Fatigue Indicator Parameters Research Articles

Strategies for rapid parametric assessment of microstructure-sensitive fatigue for HCP polycrystals

Traditionally, crystal plasticity finite element method (CPFEM) simulations have been used to capture the variability in the microstructure-scale response of polycrystalline metals. However, these types of simulations are computationally expensive and require significant resources. To explore the large space of microstructures (reflecting a variety of grain shape, size, and orientation distributions) within the practical constraints of computational resources, a more efficient strategy is required. The purpose of this work is to explore the viability of leveraging the recently established, high-throughput Materials Knowledge System (MKS) for fast evaluation of high cycle fatigue (HCF) performance of candidate microstructures. More specifically, we explore the feasibility of estimating the mesoscale strain fields in hexagonal close packed (HCP) α-titanium polycrystals during HCF loading conditions using the computationally low-cost MKS approach, and subsequently estimating the slip system activities via decoupled numerical integration of the relevant crystal plasticity (CP) constitutive relations. The computed slip activities are then used to arrive at extreme value distributions (EVDs) of fatigue indicator parameters (FIPs). As critical validation of this reduced-cost computational strategy, it is shown that the FIP distributions in the HCF regime estimated using this novel strategy are in reasonable agreement with those computed directly using the conventional CPFEM approach. Additionally, the computational advantages of the MKS and decoupled numerical integration approach over the traditional, computationally-expensive, CPFEM approach are presented and discussed.

Microstructure modeling and crystal plasticity simulations for the evaluation of fatigue crack initiation in α-iron specimen including an elliptic defect

In this study, fatigue crack initiation in pure α-iron is investigated through a microstructure-sensitive framework. At first, synthetic microstructures are modeled based on an anisotropic tessellation that accounts for the information of the grains morphology extracted from electron backscatter diffraction (EBSD) analysis. Low-cycle fatigue experiments under strain-controlled conditions are conducted in order to calibrate a crystal plasticity model and a J2 model including isotropic and kinematic hardening. A critical plane fatigue indicator parameter (FIP) based on the Tanaka-Mura model is then presented to evaluate the location and quantify the driving force for the formation of a crack. The FIP is averaged over several potential crack paths within each grain defined by the intersection between a given slip plane and the plane of the model thus accounting for both the lattice orientation and morphology of the grain. Several fatigue simulations at various stress amplitudes are conducted using a sub-modeling technique for the attribution of boundary conditions on the polycrystalline aggregate models including an elliptic defect. The influence of the microstructure attributes and stress level on the location and amplitude of the FIP are then quantified and discussed.

Fatigue hot spot simulation for two Widmanstätten titanium microstructures

A simulated microstructure-sensitive fatigue study has been performed for two titanium alloy microstructures. The investigated materials exhibit a Widmanstätten structure and include the α–β alloy Ti–6Al–4V and the near β alloy Ti-18 in a β-annealed, slow-cooled, and aged condition (BASCA). In other work [1], crystal plasticity models implemented into ABAQUS (2011) [2] UserMATerial subroutines have been calibrated to experimental cyclic deformation data for both materials. The current study utilizes calibrated crystal plasticity models to simulate fatigue loading of varying microstructures for each material to study the influence of key morphological and crystallographic aspects on the fatigue performance, e.g., the mean colony size, phase volume fraction, and crystallographic texture. Localized stress and plastic strain are studied via computation of fatigue indicator parameters (FIPs), which represent the driving force for fatigue crack formation and early propagation in the microstructure. The maximum FIP values are sampled over several stochastic simulations and are utilized to determine extreme value statistical distributions which demonstrate the trends in the microstructural influence on fatigue performance. Marked radial correlation functions developed by Przybyla and McDowell [3] have also been employed to study the correlation between favorably oriented slip systems and the extreme value FIP locations within the instantiated microstructures. The simulation results suggest that reduced lamellar colony sizes, reduced α-phase, and a transverse texture within a reference plane normal to the applied uniaxial loading direction can enhance resistance to formation and early growth of fatigue cracks.

Simulating the effect of grain boundaries on microstructurally small fatigue crack growth from a focused ion beam notch through a three-dimensional array of grains

Microstructurally small crack (MSC) growth strongly depends on local microstructure and often displays oscillatory character in terms of crack growth rate (da/dN) as a function of the conventional stress intensity range due to crack tip/grain boundary interactions of MSCs. A fatigue indicator parameter (FIP)-based MSC growth model is presented for high temperature MSC growth in polycrystalline Ni-base superalloy IN100 that takes into account crack tip/grain boundary interaction. An expression for FIP evolution is evoked based on a sequence of finite element simulations for stationary cracks. The MSC growth model was fit to experiments within the context of a simple 1D crack growth model and then applied to model 3D crack growth from a simulated focused ion beam (FIB) notch. Simulations showed that the MSC growth rate became less oscillatory as the MSC front sampled more grains, and eventually converged to the LEFM response with further crack extension.

COMPUTATIONAL STUDY ON MICROSTRUCTURE-SENSITIVE HIGH CYCLE FATIGUE DISPERSIVITY

Empirical approaches to characterize the variability of high cycle fatigue have been widely used. However, little is understood about the intrinsic relationship of randomness of microstructure attributes on the overall variability in high cycle fatigue. The ability of quantifying the dispersivity of high cycle fatigue with physics based computational methods has great potential in design of minimum life and can aid in the improvement of fatigue resistance. To investigate the effects between microstructure attributes and high cycle fatigue dispersivity, the microstructure-sensitive extreme value probabilistic framework is introduced. First, the Voronoi algorithm is used to construct random polycrystalline microstructure representative volume elements. Different kinds of periodic boundary conditions are proposed to simulate the interior and surface constraints in polycrystalline microstructure representative volume elements. Then mechanical responses of both interior and surface microstructure representative volume elements under different strain amplitudes are simulated by internal state variable based crystal plasticity. The fatigue indicator parameter is introduced to characterize the driving force for fatigue crack formation dominated by maximum shear plastic strain amplitude. By computing a limited number of random polycrystalline microstructure representative volume elements, the distributions of fatigue indicator parameter under different strain amplitudes are obtained and analyzed with extreme value probability theory. The study with a kind of titanium alloy with material grade TC4 supports that the high cycle fatigue dispersivity increases with the decrease of the strain *国家重点基础研究发展计划资助项目2015CB057400 收到初稿日期: 2015-06-23,收到修改稿日期: 2015-12-01 作者简介:韩世伟,男, 1987年生,博士生 DOI: 10.11900/0412.1961.2015.00322 第289-297页 pp.289-297

Micromechanical finite element modelling of thermo-mechanical fatigue for P91 steels

In this paper, the cyclic plasticity and fatigue crack initiation behaviour of a tempered martensite ferritic steel under thermo-mechanical fatigue conditions is examined by means of micromechanical finite element modelling. The crystal plasticity-based model explicitly reflects the microstructure of the material, measured by electronic backscatter diffraction. The predicted cyclic thermo-mechanical response agrees well with experiments under both in-phase and out-of-phase conditions. A thermo-mechanical fatigue indicator parameter, with stress triaxiality and temperature taken into account, is developed to predict fatigue crack initiation. In the fatigue crack initiation simulation, the out-of-phase thermo-mechanical response is identified to be more dangerous than in-phase response, which is consistent with experimental failure data. It is shown that the behaviour of thermo-mechanical fatigue can be effectively predicted at the microstructural level and this can lead to a more accurate assessment procedure for power plant components.

Failure of metals II: Fatigue

In this interpretive review, fatigue in metallic systems is considered primarily from the perspective of interactions between the microstructure, the deformation mode and the mechanical state at both low and high temperatures. In Part 1 the development and early propagation of cracks is considered in terms of the basic damage mechanisms and the relative size of the crack with respect to applicable microstructural feature(s). In this section, a multistage grain scale approach to microstructure-sensitive fatigue crack formation and growth is presented which uses Fatigue Indicator Parameters (FIPs) to correlate these processes. Various FIPs parameters are discussed in terms of their indication of the state of fatigue. The development and early crack propagation is considered in the context of microstructure and notches, and probabilistic aspects of the notch fatigue problem are discussed. These features are integrated into a systematic approach for the selection of fatigue resistant microstructures for given applications. In Part 2, attention is focused on Ni-base superalloys and the interaction between oxidation, creep and microstructure (including coatings) in the formation and propagation of cracks. This part of the overview addresses both experimental and modelling aspects. Methodologies based upon fundamental physical processes are presented for understanding and predicting the development and propagation of fatigue cracks, including effects of sequential oxide type formation and of creep on either restraining or accelerating damage by oxidation. The variable fatigue resistance of discs in jet engines is seen to depend upon the variability of microstructure and its influence on the severity of creep/oxidation interactions. All of these factors are considered in the practical case where both temperature and loading parameters vary simultaneously (thermomechanical fatigue). A physics-based life prediction model considering the interactions of deformation and environmental damage is reviewed in terms of its applicability to life prediction of components.

Microstructure and mesh sensitivities of mesoscale surrogate driving force measures for transgranular fatigue cracks in polycrystals

The number of cycles required to form and grow microstructurally small fatigue cracks in metals exhibits substantial variability, particularly for low applied strain amplitudes. This variability is commonly attributed to the heterogeneity of cyclic plastic deformation within the microstructure, and presents a challenge to minimum life design of fatigue resistant components. This paper analyzes sources of variability that contribute to the driving force of transgranular fatigue cracks within nucleant grains. We employ crystal plasticity finite element simulations that explicitly render the polycrystalline microstructure and Fatigue Indicator Parameters (FIPs) averaged over different volume sizes and shapes relative to the anticipated fatigue damage process zone. Volume averaging is necessary to both achieve description of a finite fatigue damage process zone and to regularize mesh dependence in simulations. Results from constant amplitude remote applied straining are characterized in terms of the extreme value distributions of volume averaged FIPs. Grain averaged FIP values effectively mitigate mesh sensitivity, but they smear out variability within grains. Volume averaging over bands that encompass critical transgranular slip planes appear to present the most attractive approach to mitigate mesh sensitivity while preserving variability within grains.

Micro-scale testing and micromechanical modelling for high cycle fatigue of CoCr stent material

This paper presents a framework of experimental testing and crystal plasticity micromechanics for high cycle fatigue (HCF) of micro-scale L605 CoCr stent material. Micro-scale specimens, representative of stent struts, are manufactured via laser micro-machining and electro-polishing from biomedical grade CoCr alloy foil. Crystal plasticity models of the micro-specimens are developed using a length scale-dependent, strain-gradient constitutive model and a phenomenological (power-law) constitutive model, calibrated from monotonic and cyclic plasticity test data. Experimental microstructural characterisation of the grain morphology and precipitate distributions is used as input for the polycrystalline finite element (FE) morphologies. Two microstructure-sensitive fatigue indicator parameters are applied, using local and non-local (grain-averaged) implementations, for the phenomenological and length scale-dependent models, respectively, to predict fatigue crack initiation (FCI) in the HCF experiments.

Modeling the microstructure influence on fatigue life variability in structural steels

The endurance and HCF lifetime of multiphase steel components depend mainly on the phase of fatigue microcrack initiation and early propagation. A numerical study, which quantitatively describes the influence of microstructural features on the initiation and growth of cyclic microcracks, is presented within the context of microstructure-sensitive modeling. The implementation of kinematic hardening on each slip system in a crystal plasticity model allows for capturing the local accumulation of plastic microdeformation representing slip irreversibility occurring in the crack incubation phase. A load increasing testing technique with continuous temperature measurement and interrupted cyclic bending experiments deliver information about the endurance strength of a structural steel and allow for metallographic observation of cyclic microcrack propagation and thereby provide the experimental basis for the numerical simulations. The material model is implemented in cyclic computations with statistically representative volume elements, which are based on experimental microstructure description using the electron backscatter diffraction technique (EBSD). The extreme value distributions of the computed accumulation of local dislocation slip are then correlated to the microstructure in an approach to assess and explore the validity extent of microstructure-sensitive modeling using fatigue indicator parameters (FIPs) to correlate to the endurance limit and fatigue life under high-cycle fatigue conditions. The eligibility of consideration of the stresses normal to the planes of localized plastic damage assisting fatigue crack formation into these FIPs is investigated.

Finite Element Simulation of Shielding/Intensification Effects of Primary Inclusion Clusters in High Strength Steels Under Fatigue Loading

The change of potency to nucleate cracks in high cycle fatigue (HCF) at a primary nonmetallic inclusion in a martensitic gear steel due to the existence of a neighboring inclusion is computationally investigated using two-and three-dimensional elastoplastic finite element (FE) analyses. Fatigue indicator parameters (FIPs) are computed in the proximity of the inclusion and used to compare crack nucleation potency of various scenarios. The nonlocal average value of the maximum plastic shear strain amplitude is used in computing the FIP. Idealized spherical (cylindrical in 2D) inclusions with homogeneous linear elastic isotropic material properties are considered to be partially debonded, the worst case scenario for HCF crack nucleation as experimentally observed for similar systems (Furuya et al., 2004, “Inclusion-Controlled Fatigue Properties of 1800 Mpa-Class Spring Steels,” Metall. Mater. Trans. A, 35A(12), pp. 3737–3744; Harkegard, 1974, “Experimental Study of the Influence of Inclusions on the Fatigue Properties of Steel,” Eng. Fract. Mech., 6(4), pp. 795–805; Lankford and Kusenberger, 1973, “Initiation of Fatigue Cracks in 4340 Steel,” Metall. Mater. Trans. A, 4(2), pp. 553–559; Laz and Hillberry, 1998, “Fatigue Life Prediction From Inclusion Initiated Cracks,” Int. J. Fatigue, 20(4), pp. 263–270). Inclusion-matrix interfaces are simulated using a frictionless contact penalty algorithm. The fully martensitic steel matrix is modeled as elastic-plastic with pure nonlinear kinematic hardening expressed in a hardening minus dynamic recovery format. FE simulations suggest significant intensification of plastic shear deformation and hence higher FIPs when the inclusion pair is aligned perpendicular to the uniaxial stress direction. Relative to the reference case with no neighboring inclusion, FIPs decrease considerably when the inclusion pair aligns with the applied loading direction. These findings shed light on the anisotropic HCF response of alloys with primary inclusions arranged in clusters by virtue of the fracture of a larger inclusion during deformation processing. Materials design methodologies may also benefit from such cost-efficient parametric studies that explore the relative influence of microstructure attributes on the HCF properties and suggest strategies for improving HCF resistance of alloys.

Statistical assessment of multiaxial HCF criteria at the grain scale

Abstracts Multiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed.

Experimental characterisation for micromechanical modelling of CoCr stent fatigue

Fatigue of CoCr alloy stents has become a major concern in recent times, owing to cases of premature fracture, often driven by microstructural phenomena. This work presents the development of a micromechanical framework for fatigue design, based on experimental characterisation of a biomedical grade CoCr alloy, including both microscopy and mechanical testing. Fatigue indicator parameters (FIPs) within the micromechanical framework are calibrated for the prediction of microstructure-sensitive fatigue crack initiation (FCI). A multi-scale CoCr stent model is developed, including a 3D global J2 continuum stent-artery model and a 2D micromechanical sub-model. Several microstructure realizations for the stent sub-model allow assessment of the effect of crystallographic orientations on stent fatigue crack initiation predictions. Predictions of FCI are compared with traditional Basquin-Goodman total life predictions, revealing more realistic scatter of data for the microstructure-based FIP approach. Comparison of stent predictions with performance of a 316L stent for the same generic design exposes the design as over-conservative for the CoCr alloy. In response, the micromechanical framework is used to modify the stent design for the CoCr alloy, improving design efficiency.

Microstructure-sensitive prediction and experimental validation of fretting fatigue

This paper is concerned with the development of a micro-mechanical methodology for prediction of fretting fatigue crack nucleation life and short crack propagation. The methodology employs critical accumulated plastic slip as a fatigue indicator parameter for microstructure-sensitive crack nucleation. Crystal plasticity unit-cell models are employed for calibration of constitutive and crack nucleation parameters and a crystal plasticity frictional contact model of the fretting test rig is developed to predict the micro-scale surface fretting damage, crack nucleation and estimated micro-crack propagation. The methodology is validated against fretting fatigue tests using a fretting bridge arrangement for 316L stainless steel.

The role of elastic anisotropy, length scale and crystallographic slip in fatigue crack nucleation

Fatigue crack nucleation in polycrystal ferritic steel is investigated through experimental observation of multiple large-grained, notched, four-point bend tests combined with explicit microstructural representation of the same samples using crystal plasticity finite element techniques in order to assess fatigue indicator parameters, together with the roles of elastic anisotropy and length scale effects in slip development, and hence in crack nucleation.Elastic anisotropy has been demonstrated to play a pivotal role in the distribution and magnitude of polycrystal slip relative to observed crack nucleation sites in the context of constrained cyclic microplasticity. Length scale effects were found not to alter substantively the distributions or magnitudes of slip relative to the observed crack nucleation site, but in detailed analyses of an experimental sample, the location of highest magnitude of geometrically necessary dislocations was found to coincide precisely with the position of predicted peak plasticity and the experimentally observed crack nucleation site.The distributions of microplasticity within polycrystal samples were found to change quite significantly between the first yield and after multiple cycles. As a result, the effective plastic strain per cycle was found to be a better indicator of fatigue crack nucleation than peak effective plastic strain. In nine independently tested and analysed polycrystal samples, the cyclic effective plastic strain and crystallographic system peak accumulated slip were found to be good indicators of a fatigue crack nucleation site.

Development of life assessment procedures for power plant headers operated under flexible loading scenarios

A finite element methodology for thermo-mechanical fatigue analysis of a subcritical power plant outlet header under realistic loading conditions is presented. The methodology consists of (i) a transient heat transfer model, (ii) a sequential anisothermal cyclic viscoplastic model and (iii) a multiaxial, critical-plane implementation of the Ostergren fatigue indicator parameter. The methodology permits identification of the local thermo-mechanical stress–strain response at critical locations and prediction of fatigue life and cracking orientation for complex transient, anisothermal, cyclic elastic–plastic-creep material behaviour. Measured plant data, in the form of steam and pipe temperature transients and steam pressure data, are employed to identify heat transfer constants and validate the predicted thermal response, with particular attention given to plant start-up and attemperation effects. The predictions indicate out-of-phase temperature-strain response at the header inside surface and in-phase response on the outside surface. Cooling transients are predicted to control damage and crack initiation at the inner bore, whereas heating transients are predicted to have a more damaging effect at weld locations. A representative test cycle is presented, which is shown to capture the salient thermo-mechanical cyclic damage of the realistic cycle. The predicted results correlate well with industrial experience in terms of crack (initiation) orientation, location and life.

Effect of annealing twins on crack initiation under high cycle fatigue conditions

Several experimental studies have shown that fatigue cracks in Ni-based superalloys preferentially form in the vicinity of favorably oriented annealing twin boundaries. However, this increase in the probability of crack nucleation has not been quantified in detail since 3 material modeling has not typically considered twins. The present work employs finite element simulations and a continuum crystal plasticity constitutive model for RR1000 Ni-based superalloy to assess the potential enhancement of nonlocal fatigue indicator parameters (FIPs) incurred by the presence of Σ3 twins. Two cases are analyzed: single crystals with twins of different widths subjected to single slip cyclic shear deformation aligned with the twin plane and polycrystals with 20 % of the grains half-twinned. Simulations with and without twins are compared in both cases. The results demonstrate the detrimental effect of twins in shifting the upper tail of the FIP distribution to higher values; this shift is more pronounced with an increase of twin thickness.

Microstructure-sensitive HCF and VHCF simulations

This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding the effects of stress amplitude, R-ratio, and microstructure on fatigue crack formation and early growth at notches, including pores and non-metallic inclusions for Ti alloys and Ni-base superalloys. The simulations employ fatigue indicator parameters (FIPs) computed over finite volumes that relate to processes of fatigue crack formation and early growth at the scale of individual grains. It is argued that both coarse scale (uncracked, mesoscale) and fine scale FIPs (computed in the vicinity of cracks in single grains or crystals) serve as a driving force for crystallographic fatigue crack growth, and correlate directly with the cyclic crack tip displacement (CTD). Furthermore, variability in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) responses is computationally assessed using multiple statistical volume elements and the distribution of FIPs of extreme value character. The concepts of marked correlation functions and weighted probability density functions are reviewed as a means to quantify the role of multiple microstructure attributes that couple to enhance the extreme value FIPs in the HCF regime. An algorithm for estimation of the cumulative probability distribution of cycles for crack formation and growth from notches in HCF and VHCF is also described.

Assessment of small fatigue crack growth driving forces in single crystals with and without slip bands

Strain localization under low amplitude cyclic loading is a manifestation of plastic irreversible deformation associated with early crack growth. However, traditional constitutive models cannot usually reproduce strain localization in smooth single crystals, which can affect crack growth predictions for crystallographic fatigue cracks. This work analyzes the influence of bands of localized plastic shear strain on the cyclic crack tip displacement and on a fatigue indicator parameter by making special provision of a crack along the interface of a deformation band. Furthermore, the quality of local and volume-averaged fatigue indicator parameters are assessed using finite element models of a Cu single crystal cycled to induce plastic deformation under multiple loading conditions.

Microstructure-sensitive extreme-value probabilities of high-cycle fatigue for surface vs. subsurface crack formation in duplex Ti–6Al–4V

The distributions of the extreme-value driving force(s) for surface vs. subsurface fatigue crack formation (nucleation and early growth) in high-cycle fatigue are evaluated for a microstructure variant of duplex Ti–6Al–4V. In polycrystalline metals, previous work has explored estimation of the driving force(s) for fatigue crack formation at the scale of the grains by computing non-local fatigue indicator parameters (FIPs) based on the cyclic plastic strain averaged over domains on the length scale of the grains. Instantiated statistical volume elements (SVEs), which sample the distributed microstructure attributes of interest for a given material system, can be simulated via the finite element method with embedded polycrystalline plasticity models to estimate the distributed plasticity and resulting FIPs. This strategy of simulating multiple SVEs is in contrast to the simulation of a single representative volume element which is typically untenably large for extreme-value distributions of microstructure attributes or response variables. In this work, multiple SVEs are instantiated with both traction-free (i.e. surface) boundary conditions and fully periodic (i.e. subsurface) boundary conditions. In addition to estimating the extreme-value distributions of the FIPs, newly introduced extreme-value marked correlation functions are applied to characterize the coupled crystallographic microstructure attributes (e.g. grain size, grain orientation, grain misorientation) that most influence the extreme-value distributions of the FIPs. It is shown that there is overlap in the distributions of the driving forces for surface vs. subsurface crack formation in the low to moderate range of failure probability based on FIPs; however, at higher failure probability levels, the driving forces are highest for surface crack formation. The overlap in the distributions of the driving forces for fatigue crack formation in the low to moderate probability range may assist in describing the competing surface vs. subsurface failure modes that are observed experimentally.