Modelling fatigue crack growth in Shape Memory Alloys

We present a phase field-based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalised phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker-Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearised system is solved using a robust monolithic scheme, based on quasi-Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress-strain hysteresis and temperature. Namely, we compute ∆ε−N curves, quantify Paris law parameters and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large-scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.

[1]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[2]  Hirshikesh,et al.  Phase field modelling of crack propagation in functionally graded materials , 2019, Composites Part B: Engineering.

[3]  Emilio Mart'inez-Paneda,et al.  A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement , 2020, Journal of the Mechanics and Physics of Solids.

[4]  S. W. Robertson,et al.  Mechanical fatigue and fracture of Nitinol , 2012 .

[5]  A. Heckmann,et al.  Structural and functional fatigue of NiTi shape memory alloys , 2004 .

[6]  Vikram Deshpande,et al.  The compressive and shear responses of corrugated and diamond lattice materials , 2006 .

[7]  Peter Wriggers,et al.  A global-local approach for hydraulic phase-field fracture in poroelastic media , 2020, Comput. Math. Appl..

[8]  M. Kadkhodaei,et al.  Fatigue analysis of shape memory alloy helical springs , 2019, International Journal of Mechanical Sciences.

[9]  D. Lagoudas,et al.  On the Fracture Toughness of Pseudoelastic Shape Memory Alloys , 2014 .

[10]  M. Paggi,et al.  Phase field modeling of fracture in Functionally Graded Materials: Γ-convergence and mechanical insight on the effect of grading , 2020 .

[11]  Vinh Phu Nguyen,et al.  Phase-field modeling of fracture , 2019 .

[12]  Cv Clemens Verhoosel,et al.  A phase-field description of dynamic brittle fracture , 2012 .

[13]  A. Y. Elghazouli,et al.  A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver , 2021, ArXiv.

[14]  D. Lagoudas,et al.  Fracture mechanics of shape memory alloys: review and perspectives , 2015, International Journal of Fracture.

[15]  Phase-field modelling of crack propagation , 2021 .

[16]  E. Mart'inez-Paneda,et al.  A mechanism-based gradient damage model for metallic fracture , 2021, ArXiv.

[17]  Julien Michels,et al.  Fatigue behavior of a Fe-Mn-Si shape memory alloy used for prestressed strengthening , 2017 .

[18]  Zhi-qian Zhang,et al.  Fourth‐order phase field model with spectral decomposition for simulating fracture in hyperelastic material , 2021 .

[19]  Z. D. Wang,et al.  Effects of triaxial stress on martensite transformation, stress–strain and failure behavior in front of crack tips in shape memory alloy NiTi , 2010 .

[20]  Philip K. Kristensen,et al.  Applications of phase field fracture in modelling hydrogen assisted failures , 2020, Theoretical and Applied Fracture Mechanics.

[21]  C. Maletta,et al.  Crack tip stress distribution and stress intensity factor in shape memory alloys , 2013 .

[22]  Emilio Mart'inez-Paneda,et al.  A phase field formulation for hydrogen assisted cracking , 2018, Computer Methods in Applied Mechanics and Engineering.

[23]  Philip K. Kristensen,et al.  An assessment of phase field fracture: crack initiation and growth , 2021, Philosophical Transactions of the Royal Society A.

[24]  George Papazafeiropoulos,et al.  Abaqus2Matlab: A suitable tool for finite element post-processing , 2017, Adv. Eng. Softw..

[25]  L. Anand,et al.  On modeling fracture of ferritic steels due to hydrogen embrittlement , 2019, Journal of the Mechanics and Physics of Solids.

[26]  Peter K. Liaw,et al.  The fatigue behavior of shape-memory alloys , 2000 .

[27]  Wei Tan,et al.  Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites , 2020, Composites Science and Technology.

[28]  R. Ritchie,et al.  Hyperelastic phase-field fracture mechanics modeling of the toughening induced by Bouligand structures in natural materials , 2019, Journal of the Mechanics and Physics of Solids.

[29]  Ferdinando Auricchio,et al.  Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior , 1997 .

[30]  J. Marigo,et al.  Gradient Damage Models and Their Use to Approximate Brittle Fracture , 2011 .

[31]  Vinh Phu Nguyen,et al.  On the BFGS monolithic algorithm for the unified phase field damage theory , 2020 .

[32]  Emilio Mart'inez-Paneda,et al.  Phase field modelling of fracture and fatigue in Shape Memory Alloys , 2020, Computer Methods in Applied Mechanics and Engineering.

[33]  Emilio Mart'inez-Paneda,et al.  A phase field model for hydrogen-assisted fatigue , 2021, International Journal of Fatigue.

[34]  Yao Xiao,et al.  Constitutive modelling of transformation pattern in superelastic NiTi shape memory alloy under cyclic loading , 2020 .

[35]  Jean-Jacques Marigo,et al.  Crack nucleation in variational phase-field models of brittle fracture , 2018 .

[36]  Hehua Zhu,et al.  Phase field modelling of crack propagation, branching and coalescence in rocks , 2018, Theoretical and Applied Fracture Mechanics.

[37]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[38]  E. Hornbogen.  Some effects of martensitic transformation on fatigue resistance , 2002 .

[39]  Dimitris C. Lagoudas,et al.  Aerospace applications of shape memory alloys , 2007 .

[40]  D. Lagoudas,et al.  A unified description of mechanical and actuation fatigue crack growth in shape memory alloys , 2021 .

[41]  Jihong Zhu,et al.  Finite element simulation of thermomechanical training on functional stability of shape memory alloy wave spring actuator , 2019, Journal of Intelligent Material Systems and Structures.

[42]  B. Bourdin,et al.  Numerical experiments in revisited brittle fracture , 2000 .

[43]  H. Sehitoglu,et al.  Effects of Temperature on Fatigue Crack Propagation in Pseudoelastic NiTi Shape Memory Alloys , 2019, Shape Memory and Superelasticity.

[44]  D. Lagoudas,et al.  On the Experimental Evaluation of the Fracture Toughness of Shape Memory Alloys , 2018 .

[45]  Chuanjie Cui,et al.  A phase field formulation for dissolution-driven stress corrosion cracking , 2020, ArXiv.

[46]  Emilio Mart'inez-Paneda,et al.  Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme , 2019, Theoretical and Applied Fracture Mechanics.

[47]  A. A. Griffith.  The Phenomena of Rupture and Flow in Solids , 1921 .

[48]  Albert Turon,et al.  A phase field approach to simulate intralaminar and translaminar fracture in long fiber composite materials , 2019, Composite Structures.

[49]  Nikolas Provatas,et al.  Phase-Field Methods in Materials Science and Engineering , 2010 .

[50]  P. Alam.  ‘E’ , 2021, Composites Engineering: An A–Z Guide.

[51]  B. Bourdin,et al.  The Variational Approach to Fracture , 2008 .

[52]  Shuichi Miyazaki,et al.  Effect of mechanical cycling on the pseudoelasticity characteristics of TiNi and TiNiCu alloys , 1995 .

[53]  D. Lagoudas.  Shape memory alloys : modeling and engineering applications , 2008 .

[54]  Vinh Phu Nguyen,et al.  A length scale insensitive phase field model for brittle fracture of hyperelastic solids , 2020 .

[55]  Tinh Quoc Bui,et al.  A review of phase-field models, fundamentals and their applications to composite laminates , 2021 .

[56]  L. De Lorenzis,et al.  A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach , 2018, 1811.02244.

[57]  D. Lagoudas,et al.  A UNIFIED THERMODYNAMIC CONSTITUTIVE MODEL FOR SMA AND FINITE ELEMENT ANALYSIS OF ACTIVE METAL MATRIX COMPOSITES , 1996 .

[58]  Klaus Neuking,et al.  Direct physical evidence for the back-transformation of stress-induced martensite in the vicinity of cracks in pseudoelastic NiTi shape memory alloys , 2009 .

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

[60]  Thomas J. R. Hughes,et al.  A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects , 2016 .

[61]  G. Wang,et al.  A finite element analysis of evolution of stress-strain and martensite transformation in front of a notch in shape memory alloy NiTi , 2007 .

[62]  Robert O Ritchie,et al.  In vitro fatigue-crack growth and fracture toughness behavior of thin-walled superelastic Nitinol tube for endovascular stents: A basis for defining the effect of crack-like defects. , 2007, Biomaterials.

[63]  Stefano Vidoli,et al.  Comparison of Phase-Field Models of Fracture Coupled with Plasticity , 2018 .

[64]  D. Lagoudas,et al.  On the fracture toughness enhancement due to stress-induced phase transformation in shape memory alloys , 2013 .

[65]  D. Lagoudas,et al.  Fracture toughness of NiTi–Towards establishing standard test methods for phase transforming materials , 2019, Acta Materialia.

[66]  Michael Ortiz,et al.  A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture , 2021, ArXiv.

[67]  Dimitris C. Lagoudas,et al.  Thermomechanical fatigue of shape memory alloys , 2009 .

[68]  L. Banks‐Sills,et al.  Crack growth resistance of shape memory alloys by means of a cohesive zone model , 2007 .

[69]  Ferdinando Auricchio,et al.  Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior , 1997 .

[70]  Xiaoping Zhou,et al.  Simulation of cracking behaviours in interlayered rocks with flaws subjected to tension using a phase‐field method , 2019, Fatigue & Fracture of Engineering Materials & Structures.

[71]  Emilio Mart'inez-Paneda,et al.  A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine , 2021, Materials.

[72]  Erhard Hornbogen,et al.  Review Thermo-mechanical fatigue of shape memory alloys , 2004 .