Microstructurally Small Crack Research Articles

Statistical analysis of microstructurally small fatigue crack growth in three-dimensional polycrystals based on high-fidelity numerical simulations

Microstructurally small cracks (MSCs) are sensitive to their local microstructural neighborhoods, resulting in highly variable 3D crack propagation within individual samples and among a population of samples. Statistically quantifying this complex spatiotemporal variability requires collecting and analyzing a large number of 3D MSC growth observations, which remains challenging due to experimental constraints that limit the availability of 3D observations of MSCs in the existing literature. We address this gap by leveraging virtual observations of MSC growth using a state-of-the-art, high-fidelity simulation framework to provide a statistical perspective on 3D MSC growth behavior. The MSC growth simulations were performed in 40 unique but statistically similar polycrystalline microstructures, and the data extracted from the virtual observations were collectively analyzed to quantify variability in geometric, microstructural, and micromechanical aspects of MSCs. Variability in tortuosity, crack surface crystallography, and MSC growth parameters (local crack extension and kink angle) were quantified statistically. The results show that 3D MSC surfaces do not necessarily propagate along {111} crystallographic planes despite crack traces on radial planes being closely aligned with {111} slip plane traces. Also, the 3D MSC surfaces exhibit increasingly tortuous propagation and spatially varying local crack growth rates (with variability as high as 59% among the population). Moreover, a correlation study revealed some of the highly influential microstructural and micromechanical features controlling MSC growth parameters. The quantified variability holds direct implications for advanced materials prognosis in engineering applications, and the identified features from the correlation study can be leveraged to train machine learning models for rapidly predicting MSC growth behavior in the future.

Microstructurally and mechanically small fatigue crack growth behaviors of 316LN stainless steel in high-temperature pressurized water

Corrosion fatigue behaviors at different stages of microstructurally small crack (MSC) and mechanically small crack (MeSC) for 316LN stainless steel were investigated in high-temperature pressurized water by interrupted tests. An improved model about the proportion in total fatigue life and growth rate for the MSC and MeSC has been proposed. It is found that the proportion in total fatigue life for the MSC is lower and the crack growth rate is higher at a lower strain rate due to the high plastic deformation and dislocation density at grain boundary. Mechanism of crack growth in high-temperature pressurized water is discussed.

Four-dimensional microstructurally small fatigue crack growth in cyclically loaded nickel superalloy specimen

We nondestructively image a low-solvus high refractory (LSHR) nickel base specimen microstructure during cyclic loading to characterize crack propagation during the microstructurally small crack (MSC) growth regime. Micro-computed tomography (μCT) is used to characterize the material density and identify crack interfaces, while high-energy diffraction microscopy (HEDM) provides snapshots of the microstructural orientation field changes. From these measurements, data are computationally reconstructed and coregistered to describe the specimen’s configuration before load, before crack nucleation, and throughout the crack propagation/loading process. An MSC forms at a FIB-cut notch, which was previously placed to concentrate stress at the center of the specimen gauge, and propagates along a facet parallel to the local {111} crystallographic plane. Analysis of available crystallographic slip directions and measured point-to-point disorientation axes indicate probable single and coplanar slip activity along FCC octahedral planes within this region. Similar analyses of other crack propagation facets reveal generally slower growth along directions favoring zig-zag cross and codirectional cross slip, which are often disfavored at room temperature.

Convolutional neural networks for expediting the determination of minimum volume requirements for studies of microstructurally small cracks, part II: Model interpretation

A significant question in the study of microstructurally small cracks (MSCs) is: What is the minimum microstructural volume that should be included in studies involving MSCs? To answer this, representative volume elements for microstructurally small cracks (RVEMSC), or the minimum volume of microstructure required around an MSC to achieve convergence of crack-front parameters with respect to volume size, were previously determined using finite element (FE) simulations. The large computational expense of determining RVEMSC via FE simulations motivated the implementation of convolutional neural networks (CNNs) to expedite the determination of RVEMSC (Part I). In addition to expediting the determination of RVEMSC, trained CNNs provide the opportunity to gain insights about RVEMSC predictions through various interpretation methods, which we investigate in the current work. First, an inspection of CNN predictions reveals trends learned by the CNN. Second, an input sampling grid study offers insights into the volume of microstructure around an MSC that most influences predictions of RVEMSC. Third, an input feature sensitivity analysis compares the influence of microstructural and geometrical features on RVEMSC predictions. Fourth, visual inspections of saliency maps reveal the local microstructure that is most important to the CNN when predicting RVEMSC. The CNN interpretation results show that microstructural features are more critical than geometrical features to the CNN predictions. Despite inherent limitations in interpreting saliency maps, the results demonstrate that the CNN can learn to identify various microstructural arrangements at individual crack-front points. Overall, this study highlights the importance of considering a variety of microstructural instantiations when determining RVEMSC, as RVEMSC should be a conservative minimum volume requirement that applies across a wide range of microstructural instantiations.

Convolutional neural networks for expediting the determination of minimum volume requirements for studies of microstructurally small cracks, Part I: Model implementation and predictions

Convolutional neural networks (CNNs) are implemented to expedite the determination of representative volume elements for microstructurally small cracks (RVEMSC). By definition, RVEMSC is the minimum volume of microstructure required around a microstructurally small crack (MSC) to achieve convergence of crack-front parameters with respect to volume size. In a previous study, RVEMSC was determined using a computationally expensive finite-element (FE) framework involving the simulation of many microstructural instantiations. With the aim of increasing the computational efficiency of determining RVEMSC, CNNs are leveraged herein to reduce the number of FE simulations required to determine RVEMSC. Using data from the previous FE-based RVEMSC study, CNNs are trained to predict RVEMSC,ip values, which quantify crack-front parameter convergence with respect to volume size for microstructural instantiation i evaluated at individual crack-front points p, given local microstructural and geometrical information. Predicted RVEMSC,ip values are subsequently used to estimate RVEMSC values. Studies are carried out to determine the optimal amount of training data, assess CNN-based RVEMSC estimation performance, and demonstrate the use of CNNs as microstructural-instantiation screening tools by enabling downselection of microstructures that are considered critical in terms of volume requirements. Individual and ensemble CNN predictions are compared. While CNNs are not found to be accurate enough to replace all FE simulations, CNNs are found to be effective as a rapid screening tool for improving the efficiency of the FE-based RVEMSC determination framework and for expediting future RVEMSC studies.

Fatigue life prediction of nickel-based GH4169 alloy on the basis of a multi-scale crack propagation approach

This paper was concerned with an approach to predict fatigue life based on a multi-scale crack propagation model. The expressions of crack propagation rates in microstructurally small crack (MSC), physically small crack (PSC) and long crack (LC) stages were unified in the multi-scale crack propagation model. Its integral form presented a fatigue life prediction approach. The nickel-based GH4169 alloy was employed to validate the prediction capacity of present approach. The prediction results of lives of specimens with different initial defects sizes were compared with the experimental data.

Effect of Stress Ratio on the Fatigue Crack Propagation Behavior of the Nickel-based GH4169 Alloy

The fatigue crack growth behavior of the newly developed GH4169 nickel-based alloy at a maximum stress of 700 MPa and different stress ratios was investigated in the present work employing the specimens with a single micro-notch at a frequency of 129 Hz at room temperature. The results demonstrate a typical three-stage process of fatigue crack propagation processing from the microstructurally small crack (MSC) stage to the physically small crack (PSC) stage, and finally to the long crack stage. The crack growth rate in the MSC stage is relatively high, while the crack growth rate in the PSC stage is relatively low. A linear function of crack-tip reversible plastic zone size was proposed to predict the crack growth rate, indicating an adequate prediction solution.

Cyclic behavior and modeling of small fatigue cracks of a polycarbonate polymer

The fatigue behavior of a polycarbonate (PC) thermoplastic material was experimentally investigated and modeled using a MultiStage Fatigue (MSF) model that evaluates fatigue crack incubation, Microstructurally Small Crack (MSC) growth, and Long Crack (LC) growth. A set of fully reversed strain controlled tests were conducted, and an analysis of the fracture surfaces was performed using Scanning Electron Microscopy (SEM) in order to quantify the structure-property relationships for the MSF model. Fractography of the microstructure revealed that incompletely melted PC pellets were present in the polymer material that nucleated the cracks along with crazes generated on the surface. Crack lengths and fatigue crack growth rates for the MSC regime were measured from striation observations on the fracture surfaces. Discontinuous crack growth (DCG) cycles between fatigue striations, for the current iteration of the model, are accounted for by the MSF crack incubation regime. Finally, the microstructure sensitive MSF model was implemented using the observed fatigue crack growth measurements. In addition, a Monte Carlo (MC) Simple Random Sampling (SRS) routine was implemented to quantify the model uncertainty for crack growth.

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.

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.

Multistage Fatigue Modeling of Cast A356-T6 and A380-F Aluminum Alloys

This article presents a microstructure-based multistage fatigue (MSF) model extended from the model developed by McDowell et al.[1,2] to an A380-F aluminum alloy to consider microstructure-property relations of descending order, signifying deleterious effects of defects/discontinuities: (1) pores or oxides greater than 100 μm, (2) pores or oxides greater than 50 μm near the free surface, (3) a high porosity region with an area greater than 200 μm, and (4) oxide film of an area greater than 10,000 μm2. These microconstituents, inclusions, or discontinuities represent different casting features that may dominate fatigue life at stages of fatigue damage evolutions. The incubation life is estimated using a modified Coffin–Mansion law at the microscale based on the microplasticity at the discontinuity. The microstructurally small crack (MSC) and physically small crack (PSC) growth was modeled using the crack tip displacement as the driving force, which is affected by the porosity and dendrite cell size (DCS). When the fatigue damage evolves to several DCSs, cracks behave as long cracks with growth subject to the effective stress intensity factor in linear elastic fracture mechanics. Based on an understanding of the microstructures of A380-F and A356-T6 aluminum alloys, an engineering treatment of the MSF model was introduced for A380-F aluminum alloys by tailoring a few model parameters based on the mechanical properties of the alloy. The MSF model is used to predict the upper and lower bounds of the experimental fatigue strain life and stress life of the two cast aluminum alloys.