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Relation of craze to crack length during slow crack growth phenomena in high‐density polyethylene
(2024)
The craze‐crack mechanism occurring in high‐density polyethylene (HDPE) causing slow crack growth and environmental stress cracking is investigated in detail with respect to the relation of crack length and the related craze zone. This is essential for the understanding of the resulting features of the formed fracture surface and their interpretation in the context of the transition from crack propagation to ductile shear deformation. It turns out that an already formed craze zone does not inevitably result in formation of a propagating crack, but could also undergo ductile failure. For the examination, the full notch creep test (FNCT) was employed with a subsequent advanced fracture surface analysis that was performed using various imaging techniques: light microscopy, laser scanning microscopy, scanning electron microscopy, and X‐ray micro computed tomography scan. FNCT specimens were progressively damaged for increasing durations under standard test conditions applying Arkopal, the standard surfactant solution, and biodiesel as test media were used to analyze the stepwise growth of cracks and crazes. From considerations based on well‐established fracture mechanics approaches, a theoretical correlation between the length of the actual crack and the length of the preceding craze zone was established that could be evidenced and affirmed by FNCT fracture surface analysis. Moreover, the yield strength of a HDPE material exposed to a certain medium as detected by a classic tensile test was found to be the crucial value of true stress to induce the transition from crack propagation due to the craze‐crack mechanism to shear deformation during FNCT measurements.
Highlights
- Progress of crack formation in high‐density polyethylene is analyzed by different imaging techniques
- Determined growth rates depend on distinction between craze zone and crack
- The ratio of the present crack to the anteceding craze zone is validated theoretically
- The transition from crack propagation to ductile shear deformation is identified
- An already formed craze zone may still fail by ductile mechanisms
A widespread recovery of waste heat requires a cost‐effective production of thermoelectric generators. Thermoelectric oxides are predestined for use at high temperatures. For manufacturing reasons, a multilayer generator design will be easily scalable and cost‐effective. To evaluate the potential of ceramic multilayer technology for that purpose, a multilayer of the promising thermoelectric oxides calcium cobaltite (Ca3Co4O9), calcium manganate (CMO, CaMnO3), and glass–ceramic insulation layers is fabricated. Cracks and reaction layers at the interfaces are observed in the microstructure. The compositions of these reaction layers are identified by energy‐dispersive X‐ray spectroscopy and X‐ray diffraction. Mechanical and thermal properties of all layers are compiled from literature or determined by purposeful sample preparation and testing. Based on this data set, the internal stresses in the multilayer after co‐firing are calculated numerically. It is shown that tensile stresses in the range of 50 MPa occur in the CMO layers. The reaction layers have only a minor influence on the level of these residual stresses. Herein, it is proven that the material system is basically suitable for multilayer generator production, but that the co‐firing process and the layer structure must be adapted to improve densification and reduce the tensile stresses in the CMO.
The current lack of quantitative knowledge on processing-microstructure–property relationships is one of the major bottlenecks in today’s rapidly expanding field of additive manufacturing. This is centrally rooted in the nature of the processing, leading to complex microstructural features. Experimentally-guided modeling can offer reliable solutions for the safe application of additively manufactured materials. In this work, we combine a set of systematic experiments and modeling to address creep anisotropy and its correlation with microstructural characteristics in laser-based powder bed fusion (PBF-LB/M) additively manufactured Inconel-738LC (IN738LC). Three sample orientations (with the tensile axis parallel, perpendicular, and 45° tilted, relative to the building direction) are crept at 850 °C, accompanied by electron backscatter secondary diffraction (EBSD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) investigations. A crystal plasticity (CP) model for Ni-base superalloys, capable of modeling different types of slip systems, is developed and combined with various polycrystalline representative volume elements (RVEs) built on the experimental measurements. Besides our experiments, we verify our modeling framework on electron beam powder bed fusion (PBF-EB/M) additively manufactured Inconel-738LC. The results of our simulations show that while the crystallographic texture alone cannot explain the observed creep anisotropy, the superlattice extrinsic stacking faults (SESF) and related microtwinning slip systems play major roles as active deformation mechanisms. We confirm this using TEM investigations, revealing evidence of SESFs in crept specimens. We also show that the elongated grain morphology can result in higher creep rates, especially in the specimens with a tilted tensile axis.
Extended X-ray absorption fine structure (EXAFS) conducted on an equiatomic MoNbTaW bcc medium-entropy alloy that was annealed at 2273 K reveals unexpectedly small 1st and 2nd shell element-specific lattice distortions. An experimental size-mismatch parameter, δexp, is determined to be ca. 50% lower than the corresponding calculated value. Around W, short-range order (SRO) preferring 4d elements in the 1st and 2nd shells persists. A Nb-W ordering is found, which is reminiscent of ordering emerging at lower temperatures in the B2(Mo,W;Ta,Nb)- and B32(Nb,W)-phases. With high-temperature ordering preferences in fcc also foreshadowing low-temperature phase, these findings suggest a general feature of high-temperature SRO.
A density-based phase field model is developed where the free energy functional is explicitly linked with molecular dynamics and is referred to as the Molecular Phase Field Method (MoPF). MoPF simulations involve expressing interatomic potentials in terms of density to form a density based free energy functional. Inputs to this functional are taken from atomistics such that the phase field density profile matches the corresponding density profile from atomistic simulations. We analyze our results by comparing the MoPF calculated excess interfacial energies with excess interfacial energies calculated using molecular dynamics associated with several nickel grain boundaries. Additionally, a comparison is made between our results and the interfacial energies of a \Sigma7 boundary across a variety of FCC systems simulated using density functional theory. The MoPF method is able to successfully predict grain boundary free energy trends between grain boundary and material types offering an atomistically informed mesoscale formulation for studying grain boundary physics.
Mean-field modeling and phase-field simulation of grain growth under directional driving forces
(2024)
Directional grain growth is a common phenomenon in the synthetic and natural evolution of various polycrystals. It occurs in the presence of an external driving force, such as a temperature gradient, along which grains show a preferred, yet competitive, growth. Novel additive manufacturing processes, with intense, localized energy deposition, are prominent examples of when directional grain growth can occur, beneath the melting pool. In this work, we derive a phenomenological mean-field model and perform 3D phase-field simulations to investigate the directional grain growth and its underlying physical mechanisms. The effect of the intensity of driving force is simulated and systematically analyzed at the evolving growth front as well as various cross-sections perpendicular to the direction of the driving force. We found that although the directional growth significantly deviates from normal grain growth, it is still governed by a power law relation <R> α tⁿ with an exponent n ~ 0.6–0.7. The exponent n exhibits a nontrivial dependence on the magnitude of the directional driving force, such that the lowest growth exponent is observed for intermediate driving forces. We elaborate that this can originate from the fact that the forces at grain boundary junctions evolve out of balance under the influence of the directional driving force. With increasing the driving forces, the growth exponent asymptotically approaches a value of n ≈ 0.63, imposed by the largest possible grain aspect ratio for given grain boundary energies. The current combined mean-field and phase-field framework pave the way for future exploration in broader contexts such as the evolution of complex additively manufactured microstructures.
A giant Zn segregation transition is revealed using CALPHAD-integrated density-based modeling of segregation into Fe grain boundaries (GBs). The results show that above a threshold of only a few atomic percent Zn in the alloy, a substantial amount of up to 60 at.% Zn can segregate to the GB. We found that the amount of segregation abruptly increases with decreasing temperature, while the Zn content in the alloy required for triggering the segregation transition decreases. Direct evidence of the Zn segregation transition is obtained using high-resolution scanning transmission electron microscopy. Base on the model, we trace the origin of the segregation transition back to the low cohesive energy of Zn and a miscibility gap in Fe-Zn GB, arising from the magnetic ordering effect, which is confirmed by ab-initio calculations. We also show that the massive Zn segregation resulting from the segregation transition greatly assists with liquid wetting and reduces the work of separation along the GB. The current predictions suggest that control over Zn segregation, by both alloy design and optimizing the galvanization and welding processes, may offer preventive strategies against liquid metal embrittlement.
Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers.
Liquid-metal embrittlement (LME) of galvanized (Zn-coated) advanced high-strength steels is a long-known problem in materials science. Here we reveal the initial microstructural processes underneath the Zn-coating that lead to LME-microcrack initiation in the steel substrate. We track the microstructural evolution during the first tens of milliseconds and find pronounced signatures of Fe-Zn intermetallic precipitation in both ferrite grain boundaries and at internal ferrite-oxide phase boundaries. In concert with novel CALPHAD-integrated density-based thermodynamic modelling, we demonstrate that Zn-rich intermetallic phase-nucleation can occur at markedly low processing temperatures due to a segregation transition. We show that a small Znenrichment caused by Zn bulk-diffusion during the initial temperature rise in a joining process is sufficient to induce the segregation transition and subsequent nucleation of Fe-Zn intermetallic grain-boundary phases, which the experiments link to crack initiation sites. These findings direct focus onto LME-controlling microstructural and thermodynamic phenomena at temperatures below the ductility trough and the austenite formation temperature.
The embrittlement of metallic alloys by liquid metals leads to catastrophic material failure and severely impacts their structural integrity. The weakening of grain boundaries by the ingress of liquid metal and preceding segregation in the solid are thought to promote early fracture. However, the potential of balancing between the segregation of cohesion-enhancing interstitial solutes and embrittling elements inducing grain boundary decohesion is not understood. Here, we unveil the mechanisms of how boron segregation mitigates the detrimental effects of the prime embrittler, zinc, in a Σ5 [0 0 1] tilt grain boundary in α −Fe (4 at.% Al). Zinc forms nanoscale segregation patterns inducing structurally and compositionally complex grain boundary states. Ab-initio simulations reveal that boron hinders zinc segregation and compensates for the zinc induced loss in grain boundary cohesion. Our work sheds new light on how interstitial solutes intimately modify grain boundaries, thereby opening pathways to use them as dopants for preventing disastrous material failure.
Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement 𝛥CTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of 𝛥CTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of 𝛥CTOD, they require an about ten times coarser mesh and show less sensitivity
w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and 𝛥CTOD value.
This contribution contains the raw data used to compare experimental results with thermodynamic calculations using the CALPHAD method, which is related to the research article “The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: experimental findings and comparison with calculations using the CALPHAD method” [1] , and therefore this article can be used as a basis for interpreting the data contained therein. The AlMo0.5NbTa0.5TiZr refractory superalloy was characterized in the cast and annealed condition (1400 °C for 24 h) in order to measure grain size and to identify and measure the size and area fraction of the phases present. The raw data of this article include X-ray diffraction (XRD) measurements, microstructural characterization by scanning and transmission electron microscopy (SEM and TEM), and elemental analysis by energy dispersive X-ray spectroscopy (EDX). XRD includes the determination of phases and the lattice parameters (A2, B2, and hexagonal structure). Microstructural analysis by scanning and transmission electron microscopy includes (1) identification of composition, size, and volume fraction of the present phases and (2) determination of grain size. Based on these experimental data, it is possible to identify similarities and discrepancies with the data calculated using the CALPHAD method for the alloy under study in Ref. [1] , which provides the basis for better and more efficient development of reliable databases.
Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The actual part qualification and certification procedures make use of spin-tests conducted on production-similar disks. While these tests provide, on the one hand, a reliable definition of the critical conditions for real components, on the other hand they represent a relevant cost item for engine manufacturers. The aim of this work is to present two alternative burst speed assessment methods under development based on the Failure Assessment Diagram (FAD) and a global stability criterion, respectively. In the scope of the fracture mechanics assessment, the failure modes hoop-burst and rim-peeling are investigated with semicircular surface cracks modelled at the critical regions on the turbine disk. The comparison of the predicted critical rotational speed shows good agreement between the assessment methods.
Along with the desire for developing novel multi-principal element alloys, also known as high-entropy alloys, the concern about their safe application is also increasingly growing. This relates to the alloys’ phase stability, in particular, the control required over unexpected phase decompositions resulting from solute segregation at grain boundaries. Yet, the mechanisms of co-segregation and grain boundary phase decomposition in multi-component alloys are rather challenging to explore. In fact, quantitative investigation of grain boundary behaviors is mostly conducted for binary and a few ternary alloys. In this work, we apply the recently introduced CALPHAD-integrated density-based formalism [RSC Advances 10 (2020) 26728-26741] for considering co-segregation phenomena in alloys with an arbitrary number of components —the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solute atoms during their interaction with a grain boundary. Quaternary Fe-Co-Mn-Cr alloy system is studied. We present two major advances beyond previous results: First, a co-segregation-induced multi-component grain boundary spinodal decomposition is quantitatively simulated for the first time. We found that in addition to its low cohesive energy and asymmetrical mixing enthalpy due to magnetic ordering, Mn plays a leading role in triggering interfacial phase decomposition by having a relatively large, concentration-dependent atomic mobility. Second, as an alternative to grain boundary phase diagrams proposed for binary and ternary alloys, we introduce the concept of co-segregation maps for grain boundary segregation screening and design in multi-component alloys. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation are discussed. Depicted on the alloying composition and phase space, the co-segregation maps enable the required insights to guide a safer, more controlled design of high-entropy alloys.
Grain boundaries (GBs)’s role in determining the functional and mechanical properties of polycrystalline materials is inscribed in both their structure and chemistry. Upon solute segregation, the structure and composition of a GB can change concurrently. We study the co-evolution of GB’s structure and segregation by enhancing the density-based phase-field model to account for the in-plane structural variations in the GB. Significant mutual coupling is revealed between the GB’s chemical and structural states during Mn segregation in Fe-Mn alloys. We found that the structural degrees of freedom in a GB (the ability of the GB structure to respond to the chemical variation) amplifies Mn segregation transition, even when the GB structure stays unchanged. When the GB structure is not uniform, that is the usual case, the coupling between GB structure and segregation evolution also enables the spinodally formed low- and high-Mn phases (upon segregation transition) to co-exist within the GB region. These findings explain the stabilizing mechanism of pronounced interfacial segregation fluctuations, experimentally evidenced in Fe-Mn GBs, and give new insights on the structural sensitivity of GBs’ segregation phenomena and the mutual chemo-structural interplay.
The large surface-to-volume ratio of nanoparticles is understood to be the source of many interesting phenomena. The melting temperature of nanoparticles is shown to dramatically reduce compared to bulk material. Yet, at temperatures below this reduced melting point, a liquid-like atomic arrangement on the surface of nanoparticles is still anticipated to influence its properties. To understand such surface effects, here, we study the coalescence of Au nanoparticles of various sizes using molecular dynamics simulations. Analysis of the potential energy and Lindemann index distribution across the nanoparticles reveals that high-energy, high-mobility surface atoms can enable the coalescence of nanoparticles at temperatures much lower than their corresponding melting point. The smaller the nanoparticles, the larger the difference between their melting and coalescence temperatures. For small enough particles and/or elevated enough temperatures, we found that the coalescence leads to a melting transition of the two nominally solid nanoparticles, here discussed in relation to the heat released due to the surface reduction upon the coalescence and the size dependence of latent heat. Such discontinuous melting transitions can lead to abrupt changes in the properties of nanoparticles, important for their applications at intermediate temperatures.
Detailed microstructural characterization of the AlMo0.5NbTa0.5TiZr refractory high entropy superalloy in the as-cast state is reported for first time and compared with the state annealed at 1400 oC for 24 h. The former shows a dendritic structure, with a mixture of A2/B2 phases < 20 nm in both the dendritic and interdendritic regions. A mostly amorphous phase, rich in Al and Zr, is found within the interdendritic region. The annealed state reproduced the combination of A2/B2/Al-Zr-rich phases reported previously. Calculations from two relevant ThermoCalc databases were compared with the experimental results. Equilibrium calculations were compared with results for the annealed alloy, whereas solidification paths calculated using Scheil-Gulliver model were used for comparison with the as-cast alloy. A previously hypothesized spinodal decomposition during cooling as the mechanism responsible for the patterned A2/B2 microstructure is confirmed via the CALPHAD calculations, pointing to its use as an efficient design tool for such alloys. Finally, the comparison between the experimental and computational findings allowed better understanding the solidification path and equilibrium stability of this alloy, giving a base to make better decisions on the field of new refractory superalloy design.
Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical features, owing to the experimental difficulties to probe these features at the atomic length scale inside bulk material specimens. Atom probe tomography (APT) is a tool capable of accomplishing this task, with an ability to quantify chemical characteristics at near-atomic scale. Using APT data sets, we present here a machine-learning-based approach for the automated quantification of chemical features of GBs. We trained a convolutional neural network (CNN) using twenty thousand synthesized images of grain interiors, GBs, or triple junctions. Such a trained CNN automatically detects the locations of GBs from APT data. Those GBs are then subjected to compositional mapping and analysis, including revealing their in-plane chemical decoration patterns. We applied this approach to experimentally obtained APT data sets pertaining to three case studies, namely, Ni-P, Pt-Au, and Al-Zn-Mg-Cu alloys. In the first case, we extracted GB specific segregation features as a function of misorientation and coincidence site lattice character. Secondly, we revealed interfacial excesses and in-plane chemical features that could not have been found by standard compositional analyses. Lastly, we tracked the temporal evolution of chemical decoration from early-stage solute GB segregation in the dilute limit to interfacial phase separation, characterized by the evolution of complex composition patterns. This machine-learning-based approach provides quantitative, unbiased, and automated access to GB chemical analyses, serving as an enabling tool for new discoveries related to interface thermodynamics, kinetics, and the associated chemistry-structure-property relations.
Single-crystal components made of nickel base superalloys contain pores after casting and homogenization heat treatment. Hot isostatic pressing (HIP), which is carried above the γ' -solvus temperature of the alloy, is industrially applied to reduce porosity. A modeling of HIP based on continuously distributed dislocations is developed in a 2D setting. Glide and climb of straight-edge dislocations, as well as vacancy diffusion, are the deformation mechanisms taken into account.
Thereby, dislocation glide is controlled by dragging a cloud of large atoms, and climb is controlled by vacancy diffusion. Relying on previous investigations of the creep behavior at HIP temperatures, it is assumed that new dislocations are nucleated at low-angle boundaries (LAB) and move through subgrains until they either reach the opposite LABs or react with other dislocations and annihilate.
Vacancies are created at the pore surface and diffuse through the alloy until they are either consumed by climbing dislocations or disappear at the LABs. The field equations are solved by finite elements. It is shown that pore shrinking is mostly controlled by vacancy diffusion as the shear stresses at the LABs are too low to
nucleate a sufficient amount of dislocations.
The formation of pores in CMSX-4 nickel based superalloys is detrimental to the service life of the material. A way to avoid the problem is to treat the superalloys under Hot Isostatic Pressing (HIP), which enables a large volume fraction of pores to be annihilated. This paper aims to understand the contribution of plastic activity related to the gliding of dislocations on the pore annihilation. Simulations based on a phase-field model of dislocation are performed and make it possible to consider the strong anisotropy of the CMSX-4 under HIP conditions in conjunction to the strong elastic heterogeneity introduced by the pore. For pores with a radius of few micrometers, it is shown that edge parts of dislocation lines that present an extra half atomic plane oriented towards the pore are stacked above and under it in the direction which is perpendicular to their slip-planes, causing an increase of the number of dislocation along the four octahedral directions of the FCC single crystal which intersect the pore center. Results are streamlined within the isotropic elastic theory of dislocations. Effects of elastic anisotropy and dislocation reactions are also investigated in order to specify what would be the dislocation configuration around a pore in CMSX-4 under HIP conditions. Notably, the elastic anisotropy is shown to significantly modify the arrangement of dislocations close to the pore equator. Simulations also allow for the characterization of pore/dislocation interactions when dislocations are involved in Low Angle Boundaries as experimentally observed.