Amorphous alloys were first developed over 40 years ago and found applications as magnetic core or reinforcement added to other materials. The scope of applications is limited due to the small thickness in the region of only tens of microns. The research effort in the past two decades, mainly pioneered by a Japanese- and a US-group of scientists, has substantially relaxed this size constrain. Some bulk metallic glasses can have tensile strength up to 3000 MPa with good corrosion resistance, reasonable toughness, low internal friction and good processability. Bulk metallic glasses are now being used in consumer electronic industries, sporting goods industries, etc. In this paper, the authors reviewed the recent development of new alloy systems of bulk metallic glasses. The properties and processing technologies relevant to the industrial applications of these alloys are also discussed here. The behaviors of bulk metallic glasses under extreme conditions such as high pressure and low temperature are especially addressed in this review. In order that the scope of applications can be broadened, the understanding of the glass-forming criteria is important for the design of new alloy systems and also the processing techniques.

https://www.tcd.ie/Physics/people/Graham.Cross/SF%20Poster%202011/Shek-MaterSciEng04-Bulk%20Metallic%20Glasses.pdf

Bulk metallic glasses

The elastic properties, elastic models and elastic perspectives of metallic glasses

Recent experimental evidence points to limitations in characterizing the critical strain in ductile fracture solely on the basis of stress triaxiality A second measure of stress state, such as the Lode parameter, is required to discriminate between axisymmetric and shear-dominated stress states This is brought into the sharpest relief by the fact that many structural metals have a fracture strain in shear, at zero stress triaxiality, that can be well below fracture strains under axisymmetric stressing at significantly higher triaxiality Moreover, recent theoretical studies of void growth reveal that triaxiality alone is insufficient to characterize important growth and coalescence features As currently formulated, the Gurson Model of metal plasticity predicts no damage change with strain under zero mean stress, except when voids are nucleated Consequently, the model excludes shear softening due to void distortion and inter-void linking As it stands, the model effectively excludes the possibility of shear localization and fracture under conditions of low triaxiality if void nucleation is not invoked In this paper, an extension of the Gurson model is proposed that incorporates damage growth under low triaxiality straining for shear-dominated states The extension retains the isotropy of the original Gurson Model by making use of the third invariant of stress to distinguish shear dominated states The importance of the extension is illustrated by a study of shear localization over the complete range of applied stress states, clarifying recently reported experimental trends The extension opens the possibility for computational fracture approaches based on the Gurson Model to be extended to shear-dominated failures such as projectile penetration and shear-off phenomena under impulsive loadings

Modification of the Gurson Model for shear failure

A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu-Leblond-Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature. has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model. (C) 2000 Elsevier Science Ltd. All rights reserved.

An extended model for void growth and coalescence

Failure of metals I : brittle and ductile fracture

Many metals which fail by a void growth mechanism display a macroscopically planar fracture process zone of one or two void spacings in thickness characterized by intense plastic flow in the ligaments between the voids; outside this region, the voids exhibit little or no growth. To model this process a material layer containing a pre-existing population of similar sized voids is assumed. The thickness of the layer, D, can be identified with the mean spacing between the voids. This layer is represented by an aggregate of computational cells of linear dimension D. Each cell contains a single void of some initial volume. The Gurson constitutive relation for dilatant plasticity describes the hole growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity. The collection of cells softened by hole growth constitutes the fracture process zone of length l1. Two fracture mechanism regimes can be identified corresponding to l1 ≈ D and l1 ⪢ D. The connection between these mechanisms and fracture resistance is discussed.

Finite element calculations have been carried out to determine crack growth resistance curves for plane strain, mode I crack growth under small scale yielding. A row of voided cells is placed on the symmetry plane ahead of the initial crack. These cell elements are embedded within a conventional elastic-plastic continuum. Under increasing load, the voids in the cells grow and coalesce to form a new crack surface thereby advancing the crack. Resistance curves are calculated for crack growth exceeding many multiples of D. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material. The effect of crack tip constraint on fracture resistance is examined under small scale yielding by way of the T-stress. As a final application, resistance curves for a deep and a shallow crack bend bar are computed. These are compared with experimental data.

Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales

Mode I crack initiation and growth under plane strain conditions in tough metals is computed using an elastic-plastic continuum model which accounts for void growth and coalescence ahead of the crack tip. The material parameters are the Young’s modulus, yield stress and strain hardening exponent of the metal, along with the parameters characterizing the spacing and volume fraction of voids in material elements lying in the plane of the crack. For a given set of these parameters and a specific specimen, or component, subject to a specific loading, relationships among load, load-line displacement and crack advance can be computed with no restrictions on the extent of plastic deformation. Similarly, there is no limit on crack advance, except that it must take place on the symmetry plane ahead of the initial crack. Suitably defined measures of crack tip loading intensity, such as those based on the J-integral, can also be computed, thereby directly generating crack growth resistance curves. In this paper, the model is applied to five specimen geometries which are known to give rise to significantly different crack tip constraints and crack growth resistance behaviors. Computed results are compared with sets of experimental data for two tough steels for four of the specimen types. Details of the load, displacement and crack growth histories are accurately reproduced, even when extensive crack growth takes place under conditions of fully plastic yielding.

http://web-static-aws.seas.harvard.edu/hutchinson/papers/447.pdf

A computational approach to ductile crack growth under large scale yielding conditions

The fracture resistance of ferritic steels in the ductile/brittle transition regime is controlled by the competition between ductile tearing and cleavage fracture. Under typical conditions, a crack initiates and grows by ductile tearing but ultimate failure occurs by catastrophic cleavage fracture. In this study the tearing process is simulated using void-containing cell elements embedded within a conventional elastic-plastic continuum; details of the cell model are discussed in Parts I and II of this article. Weakest link statistics is incorporated into the cell element model and this new model is employed to predict the onset of unstable cleavage fracture. Our approach differs from previous analyses in several important ways. The elastic-plastic field computed for crack growth by ductile tearing is fully integrated with a weakest link cleavage fracture model. The model also accounts for the competition between the nucleation of voids from carbide inclusions and the unstable cracking of inclusions precipitating catastrophic cleavage fracture. This model leads immediately to a natural definition of the Weibull stress measure pertinent to cleavage fracture. The model is not restricted by the extent of plastic deformation and ductile tearing. Two effects are associated with ductile crack growth: the cumulative sampling volume is increased and the crack tip constraint is altered. Both effects have important roles which are treated within the present cleavage fracture model. Load-displacement behavior, ductile tearing resistance and transition to cleavage fracture are investigated for several different test geometries and a range of microstructural parameters. It is found that certain variations in microstructure can result in pronounced effects on the cleavage fracture toughness though they have no effect on the ductile tearing resistance preceding cleavage. Rate effects on ductile tearing and transition to cleavage fracture are also discussed. The model predicts trends in ductile/brittle transition that are consistent with available experimental data.

Ductile crack growth−III. Transition to cleavage fracture incorporating statistics

Many metals that fail by void growth and coalescence display a macroscopically planar fracture process zone of one or two void spacings in thickness; outside this region, the voids exhibit little or no growth. A finite element model of this mode of failure was described in Part I of this paper [J. Mech. Phys. Solids, 43, 233–259 (1995)]. A row of void-containing cell elements is placed on the symmetry plane ahead of the initial crack. The cells incorporate the softening characteristics of hole growth and dependence on stress triaxiality. These cells are embedded within a conventional elastic-plastic continuum. Under increasing strain, the voids grow and coalesce to form new crack surfaces, thereby advancing the crack. Parametric studies reveal that the important microstructural parameters in the model are D and f0, characterizing the spacing and the initial volume fraction of voids on the fracture plane. Using this model, Xia et al. [J. Mech. Phys. Solids, 43, 389–413 (1995)] have successfully predicted details of the load, displacement and crack growth histories—collectively referred to as the macroscopic fracture behavior—of four specimen geometries, which give rise to significantly different crack tip constraints under fully plastic conditions. Here we study the quantitative effects of void nucleation by a stress and strain criterion on the macroscopic fracture behavior. This behavior is compared with predictions using a similar volume of voids present from the very beginning. Geometry effects on macroscopic fracture behavior under contained and fully yielded conditions are discussed for the three-point-bend specimen and the center-crack-panel loaded in tension. Here the objective is to show the connection between the crack growth resistance and the fracture environment, namely, the constraint ahead of the crack tip and the tensile stress on the fracture plane.

Ductile crack growth—II. Void nucleation and geometry effects on macroscopic fracture behavior

Microelectronic circuits often fail because cracks and voids cause open circuits in their interconnects. Many of the mechanisms of failure are believed to be associated with diffusion of material along the surfaces, interfaces or grain boundaries in the line; material may also flow through the lattice of the crystal. The diffusion is driven by variations in elastic strain energy and stress in the solid, and by the flow of electric current. To predict the conditions necessary for failure to occur in an interconnect, one must account for the influence of both deformation and electric current flow through the interior of the solid, and also for the effects of mass flow. To this end, we describe a two dimensional finite element method for computing the motion and evolution of voids by surface diffusion in an elastic, electrically conducting solid. Various case studies are presented to demonstrate the accuracy and capabilities of the method, including the evolution of a void towards a circular shape due to diffusion driven by surface energy, the migration and evolution of a void in a conducting strip due to electromigration induced surface diffusion, and the evolution of a void in an elastic solid due to strain energy driven surface diffusion.

Lin Xia

Papers

Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales

A computational approach to ductile crack growth under large scale yielding conditions

Ductile crack growth−III. Transition to cleavage fracture incorporating statistics

Ductile crack growth—II. Void nucleation and geometry effects on macroscopic fracture behavior

A finite element analysis of the motion and evolution of voids due to strain and electromigration induced surface diffusion