Void Growth Research Articles

Effects of loading rate on void growth in amorphous glassy polymers

Initiation, growth, and coalescence of microscopic voids are precursors to failure in amorphous glassy polymers. Hence, void growth analysis is important for understanding the failure in these polymers. Under quasi-static conditions, void growth in polymers is well understood; however, a similar analysis under dynamic conditions is not available in the literature. In the present work, we analyse the effect of loading rate on the void growth behaviour using large deformation finite element simulations. An axisymmetric unit cell model of a spherical void is considered for the analysis. The void is subjected to a range of strain rates (10−3s−1 to 105s−1). Remote triaxialities equivalent to uniaxial loading, biaxial loading, and higher triaxiality conditions are considered. Remote mean stresses, which are important from the perspective of void growth, have been characterized as a function of void size, strain rate, and triaxiality. Results show that the critical mean stresses required for unstable void growth increase with increasing triaxiality. Higher loading rates further amplify the critical mean stresses, and the amplification depends upon the material rate sensitivity of polymers. The void growth mechanism does not change because of material rate-sensitivity. During void growth, inertia effects are found to be significant after a strain rate of 103s−1. It is found that inertia increases with increasing triaxiality and increasing void size. It stabilizes the void growth and makes them expand in a more spherical shape, even at low triaxialities.

Mg2Al4Si5O18 as a novel bond coat material for advanced thermal/environmental barrier coatings on SiCf/SiC composites

This study proposes cordierite (Mg2Al4Si5O18, MAS) as a novel bond coat material for thermal/environmental barrier coatings (T/EBC), deposited using atmospheric plasma spray on SiC fiber reinforced SiC matrix composites (SiCf/SiC-CMCs) coupons, forming a Mg2Al4Si5O18/Yb2Si2O7/Yb2SiO5/LaMgAl11O19 coating system. The phase composition and thermal properties of the as-sprayed MAS coating were investigated, revealing cordierite as the primary phase in the as-sprayed coating with minor amounts of spinel and quartz phases which disappeared after heat treatment. Additionally, the as-sprayed MAS coating exhibited a low thermal expansion coefficient (3.19 × 10−6 K−1). The thermal cycling behavior and steam corrosion performance of the T/EBC coating system with cordierite as the bond coat were studied. Detailed analysis revealed that during thermal cycling tests, the coating failure was primarily related to liquid-phase sintering caused by eutectic reactions. In steam corrosion tests, the coating delamination was linked to the formation and growth of cracks and corrosion voids due to the residual stress release.

M-Voronoi and other random open and closed-cell elasto-plastic cellular materials: Geometry generation and numerical study at small and large strains

The present study deals with a numerical design strategy of a novel class of three-dimensional random Voronoi-type geometries, called M-Voronoi. These materials comprise random, non-quadratic convex void shapes and non-uniform intervoid ligament thicknesses, and can span high-to-low relative densities. The starting point for their generation is a random adsorption algorithm (RSA) construction with spherical voids embedded in an incompressible, nonlinear elastic matrix phase. The initial RSA geometry is subjected to large elastic volume changes by prescribing Dirichlet boundary conditions. Due to the incompressibility of the matrix phase, the externally imposed volume changes lead to significant void growth. The numerical growth process may be stopped at any desired porosity. The proposed M-Voronoi process is general and allows the formation of isotropic (or anisotropic) designs. As a byproduct of the developed approach, we also present a novel remeshing technique allowing to read arbitrary geometries of one or multiple phases. The elasto-plastic properties of the M-Voronoi porous materials are numerically investigated at small strains as well as large compressive and shear loads. Their response is assessed by comparison with other well-known random and periodic porous geometries such as polydisperse porous materials with spherical voids (RSA), classical TPMS Gyroid geometries and random Spinodoid topologies. The results show that M-Voronoi and RSA (with spherical voids) geometries exhibit the stiffest elastic and highest flow stress response compared to the other two geometries. This study shows unambiguously that randomness may or may not lead to enhanced mechanical response such as higher stiffness or flow stress.

A coupled ductile damage model for metal matrix composites: Development and application

The prediction of failure behavior in metal matrix composites remains a significant challenge in both composition design and process optimization. An accurate prediction of metal matrix composites damage evolution is a crucial for enhancing the quality of metal matrix composites forming. As the material undergoes plastic deformation, it experiences void initiation and growth, resulting in consequential microstructural transformations, stiffness degradation, and mechanical property shifts. In this work, we employed a model to predict damage progression and stiffness decay in metal matrix composites. Leveraging the Gurson-Tvergaard-Needleman framework, this homogenization model accounts for the impact of the evolution of voids and reinforcing phases, on the composite's mechanical properties. The influences of reinforcing phases on voids nucleation and growth were particularly considered, and also the interaction of voids, matrix, reinforcing phases, and stiffness were integrated to discuss their impacts on damage evolution and mechanical performances of the metal matrix composites. The model was implemented as an Abaqus VUMAT subroutine, with its validity gauged by analyzing the influence of model parameters on failure mechanisms and inherent elastoplastic traits. Utilizing the flanging process of carbon nanotube-reinforced aluminum matrix composites as a case study, a significant agreement was observed between experimental and simulated force-displacement profiles, as well as crack evolution routes.

Understanding the damage initiation and growth mechanisms of two DP800 dual phase grades

Dual phase (DP) steels are amongst the most widely used structural steels for automotive applications. It is essential to understand the damage initiation and damage growth in these high strength steels and further shed light on improving mechanical properties. In this work, two DP800 dual phase grades are investigated, which exhibit identical ultimate tensile stress but significantly different elongation in the uniaxial tensile test. To explain the difference in ductility, particularly described by uniform elongation, we investigate the damage initiation and growth mechanisms by analyzing microstructural changes upon deformation, such as voids, dislocation structures and the grain morphology. Furthermore, ferrite micropillars in pre-strained samples are tested in situ to capture the strain hardening capability of ferrite. We found that the DP steel with harder martensite and softer ferrite exhibits more damage initiation sites after deforming to an identical strain. However, void growth is much slower compared to the DP steel grade with fewer initiation sites. We explain the suppressed void growth by significant strain-hardening of ferrite surrounding the voids, which is observed in the micropillar compression experiments. The improved strain hardening of ferrite originates primarily from the difference in chromium content considering the negligible influence of dispersed particles.

Effect of Shape and Distribution of Secondary Voids on Ductile Crack Path

Ductile fracture in structural metals and alloys comprises of three distinct stages: namely nucleation, growth, and coalescence of voids. In this failure mode voids, either pre-existing in the material or nucleated during deformation grow until they coalesce to form a continuous fracture path. The larger voids nucleating early in the deformation history are often referred to as the primary voids whereas the smaller ones (typically around 0.1 to 0.01 times the size of the primary voids) nucleate much later and are described as the secondary voids. As the imposed deformation increases, voids grow, and the ductile crack path is influenced by the interaction and coalescence of the two-scale voids. The present work numerically models the interaction between the two populations of pre-existing voids lying ahead of the crack tip. The influence of secondary voids attributes, in particular, the shape and distribution of secondary voids on ductile crack propagation is analysed. A plane-strain modified boundary layer (MBL) model, under small-scale yielding condition, subjected to remote mode-I loading is analysed. Both primary and secondary voids lying near the crack tip are modelled explicitly. In the absence of secondary voids, as expected, the crack path is controlled by the distribution of primary voids. The presence of small secondary voids, however, influences the crack growth and, hence, the crack driving force. Various initial configurations of secondary voids are modelled and some details of crack propagation and the numerically computed driving force versus crack extension (J-Δa) curves are presented.

Characteristics of Quasi-static and Dynamic Failure of Inconel 625 Superalloy under Simple Shear

The shear flow and failure of a superalloy Inconel 625, conceived for jet engine applications, are investigated by using a modified flat gauge shear specimen with the assistance of Digital Image Correlation (DIC). The constant strain rate shear tests were successfully performed by using a screw driven Zwick machine and a bespoke spilt Hopkinson tension bar (SHTB). Nearly all gauge section is in a uniform strain state at dynamic force equilibrium condition. The constitutive relationships and the crystallographic texture show strain rate dependence. Different from the void growth induced failure at quasi-isothermal condition, the Inconel 625 fails by adiabatic shear at high strain rates. The present shear testing provides an opportunity to study the shear flow and failure of superalloy of small structural components in turbine engine.

Yield criterion for intergranular void coalescence under combined tension and shear

Intergranular ductile fracture is a failure mode that may arise in many metallic alloys used in industrial applications. It manifests as the successive nucleation, growth, and coalescence of cavities at grain boundaries. Thus, simulation of intergranular ductile fracture in polycrystals requires modeling those three different stages at the scale of grain boundaries, i.e. at the interface between two different crystals. In this study, a yield criterion for the coalescence of cavities at the interface between two isotropic materials obeying Mises plasticity is first developed by limit analysis in order to provide some insights into that phenomenon. This criterion is checked against numerical limit analysis under combined tension and shear and is found to agree with unit-cell simulations quantitatively. The model is then extended to crystals so as to account for the complex coupling between loading state, crystallographic orientations, and void microstructure in intergranular coalescence. This second criterion is also assessed through comparisons to numerical limit analysis for an FCC crystal lattice. The agreement is very good in the case of coalescence by internal necking and the trends displayed by coalescence under combined tension and shear are captured correctly. Some implications of the model on the competition between transgranular and intergranular ductile fracture are discussed. Finally, by combining this model with an existing criterion for void growth at grain boundaries, a multi-surface yield function relevant to intergranular ductile fracture is obtained and compared to unit-cell simulations.

Void Growth Dynamics in Solid-State Batteries

Solid-state batteries (SSBs) can potentially offer improved energy density and safety, when compared to current lithium-ion batteries. Despite their irrefutable theoretical promise, further advancement of SSBs relies on developing a comprehensive understanding of various fundamental aspects including electro-chemo-mechanics, transport interactions, morphological evolution and related failure modes at solid-solid interfaces. Amongst the wide range of challenges, the formation and evolution of interfacial voids at the lithium-metal/solid-electrolyte interface during stripping is critical, due to its associated effect on internal short-circuit and cell failure during subsequent plating. The void growth phenomenon in SSBs is jointly determined by different factors such as the self-diffusion kinetics and mechanical response of lithium, reaction distribution at the solid-solid interface, and operating conditions such as external pressure and temperature. In this presentation, the pivotal role of reaction heterogeneity on the contact evolution process, along with key descriptors such as the lithium microstructure, surface morphology and contact percolation are discussed. The underlying asymmetry in terms of the competing electrochemical/mechanical processes and contact evolution during plating and stripping is highlighted. Lastly, the influence of non-uniformities in external pressure and temperature on the occurrence of disparate void growth patterns and electrochemical response is examined in this presentation.

(Keynote) Thermo-Electrochemical Interactions in Solid-State Batteries

Solid-state batteries (SSBs) with a lithium metal anode hold tremendous promise to enable long-range electric vehicles and electric aviation. However, the successful realization of practical SSBs necessitates gaining a fundamental understanding of the complex nature of solid-solid interface evolution including the origin of various failure/degradation mechanisms such as lithium filament penetration, void growth and interphase formation. While the influence of chemo-mechanics at such interfaces has received significant research attention, the underpinnings of thermo-electrochemical coupling and the thermal stability of solid-solid interfaces still require critical investigation. In this presentation, we mechanistically delineate the spatio-temporal attributes and implications of thermal interactions in SSBs, including their critical role on interface stability of the anode, electrochemical-transport response in the cathode and crosstalk between the cathode/solid-electrolyte/anode interfaces. The effect of architectural asymmetry in a solid-state cell, consisting of a heat-generating cathode and a lithium-metal anode, on the occurrence of an intrinsic thermal gradient and associated degradation modes have been highlighted. A comprehensive description of mechanisms underlying the thermo-electrochemical stability of solid-solid interfaces in SSBs is presented.

A Noncontact Method for Estimating Thin Metal Film Adhesion Strength Through Current-Induced Void Growth

Abstract Studies have reported that the electromigration-induced void growth velocity in metal thin films is inversely related to the adhesion strength of the metal thin film with the base and passivation layers. It was also observed that the contribution of interface adhesion strength to electromigration resistance decreases with an increase in temperature. In this study, an expression is derived for the diffusive void growth velocity induced by electromigration from a generalized thermodynamically consistent continuum-based theory for reaction–diffusion driven solid-state interface evolution. This relation captures the effect of adhesion with the base and passivation layers on electromigration resistance of thin metal films. Electromigration experiments were carried out at elevated temperatures and high current density to induce voiding in thin Cu metal film deposited on a base layer of TiN and passivated with TiN or SiNx. The degradation of interface adhesion strength with temperature is modeled using an Andrade-type of relationship. The void growth rates characterized in these experiments are combined with the expression for void growth rate to estimate the interface adhesion strength for the Cu–TiN and Cu–SiNx interfaces. The methodology for estimating the adhesion strength of the metal-passivation layer interface is validated through comparison with interface adhesion strengths from mechanical de-adhesion tests reported in the literature.

A material-component-structure coupling damage model for the cyclic elastoplastic design of a large-span photovoltaic structure

To reduce structural deadweight without sacrificing stiffness and strength, a large-span offshore fixed truss is designed for bearing photovoltaic devices, and correspondingly, a material-component-structure coupling methodology of cross-scale damage evolution modelling is proposed for analysing the cyclic elastoplastic behaviours of this lightweight and high-strength structure under extreme environmental loads. Utilising this methodology, the mechanical intra-action among microscale defect propagation, mesoscale component failure and macroscale offshore-truss deterioration were characterised, in which a physical relation was established through the reciprocation of the material defect propagation model and refined bulk-member elements. The cyclic elastoplastic performance of the long-span offshore fixed truss was efficiently and accurately simulated. Moreover, this damage evolution modelling provides a reasonable framework for crack prediction by considering microstructure characteristics, stress redistribution and ductile damage, because the crack of the material is caused by void nucleation, growth, and coalescence. A cross-scale modelling approach for the offshore photovoltaic structure was presented and employed to assess the key design issue that affects typhoon performance, in which a coupled solution for the micro-defects in the material and large-scale structural bearing capacity was realised. This proposed methodology can be an alternative design technique for considering the structural features and material properties in practical engineering applications.

In situ measurement of damage evolution in shocked magnesium as a function of microstructure

Accurate modeling and prediction of damage induced by dynamic loading in materials have long proved to be a difficult task. Examination of postmortem recovered samples cannot capture the time-dependent evolution of void nucleation and growth, and attempts at analytical models are hindered by the necessity to make simplifying assumptions, because of the lack of high-resolution, in situ, time-resolved experimental data. We use absorption contrast imaging to directly image the time evolution of spall damage in metals at ∼1.6-μm spatial resolution. We observe a dependence of void distribution and size on time and microstructure. The insights gained from these data can be used to validate and improve dynamic damage prediction models, which have the potential to lead to the design of superior damage-resistant materials.

Role of grain boundary crystallography on void growth in FCC metals

The growth of an isolated spherical void at and near a grain boundary or a triple junction is studied by means of full-field crystal plasticity simulations with explicit representation of the void. To examine the fundamental aspects of void/grain boundary interactions in these cases, a three-dimensional large-strain elasto-viscoplastic fast-Fourier transform (LS-EVP-FFT) model with axisymmetric tensile periodic boundary conditions was developed. We employ this model to reveal the role of crystallography (grain orientations, grain boundary misorientation and inclination angle with respect to the largest component of the applied stress) and type of loading on void growth. It was found that grain orientation was the primary crystallographic feature governing void growth in strain-rate controlled simulations. For strains small enough to not significantly alter the local geometry, the overall growth of the void in bicrystal boundaries was not strongly affected by grain boundary inclination angle. The relative amount of void growth experienced within each grain in a bicrystal or tri-crystal was strongly dependent on the grain boundary inclination angle. We found a subset of orientations that exhibit faster void growth in bicrystal boundaries than inside the constituent single crystals. Last, we show that when placed primarily in one grain but near the grain boundary, void growth was similar to void growth when placed at the grain boundary. The growing void remained in the original grain and did not grow into the other grain, regardless of crystallographic character.

Correlation between grain size and dynamic response of NiTi alloy during intense shock-induced multi-spallation

This work committed to performing non-equilibrium molecular dynamics simulations to explore the influence of grain size on multi-spall performance of nanocrystalline nickel-titanium (NiTi) alloy. By comparing the calculated Hugoniot relationship with present experimental results, the Finnis-Sinclair (FS) type potential used in this work was verified to be suited for reproducing the shock behavior of NiTi alloy at high strain rate. During shock wave evolution, a single plastic wave was clearly observed in the sample with grain size of 5 nm, while there was a more pronounced elastic-plastic double wave structure at larger grain size. According to the free surface velocity history, the predicted spall strength exhibited a decreasing tendency and subsequently increased when the grain size decreased from 50 to 5 nm, indicative of a critical grain size (10 nm). Correspondingly, there were multiple spall planes appearing in the sample, the grain size of which was not smaller than the critical one. Contrarily, a single spall plane was observed at 5 nm. By counting the void distribution statistic, we found that as the grain size increased, the void-nucleation behavior changed from the intergranular to intergranular/transgranular coexisting pattern. In consequence, more nucleation sites were provided to promote an increase in the number of voids. Interestingly, for intergranular, there were much more voids involved in spallation at smaller grain size, which was attributed to grain boundary effect. The results demonstrated that void evolutions rarely occurred at the grain boundaries parallel to the loading direction. Moreover, when the grain size was larger than 5 nm, the B19 phases were found to be produced around those potential void-nucleation sites. After void nucleation, these B19 phases decreased till disappearance, accompanied by the proliferation of a large number of [100] dislocations. Such dislocations accumulated in the region without voids could block the void growth in this region, which was expected to be the reason for the formation of multiple spall planes. On the contrary, the absence of dislocations at 5 nm was inclined to the fact that the space for dislocation emission and aggregation was preoccupied by nucleated voids.

Coupling a void growth model with an elastoplastic material model for a simultaneous prediction of the borehole plastic zone and critical collapse pressure

The elastoplastic shear stability of an inclined borehole is explored in this study. Unlike other previously published elastoplastic wellbore stability solutions, this work considered the contributions of the anti-plane shear stresses. A new framework for estimating the critical elastoplastic collapse pressure and the extent of the plastic zone around the borehole is presented. In this approach an elastoplastic material model is coupled with a void-growth model to simultaneously predict the collapse pressure and plastic zone. In this paper, the Gurson void-growth model is coupled with an elastic-brittle plastic material model, and the critical collapse mudweight and plastic radius at the orientation of maximum compression are solved simultaneously from the resulting system of equations. The predicted collapse mudweights from the proposed approach compared very well with observed field data. When compared with the conventional method (NYZA = 1), the proposed framework performed better, although the difference can be negligible in some cases.

Investigation of ductile damage in dual phase steel during tensile deformation by in situ X-ray computed tomography

In situ synchrotron radiation X-ray computed tomography (CT) is used to understand the void nucleation and growth behaviour of dual phase (DP) steel, DP800, during uniaxial tensile deformation. The voids were identified post mortem as having nucleated primarily in the (41 vol%) martensite phase. The behaviour of individual voids was found to be broadly in line with a Rice and Tracey style growth model (their volume increasing by a factor of 10), while the mean void size was broadly in line with a model that included the continuous nucleation of new voids, as well as the growth of existing voids, throughout straining. Voids tended to elongate during uniaxial (low stress triaxiality) straining, but then to dilate more isotropically as necking led to increased triaxiality. One large pre-existing void was found to elongate quicky at first, but then for growth to slow, presumably because it was not located in the highest triaxial stress (necked) region. Perhaps surprisingly the average size of the void population grows only slowly (by a factor of 2) during straining; this is because while the size of each void grows, new small voids are always being nucleated. Finally, the changes of stress triaxiality and shear stress state during tensile deformation of the square cross-section smooth tensile specimen are investigated via finite element modelling, to qualitatively assess the impact of sample geometry on void nucleation behaviour and fracture strain in the current study.

DETECTION OF VOID NUCLEATION, COALESCENCE AND COLLAPSE IN ATOMISTIC SIMULATIONS

Extraction of required information from atomic configurations is crucial for efficient use of molecular dynamics (MD) simulations, and automating this process allows the collection of statistical data to develop and validate physical models and data-driven approaches. Here we update the previously developed pore searching algorithm to automatically detect the events of void nucleation, collapse and coalescence by comparing pairs of atomic configurations. We calculate an intersection matrix, which shows common regions between voids of current and previous time frames, and analysis of this intersection matrix gives a numerical criterion for determination of the considered events. The updated algorithm is verified in the case of small MD system and further used to analyze a large MD system with many hundreds of voids. The predominance of void collapse is confirmed in the case of uniform triaxial tension of solid aluminum, while void coalescence instead of collapse is detected in the case of a more complex loading with axial compression and lateral tension. This dependence of the predominant mechanism on the loading path correlates with previous finite element analysis in the literature. Another interesting finding is a continuing nucleation and collapse of voids far beyond the fracture beginning at a level of negative pressure much lower than the spall strength, which can be attributed to a developed defect structure of material produced by plastic growth of voids.

Predicting porosity distribution effects on the orientation induced plastic anisotropy of ductile solids: A crystal plasticity investigation

This paper investigates the role of crystallographic orientation and heterogeneous void distribution on void growth using three-dimensional crystal plasticity simulations. Face-centered cubic crystal structure is chosen as the model system. The role of crystallographic orientation on void growth is mapped by modeling single crystals as cubic unit cells with an embedded spherical void. Reminiscent of real aggregates, porosity is then re-distributed in single crystals to assess the role played by heterogeneous distribution of voids. Simulations are coupled with statistical analysis tools to decode the complex interplay involved in orientation dependent anisotropic plasticity and stochastic parameters governing heterogeneous void distribution like void size and placement. The applicability of the obtained results for single crystals is appraised for polycrystals as well by embedding the porous crystal in a randomly textured polycrystalline aggregate. Statistical analysis is repeated for all the considered orientations of the central grain to highlight the intricacies associated with plastic anisotropy-randomness in the heterogeneous microstructure. The results reveal interesting variations in mechanical strength, ductility and void growth rate in the three-dimensional orientation space. Analysis of configuration-property linkage reveals critical variables regulating the material strength and ductility for single crystals as well as polycrystals. Ramifications of the obtained results in designing strong and tough ductile components for practical applications are discussed.

Unraveling the transformation of ductile damage mechanisms of void evolution and strain localization based on deformation heterogeneity

This study delves into the ductile damage mechanism via exploring the intrinsic nature of the transformation of void and strain localization induced damages. In tandem with this, tensile experiments were conducted by using ductile metals of pure titanium and austenite steel with different grain sizes (d¯) and sample thicknesses (t). Various damage behaviors were generated: the void damage (Dv) in which the damage is induced by voids and their evolution, the strain localization induced damage (Dl) in which damage is controlled by localized deformation, and their mixed mode. Examinations of damage characteristics show a transformation from Dl to Dv with the increase of t/d¯ or hardening. To identify the decisive factor behind the mechanism, crystal plasticity finite element simulations were performed, and the grain-level non-homogeneous deformation was carefully examined. The materials with severe inhomogeneous deformation were found to have fewer voids, while the ones with more uniform deformation possessed evident void growth. Deformation heterogeneity was thus identified as a pivotal factor for the Dl - Dv transformation. The change of micro-defect configuration of void and grain boundary (GB) with deformation heterogeneity was discovered to be the underlying cause. In the Dv case, the large number of strain localization zones penetrating within the bulk promotes void nucleation and growth from vacancies and dislocations. The Dl case, on the other hand, gets more new GBs but smaller number of voids during deformation. The larger continuous strain localization zone facilitates the dislocation-consuming process of GB formation, resulting in the difficulty of void formation. Additionally, a characteristic parameter representing the deformation heterogeneity degree was defined. A Dl - Dv paradigm, which involves the change of damage mode and micro-defect configuration with deformation heterogeneity, and the characteristic parameter was established. The paradigm was validated to have a wide applicability with its efficiency in interpreting extensive damage phenomena. These explorations are expected to add new insights into the understanding of damage mechanism and support the development of a unified damage prediction platform.