise at shear bands in metallic glasses, Nat. mater. 5, 15-18 (2006)</td> </tr><tr> <td>[32]</td> <td class="space">Lewandowski, J. J.; Lowhaphandu, P.: Effects of hydrostatic pressure on the flow and fracture of a bulk amorphous metal, Philos. mag. A 82, 3427-3441 (2002)</td> </tr><tr> <td>[33]</td> <td class="space">Lewandowski, J. J.; Wang, W. H.; Greer, A. L.: Intrinsic plasticity or brittleness of metallic glasses, Phil. mag. Lett. 85, 77-87 (2005)</td> </tr><tr> <td>[34]</td> <td class="space">Lewandowski, J. J.; Shazly, M.; Nouri, A. S.: Intrinsic and extrinsic toughening of metallic glasses, Scripta mater. 54, 337-341 (2006)</td> </tr><tr> <td>[35]</td> <td class="space">Li, H.; Ghosh, A.; Han, Y. N.; Bradt, R. C.: The frictional component of the indentation size effect in low load microhardness testing, J. mater. Res. 8, 1028-1032 (1993)</td> </tr><tr> <td>[36]</td> <td class="space">Lockett, F. J.: Indentation of a rigid plastic material by a conical indenter, J. mech. Phys. solids 11, 345-355 (1963)</td> </tr><tr> <td>[37]</td> <td class="space">Lund, A. C.; Schuh, C. A.: Yield surface of a simulated metallic Glass, Acta mater. 51, 5399-5411 (2003)</td> </tr><tr> <td>[38]</td> <td class="space">Lund, A. C.; Schuh, C. A.: The mohr – Coulomb criterion from unit shear processes in metallic Glass, Intermetallics 12, 1159-1165 (2004)</td> </tr><tr> <td>[39]</td> <td class="space">Ma, C.; Ishihara, S.; Soejima, H.; Nishiyama, N.; Inoue, A.: Formation of new ti-based metallic glassy alloys, Mater. trans. 45, 1802-1806 (2004)</td> </tr><tr> <td>[40]</td> <td class="space">Manika, I.; Maniks, J.: Size effects in micro- and nanoscale indentation, Acta mater. 54, 2049-2056 (2006)</td> </tr><tr> <td>[41]</td> <td class="space">Mukhopadhyay, N. K.; Paufler, P.: Micro- and nanoindentation techniques for mechanical characterisation of materials, Int. mater. Rev. 51, 209-245 (2006)</td> </tr><tr> <td>[42]</td> <td class="space">Narasimhan, R.: Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model, Mech. mater. 36, 633-645 (2004)</td> </tr><tr> <td>[43]</td> <td class="space">Nix, W. D.; Gao, H.: Indentation size effects in crystalline materials: A law for strain gradient plasticity, J. mech. Phys. sol. 46, 411-425 (1998) · <a href="/0977.74557" class="nowrap">Zbl 0977.74557</a> · <a href="https://doi.org/10.1016/S0022-5096(97)00086-0" class="nowrap">doi:10.1016/S0022-5096(97)00086-0</a></td> </tr><tr> <td>[44]</td> <td class="space">Ogata, S.; Shimizu, F.; Li, J.; Wakeda, M.; Shibutani, Y.: Atomistic simulation of shear localization in cu – zr bulk metallic Glass, Intermetallic 14, 1033-1037 (2006)</td> </tr><tr> <td>[45]</td> <td class="space">Oliver, W. C.; Pharr, G. M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. mater. Res. 7, 1564-1583 (1992)</td> </tr><tr> <td>[46]</td> <td class="space">Park, J. M.; Chang, H. J.; Han, K. H.; Kim, W. T.; Kim, D. H.: Enhancement of plasticity in ti-rich ti – zr – be – cu – ni bulk metallic glasses, Scripta mater. 53, 1-6 (2005)</td> </tr><tr> <td>[47]</td> <td class="space">Patnaik, M. N. M.; Narasimhan, R.; Ramamurty, U.: Spherical indentation response of metallic glasses, Acta mater. 52, 3335-3345 (2004)</td> </tr><tr> <td>[48]</td> <td class="space">Schuh, C. A.; Lund, A. C.: Atomistic basis for the plastic yield criterion of metallic Glass, Nature mater. 2, 449-452 (2003)</td> </tr><tr> <td>[49]</td> <td class="space">Schuh, C. A.; Nieh, T. G.: A survey of instrumented indentation studies on metallic glasses, J. mater. Res. 19, 46-57 (2004)</td> </tr><tr> <td>[50]</td> <td class="space">Schuh, C. A.; Lund, A. L.; Nieh, T. G.: New regime of homogeneous flow in the deformation map of metallic glasses: elevated temperature nanoindentation experiments and mechanistic modeling, Acta mater. 52, 5879-5891 (2004)</td> </tr><tr> <td>[51]</td> <td class="space">Schuh, C. A.; Hufnagel, T. C.; Ramamurty, U.: Overview no. 144 – mechanical behaviour of amorphous alloys, Acta mater. 55, 4067-4109 (2007)</td> </tr><tr> <td>[52]</td> <td class="space">Spaepen, F.: Microscopic mechanism for steady-state inhomogeneous flow in metallic glasses, Acta metall. 25, 407-415 (1977)</td> </tr><tr> <td>[53]</td> <td class="space">Telford, M.: The case for bulk metallic glasses, Mater. today 7, 36-43 (2004)</td> </tr><tr> <td>[54]</td> <td class="space">Vaidyanathan, R.; Dao, M.; Ravichandran, G.; Suresh, S.: Study of mechanical deformation in bulk metallic Glass through instrumented indentation, Acta. mater. 49, 3781-3789 (2001)</td> </tr><tr> <td>[55]</td> <td class="space">Van Aken, B.; De Hey, P.; Sietsma, J.: Structural relaxation and plastic flow in amorphous la50 al25 ni25, Mater. sci. Eng. A 278, 247-254 (2000)</td> </tr><tr> <td>[56]</td> <td class="space">Van Steenberge, N.; Sort, J.; Concustell, A.; Das, J.; Scudino, S.; Suriñach, S.; Eckert, J.; Baró, M. D.: Dynamic softening and indentation size effect in a zr-based bulk Glass-forming alloy, Scripta mater. 56, 605-608 (2007)</td> </tr><tr> <td>[57]</td> <td class="space">Wang, W. H.: Correlations between elastic moduli and properties in bulk metallic glasses, J. appl. Phys. 99, 093506 (2006)</td> </tr><tr> <td>[58]</td> <td class="space">Wang, W. -H.; Wang, R. J.; Li, F. Y.; Zhao, D. Q.; Pan, M. X.: Elastic constants and their pressure dependence of zr41ti14cu12.5ni9be22.5c1 bulk metallic Glass, Appl. phys. Lett. 74, 1803-1805 (1999)</td> </tr><tr> <td>[59]</td> <td class="space">Xi, X. K.; Zhao, D. Q.; Pan, M. X.; Wang, W. H.; Wu, Y.; Lewandowski, J. J.: Fracture of brittle metallic glasses: brittleness or plasticity, Phys. rev. Lett. 94, 125510 (2005)</td> </tr><tr> <td>[60]</td> <td class="space">Yang, B.; Nieh, T. G.: Effect of the nanoindentation rate on the shear band formation in an au-based bulk metallic Glass, Acta mater. 55, 295-300 (2007)</td> </tr><tr> <td>[61]</td> <td class="space">Yang, B.; Liu, C. T.; Nieh, T. G.: Unified equation for the strength of bulk metallic glasses, Appl. phys. Lett. 88, 221911 (2006)</td> </tr><tr> <td>[62]</td> <td class="space">Yavari, A. R.; Lewandowski, J. J.; Eckert, J.: Mechanical properties of bulk metallic glasses, MRS bull. 32, 635-638 (2007)</td> </tr><tr> <td>[63]</td> <td class="space">Zhang, Z. F.; Eckert, J.; Schultz, L.: Difference in compressive and tensile fracture mechanisms of zr59 cu20 al1 0Ni8 ti3 bulk metallic Glass, Acta mater. 51, 1167-1179 (2003)</td> </tr><tr> <td>[64]</td> <td class="space">Zhang, Z. F.; He, G.; Eckert, J.; Schultz, L.: Fracture mechanisms in bulk metallic glassy materials, Phys. rev. Lett. 91, 045505 (2003)</td> </tr><tr> <td>[65]</td> <td class="space">Zhang, B.; Pan, M. X.; Zhao, D. Q.; Wang, W. H.: ”Soft” bulk metallic glasses based on cerium, Appl. phys. Lett. 85, 61-63 (2004)</td> </tr><tr> <td>[66]</td> <td class="space">Zhang, H. W.; Jing, X.; Subhash, G.; Kecskes, L. J.; Dowding, R. J.: Investigation of shear band evolution in amorphous alloys beneath a vickers indentation, Acta mater. 53, 3849-3859 (2005)</td> </tr><tr> <td>[67]</td> <td class="space">Zhang, H. W.; Subhash, G.; Jing, X. N.; Kecskes, L. J.; Dowding, R. J.: Evaluation of hardness-yield strength relationships for bulk metallic glasses, Phil. mag. Lett. 86, 333-345 (2006)</td> </tr><tr> <td>[68]</td> <td class="space">Zhang, J.; Park, J. M.; Kim, D. H.; Kim, H. S.: Effect of strain rate on compressive behaviour of ti45 zr16 ni9 cu10 be20 bulk metallic Glass, Mater. sci. Eng. A, 290-294 (2007)</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>