Void Growth Research Articles

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.

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.

Influence of temperature on deformation and damage mechanisms of wire + arc additively manufactured 2219 aluminum alloy

This work investigates the deformation and damage mechanisms of wire + arc additive manufacturing (WAAM) 2219 aluminum alloy over a broad temperature range of 77 K to 523 K. It is found that the strength and work hardening rate increase significantly with decreasing the temperature from 523 K to 77 K, and the fracture mode transitions from transgranular fracture mode to a mixture of intergranular and transgranular fracture ones. The large elongations to fracture are very similar for the specimens tested at 77 K and 523 K. This is mainly attributed to higher uniform elongation before necking at 77 K and higher post-necking elongation at 523 K. The cracking of α-Al + θ (Al2Cu) eutectics is the primary mechanism of micro-void nucleation, independent of the test temperature. The nucleated micro-voids, along with larger gas pore defects introduced by WAAM, extend along the tensile direction. In addition, as the temperature increases from 77 K to 523 K, the fracture mechanism transitions from high strain localization to extensive necking, leading to higher dislocation density, more grain fragmentation and micro-void nucleation, and more significant grain elongation and void growth. True stress and strain responses over the studied temperature range (77 ∼ 523 K) and strain rate range (0.0001 ∼ 0.01 s−1) are well predicted using an improved Arrhenius-type constitutive model, by considering the activation energy of deformation as a function of temperature.

Towards ultra-high strength dual-phase steel with excellent damage tolerance: The effect of martensite volume fraction

Ultra-high strength (> 1 GPa) dual-phase (DP) steels have been extensively investigated in literature. Yet, the damage tolerance of these DP steels remains mostly unexplored, whereas this parameter is crucial for the sheet formability and anti-crushing performance. In this work, a medium-Mn DP steel was proposed in order to develop strong but damage-resistant DP steel by refining the microstructure. Ultra-fine grained (< 1 µm) DP steels were obtained by a simple cold rolling and intercritical annealing process. The developed DP steel can achieve an outstanding ultimate tensile strength (UTS) of over 1470 MPa with appreciable elongation to failure (EtF) of over 9 % when the martensite volume fraction (Vm) is 55 %. Higher Vm results in higher strength. However, the fracture strain, which is connected with damage tolerance, decreases significantly with increasing Vm, and it is even much lower than that of a full-martensite steel. Furthermore, the necking behaviour transfers from diffuse plus localized necking to diffuse necking with increasing Vm. The sufficient ferrite content in the proposed DP1470 steel enables void growth after nucleation, consequently leading to the occurrence of localized necking and higher fracture strain. Thus, a moderate Vm ranging from 45 % to 65 % is suggested for the development of a 1470 MPa grade DP steel with excellent damage tolerance.

Very low-cycle fatigue failure behaviours of pipe elbows under displacement-controlled cyclic loading

In this study, quasi-static very low-cycle fatigue tests were conducted on pipe elbows at room temperature to investigate the effects of the pipe thickness, internal pressure, and material on the failure behaviours under large-amplitude cyclic loads. Three types of elbow specimens comprising two different materials and two different pipe thicknesses were used in the tests. Elbow specimens were subjected to displacement-controlled, fully reversed, in-plane mode cyclic bending with and without internal pressure. All specimens failed due to through-wall cracking of which the location and orientation depend only on the pipe thickness regardless of the internal pressure and elbow material. For thin-walled elbows of Schedule 40, the axial crack at flank was developed, whereas for thick-walled elbows of Schedule 160, the circumferential crack at intrados. The number of cycles to failure decreased with increasing internal pressure in thin-walled elbows. However, the effect of internal pressure on the number of cycles to failure was negligible in thick-walled elbows. Regardless of internal pressure level, stainless steel elbows were more resistant to failure, compared with carbon steel elbows of identical dimensions. Finally, the strain-based evaluation model considering the void growth and shrinkage effect was applied to predict fatigue failure location and cycles. Two parameters in the model, the multi-axial fracture strain locus and void shrinkage ratio, were determined from monotonic tensile test data and the fatigue life curve of the material. The predicted crack initiation site and orientation were consistent with experimental finding. For all cases, the predicted failure cycles were less but overall close to experimental data.

A shear modified GTN model based on stress degradation method for predicting ductile fracture

The Gurson–Tvergaard–Needleman (GTN) model has provided a powerful description of the nucleation growth and coalescence of micro voids, but it has limitations in simulating shear fracture due to the absence of a description of shear localization behavior. A shear improvement method is proposed for simulating the ductile fracture of materials under different stress states. The modified model not only allows for strain hardening of the matrix material, but also accounts for the stress degradation caused by shear. The strength equation of the material is described by both the shear stress state function and a decay function, making it easier for materials under shear stress state to experience material softening and further inducing shear fracture. The modified GTN model is developed by incorporating the shear stress degradation factor into the yield function, while taking into account both void growth and shear failure mechanisms. By carefully calibrating the model’s parameters, the deformation and fracture processes of tensile, plane strain, notch tensile, and compression specimens in the 7A52 aluminum alloy are simulated. The damage evolution behavior of the material under different stress states is analyzed. The results indicate that the damage include void growth mechanism and void shear mechanism. The proportions of these two mechanisms vary under different levels of stress triaxiality. Upon localizing material deformation, the shear stress state intensifies, and the shear damage mechanism assumes a critical role in fracture. The modified GTN model accurately predicts the load-displacement response and fracture path of the 7A52 aluminum alloy under a wide range of stress states.

Nonlinear ultrasonic techniques to quantify oxidation damage in carbon/carbon composite material

This research applies linear and nonlinear ultrasonic (NLU) techniques to quantify oxidation damage in a carbon/carbon (C/C) composite material cut from an automotive friction disc ring. The oxidation as a result of gasification of carbon at high temperatures (T >∼ 500 °C) is a major degradation mechanism in C/C composites. This is the first research to successfully use a dry-contact mediator wedge setup for nonlinear ultrasonic applications, enabling repeatable in-situ Rayleigh wave measurements on slow wave velocity materials where submersion is impractical. The samples are subjected to thermal damage by exposure to a high temperature atmosphere over multiple holding times, and the oxidation damage is visualized using scanning electron microscopy (SEM). The sample mass is recorded and both linear (velocity and attenuation) and nonlinear (β′) ultrasonic measurements are performed after each holding time. Superior sensitivity to early stage oxidation affirms the suitability of nonlinear Rayleigh wave measurements for the quantification of thermally induced oxidation damage in C/C composites, while the double mediator wedge setup is well suited for high attenuation, slow wave velocity materials, demonstrating potential applicability for in-situ condition monitoring. The results show that a systematic oxidation starts after 3 min of exposure to the temperature in this C/C composite. The oxidation induced fiber–matrix debonding, matrix defects (appearing to be microcracking), and void growth are consistently detected by the Rayleigh wave velocity and acoustic nonlinearity. In addition to the higher sensitivity, the nonlinearity parameter has the capability of selectively measuring the strength related damage such as the observed fiber–matrix debonding, while the wave velocity can detect the oxidation voids. A combined use of these two parameters can provide useful information on the microstructural evolution in C/C composites subjected to high temperatures.

Atomic-level insights on enhanced strength and ductility of Al−Mg−Si alloys with β″-Mg5Si6 at cryogenic temperatures

The influences of β″ phase volume fractions (PVF) and cryogenic temperatures on nanomechanical properties of Al−Mg−Si alloys were simulated by molecular dynamics. The simulation results show that when the β″ PVF is 0.107 at 77 K, the peak stress of Al−Mg−Si alloy is increased by 97.05% compared to that of pure aluminum. When the β″ PVF is 0.107, the peak stress of the sample at 27 K is increased by up to 23.55% compared to peak stress of sample at 300 K. Cryogenic environments help to enhance total dislocation density, allowing samples to withstand greater stress, which can provide additional strength and ductility. Temperature decrease can also appreciably inhibit the initiation and growth of voids (growth rate is decreased by 88.5% at 27 K), which contributes to the enhanced ductility.

A unified viscoelastic model of progressive damage and failure for solid propellants

A general viscoelastic model incorporating the progressive damage evolution and failure criterion is developed for solid propellants across a wide range of temperatures (223 K to 333 K) and strain rates (2.38 × 10−4 /s to 4.76×10−2/s). (i) The progressive damage evolution, characterized by continuous void cavitation and growth, is linked to a macroscopic damage variable derived from a simple damage potential threshold, making it possible to determine the microstructural damage from experimental data. (ii) The failure criterion introduces two microstructural ingredients: the strain energy density, which accounts for both the glassy and rubbery failure of the polymer matrix, capturing brittle and ductile fracture modes at low and high temperatures respectively; and the void volume limit accounts for interface debonding, a process of particle detachment from the matrix. The implementation of the model effectively predicts the damage response and failure strains under uniaxial tension, cyclic and complex loading as well as superimposed pressure. Results reveal strong temperature/strain-rate dependency in the tensile strength, volume dilatation, and failure strains. Given that the model unifies progressive damage with ultimate failure and requires only a few model parameters, it assists in establishing a fracture criterion for the nonlinear fracture behavior of viscoelastic materials.

EPOXY-SILICA NANOCOMPOSITE: CREEP RESISTANCE AND TOUGHENING MECHANISMS

In this article, the effect of modified nanosilica (m-nanosilica) on the mechanical and creep performance of epoxy resin were investigated. At the same time, the toughnening mechanisms of epoxy resin with m-nanosilica were also considered. The results show that the crack pinning and crack deflection mechanism contributes only a small part to nanocomposite, this due to the size of the nanosilica particles is such smaller than crack-opening displacement. The FE-SEM surface fracture shows evidence of the debonding of the nanoparticles from the polymer matrix and the expansion of the holes around the nanoparticles as well as the existence of the plastic deformation zone. Plastic deformation and plastic void growth are the main toughening mechanism in nanocomposite material.

Novel and Accessible Physical Recycling for Expanded Polystyrene Waste with the Use of Acetone as a Solvent and Additive Manufacturing (Direct Ink-Write 3D Printing).

The current high production of plastics has prompted the exploration of alternative pathways to facilitate recycling, aiming for a progressively sustainable society. This paper presents an alternative and affordable technology for treating waste expanded polystyrene (EPS) mixed with acetone in a 100:1 volume ratio to be used as 3D printing ink for Direct Ink Write technology. In order to optimize the printing parameters, a comprehensive study was conducted, evaluating different needle diameters, printing speeds, and bed temperature values to achieve homogenous pieces and a highly repeatable 3D printing process. Results showed that the main optimum printing parameters were using needles with diameters of 14 to 16 G and printing speeds ranging from 2 to 12 mm/s, which were found to yield the most uniform ribbons. Increasing the bed temperature, despite favoring acetone evaporation, led to the generation of more heterogeneous structures due to void growth inside the printed ribbons. Thus, employing room temperature for the bed proved to be the optimal value. Lastly, a comparative study between the starting material and the EPS after the printing process was conducted using FTIR-ATR and GPC analyses, ensuring the preservation of the original polymer's integrity during physical recycling.

Uncoupled fracture model for E250, E350, and E450 grades of structural steel under monotonic loading

Forty-eight specimens with four notch specimen configurations have been extracted from three structural steel grades used in the Indian construction industry. The extracted specimen simulates stress states of ductile fracture initiation similar to the sacrificial element installed in seismic-resistant steel structures. All the specimens are monotonically tested under a displacement-controlled loading protocol. With the help of a universal testing machine and digital image correlation, the load versus notch elongation until the point of ductile fracture initiation has been captured for all the specimens. A validated numerical model is then developed to extract the ductile fracture initiation parameters, namely stress Triaxiality (T), Lode function (L - ξ or θ or Lp), and Equivalent Plastic Strain (PEEQ). The extracted T, L, and PEEQ are then used to construct a three-dimensional fracture locus for all three study grades. In addition, a new uncoupled ductile fracture model named the Exponential based Lode parameter Void Growth Model (ELVGM) is proposed to predict the point of ductile fracture initiation and is then compared with six well-established existing uncoupled ductile fracture models using eight error measures. The proposed ELVGM with two free parameters is observed to provide better prediction accuracy for both low and high-yield strength steel corresponding to the considered stress states.

Computational modeling of fracture in polymer nano‐composites undergoing large deformations via the graded‐interphase‐enhanced phase‐field fracture approach

AbstractThe phenomenon of fracture in polymer composites, polymer nano‐composites in particular, entails a multitude of intricate mechanisms including branching and merging of several cracks along with particle debonding and subsequent plastic void growth. This work involves an extension of the standard phase‐field fracture approach by means of the graded interphase concept in order to facilitate the modeling of a wide‐spectrum of fracture responses, which can be observed in experimental studies concerning the fracture behavior of polymer nano‐composites. Herein, motivated by the microstructure morphology of polymer nano‐composites, a continuous grading of the elastic and fracture properties is considered within a finite thickness interphase region around the filler particles. Appropriate tuning of the graded‐interphase model parameters enables to capture a variety of fracture responses, including cohesive failure between the filler particle and the matrix, as demonstrated via the presented numerical examples, which focus on polymer nano‐composites undergoing large deformations prior to fracture.

Use of a modified critical fracture strain model for fracture toughness estimation of high strength rail steels

This paper explores the feasibility of estimating fracture toughness (KIC,pred) for nine high-strength rail steels using data from smooth tensile and instrumented ball indentation test methods via a modified critical fracture strain model. The modification focuses on determining the equivalent plastic fracture strain and equivalent plastic strain from tensile and indentation tests, respectively, as well as the characteristic distance needed for estimation of fracture initiation. It shows that stress triaxiality plays a vital role by decreasing the ductility required to initiate fracture, based on the kinetic damage evolution law for a multiaxial stress state. A void growth index model was established from average grain sizes, and then used as the characteristic distance for fracture initiation. At the end, the KIC,pred defined based on equivalent plastic strain from tensile tests showed a strong correlation with KIC determined from ASTM standard method. KIC,pred from indentation also offers the opportunity for ascertaining the possibility of estimating the fracture toughness of high strength rail steels, non-destructively by focusing on the equivalent plastic strain and pressure at the tip of the indenter.

Size-dependent yield criterion for single crystals containing spherical voids

A micromechanics-based yield criterion is derived for a porous single crystal containing a random distribution of spherical voids, using homogenization and limit analysis of a hollow spherical representative volume element obeying a strain gradient crystal plasticity model. The criterion captures the effect of plastic anisotropy due to crystallographic slip on a set of discrete slip systems, as well as the void size dependence of yielding. The yield criterion is formally similar to the well known Gurson model for isotropic porous materials, and reduces to existing results in the literature in the limiting case of large void sizes relative to the length scale in the gradient plasticity model. The yield criterion is validated by comparison with rigorous upper bound yield loci obtained using a numerical limit analysis procedure. Predictions for the size dependence of void growth are obtained by integrating the porous plasticity model, and shown to be consistent with the observations from lower scale discrete dislocation dynamics simulations. The loading path dependence of void growth in the size-independent limit are compared with finite element simulations of void growth in a single crystal using the unit cell model.

An uncoupled ductile fracture model considering void shape change and necking coalescence

In order to accurately describe the fracture behaviour of ductile metals in a wide range of stress states, based on the mechanism of void nucleation, growth, and coalescence during plastic deformation, an uncoupled isotropic ductile fracture model was established, which considered the combination of void shape change and void coalescence through internal necking. Firstly, the effect of the volume and shape changes on the fracture behaviour of the material was summarized and discussed, and the mechanism of interpore dimple shrinkage and consolidation during the void coalescence was studied. Secondly, the parameters of the proposed model are studied in detail to verify the flexibility of the new model. Then, the proposed ductile fracture model was used to construct the 3D fracture locus of AA 2024-T351, AISI 1045, Q460, Mg-Al-Zn-RE, and Ti-6Al-4V materials, and the predicted fracture strain values under corresponding stress states were compared with the experimental results of previous scholars. The effectiveness of the proposed new model is verified. Finally, to demonstrate the superiority of the proposed new model, the predicted results were compared with those of the widely used DF2016, MMC, and Hu models. The prediction results show that the new model has the highest precision compared to the other three. The void shape change and the void coalescence through internal necking play an essential role in the ductile metal fracture process, which should be fully considered.

The damage mechanism of the metastable β-titanium alloy Ti5321 with specific microtexture using synchrotron X-ray microtomography

In order to investigate damage mechanism of metastable β-titanium alloy Ti5321 with bimodal microstructure and specific microtexture, in situ tensile test was performed facilitating with synchrotron X-ray microtomography. The damage evolution of metastable β-titanium alloy Ti5321 can be predicted in three dimensions by proper micromechanics-based modelling methods, the Rice and Tracey model and Huang model. Through comparisons of the Rice and Tracey model and Huang model validated using the values of stress triaxiality calculated from experimental data and Finite Element (FE) simulations, the prediction accuracy of growth rates of voids can be enhanced. The results also show that the void growth is strongly related to microtexture of α plates. It is found that the growth path of largest voids is along α plates which have their c-axes with similar inclination angle of ∼45° from rolling direction (RD). Electron backscatter diffraction (EBSD) was also used to reveal the damage mechanism. This result is important enlightenment for study of damage mechanism of metastable β-titanium alloys.

A micro-mechanics based extension of the GTN continuum model accounting for random void distributions

Randomness in the void distribution within a ductile metal complicates quantitative modeling of damage following the void growth to coalescence failure process. Though the sequence of micro-mechanisms leading to ductile failure is known from unit cell models, often based on assumptions of a regular distribution of voids, the effect of randomness remains a challenge. In the present work, mesoscale unit cell models, each containing an ensemble of four voids of equal size that are randomly distributed, are used to find statistical effects on the yield surface of the homogenized material. A yield locus is found based on a mean yield surface and a standard deviation of yield points obtained from 15 realizations of the four-void unit cells. It is found that the classical GTN model very closely agrees with the mean of the yield points extracted from the unit cell calculations with random void distributions, while the standard deviation S varies with the imposed stress state. It is shown that the standard deviation is nearly zero for stress triaxialities T≤1/3, while it rapidly increases for triaxialities above T≈1, reaching maximum values of about S/σ0≈0.1 at T≈4. At even higher triaxialities it decreases slightly. The results indicate that the dependence of the standard deviation on the stress state follows from variations in the deformation mechanism since a well-correlated variation is found for the volume fraction of the unit cell that deforms plastically at yield. Thus, the random void distribution activates different complex localization mechanisms at high stress triaxialities that differ from the ligament thinning mechanism forming the basis for the classical GTN model. A method for introducing the effect of randomness into the GTN continuum model is presented, and an excellent comparison to the unit cell yield locus is achieved.