Emilio Martínez-Pañeda

On fracture in finite strain gradient plasticity

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.

Modeling damage and fracture within strain-gradient plasticity

In this work, 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. Since large deformations generally occur in the vicinity of a crack, 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. Since the distance from the crack tip at which the strain gradient significantly alters the stress field could be one order of magnitude higher when large strains are considered, results reveal that the plastic size effect could have important implications in the modelization of several damage mechanisms where its influence has not yet been considered in the literature.

Numerical analysis of quasi-static fracture in functionally graded materials

This work investigates the existing capabilities and limitations in numerical modeling of fracture problems in functionally graded materials (FGMs) by means of the well-known finite element code ABAQUS. Quasi-static crack initiation and growth in planar FGMs is evaluated. Computational results of fracture parameters are compared to experimental results and good agreement is obtained. The importance of the numerical fit of the elastic properties in the FE model is analyzed in depth by means of a sensitivity study and a novel method is presented. Several key computational issues derived from the continuous change of the material properties are also addressed and the source code of a user subroutine USDFLD is provided in the Appendix for an effective implementation of the property variation. The crack propagation path is calculated through the extended finite element method and subsequently compared to available experimental data. Suitability of local fracture criteria to simulate crack trajectories in FGMs is discussed and a new crack propagation criterion is suggested.

A finite element framework for distortion gradient plasticity with applications to bending of thin foils

Abstract A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the constitutive inclusion of the plastic spin, as proposed by Gurtin (2004) through the prescription of a free energy dependent on Nye’s dislocation density tensor. The proposed numerical scheme is developed by following and extending the mathematical principles established by Fleck and Willis (2009). The modeling of thin metallic foils under bending reveals a significant influence of the plastic shear strain and spin due to a mechanism associated with the higher-order boundary conditions allowing dislocations to exit the body. This mechanism leads to an unexpected mechanical response in terms of bending moment versus curvature, dependent on the foil length, if either viscoplasticity or isotropic hardening are included in the model. In order to study the effect of dissipative higher-order stresses, the mechanical response under non-proportional loading is also investigated.

Abaqus2Matlab: A suitable tool for finite element post-processing

Abstract A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from the image processing and the integrated graph-plotting features of Matlab but also opens up new opportunities in results post-processing, statistical analysis and mathematical optimization, among many other possibilities. The software architecture and usage are appropriately described and two problems of particular engineering significance are addressed to demonstrate its capabilities. Firstly, the software is employed to assess cleavage fracture through a novel 3-parameter Weibull probabilistic framework. Then, its potential to create and train neural networks is used to identify damage parameters through a hybrid experimental–numerical scheme, and model crack propagation in structural materials by means of a cohesive zone approach. The source code, detailed documentation and a large number of tutorials can be freely downloaded from www.abaqus2matlab.com .

Strain gradient plasticity modeling of hydrogen diffusion to the crack tip

Abstract In this work 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.

Gradient plasticity crack tip characterization by means of the extended finite element method

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from www.empaneda.com/codes.

Non-local plasticity effects on notch fracture mechanics

The authors gratefully acknowledge financial support from the Ministry of Economy and Competitiveness of Spain through grant MAT2014-58738-C3. E. Martinez-Paneda also acknowledges financial support from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° 609405 (COFUNDPostdocDTU).

A cohesive zone framework for environmentally assisted fatigue

Abstract We present a compelling finite element framework to model hydrogen assisted fatigue by means of a hydrogen- and cycle-dependent cohesive zone formulation. The model builds upon: (i) appropriate environmental boundary conditions, (ii) a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, (iii) a mechanical behavior characterized by finite deformation J2 plasticity, (iv) a phenomenological trapping model, (v) an irreversible cohesive zone formulation for fatigue, grounded on continuum damage mechanics, and (vi) a traction-separation law dependent on hydrogen coverage calculated from first principles. The computations show that the present scheme appropriately captures the main experimental trends; namely, the sensitivity of fatigue crack growth rates to the loading frequency and the environment. The role of yield strength, work hardening, and constraint conditions in enhancing crack growth rates as a function of the frequency is thoroughly investigated. The results reveal the need to incorporate additional sources of stress elevation, such as gradient-enhanced dislocation hardening, to attain a quantitative agreement with the experiments.

Damage modeling in Small Punch Test specimens

Ductile damage modeling within the Small Punch Test (SPT) is extensively investigated. The capabilities of the SPT to reliably estimate fracture and damage properties are thoroughly discussed and emphasis is placed on the use of notched specimens. First, different notch profiles are analyzed and constraint conditions quantified. The role of the notch shape is comprehensively examined from both triaxiality and notch fabrication perspectives. Afterwards, a methodology is presented to extract the micromechanical-based ductile damage parameters from the load-displacement curve of notched SPT samples. Furthermore, Gurson-Tvergaard-Needleman model predictions from a top-down approach are employed to gain insight into the mechanisms governing crack initiation and subsequent propagation in small punch experiments. An accurate assessment of micromechanical toughness parameters from the SPT is of tremendous relevance when little material is available.