Stress intensity factor calculation through thermoelastic stress analysis, finite element and RPIM meshless method

Abstract This work aims at determining the stress intensity factor (SIF) for a compact tension specimen (CT) during a fatigue crack growth test with Thermoelastic Stress Analysis (TSA). Additionally, the problem is addressed using advanced discretization techniques, Radial Point Interpolation Meshless method (RPIM) and Finite Element Method (FEM) to obtain a stress distribution and calculate SIF range. Based on an optimization procedure, a functional stress relation was designated where the TSA analysis relies upon. The stress fields obtained with the FEM and the RPIM, are graphically represented and both methodologies are compared with the experimental TSA analysis in the presence of mode I fatigue loading test. The stress field in front of the crack tip is obtained with TSA and used in Williams series expansion, together with an overdeterministic algorithm to compute the SIF under mode I loading. This proposed procedure possesses a hybrid experimental-computational feature in which the SIF determination hinges on a stress field obtained with an optical technique, TSA. The robustness of the numerical FE and RPIM computations were thereby experimentally validated with the achieved SIF solution.

[1]  J. M. Dulieu-Barton,et al.  Introduction to thermoelastic stress analysis , 1999 .

[2]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[3]  Sharif Rahman,et al.  A coupled meshless-finite element method for fracture analysis of cracks , 2001 .

[4]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[5]  Rinze Benedictus,et al.  A review of T-stress and its effects in fracture mechanics , 2015 .

[6]  Haim Waisman,et al.  An analytical stiffness derivative extended finite element technique for extraction of crack tip Strain Energy Release Rates , 2010 .

[7]  O. Zienkiewicz,et al.  The finite element method in structural and continuum mechanics, numerical solution of problems in structural and continuum mechanics , 1967 .

[8]  Aaron Kuchle,et al.  Finite elements in fracture mechanics : theory, numerics, applications , 2013 .

[9]  S. Rahman,et al.  Probabilistic fracture mechanics by Galerkin meshless methods – part I: rates of stress intensity factors , 2002 .

[10]  Neal F. Enke,et al.  An Enhanced Theory for Thermographic Stress Analysis of Isotropic Materials , 1989, Other Conferences.

[11]  L. P. Pook,et al.  A fracture mechanics analysis of fatigue crack growth data for various materials , 1971 .

[12]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[13]  D. Rooke,et al.  Numerical Fracture Mechanics , 1990 .

[14]  Robert E. Rowlands,et al.  Determining stress intensity factors in orthotropic composites from far-field measured temperatures , 2004 .

[15]  Esben Byskov,et al.  The calculation of stress intensity factors ssing the finite element method with cracked elements , 1970 .

[16]  Behzad V. Farahani,et al.  The Axisymmetric Analysis of Circular Plates Using the Radial Point Interpolation Method , 2015 .

[17]  P. Stanley,et al.  Quantitative stress analysis by means of the thermoelastic effect , 1985 .

[18]  R. Tomlinson,et al.  Thermoelasticity for the analysis of crack tip stress fields — a review , 1999 .

[19]  Alberto Carpinteri,et al.  Numerical analysis of fracture mechanisms and failure modes in bi-layered structural components , 2007 .

[20]  Behzad V. Farahani,et al.  A meshless method in the non-local constitutive damage models , 2016 .

[21]  J. Z. Zhu,et al.  The finite element method , 1977 .

[22]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[23]  Guirong Liu,et al.  On the optimal shape parameters of radial basis functions used for 2-D meshless methods , 2002 .

[24]  Bo Wang,et al.  On the computation of stress intensity factors for interfacial cracks using quarter-point boundary elements , 1997 .

[25]  O. W. Dillon,et al.  A nonlinear thermoelasticity theory , 1962 .

[26]  W. Thomson.  LV. On the dynamical theory of heat.—Part VI. Thermoelectric currents , 1856 .

[27]  T. Belytschko,et al.  A new implementation of the element free Galerkin method , 1994 .

[28]  Jorge Belinha,et al.  Meshless Methods in Biomechanics: Bone Tissue Remodelling Analysis , 2014 .

[29]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[30]  R. J. Sanford,et al.  A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns , 1979 .

[31]  Majid R. Ayatollahi,et al.  Mixed mode fatigue crack initiation and growth in a CT specimen repaired by stop hole technique , 2015 .

[32]  Janice M. Dulieu-Barton,et al.  Thermoelastic stress analysis of damage mechanisms in composite materials , 2010 .

[33]  P.M.S.T. de Castro,et al.  Three-dimensional stress intensity factor calibration for a stiffened cracked plate , 2009 .

[34]  Meinhard Kuna,et al.  Finite Elements in Fracture Mechanics , 2013 .

[35]  G. M. Everett.  Comparison Between The Thermoelastic Method And Other Experimental Techniques For Stress Measurement , 1989, Other Conferences.

[36]  Antonino Squillace,et al.  Thermoelasticity and CCD analysis of crack propagation in AA6082 friction stir welded joints , 2009 .

[37]  Gianluca Rossi,et al.  Thermoelasticity for the evaluation of fatigue behavior of 7005/Al2O3/10p metal matrix composite sheets joined by FSW , 2008 .

[38]  T. Belytschko,et al.  Fracture and crack growth by element free Galerkin methods , 1994 .

[39]  T. Anderson,et al.  Fracture mechanics - Fundamentals and applications , 2017 .

[40]  Paulo J. Tavares,et al.  SIF determination with digital image correlation , 2015 .

[41]  S. Rahman,et al.  An efficient meshless method for fracture analysis of cracks , 2000 .

[42]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..

[43]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[44]  Behzad V. Farahani,et al.  Extending a radial point interpolation meshless method to non-local constitutive damage models , 2016 .

[45]  J. Altenbach.  Zienkiewicz, O. C., The Finite Element Method. 3. Edition. London. McGraw‐Hill Book Company (UK) Limited. 1977. XV, 787 S. , 1980 .

[46]  M. Sutton,et al.  Estimation of stress intensity factor by digital image correlation , 1987 .

[47]  M. Aliabadi,et al.  Boundary Element Methods in Engineering and Sciences , 2010 .

[48]  On the computation of two-dimensional stress intensity factors using the boundary element method , 1988 .

[49]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[50]  Robert J. Sanford,et al.  Application of the least-squares method to photoelastic analysis , 1980 .

[51]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[52]  Michael B. Bever,et al.  The thermoelastic effect in iron and nickel as a function of temperature , 1950 .

[53]  Ted Belytschko,et al.  An extended finite element method for modeling crack growth with frictional contact , 2001 .