Numerical and experimental comparisons of the coplanar coalescence of two fluid-driven fractures

Brice Tanguy Alphonse Lecampion, Carlo Peruzzo
2021
Discussion par affiche

Résumé

The coalescence of two coplanar fractures growing under the symmetric injection of a Newtonian fluid from two point sources provides a unique data set to validate theoretical predictions of hydraulic fracture (HF) growth. We test the theoretical predictions resulting from the combination of linear elastic fracture mechanics and lubrication flow in the growing fracture. We use a numerical solver based on an implicit level set algorithm which notably combines a finite discretization with the asymptotic solution for a steadily moving HF locally near the crack front. For the first time, we compare blindly numerical predictions with data from coalescence experiments performed in hydrogel in the toughness dominated growth regime. Initially, the two fractures propagate radially independently until they start to interact and coalesce. The fracture front then exhibits a transition from a locally concave shape back toward a radial geometry at later times. Apart from material heterogeneities and resolution of the experimental techniques, the time evolution of the fracture footprint before and after coalescence is captured by the numerical predictions. The fluid velocity field and fracture opening at different times obtained experimentally and numerically are also in quantitative agreement.

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Assessment of mechanical properties in unirradiated and irradiated zircaloys and steels with non-standard tests and finite element calculations

Emiliano Campitelli

Nuclear materials have been successfully employed in commercial fission reactors for many decades. Research and material development for advanced fission system and future thermo-nuclear fusion reactors have acquired maturity while great challenges remain to be taken up. The goal of the material scientist is to understand the way neutron irradiation and aggressive reactor environment alter the original material properties and to safely manage the operation conditions for each particular reactor component. In the framework of surveillance programme, the need has arisen to design experimental methods to be used with a limited amount of material for Post Irradiation Examination (PIE) of reactor components to test the integrity of those on a regular time basis. Having to deal with radioactive material, it is particularly important to devise experimental testing procedures as simple as possible but from which reliable information can be drawn. Within materials development programme, irradiations have continuously been performed either in reactors or with particle accelerators. In both cases, the irradiation volumes are usually limited. The concern was to optimize the volume of the irradiated samples in order to increase their number to obtain a good statistical representation of their mechanical behavior after irradiation, and to have a very definite and homogeneous damage dose and irradiation temperature. The concerns explained above originated the development of small-scale specimen testing methods. Advantage is taken of the fact that, within size and geometry limitations, some mechanical properties of a sample are independent of its absolute size. In this way it is possible to perform mechanical tests on samples of reduced volume that represents big advantages to face the aforementioned challenges. Non-standard test on very small specimen have also been proposed to extract mechanical properties of the bulk. If these non-standard testing methods are to be employed for PIE, it becomes necessary to develop modeling tool to understand under what circumstances they can provide useful information and specially how to obtain it. Finite element modeling (FEM) of the non-standard tests has played a key role in this sense, providing a link between standard test analysis and that of the non-standard ones. The goal of this work was to implement finite element models for non-standard tests to ultimately study the mechanical properties of Zircaloy cladding tube and tempered martensitic steels in the unirradiated and irradiated condition. One model was developed for ring tensile tests. It was first validated with a quite ductile iron-chromium ferritic alloy, for which ring and uniaxial tensile test were performed at room temperature. Using the constitutive behavior determined from the uniaxial tensile tests, the load – displacement curves of the ring tensile tests were very well reproduced. Another model was developed for the so-called small ball punch test, which consists in deforming a 3 mm diameter disk clamped between two dies with a ball puncher and to record the load – displacement curve. In order to validate the model, a series of ball punch tests and of tensile tests were carried out on the austenitic steel 316L at room temperature. In this last case, the ball punch test curves were also well reconstructed with the model. Based upon a simple analysis and simulation results, we showed that it is possible to obtain, by ring tensile tests, a quick and accurate assessment of the constitutive behavior of an unknown material, simply by processing the experimental force-elongation data in the same way as for uniaxial tests, taking half the ring perimeter as initial length and twice the ring cross section as the sample cross section. The ring tensile test method was used to determine the hoop mechanical properties of Zircaloy tubes used in fission reactors. Tensile tests were also performed in the axial direction of the Zircaloy tubes. Differences between the yield stress as well as the post-yield behaviors in the axial direction and those in the circumferential direction of the tube could be measured reflecting some component of the anisotropy of the tube. Ball punch specimens were cut also out of the tube in the radial direction and tested. Using the FE model for punch test, in which the anisotropy of the mechanical properties are taken into account through the Hill's theory, the values of the Hill's yield function parameters were estimated. The irradiation hardening of neutron irradiated Zircaloy tube was finally determined. The ball punch test model was extensively used for numerical investigations, to determine how the constitutive behavior of the materials (uniaxial true stress – true strain) employed as input acts in combination with other experimental factors (specimen thickness, friction coefficient) in mediating the shape of the experimental curves. In the light of the results, we derived calibrations between parameters of the non-standard and standard tests. For instance we proposed a new approach to determine the yield stress from the ball punch test. We also showed how the slope of the punch tests scales with the average flow stress of the material. The calibrations proposed in the past by authors and published in the open literature have been revisited and critically reviewed. Based upon the findings of the numerical studies, we propose a given methodology to unambiguously evaluate the material constitutive behavior of a material in a case where the only available data comes from various non-standard tests. Experimental ball punch test results obtained on proton-irradiated specimen (0.5 dpa and Tirr = 523 K), of the tempered martensitic steel, EUROFER97, have been obtained. The irradiation hardening was found equal to about 150 MPa, consistently with previous data on similar steels and irradiation conditions. From the simulations of the ball punch test curves of the irradiated specimens, it was concluded that the irradiation does not affect the strain hardening at relatively low fluence.

EPFL2005

Chargement

Geo-energy is a comprehensive term used to describe any form of energy that comes from the Earth. This includes hydrocarbons such as gas, oil, and coal, but also geothermal energy (shallow and deep). The focus of this thesis is on Enhanced Geothermal Systems (EGS), which are renewable sources of energy. In EGS, hydraulic stimulation is the technique employed to enhance the permeability e.g. of the granite basements at great depths, which might exceed 5 kilometers. Rocks have natural fractures which affect the behavior of the rock mass. The mechanical goal of hydraulic stimulation is to open these pre-existing fractures. Due to the generally great depths, only indirect information such as in-situ stress, pumping records, and micro-seismicity, are available. Many issues in the field of reservoir geothermal (but also petroleum) production, are attributed to the lack of proper understanding of how these fractures interact with each other. The main goal of this study is to provide an insight into how the pre-existing fractures in rocks interact with each other. Specifically, this research answers the question of how pre-existing flaws of different geometrical parameters contained in rock specimens subjected to various loading configurations, affect the mode and the location of the mechanism of crack initiation. We develop a finite element (FE) linearly elastic MATLAB Partial Differential Equation (PDE) code. This numerical model predicts the mode and the location of the initiation of the local fractures at the inner tips of two interacting pre-existing flaws in Barre granite in the context of EGS. We investigate different combinations of double-flaw geometries (flaw inclination angle β, bridging angle α, and ligament length L) contained in specimens subjected to various loading scenarios (Combination of Vertical Load VL, Lateral Load LL, and Internal Flaw Pressure FP) likely to induce first local tensile and shear fractures, and we determine their corresponding predicted locations around the inner flaw tips. For a given double-flaw pair geometry, we subject the specimen to a certain loading configuration (Combination of VL, LL, and FP). We then retrieve the state of stress (maximum and minimum principal stresses 𝜎1 and 𝜎3, and maximum shear stresses 𝜏𝑚𝑎𝑥) at the Finite Element (FE) corner nodes on the boundary of the inner tips, from which we plot the corresponding Mohr’s circles. We study the interaction of these Mohr’s circles with the Griffith-Coulomb failure envelope. Since the main objective is to predict the first local failure’s mechanism and location, we iteratively vary the magnitude of the loading component until the first Mohr’s circle touches the failure envelope. Depending on where it does, the mechanism of the local fracture is inferred. If the maximum principal stress (𝜎1) of this Mohr’s circle is equal to the tensile strength of the granite (𝜎𝑇=7.5𝑀𝑃𝑎), a local tensile fracture is numerically predicted. If this Mohr’s circle touches the linear shear Coulomb portion of the envelope, it is a predicted local shear failure. The corresponding location of the FE node is then determined at the inner tip of the flaw, and this is where for the given geometry and loading scenarios, the first local fracture’s initiation is numerically expected. We follow this procedure for several double-flaw geometrical configurations. We compare the numerical predictions with the previously obtained experimental results in the MIT CEE Rock Mechanics Laboratory. This allows us to validate our set-up numerical model. 4 This study provides a solid ground to the understanding of the initiation and the interaction of pre-existing fractures in EGS. This thesis comes as an answer to a problem of major practical importance in the field of rock mechanics, and beyond. Typical geotechnical problems, such as rock slope stability and tunnel support, can also be better addressed when clearly understanding the process of crack initiation in rocks. This study also enables the correlation between numerical models and experimental findings, a challenge that has always existed in the research world. This thesis shows how our developed FE code can be used as a tool to predict the location and the mode of fractures in the laboratory, but also in the real world.

2020

Chargement

Assessment of mechanical properties in unirradiated and irradiated zircaloys and steels with non-standard tests and finite element calculations

Emiliano Campitelli

EPFL2005

2020