<p>Polymethyl methacrylate (PMMA) is a benchmark brittle material for dynamic crack propagation studies. Despite extensive research, significant inconsistencies persist in reported fracture parameter values, complicating the establishment of a consensus on their sensitivity to the cracking regime. This study aims to rigorously determine these properties while identifying the origins of these discrepancies. To minimize microbranching effects that can strongly influence fracture surface roughness, crack propagation was restricted to subcritical velocities using a strip-band-specimen (SBS) geometry and a dedicated experimental setup. This approach ensured a quasi-steady propagation regime with minimal inertial effects. Dynamic toughness was evaluated using resistance curves constructed from Williams series expansion and displacement fields obtained via digital image correlation (DIC). Fracture energy was assessed through two complementary methods: a global energy balance and an indirect analytical approach based on Irwin’s generalized relation. Two distinct propagation regimes were identified: a stable regime (90 – 180 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2025_865_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbox {m}.\hbox {s}^{-1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>m</mtext> <mo>.</mo> <msup> <mtext>s</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>) with smooth fracture surfaces and an unstable regime (180 – 320 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2025_865_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbox {m}.\hbox {s}^{-1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>m</mtext> <mo>.</mo> <msup> <mtext>s</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>) characterized by the emergence of conical microstructures, followed by a transition to fully disrupted propagation beyond 320 <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10704_2025_865_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbox {m}.\hbox {s}^{-1}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>m</mtext> <mo>.</mo> <msup> <mtext>s</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, marking the onset of microbranches. A key outcome of this study is the validation of global fracture energy estimation through the local approach, and <i>vice versa</i>, allowing the derivation of one fracture property from the other – an unprecedented achievement for PMMA in dynamic crack propagation. This was made possible by the experimental setup and specimen geometry, which effectively minimized parasitic effects such as inertia and microbranching. Additionally, the findings confirm a strong correlation between surface roughness and the evolution of fracture energy from the earliest stages of dynamic propagation.</p>

Revisiting Dynamic Fracture in PMMA: The Interplay Between Local and Global Methods

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2025年6月27日

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Vincent Fournier,
Jérémie Girardot,
Jean-Benoit Kopp

摘要

Polymethyl methacrylate (PMMA) is a benchmark brittle material for dynamic crack propagation studies. Despite extensive research, significant inconsistencies persist in reported fracture parameter values, complicating the establishment of a consensus on their sensitivity to the cracking regime. This study aims to rigorously determine these properties while identifying the origins of these discrepancies. To minimize microbranching effects that can strongly influence fracture surface roughness, crack propagation was restricted to subcritical velocities using a strip-band-specimen (SBS) geometry and a dedicated experimental setup. This approach ensured a quasi-steady propagation regime with minimal inertial effects. Dynamic toughness was evaluated using resistance curves constructed from Williams series expansion and displacement fields obtained via digital image correlation (DIC). Fracture energy was assessed through two complementary methods: a global energy balance and an indirect analytical approach based on Irwin’s generalized relation. Two distinct propagation regimes were identified: a stable regime (90 – 180 $\hbox {m}.\hbox {s}^{-1}$ $m . s^{- 1}$ ) with smooth fracture surfaces and an unstable regime (180 – 320 $\hbox {m}.\hbox {s}^{-1}$ $m . s^{- 1}$ ) characterized by the emergence of conical microstructures, followed by a transition to fully disrupted propagation beyond 320 $\hbox {m}.\hbox {s}^{-1}$ $m . s^{- 1}$ , marking the onset of microbranches. A key outcome of this study is the validation of global fracture energy estimation through the local approach, and vice versa, allowing the derivation of one fracture property from the other – an unprecedented achievement for PMMA in dynamic crack propagation. This was made possible by the experimental setup and specimen geometry, which effectively minimized parasitic effects such as inertia and microbranching. Additionally, the findings confirm a strong correlation between surface roughness and the evolution of fracture energy from the earliest stages of dynamic propagation.