TY - JOUR
T1 - Energy release rate, the crack closure integral and admissible singular fields in fracture mechanics
AU - Piccolroaz, Andrea
AU - Peck, Daniel
AU - Wrobel, Michal
AU - Mishuris, Gennady
N1 - Funding Information:
A.P. gratefully acknowledges the funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 955944 - RE-FRACTURE2. D.P. and G.M. would like to thank Ser-Cymru II Research Programme by Welsh Government supported by European Regional Development Fund. M.W. was supported by European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation (RESTART 2016 - 2020 PROGRAMMES, Excellence Hubs, Project EXCELLENCE/1216/0481).
Funding Information:
The authors are grateful to Profs. D. Bigoni, D. Garagash, P. Papanastasiou, J.R. Rice and L.I. Slepyan for fruitful discussions and useful comments. G.M. acknowledges Wolfson Research Merit Award from the Royal Society and Ser-Cymru Future Generations Industrial Fellowship.
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/7/1
Y1 - 2021/7/1
N2 - One of the assumptions of Linear Elastic Fracture Mechanics is that the crack faces are traction-free or, at most, loaded by bounded tractions. The standard Irwin's crack closure integral, widely used for the computation of the Energy Release Rate, also relies upon this assumption. However, there are practical situations where the load acting on the crack boundaries is singular. This is the case, for instance, in hydraulic fracturing, where the fluid inside the crack exerts singular tangential tractions at its front. Another example of unbounded tractions is the case of a rigid line inclusion (anticrack) embedded into an elastic body. In such situations, the classical Irwin's crack closure integral fails to provide the correct value of the Energy Release Rate. In this paper, we address the effects occurring when square-root singular tractions act at the boundary of a line defect in an elastic solid and provide a generalisation of Irwin's crack closure integral. The latter yields the correct Energy Release Rate and allows broad applications, including, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface stress elasticity. We present the results in the most general form, where six Stress Intensity Factors are present: three of them are classical SIFs corresponding to the Modes I-II-III and computed under the assumption of homogeneous boundary conditions at the defect surfaces, while the other three SIFs are associated with singular admissible tractions (those that lead to a finite ERR value). It is demonstrated that this approach resolves an ambiguity in using the same SIF's terminology in the cases of open cracks and rigid inclusions, among other benefits.
AB - One of the assumptions of Linear Elastic Fracture Mechanics is that the crack faces are traction-free or, at most, loaded by bounded tractions. The standard Irwin's crack closure integral, widely used for the computation of the Energy Release Rate, also relies upon this assumption. However, there are practical situations where the load acting on the crack boundaries is singular. This is the case, for instance, in hydraulic fracturing, where the fluid inside the crack exerts singular tangential tractions at its front. Another example of unbounded tractions is the case of a rigid line inclusion (anticrack) embedded into an elastic body. In such situations, the classical Irwin's crack closure integral fails to provide the correct value of the Energy Release Rate. In this paper, we address the effects occurring when square-root singular tractions act at the boundary of a line defect in an elastic solid and provide a generalisation of Irwin's crack closure integral. The latter yields the correct Energy Release Rate and allows broad applications, including, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface stress elasticity. We present the results in the most general form, where six Stress Intensity Factors are present: three of them are classical SIFs corresponding to the Modes I-II-III and computed under the assumption of homogeneous boundary conditions at the defect surfaces, while the other three SIFs are associated with singular admissible tractions (those that lead to a finite ERR value). It is demonstrated that this approach resolves an ambiguity in using the same SIF's terminology in the cases of open cracks and rigid inclusions, among other benefits.
KW - Energy Release Rate
KW - Fracture Mechanics
KW - Hydraulic Fracture
KW - Singularity
UR - http://www.scopus.com/inward/record.url?scp=85106489403&partnerID=8YFLogxK
U2 - 10.1016/j.ijengsci.2021.103487
DO - 10.1016/j.ijengsci.2021.103487
M3 - Article
AN - SCOPUS:85106489403
SN - 0020-7225
VL - 164
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
M1 - 103487
ER -