Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100

To quantify the effects of interactions between various microstructure attributes on fatigue life in the high cycle fatigue (HCF) regime, we have proposed a new microstructure-sensitive extreme value statistical framework. This framework couples the extreme value distributions of certain fatigue indicator parameters (FIPs) or response functions to the correlated microstructure attributes that exist at the extreme value locations of these FIPs. We demonstrate the application of this statistical framework to investigate the microstructure-sensitive fatigue response of the PM Ni-base superalloy IN100 at 650 °C. To accomplish this task, we construct statistical volume elements (SVEs) used to compute the local response for 200 instantiations of IN100. These SVEs are constructed and simulated via the finite element method with crystal plasticity constitutive relations. The results of the simulations are used to explore extreme value statistics of the FIPs for these microstructures. The extreme value distributions of the Fatemi–Socie FIP are fit with high confidence by the Gumbel distribution and are defined in a representative nature with as few as 25 simulated microstructure instantiations (i.e., SVEs). The extreme value marked correlation functions of the apparent Schmid factor based on the geometry of the slip systems relative to the loading direction indicate that cube slip may be important to fatigue crack formation in this material system. This supports previous experimental observations of fatigue crack formation and microstructurally small fatigue crack growth along cube planes in IN100 in grains that are unfavorably oriented for octahedral slip at elevated temperatures.     

Microstructure-based crystal plasticity modeling of cyclic deformation of Ti–6Al–4V

Ti–6Al–4V is a dual phase material with range of possible complex microstructures. It is well known that mechanical behavior of Ti–6Al–4V is significantly affected by its texture and microstructure morphology. A three-dimensional microstructure-based constitutive model for monotonic and cyclic deformation of duplex Ti–6Al–4V is developed and implemented. The model includes length scale effects associated with dislocation interactions with different microstructure features, and is calibrated using polycrystalline finite element simulations to fit the measured macroscopic responses (overall stress–strain behavior) of a duplex heat treated Ti–6Al–4V alloy subjected to a complex cyclic loading history. Representative microstructures are simulated using a three-dimensional finite element mesh with periodic boundary conditions imposed in all directions. The measured orientation and misorientation distributions of grains of this duplex Ti–6Al–4V are considered, and similar probability density distributions of the crystallographic orientations are assigned to the finite element mesh. The misorientation distributions are then fit using the simulated annealing method. Effects of microstructural features are examined and compared with the experimental data in terms of their influence on the material yield strength. The results are shown to be in good agreement with the experimental observations.     

Constitutive modeling of cyclic plasticity deformation of a pure polycrystalline copper

Cyclic plasticity experiments were conducted on a pure polycrystalline copper and the material was found to display significant cyclic hardening and nonproportional hardening. An effort was made to describe the cyclic plasticity behavior of the material. The model is based on the framework using a yield surface together with the Armstrong–Frederick type kinematic hardening rule. No isotropic hardening is considered and the yield stress is assumed to be a constant. The backstress is decomposed into additive parts with each part following the Armstrong–Frederick type hardening rule. A memory surface in the plastic strain space is used to account for the strain range effect. The Tanaka fourth order tensor is used to characterize nonproportional loading. A set of material parameters in the hardening rules are related to the strain memory surface size and they are used to capture the strain range effect and the dependence of cyclic hardening and nonproportional hardening on the loading magnitude. The constitutive model can describe well the transient behavior during cyclic hardening and nonproportional hardening of the polycrystalline copper. Modeling of long-term ratcheting deformation is a difficult task and further investigations are required.     

Thermomechanical coupling in shape memory alloys under cyclic loadings: Experimental analysis and constitutive modeling

In this paper, we examine the influence of thermomechanical coupling on the behavior of superelastic shape memory alloys subjected to cyclic loading at different loading rates. Special focus is given to the determination of the area of the stress-strain hysteresis loop once the material has achieved a stabilized state. It is found that this area does not evolve monotonically with the loading rate for either transient or asymptotic states. In order to reproduce this observation analytically, a new model is developed based on the ZM model for shape memory alloys which was modified to account for thermomechanical coupling. The model is shown to predict the non-monotonic variation in hysteresis area to good accord. Experimentally observed variations in the temperature of SMA test samples are also correctly reproduced for lower strain rates.     

Multiscale modeling of irradiated polycrystalline FCC metals

We propose a set of models for the post-irradiation deformation response of polycrystalline FCC metals. First, a defect- and dislocation-density based evolution model is developed to capture the features of irradiation-induced hardening as well as intra-granular softening. The proposed hardening model is incorporated within a rate-independent single crystal plasticity model. The result is a non-homogeneous deformation model that accounts for defect absorption on the active slip planes during plastic loading. The macroscopic non-linear constitutive response of the polycrystalline aggregate of the single crystal grains is then obtained using a micro–macro transition scheme, which is realized within a Jacobian-free multiscale method (JFMM). The Jacobian-free approach circumvents explicit computation of the tangent matrix at the macroscale by using a Newton–Krylov process. This has a major advantage in terms of storage requirements and computational cost over existing approaches based on homogenized material coefficients in which explicit Jacobian computation is required at every Newton step. The mechanical response of neutron-irradiated single and polycrystalline OFHC copper is studied and it is shown to capture experimentally observed grain-level phenomena.     

Plasticity in polycrystalline fretting fatigue contacts

Plastic deformation at the scale of microstructure plays an important role in fretting fatigue failure of metals under cyclic loading. In this study, crystal viscoplasticity theory with a planar triple slip idealization is employed to represent crystallographic plasticity in two-dimensional fretting analyses of Ti-6Al-4V. Subsurface deformation maps, fretting maps, and shakedown maps are constructed based on application of J₂ plasticity theory for the polycrystalline substrate. Comparisons are then made with polycrystal viscoplasticity simulations, the latter suggesting that plastic ratchetting plays a significant role in the fretting fatigue process.     

Fatigue life predictions by integrating EVICD fatigue damage model and an advanced cyclic plasticity theory

An event independent cumulative damage (EVICD) fatigue prediction model was previously developed for the fatigue damage prediction under general multiaxial stress state and loading conditions. The model takes the plastic strain energy as the major contributor to the fatigue damage. The application of the EVICD model does not require a cycle counting method for general random loading. In the current effort, derivations were made to explicitly and directly relate the material constants in the fatigue model to the parameters in the Manson–Coffin equations and the cyclic stress–strain curve of the material. In addition, an advanced cyclic plasticity theory was implemented for the determination of the detailed stress–strain response that was required as the input for the EVICD fatigue model. Three metallic materials were used to demonstrate the capability of the modified fatigue model for the predictions of fatigue lives under different loading conditions. The results show that the fatigue model can provide fatigue life predictions in close agreement with the experimental observations.     

An experimental study of cyclic deformation of extruded AZ61A magnesium alloy

Thin-walled tubular specimens were employed to study the cyclic deformation of extruded AZ61A magnesium alloy. Experiments were conducted under fully reversed strain-controlled tension-compression, torsion, and combined axial-torsion in ambient air. Mechanical twinning was found to significantly influence the inelastic deformation of the material. Cyclic hardening was observed at all the strain amplitudes under investigation. For tension-compression at strain amplitudes higher than 0.5%, the stress-strain hysteresis loop was asymmetric with a positive mean stress. This was associated with mechanical twinning in the compression phase and detwinning in the subsequent tension phase. Under cyclic torsion, the stress-strain hysteresis loops were symmetric although mechanical twinning was observed at high shear strain amplitudes. When the material was subjected to combined axial-torsion loading, the alternative occurrence of twinning and detwinning processes under axial stress resulted in asymmetric shear stress-shear strain hysteresis loops. Nonproportional hardening was not observed due to limited number of slip systems and the formation of mechanical twins. Microstructures after the stabilization of cyclic deformation were observed and the dominant mechanisms governing cyclic deformation were discussed. Existing cyclic plasticity models were discussed in light of their capabilities for modeling the observed cyclic deformation of the magnesium alloy.     

Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic-plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material's local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length was 870-890 μm with deformation imposed through a Split-Hopkinson Pressure Bar system at maximum top-to-bottom velocity in the range of 8-25 m/s. The deformation behavior of tantalum tophat samples is modeled through direct polycrystal simulations. An embedded Voronoï-tessellated two-dimensional microstructure is used to represent the material within the shear zone of the sample. A thermo-mechanically coupled elasto-viscoplastic single crystal model is presented and used to represent the response of the grains within the aggregate shear zone. In the shoulder regions away from the shear zone where strain levels remain on the order of 0.05, the material is represented by an isotropic J₂ flow theory based upon the elasto-viscoplastic Mechanical Threshold Stress (MTS) model for flow strength. The top surface stress versus displacement results were compared to those of the experiments and over-all the simulated stress magnitude is over-predicted. It is believed that the reason for this is that the simulations are two-dimensional. A region within the numerical shear zone was isolated for statistical examination. The vonMises stress state within this isolated shear zone region suggests an approximate normal distribution with a factor of two difference between the minimum and maximum points in the distribution. The equivalent plastic strain distribution within this same region has values ranging between 0.4 and 1.5 and is not symmetric. Other material state distributions are also given. The crystallographic texture within this isolated shear zone is also compared to the experimental texture and found to match reasonably well considering the simulations are two-dimensional.     

High temperature strength and failure of the Ni-base superalloy PM 3030

The strength, fatigue life and fracture behavior of the oxide dispersion strengthened (ODS) nickel-base superalloy PM 3030 are investigated. The high Al content in PM 3030 leads to the formation of coherent γ′ particles and, thus, to additional precipitation strengthening. A coarse and elongated grain structure (R34) and two isotropic batches with mean grain sizes of 1 μm (R90) and 17 μm (R901315) are considered. Compressive constant strain rate tests and high cycle fatigue (HCF) tests are performed. Optical, scanning and transmission electron microscopy (OM, SEM and TEM) are carried out. The properties are compared with those of the solely oxide dispersion strengthened Ni-base alloy PM 1000 [Estrin, Y., Heilmaier, M., Drew, G., 1999. Creep properties of an oxide dispersion strengthened nickel-base alloy: the effect of grain orientation and grain aspect ratio. Mater. Sci. Eng. A 272(1), 163–173]. It is found that additional γ′ hardening provides an increase in quasi-static strength by about a factor 2 and in HCF life by about a factor 10²–10³ at temperatures up to 850 °C. When fatigue life is compared at a fixed ratio of stress amplitude-to-yield or ultimate compressive strength, R34 shows a fatigue life similar to that of PM 1000 at lower temperature (e.g. 600 °C) indicating that the quasi-static strength advantage is proportionally translated into improved fatigue performance; for higher temperatures (850 °C) however, R34 shows a shorter fatigue life as compared to PM 1000. Grain size reduction, as exemplified with the fine grain R90 batch, also provides an increase in strength up to the equicohesion temperature (T_E) [Dieter, G.E., 1986. Mechanical Metallurgy. SI Metric ed. McGraw-Hill Book Company, London]. Above T_E, faster diffusion and grain boundary sliding [Raj, R., Ashby, M.F., 1971. On the grain boundary sliding and diffusional creep. Metall. Trans. 2, 1113–1127; Spingarn, J.R., Nix, W.D., 1978. Diffusional creep and diffusionally accommodated grain rearrangement. Acta Metall. 26, 1389–1398] lead to a drastic drop in strength for the R90 material. In contrast, the batch with intermediate grain size (R901315) shows strength comparable to that of R34 up to 850 °C. Furthermore, R901315 shows improved crack tolerance compared to its coarse grain counterpart R34. Due to premature crack initiating coarse oxide particles however, R901315 does not show any improvement in elongation to failure during tensile tests. Eliminating those coarse particles is expected to improve the ductility and toughness of this isotropic batch.     

Finite element modeling of tube hydroforming of polycrystalline aluminum alloy extrusions

Finite element modeling of tube hydroforming requires information about the anisotropy of the extruded aluminum tube. Unlike sheet metals, the complex geometry of extruded tubes makes it difficult, except in extrusion direction, to directly measure material properties. Therefore, polycrystalline models provide a good alternative for calculating the anisotropy of the tube in all directions and under various loading conditions. Using a rate-independent single crystal yield surface and rigid plasticity, a Taylor-type polycrystalline model was developed and implemented into ABAQUS/Explicit finite element (FE) code using VUMAT. The constitutive model was then used to calculate the crystallographic texture evolution during the hydroforming of an extruded aluminum tube. Initial crystallographic texture measured using orientation imaging microscopy (OIM) and uniaxial tensile test data obtained along the extrusion direction were input to this FEA model. In order to efficiently and practically simulate the tube hydroforming process using the polycrystalline model, sensitivity to the number of grain orientation, total simulation time, and number of finite elements were studied. Predicted results agreed very well with experimentally measured strain obtained from tube hydroforming process.     

The effect of microstructural representation on simulations of microplastic ratcheting

This paper assesses the sensitivity of cyclic plasticity to microstructure morphology by examining and comparing the microplastic ratcheting behavior of different idealized microstructures (square, hexagonal, tessellated, and digitized from experimental data). This analysis demonstrates the sensitivity of computational accuracy to the various approximations in microstructural representation. The methodology used to perform this study relies on a coupling between microstructural characterization, mechanical testing and numerical simulations to investigate the influence of the microstructure on the purely tensile uniaxial microplastic ratcheting behavior of pure nickel polycrystals. The morphology and deformation behavior of polycrystals were characterized using electron back-scatter diffraction (EBSD), while a finite element model (FEM) of crystal plasticity was used in a computational framework. The predicted cyclic behavior is compared to experimental results both at the macroscopic and microstructural scales. The stress–strain response is less sensitive to the details of the microstructural representation than might be expected with all representations displaying similar macroscopic constitutive response. However, the details of the plastic strain distribution at the microstructural scale and the related estimations of damage mechanics vary substantially from one microstructural representation to another.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

镍基单晶合金蠕变变形过程的描述

基于强化相γ’的筏化－解筏和粗化的细观过程,本文推导了一组用于描述基单在合金蠕变变形过程的蠕变方程,并在９５０℃和７６０℃标定了国产ＤＤ３镍基单晶合金不同晶体取向的模型参数,与实验结果比较,所提模型可以准确地描述蠕变的主要阶段。     

A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals

Modeling of scale-dependent characteristics of mechanical properties of metal polycrystals is studied using both discrete dislocation dynamics and continuum crystal plasticity. The initial movements of dislocation arc emitted from a Frank-Read type dislocation source and bounded by surrounding grain boundaries are examined by dislocation dynamics analyses system and we find the minimum resolved shear stress for the FR source to emit at least one closed loop. When the grain size is large enough compared to the size of FR source, the minimum resolved shear stress levels off to a certain value, but when the grain size is close to the size of the FR source, the minimum resolved shear stress shows a sharp increase. These results are modeled into the expression of the critical resolved shear stress of slip systems and continuum mechanics based crystal plasticity analyses of six-grained polycrystal models are made. Results of the crystal plasticity analyses show a distinct increase of macro- and microscopic yield stress for specimens with smaller mean grain diameter. Scale-dependent characteristics of the yield stress and its relation to some control parameters are discussed.     

Influence of surface effects on fatigue of microcracks nucleation

Cyclic plastic slips in persistent slip bands (PSBs) at the free surface and in the bulk are evaluated for high-cycle fatigue of polycrystals. Analytical results are obtained for PSBs in the bulk and for surface type A PSBs, but the finite element method is used for surface type B PSBs. For practical applications, the results are presented in the form of amplification factors, which are almost insensitive to the PSB aspect ratio and other material parameters. These values are then used to include surface effects in an evaluation of the post-saturation number of cycles to crack nucleation. Some environmental effects are also taken into account. An energy balance criterion is used, and the effect of microslip irreversibilities is evaluated on a statistical basis.     

Elastoplastic modeling for the ductile behavior of polycrystalline sodium chloride with suvic

A unified viscoplastic model with evolutionary state variables, called SUVIC, is reduced to its rate-independent counterpart, and is applied to the inelastic behavior of polycrystalline sodium chloride (salt) in the ductile regime. The proposed model includes a von Misestype yield criterion, an associated flow rule, and three state variables, producing a mixed (kinematic and isotropic) hardening. The evolution laws are expressed through a particular formulation of the Voce law, which is mathematically similar to the Armstrong-Frederick formulation used in numerous mechanical models. This rate-independent version of SUVIC is a simple extension of the well-known two-surface models and can be reduced to various classical elastoplastic models.     

Micro-experimental study of large plastic deformation for high-purity polycrystalline aluminum

This paper aims at revealing various micro- deformation characteristics, such as crystalline slip and grain boundary slide, which are recorded under scanning electronic microscope for high-purity aluminum tensile specimen at room temperature. These experimental data provide us direct evidence for shear localization near the grain boundary network via multi- directional grain boundary slide. The nonuniform deformation induced in the grain interiors would have decisive effect on the plastic flow and failure of polycrystalline materials. Sponsored by the National Natural Science Foundation of China and the Fok Ying- Tung Education Foundation.     

Micro-macro investigations about the fatigue behavior of pre-hardened 304L steel

In this work, the effect of cyclic pre-hardening (CPH) and monotonic pre-hardening (MPH), on the Cyclic Stress-Strain Curve (CSSC) and fatigue are considered. New tension-compression tests on two types of 304L alloys used in nuclear power plants are carried out under the following conditions: (i) strain or stress control near endurance limit; (ii) zero or positive mean stress; (iii) virgin, CPH or MPH specimens. Macroscopic results show a detrimental effect of pre-hardening in strain control and a beneficial one in stress control. Some macroscopic considerations are given to explain this result and the effects of an applied mean stress which differ under stress and strain control. Relations between macroscopic results and microstructures at failure are investigated using SEM and TEM. SEM is used for analysis of fatigue striation space.TEM analyses suggest that cyclic pre-hardening mainly promotes wavy slip during subsequent fatigue testing, while monotonous pre-loading favors planar slip. For CPH case it seems that primary cells which are preserved and refined for the most part during fatigue testing, constitute the hard stable structure. After MPH and subsequent fatigue testing, a hard structure is constituted by embedding of three kinds of microstructures, small twins, small cells, crossing twin systems. The formation of a hard structure creates an important internal stress. Observation shows that in pre-hardened specimens, softening arrays as veins and PSBs are frequent under strain control and rather scarce under stress control. It can be so deduced that the increase of fatigue life by pre-hardening in stress control is related to reduced mean free path of mobile dislocations due to internal stress.The obtained results may help to understand some aspects about linear versus non linear fatigue damage accumulation.