XFEM裂纹扩展范例

Variable Amplitude Fatigue Crack Growth Using Surrogate Models and Exact XFEM Reanalysis

Matthew PaisMarch 31, 2011

Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

Acknowledgements Dr. Kim for your comments and help throughout my time at UF, you have taught me how to research and deal with obstacles encountered along the way

Alex Coppe for our collaboration on the identification of equivalent damage parameters from XFEM data Dr. Davis and Nuri Yeralan for our collaboration on the formulation and implementation of the exact XFEM reanalysis algorithm Dr. Peters for our collaboration on the use of an element-based enrichment scheme for modeling weak discontinuities independent of the FE mesh Richard Pippy who originally created the finite element wing box model which was modified as part of the analysis of AFRL flight data Ben Smarslok and Eric Teugel at ARFL for providing the flight data Felipe Viana for our collaboration on the use of kriging for enabling higher-order integration of fatigue crack growth models and Dr. Haftka for an idea leading to the creation of the variable step size algorithmCommittee members for your willingness to serve and contributions to the improvement of my dissertation

MDO group for all the feedback which contributed to the improvement of this workStructural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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Acoustic Emission Sensors Data Estimate of Damage Size3 Estimate of Material Properties/Remaining Life2

Add Weight Traditional Sensors Data Convert Data to Stress History Damage Growth on Digital Twin Life Estimate of Panel/Airplane

Uncertainty in Location/Size

In Development

Conditional Maintenance1Black, 2Coppe,

Structural health monitoring: Composites get smart, 2008. Simplified damage growth models can still yield accurate prognosis, submitted. 3An, Experimental study on identifying cracks of increasing size using ultrasonic excitation, 2011. Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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Constant Amplitude Loading

Overload

R= min N Variable Amplitude Loading Biaxial Variable Amplitude Loading

max

Underload

N

xx xy yyN

N Proportional loading Non-proportional loading

xx : xy : yy – ratio is constant as a function of N xx : xy : yy – ratio changes as a function of NStructural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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xx xy yyN N

N

a or N

?

Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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Overview Fatigue crack growth Stress intensity factor evaluation – Extended Finite Element Method (XFEM) – Exact XFEM reanalysis algorithm Integration of fatigue crack growth models – Surrogate models for high-order in

tegration – Surrogate models for variable integration step size Variable amplitude fatigue crack growth from flight data – Crack tip plasticity – Conversion of flight data to biaxial stress histories – Example problem and discussion ConclusionsStructural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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Computational Fatigue High-cycle fatigue (104-108 cycles to failure) Fatigue growth model is ordinary differential equation Some analytical equations for K for simple geometries Finite element method to calculate K for complex geometryda f K , R dN

Constant amplitude fatigue – Crack growth increment a or N reduces number of simulations – Creates error in integration of fatigue growth model/crack path Biaxial variable amplitude fatigue – Crack has preferred growth direction for history or for each cycle (nonproportional) – No prior knowledge of crack path, how to have a- K relationship? – Plasticity accelerates/slows crack growth

Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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Paris Modelda , log scale dN da m C K dNm

C11Paris, A rational

Kth

K , log scaleStructural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

analytic theory for fatigue, The Trend in Eng., 1961.

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Direct and Indirect Solution to ODE Direct Solution to ODENumber of elapsed cycles for iteration, N. Given a crack Calculate KI, KII Calculate crack growth direction Convert KI, KII into Keq Calculate a from fatigue model Grow crack by calculated direction/magnitudeStructural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

Indirect solution to ODEAssumed crack growth for iteration, a.

Use given a

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Extended Finite Element Method Contour integrals to calculate KI, KII

The extended finite element method1 (XFEM) eliminates need to recreate mesh2 locally around crack tip as crack growthsEnrichment functions/DOFs added to displacement approximation and are active in elements with discontinuity – Enriched element – Traditional element – Crack tip enriched node – Heaviside enriched noden u N I u I H Ia I I, b I 1 h

1Belytschko,

Elastic crack growth in finite elements with minimal remeshing, Int. J. Num. Meth. Eng., 1999. numerical study of fatigue crack growth using remeshing, Eng. Frac. Mech., 2010. 3Osher, Fronts propagating with curvature dependent speed, J. Comp. Phys., 1988.2Maligno, A three-dimensional

Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department

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