Commercial FEM Codes Customisations for Creep-Fatigue Damage Assessment. University of Naples Federico II Italy

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1 Industry Sector Aerospace RTD Thematic Area Durability and Life Extension Date 3 th June 2002 Commercial FEM Codes Customisations for Creep-Fatigue Damage Assessment Summary Mauro Fontana, Leonardo Lecce, Antonio De Iorio *, Francesco Penta * ( ) Dipartimento di Progettazione Aeronautica Via Claudio, Napoli (*) Dipartimento di Progettazione e Gestione Industriale P.le Tecchio, Napoli University of Naples Federico II Italy mfontana@unina.it - leonardo@unina.it - antdeior@unina.it - penta@unina.it Introduction; Fatigue damage assessment for non-linear solids; Creep-Fatigue damage evaluation; FE creep-fatigue evaluation example; FE Kachanov-Rabotnov creep model; Conclusions; References.

2 Introduction Finite Element Analysis (FEA) gives the possibility of doing fatigue and creep calculations before making prototypes. Fatigue assessment strain-life approach let deal with local plasticity effects that are the primary cause of crack initiation. The local time history of stress and strain, where the crack is going to start, is the critical factor that is put in evidence using FEA. Most commercial codes have already tools for fatigue and creep life assessment, however they do not allow to evaluate automatically the effect of creep-fatigue interaction, nor to carry out coupled analysis when material degradation strongly affects stress and strain distributions Difficulties arise when interaction of the fatigue and creep damages has to be simulated and, moreover, when Damage Mechanics models are implemented. 2

3 Introduction Creep-Fatigue interaction, Crack Propagation, Damage Mechanics, Material degradation, are among the new requirements for mechanical CAE design phase in industry, and FE codes suitable to be user customised are well suited for this aim. Research activities in this field are carried out by the authors for jet-engine components damage assessment, in collaboration with Fiat Avio, plant of Naples, one of outstanding industry for aeronautic propulsion systems. FE software let user programmable features that are not always so user friendly, even if they are among the most attractive items in software purchasing. Very often, in code customisation, most of the work is done to manage the exchange of the standard and user-defined variables, between the main and the sub-routines. Another critical step is the identification of suitable benchmarks to validate user procedures, as in the case of user defined material behaviour. A method for customised fatigue analysis, a first attempt of introducing creep-fatigue damage interaction and creep damage mechanic, made among the current research activities using commercial FE, are reported in the following slides. 3

4 Fatigue damage assessment for non-linear solids At present, the most reliable methods are based on the results of an elastic stress analysis of the component: evaluation of the theoretical stress concentration factor K T from which the fatigue notch factor K f is deduced by the expression of the notch sensitivity factor q (if the stress life approach is adopted), otherwise the plastic strain amplitude at the notch root is evaluated by the Neuber rule and the tensile stress-strain curve (strain-life approach). Several post-processors have special routines by which it is possible to carry out automatically the following fundamental tasks: load or nominal stress-history analysis to the definition of the load spectrum by a cycle counting technique; specific damage evaluation by the ε - N or S - N experimental curves; cumulated damage evaluation for the whole load-history of the component. The previous methods can not be used to evaluate multi-axial fatigue damage. In this latter case, when ad hoc software are not available, a special tool has to be prepared to analyse the numerical data supplied by the solver of the commercial FE code by a multi-axial fatigue strength criterion. This problem can be solved if the post-processor can be programmed by means of an high level language able to operate directly on the data structures of the solver. 4

5 Fatigue damage assessment for non-linear solids In the problem that was solved by Iannuzzi [], multi-axial fatigue damage was calculated by the Dang Van Papadopoulos criterion [2,3]: failure takes place when the amplitude C a of the shear stress vector C (which describes a closed curve Ψ ) attains a critical value that is dependent on the material. In this procedure, the elastic stress distribution was calculated by the ANSYS code. Output data of the solver were analysed by the ANSYS post-processor using an APDL macro (Ansys Parametric Design Language). Indeed, the APDL has the control structures (repeating, branching, looping) for the implementation of any algorithm and the functions to fetch the output data of the solver that are stored in the Ansys database (*GET command). The closed curves described by the stress vectors 5

6 Creep-Fatigue damage evaluation A very effective and promising approach to evaluate the creep-fatigue life is that inspired to Continuum Damage Mechanics [see ref 4-6]: the effects of creep-fatigue interaction are quantified by a damage variable that is representative of the material weakening due to the interaction of the phenomena. The analysis by the finite element method of a component, when a significant stress or strain rate redistribution can take place due to damage accumulation, has to be carried out by specialized codes, since the constitutive models need of special routines both for the stresses updating at the integration points, the evaluation of internal nodal forces and the data storing. The problem has to be solved by the incremental technique: the load history is divided in steps small enough and, to solve the non linear equilibrium equation, the iterative Newton- Raphson solution method has to be adopted; each iteration produces a correction for the nodal displacements vector: [ ] T nr { u } = [ K ] ( { F } { F }) i i T being K i the structure tangent stiffness matrix, the actual load vector and the restoring force vector calculated from the element stresses. At the end of each iteration the updating of the stresses at the element integration point has to be executed in order to evaluate the new restoring force vector and to assembly the structure tangent matrix. a i 6

7 Creep-Fatigue damage evaluation Commercial codes having an open architecture allows the customisation by C or Fortran subroutines that have to be linked to the main code. When special constitutive models have to be implemented (such as Continuum Damage Mechanic models) the ANSYS code offers the possibility to carry out the link with the following user-written subroutines: userpl to calculate the plastic strain changes at the integration points and the corresponding tangent stiffness matrix; usercr, usercreep to calculate the creep strain changes; uservp to evaluate the changes of visco-plastic strain and update the stresses at the integration points of the VISCOXXX elements. When the constitutive model has internal variables, e.g. damage variable, their values at the end of each stress and/or strain updating have to be saved (to trace the state of the elements at the next stress and/or strain updating) and at the end of each load step for the data post-processing. A first step to creep-fatigue interaction analysis has been carried out by the linear damage summation, integrating FE results with experimental data. 7

8 Creep - Fatigue linear damage summation in a cylindrical combustor by FE software Research activities in collaboration with Fiat Avio, Naples ANSYS was used for stress-strain analyses, submodelling and post-processing [7]: Linear analysis for global coarse model Non-linear analysis for fine meshed sub-models of devices LCF analysis based on experimental ε -N curves Creep analysis based on Norton model φ holes = 0.4 mm Cooling Device 30 Thermal distribution on liner (Tmax) Tref = 20 C length = 56.5 mm radius = 47 mm thickness = 0.8 mm p = 5 bar p = 8 kpa Sub-models φ hole = 5 mm Dilution hole Fuel flow φ holes = 0.4 mm Cooling Device 90 8

9 Radial displacements (mm) for a thermal load Tmax-Tref cycle Non linear analysis let residual plastic deformation evaluation Device 30 Device 90 Temperature T max Tref Dilution hole Cooling air flow Unwrapped liner cylindrical surface t Tmax temperature distribution [ C] Liner at Tmax Device 30deg at Tref Device 90deg at Tref Dilution hole at Tref 9

10 LCF cycles to failure assessment for one Tmax -Tref cycle Total strain amplitude let N f assess in a cycle LCF experimental data R=- Von Mises equivalent strain at Tmax Von Mises equivalent strain at Tref Device 30 deg ε Total Strain % N f cycles 800 C 600 C 300 C Cycles to failure Fatigue D f = damage n N f 0

11 Creep Fatigue damage after one cycle FE creep after hour a Tmax and experimental creep data let damage evaluation Creep Damage Creep strain Part of Device 30 deg Total damage is given by linear sum of two damages Both them have been calculated by the integration of FE results with experimental data, by an external to FE software elaboration. D c c = ε ε ( σ ) Ductility exhaustion R D = D + D T f c Creep damage Total damage

12 2 Kachanov-Rabotnov Creep model by user routine in ANSYS Research activities in collaboration with Fiat Avio, Naples The model describes creep brittle fracture, considering damage influence on creep rate [8]. Creep rate Damage rate t=0 ω = 0 & ε c = 0 t σ=cost Solution is: ; integer 0 < ω < damaged material Creep test are simulated by FE, based on experimental database to evaluate material parameters ν, φ, n, ε f, t f [9]. Plain specimen for lab creep test: 90 mm length; φ min = 8 mm Creep test at constant stress and temperature FEM model: 575 Axial symmetric PLANE42 elements, 696 nodes User customisation for Kachanov-Rabotnov model Element killing technique was applied to damaged elements n o o c = ) ( ω σ σ ε ε & & ϕ ν ω σ σ ω ω ) ( = o o & & ϕ ω + = f t t = + + ϕ ϕ ε ε n f f c t t

13 K-R Creep customisation routine Example test: Temp. = 600 C Constant Tensile = 400MPa Solution User routine 0 t t f automatic time step t usercr (elem, t, t,τ, σ, ε cr, ε cr ) yes Ansys-main Selection & Killing of elements in data tables with critical damage values ω c G.E t.0e-6 no stress and temperature dependent Kachanov-Rabtonov ν, φ, n, ε f, t f parameters evaluation ε cr, ε cr, ω end usercr Input files data tables in main Files Print (elem, ω) Data table 3

14 Kachanov-Rabotnov creep strain curves FE model creep strain curves at several stress and temperature value couples Secondary and tertiary creep is represented Small differences between experimental data and model 400MPa 450MPa 500MPa 550 MPa Experimental FE model T= 600 C epcr E+00.00E E E E E E E E E+02.00E+03 tim e (hour s) 600 C - 400MPa epcr time(hours) epcr epcr Experimental T=550 C T=600 C T=630 C FE model Stress=500MPa E+00.00E E E E E E E E E+02 time(hours) 950 C-35MPa time(hours) 4

15 Kachanov-Rabotnov specimen damage Damage starts near specimen axis at notch, where element killing starts FE damage ω evolution rupture at notch for 600 C and 400 MPa test, and stress distribution. killed elements (ω G.E. ω c ). Symmetry axis Symmetry axis middle gage length middle gage length Rupture 600 C 400MPa Time = 904hr t f = 925hr 600 C 400MPa Time = 924hr t f = 925hr Symmetry axis Symmetry axis middle gage length middle gage length 600 C 400MPa Time = 93hr t f = 925hr Stress at t = 924hr 5

16 Conclusions Software customisation let us: Fatigue damage assessment for non-linear solids; A first approach to creep-fatigue life assessment by summing of damage ; Tools for local analyses until rupture (tertiary creep) for mechanical components; The possibility to use a virtual laboratory for creep tests; Damage distribution post-processing; Work in progress is: Management of user defined variables for damage post-processing in main software; Combination of plastic and creep by user defined routines; Introduction of statistic and probabilistic aspects in damage prediction. 6

17 References [] R. Iannuzzi, Multi-axial H.C.F. Application, Seminar on Multiaxial Fatigue, (scientific coordinator: A. De Iorio), Capri, 20-2 July 2000, Naples, Italy. [2] K. Dang Van, A. Le Douron, H.P. Lieurade, Multiaxial fatigue limit: a new approach, Advance in Fracture Research, Proc. 6 th Int. Conf. Fract. (I.C.F. 6), pp , Pergamon Press, Oxford, 984. [3] I.V. Papadopoulos, Fatigue polycyclic des metaux : une nouvelle approche, These de Doctorate, Ecole Nationale des Ponts et Chaussées, Paris, 987. [4] F.P.E. Dunne, D.R. Hayrust, Efficient cycle jumping techniques for the modelling of materials and structures under cyclic mechanical and thermal loading, Eur. J. Mech., A/Solids, 3, 5, , 994. [5] J. Lemaitre, J.L. Chaboche, Machanique des Materiax Solides, Dunod Publ., Paris, 985. [6] A. Plumtree, J. Lemaitre, Application of Damage Concepts to predict creep-fatigue failures, ASME, Press. Vessels and Piping Conf., Montreal, 979. [7] M. Fontana, Metodologie per la Valutazione del Danno da Creep-Fatica, Tesi di Dottorato, CUEN s.r.l - Napoli, Febbraio 200. [8] L.M. Kachanov, On the Time to Failure under Creep Conditions, Izv. Akd. Nauk. SSR. Otd. Tekhen N.8 (958), 26 3 [9] A. Lagreca, Analisi numerica del danneggiamento da creep mediante il modello di Kachanov, Tesi di Laurea, D.P.A., Luglio