Numerical Modeling of Fatigue Crack Growth in Single Crystals Based on Microdamage Theory

Abstract

Proper life-time prediction modeling of single crystalline components is of increasing importance due to their common use in turbine industry. Viscoplastic damage approaches are of great interest in that context. However, mechanical properties of single crystals are strongly anisotropic and nonlinear in service conditions, bringing certain complexity into constitutive and numerical modeling. The aim of this work is to develop a thermodynamically consistent constitutive model based on generalized continua in order to simulate fatigue crack initiation and growth in single crystals. For that purpose, a standard crystal plasticity model is taken as a basis and coupled with the continuous damage model developed by Marchal et al. MoretSurLoing, France, Presses de l'Ecole des mines de Paris, pp. 353358]. As a variant of micromorphic theory, microdamage approach is applied to the model in order to obtain a regularized continuum damage formulation which solves mesh dependency problem by introducing an intrinsic length scale. A detailed finite element implementation procedure and its validation for monotonic crack growth areshown. Fatigue crack growth analyses have been performed on a single edge notched geometry and a comparison between numerical and experimental results is presented.

Experimental and Computational Approach to Fatigue Behavior of Polycrystalline Tantalum

“…In that case, intergranular and transgranular cracks can be distinguished. Such a coupled crystal plasticity and damage model was proposed and applied to crack initiation and propagation in single crystal superalloys in [86]. This includes a gradient damage term which is necessary to obtain mesh-independent crack simulation results.…”

A Large-Deformation Gradient Damage Model for Single Crystals Based on Microdamage Theory

“…where I is a unit elastic modulus which converts unit strain into unit energy and β * is equivalent to β/B of the conventional approach. Note that in this framework the higher order terms 1 2 I(d − χ d) 2 and 1 2 β * |∇ χ d| 2 are very small compared to the standard elasticity terms, thus, the energy stored through higher order continuum can be ignored. Accordingly, the energetic terms become:…”

“…Highly anisotropic behavior of single crystals necessitates the consideration of microstructurally motivated life time estimation models. Considering the general use of single crystals in complex geometries under harsh environments such as turbine blades, modeling of crack growth due to the coupling of plasticity and damage becomes essential [1,2]. The chosen constitutive model should satisfactorily demonstrate the extremely anisotropic and nonlinear behavior of single crystals under severe thermomechanical loading conditions.…”

Analytical Solutions of Model Problems for Large-Deformation Micromorphic Approach to Gradient Plasticity

“…By Eringen's theory the gradient terms are naturally introduced through higher order degrees of freedom and thermodynamical consistency can be achieved in a systematic fashion by using the principle of virtual power. That track of micromorphic approach is further adopted to several strain gradient problems by Forest and Aslan [21][22][23][24][25] and unified to Gurtin's thermodynamics [26] by Anand et al [8].…”