Combined Thermal Cycling Research Articles

Survival dependence of 3D-printed temporary materials on the filler content.

The aim of the present study was the evaluation of the in vitro performance and fracture force of 3D-printed anterior implant-supported temporary partial dentures (TPDs) with different filler content. Identical anterior resin-based TPDs (tooth sites 11 to 13; n = eight per material) were 3D printed from methacrylate resins with different filler content. A cartridge polymethyl methacrylate (PMMA) material was used as a reference. After temporary cementation, combined thermal cycling and mechanical loading (TCML) was performed on all the restorations to mimic clinical application. Behavior during TCML and fracture force was determined, and failures were analyzed. Data were statistically investigated (Kolmogorov-Smirnov test, one-way ANOVA; post hoc Bonferroni, Kaplan-Meier survival; α = 0.05). Failure during TCML varied between three failures and total failure during loading time. Mean survival time varied between 93 ± 206 x 103 cycles and 329 ± 84 x 103 cycles. Significantly different survival cycles between the individual materials could be determined (Mantel Cox log-rank test: chi-square: 21,861; degrees of freedom (df) = 4, P < 0.001). A correlation between filler level and survival cycles could be found (Pearson: 0.186, P = 0.065). Fracture values of the surviving TPDs varied between 499 and 835 N. Failures were characterized by fracture of the connector (n = 24) followed by fractures at the abutment (n = 10). TDPs showed different filler-dependent survival. Individual 3D-printed materials provided comparable or even better performance than a standard cartridge system and might be sufficient for temporary application of at least half a year.

Impact of the occlusal contact pattern and occlusal adjustment on the wear and stability of crowns

ObjectivesTo investigate the impact of the occlusal contact situation and occlusal adjustment on wear, roughness, and fracture force of molar crowns. Materials and methodsCAD/CAM crowns (lower right first molar, n = 64; 4 groups à 8, 3Y-TZP zirconia and resin composite) and corresponding antagonists (upper right first molar; 3Y-TZP zirconia) were manufactured. Crowns were constructed according to two principles of occlusion (group “T”: Peter K. Thomas’ “point-centric” cusp-to-fossa tripodization concept, with 15 contact points; group ”RA” Sigurd P. Ramfjord and Major M. Ash, “freedom in centric” concept with four contacts). On one half of the crowns, occlusal adjustment was performed (groups “T adjusted” and “RA adjusted”). All crowns underwent combined thermal cycling (TC) and mechanical loading (ML) (ML: 1.2 × 106 cycles, 50 N, 2 Hz, mouth opening 1 mm; TC: 2 × 3000 cycles, 5/55°C). Wear area and depth of each contact point on the occlusal surfaces of crowns and antagonists were determined using a digital microscope. Surface roughness (Ra, Rz) was measured in and besides (reference) the worn area (3D laser-scanning microscope). Fracture force of the crowns was determined (statistics: Levene-test, one-way-ANOVA; Bonferroni-post-hoc-test; between-subjects effects, Pearson correlation, α=0.05). ResultsThe resin composite crowns yielded significantly higher mean values for wear area and depth (p < 0.001) and lower fracture forces (p < 0.001). Resin composite surfaces showed increased roughness after TCML while zirconia exhibited smoothened surfaces. The occlusal design significantly impacted wear depth (p = 0.012) and fracture force (p < 0.001). Resin composite crowns with fewer contact points (group RA) showed more wear and lower fracture force. Adjusted resin composite crowns showed increased wear areas and depths (p = 0.009-0.013). For zirconia crowns, the adjustment impacted wear area (p = 0.013), wear depth (p = 0.008), and fracture force (p = 0.006), with adjusted zirconia crowns exhibiting more wear and lower maximum forces until fracture. Zirconia wear depth was also impacted by the occlusal design (p = 0.012). Antagonistic wear was influenced by the restorative material, the occlusal contact pattern, and the adjustment. ConclusionsThe investigated materials show strongly varying performances with zirconia being significantly influenced by the adjustment, while for resin composites, contact design and adjustment had a major impact. Clinical relevanceThe results show the necessity of adapting occlusal design and adjustment in order to improve roughness, wear, and stability of zirconia and resin composite crowns.

Surface Microhardness, Flexural Strength, and Clasp Retention and Deformation of Acetal vs Poly-ether-ether Ketone after Combined Thermal Cycling and pH Aging

To evaluate the effect of combined thermocycling and artificial saliva pH on flexural strength, surface microhardness, as well as clasp retention and deformation of two different thermoplastic polymers. Three groups were created, heat-cured polymethyl methacrylate, acetal, and poly-ether-ether ketone (PEEK) resins. Specimens were wrapped in plastic bags containing artificial saliva with three pH values (acidic 5.8, neutral 7.2, and alkaline 8.3). Two Aker clasps materials (acetal and PEEK), for premolar and molar, were stored in neutral salivary pH. Specimens were subjected to 2,000 thermocycles (5-55°C). Surface microhardness, flexural strength, and clasp retention and deformation were evaluated before and after aging. Data were analyzed by ANOVA, Tukey's test, Student's t-test, and paired t-tests (p < 0.05). Thermal cycling at acidic and alkaline pH significantly decreased flexural strength and surface microhardness of acetal. It had no significant effect on PEEK properties. Poly-ether-ether ketone showed statistically significant higher mechanical properties in all groups. Acetal clasps exhibited a statistically significant deformation and a corresponding decrease in retention after thermocycling at neutral pH. Mechanical properties of acetal, as well as its clasp retention and deformation, significantly decreased after combining thermal and pH aging and thermal cycling in neutral pH, respectively. Meanwhile, PEEK clasps were not significantly affected. Different intraoral variables may significantly affect mechanical performance, retention, and deformation of TMs used for denture base and clasp construction. Some of these TMs may behave better than the other types with recommended improvement of the design like increasing clasp cross-section area.

Study of deuterium permeation, retention, and desorption in SiC coatings submitted to relevant conditions for breeder blanket applications: thermal cycling effect under electron irradiation and oxygen exposure

In this paper we report on the performance as deuterium permeation barriers of sputtered amorphous, dense and not fully stoichiometric SiC coatings under relevant conditions for breeder blanket applications in fusion reactors. To do that, we investigate the following effects on permeation values: (i) thermal cycling at 450 °C, (ii) combined thermal cycling and e− irradiation (1.8 MeV up to a total dose of 1 MGy), as well as (iii) oxygen exposure at a temperature of 450 °C during e− irradiation. Data show that the permeation reduction factor (PRF) for the as-deposited SiC coated is ∼10 4, even at the predicted operation temperature for the breeder and it is slightly reduced either by thermal cycling without and during e− irradiation. However, the exposure to oxygen at 450 °C during e− irradiation leads to degradation of the coating and of its PRF of about three orders of magnitude. The origin of the coating degradation is discussed.

A rapid life-prediction approach for solder joints based on modified Engelmaier fatigue model

Accelerated life test (ALT) is widely used to predict life of solder joints nowadays, and how to shorten the test time and improve the precise of evaluation is one of the most important issues. Based on statistical results of field failure for solder joints, improved ALT under combined thermal cycling and vibration loading conditions was designed and carried out. This paper presents a modified Engelmaier fatigue model to predict life of solder joints, by taking into account field failure data and ALT testing data. The results show that test time of improved ALT is more shorter than conventional one, and the result of remaining life prediction based on modified Engelmaier fatigue model becomes more precise due to improving life model and increasing information.

Effect of thermal and vibrational combined ageing on QFN terminal pads solder reliability

Automotive environment generates vibration and temperature fluctuation, which reduces the life of electronic boards. The heavy trucks passing at relatively high speed on uneven road pavement is considered as the main reason of the traffic vibration. In fact, interaction between wheels and road surface causes a dynamic excitation which generates waves propagating in the soil affecting nearby structures. In addition, Thermal Cycling Test reveals the strict impact of environment conditions and slow cycles of temperature caused during operation. In this paper, vibration tests are performed continuously throughout thermal cycling to investigate the combined effect of temperature and vibration on the SAC305 solder of Quad Flat No-lead (QFN) terminals pads bonded on Printed Circuit Board (PCB). Power Spectral Density (PSD), which can be linked to the strain rate, is calculated from the acceleration, during combined ageing. Experimental results imply that the number of combined cycles affects the PCB responses: the value of the first natural frequencies and the corresponding PSDs. Fifty thermal cycles of combined thermal cycling and fatigue random vibration tests have been carried out on 100 QFN terminal pads solder. Statistical evaluation of the State of Health of the solder showed that cracking has started in 68% of them. An in-depth analysis was conducted to understand the reasons behind this degradation. On the other hand, an accurate numerical model for simultaneous combined thermal cycling and vibration simulation is developed and validated using experiments. These simulations make it possible to assess the displacement evolution due to combined loadings.

Microstructure, isothermal and thermomechanical fatigue behaviour of leaded and lead-free solder joints

The reliability of solder joints is a critical issue in the microelectronics industry. The requirement of permanent electrical and thermal connections between solder alloys and the various components of a surface mount device is dependent upon the mechanical integrity of the solder and its interfaces.Accordingly, in this paper, the reliability of lead-free, Sn-3.8Ag-0.7Cu, and leaded, Sn-37Pb, solder alloys was investigated under both thermal-mechanical fatigue (TMF) and isothermal mechanical fatigue (IF) conditions. The investigation included material characterisation and fatigue testing on 4-ball grid array (BGA) specimens. The IF tests were carried out under load control at three different temperatures including Room Temperature (RT), 35 °C and 75 °C. Also, a set of ‘not-in-phase’ (nIP), ‘in-phase’ (IP) and ‘out-of-phase’ (OoP) combined thermal and mechanical cycling tests were carried out to investigate the TMF behaviour of the solders. The stress-life curves for each test condition were generated and then compared taking into account the observations on microstructure.It was found that the IF and TMF performance of Sn-3.8Ag-0.7Cu alloy was better than Sn-37Pb alloy when expressed as stress-life curves. Additionally, the Sn-3.8Ag-0.7Cu was less susceptible to the changes in temperature. This study provides a comprehensive insight into the reliability of solder alloys under a wide range of loading conditions.

Analysis of performance degradation during steady-state and load-thermal cycles of proton exchange membrane water electrolysis cells

A membrane-electrode assembly based on a 90 μm short-side-chain Aquivion® proton exchange membrane and containing low catalyst loadings, 0.4 mg IrRuOx cm−2 and 0.1 mg Pt cm−2 at anode and cathode, respectively, is investigated for combined thermal and load cycling at high current density (3 A cm−2) in water electrolysis cell. Durability tests under steady-state and load-thermal cycles are compared to evaluate the efficiency losses under specific operating conditions. Ac-impedance spectra and post-operation analyses are carried out to investigate the degradation mechanism. Catalyst degradation occurs more rapidly under cycled operation whereas mass transfer issues are relevant especially under steady-state mode. Membrane thinning appears to be affected by the uptime hours at high current density. The overall cell voltage increase is slightly larger for the cycled operation compared to the steady-state mode. However, this is essentially related to a compensation effect associated to a larger decrease of series resistance during the steady-state durability test. The dynamic electrolysis mode at high current density does not exacerbate significantly the degradation issues of low catalyst loading MEAs compared to a steady-state operation. This confirms the proper dynamic characteristics of the polymer electrolyte membrane electrolyser.

Sequential combined thermal cycling and vibration test and simulation of printed circuit board

Automotive environment generates vibration and temperature fluctuation, which can be damaging for electronic boards. Furthermore, combined temperature and vibration is a type of testing that recreates environments approximating more closely operating environments. In this paper, vibration tests are performed during thermal cycling to investigate the influence of temperature on Printed Circuit Board (PCB) responses. A combined test of temperature and vibration is designed to evaluate the PCB response after each step of one thermal cycle [−40/125] °C. The frequency and displacement can be linked to the strain and strain rate during a board level vibration test. They are obtained from the acceleration during a sine sweep application on a shaker, which is measured using a light weight accelerometer. Experimental results show that temperature significantly affects the PCB responses. Temperature variation leads to striking differences in vibration loading intensity. The PCB first natural frequency shifts from 328 Hz to 313 Hz with temperature increase from 25 °C to 125 °C. A complex PCB is characterized using tension and flexure tests at different temperatures, to extract user input parameter for simulations. An accurate numerical model for sequential combined thermal cycling and vibration simulation is developed and validated using experiments. Thanks to these simulations, the displacement evolution due to combined loading is possible.

Influence of Cycle Temperature on the Wear Resistance of Vermicular Iron Derivatized with Bionic Surfaces

Depending on their applications, such as in brake discs, camshafts, etc., the wear behavior of vermicular iron is influenced by the thermal cycling regime. The failure of a working part during its service life is a consequence of both thermal fatigue and wear. Previously, the wear and thermal fatigue resistance properties of vermicular iron were separately investigated by researchers, rather than a study combining these two factors. In the present work, the effect of cycle temperature on the wear resistance of specimens with bionic units processed by laser has been investigated experimentally. The wear behavior pre- and post-thermal cycling has also been investigated, and the influence of different cycle temperatures on the wear resistance is discussed. The results indicate that the thermal cycling regime brought about negative influences with varying degrees, on the material properties, such as the microstructures, micro-hardness, cracks, and oxidation resistance properties. All these factors synergistically reduced the wear resistance of vermicular iron. In particular, the negative influence apparently increased with an increase in cycle temperature. Nevertheless, the post-thermal-cycle wear resistance of the specimens with bionic units was superior to those without bionic units. Hence, the laser bionic process is an effective way to improve the performance of vermicular iron in combined thermal cycling and wear service conditions.

Structure and electrical properties of silicone rubber filled with thermally reduced graphene oxide

Graphene oxide (GO) was heat treated at different temperatures between 120 and 220 °C and the structural changes were assessed by thermogravimetry, infrared spectroscopy, X-ray photoelectron spectroscopy and scanning electron microscopy (SEM). The resulting reduced graphene oxide (rGO) fillers showed markedly lower oxygen contents (primarily by reduction of epoxide and hydroxyl groups) than GO. SEM of silicone rubber composites containing 3 wt.% rGO or GO filler showed that the nanoparticles were uniformly distributed in the polymer. The rGO-filled composites exhibited electric field-dependent resistivity; the resistivity decreased from 1014 to 1011 ohm m as the electric field was increased from 0.2 to 6 kV (mm)−1. The composites exhibited an increased resistivity after being exposed to a combined thermal cycling and electrical field. An increase in the resistivity of samples aged at 120 °C for more than 17 h was observed; the resistivity-electric field behavior and the dielectric constant of the aged composite resembled that of GO-filled composite. The composites exhibited dielectric constant values between 4.0 and 5.2 and a low tan delta (≤ 0.015) at frequencies between 10−2 and 104 Hz. The results suggest that the resistivity of the composites can be tuned by adjusting the degree of reduction of GO. The low rGO-filler content that was required to achieve this adequate property profile is attractive, which makes these composites potentially useful as electric field-grading material in HVDC cable accessories. However, this requires that the long-term stability problem can be sensible addressed.

Microstructural Modifications in AISI 1080 Eutectoid Steel Under Combined Cyclic Heat Treatment

In this research work annealed AISI 1080 steel bars are subjected to a typical combined cyclic heat treatment involving two cycles. The first cycle consist of inserting the specimen in an electric resistance furnace at a temperature of 775 °C (in fully austenitic region) and holding for a short duration (6 min), followed by forced air cooling to the room temperature. In second cycle holding temperature and time being same, the specimen is subjected to oil quenching. Such a typical combined thermal cycling results in the evolution of a novel microstructure that comprises of submicroscopic cementite spheroids and fine microscopic cementite clusters in a matrix of martensite. Accordingly, very high hardness (894 HV) is achieved which envisaged a new heat treatment route of the development of plain carbon tool steel.

Influence of cementation on in vitro performance, marginal adaptation and fracture resistance of CAD/CAM-fabricated ZLS molar crowns

ObjectivesThis study investigated the influence of conventional cementation, self-adhesive cementation, and adhesive bonding on the in vitro performance, fracture resistance, and marginal adaptation of zirconia-reinforced lithium silicate (ZLS) crowns. MethodsHuman molar teeth (n=40) were prepared and full-contour crowns of a ZLS ceramic (Celtra Duo, DeguDent, G, n=32) and a lithium disilicate ceramic (LDS; IPS e.max CAD, Ivoclar-Vivadent, FL, n=8) were fabricated and glazed. Four groups of ZLS crowns were defined (n=8/group) and cemented with different glass-ionomer cements, resin, and resin-modified self-adhesive luting materials. The LDS crowns served as reference group with adhesive bonding.A combined thermal cycling and mechanical loading (TCML: 3000×5°C/3000×55°C; 1.2×106 cycles à 50N) with human antagonists was performed in a chewing simulator. Fracture force of surviving crowns was determined. Marginal adaptation at the cement/tooth and cement/crown interface was investigated by scanning electron microscopy before and after TCML, and the share of perfect margins was determined. Data were statistically analyzed (one-way ANOVA; post hoc Bonferroni, α=0.05). ResultsOne crown of the adhesive group failed during TCML (879,000 cycles=3.7 years). No statistically significant (p=0.078) differences in fracture resistance were found between different cementations, although highest data in tendency were found for adhesive bonding. Shares of perfect margins at the cement/tooth (93.8±5.6–99.6±0.8%) and cement/crown (84.7±6.6–100.0±0.0%) interfaces did not differ significantly (p>0.05) between the different cementation groups. SignificanceMarginal adaptation and fracture forces of all tested groups are in a range, where no restrictions should be expected for clinical application.

Heat flux across an open pore enables the continuous replication and selection of oligonucleotides towards increasing length.

The replication of nucleic acids is central to the origin of life. On the early Earth, suitable non-equilibrium boundary conditions would have been required to surmount the effects of thermodynamic equilibrium such as the dilution and degradation of oligonucleotides. One particularly intractable experimental finding is that short genetic polymers replicate faster and outcompete longer ones, which leads to ever shorter sequences and the loss of genetic information. Here we show that a heat flux across an open pore in submerged rock concentrates replicating oligonucleotides from a constant feeding flow and selects for longer strands. Our experiments utilize the interplay of molecular thermophoresis and laminar convection, the latter driving strand separation and exponential replication. Strands of 75 nucleotides survive whereas strands half as long die out, which inverts the above dilemma of the survival of the shortest. The combined feeding, thermal cycling and positive length selection opens the door for a stable molecular evolution in the long-term microhabitat of heated porous rock.

A comparison of the fracture resistance of three machinable ceramics after thermal and mechanical fatigue

Mechanical and thermal fatigue may affect ceramic restorations in the oral environment. The purpose of this study was to determine the influence of thermal and mechanical cycling on the fracture load and fracture patterns of 3 machinable ceramics. Seventy-two human third molar teeth were prepared for bonding ceramic specimens of Sirona CEREC Blocs, IPS e.maxCAD, or inCoris ZI meso blocks. The 24 specimens of each ceramic were divided into 4 groups (n=6), which underwent no preloading (control), thermocycling (5°C-55°C, 2000 cycles), mechanical cycling (10(5) cycles, 100 N), and thermocycling (5°C-55°C, 2000 cycles) plus mechanical cycling (10(5) cycles, 100 N). The specimens were subsequently loaded to failure, and both stereomicroscopy and scanning electron microscopy were used to investigate the fracture patterns. The data were analyzed with 2-way ANOVA and the Fisher exact probability test (α=.05). Mechanical and thermal cycling had a significant influence on the critical load to failure of the 3 ceramics. No significant difference was found between mechanical cycling for 10(5) times and thermocycling for 2000 times within the same ceramic. The specimens of inCoris ZI experienced significantly higher fracture loads for all the groups. The fracture patterns of the 3 machinable ceramics showed that failure mainly occurred at the cement-dentin interface. The effects of combined thermal and mechanical cycling on the fracture load of ceramics were more significant than any individual mode of cyclic fatigue. Overall, the inCoris ZI resisted thermal and mechanical fatigue better than the Sirona CEREC and IPS e.maxCAD.

Numerical Investigation on Void Nucleation around Inclusions under Combined Mechanical and Thermal Cycling Conditions

In this paper a numerical investigation on the void nucleation behaviors under combined mechanical and thermal cycling conditions have been performed. A finite element unit cell model is conduct to calculate the local stress-strain field and describe the process of void nucleation from inclusion. Numerical results show that the thermal mismatch stress between the particles and matrix can assist the external load to cause interface debonding. Under certain mechanical and thermal cycling conditions, complicated stress and strain hystereses developed in the matrix. Both the plastic strain and plastic energy density of the interface will be accumulated during every thermal cycle. The plastic energy accumulation of the interface will first reach the debonding value and failure occurs. Based on the numerical calculation, a new energy based failure criteria is proposed to characterize the behaviors of void nucleation under combine mechanical and thermal cycling conditions.

Shape memory properties of ionic polymer–metal composites

The shape memory properties of hydrated Nafion ionic polymer–metal composite (IPMC) actuators under combined thermal cycling and electrical shape fixing are presented and experimentally demonstrated. By exploiting these new properties the utility of such ionic actuators can be greatly enhanced to include bistability, multi-modal operation and increased actuation range. Shape memory effects were shown when the IPMC was deformed during programming by either an external force or by voltage-induced actuation. Comparison is made to the shape memory effects in hydrated raw Nafion membrane. It was observed that shape memory effects undergo slow decay, with different programming methods and subsequent electrical excitation exhibiting different decay profiles.

Sensitivity of Stresses and Failure Mechanisms in SOFCs to the Mechanical Properties and Geometry of the Constitutive Layers

AbstractA model based on the Euler–Bernoulli theory is used to assess the sensitivity of residual stresses in solid oxide fuel cells to the mechanical properties and geometry of the constituents. It considers different cell configurations, characterised by the presence or not of a compensating layer, and a cathode based on either lanthanum strontium manganite (LSM) or lanthanum strontium cobaltite ferrite (LSCF). The implementation of creep in the model provides insights into the parameters that affect the zero‐stress temperature and behaviour during ageing. The amount of irreversible deformation generated in the cell layers after the sintering step depends on the mechanical properties of the layers, type of cell and to some extent, cooling rate. X‐ray diffraction measurements from literature are used to verify the prediction. Depending on the mechanical properties, the stress state in the LSM cathode changes from tensile to compressive with respect to temperature. During combined ageing and thermal cycling, tensile stress might arise in the compatibility layer of LSCF‐based cells, due to the relief of the initial compressive stress at operating temperature. The Weibull analysis provides the assessment of mechanical failure. A simplified approach is used for buckling‐driven delamination, but the propagation of cracks is predicted for unlikely large pre‐existing defects.

System Relevant Redox Cycling in SOFC Stacks

staxera GmbH is a manufacturer of commercial available solid oxide fuel cell (SOFC) stacks and Integrated Stack Modules (ISM). The aim of development and testing is to meet the requirements of existing customers and the needs of the market. Besides high power densities, low degradation rates in long term operation and thermal cycling capability, the possibility for oxidation and reduction (redox) cycles as a requirement of system operation or in case of a system failure is a big challenge in today's SOFC stack development. In this publication, data for different types of redox cycles at stack level is reported, including system relevant combined thermal and redox cycling.

Three-dimensional thermal response and thermo-mechanical fatigue analysis for a large LCD TV frame mould in steam-assisted rapid heat cycle moulding

Rapid heat cycle moulding (RHCM) is a newly developed moulding technique to improve the surface appearance of plastic parts and eliminate the polluting secondary operations such as primers and painting. In steam-assisted RHCM, the mould surface temperature should be thermally cycled by alternatively cycling the high temperature steam and cooling water in the heating/cooling channels of the mould. The mould design is of great importance for RHCM because it not only has a great effect on the heating/cooling efficiency and hence the productivity but also directly affects the mould surface temperature uniformity and accordingly the final part quality. Furthermore, the service life of the RHCM mould with steam heating is also very much dependent on the mould structure or the layout of the heating/cooling channels as the fatigue crack is likely to occur at the wall of the heating/cooling channels under combined thermal cycling and mechanical loading. In this study, an RHCM mould for a type of 52-inch LCD TV frame was designed. A three-dimensional (3D) transient thermal analysis was performed to determine the thermal response efficiency of the designed RHCM mould cavity and investigate the factors affecting the heating efficiency. Then, by using the results obtained from the heat transfer simulation, the thermal-structure coupling analysis comprehensively considering the cavity pressure and clamp force was conducted to analyse the stress distribution in the mould cavity, which is helpful to find the weak position in the mould cavity. We found that the spots where the maximum stresses occur are similar to the region where fatigue cracks come into being in the actual RHCM mould. Based on the simulation results, the mechanism of the cavity cracks formation on the cavity surface was proposed. Finally, the fatigue analysis was conducted to predict the fatigue life of the RHCM mould. The analysis results show that the regions at the top edges of the heating/cooling channels have the lowest fatigue life and safety factor. The discrepancy between the available life predicted by simulation and the actual service life of the RHCM mould is also discussed.