Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics

Chemical weathering induced by reactive fluid circulation critically affects the mechanical properties of sedimentary rocks involved in subsurface energy applications such as geothermal systems and underground energy storage. This work investigates chemo-mechanical degradation in bonded granular geomaterials through a multiscale approach combining discrete and continuum modeling.At the grain scale, Discrete Element Method (DEM) simulations are used to study dissolution-driven debonding under oedometric conditions. The evolution of the lateral earth pressure coefficient k0 used as a proxy for stress state, is analyzed as a function of cementation degree, confining pressure, initial stress anisotropy, and loading history. Progressive dissolution leads to convergence toward an attractor stress state, with k0​ stabilizing between 0.3 and 0.4 independently of initial conditions. This behavior results from the collapse of cement-stabilized force chains and chemical softening of grains.At the continuum scale, a phase-field fracture model coupled with damage-enhanced reactive diffusion is developed, informed by micromechanically derived degradation laws from DEM simulations. The model reveals that higher initial cementation delays brittle fracture initiation, while increased acidity may induce a chemical ductilization effect that counter-intuitively postpones fracture due to localized softening ahead of crack tips. The competing effects of chemical softening and degradation of fracture toughness are quantitatively characterized.

Modeling damage and ductile crack growth in metallic materials has been of interest over the last four decades. Damage models of increasing complexity have been employed to characterize and predict the ductile crack growth in materials. A short review of the existing ductile crack growth models has been provided. Recently, a strain-based damage model has been advanced by researchers, which is capable of capturing the stress and strain states for the incipient damage within the material while being able to capture the triaxiality parameter. In this work a strain based ductile fracture damage model has been employed to model specimens with three different crack geometries, namely a single-edge notch tension SEN(T), compact-tension C(T), and outer diameter (OD) axial surface-cracked pipe. The predictions from the ductile crack growth model have been compared to experimental findings of the crack growth (obtained using a d-c Electric Potential measurement technique) and the corresponding load levels and crack opening displacements (CODs). The points of similarity between the experimental measurements and the fracture surface observations of crack growth and the predictions from the finite element modeling (FEM) approach have been discussed. The same X80 material properties and damage model parameters were employed to benchmark the ductile crack growth in two different SEN(T) specimens with differing normalized crack depths (crack/width ratios, a/W), a C(T) specimen (a/W = 0.5), and an OD SC pipe (a/t = 0.6) to shed light on the predictability of the crack initiation event and the subsequent ductile crack growth until failure. The findings provide credence to the applicability of the new approach for piping materials while providing a framework for flaw evaluation methodologies. The investigation also opens the doors for regions where mesh regularization methods and modeling approaches along with mathematical relations can be developed to form a more efficient framework for modeling specimens with diverse constraints efficiently.

ABSTRACT: To study the effects of loading rate on the fracture characteristics, sandstone samples with a center notch were used in three-point bend experiment for the loading rates of 0.0004, 0.004, 0.04, 0.4 and 4mm/min of crack mouth opening displacement. We divided the fracture process zone into elastic zone (εxx < 0.08%), plastic zone (0.08% < εxx < 0.4%) and damage zone (εxx > 0.4%) based on the displacement and strain field around the fracture tip. The shape of the fracture process zone is candle-like, and the damage zone is within the plastic zone. The fracture process zone length and width are reduced by 36% and 23% when the loading rate increases by 3 orders of magnitude. The damage zone decreases from 56% to 40% with 3 orders' increase in loading rate; that is, the plasticity is enhanced from high fracture velocity. The rough fracture surface is induced by local microcrack slip and expansion in the fracture process zone from high loading rates. The proposed method of dividing the fracture process zone into a plastic-damage zone is of significance for studying the stress distribution and fracture energy calculation in the rock fracture. 1. INTRODUCTION The rock is a quasi-brittle material with mineral particles, cracks and pores, leading to a micro-crack zone in the fracture tip subjected to an external load, called fracture process zone (FPZ). FPZ generally refers to the region of fracture from fracture initiation to instability, and its length can be considered as subcritical propagation length. The mechanisms of microcrack, branching and slip along cracks lead to nonlinear fracture growth behaviors of rock. The stress-intensity factor (k) describes the elastic stress distribution with little yield zone at the crack tip. The crack growth occurs when k equals to fracture toughness (kc), a material property independent of fracture velocity. In general, the fracture velocity is positively correlated with loading rate. The relationship between fracture velocity and crack driving force is often described by a power law or an Arrhenius law (Ponson L, 2009). To involve the effects of fracture velocity, Paris, (1961) proposed the power law relationship between stress-intensity factor range Δk and crack growth rate da/dN to study fatigue failure. Atkinson, (1984) reviewed the experimental data on the subcritical crack growth in geological materials, indicating that a power equation (v∼kn) can be capable of describing fracture velocity - stress intensity factor. Zhou, (2009) et al. used three-point bend tests to determine the critical strain energy density factor of Huanglong limestone with loading rate ranging from 10-4∼10-1mm/s. A cohesive zone model (CZM) was proposed based on the traction-separation law (TSL) to study both crack initiation and propagation (Dugdale D S, 1960). To add rate effect to the CZM, two methods were raised, including the rate-dependent constitutive model in the bulk material and the rate-dependency in the TSL (Salih S, 2018). The non-negligible nonlinear deformation around the fracture tip, namely the FPZ, is responsible for rate-dependent rock fracture growth.

Many anisotropic damage models have been proposed for different materials, ductile as well as quasi-brittle. The main drawback of the corresponding analyzes is that a large number of material parameters is often introduced, leading to identification difficulties and also to model complexity and associated numerical difficulties. It is also sometimes difficult to ensure the continuity of the stresses if the quasi-unilateral effect of microcracks closure and the dissymmetry tension/ compression are represented. In order to solve those difficulties, one proposes to write the damage models in a specific nonstandard thermodynamics framework. The damage states are represented by a symmetric second-order tensor and the damage rate is assumed governed by a positive second-order tensor having a clear meaning: the absolute or the positive value of the plastic strain rate tensor for ductile materials, the positive part of the total strain tensor in quasi-brittle materials. Such a nonstandard feature makes the proof of the the positivity of the intrinsic dissipation necessary. This important proof is given in the considered framework for any damage law ensuring (anisotropic) damage increase and for any case, 3D, proportional or nonproportional. This extends then to induced anisotropy the isotropic case property of a positive damage rate as a sufficient condition for the thermodynamics second principle to be fulfilled. Altogether with the fact that the thermodynamics potential can be continuously differentiated, the example of an anisotropic damage model for concrete (build in this framework) is given. It allows for robust finite element implementation. Both space (classical nonlocal with internal length, nonlocal with internal time) and time regularizations (visco- or delay-damage) are used and applied to quasi-static and dynamic cases. Examples on concrete and reinforced concrete structures are given.

The response of underground structures and transportation facilities under various external loadings and environments is critical for human safety as well as environmental protection. Since quasi-brittle materials such as concrete and rock are commonly used for underground construction, the constitutive modeling of these engineering materials, including post-limit behaviors, is one of the most important aspects in safety assessment. From experimental, theoretical, and computational points of view, this report considers the constitutive modeling of quasi-brittle materials in general and concentrates on concrete in particular. Based on the internal variable theory of thermodynamics, the general formulations of plasticity and damage models are given to simulate two distinct modes of microstructural changes, inelastic flow and degradation of material strength and stiffness, that identify the phenomenological nonlinear behaviors of quasi-brittle materials. The computational aspects of plasticity and damage models are explored with respect to their effects on structural analyses. Specific constitutive models are then developed in a systematic manner according to the degree of completeness. A comprehensive literature survey is made to provide the up-to-date information on prediction of structural failures, which can serve as a reference for future research.

A multiscale modeling of damage accumulation and permeability variation in shale rocks under mechanical loading

On the equivalence of Eulerian Smoothed Particle Hydrodynamics, Total Lagrangian Smoothed Particle Hydrodynamics and molecular dynamics simulations for solids

Lithium-ion batteries are a key enabler for a low-carbon future, however their performance and lifetime are influenced by complex and coupled electrochemical, thermal and mechanical factors across different length and time scales. In this talk, we explore the key degradation modes which limit battery lifetime and how multi-scale models can help describe these effects towards improved cell designs and device control. At the particle level, we explore how phase field fatigue models of cathode particles can be used to understand crack growth, leading to loss of active material [1]. Here, non-linear crack growth is observed due to the fatigue of material properties and crack merger, leading to a transition from slow to rapid crack growth rate. Use of these models can identify critical C-rates and particle sizes which mitigate cracking.At the continuum scale, we then investigate how these stresses evolve during cycling, with stress heterogeneities arising initially at the electrode-separator interface, but later propagating to the electrode-current collector interface [2]. We then extend this study to composite anodes of graphite and silicon, where highly non-linear behaviour is observed [3]. Here, the graphite phase provides the majority of the reaction current density at high state-of-charge operation, with this then shifting to the silicon phase at low state-of-charge operation, with hysteresis effects observed due to the silicon. This behaviour is attributed mostly to the different open circuit potentials of the two different phases. Finally, we explore how these effects propagate to the battery pack scale and highlight the divergence of material level performance from their real-world implementation [4].

Smoothing gradient damage model with evolving anisotropic nonlocal interactions tailored to low-order finite elements

Particle breakage in milling operations is often modeled using population balance models (PBMs). A discrete element method (DEM) model can be coupled with a PBM in order to explicitly identify the effect of material properties on breakage rate. However, the DEM-PBM framework is computationally expensive to evaluate due to high-fidelity DEM simulations. This limits its application in continuous process modeling for dynamic simulation, optimization, or control purposes. The current work proposes the use of surrogate modeling (SM) techniques to map mechanistic data obtained from DEM simulations as a function of processing conditions. To demonstrate the benefit of the SM-PBM approach in developing integrated process models for continuous pharmaceutical manufacturing, a comill-tablet press model integration utilizing the proposed framework is presented. The SM-PBM approach is in excellent agreement with the DEM-PBM approach to predict particle size distributions (PSDs) and dynamic holdup, with a maximum sum of square errors of 0.0012 for PSD in volume fraction and 0.93 for holdup in grams. In addition, the time taken to run a DEM simulation is in the order of days whereas the proposed hybrid model takes few seconds. The SM-PBM approach also enables comill-tablet press model integration to predict tablet properties such as weight and hardness. The proposed hybrid framework compares well with a DEM-PBM framework and addresses limitations on computational expense, thus enabling its use in continuous process modeling.

Modelling Crack Growth within Graphite Bricks due to Irradiation and Radiolytic Oxidation

In recent years, growing human population is more and more dependent on production of various wares which are dependent on the functionality of manufacturing technologies. The Laboratory of bulk materials solves many problems of flow failure in different technologies and processes with particulate materials. A perfect understanding of powder behaviour is very important for optimization processes. Due different mechanical and physical properties of a wide scale of particulate materials it is very hard to design appropriate technologies. Goal of this paper is to subscribe some samples of powdered coal by the measurement of its mechanical and physical properties important for storage of the bulk solids. Experimental work was performed by the Freeman Technology FT4 Powder Rheometer and Cilas 1190 Particle Size Analyser. The device allows obtaining a considerable amount of information about powder behaviour from basic bulk density until friction or mechanical interlocking. It was found that dominant parameter in storage process is compressibility. Dependence between compressibility and the ratio of the microparticles and nanoparticles was observed. Depending on the granulometry of samples different compressibility and angle of internal friction was observed. The measured properties of powdered coal have been used for determine cohesion and easy-flowing to free flowing regime. The aim of this article is bulk solid behaviour prediction based on specific properties like compressibility, angle of internal friction, wall friction, angle of repose, humidity, cohesion and others. We need to find a way how to completely describe powders and bulk solids by a few parameters. The problem is bulk solids are very complex and wide field of specialization. Laboratory of Bulk Materials at Technical University of Ostrava is focused on measurement of mechanical and physical properties of the bulk solids and powders and simultaneously it deals with virtual DEM (Discrete Element Method) simulations of particulate matters. Nowadays we are able to predict behavior of bulk materials based on verified models in DEM simulations and flow properties measurement. These simulations are used in innovative way of designing storage and process devices in all kinds of industry.

Since the flux leakage phenomenon is dominant in the inner and outer radii of axial flux magnetic gears (AFMGs), a prominent overestimation of torque prediction is obtained by the 2-D analytical method (AM) in comparison with the 3-D finite-element method (FEM) simulations. The main motivation of this paper is to present an improved quasi-3-D AM (IQAM), which is an improvement and amendment of the 2-D AM by a simple and effective radial dependence modeling of the axial and tangential magnetic field distribution in AFMGs. This IQAM plays an important role in a reliable and accurate prediction of static and transient behavior of AFMGs. The cogging torque of the AFMG is predicted using the obtained IQAM and Maxwell’s stress tensor. However, the proposed IQAM will become more prominent by focusing on the effects of single- and dual-skews’ designs for ferromagnetic pole-pieces and permanent magnets through suitable step changes in a combined skewed-MG model, as an effective passive method, in order to mitigate the cogging torque and thereby intensively augmenting torque quality in an exemplary AFMG. The accuracy of the developed skewing method is verified using 3-D FEM simulations.

A novel microstructure-informed machine learning framework for mechanical property evaluation of SiCf/Ti composites

Many material properties of alloys are strongly influenced by the precipitation of secondary phases in the bulk material. Traditional alloys have been polycrystalline, but over the years many types of advanced alloys have been obtained by precise tailoring of microstructure. One of these advanced alloys is the metallic glass, which is obtained by rapid quenching of a liquid into a metastable amorphous solid. The lack of long-range ordering in this phase has been shown to yield remarkable material properties such as extremely high yield strength and high corrosion resistance. One drawback of the amorphous phase is that it is very brittle and critical failure caused by a heterogeneous dislocation density is common. At the frontier of research on glassy-type alloys are the nanocrystalline composite alloys, where a controlled dispersion of nanosized crystallites is allowed to form by controlled heat treatment of the alloy system, yielding even more refined material properties. For example, alloys with high ductility and high strength, tunable corrosion resistance, or excellent soft-magnetic properties have been obtained. Regardless of whether the alloy is glassy, nanocrystalline, or polycrystalline, engineering of the microstructure is key, but far from trivial. A theoretical method well suited for simulating distributions of precipitates on a continuum scale is the classical nucleation and growth theory (CNGT), where the statistical precipitate population within a unit volume can be simulated. To quantitatively study colloid distributions of precipitates experimentally, small-angle scattering (SAS) is an advantageous method.This licentiate thesis is based on two research papers on precipitation in glassy alloys. Paper I is about oxygen-induced, unwanted, crystallization in the commercially available glassy alloy AMLOY-ZR01 (Zr Cu Al Nb ). Using X-ray characterization tech- niques and CNGT, the impact on phase transformations of this hard, ductility-deteriorating phase was investigated at various oxygen concentrations during rapid heating. The oxygen concentration is shown to be strongly correlated with the phase-formation hierarchy. This study thoroughly elucidates how oxygen impurities affect the devitrification of Zr-based bulk metallic glass (BMG), which is one of the main obstacles in overcoming the pro- cessing of BMG with additive manufacturing (AM). Paper II focuses on the analysis of SAS data from X-rays (SAXS) using the indirect Fourier-based model fitting approach. A method for separating model parameters is implemented and thoroughly benchmarked toward the standard method. A reduced computational wall time is obtained while the parameter precision is maintained. The Fourier-based model is found to inherently suffer from parameter correlations, and large discrepancies to the true values are observed when the intensity peak in the signal is not well defined. Based on the obtained results, a program called pySASA, which is built with parallelization using message passing interface to rapidly fit large batches of data, is presented. The solution structure around which this program is built can be one of the keys to keeping the full model analysis of SAS datarelevant in the future.