Numerical modelling of the microstructure effect on fatigue behaviour of Ni-base superalloys for turbine disk

Nickel-based alloy like N18 can present various types of precipitate distributions according to the applied heat treatment. A model involving a three scale homogenization procedure is developed to characterize the influence of this microstructure on fatigue life. The microstructural parameters are the size and the volume fraction of the secondary and tertiary precipitates of γ\u27 phase. Experimental results at 450 °C, specially designed to calibrate the model, allow to understand the role of tertiary precipitation. The first identification of the three scale homogenization model is shown

Link between the microstructure and the durability of polycrystalline materials: a fatigue damage model in an aluminium alloy

In polycrystalline alloys, fatigue damage is strongly influenced by the microstructure. Nowadays crystal plasticity models are used in order to take into account the crystallography and microstructural mechanisms but there is no consensus on crack initiation sites and their most significant mechanisms. The present work combines experimental tests and numerical simulations in order to understand and predict the physical mechanisms that lead to crack formation in high cycle fatigue in high-strength aluminium alloys for aerospace applications. The numerical simulations include a two parameters kinematic hardening. Experiments highlight the importance of two phenomena in fatigue crack initiation in connection with the microstructure. The first aspect is the surface roughness [1]; and our simulations succeed in putting forward the intrusion/extrusion phenomenon. The interest of large deformations in simulations is also discussed because of their effect on grain re-orientation and thus in surface roughness. The second phenomenon is progressive deformations; and the model achieves to account for it through local ratchetting and its effect on the crack initiation. We also intend to model stress relaxation, as its role is yet to be determined. In order to be able to extrapolate the mechanical behaviour over a large number of cycles, it is important to find the stabilized cycle [2]. Parallel simulations allow this to be done for representative crystalline aggregates. Finally, different macroscopic and mostly microscopic fatigue initiation parameters [3] are compared such as the Fatemi-Socie parameter, the stored energy or the commonly used cumulative plastic strain. It leads us to multiple fatigue site initiations, which we can compare with experimental results. The aim is to more accurately predict the site of fatigue crack initiation and the predominant mechanisms in fatigue crack initiation

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

This article has been made available through the Brunel Open Access Publishing Fund.A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations

Influence of residual stress and work hardening on instrumented indentation

Many forming and surface treatments for metallic materials introduce residual stresses and work hardening simultaneously in mechanical components. Instrumented indentation is a technique which is sensitive to both phenomena and can thus be used to quantify them provided that their influences on the experimental response can be separated. In the present paper, this question was addressed through a series of Finite Elements simulations of a spherical indentation test in which the residual stress and work hardening levels were varied independently. It was found that, for each given value of the compressive residual stress, there is a corresponding work hardening level (cumulated plastic strain) for which the two P-h curves (Force vs. Penetration Depth curves) are almost completely superposed. Therefore, it will be impossible to obtain a unique set of residual stress and work hardening from the analysis of the sole P-h curves. However, when the dimples left by the indenter are analyzed, it can be found that, for the same P-h curve, the two phenomena lead to a difference in pile-up value which is about 2% of the maximum penetration depth. The numerical simulations presented in the paper are obtained on a specific material with a spherical indenter but similar results were obtained on other materials with a spherical or a conical indenter

Cyclic inelastic constitutive equations of the hot turboengine components

International audienceThe hot section of aeronautical structures are subjected to complex thermal and mechanicalloads involving fatigue, creep and also creep-fatigue interaction and crack propagation.In order to correctly estimate the life assessment of components, a 3D cyclic inelastic analysis isnecessary. To do so, inelastic constitutive equations that are able to account all or major materialexperimental observations at different temperatures are used.In this contribution elasto-viscoplastic constitutive equations used in cyclic inelastic analysisare given. In particular, the recent progress of the crystal anisotropic law for the description ofsingle crystal superalloys (blades). Also, a new behavior model to better reflect the most frequentexperimental facts on combustion chambers materials under cyclic loading as very pronouncedhardening, dynamic strain aging, memory effect and static recovery at high temperature

Non-local damage-enhanced MFH for multiscale simulations of composites

In this work, a gradient-enhanced mean-field homogenization (MFH) procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material obeys an elasto-plastic behavior enhanced by a damage model. As classical finite element simulations face the problems of losing uniqueness and strain localization when strain softening of materials is involved, we develop the mean-field homogenization in a non-local way. Toward this end we use the so-called non-local implicit approach, reformulated in an anisotropic way to describe the damage in the matrix. As a result we have a multi-scale model that can be used to study the damage process at the meso-scale, and in particular the damaging of plies in a composite stack, in an efficient computational way. As a demonstration a stack with a hole is studied and it is shown that the model predicts the damaging process in bands oriented with the fiber directions.SIMUCOMP no 1017232 (CT-EUC 2010-10-12