<p>The dynamic fracture properties of porous ceramics were studied using single bunch synchrotron X-ray phase contrast imaging. The modified brazilian geometry was used to initiate and propagate a pure mode I crack. The specimen was compressed using the Split Hopkinson bars at strain rates of the order of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>&#xa0;s<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq5.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>. Main cracks were isolated for four different grades of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(Al_2O_3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <msub> <mi>l</mi> <mn>2</mn> </msub> <msub> <mi>O</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, one dense alumina, and three porous grades with <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(20~\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mspace width="3.33333pt" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(60~\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>60</mn> <mspace width="3.33333pt" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> porosity. The maximum measured crack velocities for three grades is of the order of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(0.6c_R\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.6</mn> <msub> <mi>c</mi> <mi>R</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(0.4c_R\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.4</mn> <msub> <mi>c</mi> <mi>R</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> for the most porous. The fracture energy was estimated using a FE numerical simulation to quantify the influence of inertial effects induced by crack propagation. The results show that these inertial effects are far from negligible (up to <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq11.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(80~\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>80</mn> <mspace width="3.33333pt" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the stored energy) and that the dynamic correction factors known from the literature tend to overestimate the fracture energy. The values obtained vary from 22&#xa0;J/m<InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> for the densest to 5&#xa0;J/m<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2024_816_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> for the most porous.</p>

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In situ characterisation of dynamic fracture in \(Al_2O_3\) using ultra-fast X-ray phase contrast radioscopy: effects of porosity and crack speed

  • Q. Henry,
  • J.-B. Kopp,
  • L. Le Barbenchon,
  • J. Girardot,
  • B. Lukić,
  • A. Cohen,
  • A. Cosculluela,
  • P. Viot

摘要

The dynamic fracture properties of porous ceramics were studied using single bunch synchrotron X-ray phase contrast imaging. The modified brazilian geometry was used to initiate and propagate a pure mode I crack. The specimen was compressed using the Split Hopkinson bars at strain rates of the order of \(10^2\) 10 2  s \(^{-1}\) - 1 . Main cracks were isolated for four different grades of \(Al_2O_3\) A l 2 O 3 , one dense alumina, and three porous grades with \(20~\%\) 20 % to \(60~\%\) 60 % porosity. The maximum measured crack velocities for three grades is of the order of \(0.6c_R\) 0.6 c R and \(0.4c_R\) 0.4 c R for the most porous. The fracture energy was estimated using a FE numerical simulation to quantify the influence of inertial effects induced by crack propagation. The results show that these inertial effects are far from negligible (up to \(80~\%\) 80 % of the stored energy) and that the dynamic correction factors known from the literature tend to overestimate the fracture energy. The values obtained vary from 22 J/m \(^2\) 2 for the densest to 5 J/m \(^2\) 2 for the most porous.