Modeling the mechanics of intergranular crack propagation

Strain, 2011

Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First, 3D grain boundary geometries comprise a five-dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation.

Computational Materials Science, 1998

A computational model is presented to analyze intergranular creep crack growth in a polycrystalline aggregate in a discrete manner and based directly on the underlying physical micromechanisms. A crack tip process zone is used in which grains and their grain boundaries are represented discretely, while the surrounding undamaged material is described as a continuum. The constitutive description of the grain boundaries accounts for the relevant physical mechanisms, i.e. viscous grain boundary sliding, the nucleation and growth of grain boundary cavities, and microcracking by the coalescence of cavities. Discrete propagation of the main crack occurs by linking up of neighbouring facet microcracks. Assuming small-scale damage conditions, the model is used to simulate the initial stages of crack growth under g à controlled, model I loading conditions. Initially sharp or blunted cracks are considered. The emphasis in this study is on the eect of the grain microstructure on crack growth. Ó

Predicting the effects of material aging in view of development of intergranular damage is of particular importance in a number of nuclear installations and especially in structural integrity assessments for critical components in energy generating power plants. In 2007 a bilateral research project between Jozef Stefan Institute and Materials Performance Centre of The University of Manchester started. The main purpose is to develop improved models that represent the effects of microstructure on crack growth kinetics, described by the influence of grain size, shape, crystal orientation and grain boundary structure. The University of Manchester partners have pioneered unique techniques for 3D in-situ observation of intergranular stress corrosion cracking with 3D characterisation of microstructures. The Jožef Stefan Institute partners have developed advanced 2D models of transgranular cracking of microstructure where size, shape and orientation of grains are explicitly modeled. We are now in the process of further developing these models and expanding modelling capabilities to 3D. The presented work reports on the latest efforts pertaining to the above research project.

JOM, 2008

Multiscale Approaches to Fatigue and Fracture How would you… …describe the overall signifi cance of this paper? This paper is an effort to study numerically the deformation of a material that contains multiple cracks with different shapes and sizes, under fatigue loading conditions. The yield stresses were found and compared with the uncracked material. The analysis shows that the cracked area size affects the yield stress, as well as the crack shape and stress fi eld. …describe this work to a materials science and engineering professional with no experience in your technical specialty? The effect of different shaped cracks on fatigue behavior in metals is investigated. The cracks are represented as distributions of infi nitesimal dislocation loops. The stress fi eld of the cracks is calculated using a superposition principle. The simulation results provide an insight into the 3-D dislocation structure around the cracks and its relation to the crack shapes. …describe this work to a layperson? The presence of cracks inside materials changes their mechanical behavior. Since the plastic deformation of a material depends on the dislocation motion inside the material, and the dislocation motion is affected by the presence of the cracks, the investigation of the cracksdislocation interaction is important when the deformation of a cracked material is considered. This paper tries to provide an insight into this matter. In this article, the effect of different shape cracks on fatigue behavior in metals is investigated with the help of the discrete dislocation dynamics technique. The cracks are represented as distributions of infi nitesimal dislocation loops. The distribution is determined by an integral equation satisfying stress-free boundary conditions and containing a singular kernel of the third type. The stress fi eld in the cracked domain is calculated using a superposition principle coupled with an iterative technique. The derived stress fi elds describe the interaction between the cracks and the dislocations into the framework of dislocation dynamics. The simulation results provide an insight on the three-dimensional character of the dislocation structure around the cracks and its relation to the crack shapes. The effect of the cracks on the macroscopic yield stress is also determined for various crack sizes and shapes.

Journal of the Mechanics and Physics of Solids, 2011

Metallurgical and Materials Transactions A, 2006

At hree-dimensional multiple-slip dislocation-density-basedc rystalline formulation and specialized finite-element formulation wereused to investigate dislocation-density transmission and blockage in nickel-aluminide polycrystalline aggregates, which were subjected to dynamic loading conditions, with am acroscopic crack and different distributions of randoml ow-anglea nd coincident site lattice (CSL) grain boundaries(GBs). An interfacial GB schemew as developed to determine whether dislocation-density pileups or transmissions occur as immobile and mobile dislocation densities evolvea long different slip systems. Thet hree-dimensionald islocation-density-basedc rystalline formulation is based on interrelated mechanisms that can occur due to the generation, trapping, interaction, and annihilation of mobile and immobile dislocation densities that are generally associated with large strain-high-strain-rate plasticity in L1 2-orderedintermetallics. Acrack-tip shielding factor was also formulated to delineate betweent ransgranular and intergranular crack growth. The current results indicatet hat aggregates with ah igh frequency of S 33a GBs would be susceptiblet ob lunted transgranular crackg rowth due to high dislocation-density transmission rates and shear-stress accumulations, and that an aggregate with ah igh frequency of S 17b GBs would be susceptible to sharp intergranular growth due to al arge number of dislocation-density pileups and an accumulation of large normal stresses ahead of the crack tip.

2011

The road has been rather long-not to mention somewhat winding. Journeying through the dim realm of research requires more than personal effort and firm conviction. The extending hands of the following people have been my recourse in encountering numerous periods of disillusionment and anxiety. Prof. Dr. Ir. L. J. Sluys and Prof. Dr. Ir. Miguel A. Gutierrez have to be solemnly acknowledged as the committee members of this project. I am also deeply indebted to Dr. Ir. A. Simone for his gracious manners and enlightening advices. His heartwarming good will infused me with selfconfidence and determination. Finally, My daily supervisor Ir. Z. Shabir, who did a seamless job of supervision by patiently answering my questions, has to be particularly thanked. I shall express my deepest gratitude to my parents without whose unconditional, selfless and perpetual supports I would not be even close to where I am now. Words would not be able to convey the true degree of my appreciations and thanks for their dedications and surpassing the paternal responsibilities. Last but not least, all my benevolent friends and people whose help sustained me with hope and passion during my studies in the Netherlands have to be particularly thanked.

Mechanics of Materials, 1997

A new numerical method is proposed to simulate intergranular creep fracture in large polycrystalline aggregates. The method utilizes so-called grain elements to represent the polycrystal. These grain elements take care of the average elastic and creep deformation of individual grains. Grain boundary processes, like cavitation and sliding, are accounted for by grain boundary elements connecting the grains. Results are compared with full-field finite element calculations. The method is demonstrated to capture the essential features of creep fracture, like creep constrained cavitation and the interlinkage of microcracks. Also the: performance in polycrystals with random variations in microstructure, in terms of grain shape, is shown to be reasonably well. For the size of the unit-cell considered, a factor of around 600 is gained in computer time as compared with the full-field calculations.

PAMM, 2009

Service life of cyclically loaded components is often determined by the propagation of short fatigue cracks, which is highly influenced by microstructural features such as grain boundaries. A two-dimensional model to simulate the growth of such stage I-cracks is presented. The crack is discretised by dislocation discontinuity boundary elements and the direct boundary element method is used to mesh the grain boundaries. A superposition procedure couples these different boundary element methods to employ them in one model. Varying elastic properties of the grains are considered and their influence on short crack propagation is studied. A change in crack tip slide displacement determining short crack propagation is observed.

The intrinsic lattice resistance to dislocation motion, or Peierls stress, depends on the core structure of the dislocation and is one essential feature controlling plastic anisotropy in materials such as HCP Zn, Mg, and Ti. Here, we implement an anisotropic Peierls model as a friction stress within a 2d discrete dislocation (DD) plasticity model and investigate the role of plastic anisotropy on the crack tip stress fields, crack growth, toughening, and micro-cracking. First, tension tests for a pure single crystal with no obstacles to dislocation motion are carried out to capture the general flow behavior in pure HCP-like materials having slip on basal and pyramidal planes. Then Mode-I crack growth in such a single crystal of the HCP material is analyzed using the 2d-DD model. Results show that the fracture toughness scales inversely with the tensile yield stress, largely independent of the plastic anisotropy, so that increasing Peierls stress on the pyramidal planes gives decreasing resistance to crack growth, consistent with recent experiments on Zn. Analyzing the results within the framework of Stress Gradient Plasticity concepts shows that the equilibrium dislocation dipole spacing serves as an internal material length scale for controlling fracture toughness. Furthermore, the fracture toughness of materials with flow stress controlled by a Peierls stress (this work) and of materials with flow stress controlled by dislocation obstacles (prior literature) is unified through the Stress Gradient Plasticity concept. Finally, the DD simulations show that local stress concentrations exist sporadically along the pyramidal plane(s) that emanate from the current crack tip, suggesting an origin for experimentally observed basal-plane microcracking near the tip of large cracks.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005

The influence of the material texture (substructure) on the force driving the crack tip in complex materials admitting Ginzburg-Landau-like energies is analyzed in a three-dimensional continuum setting. The theory proposed accounts for finite deformations and general coarse-grained order parameters. A modified expression of the J-integral is obtained together with other path-integrals which are necessary to treat cases where the process zone around the tip has finite size. The results can be applied to a wide class of material substructures. As examples, cracks in ferroelectrics and in materials with strain-gradient effects are discussed: in these cases the specializations of the general results fit reasonably experimental data.

Journal of the Mechanical Behavior of Materials, 2003

Although statistical methods are widely used to study a large amount of phenomena ranging from random walk to percolation and particle charging, the application of these methods to mechanics is limited.

Philosophical Magazine, 2005

Small scale yielding around a mode I crack is analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. The polycrystalline material is taken to consist of two types of square grains, one of which has a bcc-like orientation and the other an fcc-like orientation. For both orientations there are three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains is used to construct the polycrystalline materials. Consistent with the increasing yield strength of the polycrystalline material with decreasing grain size, the calculations predict a decrease in both the plastic zone size and the crack-tip opening displacement for a given applied mode I stress intensity factor. Furthermore, slip-band and kink-band formation is inhibited by all grain arrangements and, with decreasing grain size, the stress and strain distributions more closely resemble the HRR fields with the crack-tip opening approximately inversely proportional to the yield strength of the polycrystalline materials. The calculations predict a reduction in fracture toughness with decreasing grain size associated with the grain boundaries acting as effective barriers to dislocation motion.

Acta Materialia, 1996

Brittle intergranular fracture (BIF) is a common mode of failure for monolithic ceramics and intermetallics, as well as for some refractory metals and metals exposed to environmental corrosion, stress corrosion cracking or high temperature creep. As interest in applications for these materials grows, research programs have been developed to characterize and predict their fracture behavior. In order to experimentally quantify the effects of microstructure on local BIF, systems which have a minimum number of variables which influence fracture must be used. Evaluation of materials with two dimensional (2D) microstructures can considerably reduce the complexity of the system. In addition, providing a biaxial stress state in the 2D microstructure ensures that all boundaries experience exclusively Mode I loading prior to failure. Biaxial elastic loading of this simplified microstructure allows the calculation of (a) local stress and strain fields (and their concentrations) prior to failure, as well as (b) prediction of grain boundary strength criteria, and (c) prediction of intergranular crack paths. This can be achieved by conducting computer simulations of the experimentally observed fracture phenomena in polycrystalline specimens having a given texture and microgeometry. These simulations use high resolution finitedifference grids below the crystal scale, and involve the derivation of a spring-network model for arbitrary in-plane crystal anisotropy. Since the grain boundary strength criterion is easily controllable in such simulations, it can be inferred by a comparison with actual experimental results. The latter is complemented by results on fracture of materials with very weak grain boundaries, thus providing a clear perspective on evolution of the failure process for varying degrees of embrittlement.