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2018 | Buch

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Strain Gradient Plasticity-Based Modeling of Damage and Fracture

verfasst von: Emilio Martínez Pañeda

Verlag: Springer International Publishing

Buchreihe : Springer Theses

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book provides a comprehensive introduction to numerical modeling of size effects in metal plasticity. The main classes of strain gradient plasticity formulations are described and efficiently implemented in the context of the finite element method. A robust numerical framework is presented and employed to investigate the role of strain gradients on structural integrity assessment. The results obtained reveal the need of incorporating the influence on geometrically necessary dislocations in the modeling of various damage mechanisms. Large gradients of plastic strain increase dislocation density, promoting strain hardening and elevating crack tip stresses. This stress elevation is quantified under both infinitesimal and finite deformation theories, rationalizing the experimental observation of cleavage fracture in the presence of significant plastic flow. Gradient-enhanced modeling of crack growth resistance, hydrogen diffusion and environmentally assisted cracking highlighted the relevance of an appropriate characterization of the mechanical response at the small scales involved in crack tip deformation. Particularly promising predictions are attained in the field of hydrogen embrittlement. The research has been conducted at the Universities of Cambridge, Oviedo, Luxembourg, and the Technical University of Denmark, in a collaborative effort to understand, model and optimize the mechanical response of engineering materials.

Inhaltsverzeichnis

Frontmatter

Numerical Framework

Frontmatter

Chapter 1. Introduction

Abstract

In recent years there has been an increasing interest in characterizing the behavior of metallic materials at the micrometer scale. Numerous formulations - referred to as Strain Gradient Plasticity models - have been proposed to extend plasticity theory to small scales. However, the presently available constitutive models are far from being firmly established and uncertainties remain regarding the constitutive prescriptions that best capture increased geometrically necessary dislocations density associated with a plastic strain gradient.

Emilio Martínez Pañeda

Chapter 2. Gradient Plasticity Formulations

Abstract

A theoretical framework that has potential to cover a large range of gradient plasticity effects in isotropic materials is presented. Four classes of strain gradient plasticity theories are considered, aiming to span a wide domain of gradient plasticity formulations. The compatibility, balance and constitutive equations of the different classes of strain gradient plasticity models are described and discussed.

Emilio Martínez Pañeda

Chapter 3. Numerical Implementation

Abstract

While solving analytically (or semi-analytically) simple problems, such as pure bending or shear of an infinite layer, has been particularly useful to compare and benchmark SGP theories, quantitative assessment of gradient effects in engineering applications requires the use of numerical methods. A wide range of ad hoc numerical solutions have been proposed for each gradient plasticity model, ranging from the relatively easy to implement lower order theories to the more complicated gradient plasticity formulations falling within the mathematical framework of Cosserat-Koiter-Mindlin theories of higher order elasticity. Verification of each numerical implementation is performed by solving different boundary value problems and comparing the output with numerical results from other authors.

Emilio Martínez Pañeda

Results

Frontmatter

Chapter 4. Mechanism-Based Crack Tip Characterization

Abstract

The influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. The numerical framework of the chosen SGP theory is developed for allowing large strains and rotations. The material model is implemented in a commercial finite element (FE) code by a user subroutine, and crack-tip fields are evaluated thoroughly for both infinitesimal and finite deformation theories by a boundary-layer formulation. An extensive parametric study is conducted and differences in the stress distributions ahead of the crack tip, as compared with conventional plasticity, are quantified. As a consequence of the strain-gradient contribution to the work hardening of the material, FE results show a significant increase in the magnitude and the extent of the differences between the stress fields of SGP and conventional plasticity theories when finite strains are considered.

Emilio Martínez Pañeda

Chapter 5. On Fracture in Finite Strain Gradient Plasticity

Abstract

A general framework for damage and fracture assessment including the effect of strain gradients is provided. Both mechanism-based and phenomenological strain gradient plasticity (SGP) theories are implemented numerically using finite deformation theory and crack tip fields are investigated. Differences and similarities between the two approaches within continuum SGP modeling are highlighted and discussed. Local strain hardening promoted by geometrically necessary dislocations (GNDs) in the vicinity of the crack leads to much higher stresses, relative to classical plasticity predictions. These differences increase significantly when large strains are taken into account, as a consequence of the contribution of strain gradients to the work hardening of the material. The magnitude of stress elevation at the crack tip and the distance ahead of the crack where GNDs significantly alter the stress distributions are quantified. The SGP dominated zone extends over meaningful physical lengths that could embrace the critical distance of several damage mechanisms, being particularly relevant for hydrogen assisted cracking models.

Emilio Martínez Pañeda

Chapter 6. The Role of Energetic and Dissipative Length Parameters

Abstract

Introduced by Gudmundson (J Mech Phys Solids 52:1379–1406, 2004, [1]) (see also the works by Gurtin (J Mech Phys Solids 52:2545–2568, 2004, [2]) and Gurtin and Anand (J Mech Phys Solids 53:1624–1649, 2005, [3]) to ensure positive plastic dissipation, energetic (or recoverable) and dissipative (or unrecoverable) gradient contributions are a common feature among the vast majority of the most recent SGP formulations. Two different gradient plasticity models are employed to assess the role of energetic and dissipative length parameters in fracture problems. The analysis of crack tip fields within a stationary crack reveals that both energetic and dissipative length scales lead to the same qualitative response, with their role weighted by the different constitutive prescriptions employed to account for the effect of GNDs. Larger differences arise when crack growth resistance is modeled by means of a cohesive zone formulation. The material response after crack initiation is therefore sensitive to the identification of the gradient contributions as energetic or dissipative.

Emilio Martínez Pañeda

Chapter 7. Hydrogen Diffusion Towards the Fracture Process Zone

Abstract

Hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental measurements of crack tip deformation and high levels of lattice hydrogen concentration are predicted within microns to the crack tip. The important implications of the results in the understanding of hydrogen embrittlement mechanisms are thoroughly discussed.

Emilio Martínez Pañeda

Chapter 8. SGP-Based Modeling of HEAC

Abstract

Finite element analysis of stress about a blunt crack tip, emphasizing finite strain and phenomenological and mechanism-based strain gradient plasticity (SGP) formulations, is integrated with electrochemical assessment of occluded-crack tip hydrogen (H) solubility and two H-decohesion models to predict hydrogen environment assisted crack growth properties. SGP elevates crack tip geometrically necessary dislocation density and flow stress, with enhancement declining with increasing alloy strength. Elevated hydrostatic stress promotes high-trapped H concentration for crack tip damage; it is imperative to account for SGP in H cracking models. Predictions of the threshold stress intensity factor and H-diffusion limited Stage II crack growth rate agree with experimental data for a high strength austenitic Ni-Cu superalloy (Monel\(\textregistered \)K-500) and two modern ultra-high strength martensitic steels (AerMet™100 and Ferrium™M54) stressed in 0.6MNaCl solution over a range of applied potential.

Emilio Martínez Pañeda

Chapter 9. Conclusions

Abstract

A general purpose numerical framework to assess fracture and damage by means of gradient plasticity models has been developed. The main classes of SGP formulations have been successfully implemented, validated and used to address several applications of particular interest from the structural integrity perspective. The main achievements, conclusions and future work are presented.

Emilio Martínez Pañeda

Backmatter

Titel: Strain Gradient Plasticity-Based Modeling of Damage and Fracture
verfasst von: Emilio Martínez Pañeda
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-63384-8
Print ISBN: 978-3-319-63383-1
DOI: https://doi.org/10.1007/978-3-319-63384-8

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