Viscous control of shallow elastic fracture: peeling without precursors
Viscous control of shallow elastic fracture: peeling without precursors
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浅层弹性断裂的粘性控制：无前兆剥离
DOI：
10.1017/jfm.2019.185
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发表时间：
2019
影响因子：
3.7
通讯作者：
Timothy Large
中科院分区：
文献类型：
--
作者：
J. Lister;Dominic J. Skinner;Timothy Large
我们考虑通过沿两者之间的界面传播充满流体的裂纹，使弹性薄片从弹性基材上剥离。剥落是由施加在薄板上的弯矩驱动的，并由流向裂纹尖端的粘性流动和薄板与基材之间的任何粘合的韧性来抵抗。行波解是用润滑理论结合弹性和断裂完整方程确定的。传播速度$v$的尺度为$M^{3}/\unicode[STIX]{x1D707}\bar{E}^{2}d^{5}=Bd\unicode[STIX]{x1D705}}，其中$d$为板材的厚度，$B=\bar{E}d^{3}/ 144\unicode[STIX]{x1D707}$为其刚度，$\bar{E}=E/(1-\unicode[STIX]{x1D708}^{2})$为其平面应变模量，$\unicode[STIX]{x1D707}$为流体粘度，$M$为施加的弯矩，$\unicode[STIX]{x1D705}=M/B$为板材由于弯曲而产生的曲率；预因子取决于无量纲韧性。如果韧性较小，则在充液区之前存在干剪切破坏区。利用传播速度表达式导出了轴对称充液泡在不同状态下扩散的相似解：在尖端受弹性流体力学阻力的恒定通量注入导致弯曲剥离、重力扩展和拉剥离的扩散分别成正比于$t^{4/13}$、$t^{4/17}$和$t^{7/19}$。
We consider peeling of an elastic sheet away from an elastic substrate through propagation of a fluid-filled crack along the interface between the two. The peeling is driven by a bending moment applied to the sheet and is resisted by viscous flow towards the crack tip and by the toughness of any bonding between the sheet and the substrate. Travelling-wave solutions are determined using lubrication theory coupled to the full equations of elasticity and fracture. The propagation speed $v$ scales like $M^{3}/\unicode[STIX]{x1D707}\bar{E}^{2}d^{5}=Bd\unicode[STIX]{x1D705}^{3}/144\unicode[STIX]{x1D707}$ , where $d$ is the sheet’s thickness, $B=\bar{E}d^{3}/12$ its stiffness, $\bar{E}=E/(1-\unicode[STIX]{x1D708}^{2})$ its plane-strain modulus, $\unicode[STIX]{x1D707}$ the fluid viscosity, $M$ the applied bending moment and $\unicode[STIX]{x1D705}=M/B$ the sheet’s curvature due to bending; and the prefactor depends on the dimensionless toughness. If the toughness is small then there is a region of dry shear failure ahead of the fluid-filled region. The expressions for the propagation speed have been used to derive new similarity solutions for the spread of an axisymmetric fluid-filled blister in a variety of regimes: constant-flux injection resisted by elastohydrodynamics in the tip leads to spread proportional to $t^{4/13}$ , $t^{4/17}$ and $t^{7/19}$ for peeling-by-bending, gravitational spreading and peeling-by-pulling, respectively.
影响因子：
8.6
作者：
Pihler-Puzovic, D.;Illien, P.;Juel, A.
通讯作者：
Juel, A.
位移在弹性膜下流动。
影响因子：
3.7
作者：
Pihler-Puzovic D
通讯作者：
Pihler-Puzovic D