Modeling and Simulation of Microstructurally Small Crack Formation and Growth in Notched Nickel-base Superalloy Component

Studies on microstructurally small fatigue cracks have illustrated that heterogeneous microstructural features such as inclusions, pores, grain size distribution as well as precipitate size distribution and volume fraction create stochasticity in their behavior under cyclic loads. Therefore, to enhance safe-life and damage-tolerance approaches, accurate modeling of the influence of these heterogeneous microstructural features on microstructurally small crack formation and growth from stress raisers is necessary. In this work, computational micromechanics was used to predict the high cycle fatigue of microstructurally small crack formation and growth in notched polycrystalline nickel-base superalloys and to quantify the variability in the driving force for formation and growth of microstructurally small crack from notch root in the matrix with non-metallic inclusions. The framework involves computational modeling to obtain three-dimensional perspectives of microstructural features influencing fatigue crack growth in notched nickel-base superalloys, which accounts for the effects of nonlocal notch root plasticity, loading, microstructural variability, and extrinsic defects on local cyclic plasticity at the microstructure-scale level. This approach can be used to explore sensitivity of minimum fatigue lifetime to microstructures. The simulation results obtained from this framework were calibrated to existing experimental results for polycrystalline nickel-base superalloys.     

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.     

Material defects as the basis of fatigue design

Microstructural inhomogeneities can exist in metals, such as precipitates and inclusions. These can be introduced purposely to strengthen the metal matrix (e.g.: CuAl₂ in α-phase aluminium) or by faulty manufacture (e.g.: large inclusions). A major part of the history of metal fatigue has been to eliminate, or at least reduce, detrimental precipitates, inclusions and manufacture defects such as scratches, surface roughness and shrinkages in cast irons since these can initiate fatigue cracks. The deleterious nature of foreign bodies or other forms of inhomogeneities, e.g.: pores or de-bonded zones within a microstructure are related to their size, position, shape, orientation and physical properties.Small sizes of precipitates and inclusions are to be preferred to large ones; such defects being less detrimental inside a grain rather than at grain boundaries where they can simultaneously affect two or three near-neighbour grains. The orientation of a defect is dangerous should it be inclined to the future direction of Stage I and/or Stage II crack growth planes. An important duty of a metallurgist is to reduce the effectiveness of these different forms of micro-defects produced during manufacture whilst a mechanical engineer is required to derive a suitable form of fracture mechanics in order to account for their behaviour in a quantitative fatigue fracture analysis.In this paper, some important types of microstructural defects will be illustrated and discussed in terms of their size, position, shape, orientation and properties, together with their effect on the fatigue resistance of a material. This will be coupled with a fracture mechanics (FMs) approach that quantifies their behaviour in terms of their relationship to fatigue crack propagation. In this approach, the boundary condition between failure and non-failure is explored using FM as a threshold condition for a small crack coupled with the Vickers hardness HV of the material that represents the condition (ΔK_th) for the onset of micro-plasticity (yielding) required for the growth of a crack from the defect and the non-propagation behaviour of the crack.Statistical scatters of microstructures, defects and inclusions are the major factors of statistical scatters of fatigue strength and fatigue life. Directions for optimizing microstructure to improve fatigue strength are explained from the viewpoint of equality control based on the statistics of extremes of defects and inclusions.A new efficient and reliable inclusion rating method for high strength steels based on the statistics of extremes using the phenomenon of hydrogen embrittlement is proposed.     

Effects of Microstructure Variability on Intrinsic Fatigue Resistance of Nickel-base Superalloys – A Computational Micromechanics Approach

Understanding the effects of microstructure variability on fatigue resistance is a key to selection and design of materials for fatigue applications. The traditional empirical approach rooted in experiments is being increasingly combined with systematic computational modeling. This work is concerned with demonstrating the feasibility of linking effects of microstructure variability on cyclic plasticity at the scale of intrinsic microstructure of a single crystal nickel-base superalloy. The precipitate and the matrix phases of the alloy are modeled explicitly using a physically based crystal viscoplasticity constitutive framework with appropriate scale and spacing effects to reflect dislocation–precipitate interactions. The model is implemented as a user material subroutine within a finite element code. Various realizations of different microstructures are generated using a constrained Poisson point process. Statistical volume elements (SVEs) with random-periodic boundary conditions are simulated under fully reversed cyclic loading at 650°C. Primary cooling γ′ precipitate size and volume fraction are considered in terms of their effects on the macroscopic stress–strain response and on distributed cyclic microplasticity within the SVE. To compare various microstructures in terms of probability of fatigue crack formation, an appropriate nonlocal measure of cyclic plastic shear strain range is proposed based on percolation of cyclic microplasticity at the scale of the SVE.     

3D modeling of subsurface fatigue crack nucleation potency of primary inclusions in heat treated and shot peened martensitic gear steels

A computational strategy is developed to characterize the driving force for fatigue crack nucleation at subsurface primary inclusions in carburized and shot peened C61^® martensitic gear steels. Experimental investigation revealed minimum fatigue strength to be controlled by subsurface fatigue crack nucleation at inclusion clusters under cyclic bending. An algorithm is presented to simulate residual stress distribution induced through the shot peening process following carburization and tempering. A methodology is developed to analyze potency of fatigue crack nucleation at subsurface inclusions. Rate-independent 3D finite element analyses are performed to evaluate plastic deformation during processing and service. The specimen is subjected to reversed bending stress cycles with R = 0.05, representative of loading on a gear tooth. The matrix is modeled as an elastic–plastic material with pure nonlinear kinematic hardening. The inclusions are modeled as isotropic, linear elastic. Idealized inclusion geometries (ellipsoidal) are considered to study the fatigue crack nucleation potency at various subsurface depths. Three distinct types of second-phase particles (perfectly bonded, partially debonded, and cracked) are analyzed. Parametric studies quantify the effects of inclusion size, orientation and clustering on subsurface crack nucleation in the high cycle fatigue (HCF) or very high cycle fatigue (VHCF) regimes. The nonlocal average values of maximum plastic shear strain amplitude and Fatemi–Socie (FS) parameter calculated in the proximity of the inclusions are considered as the primary driving force parameters for fatigue crack nucleation and microstructurally small crack growth. The simulations indicate a strong propensity for crack nucleation at subsurface depths in agreement with experiments in which fatigue cracks nucleated at inclusion clusters, still in the compressive residual stress field. It is observed that the gradient from the surface of residual stress distribution, bending stress, and carburized material properties play a pivotal role in fatigue crack nucleation and small crack growth at subsurface primary inclusions. The fatigue potency of inclusion clusters is greatly increased by prior interfacial damage during processing.     

Initiation and early growth mechanisms of corrosion fatigue cracks in stainless steels

The mechanism of corrosion fatigue crack initiation in stainless steels was examined in both air and chloride solutions. For a tempered martensitic, a duplex and a soft martensitic steel it is shown that the decrease of the fatigue strength from the value measured in air to that measured in corrosive environments depends primarily upon the stability of the protective film. If the passivity is stable, cracks are found to originate almost exclusively at oxide inclusions. Cracking or debonding were found to occur. For the duplex steel in the vicinity of the inclusion there were pronounced emerging persistent slip bands. They cause localized corrosion attack, thus allowing cracks to be formed more easily. If pitting is superposed, crack nucleation always occurs at the base of the pit. Pit formation and growth rate are accelerated by cyclic loading.     

Effect of microstructural modification on damage tolerance of 34CrMo4 shaft steel

Overall damage tolerances of the heat‐treated 34CrMo4 steels having ferritic‐pearlitic, bainitic, and tempered‐martensitic microstructures were evaluated based on their threshold stress intensity factor prior to small crack propagation, fatigue strength, and fracture toughness under static loading. Kitagawa‐Takahashi diagrams were constructed to determine the limiting size of small crack propagation. The micromechanical effects of carbide morphology and phase distribution on quasi‐static and dynamic mechanical properties were also elaborated. Fractographic investigations were carried out on the notched fatigue test specimens to distinguish deterioration and deformation mechanism of the microstructure under reversed cyclic loads. Finally, improvements in the damage tolerance were discussed to present the advantages and disadvantages of each heat treatment procedure to minimize in‐service fatigue failures.     

Fatigue studies on dual-phase low carbon steel

Low cycle fatigue studies have been carried out on 2 wt% Mn, 2 wt% Si and 0.1 wt% C steels with dual-phase and tempered martensitic structures. Fatigue crack initiation and propagation were investigated using scanning electron microscopy as well as optical microscopy. In addition, taper-section and cross-section techniques were also performed for more detail studies on the correlation of crack initiation with the internal microstructures of the testing samples. Internal microstructures were also investigated on the dual-phase steel sample before and after fatigue fracture by transmission electron microscopy.     

A study on fatigue crack growth in dual phase martensitic steel in air environment

Dual phase (DP) steel was intercritically annealed at different temperatures from fully martensitic state to achieve martensite plus ferrite, microstructures with martensite contents in the range of 32 to 76%. Fatigue crack growth (FCG) and fracture toughness tests were carried out as per ASTM standards E 647 and E 399, respectively to evaluate the potential of DP steels. The crack growth rates (da/dN) at different stress intensity ranges (ΔK) were determined to obtain the threshold value of stress intensity range (ΔK_th). Crack path morphology was studied to determine the influence of microstructure on crack growth characteristics. After the examination of crack tortuosity, the compact tension (CT) specimens were pulled in static mode to determine fracture toughness values. FCG rates decreased and threshold values increased with increase in vol.% martensite in the DP steel. This is attributed to the lower carbon content in the martensite formed at higher intercritical annealing (ICA) temperatures, causing retardation of crack growth rate by crack tip blunting and/or deflection. Roughness induced crack closure was also found to contribute to the improved crack growth resistance at higher levels of martensite content. Scanning electron fractography of DP steel in the near threshold region revealed transgranular cleavage fracture with secondary cracking. Results indicate the possibility that the DP steels may be treated to obtain an excellent combination of strength and fatigue properties.     

A new approach to model the fatigue anisotropy due to non-metallic inclusions in forged steels

The objective of this work is to propose an anisotropic fatigue criterion for the sizing of industrial forged components. The results from different experimental campaigns using three different rolled steels are first presented. The effect of inclusions and the microstructure on the fatigue behaviour are investigated. For the two ferrite–pearlitic steels tested, the presence of a microstructure consisting of elongated grains has no observable effects on the fatigue behaviour. For two of the three steels studied the presence of non-metallic inclusions, elongated in the rolling direction, form the origin of the anisotropic fatigue behaviour.The proposed probabilistic model is based on the competition between two possible fatigue crack initiation mechanisms. The anisotropic character of the fatigue resistance of forged components is taken into account by the definition of the geometry and the orientation of the non-metallic inclusion. This criterion results in the establishment of a probabilistic Kitagawa type diagram.     

A study of microcrack formation in multiphase steel using representative volume element and damage mechanics

Multiphase steels have become a favoured material for car bodies due to their high strength and good formability. Concerning the modelling of mechanical properties and failure behaviour of multiphase steels, representative volume elements (RVE) have been proved to be an applicable approach for describing heterogeneous microstructures. However, many multiphase steels exhibit inhomogeneous microstructures which result from segregation processes during continuous casting. These segregations lead to a formation of martensite bands in the microstructure causing undesirable inhomogeneities of material properties. The aim of this work is to develop an FE evaluation procedure for predicting a microcrack formation provoked by banded martensitic structures. A micromechanism based damage curve was applied as a failure criterion for the softer ferritic matrix in the microstructure in order to simulate the propagation of cracks resulting from the failure of martensitic bands. The parameters of the damage curve were determined by in situ miniature bending tests and tensile tests with notched samples. The presented approach provides the basis for an assessment criterion of the component safety risk of multiphase steels with inhomogeneous microstructures.     

Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach

A computational study is conducted to determine the influence of microstructure attributes and properties on driving forces for fatigue crack formation and microstructurally small crack growth in a polycrystalline Ni‐base superalloy, IN100, a turbine disk alloy. A principal objective is to obtain quantitative estimates of the effect of variability of microstructure features on scatter in fatigue life or fatigue strength for a given life. Understanding is sought regarding sensitivity of driving forces to various microstructure attributes that may guide selection of the process route to tailor microstructure to achieve fatigue resistance. A microstructure‐sensitive crystal plasticity model is used to explicitly model individual grains and polycrystals, which is then used to explore effects of: (a) grain size distribution and (b) secondary and tertiary coherent γ′ precipitate size distributions and volume fractions on the cyclic inelastic strain distribution. Multiple statistical volume elements (SVEs) are subjected to random periodic boundary conditions to build up statistically significant measures of distributions of cyclic microplasticity. Multiaxial fatigue criteria with critical plane approaches are used to estimate the crack initiation life. Methods are developed for assessing crack formation and microstructurally small crack growth as a function of microstructure attributes.     

Deformation and Failure of Single-Packets in Martensitic Steels

A three-dimensional multiple-slip dislocation-density-based crystalline formulation, and specialized finite-element formulations were used to investigate dislocation-density evolution and crack behavior in single-packet lath martensite in high strength martensitic steels. The formulation is based on accounting for variant morphologies and orientations, and initial dislocations-densities that are uniquely inherent to martensitic microstructures. The effects of loading plane with respect to the orientation o the habit plane are investigated. Furthermore, the formulation was used to investigate single-packet microstructure mapped directly from SEM/EBSD images of maraging and ausformed martensitic steel alloys. This analysis underscores that shear pipe effects in martensitic steels, where the long direction of the laths is aligned with specific slip-directions, can result in shear-strain localization along specific variants. Furthermore, the results indicate that the strength and ductility are higher for the loading plane parallel to the habit plane as compared to those normal to the habit plane.     

Influence of sulphur additions on impact properties of bainitic or martensitic steels

Abstract

Effects of sulphur addition on the Charpy impact properties of various continuously cooled bainitic steels with different prior austenite grain size, hardness, and content of retained austenite were investigated and compared with martensitic steels. The impact properties of 1473 K austenitised bainitic steels were improved with increasing sulphur content up to 0·1 wt-%, while the impact properties of martensitic steels were deteriorated with increasing sulphur content. The crack initiation energy of bainitic steels increased with the increase of sulphur content because the structure units surrounded by the high angle boundaries were refined with the increase of manganese sulphide inclusions which caused the expansion of ductile fracture area. On the other hand, the impact energy, particularly the crack propagation energy, of martensitic steels decreased with increasing sulphur content because the nucleation sites of voids increased with the increase of manganese sulphide inclusions in the ductile fracture region.     

Cyclic plasticity at pores and inclusions in cast Al-Si alloys

Finite element analyses of micronotches including pores and silicon particles of an A356 aluminum alloy were performed to elucidate microstructure-property relations for fatigue crack incubation. Several important findings resulted. By varying the particle and pore size, spacing, aspect ratio, and clustering, the relative microstructural differences were quantified related to micronotch root cyclic plasticity. Results from realistic two-dimensional microstructures showed that minimal microstructure-scale cyclic plasticity corresponds well to the measured fatigue strength at 10⁷ cycles for low porosity A356 aluminum alloy specimens. “Realistic” and idealized particles/pores simulations were used to formulate a local Coffin-Manson type law for crack incubation.     

Micromechanical methodology for fatigue in cardiovascular stents

A finite element based micromechanical methodology for cyclic plasticity and fatigue crack initiation in cardiovascular stents is presented. The methodology is based on the combined use of a (global) three-dimensional continuum stent-artery model, a local micromechanical stent model, the development of a combined kinematic–isotropic hardening crystal plasticity constitutive formulation, and the application of microstructure sensitive crack initiation parameters. The methodology is applied to 316L stainless steel stents with random polycrystalline microstructures, based on scanning electron microscopy images of the grain morphology, under realistic elastic–plastic loading histories, including crimp, deployment and in vivo systolic–diastolic cyclic pressurisation. Identification of the micromechanical cyclic plasticity and failure constants is achieved via application of an objective function and a unit cell representative volume element for 316L stainless steel. Cyclic stent deformations are compared with the J₂-predicted response and conventional fatigue life prediction techniques. It is shown that micromechanical fatigue analysis of stents is necessary due to the significant predicted effects of material inhomogeneity on micro-plasticity and micro-crack initiation.     

Mechanical properties of martensitic steels in gaseous hydrogen

We present the regularities of hydrogen degradation of 03Kh12N10MT, 15Kh12N2MFAV and 13Kh11N2V2MF steels under a pressure of 30 MPa within the temperature range of 293–673 K. The minimum values for plasticity, low-cycle fatigue, and static crack resistance, which do not decrease with an increase in pressure of hydrogen atmosphere and content of the absorbed hydrogen, are found. The difference between temperature dependences of the coefficients of influence of hydrogen on static and cyclic crack resistance of martensitic steels with various content of austenite is established. The main fractographic features of the influence of hydrogen on the micromechanism of fracture of steels under different types of loading and temperatures are determined.     

The Effect of Hydrogen on Fatigue Properties of Metals used for Fuel Cell System

The effect of hydrogen on the fatigue properties of alloys which are used in fuel cell (FC) systems has been investigated. In a typical FC system, various alloys are used in hydrogen environments and are subjected to cyclic loading due to pressurization, mechanical vibrations, etc. The materials investigated were three austenitic stainless steels (SUS304, SUS316 and SUS316L), one ferritic stainless steel (SUS405), one martensitic stainless steel (0.7C-13Cr), a Cr-Mo martensitic steel (SCM435) and two annealed medium-carbon steels (0.47 and 0.45%C). In order to simulate the pick-up of hydrogen in service, the specimens were charged with hydrogen. The fatigue crack growth behaviour of charged specimens of SUS304, SUS316, SUS316L and SUS405 was compared with that of specimens which had not been hydrogen-charged. The comparison showed that there was a degradation in fatigue crack growth resistance due to hydrogen in the case of SUS304 and SUS316 austenitic stainless steels. However, SUS316L and SUS405 showed little degradation due to hydrogen. A marked increase in the amount of martensitic transformation occurred in the hydrogen-charged SUS304 specimens compared to specimens without hydrogen charge. In case of SUS316L, little martensitic transformation occurred in either specimens with and without hydrogen charge. The results of S-N testing showed that in the case of the 0.7C–13Cr stainless steel and the Cr–Mo steel a marked decrease in fatigue resistance due to hydrogen occurred. In the case of the medium carbon steels hydrogen did not cause a reduction in fatigue behaviour. Examination of the slip band characteristics of a number of the alloys showed that slip was more localized in the case of hydrogen-charged specimens. Thus, it is presumed that a synergetic effect of hydrogen and martensitic structure enhances degradation of fatigue crack resistance.     

基于内部失效机理预测评估渗碳Cr-Ni齿轮钢的超高周疲劳强度

对渗碳Cr-Ni齿轮钢进行应力比为0和0.3的室温超高周疲劳实验,观测试样中诱发裂纹萌生的夹杂和疲劳断口形貌,以全面评估渗碳Cr-Ni齿轮钢疲劳性能。将疲劳失效模式分为有细颗粒区(Fine granular area,FGA)的内部疲劳失效和有表面光滑区(Surface smooth area, SSA)的表面疲劳失效,并阐明了渗碳Cr-Ni齿轮钢的超高周内部疲劳破坏机制。基于累积损伤和位错能量法并结合细颗粒区形成机理和夹杂的最大评估尺寸,分别构建了两种渗碳Cr-Ni齿轮钢内部疲劳强度的预测模型。利用FGA尺寸与夹杂尺寸的比值和夹杂应力强度因子及应力比之间的关系,修正所提出的两种疲劳强度预测模型并给出了最大夹杂尺寸下的l_FGA-S-N曲线。结果表明,基于累积损伤法和位错能量法分别构建的疲劳强度预测模型都可用于预测评估渗碳Cr-Ni齿轮钢在多种应力比下的内部疲劳强度,基于位错能量法的强度预测模型精度较高。