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class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Thermal shock resistance</span> </div> </a> <button aria-controls="toc-Thermal_shock_resistance-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Thermal shock resistance subsection</span> </button> <ul id="toc-Thermal_shock_resistance-sublist" class="vector-toc-list"> <li id="toc-Strength-controlled_thermal_shock_resistance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Strength-controlled_thermal_shock_resistance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Strength-controlled thermal shock resistance</span> </div> </a> <ul id="toc-Strength-controlled_thermal_shock_resistance-sublist" class="vector-toc-list"> <li id="toc-Perfect_heat_transfer" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Perfect_heat_transfer"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Perfect heat transfer</span> </div> </a> <ul id="toc-Perfect_heat_transfer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Poor_heat_transfer" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Poor_heat_transfer"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Poor heat transfer</span> </div> </a> <ul id="toc-Poor_heat_transfer-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Fracture_toughness_controlled_thermal_shock_resistance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fracture_toughness_controlled_thermal_shock_resistance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Fracture toughness controlled thermal shock resistance</span> </div> </a> <ul id="toc-Fracture_toughness_controlled_thermal_shock_resistance-sublist" class="vector-toc-list"> <li id="toc-Perfect_heat_transfer_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Perfect_heat_transfer_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Perfect heat transfer</span> </div> </a> <ul id="toc-Perfect_heat_transfer_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Poor_heat_transfer_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Poor_heat_transfer_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Poor heat transfer</span> </div> </a> <ul id="toc-Poor_heat_transfer_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kingery_thermal_shock_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kingery_thermal_shock_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Kingery thermal shock methods</span> </div> </a> <ul id="toc-Kingery_thermal_shock_methods-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Testing" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Testing"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Testing</span> </div> </a> <ul id="toc-Testing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples_of_thermal_shock_failure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples_of_thermal_shock_failure"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Examples of thermal shock failure</span> </div> </a> <ul id="toc-Examples_of_thermal_shock_failure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" 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.sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title">Mechanical failure modes</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Buckling" title="Buckling">Buckling</a></li> <li><a href="/wiki/Corrosion" title="Corrosion">Corrosion</a></li> <li><a href="/wiki/Corrosion_fatigue" title="Corrosion fatigue">Corrosion fatigue</a></li> <li><a href="/wiki/Creep_(deformation)" title="Creep (deformation)">Creep</a></li> <li><a href="/wiki/Fatigue_(material)" title="Fatigue (material)">Fatigue</a></li> <li><a href="/wiki/Fouling" title="Fouling">Fouling</a></li> <li><a href="/wiki/Fracture" title="Fracture">Fracture</a></li> <li><a href="/wiki/Hydrogen_embrittlement" title="Hydrogen embrittlement">Hydrogen embrittlement</a></li> <li><a href="/wiki/Impact_(mechanics)" title="Impact (mechanics)">Impact</a></li> <li><a href="/wiki/Liquid_metal_embrittlement" title="Liquid metal embrittlement">Liquid metal embrittlement</a></li> <li><a href="/wiki/Mechanical_overload" title="Mechanical overload">Mechanical overload</a></li> <li><a href="/wiki/Metal-induced_embrittlement" title="Metal-induced embrittlement">Metal-induced embrittlement</a></li> <li><a href="/wiki/Stress_corrosion_cracking" title="Stress corrosion cracking">Stress corrosion cracking</a></li> <li><a href="/wiki/Sulfide_stress_cracking" title="Sulfide stress cracking">Sulfide stress cracking</a></li> <li><a class="mw-selflink selflink">Thermal shock</a></li> <li><a href="/wiki/Wear" title="Wear">Wear</a></li> <li><a href="/wiki/Yield_(engineering)" title="Yield (engineering)">Yielding</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Mechanical_failure_modes" title="Template:Mechanical failure modes"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mechanical_failure_modes" title="Template talk:Mechanical failure modes"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mechanical_failure_modes" title="Special:EditPage/Template:Mechanical failure modes"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Thermal shock</b> is a phenomenon characterized by a rapid change in temperature that results in a transient <a href="/wiki/Mechanical_load" title="Mechanical load">mechanical load</a> on an object. The load is caused by the differential expansion of different parts of the object due to the temperature change. This differential expansion can be understood in terms of <a href="/wiki/Strain_(materials_science)" class="mw-redirect" title="Strain (materials science)">strain</a>, rather than <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a>. When the strain exceeds the <a href="/wiki/Tensile_strength" class="mw-redirect" title="Tensile strength">tensile strength</a> of the material, it can cause cracks to form, and eventually lead to structural failure. </p><p>Methods to prevent thermal shock include:<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Minimizing the <a href="/wiki/Thermal_gradient" class="mw-redirect" title="Thermal gradient">thermal gradient</a> by changing the temperature gradually</li> <li>Increasing the <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a> of the material</li> <li>Reducing the coefficient of <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal expansion</a> of the material</li> <li>Increasing the strength of the material</li> <li>Introducing <a href="/wiki/Compressive_stress" title="Compressive stress">compressive stress</a> in the material, such as in <a href="/wiki/Tempered_glass" title="Tempered glass">tempered glass</a></li> <li>Decreasing the <a href="/wiki/Young%27s_modulus" title="Young's modulus">Young's modulus</a> of the material</li> <li>Increasing the <a href="/wiki/Toughness" title="Toughness">toughness</a> of the material through crack tip blunting or crack deflection, utilizing the process of <a href="/wiki/Plastic_Deformation" class="mw-redirect" title="Plastic Deformation">plastic deformation</a>, and <a href="/wiki/Phase_Transformation" class="mw-redirect" title="Phase Transformation">phase transformation</a></li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Effect_on_materials">Effect on materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=1" title="Edit section: Effect on materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Borosilicate_glass" title="Borosilicate glass">Borosilicate glass</a> is made to withstand thermal shock better than most other glass through a combination of reduced expansion coefficient, and greater strength, though <a href="/wiki/Fused_quartz" title="Fused quartz">fused quartz</a> outperforms it in both these respects. Some <a href="/wiki/Glass-ceramic" title="Glass-ceramic">glass-ceramic</a> materials (mostly in the <a href="/w/index.php?title=Lithium_aluminosilicate&action=edit&redlink=1" class="new" title="Lithium aluminosilicate (page does not exist)">lithium aluminosilicate</a> (LAS) system<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>) include a controlled proportion of material with a negative expansion coefficient, so that the overall coefficient can be reduced to almost exactly zero over a reasonably wide range of temperatures. </p><p>Among the best thermomechanical materials, there are <a href="/wiki/Alumina" class="mw-redirect" title="Alumina">alumina</a>, <a href="/wiki/Zirconia" class="mw-redirect" title="Zirconia">zirconia</a>, <a href="/wiki/Tungsten" title="Tungsten">tungsten</a> alloys, <a href="/wiki/Silicon_nitride" title="Silicon nitride">silicon nitride</a>, <a href="/wiki/Silicon_carbide" title="Silicon carbide">silicon carbide</a>, <a href="/wiki/Boron_carbide" title="Boron carbide">boron carbide</a>, and some <a href="/wiki/Stainless_steel" title="Stainless steel">stainless steels</a>. </p><p><a href="/wiki/Reinforced_carbon-carbon" class="mw-redirect" title="Reinforced carbon-carbon">Reinforced carbon-carbon</a> is extremely resistant to thermal shock, due to <a href="/wiki/Graphite" title="Graphite">graphite</a>'s extremely high thermal conductivity and low expansion coefficient, the high strength of <a href="/wiki/Carbon_fiber" class="mw-redirect" title="Carbon fiber">carbon fiber</a>, and a reasonable ability to deflect cracks within the structure. </p><p>To measure thermal shock, the <a href="/wiki/Impulse_excitation_technique" title="Impulse excitation technique">impulse excitation technique</a> proved to be a useful tool. It can be used to measure Young's modulus, <a href="/wiki/Shear_modulus" title="Shear modulus">Shear modulus</a>, <a href="/wiki/Poisson%27s_ratio" title="Poisson's ratio">Poisson's ratio</a>, and <a href="/wiki/Damping_ratio" class="mw-redirect" title="Damping ratio">damping</a> coefficient in a non destructive way. The same test-piece can be measured after different thermal shock cycles, and this way the deterioration in physical properties can be mapped out. </p> <div class="mw-heading mw-heading2"><h2 id="Thermal_shock_resistance">Thermal shock resistance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=2" title="Edit section: Thermal shock resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal shock resistance measures can be used for material selection in applications subject to rapid temperature changes. A common measure of thermal shock resistance is the maximum temperature differential, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e61e7deb9c7c7b7dda762b0935e757add2acc559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.572ex; height:2.176ex;" alt="{\displaystyle \Delta T}"></span>, which can be sustained by the material for a given thickness.<sup id="cite_ref-:2_3-0" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Strength-controlled_thermal_shock_resistance">Strength-controlled thermal shock resistance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=3" title="Edit section: Strength-controlled thermal shock resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal shock resistance measures can be used for material selection in applications subject to rapid temperature changes. The maximum temperature jump, <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e61e7deb9c7c7b7dda762b0935e757add2acc559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.572ex; height:2.176ex;" alt="{\displaystyle \Delta T}"></span>,</span> sustainable by a material can be defined for strength-controlled models by:<sup id="cite_ref-:3_4-0" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_3-1" class="reference"><a href="#cite_note-:2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B\Delta T={\frac {\sigma _{f}}{\alpha E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow> <mi>α</mi> <mi>E</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\Delta T={\frac {\sigma _{f}}{\alpha E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23c9c27c22aa16e8688ea3a158ae9c1f9bc3bace" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.534ex; height:5.009ex;" alt="{\displaystyle B\Delta T={\frac {\sigma _{f}}{\alpha E}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1faac91a4f954c5707a88c07bfed70b9b92b3785" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.464ex; height:2.343ex;" alt="{\displaystyle \sigma _{f}}"></span> is the failure stress (which can be <a href="/wiki/Yield_(engineering)" title="Yield (engineering)">yield</a> or <a href="/wiki/Fracture" title="Fracture">fracture stress</a>), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> is the coefficient of thermal expansion, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is the Young's modulus, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> is a constant depending upon the part constraint, material properties, and thickness. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B={\frac {C}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>C</mi> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B={\frac {C}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce12ca0ab57374c6e1a73e59aca5a8a4f70233c0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.465ex; height:5.509ex;" alt="{\displaystyle B={\frac {C}{A}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> is a system constrain constant dependent upon the Poisson's ratio, <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span>,</span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> is a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">non-dimensional parameter</a> dependent upon the <a href="/wiki/Biot_number" title="Biot number">Biot number</a>, <span class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Bi} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Bi} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9f009e6039b05e7b6e40937148ad32b5cab2282" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.292ex; height:2.176ex;" alt="{\displaystyle \mathrm {Bi} }"></span>.</span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C={\begin{cases}1&{\text{axial stress}}\\(1-\nu )&{\text{biaxial constraint}}\\(1-2\nu )&{\text{triaxial constraint}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>axial stress</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>biaxial constraint</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mn>2</mn> <mi>ν</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>triaxial constraint</mtext> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\begin{cases}1&{\text{axial stress}}\\(1-\nu )&{\text{biaxial constraint}}\\(1-2\nu )&{\text{triaxial constraint}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/775ad43c19c57f28637d7cc6402292cef671727e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:36.328ex; height:8.509ex;" alt="{\displaystyle C={\begin{cases}1&{\text{axial stress}}\\(1-\nu )&{\text{biaxial constraint}}\\(1-2\nu )&{\text{triaxial constraint}}\end{cases}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> may be approximated by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {Hh/k}{1+Hh/k}}={\frac {\mathrm {Bi} }{1+\mathrm {Bi} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>H</mi> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>k</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>H</mi> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>k</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {Hh/k}{1+Hh/k}}={\frac {\mathrm {Bi} }{1+\mathrm {Bi} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e26ea9af8fdb29ff2d34cbb281771bbd5c08a09c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.687ex; height:6.509ex;" alt="{\displaystyle A={\frac {Hh/k}{1+Hh/k}}={\frac {\mathrm {Bi} }{1+\mathrm {Bi} }}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span> is the thickness, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> is the <a href="/wiki/Heat_transfer_coefficient" title="Heat transfer coefficient">heat transfer coefficient</a>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> is the <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Perfect_heat_transfer">Perfect heat transfer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=4" title="Edit section: Perfect heat transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If perfect heat transfer <span class="nowrap">(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Bi} =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Bi} =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc34fe6b61ea2f0148f08593178213b05fb7b9e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.715ex; height:2.176ex;" alt="{\displaystyle \mathrm {Bi} =\infty }"></span>)</span> is assumed, the maximum heat transfer supported by the material is:<sup id="cite_ref-:3_4-1" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fleck_96_5-0" class="reference"><a href="#cite_note-Fleck_96-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T=A_{1}{\frac {\sigma _{f}}{E\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T=A_{1}{\frac {\sigma _{f}}{E\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46665909f17d33ff3d2c7372f6b4074b671856f1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.567ex; height:5.009ex;" alt="{\displaystyle \Delta T=A_{1}{\frac {\sigma _{f}}{E\alpha }}}"></span> </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}\approx 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≈</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}\approx 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e9782da5f9b6610203b7b4b692d726947835e8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.058ex; height:2.509ex;" alt="{\displaystyle A_{1}\approx 1}"></span> for cold shock in plates</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}\approx 3.2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≈</mo> <mn>3.2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}\approx 3.2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a97464372c2eb459078efe9eb7a64f01154d2c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.868ex; height:2.509ex;" alt="{\displaystyle A_{1}\approx 3.2}"></span> for hot shock in plates</li></ul> <p>A <a href="/wiki/Material_selection" title="Material selection">material index</a> for material selection according to thermal shock resistance in the fracture stress derived perfect heat transfer case is therefore: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\sigma _{f}}{E\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\sigma _{f}}{E\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6952be3fdb82e65a5b0fc957e770942454bd3b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.099ex; height:5.009ex;" alt="{\displaystyle {\frac {\sigma _{f}}{E\alpha }}}"></span> </p> <div class="mw-heading mw-heading4"><h4 id="Poor_heat_transfer">Poor heat transfer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=5" title="Edit section: Poor heat transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For cases with poor heat transfer <span class="nowrap">(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Bi} <1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Bi} <1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a138bf140cffc0a7517699af818d915a161cebcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.553ex; height:2.176ex;" alt="{\displaystyle \mathrm {Bi} <1}"></span>),</span> the maximum heat differential supported by the material is:<sup id="cite_ref-:3_4-2" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fleck_96_5-1" class="reference"><a href="#cite_note-Fleck_96-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T=A_{2}{\frac {\sigma _{f}}{E\alpha }}{\frac {1}{\mathrm {Bi} }}=A_{2}{\frac {\sigma _{f}}{E\alpha }}{\frac {k}{hH}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <mrow> <mi>h</mi> <mi>H</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T=A_{2}{\frac {\sigma _{f}}{E\alpha }}{\frac {1}{\mathrm {Bi} }}=A_{2}{\frac {\sigma _{f}}{E\alpha }}{\frac {k}{hH}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/318afbdecca663ae663ee0446d025ba17b086cdc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:30.93ex; height:5.509ex;" alt="{\displaystyle \Delta T=A_{2}{\frac {\sigma _{f}}{E\alpha }}{\frac {1}{\mathrm {Bi} }}=A_{2}{\frac {\sigma _{f}}{E\alpha }}{\frac {k}{hH}}}"></span> </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{2}\approx 3.2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≈</mo> <mn>3.2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2}\approx 3.2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0e0bd098599e3ae82001f0e34de8d0ceb5fef47" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.868ex; height:2.509ex;" alt="{\displaystyle A_{2}\approx 3.2}"></span> for cold shock</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{2}\approx 6.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≈</mo> <mn>6.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{2}\approx 6.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8e7487ee0a34c33788a156e063b93aa8e1b0dc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.868ex; height:2.509ex;" alt="{\displaystyle A_{2}\approx 6.5}"></span> for hot shock</li></ul> <p>In the poor heat transfer case, a higher thermal conductivity is beneficial for thermal shock resistance. The material index for the poor heat transfer case is often taken as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {k\sigma _{f}}{E\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {k\sigma _{f}}{E\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b266f4eda3431ac6f946b44f52ebe5ee9cce637a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.511ex; height:5.676ex;" alt="{\displaystyle {\frac {k\sigma _{f}}{E\alpha }}}"></span> </p><p>According to both the perfect and poor heat transfer models, larger temperature differentials can be tolerated for hot shock than for cold shock. </p> <div class="mw-heading mw-heading3"><h3 id="Fracture_toughness_controlled_thermal_shock_resistance">Fracture toughness controlled thermal shock resistance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=6" title="Edit section: Fracture toughness controlled thermal shock resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In addition to thermal shock resistance defined by material fracture strength, models have also been defined within the <a href="/wiki/Fracture_mechanics" title="Fracture mechanics">fracture mechanics</a> framework. Lu and Fleck produced criteria for thermal shock cracking based on <a href="/wiki/Fracture_toughness" title="Fracture toughness">fracture toughness</a> controlled cracking. The models were based on thermal shock in ceramics (generally brittle materials). Assuming an infinite plate, and <a href="/wiki/Mode_I_crack" class="mw-redirect" title="Mode I crack">mode I</a> cracking, the crack was predicted to start from the edge for cold shock, but the center of the plate for hot shock.<sup id="cite_ref-:3_4-3" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Cases were divided into perfect, and poor heat transfer to further simplify the models. </p> <div class="mw-heading mw-heading4"><h4 id="Perfect_heat_transfer_2">Perfect heat transfer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=7" title="Edit section: Perfect heat transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The sustainable temperature jump decreases, with increasing convective heat transfer (and therefore larger Biot number). This is represented in the model shown below for perfect heat transfer <span class="nowrap">(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Bi} =\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">i</mi> </mrow> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Bi} =\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc34fe6b61ea2f0148f08593178213b05fb7b9e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.715ex; height:2.176ex;" alt="{\displaystyle \mathrm {Bi} =\infty }"></span>).</span><sup id="cite_ref-:3_4-4" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fleck_96_5-2" class="reference"><a href="#cite_note-Fleck_96-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T=A_{3}{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>c</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>π</mi> <mi>H</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T=A_{3}{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e71a30dd0ef3f391ea087a1cb1116da6884d661" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:18.899ex; height:6.176ex;" alt="{\displaystyle \Delta T=A_{3}{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{Ic}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{Ic}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e78591056fee2484c707fe8c0a8eb1260367c7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.746ex; height:2.509ex;" alt="{\displaystyle K_{Ic}}"></span> is the mode I <a href="/wiki/Fracture_toughness" title="Fracture toughness">fracture toughness</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is the Young's modulus, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> is the thermal expansion coefficient, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span> is half the thickness of the plate. </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{3}\approx 4.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>≈</mo> <mn>4.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{3}\approx 4.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/044a30c34aaa5beb2a8c6d35c5207b0e5edc24db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.868ex; height:2.509ex;" alt="{\displaystyle A_{3}\approx 4.5}"></span> for cold shock</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{4}\approx 5.6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>≈</mo> <mn>5.6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{4}\approx 5.6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0efb3a600908a7af0db7e05eb52e4c8ad3611119" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.868ex; height:2.509ex;" alt="{\displaystyle A_{4}\approx 5.6}"></span> for hot shock</li></ul> <p>A material index for material selection in the fracture mechanics derived perfect heat transfer case is therefore: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {K_{Ic}}{E\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>c</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {K_{Ic}}{E\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6e192997ef24a1af7c6c547a8439c00d0ae4e4d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.582ex; height:5.176ex;" alt="{\displaystyle {\frac {K_{Ic}}{E\alpha }}}"></span> </p> <div class="mw-heading mw-heading4"><h4 id="Poor_heat_transfer_2">Poor heat transfer</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=8" title="Edit section: Poor heat transfer"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For cases with poor heat transfer, the Biot number is an important factor in the sustainable temperature jump.<sup id="cite_ref-:3_4-5" class="reference"><a href="#cite_note-:3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fleck_96_5-3" class="reference"><a href="#cite_note-Fleck_96-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T=A_{4}{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}{\frac {k}{hH}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>c</mi> </mrow> </msub> <mrow> <mi>E</mi> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>π</mi> <mi>H</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>k</mi> <mrow> <mi>h</mi> <mi>H</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T=A_{4}{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}{\frac {k}{hH}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35f99b8de8bfa57e430ded2968a72bc8664296b5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:23.138ex; height:6.343ex;" alt="{\displaystyle \Delta T=A_{4}{\frac {K_{Ic}}{E\alpha {\sqrt {\pi H}}}}{\frac {k}{hH}}}"></span> </p><p>Critically, for poor heat transfer cases, materials with higher thermal conductivity, <span class="texhtml"><i>k</i></span>, have higher thermal shock resistance. As a result, a commonly chosen material index for thermal shock resistance in the poor heat transfer case is: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {kK_{Ic}}{E\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mi>c</mi> </mrow> </msub> </mrow> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {kK_{Ic}}{E\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13d93585deca7562583251d6f511ba1cd5e8aad7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.793ex; height:5.343ex;" alt="{\displaystyle {\frac {kK_{Ic}}{E\alpha }}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Kingery_thermal_shock_methods">Kingery thermal shock methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=9" title="Edit section: Kingery thermal shock methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The temperature difference to initiate fracture has been described by <a href="/wiki/W._David_Kingery" title="W. David Kingery">William David Kingery</a> to be:<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_7-0" class="reference"><a href="#cite_note-:1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta T_{c}=S{\frac {k\sigma ^{*}(1-\nu )}{E\alpha }}{\frac {1}{h}}={\frac {S}{hR^{'}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>h</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>S</mi> <mrow> <mi>h</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mo>′</mo> </msup> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta T_{c}=S{\frac {k\sigma ^{*}(1-\nu )}{E\alpha }}{\frac {1}{h}}={\frac {S}{hR^{'}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/948c53ab675676c1a8e4a49858dc746b5a5682df" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:30.288ex; height:6.009ex;" alt="{\displaystyle \Delta T_{c}=S{\frac {k\sigma ^{*}(1-\nu )}{E\alpha }}{\frac {1}{h}}={\frac {S}{hR^{'}}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> is a shape factor, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma ^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma ^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65f4dfaabbd9ff3a498984dd4fdc62af5ed24ecc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.385ex; height:2.343ex;" alt="{\displaystyle \sigma ^{*}}"></span> is the fracture stress, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> is the thermal conductivity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is the Young's modulus, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> is the coefficient of thermal expansion, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> is the heat transfer coefficient, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>R</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43cc152440f75fd8f842f4225a7484bb431b3343" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.509ex;" alt="{\displaystyle R'}"></span> is a fracture resistance parameter. The fracture resistance parameter is a common metric used to define the thermal shock tolerance of materials.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R'={\frac {k\sigma ^{*}(1-v)}{E\alpha }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>R</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>v</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>E</mi> <mi>α</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R'={\frac {k\sigma ^{*}(1-v)}{E\alpha }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d9c2a40361380d00b6d21971e991ff69cd7909c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.919ex; height:5.676ex;" alt="{\displaystyle R'={\frac {k\sigma ^{*}(1-v)}{E\alpha }}}"></span> </p><p>The formulas were derived for ceramic materials, and make the assumptions of a homogeneous body with material properties independent of temperature, but can be well applied to other brittle materials.<sup id="cite_ref-:1_7-1" class="reference"><a href="#cite_note-:1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Testing">Testing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=10" title="Edit section: Testing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermal shock testing exposes products to alternating low and high temperatures to accelerate failures caused by temperature cycles or thermal shocks during normal use. The transition between temperature extremes occurs very rapidly, greater than 15 °C per minute. </p><p>Equipment with single or multiple chambers is typically used to perform thermal shock testing. When using single chamber thermal shock equipment, the products remain in one chamber and the chamber air temperature is rapidly cooled and heated. Some equipment uses separate hot and cold chambers with an elevator mechanism that transports the products between two or more chambers. </p><p>Glass containers can be sensitive to sudden changes in temperature. One method of testing involves rapid movement from cold to hot water baths, and back.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples_of_thermal_shock_failure">Examples of thermal shock failure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=11" title="Edit section: Examples of thermal shock failure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Thermal_shock" title="Special:EditPage/Thermal shock">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">June 2013</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <ul><li>Hard rocks containing ore veins such as <a href="/wiki/Quartzite" title="Quartzite">quartzite</a> were formerly broken down using <a href="/wiki/Fire-setting" title="Fire-setting">fire-setting</a>, which involved heating the rock face with a wood fire, then quenching with water to induce crack growth. It is described by <a href="/wiki/Diodorus_Siculus" title="Diodorus Siculus">Diodorus Siculus</a> in Egyptian <a href="/wiki/Gold_mine" class="mw-redirect" title="Gold mine">gold mines</a>, <a href="/wiki/Pliny_the_Elder" title="Pliny the Elder">Pliny the Elder</a>, and <a href="/wiki/Georg_Agricola" class="mw-redirect" title="Georg Agricola">Georg Agricola</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2015)">citation needed</span></a></i>]</sup></li> <li>Ice cubes placed in a glass of warm water crack by thermal shock as the exterior surface increases in temperature much faster than the interior. The outer layer expands as it warms, while the interior remains largely unchanged. This rapid change in volume between different layers creates stresses in the ice that build until the force exceeds the strength of the ice, and a crack forms, sometimes with enough force to shoot ice shards out of the container.</li> <li><a href="/wiki/Incandescent_light_bulb" title="Incandescent light bulb">Incandescent bulbs</a> that have been running for a while have a very hot surface. Splashing cold water on them can cause the glass to shatter due to thermal shock, and the bulb to implode.</li> <li>An antique cast iron cookstove is a simple iron box on legs, with a cast iron top. A wood or coal fire is built inside the box and food is cooked on the top outer surface of the box, like a griddle. If a fire is built too hot, and then the stove is cooled by pouring water on the top surface, it will crack due to thermal shock.</li> <li>The strong gradient of temperature (due to the dousing of a fire with water) is believed to cause the breakage of the third <a href="/wiki/Tsar_Bell" title="Tsar Bell">Tsar Bell</a>.</li> <li>Thermal shock is a primary contributor to <a href="/wiki/Head_gasket" title="Head gasket">head gasket</a> failure in internal combustion engines.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Biot_number" title="Biot number">Biot number</a></li> <li><a href="/wiki/Impulse_excitation_technique" title="Impulse excitation technique">Impulse excitation technique</a></li> <li><a href="/wiki/Spontaneous_glass_breakage" class="mw-redirect" title="Spontaneous glass breakage">Spontaneous glass breakage</a></li> <li><a href="/wiki/Strain_(materials_science)" class="mw-redirect" title="Strain (materials science)">Strain</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thermal_shock&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFAskeland2015" class="citation book cs1">Askeland, Donald R. (January 2015). "22-4 Thermal Shock". <i>The science and engineering of materials</i>. Wright, Wendelin J. (Seventh ed.). Boston, MA. pp. 792–793. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-305-07676-1" title="Special:BookSources/978-1-305-07676-1"><bdi>978-1-305-07676-1</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/903959750">903959750</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=22-4+Thermal+Shock&rft.btitle=The+science+and+engineering+of+materials&rft.place=Boston%2C+MA&rft.pages=792-793&rft.edition=Seventh&rft.date=2015-01&rft_id=info%3Aoclcnum%2F903959750&rft.isbn=978-1-305-07676-1&rft.aulast=Askeland&rft.aufirst=Donald+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+shock" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent" id="CITEREFScott_L._Swartz2000"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6066585">US Patent 6066585</a>, Scott L. Swartz, "Ceramics having negative coefficient of thermal expansion, method of making such ceramics, and parts made from such ceramics", issued 2000-05-23,  assigned to Emerson Electric Co.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=6066585&rft.cc=US&rft.title=Ceramics+having+negative+coefficient+of+thermal+expansion%2C+method+of+making+such+ceramics%2C+and+parts+made+from+such+ceramics&rft.inventor=Scott+L.+Swartz&rft.assignee=Emerson+Electric+Co.&rft.date=2000-05-23"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-:2-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAshby,_M._F.1999" class="citation book cs1">Ashby, M. F. (1999). <i>Materials selection in mechanical design</i> (2nd ed.). Oxford, OX: Butterworth-Heinemann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7506-4357-9" title="Special:BookSources/0-7506-4357-9"><bdi>0-7506-4357-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/49708474">49708474</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Materials+selection+in+mechanical+design&rft.place=Oxford%2C+OX&rft.edition=2nd&rft.pub=Butterworth-Heinemann&rft.date=1999&rft_id=info%3Aoclcnum%2F49708474&rft.isbn=0-7506-4357-9&rft.au=Ashby%2C+M.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+shock" class="Z3988"></span></span> </li> <li id="cite_note-:3-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:3_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:3_4-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:3_4-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:3_4-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoboyejo2003" class="citation book cs1">Soboyejo, Wole O. (2003). "12.10.2 Materials Selection for Thermal Shock Resistance". <i>Mechanical properties of engineered materials</i>. Marcel Dekker. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-8900-8" title="Special:BookSources/0-8247-8900-8"><bdi>0-8247-8900-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/300921090">300921090</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=12.10.2+Materials+Selection+for+Thermal+Shock+Resistance&rft.btitle=Mechanical+properties+of+engineered+materials&rft.pub=Marcel+Dekker&rft.date=2003&rft_id=info%3Aoclcnum%2F300921090&rft.isbn=0-8247-8900-8&rft.aulast=Soboyejo&rft.aufirst=Wole+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+shock" class="Z3988"></span></span> </li> <li id="cite_note-Fleck_96-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Fleck_96_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Fleck_96_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Fleck_96_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Fleck_96_5-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFT._J._LuN._A._Fleck1998" class="citation journal cs1">T. J. Lu; N. A. Fleck (1998). <a rel="nofollow" class="external text" href="http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/96.pdf">"The Thermal Shock Resistance of Solids"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Acta_Materialia" title="Acta Materialia">Acta Materialia</a></i>. <b>46</b> (13): 4755–4768. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998AcMat..46.4755L">1998AcMat..46.4755L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1359-6454%2898%2900127-X">10.1016/S1359-6454(98)00127-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Materialia&rft.atitle=The+Thermal+Shock+Resistance+of+Solids&rft.volume=46&rft.issue=13&rft.pages=4755-4768&rft.date=1998&rft_id=info%3Adoi%2F10.1016%2FS1359-6454%2898%2900127-X&rft_id=info%3Abibcode%2F1998AcMat..46.4755L&rft.au=T.+J.+Lu&rft.au=N.+A.+Fleck&rft_id=http%3A%2F%2Fwww-mech.eng.cam.ac.uk%2Fprofiles%2Ffleck%2Fpapers%2F96.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+shock" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKINGERY1955" class="citation journal cs1">KINGERY, W. D. (Jan 1955). "Factors Affecting Thermal Stress Resistance of Ceramic Materials". <i>Journal of the American Ceramic Society</i>. <b>38</b> (1): 3–15. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1151-2916.1955.tb14545.x">10.1111/j.1151-2916.1955.tb14545.x</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-7820">0002-7820</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Ceramic+Society&rft.atitle=Factors+Affecting+Thermal+Stress+Resistance+of+Ceramic+Materials&rft.volume=38&rft.issue=1&rft.pages=3-15&rft.date=1955-01&rft_id=info%3Adoi%2F10.1111%2Fj.1151-2916.1955.tb14545.x&rft.issn=0002-7820&rft.aulast=KINGERY&rft.aufirst=W.+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+shock" class="Z3988"></span></span> </li> <li id="cite_note-:1-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoboyejo2003" class="citation book cs1">Soboyejo, Wole O. (2003). "12.10 Thermal Shock Response". <i>Mechanical properties of engineered materials</i>. Marcel Dekker. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-8900-8" title="Special:BookSources/0-8247-8900-8"><bdi>0-8247-8900-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/300921090">300921090</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=12.10+Thermal+Shock+Response&rft.btitle=Mechanical+properties+of+engineered+materials&rft.pub=Marcel+Dekker&rft.date=2003&rft_id=info%3Aoclcnum%2F300921090&rft.isbn=0-8247-8900-8&rft.aulast=Soboyejo&rft.aufirst=Wole+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThermal+shock" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">ASTM C149 — Standard Test Method for Thermal Shock Resistance of Glass Containers</span> </li> </ol></div></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output 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