Геометрически точные нелокальные модели накопления повреждений в металлических материалах тема диссертации и автореферата по ВАК РФ 01.02.04, кандидат наук Ключанцев Владислав Сергеевич

• Ключанцев Владислав Сергеевич
• кандидат наук
• 2025

Оглавление диссертации кандидат наук Ключанцев Владислав Сергеевич

Contents

Preface

Chapter 1. Introduction

1.1 Scope and motivation

1.2 General remarks regarding discretization in Space

1.3 Ductile damage model

1.4 General remarks on non-local modeling of damage

Chapter 2. Basic problem statement

2.1 Strain tensors

2.2 Stress tensors

2.3 Equation of motion

2.4 Discretization of the problem

2.4.1 Finite element method

2.4.2 Smoothed particle hydrodynamics

Chapter 3. Local constitutive equations

3.1 Hyperelastic compressible neo-Hookean material

3.2 Maxwell model according to Simo-Miehe

3.3 Elasto-plastic material

3.4 Thermodynamically consistent model

3.5 Gurson-Tvergaard-Needleman model

Chapter 4. Delocalization of integral type

4.1 General approach

4.2 Delocalization under plane strain

4.3 Delocalization under axial symmetry

4.4 Delocalization in thin plates

4.5 Volume-reducing symmetries

4.6 Combination of symmetries

4.7 New easy-to-use delocalization kernel

4.8 Receiver-based normalization

4.9 Source-based normalization

4.10 Orthotropic delocalization scheme

4.11 Stress-based modification of kernels

4.12 Strain-based modification of kernels

Chapter 5. Non-local ductile damage models

5.1 Delocalization procedure for the TDC model

5.2 Delocalization procedure for the GTN model

5.3 Basic properties of the model

5.4 Numerical procedure

Chapter 6. Boundary value problems and numerical results

6.1 Hyperelastic material

6.2 Maxwell material

6.3 Elasto-plastic material

6.4 Comparison between the non-local GTN model and the non-local

TDC model

6.5 Integral-based averaging with spatial symmetries for nonlocal

damage modelling

6.5.1 Damage of a thick-walled tube

6.5.2 Damage of a thin ring

6.6 Simulation of fracture of a CT specimen

6.6.1 Sample geometry and applied boundary conditions

6.6.2 Compact tension test under plane strain

6.6.3 Compact tension test under plane stress

6.6.4 SPH simulations with the local model

6.6.5 SPH simulations with non-local models

6.6.6 Simulations with regularized crack path predictions

6.7 SPH simulation of crack initiation

6.8 Basic set of material parameters for aluminium alloy EN AW5754

H111

6.9 Size-effect and boundary layer caused by non-locality

6.10 Fracture of compact tension—shear samples

6.10.1 Experimental set-up

6.10.2 Delocalization near the crack tip: visibility and metrics

6.10.3 Test of mesh dependence

6.10.4 Simulation results for different types of kernels

Chapter 7. Conclusions

Bibliography

Author's publications on the dissertation topic

Введение диссертации (часть автореферата) на тему «Геометрически точные нелокальные модели накопления повреждений в металлических материалах»

Preface

Relevance of the chosen research topic. The topic of non-local modelling of damage accumulation and ductile fracture holds significant relevance in modern engineering, particularly in relation to metallic materials. Traditional methods of damage modelling often struggle to accurately depict material behaviour, especially in scenarios involving large deformations and fracture. This has led to a growing interest in non-local models, which introduce internal length scales to diffuse damage throughout the damage process zone. This diffusion allows for mesh-independent numerical results and addresses convergence issues which appear when modeling strain softening materials with fine spatial discretization. In engineering, the ability to accurately model damage in metallic materials can have profound implications. It can lead to improved designs, enhanced safety measures, and more efficient use of materials. This is particularly true for industries where the structural integrity of metallic components is critical, such as aerospace, automotive, and civil engineering.

Scientific and practical relevance. The development of new advanced nonlocal damage models and corresponding numerical algorithms stands on the cutting edge of the modern solid mechanics. In addition to improving the modeling of ductile fracture, this research allows for the import substitution of foreign commercial finite element codes used in the Russian Federation.

The goal of this thesis is to develop and enhance a set of material models suitable for end-to-end simulations of damage accumulation, crack initiation, and ductile fracture.

To achieve this goal, the following tasks need to be addressed:

1. Construct an elasto-plastic model with damage accumulation suitable for applications involving large strains and deformations.

2. Resolve the issue of pathological dependence of the numerical solution on the spatial discretization.

3. Stemming from task 2, develop advanced non-local damage accumulation models: adapt the models to spatial symmetries, address issues of excessive diffusion of damage, and identify parameters suitable for delocalization.

4. Identify an acceptable method for spatial discretization.

5. Provide calibration protocols for the created non-local material models.

Scientific novelty of the work consists in the following contributions:

1. A fully coupled model for the analysis of mixed mode damage and fracture in ductile materials is introduced.

2. New families of delocalization kernels, stress-based and strain-based, are introduced and tested.

3. It is established that developed models show different performance regarding objectivity and w-invariance depending on isotropic and anisotropic delocalisation. Thermodynamic consistence of models is verified.

4. Problem-adapted delocalization kernels have been refined for dimension-reducing symmetries like plane strain, plane stress, and axial symmetry as well as for volume-reducing symmetries.

5. Two types of kernel normalisation procedures, namely mathematically convenient receiver-based and physically reasonable source-based, are considered and their differences are highlighted.

Practical significance. The developed models and algorithms can be used for improvements to commercial codes of finite element methods and smoothed particle hydrodynamics, developed for problems involving large deformations and ductile fracture. The proposed theoretical background can be used for numerical analysis of damage accumulation and fracture in real structures like pipe-lines, oil storages, bridges etc.

Methodology and research methods utilized to address the challenges presented in the thesis encompass theoretical research methods such as theoretical mechanics, continuum mechanics, and tensor analysis. Additionally, numerical methods in nonlinear mechanics of deformable solids are employed, notably the nonlinear finite element method and the method of smoothed particles hydrodynamics.

Main contributions to be defended:

1. A geometrically nonlinear non-local model of ductile damage and fracture has been developed: the TDC model.

2. A home-made research package of finite elements and the method of smoothed particle hydrodynamics have been developed.

3. The properties of objectivity and w-invariance have been studied for various types of delocalization procedure.

4. Qualitative and quantitative agreement of simulation results with actual experimental data on deformation and fracture of specimens with heterogeneous stress state is obtained.

The reliability of obtained results is ensured by the rigor of the mathematical apparatus, the application of well-established algorithms, convergence studies of the solution upon the mesh refinement, as well as a verification against the results obtained by fundamentally different algorithms.

The main contributions are in line with existing models and experimental results obtained by other authors. An additional plausibility control is achieved through cross-validation and validation against actual experimental data as well as comparisons with commercial FEM codes.

Presentation of scientific results:

The main results of the thesis were reported at the following conferences:

— Всероссийская конференция и школа для молодых ученых, посвященные 100-летию академика Л.В.Овсянникова "Математические проблемы механики сплошных сред" (Новосибирск, 2019)

— The third Russia-Japan workshop mathematical analysis of fracture phenomena for elastic structures and its applications 21st conference of continuum (Новосибирск, 2021)

— XXII зимняя школа по механике сплошных сред (Пермь, 2021)

— 16th International Conference on Computational Plasticity: Fundamentals and Applications, COMPLAS 2021 (Barcelona, 2021)

— XXI, XXII, XXIII всероссийская конференция молодых учёных по математическому моделированию и информационным технологиям (Новосибирск, 2020, 2021, 2022)

— The 8th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Congress (Oslo, 2022)

— XXIV всероссийская конференция молодых учёных по математическому моделированию и информационным технологиям (Красноярск, 2023)

— Всероссийская конференция «Математические проблемы механики сплошных сред», посвящённая 105-летию со дня рождения академика Л. В. Овсянникова (Новосибирск 2024)

Personal contribution. The author of the thesis actively participated in analyzing the current state of the field, setting research goals and analyzing the

obtained results, as well as in writing the original and revised texts of scientific publications [111, 112, 113, 114, 115, 116, 117, 118]. All the numerical experiments presented in the work and the related software solutions were personally done by the author.

Publications. The main results on the subject of the thesis are presented in 18 printed publications, 8 of which have been published in periodical scientific journals indexed by Web of Science and Scopus, 10 in abstracts of conference papers.

Volume and structure of the thesis. The dissertation consists of an introduction, 7 chapters and conclusion. The full volume of the dissertation is 148 page, including 83 figures and 12 tables. The bibliography contains 118 items.

Acknowledgments. I would like to extend my deepest appreciation to my supervisor, Alexey Valerievich Shutov. His consistent guidance, interesting problem statements, and unwavering support, especially during times of self-doubt, have been instrumental in my scientific journey. His contribution to my growth as a specialist in solid mechanics and as a researcher cannot be overstated. This work would not have been possible without his involvement. A significant portion of the research was conducted during my tenure at the Lavrentiev Institute of Hydrodynamics (Novosibirsk). I am profoundly grateful to the staff of the institute, particularly Sergey Nikolaevich Korobeinikov, for his high standards of work and meticulous review of my interim results during the seminar under his guidance. I also extend my gratitude to Vladimir Dmitrievich Kurguzov, Evgeny Viktorovich Karpov, and Alexey Yurievich Larichkin, for fruitful conversations and discussions about contemporary circumstances in our research activities. These world-class scientists have greatly influenced my research skills through our interactions. During my time in graduate school, I also engaged in teaching and organizational activities at Novosibirsk State University. I owe a debt of gratitude for my professional and personal growth to the Department of Theoretical Mechanics and the Mathematics Center. Anastasia Valerievna Karpenko and Evgeny Alexandrovich Batyaev have supported me throughout my postgraduate studies and have been mentors in the educational sphere. Lastly, I wish to express my heartfelt gratitude to my wife, Anna. Her immense support and care have been a constant source of strength for me.

Заключение диссертации по теме «Механика деформируемого твердого тела», Ключанцев Владислав Сергеевич

Chapter 7. Conclusions

The present study provides insights into the non-local modeling of ductile damage and fracture:

Refinements and additions to the strong (integral) approach to the delocalization of ductile damage models:

- Delocalisation kernels have been specified for plane strain, plane stress and spatial symmetry cases (cf. Sections 4.2, 4.4, 4.3).

- A new easy-to-use averaging kernel is suggested. Its major advantage is that no special care is needed when solving 3D, plane strain, and plane stress problems. Moreover, its universal analytical expression (4.51) is much simpler than some of the symmetry-adapted kernels (cf. (4.33)).

- Two types of kernel normalisation, namely receiver-based and source-based (see Eqs. (4.52), (4.61)) are considered and their differences are highlighted (cf. Sections 4.8, 4.9).

- Fully coupled model for the analysis of mixed mode damage and fracture in ductile materials is introduced (cf. Section 5).

- Developed material models show different performance in objectivity and w-invariance depending on isotropic and anisotropic delocalisation, with consistent thermodynamic consistency (see Table 2 in Section 5.3).

The result of the development of numerical methods of discretization in Space:

- SPH with corrected smoothing kernels preserves full energy in dealing with hyperelastic material responses (Fig. 6.3 in Section 6.1).

- Corrected smoothing kernels are implemented to mitigate undesired edge effects, leading to increased accuracy even with a small number of particles. Notably, the current version of SPH demonstrates sufficient accuracy for engineering applications (Fig. 6.2 in Sections 6.1, 6.2).

- By combining SPH techniques, advanced nonlinear material models beyond elasticity can be effectively considered, as evidenced by the implementation of a Maxwell body and TDC model for large elastic and inelastic strains. Simulation results exhibit no nonphysical behavior typically associated with cohesion, tensile, or hourglass instabilities, even without the introduction of

damping or artificial viscosities (Figs. 6.4, 6.5, 6.34, 6.36, 6.44 in Sections 6.1, 6.2, 6.6.4, 6.6.5, 6.7). The results are obtained by post-processing of numerical solutions:

— In cases where the loading direction is oblique to the orthotropic axes of structure tensor, crack paths may naturally deviate from symmetry (Figs. 6.44 & 6.45 in Section 6.6.5).

— Efficient coupling of low-order discretisation methods, such as meshless SPH, with integral-type nonlocal material models is demonstrated for large strain applications (cf. Sections 6.1, 6.2, 6.6.4, 6.6.5, 6.7).

— Averaging of the dual variable, i.e. the continuity rate Ф, in the current model leads to more physically realistic results and reduces unphysical damage diffusion (see Fig. 6.46 in Section 6.6.5).

— In fracture mode I, the apparent fracture toughness Kjc shows a moderate dependence on the internal length parameter hNL (Fig. 6.37), emphasising the advantage of procedure based on calibration against energy consumption curves (Fig. 6.38 in Section 6.6.5).

— Delocalisation schemes on the reference configuration provide larger fracture toughness than those on the current configuration in mode I fracture, attributed to the increased interaction distance across the crack path (Figs. 6.39 & 6.40 in Section 6.6.5).

— The four different approaches to the delocaliztion near the crack tip (Section 6.10.2) yield practically the same results. Nevertheless, we use the most advanced approach (concept iv), which involves re-thinking the metric near the crack tip (Fig. 6.64).

Results obtained by postprocessing and from numerical solutions for non-standard delocalization procedures:

— Anisotropic schemes show a significant dependence of Mode I fracture toughness on the interaction distance perpendicular to the crack, with minimal effect of the interaction distance along the crack (Fig. 6.43 in Section 6.6.5).

— The investigation into size effects and boundary layers induced by non-locality demonstrates the nuanced differences in simulation results obtained using different normalization procedures. While both receiver-based and source-based normalization yield slightly different results for small samples,

both approaches respect the basic principles of constitutive mechanics (Figs. 6.60 & 6.61 in Section 6.9).

— The utilization of receiver-normalized kernels, both with stress-based and strain-based modifications, provides consistent results, showcasing similar trends in fracture toughness variation with changing material parameters. Specifically, as Strain and hstress increase, there is a slight increase in fracture toughness for tests near the first fracture mode, but a drastic decrease for loading cases near the second fracture mode (Figs. 6.66 & 6.67 in Section 6.10.4).

— Non-normalized kernels, derived from both receiver-normalized and source-normalized BaZant kernels, exhibit significant reductions in apparent fracture toughness, particularly noticeable for moderate to large values of hstrain and hstress. Interestingly, the type of normalization procedure impacts the structural strength differently, with non-normalized kernels showing a drastic reduction in peak load with increasing hstress, contrary to the nearly zero impact observed for receiver-normalized kernels (Figs. 6.69 & 6.67 in Section 6.10.4).

— Analysis reveals the sensitivity of the material's structural strength to parameters like hNL, PCR, and ^press. For the analyzed alloy, Dpress plays a significant role in controlling the shape of the K\—Ku diagram, particularly affecting fracture toughness in the second mode while having minimal impact in the first mode (Figs. 6.71, 6.72, 6.74, 6.75 in Section 6.10.4).

In a separate context, a novel variant of the nonlocal Gurson-Tvergaard-Needleman (GTN) model is introduced, based on the multiplicative decomposition of the deformation gradient tensor and hyperelastic relations (cf. Section 3.5). The study emphasizes the similarity between finite element calculations for this new GTN variant and a previously proposed TDC model.

The families of delocalization kernels introduced in this study open avenues for a unified analysis of pre-damaged structures, with and without cracks, in mixed modes of fracture. These tools enable end-to-end simulations of damage accumulation followed by fracture. The framework is promising for assessing the impact of plastic anisotropy and damage on fracture toughness in diverse practical applications, from predicting fracture toughness in plastic-formed parts to designing pre-programmed fracture patterns for precise control of ductile fracture (cf. Sections 4.10 - 4.12). To maintain acceptable computational costs, we use a relatively simple

damage accumulation rule, cf. equation (3.56). Naturally, this ansatz can be further expanded for a more precise description of void nucleation and growth [49, 68, 72, 110], as well as void coalescence [71].

Due to its practical significance, the study addresses the spacial case of plane stress assumption introducing a plane-stress-adapted kernel. This kernel, while similar to the plane-strain kernel, exhibits dependency on the plate thickness and interaction distance (cf. Section 4.4). The choice of the kernel is shown to impact the simulation results, emphasizing the need for careful consideration, especially in cases involving symmetry planes (cf. Section 6.6.3).

An easy-to-use averaging kernel is proposed, exhibiting advantages like versatility and simpler analytical expression. This kernel is therefore more suitable for engineering applications (cf. Section 4.7).

A key finding in Section (6.4) is the similarity in results between GTN and TDC models, prompting the need for detailed experimental data on local damage evolution for robust parameter identification and model validation. The study highlights the importance of understanding porosity fields predicted by different models, emphasizing the necessity of detailed experimental data for accurate model validation.

Nonlocal material models are widely used to overcome mesh dependence issues and enhance predictive capabilities. The integral-based nonlocal framework, explored here, offers convergent simulation results compared to local modeling approaches. The study delves into symmetry-adapted cases, providing analytical expressions for averaging kernels in various scenarios (cf. Sections 6.4 - 6.10.4).

The proposed non-local ductile damage models an corresponding algorithms prove to be a powerful tool for simulating damage localisation during crack initiation and propagation. Furthermore, when combined with SPH, it becomes practical for analysing processes such as machining and metal forming involving large elasto-plastic deformations. The study provides a robust basis for future extensions to address nonlinear kinematics, distortional hardening and creep damage (cf. Sections 6.6, 6.7).

Nonlocal models can be used to generate virtual experimental data suitable for validation of engineering theories. This approach to creating synthetic experimental data allows systematic variations in brittleness and fracture toughness. Further details can be found in our paper [118].

Список литературы диссертационного исследования кандидат наук Ключанцев Владислав Сергеевич, 2025 год

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Author's publications on the dissertation topic

[111] A. V. Shutov and V.S. Klyuchantsev. —"Integral-based non-local approach to ductile damage and mixed-mode fracture". — In: Engineering Fracture Mechanics 292 (2023), p. 109656.

[112] Klyuchantsev V.S. and A.V. Shutov. — "A comparative analysis of two approaches to nonlocal ductile damage modeling". — In: Journal of Engineering Physics and Thermophysics 95.7 (2022), p. 1634—1646.

[113] V.S. Klyuchancev and A.V. Shutov. —"Nonlocal FEM Simulations of ductile damage with regularized crack path predictions". — In: Journal of Physics: Conference Series 194 (2021), p. 012018.

[114] A. V. Shutov and V.S. Klyuchantsev. — "On the application of SPH to solid mechanics". — In: Journal of Physics: Conference Series 1 (2019), p. 012077.

[115] A. V. Shutov and V.S. Klyuchantsev. — "Solving elasto-viscoplastic problems by smoothed particle hydrodynamics". — In: AIP Conference Proceedings 2216 (2020), p. 030006.

[116] A. V. Shutov and V.S. Klyuchantsev. —"Large strain integral-based nonlocal simulation of ductile damage with application to mode-I fracture". — In: International Journal of Plasticity 144 (2021), p. 103061.

[117] A. V. Shutov and V.S. Klyuchantsev. — "Integral-based averaging with spatial symmetries for non-local damage modelling". — In: ZAMM 103.1 (2021), e202100434.

[118] V.S. Klyuchantsev, V.D. Kurguzov, and A.V. Shutov. —"Refined Engineering Theory of Fracture with a Two-Parameter Strength Criterion". — In: Physical Mesomechanics 26.5 (2023), p. 542—556.