Finite element simulations of notch tip fields in magnesium single crystals

Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of {10 (1) over bar2}-type form profusely near a notch tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load-displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack tip stress, plastic slip and twin volume fraction distributions near the notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the notch tip. Further, deflection of the crack path at twin-twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the notch root.

Effects of Microstructure and Loading on Fracture of Sn-3.8Ag-0.7Cu Joints on Cu Substrates with ENIG Surface Finish

When dropped, electronic packages often undergo failure by propagation of an interfacial crack in solder joints under a combination of tensile and shear loading. Hence, it is crucial to understand and predict the fracture behavior of solder joints under mixed-mode high-rate loading conditions. In this work, the effects of the loading conditions (strain rate and loading angle) and microstructure interfacial intermetallic compound (IMC) morphology and solder yield strength] on the mixed-mode fracture toughness of Sn-3.8 wt.%Ag-0.7 wt.%Cu solder joints sandwiched between two Cu substrates with electroless nickel immersion gold (ENIG) metallization have been studied, and compared with the fracture behavior of joints attached to bare Cu. Irrespective of the surface finish, the fracture toughness of the solder joints decreased monotonically with strain rate and mode-mixity, both resulting in increased fracture proportion through the interfacial IMC layer. Furthermore, the proportion of crack propagation through the interfacial IMC layer increased with increase in the thickness and the roughness of the interfacial IMC layer and the yield strength of the solder, resulting in a decrease in the fracture toughness of the joint. However, under most conditions, solder joints with ENIG finish showed higher resistance to fracture than joints attached directly to Cu substrates without ENIG metallization. Based on the experimental observations, a fracture mechanism map is constructed correlating the yield strength of the solder, the morphology and thickness of the interfacial IMC, and the fracture mechanisms as well as the fracture toughness values for different solder joints under mode I loading.

A meshless adaptive multiscale method for fracture

The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the Phantom node method. A molecular statics approach is employed in the fine scale where crack propagation is modelled naturally by breaking of bonds. The triangular lattice corresponds to the lattice structure of the (111) plane of an FCC crystal in the fine scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively refined and coarsened as the crack propagates. The centro symmetry parameter is used to detect the crack tip location. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. (C) 2014 Elsevier B. V. All rights reserved.

On the variability in fracture toughness of `ductile' bulk metallic glasses

The mode I fracture toughness, K-Ic, of ductile bulk metallic glasses (BMGs) exhibits a high degree of specimen-to-specimen variability. By conducting fracture experiments in modes I and II, we demonstrate that the observed high variability in mode I, vis-a-vis mode II, is a result of highly variable propensity for the conversion of shear bands into cracks in mode I whereas in mode II, crack growth direction is fixed. Thus, the measured variability in K-Ic is intrinsic to the nature of BMGs. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Optimization of clamped beam geometry for fracture toughness testing of micron-scale samples

Fracture toughness measurements at the small scale have gained prominence over the years due to the continuing miniaturization of structural systems. Measurements carried out on bulk materials cannot be extrapolated to smaller length scales either due to the complexity of the microstructure or due to the size and geometric effect. Many new geometries have been proposed for fracture property measurements at small-length scales depending on the material behaviour and the type of device used in service. In situ testing provides the necessary environment to observe fracture at these length scales so as to determine the actual failure mechanism in these systems. In this paper, several improvements are incorporated to a previously proposed geometry of bending a doubly clamped beam for fracture toughness measurements. Both monotonic and cyclic loading conditions have been imposed on the beam to study R-curve and fatigue effects. In addition to the advantages that in situ SEM-based testing offers in such tests, FEM has been used as a simulation tool to replace cumbersome and expensive experiments to optimize the geometry. A description of all the improvements made to this specific geometry of clamped beam bending to make a variety of fracture property measurements is given in this paper.

Fracture behavior of magnesium alloys - Role of tensile twinning

In this work, Mode-I fracture experiments are conducted using notched compact tension specimens machined from a rolled AZ31 Mg alloy plate having near-basal texture with load applied along rolling direction (RD) and transverse direction (TD). Moderately high notched fracture toughness of J(C) similar to 46 N/mm is obtained in both RD and TD specimens. Fracture surface shows crack tunneling at specimen mid-thickness and extensive shear lips near the free surface. Dimples are observed from SEM fractographs suggesting ductile fracture. EBSD analysis shows profuse tensile twinning in the ligament ahead of the notch. It is shown that tensile twinning plays a dual role in enhancing the toughness in the notched fracture specimens with reduced triaxiality. It provides significant dissipation in the background plastic zone and imparts hardening to the material surrounding the fracture process zone via operation of several mechanisms which retards micro-void growth and coalescence. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Damage mechanisms in stainless steel and chromium carbide coatings under controlled environment fretting conditions

Fretting is of a serious concern in many industrial components, specifically, in nuclear industry for the safe and reliable operation of various component and/or system. Under fretting condition small amplitude oscillations induce surface degradation in the form of surface cracks and/or surface wear. Comprehensive experimental studies have been carried out simulating different fretting regimes under ambient and vacuum (10(-9) MPa) conditions and, temperature up to 400 degrees C. Studies have been carried out with stainless steel spheres on stainless steel flats, and stainless steel spheres against chromium carbide, with 25% nickel chrome binder coatings. Mechanical responses are correlated with the damage observed. It has been observed that adhesion plays a vital role in material degradation process, and its effectiveness depends on mechanical variables such as normal load, interfacial tangential displacement, characteristics of the contacting bodies and most importantly on the environment conditions. Material degradation mechanism for ductile materials involved severe plastic deformation, which results in the initiation or nucleation of cracks. Ratcheting has been observed as the governing damage mode for crack nucleation under cyclic tangential loading condition. Further, propagation of the cracks has been observed under fatigue and their orientation has been observed to be governed by the contact conditions prevailing at the contact interface. Coated surfaces show damage in the form of brittle fracture and spalling of the coatings. Existence of stick slip has been observed under high normal load and low displacement amplitude. It has also been observed that adhesion at the contact interface and instantaneous cohesive strength of the contacting bodies dictates the occurrence of material transfer. The paper discusses the mechanics and mechanisms involved in fretting damage under controlled environment conditions. (C) 2015 Elsevier B.V. All rights reserved.

Estimation of mechanical properties of single wall carbon nanotubes using molecular mechanics approach

Molecular mechanics based finite element analysis is adopted in the current work to evaluate the mechanical properties of Zigzag, Armchair and Chiral Single wall Carbon Nanotubes (SWCNT) of different diameters and chiralities. Three different types of atomic bonds, that is Carbon Carbon covalent bond and two types of Carbon Carbon van der Waals bonds are considered in the carbon nanotube system. The stiffness values of these bonds are calculated using the molecular potentials, namely Morse potential function and Lennard-Jones interaction potential function respectively and these stiffness's are assigned to spring elements in the finite element model of the CNT. The geometry of CNT is built using a macro that is developed for the finite element analysis software. The finite element model of the CNT is constructed, appropriate boundary conditions are applied and the behavior of mechanical properties of CNT is studied.

Handling large variations in mechanics: Some applications

There is a need to use probability distributions with power-law decaying tails to describe the large variations exhibited by some of the physical phenomena. The Weierstrass Random Walk (WRW) shows promise for modeling such phenomena. The theory of anomalous diffusion is now well established. It has found number of applications in Physics, Chemistry and Biology. However, its applications are limited in structural mechanics in general, and structural engineering in particular. The aim of this paper is to present some mathematical preliminaries related to WRW that would help in possible applications. In the limiting case, it represents a diffusion process whose evolution is governed by a fractional partial differential equation. Three applications of superdiffusion processes in mechanics, illustrating their effectiveness in handling large variations, are presented.

Twinning induced enhancement of fracture toughness in ultrafine grained Hydroxyapatite-Calcium Titanate composites

Despite being highly bioactive and biocompatible, the limitations of monolithic hydroxyapatite (HA) include extremely low fracture toughness, poor electrical conductivity. While addressing these issues, the present study demonstrates how CaTiO3 (CT) addition to HA can be utilized to obtain a combination of long crack fracture toughness (1.7 MPa m(1/2) SEVNB technique) and flexural strength of 98-155 MPa (3-point bending) and a moderate tensile strength (diametral compression) of 17-36 MPa. The enhancement in fracture resistance in spark plasma sintered HA-CT composites has been explained in reference to the observed twin morphology. TEM reveals the presence of twins in CT grains due to 1800 rotation about 101]. The measured properties along with our earlier reports on biocompatibility and electrical properties make HA-CT suitable for bone tissue engineering applications. When compared with other competing HA-based biocomposites, HA-CT composites are found to have a better combination of properties useful for medium load bearing implant applications. (C) 2015 Elsevier Ltd. All rights reserved.

In-situ study of microscale fracture of diffusion aluminide bond coats: Effect of platinum

The influence of Pt layer thickness on the fracture behavior of PtNiAl bond coats was studied in situ using clamped micro-beam bend tests inside a scanning electron microscope (SEM). Clamped beam bending is a fairly well established micro-scale fracture test geometry that has been previously used in determination of fracture toughness of Si and PtNiAl bond coats. The increasing amount of Pt in the bond coat matrix was accompanied by several other microstructural changes such as an increase in the volume fraction of alpha-Cr precipitate particles in the coating as well as a marginal decrease in the grain size of the matrix. In addition, Pt alters the defect chemistry of the B2-NiAl structure, directly affecting its elastic properties. A strong correlation was found between the fracture toughness and the initial Pt layer thickness associated with the bond coat. As the Pt layer thickness was increased from 0 to 5 mu m, resulting in increasing Pt concentration from 0 to 14.2 at.% in the B2-NiAl matrix and changing alpha-Cr precipitate fraction, the initiation fracture toughness (K-IC) was seen to rise from 6.4 to 8.5 MPa.m(1/2). R-curve behavior was observed in these coatings, with K-IC doubling for a crack propagation length of 2.5 mu m. The reasons for the toughening are analyzed to be a combination of material's microstructure (crack kinking and bridging due to the precipitates) as well as size effects, as the crack approaches closer to the free surface in a micro-scale sample.