Void Coalescence Research Articles

Micro-mechanics investigation of heterogeneous deformation fields and crack initiation driven by the local stored energy density in austenitic stainless steel welded joints

This work investigates the heterogeneous deformation and failure of HR3C austenitic stainless steel welded joints at room and typical service temperatures. Such types of welded joints are widely used in the new generation of fossil fuel power stations and are known to suffer from premature high temperature failure. Observation of in-service failures revealed that cracks may nucleate either in the heat affected zone or in the weld metal. The main objective of this work is to identify the local microstructural conditions and stress–strain fields responsible for both ductile failure and micro-crack nucleation within the weldment at low and high temperatures, respectively. To that purpose, a novel multi-scale micromechanics-based modelling framework is proposed. It relies on representative weld microstructure models digitally reconstructed from electron backscatter diffraction measurements, and dislocation density-based crystal plasticity models to describe the behaviour of individual grains in each weld region. A novel thermo-dynamically consistent relation for the configuration stored energy per unit volume is derived from the crystal plasticity framework.The single crystal models are calibrated and validated from a combination of uniaxial tensile tests on cross-weld specimens using high resolution digital image correlation techniques, representative volume elements of the polycrystals at the macro-scale, as well as micropillar compression tests at the scale of the individual grains. Predictions of heterogeneous inelastic deformation fields within the weldment at both 22 °C and 665 °C, and of micropillar compression behaviour of the individual weld single crystal phases are consistent with experimental data. The experimentally observed ductile failure of the weld metal at room temperature is successfully predicted using a Gurson-type void nucleation, growth and coalescence constitutive model. The suitability of the stored strain energy density and the accumulated plastic strain as crack initiation/creep failure indicators is investigated. It was found that predicted creep lifetimes with either indicator were very similar, and that they were relatively accurate for low stress levels.

Void growth and coalescence in sigmoidal hardening porous plastic solids under tensile and shear loading

Void growth and coalescence in sigmoidal hardening porous plastic solids under tensile and shear loading

Void nucleation and growth behavior of TIG welded AA2219 deformed at cryogenic temperatures

This work investigates the failure behaviour of tungsten inert gas (TIG) welded 2219 aluminum alloy butt welds deformed over a range of cryogenic temperatures relevant to liquid hydrogen/oxygen propellent storage tanks. A novel in situ tensile testing machine, able to deform samples at temperatures down to 83 K, was designed to be accommodated on synchrotron computed tomography beamlines. In this way we were able to observe the accumulation of damage from void nucleation through growth to coalescence and ultimate failure by time-lapse X-ray microtomography during tensile straining at 293 K and 123 K. The results reveal that micro-void nucleation is triggered by θ (Al2Cu) precipitates and α-Al + θ (Al2Cu) eutectics in the form of particle fracture and interface decohesion. After nucleation, these freshly nucleated voids, along with pre-existing welding defects, extend with straining along the loading direction. This leads to void linkage, a very short void coalescence stage and subsequent catastrophic failure. The probability distribution function that describes the rate at which voids nucleate by interface decohesion considering the particle orientation was determined through the Eshelby inclusion theory. The evolution of void aspect ratio and void growth were modelled using the Gurson-Tvergaard-Needleman model and Le Roy model, respectively. This suggests that pre-existing defects grow faster, but that the numerous closely spaced nucleated voids play a significant role in failure.

The effect of silica nanoparticles on the shock adiabatic relation and tensile strength in polyurethane

This work exploded the effect of silica nanoparticles on shock adiabatic relation and tensile fracture in polyurethane based on atomistic simulations. It is found that the non-uniform interface structures introduced by nanoparticles can increase the shock impedance, which also leading to increased twisting of polyurethane chains and the generation of local hotspots near the nanoparticles. The interface structures near the nanoparticle consists of polyurethane chains with a high gyration radius, and the average gyration radius increases approximately linearly with the increase in nanoparticle content. At lower shock velocity, the potential energy increment initially increases and then decreases with the increase in nanoparticle content. Bond analysis reveal that flexible segments dominate the bending and twisting deformations of polyurethane, while nanoparticles enhance the corresponding deformation degrees. Furthermore, nanoparticles can serve as void nucleation sites for early-stage tensile damage, resulting in a decrease in fracture strength. Differing from metals, the relationship between tensile strength and fracture temperature follows a more linear law. Nanoparticles inhibit the later growth and coalescence of voids by increasing the temperature and steric hindrance. The density and size distribution characteristics of voids are consistent with the changes in potential energy during the shock compression process. Unlike classical spallation, the curled polyurethane chains in the tensile region gradually orient along the shock direction, evolving into a void-fiber structure.

Extended Gurson-Tvergaard-Needleman model considering damage behaviors under reverse loading

Void nucleation, growth, deformation and coalescence are the main microscopic damage mechanisms for plastic deformation of sheet metals. To describe the effect of reverse loading on the microscopic damage accumulation and ductile fracture, the damage evolution equations in regard of void nucleation, void growth, shear void nucleation and shear deformation damage were modified. Through the further introduction of the combined hardening model, an extended Gurson-Tvergaard-Needleman (GTN) model was constructed in this study, to improve the predictive ability of ductile fracture under reverse loading conditions. Two typical reverse loading experiments including compression-tension and shear-reverse shear were performed. The number, size and shape of microscopic voids were qualitatively analyzed and compared through the microscopic observations, it is indicated that the preloading and loading sequence strongly affect the damage accumulation and the final ductile fracture, which is the microscopic damage mechanisms under reverse loading. The proposed GTN model was verified by the load responses and displacements at fracture (DAFs) of the conducted reverse loading experiments. The good agreement between numerical simulations and experimental results proves the rationality of the proposed GTN model and its accuracy to the prediction of ductile fracture under reverse loading conditions.

Elucidation of the factors controlling interface decohesion and particle fracture in a friction stir alloyed Al‒Fe alloy system

In the present study, an Al‒Fe alloy was fabricated by the solid-state friction stir alloying (FSA) technique. The FSA was carried out at a constant linear speed and variable tool rotational speed ranging from 600 to 1200 RPM. The ultimate tensile strength (UTS) and total elongation (TE) of the alloy fabricated at lower tool rotational speeds (600 and 900 RPM) are ∼ 300 MPa and ∼ 10%, respectively. Whereas the UTS and TE of the alloy fabricated at higher tool rotational speeds (1200 and 1500 RPM) are ∼ 110 MPa and ∼ 20%, respectively. The transition in the fracture behavior of the alloy from brittle to ductile was observed at a tool rotational speed of 900 RPM. The brittle fracture of alloys fabricated at low tool rotational speeds is primarily associated with Al/Fe interface decohesion and coarse Fe particle fracture. Whereas the void growth and coalescence are responsible for ductile fracture in alloys fabricated at higher tool rotational speeds. The transition of the dominant strengthening mechanism from dislocation and precipitation strengthening in alloys fabricated at lower tool rotational speeds to Hall‒Petch strengthening in alloys fabricated at high rotational speeds is the primary reason for the drastic change in the fracture behavior of these alloys. The coarse undissolved Fe particles and finely dispersed Al13Fe4 contributed significantly to kinematic and isotropic work hardening, which resulted in an extremely high work hardening rate in the alloys fabricated at lower tool rotational speeds.

Constant Strain-Rate Garofalo Creep Behavior of Intermediate 83Pb/10Sb/5Sn/2Ag and 91.5Sn/8.5Sb Solder Materials

Abstract Modern electronics reliability prediction models require materials-specific failure data across a range of conditions. Garofalo models are preferred due to their ability to accurately predict performance over a wide temperature range. However, data on intermediate solders are sparse, especially regarding performance at cold temperatures. We report Garofalo creep data for 83Pb/10Sb/5Sn/2Ag (Indalloy 236) and 91.5Sn/8.5Sb (Indalloy 264). Indalloy 236 exhibits an activation energy of 54.5 kJ/mol, n = 4.5, and α = 0.043 while Indalloy 264 exhibits an activation energy of 70.04 kJ/mol, n = 2.705, and α = 0.099 from −20 °C to 175 °C. We show that modern curve-fitting analysis should be utilized for Garofalo analysis rather than traditional linearization methods. X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy dispersive spectroscopy (EDS) were used to characterize the changes in the alloy phases during testing. Microstructural analysis indicates that Indalloy 236 can experience void coalescence at high temperatures while Indalloy 264 precipitates antimony-rich phases on the grain boundaries.

Ductile fracture prediction of additively manufactured Ti-6Al-4 V alloy based on void growth and coalescence of a unit-cell model

In this work, we have studied the fracture mechanism and proposed a micromechanical method with a unit cell model to predict the ductile fracture of additively manufactured (AMed) Ti-6Al-4 V alloy. The tensile experiments with smooth round bars and notched round bars were conducted to investigate the mechanical properties and ductile fracture behavior of materials. The proposed unit-cell model was validated by quasi-static tensile fracture tests to predict the ductile failure of titanium alloy manufactured by laser power bed fusion (L-PBF) under different stress states, which include a wide range of stress triaxialities. An equivalent initial void fraction was introduced to evaluate the ductile behavior of the titanium alloy. Our investigation shows that the stress states significantly influence the void coalescence behavior of AMed Ti-6Al-4 V alloy, and the fracture locus of L-PBF fabricated Ti-6Al-4 V alloy under different stress states was successfully predicted by the proposed unit-cell model under proportional loading. Our study provides useful guidance for the future design and application of metal materials for additive manufacturing.

Gurson-Cohesive modeling (GCM) for 3D ductile fracture simulation

A Gurson-Cohesive Model (GCM) is proposed to investigate 3D ductile fracture accounting for the void growth, coalescence, and complete failure phenomena. The proposed model idealizes the ductile fracture process as continuum damage evolution, cohesive crack initiation, nonlinear softening along the crack surface, and complete failure. The Gurson model is employed to describe continuum damage with void growth, while the cohesive zone model is utilized to introduce discontinuous cracks and represent nonlinear softening behavior. The transition from the continuum damage to discontinuous crack is taken into account systematically using a porosity-based crack initiation criterion considering stress triaxiality. The computational results successfully reproduce the experimental results of fracture tests with 15–5 PH steel and structural carbon steel 20 within the unified modeling framework. Furthermore, strong and stable convergence of both global and local responses (e.g., load-displacement curve, area reduction, crack tip location) are demonstrated under the mesh refinement without the aid of any ad hoc characteristic length scale parameter in the simulations.

Experimental Investigation of Void Coalescence in XTral-728 Plate Containing Three-Void Cluster

Void clustering effect is investigated by performing uniaxial tensile test on commercial 95% aluminum alloy XTral 728 by strategically placing an additional hole. Incorporating additional void induces strong stress and strain localization and reduces incipient coalescence strain approximately 17%. Also, two different cluster orientations with respect to applied loading and hole spacing ratios have been considered. The experimental revealed that material ductility is significantly decreased with increasing hole spacing ratios and for certain cluster orientation. To evaluate existing void coalescence models, numerical simulations are also performed and found that existing models overestimate the incipient coalescence strains for considered three-void cluster.

Use of effective multiscale cohesive models in the simulation of spall in metal plates

AbstractDuctile fracture of metals is the net result of void nucleation, growth and coalescence mechanisms that operate at the microscale. Optimal scaling analysis provides the analytical form of the effective material law that models the ductile fracture phenomena at the macroscale. The upscaled model of ductile behavior assumes the form of a cohesive relation—surface traction versus displacement—of the power‐law type with well‐defined exponents. In the present work, we demonstrate how the effective cohesive law derived from optimal scaling can be conveniently inserted into macroscale calculations by recourse to cohesive elements. The plastic deformation outside the cohesive elements is of moderate size and can be modeled by means of conventional plasticity models. In particular, the mesh size is dictated by accuracy considerations at the macroscale structural level and is not in any way constrained by microscale features and mechanisms, which happen at the subgrid level and are accounted for by the effective cohesive law. We illustrate the multiscale paradigm by means of spall calculations.

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.

Fatigue responses of metallic glass‐based stochastic network nanomaterial: Superior strain‐hardening ability

AbstractEngineering materials commonly suffer from cumulative and irreversible damage during cyclic deformation, leading to fatigue failure. Developing materials with better fatigue resistance is imperative. This work reports a metallic glass network nanomaterial that possesses superior strain‐hardening ability. After a certain number of fatigue tests, the peak stress of the nanomaterial can even be up to four times its original value. This superior strain‐hardening ability originates from the unique plastic mechanism. During cyclic deformation, localized shear transformation zones form and develop, especially in the stress concentration regions. Ligaments crosslinked to these regions cannot sustain their original configurations and contract toward these plastic hinges, resulting in the collapse and coalescence of voids. This densification enhances the engineering stress during each cycle. The fatigue features can be altered by adjusting the cyclic frequency. Stronger strain‐hardening ability can be achieved at lower cyclic frequencies.

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.

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.

In situ observations of the damage behavior of the metastable β‐titanium alloy Ti5321 using synchrotron X-ray microtomography

In situ X-ray synchrotron microtomography was used to quantify the evolution of damage in the titanium alloy Ti5321 with bimodal microstructure. The results show that voids nucleate in the equiaxed primary α grains and α plates or at α/β interfaces. There exists an approximate linear relationship between volume of voids and local strain of several largest voids. The low growth rate and delay of coalescence of voids are attributed to the dispersed distribution of the α phase in the bimodal microstructure. There are no micro-cracks formed in the interior of the sample until fracture. The deep dimples in the fracture surface indicate ductile fracture. The damage mechanism of Ti5321 is discussed with the help of post-mortem SEM. To clarify the difference in damage mechanism between metastable β and α + β titanium alloys, Ti64 is also in situ tensile tested.

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.

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.

Analysis on dynamic shear fracture based on a novel damage evolution model

Dynamic shear experiments and relevant numerical simulations are crucial for comprehensively understanding shear fracture mechanisms under diverse strain rates. In numerical simulations, damage evolution models are important for accurately capturing fractures and for guiding engineering applications under impact loading. To better predict dynamic fractures, a novel dynamic fracture model based on statistic damage mechanics is proposed. Based on the two-dimensional phase-field theory, the acceleration of void deformation is introduced into the void number continuity equation from the mesoscale. As fracture surfaces are formed by void evolution, a novel damage level is defined as the ratio of the statistical cross-sectional area of voids to the cross-sectional area of representative elements. Combining the void number continuity equation and the abovementioned damage level, a novel damage model is established based on void nucleation and ellipsoidal void growth. Based on percolation theory, a damage-softening function suitable for such a model is derived to characterize the effect of void coalescence on damage. Subsequently, dynamic shear tests are conducted at different strain rates using Split Hopkinson Pressure Bar (SHPB) and double-shear specimens with different shear zone widths. Two groups are defined to perform the dynamic shear experiments. One group is used to obtain the numerical model parameters and the other is used to investigate the fracture and void evolution. Scanning electron microscopy (SEM) tests are performed to analyze the effect of strain rate on void evolution. Moreover, the damage evolution model is used in the numerical simulation and its reliability is verified. The numerical results are consistent with the experimental results in terms of the strain signals and void number distributions. The effects of strain rate on fracture and void evolution are investigated via numerical simulations. All the results indicate that the proposed model can accurately predict dynamic shear fractures under different strain rates, thus serving as a useful reference for engineering design.

Synchrotron radiation X-ray laminography of internal damage in short-fiber-reinforced polyamide 6 under cyclic tensile loading

Fiber-reinforced plastics are lightweight materials expected to reduce greenhouse gases and the fatigue properties need to be clarified to extend the practical applications. However, the fatigue tests have been limited to the surface or cross-sectional observation of cut specimens. In this study, we conducted non-destructive through-thickness measurements using synchrotron radiation X-ray laminography to investigate the internal fatigue damage behavior in sharply notched carbon fiber (30 wt%)-reinforced polyamide 6 specimens. Under fatigue loading, a large number of voids in the matrix and delaminations at the carbon fiber sides as well as fiber ends were nucleated near the notch tip. Incremental fatigue cycles caused voids coalescence, resulting in the extension of the damaged zone. The unit volume of voids increased locally in severely damaged zone due to coalescence of the voids, while it decreased in adjacent locations because the residual voids were small, which resulted in the larger diversity of unit volume of voids. In the specimen thickness direction, the damage zone was larger near the surfaces in plane-stress condition than inside the specimen in plane-strain condition.