Mixed-mode fatigue crack growth analysis using peridynamic approach

Abstract A new method is developed in this study to extend the peridynamic fatigue model for mode-I crack case proposed by Silling (2014) to a mixed-mode (mode-I and mode-II) crack case. To determine the model parameters, application of the modified Paris law incorporating the effective stress intensity factor model of Tanaka (Tanaka, 1974), is also proposed. Furthermore, a method is developed to decompose the peridynamic J-integral separately into mode-I and mode-II. The decomposed J-integral values are then used to compute and analyze the change in the stress intensity factor of each mode during crack propagation. The proposed model is validated by comparison with existing experimental results and shows that a mixed-mode fatigue crack growth rate can accurately be predicted under various load conditions. Additionally, the associated computation time is significantly reduced by formulating a matrix-based peridynamic code that uses a graphics processing unit.

[1]  Keisuke Tanaka,et al.  Fatigue crack propagation from a crack inclined to the cyclic tensile axis , 1974 .

[2]  Thomas H. Hyde,et al.  Mixed mode fatigue crack growth at 550°c under plane stress conditions in Jethete M152 , 1991 .

[3]  Erkan Oterkus,et al.  Fatigue failure model with peridynamic theory , 2010, 2010 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems.

[4]  F. Bobaru,et al.  Studies of dynamic crack propagation and crack branching with peridynamics , 2010 .

[5]  P. Paris.  A rational analytic theory of fatigue , 1961 .

[6]  T. K. Hellen,et al.  The calculation of stress intensity factors for combined tensile and shear loading , 1975 .

[7]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[8]  Youn Doh Ha,et al.  The formulation and computation of the nonlocal J-integral in bond-based peridynamics , 2012, International Journal of Fracture.

[9]  Arun K. Subramaniyan,et al.  Validation of a peridynamic model for fatigue cracking , 2016 .

[10]  S. Silling,et al.  A meshfree method based on the peridynamic model of solid mechanics , 2005 .

[11]  R. Forman,et al.  Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures , 1967 .

[12]  Won Ho Yang,et al.  Mixed mode fatigue crack growth in aluminum plates with composite patches , 2003 .

[13]  G. C. Sih,et al.  Mixed mode fatigue crack growth predictions , 1980 .

[14]  Erdogan Madenci,et al.  Peridynamics for fatigue life and residual strength prediction of composite laminates , 2017 .

[15]  Bahattin Kilic,et al.  Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials , 2008 .

[16]  N. P. Andrianopoulos,et al.  The T-criterion applied to ductile fracture , 1982 .

[17]  G Hua,et al.  Growth of Fatigue Cracks Under Combined Mode I and Mode II Loads , 1985 .

[18]  Stewart Andrew Silling,et al.  Crack nucleation in a peridynamic solid , 2010 .

[19]  Richard B. Lehoucq,et al.  Force flux and the peridynamic stress tensor , 2008 .

[20]  Robert Badaliance,et al.  Application of strain energy density factor to fatigue crack growth analysis , 1980 .

[21]  A. P. Berens,et al.  USAF Damage Tolerant Design Handbook: Guidelines for the analysis and Design of Damage Tolerant Aircraft Structures. Revision A , 1984 .

[22]  E. Madenci,et al.  Prediction of crack paths in a quenched glass plate by using peridynamic theory , 2009 .

[23]  S. Silling,et al.  Peridynamic States and Constitutive Modeling , 2007 .

[24]  Rohan Panchadhara,et al.  Application of peridynamic stress intensity factors to dynamic fracture initiation and propagation , 2016, International Journal of Fracture.

[25]  Pericles S. Theocaris,et al.  Authors' closure on the discussion by G. C. Sih, E. T. Moyer Jr. and E. E. Gdoutos of “the mises elastic-plastic boundary as the core region in fracture criteria” , 1984 .

[26]  R. Pandey,et al.  FATIGUE CRACK GROWTH UNDER MIXED MODE LOADING , 1981 .

[27]  Erdogan Madenci,et al.  Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence , 2016 .

[28]  Jeehyun Jung,et al.  Fatigue crack growth analysis in layered heterogeneous material systems using peridynamic approach , 2016 .

[29]  H. O. Fuchs,et al.  Metal fatigue in engineering , 2001 .

[30]  F. Erdogan,et al.  Fatigue and fracture of cylindrical shells containing a circumferential crack , 1970 .

[31]  Sandia Report,et al.  Peridigm Users' Guide v1.0.0 , 2012 .

[32]  Stewart Andrew Silling,et al.  Peridynamic model for fatigue cracking. , 2014 .

[33]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[34]  Chingshen Li,et al.  VECTOR CTD CRITERION APPLIED TO MIXED MODE FATIGUE CRACK GROWTH , 1989 .

[35]  Justin Schwartz,et al.  A two‐dimensional ordinary, state‐based peridynamic model for linearly elastic solids , 2014 .

[36]  G. Sih.  Strain-energy-density factor applied to mixed mode crack problems , 1974 .