Evolution Of Stress State Research Articles

Microstructural Evolution of SAC305 Solder Joints in Wafer Level Chip-Scale Packaging (WLCSP) with Continuous and Interrupted Accelerated Thermal Cycling

Four high-strain design wafer level chip scale packages were given accelerated thermal cycling with a 10°C/min ramp rate and 10 min hold times between 0°C and 100°C to examine the effects of continuous and interrupted thermal cycling on the number of cycles to failure. The interruptions given two of the samples were the result of periodic examinations using electron backscattered pattern mapping, leading to room temperature aging of 30 days–2.5 years after increments of about 100 cycles at several stages of the cycling history. The continuous thermal cycling resulted in solder joints with a much larger degree of recrystallization, whereas the interrupted thermal cycling tests led to much less recrystallization, which was more localized near the package side, and the crack was more localized near the interface and had less branching. The failure mode for both conditions was still the same, with cracks nucleating along the high angle grain boundaries formed during recrystallization. In conditions where there were few recrystallized grains, recovery led to formation of subgrains that strengthened the solder, and the higher strength led to a larger driving force for crack growth through the solder, leading to failure after less than half of the cycles in the continuous accelerated thermal cycling condition. This work shows that there is a critical point where sufficient strain energy accumulation will trigger recrystallization, but this point depends on the rate of strain accumulation in each cycle and various recovery processes, which further depends on local crystal orientations, stress state evolution, and specific activated slip and twinning systems.

Effect of silicon configurations on the mechanical integrity of silicon–carbon nanotube heterostructured anode for lithium ion battery: A computational study

Heterostructures of silicon and carbon nanotubes (CNT) have been widely studied as Li-ion battery anodes. The focus of the current study is to investigate the role of silicon configurations on the mechanical integrity of the Si–CNT heterostructured anodes during electrochemical cycling. We hypothesize that void nucleation and growth in silicon during electrochemical cycling of Li can induce fracture and eventual failure. To test this hypothesis, we utilized a custom developed multiphysics finite element modeling framework considering the lithium diffusion induced elasto-plastic deformation of silicon. We systematically varied the silicon component configuration and enumerated the stress field within it for one complete electrochemical cycle. Resulting evolution of stress state reveals that reducing the mechanical constraints on Si reduces the plastic flow of the material, and thus possibility of void nucleation and growth. We find that the Si droplet configuration is mechanically stable while the continuous Si coating configuration is prone to void growth induced mechanical failure. Present analysis provides a mechanistic understanding of the effect of Si configurations in heterostructured electrodes on its mechanical integrity, which can help in design of next-generation hetersostructured electrodes with improved capacity retention.

Analysis of laminated crack defect in the upsetting process of heavy disk-shaped forgings

Using nonlinear finite element method, a thermo-mechanical coupled simulation model for the formation mechanism of the laminated crack defect has been established in the upsetting of heavy disk-shaped forgings. Through numerical simulation, the distributions of stress, equivalent strain and strain rate were analysed. Meanwhile the distribution diagram of stress state evolution was obtained, and the uncoordinated deformation, under tri-lateral compression, is determined as the main reason leading to laminated crack defect. To reveal the characteristics of the uncoordinated deformation, the variations of each variable and its gradient in numerical simulation were presented, and a combined prediction model of laminated crack defect were proposed based on degree of deformation and gradient of deformation speed. Subsequently, the morphology and distribution of laminated crack were obtained in the centre of forging using the prediction model. Comparison of calculation results and experimental data indicates that both of them match well. In addition, the effect of friction coefficient on the deformation is also presented. The results show that the decreasing of friction coefficient is an effective measure to restrain the laminated crack defect.

The material point method for unsaturated soils

The paper describes a three-phase single-point material point method formulation of coupled flow (water and air) for hydro-mechanical analysis of geotechnical problems involving unsaturated soils. The governing balance and dynamic momentum equations are discretised and adapted to material point method characteristics: an Eulerian computational mesh and a Lagrangian analysis of material points. General mathematical expressions for the terms of the set of governing equations are given. A suction-dependent elastoplastic Mohr–Coulomb model, expressed in terms of net stress and suction variables is implemented. The instability of a slope subjected to rain infiltration, inspired from a real case, is solved and discussed. The model shows the development of the initial failure surface in a region of deviatoric strain localisation, the evolution of stress and suction states in some characteristic locations, the progressive large strain deformation of the slope and the dynamics of the motion characterised by the history of displacement, velocity and acceleration of the unstable mass.

Comparative study of evolution of residual stress state by local mechanical tensioning and laser processing of ferritic and austenitic structural steel welds.

Complex thermal stresses generated in welded structures are undesirable but inevitable in fusion welding. The presence of residual stresses can be detrimental to the integrity of a welded joint. In this research, redistribution of residual stress magnitude and profile was studied and compared in two multi-pass welded structural alloys (API X100 and 304L stainless steel) after cold rolling and laser processing. The residual stress field was studied by neutron diffraction using the SALSA strain scanner at their reactor neutron source at ILL, Grenoble. In addition to a complex distribution of residual stress state, multi-pass welds also forms dendritic grain structure, which are repeatedly heated, resulting in segregation of alloying elements. Dendritic grain structure is weaker and segregation of alloying elements may result in formation of corrosion microcells as well as reduction in overall corrosion prevention due to depletion of alloying elements in certain areas. The modification of as-welded residual stress state was done by cold rolling which was followed by laser processing to create a recrystallized microstructure to minimise segregation. The main objective of this study is to understand the suitability of this novel manufacturing technique to create a stress free weldment with recrystallised grain structure. Hardness evolution in the welded structures was scanned following welding, post weld cold rolling and cold rolling followed by laser processing. Hardness distribution in both the structural alloys showed a significant evidence of plastic deformation near the cap pass of the weld metal. Residual stress redistribution was observed up to 4 mm from the capping pass for ferritic steel, while in austenitic steel weld, post weld cold rolling was effective in modifying the residual stress redistribution throughout the entire thickness. Laser processing in both cases reinstated the as-welded residual stress distribution and resulted in softening of the strained area.

A quantitative phase-field model for two-phase elastically inhomogeneous systems

Solid-state phase transformations are influenced by strains that are generated internally or applied externally. The stress state, composition, and microstructure evolution, which together determine the properties of solid materials can be studied using phase-field models coupled with micro-elasticity theory in the small strain limit. This coupling has been implemented using various schemes in literature. In a previous article (Durga et al., 2013), the authors evaluated three main existing schemes for a two-phase system and concluded that these schemes are not quantitative for inhomogeneous anisotropic elastic properties of the two phases. The stress states predicted by these models deviate from the expected values due to the generation of extra interfacial energy, which is an artefact of the models resulting from interfacial conditions different from local mechanical equilibrium conditions. In this work, we propose a new scheme with interfacial conditions consistent with those of the analytical results applicable to a general system where shear strains may be present. Using analytical solutions for composition and stress evolution, we validate this model for 2D and 3D systems with planar interface in the presence of misfit between phases and applied strains, and a 2D system with an elliptical second-phase particle. This extended scheme can now be applied to simulate quantitatively the microstructural evolution with coupled chemical and mechanical behaviour in any 2D or 3D two-phase system subject to internal or external strains irrespective of interface curvature.

Residual Stress Evolution during the Manufacturing Process of Bearing Rings

An innovative X-ray diffractometer was used to measure the residual stress being the source of a typical deformation failure called ovality on bearing rings. The equipment performs the measurements without sample cutting making it possible to measure the stress state of the same rings after each processing step. Thus, the stress state evolution during the complete manufacturing scenario was monitored on the same rings and the manufacturing process was revised.

Changes in fluid pathways in a calcite vein mesh (Natih Formation, Oman Mountains): insights from stable isotopes

AbstractWe present a structural, microstructural, and stable isotope study of a calcite vein mesh within the Cretaceous Natih Formation in the Oman Mountains to explore changes in fluid pathways during vein formation. Stage 1 veins form a mesh of steeply dipping crack‐seal extension veins confined to a 3.5‐m‐thick stratigraphic interval. Different strike orientations of Stage 1 veins show mutually crosscutting relationships. Stage 2 veins occur in the dilatant parts of a younger normal fault interpreted to penetrate the stratigraphy below. The δ18O composition of the host rock ranges from 21.8‰ to 23.7‰. The δ13C composition ranges from 1.5‰ to 2.3‰. This range is consistent with regionally developed diagenetic alteration at top of the Natih Formation. The δ18O composition of vein calcite varies from 22.5‰ to 26.2‰, whereas δ13C composition ranges from −0.8‰ to 2.1‰. A first trend observed in Stage 1 veins involves a decrease of δ13C to compositions nearly 1.3‰ lower than the host rock, whereas δ18O remains constant. A second trend observed in Stage 2 calcite has δ18O values up to 3.3‰ higher than the host rock, whereas the δ13C composition is similar. Stable isotope data and microstructures indicate an episodic flow regime for both stages. During Stage 1, formation of a stratabound vein mesh involved bedding‐parallel flow, under near‐lithostatic fluid pressures. The 18O fluid composition was host rock‐buffered, whereas 13C composition was relatively depleted. This may reflect reaction of low 13C CO2 derived by fluid interaction with organic matter in the limestones. Stage 2 vein formation is associated with fault‐controlled fluid flow accessing fluids in equilibrium with limestones about 50 m beneath. We highlight how evolution of effective stress states and the growth of faults influence the hydraulic connectivity in fracture networks and we demonstrate the value of stable isotopes in tracking changes in fluid pathways.

Análise numérica da alteração do estado de tensão geomecânico induzida pelo tráfego ferroviário

In this paper, a numerical study of the geomechanical stress state evolution induced by the railway traffic is presented. The numerical model is based on a 2.5D formulation with the ability to account for the dynamic train‐track interaction. For the case study, the stress state evolution is systematized in the form of stress paths. The results obtained allow to recognize the great influence of the train speed and the presence of irregularities in the track for the behavior of the railway track. Based on the knowledge acquired during the implementation of previous parametric studies, the adequacy of the hollow cylinder torsional test to simulate the complex stress paths induced in the ground of the traffic railway is evaluated. The results obtained allow to put in perspective the simulation of these loads in laboratory, with the aim of studying the damage accumulation in the specimens.

Fault constitutive relations inferred from the 2009‐2010 slow slip event in Guerrero, Mexico

AbstractThe spatiotemporal evolution of stress state is analyzed during the 2009–2010 Slow Slip Event (SSE) of Guerrero, Mexico, based on the kinematic inversion results and using an integral expression for stress changes. A linear slip weakening behavior is generally observed during the SSE with an average slope of −0.5 ± 0.2MPa/m regardless the perturbation due to the 27 February 2010 Mw = 8.8 Maule, Chile earthquake. This slope remains unchanged before and after the Maule earthquake. However, for some area, the friction behavior changes from slip hardening to slip weakening following the Maule earthquake. The complex trajectory between shear stress and slip velocity is fitted with a rate‐ and state friction law through an inversion. The direct (rate) effect (parameter A) is found to be very small, lower by an order of magnitude than the evolutional (state) effect (parameter B). The characteristic length L is obtained as 5 cm on average.

The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

We investigate the evolution of heterogeneous stress states along frictional interfaces. Using finite-element simulations, we model the occurrence of precursory slip sequences on a deformable-deformable as well as a deformable–rigid interface between two solids. Every interface rupture creates a stress concentration at its arrest position and erases the stress concentrations produced by previous slip events. While the interface is sticking perfectly between two slip events, erased stress concentrations reappear and survive several cycles of ruptures. Such reestablished stress concentrations are smaller than they were before the rupture. We show that the decrease rate of these stress concentrations is exponential with respect to the number of subsequent events and that the bulk viscoelasticity is at the origin of this history effect. During a slip event, the friction tractions at the interface change almost instantaneously, which leads, between two ruptures, to a relaxation-resembling viscous effect that restores the stress concentration. We describe the decrease rate analytically and highlight that it is proportional to the ratio of the viscous over the instantaneous Young’s moduli, and illustrate it by varying the material properties in our simulations.

Notched Fatigue Behavior under Multiaxial Stress States

Most engineering components and structures contain stress concentrations, such as notches. The state of stress at such concentrations is typically multiaxial due to the notch geometry, and/or multiaxiality of the loading. Significant portions of the fatigue life of notched members are usually spent in crack initiation (crack formation and microscopic growth) and macroscopic crack growth. Synergistic complexity of combined stress and stress concentration has been evaluated in a limited number of studies. Available experimental evidence suggests the current life estimation and fatigue damage analysis techniques commonly used may not be capable of accurate predictions for such complex and yet highly practical conditions. This paper investigates notched fatigue behavior under multiaxial loads using aluminum alloys. Many effects involved in such loading conditions are included. These include the effects of stress state (axial, torsion, combined axial-torsion), geometry condition (smooth versus notched), and damage evolution stage (nucleation and micro-crack growth versus long crack growth).

Origin and timing of layer-bound radial faulting around North Sea salt stocks: New insights into the evolving stress state around rising diapirs

3D seismic data are used to establish the origin and timing of layer-bound arrays of radial faults within a 1500-m-thick sequence of polygonally faulted, Eocene to middle Miocene claystones penetrated by two adjacent salt stocks in the UK Central Graben. Polygonal faults are organised into six laterally extensive tiers that formed during sediment compaction and dewatering during early burial. Dip and amplitude attributes of faulted horizons within the centre of the tiers shows that regional polygonal fault patterns change to radial patterns around the two salt stocks which have radii of c. 1.5 and 2.5 km respectively. Radial faults are confined to the same (120–450 m thick) tiers as those of polygonal faults, indicating that they are also layer bound. The radial-fault pattern in each tier is distinctive and commonly shows a range of fault spacings (154–356 m), maximum throws (7–40 ms), and C-shaped displacement–distribution profiles similar to those of laterally equivalent polygonal faults. These layer-bound radial faults are interpreted as a form of polygonal faults in which strikes have been strongly aligned by a local stress perturbation of salt stocks. Timing constraints indicate that layer-bound arrays of polygonal and radial faults formed in discrete phases during and at the close of sedimentation of each tier. The six tiers formed during the early Eocene, late Eocene, early Oligocene, late Oligocene, early Miocene and middle Miocene. The distance of the polygonal–radial-fault transition from the salt stocks vary from tier to tier but are typically within 800–4000 m of the salt-sediment contact. The position of the transition boundary is used to reconstruct the lateral limit of the salt/sediment-boundary-parallel stress or hoop stress field during key stages in the evolution of the Pierce salt stocks. The position of the radial–polygonal fault transition could be caused by two possible mechanisms: (1) limit of circumferential stretching caused by arching during diapiric rise or (2) lateral limit of hoop stresses produced by radial loading of the overburden from a pressurised salt stock.

Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain

An implicit gradient formulation based on the micro-dilatational approach is applied to the Gurson–Tvergaard–Needleman ductile damage model. The stability of the model is proven analytically for the considered class of materials. The damage model is implemented in an implicit finite-element code in an Updated Lagrangian formulation incorporating an objective time integration scheme and consistent tangent moduli for quadratic convergence. The model is applied to simulate a fracture mechanical test of a typical pressure vessel steel. The investigations are focused on the evolution of ductile damage and stress state at the crack tip. The results show that the model captures the different stages of crack initiation and propagation realistically. A condition for mesh-convergence in terms of the internal length parameter is suggested.

Evolution of residual stress states in surface layers of an AISI D2 steel treated by low energy high current pulsed electron beam

The quantitative evolution of the residual stress states in the surface layers of an AISI D2 steel after Low Energy High Current Pulsed Electron Beam (LEHCPEB) treatment has been investigated by using X-ray diffraction technique. The initial material contained mainly ferrite plus carbides and the ferrite had a compressive stress of about 560 MPa. After the LEHCPEB treatment, the residual stress of the ferrite in the surface layers became tensile in nature, reaching values as high as 730 MPa. A residual tensile stress also existed in the austenite formed at the surface. The stress increased from 170 MPa after 5 pulses to 700 MPa after 25 pulses of treatment. The evolution of the residual stress state in the surface layers can be explained by taking into account the fast thermal cycle, deformations induced by the dynamic thermal stress at the surface together with melting and phase transformations generated by the LEHCPEB treatment.

Applying of Integral Equation of Volterra for Determining the Section Forces in Composite Beam, Regarding Shrinkage of Concrete

During time, the equilibrium state of a steel-concrete mixed beam progresses under the concrete shrinkage. In this context, a contribution to the search of the time-dependant behaviour of mixed beams, including the shrinkage phenomenon of the concrete slab, is dealt with in this paper. The influence of the concrete shrinkage, taking into account the slab reinforcement contribution, on the strength of the mixed beams is taken into account using the linear concrete viscoelasticity theory. With the help of this theory we obtain an analytic model, based on two linear differential equations that result in the over-time-behaviour of the steel-concrete mixed beams. From this model we can determine, at any time t, the values of the normal force and bending moment due to the concrete shrinkage. So it allows us to give an account of the stress state evolution developed in the cross sections of the steel-concrete mixed beams. The results obtained from the application of the suggested model are completely comparable with the results derived by the method proposed by EUROCODE 4

Evolution of interfacial nanostructures and stress states in Mg matrix composites reinforced with coated continuous carbon fibers

Magnesium (Mg) matrix composites reinforced with 45 vol.% continuous carbon fibers (C f) were fabricated using a pressureless infiltration process in vacuum. In order to modify the interface between the C f and the Mg matrix, the C f were coated with 5.0 mol.% yttria stabilized zirconia (YSZ) in sol–gel route. The C f/Mg composite exhibited a tensile strength of 1.08 GPa which reached 90% of the theoretical prediction by means of the rule of mixture. Microstructural examinations revealed the occurrence of interfacial reaction between the YSZ coating and the Mg matrix, producing a ∼20 nm thick interfacial reaction layer consisting of nanocrystalline particles, which include MgO particles, remaining ZrO 2 particles and a small quantity of ZrC particles. Interfacial reaction could induce a large compressive stress in the interfacial layer. As a result, some nanostructured defects, such as edge dislocations, were formed in interfacial layer due to the compressive stress. In the cooling process of fabricating the composite, the phase transformation of the remaining ZrO 2 from tetragonal to monoclinic could relax the thermal residual stress of interfacial layer.

Mechanism of décollement formation in subduction zones

SUMMARY The mechanism of decollement formation was investigated through a particle-based simulation model assuming homogeneity (e.g. no weak layer or pore fluid). A decollement-like structure appeared as a spontaneously localized shear deformation near the bottom of the sediment when the thickness of the sediment was sufficient to balance the gravitational force and tectonic loading. In contrast, no such decollement-like structure was formed when the sediment was too thin; in this case, the entire prism was deformed because of plate motion. These results are consistent with various observations in real subduction zones. A precise analysis of the stress state evolution during accretion reveals that the formation of a decollement-like structure is controlled by the spatio-temporal distribution of isotropic compression states.

Covariant hypo-elasticity

The theory of constitutive behavior, with explicit reference to hypo-elastic materials, is addressed with a geometric approach which, following physical arguments, leads to a covariant formulation. The essential role played by a careful distinction between spatial vectors, material-based spatial vectors and material vectors is emphasized. Definite answers to debated issues, such as the proper definition of stress rate, the formulation of integrability conditions, the fulfilment of material frame-indifference, and the task of evaluating the stress state evolution, are given. Simple shear and extension of a specimen of a hypo-elastic material are investigated as applications of the theory. Improper statements and unsound physical responses of hypo-elastic materials are overcome by the covariant theory, thus restoring the proper role to this constitutive model, for both theoretical and computational purposes. ► Spatial and material tensor fields are carefully defined. ► Comparison of material tensors by push is compelling. ► Rates of material tensors are Lie time-derivatives along the motion. ► Elasticity is time-independent and integrable hypo-elasticity. ► Simplest hypo-elasticity is hyper-elastic.

Evolution of large Venusian volcanoes: Insights from coupled models of lithospheric flexure and magma reservoir pressurization

[1] The growth and evolution of large volcanic edifices on Venus should reflect interactions between local magma reservoir-induced stresses and broader-scale stresses resulting from flexure of the lithosphere beneath the edifice load. Here, we explore the relationship between magma movement in the lithosphere and the flexural stress state via static, gravitationally loaded, axisymmetric finite element models. We find that reservoirs situated in the lower (extensional) lithosphere fail at the bottom and are therefore not viable long-term conduits for upward magma transport. Furthermore, for high-stress conditions (e.g., large edifices or thin lithospheres), chambers in the lowermost lithosphere exceed the failure criterion even before pressurization and are therefore unstable. In contrast, magma chambers located in the upper (compressional) lithosphere fail at or somewhat above the reservoir midsection, promoting lateral sill injection; continued failure in this mode would tend to produce oblate magma chambers with zones of intrusion at their margins. Reservoirs near the flexural neutral plane require the greatest overpressure to reach failure, emplacing cone sheets that transition to sills further from the chamber. The out-of-plane orientation of principal extensional stresses in the flexed lower lithosphere predicts the presence of radial dikes that are likely the main conduits for any subsequent magma ascent from the mantle melt source region. Our results also explain how the evolving stress state in the lithosphere tends to redirect magma passage over time: magma ascending into the lithosphere beneath the edifice is diverted to lateral sills in the upper lithosphere, inhibiting summit eruptions and possibly shifting eruption locations to the lower flanks at and beyond the distal margins of an oblate chamber or sill complex. We apply these results to interpret the observed structure and tectonism of Sapas Mons, Venus, in terms of flexurally controlled intrusive processes.