Crack nucleation using combined crystal plasticity modelling, high

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    ResearchCite this article: Zhang T, Jiang J, Britton B,Shollock B, Dunne F. 2016 Crack nucleationusing combined crystal plasticity modelling,high-resolution digital image correlation andhigh-resolution electron backscatterdiffraction in a superalloy containingnon-metallic inclusions under fatigue. Proc. R.Soc. A 472: 20150792.http://dx.doi.org/10.1098/rspa.2015.0792

    Received: 16 November 2015Accepted: 11 March 2016

    Subject Areas:materials science

    Keywords:crystal plasticity, nickel, decohesion, fatiguecrack nucleation, interfacial strength

    Author for correspondence:Tiantian Zhange-mail: tiantian.zhang08@imperial.ac.uk

    Crack nucleation usingcombined crystal plasticitymodelling, high-resolutiondigital image correlation andhigh-resolution electronbackscatter diffraction in asuperalloy containingnon-metallic inclusions underfatigueTiantian Zhang1, Jun Jiang1, Ben Britton1, Barbara

    Shollock1,2 and Fionn Dunne1

    1Department of Materials, Imperial College London,London SW7 2AZ, UK2WMG, University of Warwick, Coventry CV4 7AL, UK

    JJ, 0000-0002-9050-6018

    A crystal plasticity finite-element model, whichexplicitly and directly represents the complexmicrostructures of a non-metallic agglomerateinclusion within polycrystal nickel alloy, has beendeveloped to study the mechanistic basis of fatiguecrack nucleation. The methodology is to use thecrystal plasticity model in conjunction with directmeasurement at the microscale using high (angular)resolution-electron backscatter diffraction (HR-EBSD) and high (spatial) resolution-digital imagecorrelation (HR-DIC) strain measurement techniques.Experimentally, this sample has been subjectedto heat treatment leading to the establishment ofresidual (elastic) strains local to the agglomerateand subsequently loaded under conditions of lowcyclic fatigue. The full thermal and mechanical

    2016 The Authors. Published by the Royal Society under the terms of theCreative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author andsource are credited.

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    loading history was reproduced within the model. HR-EBSD and HR-DIC elastic andtotal strain measurements demonstrate qualitative and quantitative agreement with crystalplasticity results. Crack nucleation by interfacial decohesion at the nickel matrix/agglomerateinclusion boundaries is observed experimentally, and systematic modelling studies enable themechanistic basis of the nucleation to be established. A number of fatigue crack nucleationindicators are also assessed against the experimental results. Decohesion was found to bedriven by interface tensile normal stress alone, and the interfacial strength was determinedto be in the range of 12701480 MPa.

    1. IntroductionNickel-based superalloys are widely used for turbine disc applications. Modern superalloyswith exceptional high temperature properties are produced via a powder metallurgy (PM) routein order to minimize micro/macrochemical segregation [1]. However, although great effortshave been made to reduce contamination introduced during manufacturing steps, non-metallicinclusions are inevitable in these alloys, resulting in degradation of mechanical properties andscatter in fatigue life. To address this issue, a series of studies have been carried out [2,3] toinvestigate the effects of inclusions under various conditions of loading, but it remains clearthat crack nucleation occurring at agglomerate inclusions remains a significant technological andscientific challenge [4], and this paper addresses the mechanistic basis by which it occurs in thenickel superalloys.

    The presence of non-metallic inclusions is common to a range of alloys in aluminium [57],steels [8] and nickel superalloys [9]. In the presence of these inclusions, cracks are rarelyobserved to nucleate in the surrounding metal matrix, but at the oxide inclusions either byoxide/metal decohesion or by fracture of oxide particles. Experimental observations indicate thatsuch crack nucleation occurs very early and eventually leads to the development of cracks intothe neighbouring microstructures.

    Interface decohesion has been studied extensively using cohesive zone modelling. Thecohesive zone theory relies on a phenomenological continuum framework with constitutiveequations that relate surface traction and displacement. Complete separation occurs when thecohesive traction across the decohering interfaces becomes zero [10]. The predictive capabilityof such a damage initiation model relies on accurate prediction of stress and strain fields atappropriate length scales. However, in the literature, criteria for void nucleation at interfaces arerelated to and defined with respect to macroscopic quantities [11] and typically, in these analyses,the constitutive behaviour of each phase present is not considered explicitly. Cohesive zonemodels with interface potential functions predicted by first principles density functional theory(DFT) simulations have been used for analyses of the atomistic separation of -Ni(Al)/Al2O3interfaces [12,13], and such strategies have been employed to address fracture of bimaterialinterfaces at various length scales. However, the use of DFT simulations to determine theoreticalinterfacial strengths for metalceramic systems is problematic, particularly when the detailedmetallurgy at the interface often remains elusive. An alternative strategy is to determinethe interfacial strengths at the granular length scale. The determination of cohesive zoneproperties at this scale has also remained problematic, but a potential solution exists bybringing together the results of detailed high (spatial) resolution digital image correlation (HR-DIC) and high (angular) resolution electron backscatter diffraction (HR-EBSD) measurements,together with microstructurally faithful crystal plasticity representations in order to extract outinterface properties.

    Recent advances in microstructure-sensitive crystal plasticity modelling in conjunction withexperimental validation have provided understanding of damage nucleation in dual phase (DP)steels [14], aluminium alloys [15] and tantalum oligocrystals [16]. In addition, by virtue ofdetailed microstructure-level comparison of model predictions with independent experimental

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    measurement, significant confidence has been developed in crystal modelling capabilities tocapture quantitatively microstructure-level strain, stress, stress state and dislocation density[1719].

    In previous studies [17,20], thermal residual strains and dislocation densities near non-metallicinclusions have been investigated by HR-EBSD and HR-DIC carried out in [20] have providedmicroscopic mapping of strain fields local to non-metallic inclusions. In the literature, full-fieldmapping of elastic strains and dislocation densities has been achieved by HR-EBSD in a widevariety of alloys [2123]. DIC and EBSD characterization has recently been applied for studies ofstrain partitioning between ferrite and martensitic phases in steels [14], and strain heterogeneitiesand lattice rotations in 304L stainless steel [24]. The HR-DIC and HR-EBSD techniques used inthe two consecutive analyses in [17,20] have enabled concurrent mapping of elastic strain, plasticstrain and dislocation density at key microstructural features.

    In this paper, we address the mechanistic basis of crack nucleation in nickel superalloy RR1000containing oxide particle inclusions under fatigue. Concurrent crystal plasticity modelling isemployed along with detailed HR-DIC (for total strain measurement), EBSD (for elastic strainand lattice rotation measurement) and micromechanical three-point beam testing with fullycharacterized microstructure in order to identify and quantify cracks and their nucleationsites. Grain-by-grain assessments of slip, plastic strain accumulation through ratcheting,maximum principal and hydrostatic stresses and stored energy are examined in the contextof experimentally observed fatigue crack nucleation sites in order to explain the mechanisticbasis. In 2, the overall methodology is summarized, detailing the experimental investigation,the multiscale modelling to establish appropriate submodel boundary conditions and thecrystal plasticity submodel explicit representation of the experimental beam microstructure.Computational and experimental comparison of results is presented to provide justificationfor, and confidence in, the model. This is followed by a systematic analysis of the slip, strainaccumulation, stress and stored energy occurring at sites of fatigue crack nucleation, and theassessment of the mechanistic basis for crack nucleation. In so doing, we present the extractedinterfacial strength between the nickel matrix and oxide particles forming the agglomerateinclusions in RR1000.

    2. Materials and methodology

    (a) Experimental methodology(i) Thermal treatment

    A RR1000 polycrystalline nickel-based superalloy sample was supplied by Rolls-Royce plc. Thesample was produced via a PM route, followed by extrusion, forging and a