Influence of microstructure variability on short crack growth behavior

Fatigue life in metals is predicted utilizing regression analysis of large sets of experimental data. Furthermore, a high variability in the short crack growth (SCG) rate has been observed in polycrystalline materials, in which the evolution and distribution of local plasticity is strongly influenced by the microstructure features. We aim to identify relationships between the crack driving force and the materials microstructure; specifically addressing variability of microstructure features and slip activity near a crack-tip as a means to account for the variability in the SCG behavior. To investigate the effects of microstructure variability on the SCG rate, sets of different microstructure realizations are constructed, in which cracks of different length are introduced to mimic quasi-static SCG. Through fatigue indicator parameters within crystal plasticity models, scatter within the SCG rates is related to variability in the microstructural features as a means to quantify uncertainty in fatigue behavior

Influence of microstructure variability on short crack growth behavior

Fatigue life in metals is predicted utilizing regression analysis of large sets of experimental data, thus representing the material’s macroscopic response. Furthermore, a high variability in the short crack growth (SCG) rate has been observed in polycrystalline materials, in which the evolution and distributionof local plasticity is strongly influenced by the microstructure features. The present work serves to (a) identify the relationship between the crack driving force based on the local microstructure in the proximity of the crack-tip and (b) defines the correlation between scatter observed in the SCG rates to variability in the microstructure. A crystal plasticity model based on the fast Fourier transform formulation of the elasto-viscoplastic problem (CP-EVP-FFT) is used, since the ability to account for the both elastic and plastic regime is critical in fatigue. Fatigue is governed by slip irreversibility, resulting in crack growth, which starts to occur during local elasto-plastic transition. To investigate the effects of microstructure variability on the SCG rate, sets of different microstructure realizations are constructed, in which cracks of different length are introduced to mimic quasi-static SCG in engineering alloys. From these results, the behavior of the characteristic variables of different length scale are analyzed: (i) Von Mises stress fields (ii) resolved shear stress/strain in the pertinent slip systems, and (iii) slip accumulation/irreversibilities. Through fatigue indicator parameters (FIP), scatter within the SCG rates is related to variability in the microstructural features; the results demonstrate that this relationship between microstructure variability and uncertainty in fatigue behavior is critical for accurate fatigue life prediction

A General Probabilistic Framework Combining Experiments and Simulations to Identify the Small Crack Driving Force

Identifying the small fatigue crack (SFC) driving force of polycrystalline engineering alloys is instrumental in correlating the inherent microstructure variability and the scatter exhibited by SFC during the early stage of propagation. By utilizing synchrotron images of a SFC propagating through a beta-metastable titanium alloy a general framework to identify the SFC driving force is presented. FFT-based crystal plasticity simulations are then used to computed micromechanical quantities not available from the experiment. The experimental and simulation results are consolidated into a multimodal dataset which is sampled using physically based non- local data mining techniques. Sampled data are analyzed via a machine learning Bayesian Network framework to identify statistically relevant correlations between micromechanical fields and the SFC propagation direction and rate. Statistically relevant correlations are further analyzed and critical variables are selected to formulate a data driven SFC driving force. The predictive capabilities of the identified SFC driving force are evaluated by comparing experimental data and simulations. Furthermore, a comparison between the proposed SFC driving force and the ones available in the literature is also presented. Results show the stronger quantitative behavior of the identified SFC driving force compared to most commonly used in literatur

Assessing the reliability of fast Fourier transform-based crystal plasticity simulations of a polycrystalline material near a crack tip

International audienc

Using machine learning and a data-driven approach to identify the small fatigue crack driving force in polycrystalline materials

International audienceThe propagation of small cracks contributes to the majority of the fatigue lifetime for structural components. Despite significant interest, criteria for the growth of small cracks, in terms of the direction and speed of crack advancement, have not yet been determined. In this work, a new approach to identify the microstructurally small fatigue crack driving force is presented. Bayesian network and machine learning techniques are utilized to identify relevant micromechanical and microstructural variables that influence the direction and rate of the fatigue crack propagation. A multimodal dataset, combining results from a high-resolution 4D experiment of a small crack propagating in situ within a polycrystalline aggregate and crystal plasticity simulations, is used to provide training data. The relevant variables form the basis for analytical expressions thus representing the small crack driving force in terms of a direction and a rate equation. The ability of the proposed expressions to capture the observed experimental behavior is quantified and compared to the results directly from the Bayesian network and from fatigue metrics that are common in the literature. Results indicate that the direction of small crack propagation can be reliably predicted using the proposed analytical model and compares more favorably than other fatigue metrics. INTRODUCTION Modeling the propagation of small fatigue cracks, especially cracks that are intragranular in nature, requires information about how the underlying microstructure affects the crack behavior. While, crack initiation has been modeled as both stochastic 1,2 and deterministic, 3-6 there is still an open question if the small fatigue crack behavior can be predicted. Small crack propagation follows crystallographic directions and planes, and thus is said to be a slip-mediated process. 7-9 The behavior of long cracks is well described by linear elastic fracture mechanics through the Paris law. 10 While for small cracks, the propagation rate strongly deviates from linear elastic fracture mechanics behavior and exhibits large scatter, 11-13 based on the complex interactions between the small crack and the local microstructure. Several relationships have been proposed to capture the small crack behavior, albeit these theories have not been validated at the appropriate length-scale due to prior limitations in the experimental measurements. With the advent of synchrotron-based x-ray tomography and diffraction techniques combined with in situ loading, the necessary data are available for the crack direction and propagation rate with respect to the microstructure. In this work, experimental data for the evolution of a fatigue crack relative to the local microstructure during in situ loading 14,15 are used as the foundation to build a model for the driving force of small fatigue cracks. Based on the 3D nature and intricacies of the local crack growth process, simple relationships governing the fatigue crack dynamics are very difficult to extract, thus data-driven approaches offer a promising path forward. Specifically, machine-learnin

Accurate Effective Stress Measures: Predicting Creep Life for 3D Stresses Using 2D and 1D Creep Rupture Simulations and Data

Abstract Operating structural components experience complex loading conditions resulting in 3D stress states. Current design practice estimates multiaxial creep rupture life by mapping a general state of stress to a uniaxial creep rupture correlation using effective stress measures. The data supporting the development of effective stress measures are nearly always only uniaxial and biaxial, as 3D creep rupture tests are not widely available. This limitation means current effective stress measures must extrapolate from 2D to 3D stress states, potentially introducing extrapolation error. In this work, we use a physics-based, crystal plasticity finite element model to simulate uniaxial, biaxial, and triaxial creep rupture. We use the virtual dataset to assess the accuracy of current and novel effective stress measures in extrapolating from 2D to 3D stresses and also explore how the predictive accuracy of the effective stress measures might change if experimental 3D rupture data was available. We confirm these conclusions, based on simulation data, against multiaxial creep rupture experimental data for several materials, drawn from the literature. The results of the virtual experiments show that calibrating effective stress measures using triaxial test data would significantly improve accuracy and that some effective stress measures are more accurate than others, particularly for highly triaxial stress states. Results obtained using experimental data confirm the numerical findings and suggest that a unified effective stress measure should include an explicit dependence on the first stress invariant, the maximum tensile principal stress, and the von Mises stress

Predicting the 3D fatigue crack growth rate of short cracks using multimodal data via Bayesian network: in-situ experiments and crystal plasticity simulations

International audienceSmall crack propagation accounts for most of the fatigue life of engineering structures subject to high cycle fatigue loading conditions. Determining the fatigue crack growth rate of small cracks propagating into polycrystalline engineering alloys is critical to improving fatigue life predictions, thus lowering cost and increasing safety. In this work, cycle-by-cycle data of a small crack propagating in a beta metastable titanium alloy is available via phase and diffraction contrast tomography. Crystal plasticity simulations are used to supplement experimental data regarding the micromechanical fields ahead of the crack tip. Experimental and numerical results are combined into a multimodal dataset and sampled utilizing a non-local data mining procedure. Furthermore, to capture the propensity of body-centered cubic metals to deform according to the pencil-glide model, a non-local driving force is postulated. The proposed driving force serves as the basis to construct a data-driven probabilistic crack propagation framework using Bayesian networks as building blocks. The spatial correlation between the postulated driving force and experimental observations is obtained by analyzing the results of the proposed framework. Results show that the above correlation increases proportionally to the distance from the crack front until the edge of the plastic zone. Moreover, the predictions of the propagation framework show good agreement with experimental observations. Finally, we studied the interaction of a small crack with grain boundaries (GBs) utilizing various slip transmission criteria, revealing the tendency of a crack to cross a GB by propagating along the slip directions minimizing the residual Burgers vector within the GB

Combining Experiments and Models via a Bayesian Network Approach to Predict Short Fatigue Crack Growth

International audienceIdentifying the short crack driving force of polycrystalline engineering alloys is critical to correlate the inherent microstructure variability and the uncertainty in the short crack growth behavior observed during stage I fatigue crack growth. Due to recent experimental advancements, data of a short crack propagating at the relevant length scale is available via phase and diffraction contrast tomography. To compute the micromechanical fields not available from the experiment, crystal plasticity simulations are performed. Results of the experiment and simulations are combined in a single dataset and sampled utilizing non-local mining technique. Sampled data is analyzed using a machine learning Bayesian Network framework to identify statically relevant correlations between state variables, microstructure features, location of the crack front, and experimentally observed growth rate, in order to postulate a data-driven, non-parametric short crack driving force

Combining Experiments and Models via a Bayesian Network Approach to Predict Short Fatigue Crack Growth

International audienceIdentifying the short crack driving force of polycrystalline engineering alloys is critical to correlate the inherent microstructure variability and the uncertainty in the short crack growth behavior observed during stage I fatigue crack growth. Due to recent experimental advancements, data of a short crack propagating at the relevant length scale is available via phase and diffraction contrast tomography. To compute the micromechanical fields not available from the experiment, crystal plasticity simulations are performed. Results of the experiment and simulations are combined in a single dataset and sampled utilizing non-local mining technique. Sampled data is analyzed using a machine learning Bayesian Network framework to identify statically relevant correlations between state variables, microstructure features, location of the crack front, and experimentally observed growth rate, in order to postulate a data-driven, non-parametric short crack driving force

Microstructurally-Short Crack Growth Driving Force Identification: Combining DCT, PCT, Crystal Plasticity Simulations and Machine Learning Technique

International audienceIdentifying the Microstructurally-Short Crack (MSC) growth driving force of polycrystalline engineering alloys is a critical need in assessing performances of materials subject to fatigue load and to improve both material design and component life prediction. However, due to (i) the lack of “cycle-by-cycle” experimental data, (ii) the complexity of MSC growth phenomenon, and (iii) the incomplete physics of constitutive relationships, only simple driving force metrics, inadequate to predict MSC growth, have been postulated. Based on experimental results by Ludwig, Guilhem, et al., “cycle-by-cycle” data of a MSC propagating through a beta-metastable titanium alloy are available via phase and diffraction contrast tomography. To identify the crack driving force, we developed a framework utilizing the aforementioned experimental results and FFT-based crystal plasticity simulations (to compute micromechanical fields not available from the experiment). These results are combined and converted into probability distributions for use in a Bayesian Network