A general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f(1a) and f(2a)), (ii) generation of a master-plot to determine a(c), and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints. (C) 2014 Elsevier Ltd. All rights reserved.

Cavitation in brittle metallic glasses - Effects of stress state and distributed weak zones

Experimental studies and atomistic simulations have shown that brittle metallic glasses fail by a cavitation mechanism whose origin has been traced to the presence of intrinsic atomic density fluctuations which give rise to weak zones with reduced yield strength. It has been shown recently through continuum analysis that the presence of these zones can lower the cavitation stress considerably under equibiaxial loading. The objective of the present work is to study the effect of the applied stress state on the cavitation behavior of such a heterogeneous plastic solid with distributed weak zones. To this end, 2D plane strain finite element simulations are performed by subjecting a unit cell containing a weak zone to different (biaxiality) stress ratios. The volume fraction and yield strength of the weak zone are varied over a wide range. The results show that unlike in a homogeneous plastic solid, the cavitation stress of the heterogeneous aggregate does not reduce appreciably as the stress ratio decreases from unity when the yield strength of the weak zone is low. It is found that a non-dimensional parameter characterizing the stress state prevailing in the weak zone and its yield properties uniquely control the cavitation stress. The nature of cavitation bifurcation may change from unstable bifurcation to the left at sufficiently low stress ratio to one involving snap cavitation at high stress ratio. (C) 2014 Elsevier Ltd. All rights reserved.

Ductility enhancement in nanoglass: role of interaction stress between flow defects

Using a thermodynamically consistent non-local plasticity model, the mechanistic origin of enhancement in ductility and suppression of dominant shear banding in nanoglasses (NGs) is analysed. It is revealed that the interaction stress between flow defects plays a central role in promoting global plasticity of NGs. Specifically, we find that the intrinsic length associated with this stress provides a scaling for the shear band width and its coupling with grain size governs the level of enhancement in the deformation behaviour of NGs. The present work may provide useful insights in developing highly ductile NGs for practical engineering applications.

Tailoring the interface of an immiscible polymer blend by a mutually miscible homopolymer grafted onto graphene oxide: outstanding mechanical properties

A unique strategy was adopted here to improve the compatibility between the components of an immiscible polymer blend and strengthen the interface. PMMA, a mutually miscible polymer to both PVDF and ABS, improved the compatibility between the phases by localizing at the blends interface. This was supported by the core-shell formation with PMMA as the shell and ABS as the core as observed from the SEM micrographs. This phenomenon was strongly contingent on the concentration of PMMA in the blends. This strategy was further extended to localize graphene oxide (GO) sheets at the blends interface by chemically coupling it to PMMA (PMMA-g-GO). A dramatic increment of ca. 84% in the Young's modulus and ca. 124% in the yield strength was observed in the presence of PMMA-g-GO with respect to the neat blends. A simultaneous increment in both the strength and the modulus was observed in the presence of PMMA-g-GO whereas, only addition of GO resulted in a moderate improvement in the yield strength. This study reveals that a mutually miscible polymer can render compatibility between the immiscible pair and can improve the stress transfer at the interface.

Maximum likelihood analysis of multi-stress accelerated life test data of series systems with competing log-normal causes of failure

This article presents frequentist inference of accelerated life test data of series systems with independent log-normal component lifetimes. The means of the component log-lifetimes are assumed to depend on the stress variables through a linear stress translation function that can accommodate the standard stress translation functions in the literature. An expectation-maximization algorithm is developed to obtain the maximum likelihood estimates of model parameters. The maximum likelihood estimates are then further refined by bootstrap, which is also used to infer about the component and system reliability metrics at usage stresses. The developed methodology is illustrated by analyzing a real as well as a simulated dataset. A simulation study is also carried out to judge the effectiveness of the bootstrap. It is found that in this model, application of bootstrap results in significant improvement over the simple maximum likelihood estimates.

Simultaneous enhancement in mechanical strength, electrical conductivity, and electromagnetic shielding properties in PVDF-ABS blends containing PMMA wrapped multiwall carbon nanotubes

A unique approach was adopted to drive the multiwall carbon nanotubes (MWNTs) to the interface of immiscible PVDF-ABS blends by wrapping the nanotubes with a mutually miscible homopolymer (PMMA). A tailor made interface with an improved stress transfer was achieved in the blends with PMMA wrapped MWNTs. This manifested in an impressive 108% increment in the tensile strength and 48% increment in the Young's modulus with 3 wt% PMMA wrapped MWNTs in striking contrast to the neat blends. As the PMMA wrapped MWNTs localized at the interface of PVDF-ABS blends, the electrical conductivity could be tuned with respect to only MWNTs, which were selectively localized in the PVDF phase, driven by thermodynamics. The electromagnetic shielding properties were assessed using a vector network analyser in a broad range of frequency, X-band (8-12 GHz) and Ku-band (12-18 GHz). Interestingly, enhanced EM shielding was achieved by this unique approach. The blends with only MWNTs shielded the EM waves mostly by reflection however, the blends with PMMA wrapped MWNTs (3 wt%) shielded mostly by absorption (62%). This study opens new avenues in designing materials, which show simultaneous improvement in mechanical, electrical conductivity and EM shielding properties.

Tailored mechanical behavior of magnetic particles loaded carbon nanotube foam in presence of magnetic field

The compressive behavior of carbon nanotube (CNT) foam with an entangled microstructure has become an important research area due to its excellent energy absorption capability. This report presents a tailored mechanical behavior of CNT foam under an applied magnetic field when all CNTs in the foam are coated with magnetic nanoparticles. The presence of nanoparticles not only enhanced the stiffness of the foam to four times but also revealed a nonlinear variation in both the stress and energy absorption capability with the gradual increase of the magnetic field. Magnetization of both CNT and attached nanoparticles along the magnetic field direction are shown to play a crucial role in determining the dominant deformation mechanism.

Hydrogen-induced mechanical properties of amorphous silicon thin films

Mechanical properties of thin films such as residual stress and hardness are of paramount importance from the device fabrication point of view. Intrinsic stress in sputtered films can be tensile or compressive as decided by the number density and the energy of the plasma species striking the growing film. In the presence of hydrogen we analyzed the applicability of idealized stress reversal curve for amorphous silicon thin films deposited by DC, pulsed DC (PDC) and RF sputtering. We are successfully able to correlate the microstructure with the stress reversal and hardness. We observed a stress reversal from compressive to tensile with hydrogen incorporation. It was found that unlike in idealized stress reversal curve case, though the energy of plasma species is less in DC plasma, DC deposited films exhibit more compressive stress, followed by PDC and RF deposited films. A tendency towards tensile stress from compressive stress was observed at similar to 13, 18 and 23 at%H for DC, PDC and RF deposited films respectively, which is in exact agreement with the vacancy to void transition in the films. Regardless of the sputtering power mode, the hardness of a-Si:H films is found to be maximum at C-H similar to 10 at%H. Enhancement in hardness with C-H (up to C-H similar to 10 at%H) is attributed to increase of Si-H bonds. Beyond C-H similar to 10 at%H, hardness starts falling. (C) 2015 Elsevier Ltd. All rights reserved.

Phase-field elasticity model based on mechanical jump conditions

Computational models based on the phase-field method typically operate on a mesoscopic length scale and resolve structural changes of the material and furthermore provide valuable information about microstructure and mechanical property relations. An accurate calculation of the stresses and mechanical energy at the transition region is therefore indispensable. We derive a quantitative phase-field elasticity model based on force balance and Hadamard jump conditions at the interface. Comparing the simulated stress profiles calculated with Voigt/Taylor (Annalen der Physik 274(12):573, 1889), Reuss/Sachs (Z Angew Math Mech 9:49, 1929) and the proposed model with the theoretically predicted stress fields in a plate with a round inclusion under hydrostatic tension, we show the quantitative characteristics of the model. In order to validate the elastic contribution to the driving force for phase transition, we demonstrate the absence of excess energy, calculated by Durga et al. (Model Simul Mater Sci Eng 21(5):055018, 2013), in a one-dimensional equilibrium condition of serial and parallel material chains. To validate the driving force for systems with curved transition regions, we relate simulations to the Gibbs-Thompson equilibrium condition

Real-Time Stress Measurements in Germanium Thin Film Electrodes during Electrochemical Lithiation/Delithiation Cycling

An in situ study of stress evolution and mechanical behavior of germanium as a lithium-ion battery electrode material is presented. Thin films of germanium are cycled in a half-cell configuration with lithium metal foil as counter/reference electrode, with 1M LiPF6 in ethylene carbonate, diethyl carbonate, dimethyl carbonate solution (1:1:1, wt%) as electrolyte. Real-time stress evolution in the germanium thin-film electrodes during electrochemical lithiation/delithiation is measured by monitoring the substrate curvature using the multi-beam optical sensing method. Upon lithiation a-Ge undergoes extensive plastic deformation, with a peak compressive stress reaching as high as -0.76 +/- 0.05 GPa (mean +/- standard deviation). The compressive stress decreases with lithium concentration reaching a value of approximately -0.3 GPa at the end of lithiation. Upon delithiation the stress quickly became tensile and follows a trend that mirrors the behavior on compressive side; the average peak tensile stress of the lithiated Ge samples was approximately 0.83 GPa. The peak tensile stress data along with the SEM analysis was used to estimate a lower bound fracture resistance of lithiated Ge, which is approximately 5.3 J/m(2). It was also observed that the lithiated Ge is rate sensitive, i.e., stress depends on how fast or slow the charging is carried out. (C) The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. All rights reserved.

Flow Stress of Biomorphous Metal-Matrix Composites

For metal-matrix composites (MMCs), interfacial debonding between the ductile matrix and the reinforcing hard inclusions is an important failure mode. A fundamental approach to improving the properties of MMCs is to optimize their microstructure to achieve maximum strength and toughness. Here, we investigate the flow stress of a MMC with a nanoscale microstructure similar to that of bone. Such a 'biomorphous' MMC would be made of staggered hard and slender nanoparticles embedded in a ductile matrix. We show that the large aspect ratio and the nanometer size of inclusions in the biomorphous MMC lead to significantly improved properties with increased tolerance of interfacial damage. In this case, the partially debonded inclusions continue to carry mechanical load transferred via longitudinal shearing of the matrix material between neighboring inclusions. The larger the inclusion aspect ratio, the larger is the flow stress and work hardening rate for the composite. Increasing the volume concentration of inclusion also makes the biomorphous MMC more tolerant of interfacial damage.

Mechanical effects of the self-organization of dislocations and related critical characteristics

The effects of the dislocation pattern formed due to the self-organization of the dislocations in crystals on the macroscopic hardening and dynamic internal friction (DIF) during deformation are studied. The classic dislocation models for the hardening and DIF corresponding to the homogeneous dislocation configuration are extended to the case for the non-homogeneous one. In addition, using the result of dislocation patterning deduced from the non-linear dlislocation dynamics model for single slip, the correlation between the dislocation pattern and hardening as well as DIF is obtained. It is shown that in the case of the tension with a constant strain rate, the bifurcation point of dislocation patterning corresponds to the turning point in the stress versus strain and DIF versus strain curves. This result along with the critical characteristics of the macroscopic behavior near the bifurcation point is microscopically and macroscopically in agreement with the experimental findings on mono-crystalline pure aluminum at temperatures around 0.5T(m). The present study suggests that measuring the DIF would be a sensitive and useful mechanical means in order to study the critical phenomenon of materials during deformation.

Microstructure and mechanical behaviour of a SiC particles reinforced Al-5Cu composite under dynamic loading

The mechanical behaviour of a composite of Al–5Cu matrix reinforced with 15% SiC particles was studied at different strain rates from 1×10−3 to 2.5×103 s−1 using both a conventional universal testing machine (for low strain-rate tests) and a split Hopkinson bar (for tests at dynamic strain rates). Whilst the yield stress of the composite increases as the strain rate increases, the maximum flow stresses, 440 MPa for compression and 450 MPa for tension, are independent of strain rate. The microstructures and defect structures of the deformed composite were studied with both scanning electron microscopy and transmission electron microscopy and were correlated to the observed mechanical behaviour. Fracture surface studies of samples after dynamic tensile testing indicates that failure of the composite is controlled by ductile failure of the aluminium matrix by the nucleation, growth and coalescence of voids.

Effects Analysis on the Mechanical Properties of Nanocrystalline Materials

Nanocrystalline materials are characterized by a typical grain size from 1 to 100nm. In order to study the nanocrystalline properties of nanocrystalline materials, we chose nanocrystalline coppers as the research object. The uniaxial tensile deformation of computer produced nanocrystalline coppers is simulated by using molecular dynamics with Finnis-Sinclair potential. The mean grain size of simulated nanocrystalline coppers is varied within the 5.38 to 1.79 nm range. The strength, Young's modulus and stress-strain are strongly depended on the grain size and nanocrystalline structure. The simulated nanocrystalline coppers show a reverse Hall-Petch effect.

A Thermodynamic Constitutive Model for Stress Induced Phase Transformation in Shape Memory Alloys

In this paper a thermodynamic constitutive model is developed for stress induced phase transformation in single crystalline and polycrystalline shape memory alloys (SMAs). Volume fractions of different martensite variants are chosen as internal variables to describe the evolution of microstructure state in the material. This model is then used in prediction the transformation behavior of a SMA (Cu-Al-Zn-Mn) under complex thermomechanical load (including complete and incomplete transformation in mechanical cycling, and proportional/non-proportional loading). (C) 2002 Elsevier Science Ltd. All rights reserved.