Three-dimensional in situ observations of short fatigue crack growth in magnesium

King, Andrew; Ludwig, Wolfgang; Herbig, Michael; Buffière, Jean‐Yves; Khan, Abid Ali; Stevens, Nicholas; Marrow, James

doi:10.1016/j.actamat.2011.07.034

Cited by 122 publications

(83 citation statements)

References 30 publications

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“…International Materials Reviewsfocussed on crack deflection and crack bridging of both transgranular 328 and intergranular crack growth. 334 Many natural materials are extremely anisotropic giving rise to extensive crack deflection, e.g.…”

Section: Quantitative 3d Fracture Mechanicsmentioning

confidence: 99%

“…Buffiere et al 191,325 have looked at the morphology of cracks and correlated this to the crack growth rate of longer cracks as a function of fatigue cycling. To quantify the relationship between crack growth and grain orientation 328 or the nature of the grain boundaries 152 it has been necessary to exploit the grain mapping methods summarised in the 'Crystal grain imaging' section 152 or undertake post mortem electron back scattered analysis. 329 Birosca et al 330,331 created three types of microstructure for dual phase titanium alloy, namely lamellar, duplex and a heterogeneous combination of the two.…”

Section: Quantitative 3d Fracture Mechanicsmentioning

confidence: 99%

See 1 more Smart Citation

Quantitative X-ray tomography

Maire¹,

Withers²

2013

International Materials Reviews

1,086

601

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X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information needed to optimise manufacturing processes, for example sintering or solidification, or to highlight the proclivity of specific degradation processes under service conditions, such as intergranular corrosion or fatigue crack growth. Besides the repeated application of static 3D image quantification to track such changes, digital volume correlation (DVC) and particle tracking (PT) methods are enabling the mapping of deformation in 3D over time. Finally the use of CT images is considered as the starting point for numerical modelling based on realistic microstructures, for example to predict flow through porous materials, the crystalline deformation of polycrystalline aggregates or the mechanical properties of composite materials.

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Section: Quantitative 3d Fracture Mechanicsmentioning

confidence: 99%

Section: Quantitative 3d Fracture Mechanicsmentioning

confidence: 99%

Quantitative X-ray tomography

Maire¹,

Withers²

2013

International Materials Reviews

1,086

601

View full text Add to dashboard Cite

show abstract

“…(32) are currently implemented in the matrix A(H i k+1 ), then the value of δu n is checked, to detect any interpenetration: if δu n < 0, then the separation condition is violated and the contact state of the pair must be updated; in this specific case, contact-stick state is assumed and the corresponding Eqs. (33) are implemented into the system matrix.…”

Section: Iterative Searchmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

117

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In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as threedimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incrementaliterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo-and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

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“…Their microstructure, at the grain scale, is characterized by grains morphology, size distribution, anisotropy and crystallographic orientation, by the presence of flaws and porosity and by physical and chemical properties of the intergranular interfaces [6], which have direct influence on the initiation and evolution of damage. Polycrystalline microstructures have been studied using experimental [7,8,9,10,11,12,13,14,15] and computational techniques [4,16,17]. Much research has been carried out for developing numerical models for polycrystalline microstructures and their failure processes.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture

Benedetti

Aliabadi

2015

Computer Methods in Applied Mechanics and Engineering

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In this work, a two-scale approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using a three-dimensional boundary element formulation in which the presence of damage is taken into account employing an initial stress approach for modelling the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighborhood of the selected points. A three-dimensional grain-boundary formulation is used to simulate intergranular degradation and failure in the microstructure, whose morphology is generated using Voronoi tessellations. Intergranular degradation and failure are modelled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVE as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macro-scale, integral non-local counterparts of the strains are employed. The multiscale processing algorithm is described. Some multiscale simulations are performed to investigate the capability of the method.

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Three-dimensional in situ observations of short fatigue crack growth in magnesium

Cited by 122 publications

References 30 publications

Quantitative X-ray tomography

Quantitative X-ray tomography

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture

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