Microstructure-mechanical Property Relationships Research Articles

Characterization of Microstructure–Mechanical Properties Relationship in Dissimilar Resistance Spot Welding of the Advanced High-Strength Steel DP590 Steel to the Interstitial-Free Steel DC 06: EBSD Study

Characterization of Microstructure–Mechanical Properties Relationship in Dissimilar Resistance Spot Welding of the Advanced High-Strength Steel DP590 Steel to the Interstitial-Free Steel DC 06: EBSD Study

Influence of the processing route on the mechanical properties of Cu–35Cr metal matrix composites

Cu–Cr-based composites with Cr content ranging from 20 to 50 wt% are widely used as electrical contacts for vacuum interrupters for medium voltage applications because of their excellent combination of mechanical, thermal, and electrical conductivity. Cu–Cr electrical contacts are usually processed by sintering or casting. Their mechanical properties have been the interest of some studies to enhance their percussion welding performance. However, a detailed microstructure-mechanical properties relationship for such composites is yet to be established. Herein, we report an in-depth multi-scale microstructural characterization of solid-state sintered and vacuum arc-remelted Cu–35Cr composites, coupled with the characterization of their mechanical properties. The strengthening mechanisms in both Cu and Cr phases are discussed in light of the microstructure differences caused by the processing route. The presence of large and interconnected pores at the Cu/Cr interfaces in the sintered Cu–Cr composites reduces the load transfer from the Cu matrix to the Cr reinforcing particles and leads to a lower dislocation density by differential thermal mismatch in the Cu matrix. We shed light on the influence of the processing routes on the microstructure-mechanical property relationships for Cu–35Cr composite materials.

Optimizing the Heat Treatment Method to Improve the Aging Response of Al-Fe-Ni-Sc-Zr Alloys.

This work has studied the co-addition of Sc and Zr elements into the Al-1.75wt%Fe-1.25wt%Ni eutectic alloy. The changes in the microstructure, electrical conductivity, and Vickers hardness of the Al-1.75wt%Fe-1.25wt%Ni-0.2wt%Sc-0.2wt%Zr alloy during heat treatment were studied. The results showed that two-step aging can effectively improve the aging response of the alloy over the single-step aging method. This was ascribed to the minimization of the diffusion difference between Sc and Zr elements. Furthermore, the homogenization treatment can also improve the aging response of the alloy by alleviating the uneven distribution of Sc and Zr. Nevertheless, the micro-alloyed elements exceeded the solid solubility limit in the Al-1.75wt%Fe-1.25wt%Ni-0.2wt%Sc-0.2wt%Zr alloy, and their strengthening effect has ever achieved the best prospect. Finally, both Sc and Zr contents were reduced simultaneously, and the aging response of the Al-1.75wt%Fe-1.25wt%Ni-0.15wt%Sc-0.1wt%Zr alloy was improved by optimized heat treatment. The underlying mechanisms for this alloy design and the corresponding microstructure-mechanical property relationship were analytically discussed.

Coarse-Grained Simulations on Polyethylene Crystal Network Formation and Microstructure Analysis.

Understanding and characterizing semi-crystalline models with crystalline and amorphous segments is crucial for industrial applications. A coarse-grained molecular dynamics (CGMD) simulations study probed the crystal network formation in high-density polyethylene (HDPE) from melt, and shed light on tensile properties for microstructure analysis. Modified Paul-Yoon-Smith (PYS/R) forcefield parameters are used to compute the interatomic forces among the PE chains. The isothermal crystallization at 300 K and 1 atm predicts the multi-nucleus crystal growth; moreover, the lamellar crystal stems and amorphous region are alternatively oriented. A one-dimensional density distribution along the alternative lamellar stems further confirms the ordering of the lamellar-stack orientation. Using this plastic model preparation approach, the semi-crystalline model density (ρcr) of ca. 0.913 g·cm-3 and amorphous model density (ρam) of ca. 0.856 g·cm-3 are obtained. Furthermore, the ratio of ρcr/ρam ≈ 1.06 is in good agreement with computational (≈1.096) and experimental (≈1.14) data, ensuring the reliability of the simulations. The degree of crystallinity (χc) of the model is ca. 52% at 300 K. Nevertheless, there is a gradual increase in crystallinity over the specified time, indicating the alignment of the lamellar stems during crystallization. The characteristic stress-strain curve mimicking tensile tests along the z-axis orientation exhibits a reversible sharp elastic regime, tensile strength at yield ca. 100 MPa, and a non-reversible tensile strength at break of 350%. The cavitation mechanism embraces the alignment of lamellar stems along the deformation axis. The study highlights an explanatory model of crystal network formation for the PE model using a PYS/R forcefield, and it produces a microstructure with ordered lamellar and amorphous segments with robust mechanical properties, which aids in predicting the microstructure-mechanical property relationships in plastics under applied forces.

Molecular insights into reversible and irreversible kinks formed in nanocellulose

Kink defects in nanocellulose are common, yet questions remain open regarding the unclear microstructure-mechanical property relationship. Various kink patterns without molecular-scale resolution cause confusion about how nanocellulose forms different kinks and what the fundamental mechanisms of reversible and irreversible kinks are. In atomic force microscopy images, bent nanofibrils usually exhibit small curvatures, while kinked nanofibrils feature sharp bends, in which kinks are notable due to their distinct disordered configurations. To identify the incipient kink defects formed in nanocellulose, molecular dynamics simulations of cellulose nanocrystals (CNCs) under curvature-dependent bending were subsequently carried out. Five typical bending/kinking modes were found, depending on the anisotropic microstructure and size of CNCs. More importantly, two contrasting cases of kinks were demonstrated, providing evidence that kink defects in nanocellulose depend mainly on the microstructure at the molecular scale. Kinks in CNCs with the (100) and (11¯0) crystal plane are recoverable with a few residual defects. While kinks in CNCs with the (010) crystal plane are irreversible with permanent microstructural damage. Compressive stresses accumulated in the bottom chains of CNC contribute to the main mechanism for forming incipient kinks in nanocellulose. The results can fundamentally answer the confusion in recent experiments why bond breakage did not necessarily occur even at high kink angles. The insights present intrinsic deformation mechanisms for understanding the widespread but mysterious kinks arising in nanocellulose.

Structure-Property Relationships of Granular Hybrid Hydrogels Formed through Polyelectrolyte Complexation.

Hybrid hydrogels are hydrogels that exhibit heterogeneity in the network architecture by means of chemical composition and/or microstructure. The different types of interactions, together with structural heterogeneity, which can be created on different length scales, determine the mechanical properties of the final material to a large extent. In this work, the microstructure-mechanical property relationships for a hybrid hydrogel that contains both electrostatic and covalent interactions are investigated. The hybrid hydrogel is composed of a microphase-separated polyelectrolyte complex network (PEC) made of poly(4-styrenesulfonate) and poly(diallyldimethylammonium chloride) within a soft and elastic polyacrylamide hydrogel network. The system exhibits a granular structure, which is attributed to the liquid-liquid phase separation into complex coacervate droplets induced by the polymerization and the subsequent crowding effect of the polyacrylamide chains. The coacervate droplets are further hardened into PEC granules upon desalting the hydrogel. The structure formation is confirmed by a combination of electron microscopic imaging and molecular dynamics simulations. The interpenetration of both networks is shown to enhance the toughness of the resulting hydrogels due to the dissipative behavior of the PEC through the rupture of electrostatic interactions. Upon cyclic loading-unloading, the hydrogels show recovery of up to 80% of their original dissipative behavior in less than 300 s of rest with limited plasticity. The granular architecture and the tough and self-recoverable properties of the designed hybrid networks make them good candidates for applications, such as shape-memory materials, actuators, biological tissue mimics, and elastic substrates for soft sensors.

Partially recrystallized triplex-phase medium Mn steel strengthened by B2 precipitates

We report the annealing time-dependent microstructure–mechanical properties relationship of cold-rolled and annealed Fe–6Mn-0.05C–3Ni-1.5Al (wt.%) steel, containing Ni and Al to form NiAl B2 precipitates. The microstructures of the investigated materials after cold-rolling and intercritical annealing show a mixture of lath and equiaxed zones consisting of a triplex matrix phase (ferrite, austenite, and tempered martensite) with B2 precipitates. Recovery of the deformed martensite in the cold-rolled microstructure during annealing resulted in the formation of sub-boundaries and a continuous transition from partially-recrystallized tempered martensite to recrystallized ferrite. The investigated materials showed a decrease in strength and an increase in ductility and strain-hardening rate with increasing annealing time. A decrease in the fraction of tempered martensite, an increase in the fraction of recrystallized ferrite/austenite grains, and enhanced transformation-induced plasticity (TRIP) kinetics with increasing annealing time led to enhanced ductility and strain hardening of the materials. The mixed presence of less stable equiaxed austenite and more stable lath austenite resulted in sustained TRIP effect during tensile deformation and superior strain hardening capacity of the specimen annealed for 24 h. This study provides a novel microstructure design solution for medium Mn steels, and further optimization of the composition and processing will lead to the development of medium Mn steels with superior mechanical performance.

Microstructure engineering of fusion zone in resistance spot welding of martensitic stainless steels: The role of Ni interlayer thickness

Martensitic stainless steel (MSS) spot welds show low fracture toughness due to the formation of a brittle microstructure at the joint area. To realize the full advantage of this class of steels in industrial applications, the strategy of altering the microstructure of the weld nugget through introduction of a Ni interlayer was investigated. For this purpose, Ni interlayers with variable thicknesses of 50 to 400 μm were utilized. The microstructural evolutions were thoroughly scrutinized using Scheil-Gulliver solidification modeling and electron backscatter diffraction (EBSD) analysis. Conventional quasi-static mechanical tests, namely, tensile-shear (TS) and cross-tension (CT) were used to correlate microstructure-mechanical properties relationships. In the absence of Ni interlayer, the weld nugget was predominantly composed martensite-M and presumably residual delta ferrite-δ (M+ δ-95%) phases with minor amounts of austenite-γ (5%), failing to meet the minimum peak load requirements under TS and CT loading conditions. By applying Ni interlayers of 50 and 75 μm, a noticeable increase in the fraction of austenite phase (up to 31%) in the weld nugget was detected; nevertheless, a slight to moderate improvement in the mechanical properties was observed since the solidification mode was still primary δ, and M+δ were still the predominant phases in the microstructure. A significant improvement in mechanical properties was achieved in 100 μm Ni interlayer owing to change in the solidification mode from primary δ to γ along with the formation of a mainly austenitic microstructure. However, due to the incomplete mixing of melted base metals and Ni interlayer, a different microstructure consisting of M, δ and γ was also occasionally perceptible in the weld nugget of this sample. The best mechanical properties in terms of strength and ductility occurred with increasing thickness to 200 μm and above, which coincided with the formation of a fully austenitic microstructure in the entire weld nugget.

Microstructure–Mechanical Property Relationship and Austenite Stability in Transformation-Induced Plasticity Steels: Effects of Quenching and Partitioning Processing and Quenching and Tempering Treatments

Microstructure–Mechanical Property Relationship and Austenite Stability in Transformation-Induced Plasticity Steels: Effects of Quenching and Partitioning Processing and Quenching and Tempering Treatments

Microstructure-mechanical properties relationships and strain hardening mechanism for medium-Mn steel with low yield and ultra-high tensile strength

Considering the problems of forming ultra-high strength steel, a medium-Mn steel with low yield strength was prepared. The steel exhibited a yield strength of 537 MPa, a tensile strength of 1780 MPa, and an elongation of 17.8%. The study aimed to identify the key factors contributing to the low yield-to-tensile ratio and strain hardening behavior of the steel. To achieve this, interrupted tensile tests, loading-unloading-reloading tensile tests, and microstructure characterization were used, along with theoretical calculations. The results indicated that the low dislocation density in lath ferrite, initial martensite, and retained austenite, as well as the high-volume fraction of retained austenite, were the primary factors contributing to the low yield strength. During tensile deformation, strong solid solution strengthening in strain-induced martensite was the main factor driving strain hardening. Additionally, the rapid multiplication of dislocations in ferrite and martensite, along with the heterogeneous deformation-induced hardening caused by the heterogeneous structure composed of strain-induced martensite and other phases, were also significant factors contributing to strain hardening. When considering grain boundary strengthening, dislocation strengthening, solid solution strengthening, and heterogeneous deformation-induced hardening, the theoretical yield strength and flow stress calculated in this study closely matched the actual measured values.

Review of Microstructure–Mechanical Property Relationships in Cast and Wrought Ni‐Based Superalloys with Boron, Carbon, and Zirconium Microalloying Additions

Cast and wrought Ni‐based superalloys are materials of choice for harsh high‐temperature environments of aircraft engines and gas turbines. Their compositional complexity requires sophisticated thermo‐mechanical processing. A typical microstructure consists of a polycrystalline γ‐matrix, strengthening Ni3(Al,Ti) γ′ precipitates, carbides (MC, M6C, and M23C6), borides (M2B, M3B2, and M5B3), and other inclusions. Microalloying additions of B, C, and Zr commonly improve high‐temperature strength and creep resistance, although excessive additions are detrimental. Grain boundary (GB) segregation may improve cohesion and displace embrittling impurities. Finely dispersed carbides and borides are desired to control grain size via GB pinning. However, excessive decoration of GBs may lead to failure during processing and in‐service. Hence, a systematic review on the roles of B, C, and Zr in cast and wrought Ni‐based superalloys is required. The current state of knowledge on GB segregation and precipitation is reviewed. Experimental and modeling results are compared across various processing steps. The impact of GB precipitation on mechanical properties is most well researched. Co‐precipitation in proximity to GBs interacting with local microstructure evolution and mechanical properties remains less explored. Addressing these gaps in knowledge allows a more complete understanding of processing–microstructure–properties relationships in advanced cast and wrought Ni‐based superalloys.

CALPHAD-guided alloy design of Sn–In based solder joints with multiphase structure and their mechanical properties

A CALPHAD-guided alloy design and the corresponding key experiments method were performed to study the microstructure-mechanical properties relationships for Sn–In based solder alloys with In content ranging from 0 to 52 wt %. Based on a calculated Sn0.7Cu–Sn52In isoplethal section phase diagram, six compositions (Sn52In, 42In, 35In, 18In, 8In and Sn0.7Cu) were selected with different phases such as β-In3Sn, γ-InSn4, β-Sn and β-Sn(In). The phase fractions of alloys acquired from experimental microstructures are consistent with calculated values. Their phase fractions differ and the order of hardness values is β-Sn(In) > β-Sn > γ-InSn4 > β-In3Sn, leading to an increase in strength and a decrease in ductility with the reduction of In content. Strengths of low In content alloys of 18In and 8In containing β-Sn(In) and γ-InSn4 phase are higher compared with high In content alloys of Sn52In, 42In and 35In containing γ-InSn4 and β-In3Sn phases. Meanwhile, elongations of low In content alloys are better than that of 42In and 35In alloys. Thus, the best strength and ductility combination can be achieved by low ln contents alloys. This work can provide a new strategy for the development of Sn–In based alloys via CALPHAD-guided design of phase types and fractions.

High temperature performance of 316L steel reinforced by particle inoculation and processed by laser powder bed fusion

Grade 316 L is one of the most versatile austenitic stainless-steel products whose potential in laser powder bed fusion has been recently evaluated. A way of improving its properties is to add reinforcements, such as TiC nanoparticles, to promote dispersion hardening. However, it is often difficult to assess microstructure-mechanical property relationships, since particle inoculation promotes heterogeneous nucleation of equiaxed grains during rapid solidification. In this work, two 316 L samples were manufactured by laser powder bed fusion, where the powder of one of them was inoculated with TiC nanoparticles. The effect of inoculants on the microstructure and its high temperature behavior was assessed. Electron Probe Micro Analyzer proved that inoculants did not get dissolved during the printing process and they predominately lay in the intercellular regions, which were solute enriched. Advanced characterization proved that inoculation did not affect the solidification structure, which remained cellular and with a similar size, or the grain size, although it did modify the bulk texture. Finally, the effect of dispersion hardening on the behavior at high temperature of a 316 L steel was evaluated by small punch tests, which proved that the addition of TiC improves all, ductility, yield strength and ultimate tensile strength at high temperature. Moreover, samples processed by LPBF showed high temperature behavior and superior strength and ductility, as compared to the ones obtained in a reference annealed steel, even though the grain size obtained in the former case was at least 50 times larger than the one obtained for the reference condition.

Multi-scale characterization of supersolidus liquid phase sintered H13 tool steel manufactured via binder jet additive manufacturing

Additive manufacturing (AM) of H13 tool steel by binder jet 3D printing (BJ3DP) followed by pressureless supersolidus liquid phase sintering (SLPS) provides a low-cost alternative manufacturing method for components with intricate geometric features. However, the microstructure-mechanical property relationships for BJ3DP-SLPS produced H13 tool steel are not well understood, which makes it challenging to develop printing and post-processing methods that maximize part performance. In this work, we leverage atom probe tomography and transmission electron microscopy along with thermodynamic calculations to rationalize the microstructure-mechanical property relationships in as-sintered BJ3DP H13 tool steel. We report for the first time, the presence of a continuous eutectic film-like carbide in H13 along with the more commonly observed cuboidal MX carbides in the prior liquid channels of the microstructure. Further, atom probe tomography revealed the interconnected nature of the MX carbides that appear to be discrete in two-dimensional micrographs. These continuous eutectic carbides and interconnected MX carbides result in brittle failure of the material. Characterization of these microstructural features will be critical in developing appropriate post-processing heat treatments for the improved mechanical performance of BJ3DP H13.

Solute concentration effects on microstructure and the compressive strength of ice‐templated sintered lithium titanate

AbstractThis work investigated the role of sucrose and cationic dispersant (1‐hexadecyl)trimethylammonium bromide concentration on ice‐templated sintered lithium titanate microstructure and compressive strength, to enable a comprehensive understanding of composition selection and elucidate processing–microstructure–mechanical property relationships. Sucrose and dispersant concentrations were varied to change total solute concentration in suspensions and viscosity. Dispersant was more effective in reducing viscosity than sucrose; however, their combination had an even greater impact on reducing viscosity. Based on viscosity measurements, a total of 12 suspension compositions were developed, and materials were fabricated at two different freezing front velocity (FFV) regimes. Solute concentration greatly influenced ice‐templated microstructure and microstructure development improved with solute concentration. Depending on solute concentration, type of solute, viscosity, and FFV, a wide variety of microstructures were observed ranging from lamellar to dendritic morphologies. Solute concentration effect was rationalized based on solid–liquid planar interface instability. For suspensions with comparable viscosity, solute concentration can be varied to tune microstructure, whereas for suspensions with comparable solute concentration, viscosity variation can tune microstructure. Compressive strength of sintered materials generally increased with total solute concentration, sucrose concentration, viscosity, and FFV. Due to the wide variety of microstructure, strength also varied over a wide range, 23–128 MPa.

Dynamic cryo-mechanical properties of additively manufactured nanocrystalline nickel 3D microarchitectures

Template-assisted electrodeposition is a promising microscale additive manufacturing technique allowing to deposit pure metals with high resolution. To allow the application-relevant design of metamaterials, it is necessary to establish microstructure-mechanical property relationships under extreme conditions. In this work, a novel process based on two-photon lithography was used to synthesize arrays of nanocrystalline nickel micropillars and complex microlattices. This allowed high throughput mechanical testing using a newly developed in situ nanoindenter at unprecedented combination of cryogenic temperatures (160 to 300 K) and strain rates (0.001 to 500 s−1). Strain rate sensitivity was found to increase from ∼ 0.004 at 300 K to ∼ 0.008 at 160 K. Thermal activation analysis showed a decrease in activation volume from 122b3 at 300 K to 45b3 at 160 K and an activation energy of 0.59 eV in line with collective dislocation nucleation as the rate limiting mechanism. Transmission Kikuchi Diffraction allowed quantifying microstructural changes during deformation. As such, a deformation map along with the responsible deformation mechanisms has been ascertained for additively micromanufactured nanocrystalline nickel at unique combinations of extreme temperatures and strain rates. Further, rate-dependent compression of microlattices and complementary finite element simulations using the results from micropillars as constitutive models exemplified the promise of such metal microarchitectures in space and aviation applications.

Microstructure-property relationship in binder jet produced and vacuum sintered 316 L

This work investigates the impact of vacuum sintering and the microstructure-mechanical properties relationship in binder jet additive manufacturing of 316 L. These two perspectives provide valuable understanding to an otherwise well-established area. The resulting properties are compared with those of conventionally manufactured parts. Results revealed isotropic microstructural and mechanical properties in binder jet-manufactured samples. Despite 1.9 ± 0.1% remained porosity, the ductility (elongation to fracture 73 ± 2.8%) of the binder jet specimens was remarkably higher than the conventionally manufactured 316 L alloy due to two-stage work hardening, remaining δ-ferrite, and deformation twinning. The yield strength, ultimate tensile strength, and hardness of the binder jet samples were inferior to those of conventionally manufactured parts, likely due to porosity and grain growth upon sintering.

A Control‐Cooled Hot‐Forged Medium Carbon V‐Microalloyed Steel: Strengthening Breakdown in Conjunction with the Synchrotron X‐Ray Absorption Spectroscopy

This article represents a few practical objectives for industrial research on a microalloyed medium carbon ferritic‐pearlitic 38MnSiVS6 steel, fabricated by hot forging followed by controlled cooling. The first is to determine the achievable yield strength (YS) in different process windows using an industrial‐scale sample. Second, it quantifies the contribution of different strengthening mechanisms, where less attention has been paid in the literature for the studied steel group. The process–microstructure–mechanical properties relationship is characterized by means of image analysis, synchrotron X‐Ray absorption spectroscopy (XAS), hardness, impact, and tensile tests. XAS is the key in this study to evaluate the fraction precipitated of the microalloying element to correlate its effectiveness in strengthening. It can be concluded that vanadium precipitates between 60 and 73 at‐%, which contributes to the additional YS of 221–349 MPa within the studied process window. The smaller precipitated fraction of 7–12% at a higher cooling rate shows a strengthening fraction above 100 MPa of improvement. The refined precipitates enable a lower overall precipitation amount down to 60%, which can be a good hint in case alloying optimization is required.

Interfacial investigation of explosion-welded Al/steel plate: The microstructure, mechanical properties and residual stresses

This paper presents a systematic investigation of microstructure, mechanical properties and residual stress distribution of explosion-welded Al/steel plates. It was found that vortexes resulted from the trapped jetting were surrounded by highly deformed bulk materials and Fe–Al intermetallics. The microstructure-mechanical property relationship in individual phases was established using nanoindentation tests, e.g. FeAl + FeAl2 and FeAl3 having the hardness of 16.2 GPa and 11.4 GPa, respectively. The Al/steel interface showed higher microhardness values (200–300 HV0.1). The internal stresses were evaluated by a contour method, and the tensile stresses concentrated at the Al/steel interface, reaching to 170 MPa and 160 MPa in the longitudinal and transverse directions, respectively. Smoothed particles hydrodynamics (SPH) methods was used to simulate the formation of wave boundary, vortex zone, as well as the jet moving ahead of the collision point during the high-velocity oblique process. A good agreement was observed between the simulation and experiment, especially the formation of intermetallic compounds at interfacial regions and the evolution of residual stress.

The Hardness Evolution of Cast and the High-Cycle Fatigue Life Change of Wrought Ni-Base Superalloys after Additional Heat Treatment.

Concerning the use of modern technologies and manufacturing systems in the production of high-stress components from Ni-base superalloys and the optimization of the production process, knowledge of the microstructure–mechanical properties relationship is very important. The microstructure of Ni-base superalloys is very closely related to the chemical composition. With the high number of alloying elements, various phases are presented in the structure of Ni-base superalloys, which have a predominantly positive effect on the mechanical properties, but also phases that reduce, in particular, the heat resistance of these materials. The aim of the presented paper is the quantification of structural parameters of two types of cast alloys, ZhS6K and IN738, where the effect of dwell at 10 and 15 h at 800 °C on the change in morphology and volume fraction of the γ′-phase precipitate was studied. The detected changes were verified by the Vickers hardness test. The IN718 superalloy was chosen as a representative of the wrought superalloy. This alloy was also annealed for 72 h at a temperature of 800 °C, and the quantification of structural parameters was performed by EDS mapping and TEM analysis. Another partial goal was to assess the effect of changes in the volume fraction of the γ′-phase and δ-phase on the change in the high-cycle fatigue life of superalloy IN 718. This superalloy was tested by dynamic cyclic loading with cycle asymmetry parameter R = −1 at an ambient temperature of 22 ± 5 °C and at a temperature of 700 ± 5 °C and with cycle asymmetry parameter R < 1 (three-point bending load) after annealing at 700 °C/72 h. The results of the quantitative analyses and fatigue tests will be further used in optimizing the design of Ni-base superalloy components by modern technologies such as additive technologies for the production of turbine blades and implemented within the philosophy of Industry 4.0.