Rolling Parameters Research Articles

Revealing the interdependence of load partitioning, dislocation density evolution and mechanical behavior of medium Mn steels

The load partitioning between inter-phases and intragranular of austenite, their dislocation density evolution, and mechanical behavior were investigated in two medium Mn steels by in-situ high-energy synchrotron x-ray diffraction during tensile loading. The investigated steels were produced with different hot rolling parameters resulting in different initial microstructures. The initial microstructures were characterized using scanning electron microscope and electron backscatter diffraction analysis. Transmission electron microscope with high angle annular dark field technique was furthermore used to provide the fine microstructural features of deformed specimens in order to supplement the in-situ analysis. Despite the differences in the initial microstructure, the load partitioning from the softer ferrite to the stronger α’-martensite (α’) was observed; while different degrees of load partitioning for intragranular of γ occurred. The sample with a relatively low degree of load partitioning exhibits the intersection of two bundles of stacking faults (SF), one with high density SF, and the other with low density and limited SF, as well as the occurrence of α′ in the intersecting region. The secondary SFs and the relatively intermediate density of primary SFs bundle are characterized in γ for the sample with relatively high degree of load partitioning. The load partitioning between intragranular of γ is found to have a coordination relationship with the dislocation density evolution of γ; after the load partitioning, dislocation density of γ rapidly rises. The sample with intersection of two bundles SFs and the occurrence of α′, exhibits the higher transformation rate of γ into ε-martensite/α’, resulting in the larger work hardening rate. In addition, the early load on α’ is found to contribute to a higher yield strength. These results reveal the importance of assessing both phase-specifc strain/stress and the dislocation density evolution in order to predict the macroscopic mechanical properties of medium Mn steels.

A mathematical model for longitudinal temperature evolution in strip deformation zone during cold rolling

Strip temperature is a critical control factor in the cold rolling process. In previous, most attention is paid to the total temperature rise in the strip rolling deformation zone, i.e., temperature grows approximately linearly from the entry to the exit. However, the rolling pressure, friction stress and contact condition show different characteristics in different longitudinal zones, which make the heat generation and transfer states different, so the strip temperature undergoes a complex change process. Here, an improved rolling pressure calculation model is proposed at first, where the entry-elastic and exit-elastic zones are added and the Karman differential equation is re-derived in the plastic zone. On this basis, a longitudinal temperature evolution model is proposed, which includes the temperature changes caused by the plastic deformation heat, the friction heat and the contact heat loss. Then, the effectiveness of the proposed model is verified by cold rolling plant experiments and finite element method, the results show that the new model has higher prediction accuracy in rolling force and temperature and can be applied to online control of cold rolled strip. Finally, the effects of different rolling parameters on total temperature are studied, and the results show that the temperature rise of friction heat increases slowly in the front of the rolling deformation zone, so the appearance of maximum temperature is closely related to the increment of the temperature rise of deformation heat against the temperature drop of contact heat loss. To avoid the maximum temperature appearing in the middle of deformation zone, it is useful to appropriately increase the rolling speed, reduce the strip entry temperature.

On the constant roll complex scalar field inflationary models

In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea of real field inflaton with constant rate of roll to a complex field, showing the feasibility of solving Einstein Klein-Gordon equations constrained by an appropriate form of constant roll definition. As compared to the well known (two-parametric class of) real field models, there is one more degree of flexibility in constant roll inflationary solutions which is represented by an arbitrary function of time, γ(t). We work with an arbitrary but constant function γ (where γ = 0 refers to the corresponding real field model) and find new inflationary class of potentials. In this class of models, the behavior of real and complex field models are similar in some aspects, for example the solutions with large constant roll parameter are not stable and should be considered as early time transients. These field solutions relax at late time on a dual attractor trajectory. However, complex fields phase space trajectories reach this stable regime after real fields. We performed the stability analysis on γ function space solutions and found that dynamically stable trajectories in phase space are stable under γ variations. We extended this study by considering multifield models of constant roll inflation with non-canonical kinetic terms. By enlarging the size of field space, we showed that a multifield constant roll model is dynamically a single field effective theory. If field space is parametrized by N non-canonical fields, there will be N free parameters in the potential that can be attributed to the interaction between the fields.

ANALYSIS OF DIMENSIONAL PARAMETERS OF ROLLS OF LONG PRODUCTS MILLS

For long products rolling mills, which in most cases have a significant number of sequentially located working stands, the tasks of choosing the optimal materials, structures and roll sizes are quite relevant. The dimensional parameters of the rolls, which are chosen at the stage of design of the mills, largely determine the efficiency of the technological process. Therefore, the tasks of substantiating the choice of roll sizes for long products rolling mills are relevant and have important practical significance.
 The purpose of the work is to analyze the dimensional parameters of rolls of modern long products rolling mills, to identify the characteristic features of size ratios and to develop recommendations for choosing the main sizes according to the most significant criteria.
 An analysis of the dimensional parameters of rolls of typical modern mills of long products of several leading manufacturers was performed. It was established that the actual ratios of the sizes of the main elements of the rolls only partially correspond to those given in the technical and educational literature.
 The ratio of the nominal diameter of the rolls to the initial rolling thickness varies from 3.75 to 38.5. These values indicate that over the past few decades, the range of changes in this indicator has shifted towards smaller values.
 For the ratio of the length of the barrel to the nominal diameter of the rolls, the most common range of values is from 0.93 to 2.56. That is, there is a decrease in the lower limit of this range for stands of housing and housingless type. The use of rolls with approximately the same barrel length and diameter is due to the characteristics of roll materials and the desire to reduce operating costs by simplifying equipment designs.
 The ratio of the diameters of the necks and the barrel of the rolls varies from 0.40 to 0.57. Such values indicate significant progress, both in the use of new rolls materials and in the improvement of modern bearing assemblies and stands.
 Recommendations have been developed for the selection of the main sizes of rolls by groups of stands of long products rolling mills. From the calculations of the admissible rolling force according to the conditions of the strength of the necks of the rolls, it is proved that according to the criteria of strength and wear resistance, the minimum diameter of the rolls of finishing stands is 350 mm.
 The limits of changes in the dimensional parameters of the rolls determined from the analysis and the recommendations for choosing such dimensions can be used in the design of new rolling mills.

Experimental Evaluation on the Microstructural and Mechanical Response of Ce Microalloying AZ31 Fabricated by Multi-Pass Unidirectional and Cross Rolling after TRC

Conventional billet rolling is being widely used in magnesium (Mg) alloys products, but this method gives rise to biological and environmental problems. The advantages of the short process on sheet fabrication have been widely proved in Mg alloy twin-roll casting (TRC). In this study, an attempt is made to create high-performance Mg alloy sheets via multi-pass unidirectional and cross hot rolling (UR, CR) after TRC for purposes of lowering edge defects and energy consumption. Then, the microstructural and mechanical response of Ce when microalloying AZ31 was observed using UR and CR, respectively. The mechanism of the performance improvement after the AZ31 microalloying is disclosed. In addition, the effect of the rolling parameters on the microstructural and mechanical properties are discussed. Experimental results revealed that the homogenization effect of the AZ31-0.2Ce alloy was the best after being kept at 440 °C for 24 h. The CR-rolled sheet had a more uniform and finer microstructure in the horizontal and center, while for the UR-rolled sheet, it was the opposing edge microstructure. This research is expected to prepare and optimize the microstructural and mechanical properties of microalloying AZ31 in a sheet-rolling process, a material that has important theoretical significance and engineering application value.

Study of Regression Algorithms and Influent Factors between Intelligent Compaction Measurement Values and In-Situ Measurement Values

Intelligent compaction (IC) technology have been used for quality control and quality assurance (QC/QA) in subgrade construction. The effective regression correlations between Intelligent Compaction Measurement Values (ICMV) and In-situ Measurement Values (ISMV, including compaction degree and subgrade modulus ELWD) are the essential prerequisite of using IC technology for QC/QA. This paper presents the results from an experimental research study that was conducted from a practical subgrade project of China to explore the regression relationships between ICMV and ISMV. Three types of ICMV, including CMV, CCV and Evib, were collected along with the corresponding positions of the rollers. Two types of ISMV, containing compaction degree and ELWD, were measured by ring sampler method and light weight deflectometer (LWD) at specified test points, respectively. Based on these data, the influences of roller parameters and subgrade properties on the regression relationships of ICMV and ISMV were investigated. In addition, linear regression and 5 nonlinear regression algorithms were compared. The results suggest that ICMV reflect the stiffness of subgrade more than reflecting the density. In the regression of ICMV and ISMV, subgrade properties are more important than roller parameters while both of them should not be neglected. The influences of underlying stiffness and roller amplitude are linear while that of roller speed and moisture content are nonlinear. Nonlinear algorithms, especially the random forest, have the better performance compared to linear algorithm. Moreover, the combination of random forest and linear algorithm can further improve the accuracy of ISMV prediction.

Molecular dynamics study of the effect of rolling process on subsurface strengthening of nickel-based superalloy GH4169 plastic deformation

In this paper, the molecular dynamics (MD) method is used to establish a rolling model at the nanoscale, the same depth of rolling is rolled, and three rolling methods are used, namely, one time, two times and three times respectively. The effects of three rolling methods on the workpiece are studied, and the evolution of dislocation and defect atoms, subsurface damage, surface quality and subsurface micro-strengthening mechanism of the rolled workpiece are mainly analyzed. The results show that the dislocation density increases most significantly by one rolling, and the difficulty of material deformation is reduced by multiple rolling, with the increase of rolling times, the surface roughness increases. We found that the rolling process has a directional effect on the micro-strengthening of nickel-based single crystal alloys, and the strengthening effect is most significant in the normal direction. The subsurface strengthening effect of rolled workpiece is positively correlated with dislocation density and rolling force. Compared with the previous macro rolling test research, we observed the strengthening effect of dislocation density on rolling plastic deformation of nickel-based single crystal alloy from the microscopic level, which can provide a reference for understanding the strengthening mechanism of rolling process on nickel-based single crystal alloy and the optimization of rolling parameters.

A truncated scale factor to realize cosmological bounce under the purview of modified gravity

AbstractThe present paper reports a study on bounce realization with a truncated scale factor and the holographic fluid taken in the form of holographic Ricci Dark Energy, which is a particular case of holographic Nojiri–Odintsov model (Nojiri & Odintsov, 2006, Gen. Relativ. Gravit., 38(8), 1285). We have investigated the realization of bounce due to the application of a holographic fluid in the early scenario of the universe. We started with a de‐Sitter scale factor in our study and derived two modified forms using Taylor's series expansion. After studying the behavior of the resulting Hubble parameter, we identified as the suitable form of the scale factor to realize the bounce. It satisfied the conditions , , and before, at, and after the turn‐around point. We have also observed that the resulting equation of state (EoS) parameter violates the null energy condition required by the bounce realization. We have studied the bounce scenario in a modified gravity framework and derived the slow roll parameters. We have studied the behavior of the potential along with the slow‐roll parameters in this bouncing scenario.

Automated system for analysis and calculation of cold strip rolling parameters. Message 2

Automated system for analysis and calculation of cold strip rolling parameters. Message 2

Correlation of fracture toughness with microstructural parameters and standard mechanical properties of high-strength medium-alloy steel

Fracture toughness of rolled plates of high-strength medium-alloy steel with a martensitic or martensitic- bainite microstructure can vary widely depending on the parameters of their microstructure, which depends on the specific chemical composition, rolling parameters, quenching and tempering. In previous works, the authors studied the metal of various experimental smelts. The studied materials were significantly different in the size of structural components separated by large-angle boundaries (hereditary austenitic grain, martensite packages, and bainite crystallites). The continuation of these studies is the analysis of the relationship between the fracture toughness of a metal of one smelt and the general quenching parameters and, as a consequence, with the same parameters of the microstructure formed during quenching, but with different tempering parameters. A general structural state parameter based on the obtained data, and correlated with fracture toughness is proposed.

Intelligent adaptive control method for key parameters of vibration rolling during high-speed railway subgrade compaction

To improve the intelligent construction of high-speed railway foundations using continuous subgrade compaction control techniques, a large amount of measured data was accumulated through rolling tests at four sites along the Tianjin Beichen Station high-speed railway foundation. An intelligent adaptive control program for key technical parameters of vibration rolling was then proposed using a long short-term memory neural network. The accuracy of the proposed method was verified, the corresponding calculation process presented, and case validation carried out. The results show that between the measured and predicted values of the compaction quality control index, the average absolute value percentage error (APE) was limited to within 10% with a minimum of 4%, and the mean APE was limited to within 5.5% with a minimum of 3.397%; and the root mean square error was limited to within 2.5 with a minimum of 1.135. These results demonstrate that the proposed model was successfully trained to store the non-linear function describing the relationship between the data in the system and that its learning effect was reasonable, meeting the accuracy requirements of the project. The proposed method can fulfil the requirements for real-time precise intelligent compaction by determining the key parameters of the vibratory roller. It can thereby realize modular management and precise pressure compensation to ensure the efficiency and quality of high-speed railway subgrade fill compaction by vibratory rolling.

Study on Manufacturing Technology of Ultra-Thin/Narrow Bonding Cu Strip for Electronic Packaging

The performance of rolling parameters and annealing processes on the microstructure and properties of Cu strip were studied by High Precision Rolling Mill, FIB, SEM, Strength Tester, and Resistivity Tester. The results show that with the increase of the reduction rate, coarse grains in the bonding Cu strip are gradually broken and refined, and the grains are flattened when the reduction rate is 80%. The tensile strength increased from 248.0 MPa to 425.5 MPa, while the elongation decreased from 8.50% to 0.91%. The growth of lattice defects and grain boundary density results in an approximately linear increase in resistivity. With the increase of annealing temperature to 400 °C, the Cu strip recovers, and the strength decreased from 456.66 MPa to 220.36 MPa while the elongation rose from 1.09% to 24.73%. The tensile strength and elongation decreased to 192.2 MPa and 20.68%, respectively, when the annealing temperature was 550 °C. The trend of yield strength of the Cu strip was basically the same as that of tensile strength. The resistivity of the Cu strip decreased rapidly during a 200~300 °C annealing temperature, then the trend slowed, and the minimum resistivity was 3.60 × 10−8 Ω·m. The optimum tension range annealing was 6–8 g; less or more than that will affect the quality of the Cu strip.

Investigation of the Porosity Gradient in Thickness Direction Formed by Cold Rolling in Porous Aluminum

To adapt porous material for its application as low noise trailing edge, a special rolling process, using a time-varied rolling gap, was used in previous research to produce a porosity gradient in the direction of rolling. Investigations suggest that a gradient in porosity may also be produced in the thickness direction of the material, i.e., in the rolling gap direction, without using a specialized rolling mill. Such a gradient may help to further increase acoustic efficiency of porous materials. The aim of this study was to analyze the dependency of such a gradient on the rolling parameters, and to clarify which stress components are significantly responsible for an increased near-surface compaction. Experiments using different relative compressed lengths were performed to analyze shear-dominated and friction-dominated rolling. The material was characterized using compression tests, computed tomography and flow resistance measurements. It is shown that the compressed length is an important parameter for adjusting a porosity gradient. Rolling with small values of compressed length during all rolling passes leads to increased compaction of near-surface regions, compared to interior ones. The difference in porosity achieved was up to 15%. Furthermore, the results suggested that a gradient in hydrostatic stress is responsible for the porosity gradient. Validation of the results by FE simulation is forthcoming, but not part of this publication.

Optimization of hot rolling parameters of CRNO steel with the aid of hot compression test and deformation map

Abstract Cold-rolled non-oriented (CRNO) electrical steels find a wide variety of applications in the core of electrical machines due to low core loss and high magnetic permeability. Stringent market conditions not only require CRNO steel with superior magnetic properties but also demand excellent surface conditions. CRNO steel is cold rolled to 0.5 mm in reversing mill. High hot rolled input thickness (>2.6 mm) increases the number of passes during cold rolling and adversely affects the mill productivity. It also results in surface defects such as buckling and coil break. The flow stress of this steel varies differently compared to conventional rolled steel. Thus, it becomes difficult to optimize the reduction schedule and hence safe hot rolling practice is adopted to restrict roll force within permissible limit resulting in higher thickness. A hot compression test was carried out in a Gleeble–3500 to evaluate the flow stress behaviour of this steel and a deformation map was developed to optimize the hot rolling window. The input from the hot compression test and deformation map was used to develop a mill setup model to accurately predict the roll force and optimize the reduction schedule of CRNO steel in the finishing stands of HSM. The final thickness of hot-rolled coils during industrial trials with an optimized reduction schedule was found to be in the range of 2.4–2.6 mm compared to 2.7–3.0 mm during conventional rolling. These coils were further cold rolled and finished in 4–5 passes compared to 6–7 passes with conventional rolling. Reduction in the number of passes has resulted in increased productivity during cold rolling as well as improved surface finish.

Effect of rolling motion on transient characteristics of condensation induced water hammer in an equal-height-difference passive heat removal system

The investigation of condensation-induced water hammer (CIWH) under ocean conditions is crucial to the system safety of the offshore floating nuclear plants (OFNPs). This paper establishes a CIWH numerical model under rolling conditions based on the computational fluid dynamics (CFD) code combined with user-defined functions (UDF). First, the numerical model is verified by published experimental data. Then, the transient behaviors of CIWH events under various rolling parameters are numerically investigated. The results show that the rolling motion causes a significant steam slug and enhances the steam-subcooled water contact area, which promotes the average condensation rate. The average condensation rate increases with an increase in rolling angle, decreases with an increase in rolling period. Due to the larger average condensation rate and reverse flow caused by rolling motion, the pressure peak generated by the CIWH significantly increases compared to static conditions. Similarly, the pressure peak increases as rolling angle increases, decreases as rolling period increase. Moreover, the pressure peak is proportional to steam inlet velocity, and the location of the pressure peak gradually moves back to the outlet direction as the steam velocity increases. These qualitative conclusions are useful to understand the effects of rolling motion on the CIWH and provide a reference for the CIWH simulations.

Recrystallisation Characteristics of a Cu Bearing HSLA Steel Assessed Through High Temperature Compressive Deformation

Dynamic (DRX) operative duringdeformation and static recrystallization (SRX) operative after deformation are considered responsible for the changes in microstructure and texture of deformed materials. Especially in the case of advanced steels that are required in the form of plates of various thicknesses, hot rolling is the main manufacturing process during which the steel undergoes DRX under the rolls and SRX between rolling passes/strands. Knowledge on DRX and SRX characteristics of such steels is crucial for optimisation of hot rolling parameters,achieving the desired microstructure and consequently the targeted mechanical properties.In this study, certain key aspects of both dynamic (DRX) and static recrystallisation (SRX) behaviour of aCu-bearing HSLA steel, which was developed at DMRL, have been explored through high temperature deformation studies using Gleeble thermo-mechanical simulator. Through uniaxial compression testing in the austenitic regime, domains of continuous and discontinuous DRX prevalent in the steel were identified and critical parameters for initiation of dynamic recrystallisation viz., critical strain (ec), critical stress (sc), peak stress (sp) and peak strain (ep) were determined as a function of temperature and strain rate. SRX characteristics were assessed through uniaxial double hit compression tests with fixed strain rate and strain per hit but at different temperatures and with different imposed intermediate static recrystallisation (ISRT) times. From the fractional softening data, parameters such as time for 50% recrystallisation, t0.5, temperature for 50% recrystallisation, T0.5, and activation energy, QSRX have been estimated.Although the steel exhibited good plastic deformation characteristics, the results suggest that the role of copper in retarding recrystallisation is significant.

Short-Flow Rolling Process and Heat Treatment of Seamless Titanium Alloy Tube

In view of the material characteristics of titanium alloys, such as their capability to quickly cool down and their poor machinability, in this study, we combined a new production mode for seamless tube rolling (tandem skew rolling, TSR) with titanium alloy materials and conducted systematic research. The most suitable parameters for titanium alloy rolling were determined from the unit parameters using finite-element software and an analysis of the changing laws of stress-strain, temperature, speed and tension during the rolling process. A rolling experiment was completed in the tandem skew rolling unit. Seamless titanium alloy (TC4ELI) tubes with uniform wall thickness were successfully produced and a metallurgical heat-treatment experiment was carried out. The results show that the seamless titanium alloy tubes prepared using the TSR process have a high degree of dimensional precision (the outer diameter is approximately 38.7 mm, the wall thickness is approximately 3.9 mm and the axial extension is 2.9 times) and the tube after heat treatment still presented a basketweave structure. Furthermore, the hardness level of the seamless titanium alloy tubes was improved. It can be concluded that the TSR process with a short flow is suitable for the mass production of seamless titanium alloy tubes.

Cosmology of modified holographic f(G) gravity and study of baryogenesis

Motivated by the work of Nojiri and Odintsov [Phys. Lett. B 631 (2005) 1–6, arXiv:hep-th/0508049 [hep-th]], this work reports on the cosmology and baryogenesis of modified [Formula: see text] gravity by assuming the background evolution as generalized holographic dark energy (GHDE). For vacuum energy density, modified [Formula: see text] gravity is reconstructed and found to be of positive behavior. The equation of state (EoS) parameter under the purview of vacuum energy density comes out to be quintom. The reconstructed modified [Formula: see text] gravity in GHDE shows positive behavior, and its corresponding EoS parameter is phantom. There is a chance of a big rip singularity and the slow roll parameters are analyzed. Quasi exponential expansion and warm inflation are observed. Finally, baryogenesis is studied. The study suggests that either there may be symmetry between the number density of baryons and antibaryons in the far future, or the generalized second law of thermodynamics is satisfied by the model.

Effect of High-Temperature-Assisted Ultrasonic Deep Rolling on Microstructure and Tribological Properties of Ni-WC Coatings

Cermet coatings are post-treated by a new surface microcrystallization technology, namely high-temperature-assisted ultrasonic deep rolling (HT + UDR). The process parameters of ultrasonic deep rolling significantly affect the microstructure and tribological properties of the Ni-WC coatings. In this paper, the samples were treated with different preloading depths (0.20 mm, 0.25 mm, and 0.30 mm), and the microstructure and properties of the coatings were characterized by SEM, EDS, X-ray stress analysis, and micro-Vickers hardness testing. An MMW-1A-type friction and wear tester was used for the dry friction and wear test at room temperature, respectively. Compared with the untreated sample, plastic rheology occurred on the surface of the coatings after HT + UDR, showing a phenomenon of “cutting peaks and filling valleys”. In the treated coatings, visible cracks were eliminated, and the inside of the coating was denser. The surface hard phase was increased as a “skeleton” and embedded with the soft phase, which played a role in strong and tough bonding. After HT + UDR + 0.25 mm treatment, the surface roughness increased by 68%, the microhardness of the surface layer reached a maximum of 726.3 HV0.1, and the residual tensile stress changed from 165.5 MPa to −337.9 MPa, which inhibited the germination and propagation of cracks. HT + UDR improved the wear resistance of the coating in many aspects. The coating after the 0.25 mm preloading depth treatment possessed the smallest friction coefficient and the lowest wear amount, which is 0.04 and 4.5 mg, respectively. The wear form was abrasive wear, and the comprehensive tribological performance is the best.

Production of a Non-Stoichiometric Nb-Ti HSLA Steel by Thermomechanical Processing on a Steckel Mill

Obtaining high levels of mechanical properties in steels is directly linked to the use of special mechanical forming processes and the addition of alloying elements during their manufacture. This work presents a study of a hot-rolled steel strip produced to achieve a yield strength above 600 MPa, using a niobium microalloyed HSLA steel with non-stoichiometric titanium (titanium/nitrogen ratio above 3.42), and rolled on a Steckel mill. A major challenge imposed by rolling on a Steckel mill is that the process is reversible, resulting in long interpass times, which facilitates recrystallization and grain growth kinetics. Rolling parameters whose aim was to obtain the maximum degree of microstructural refinement were determined by considering microstructural evolution simulations performed in MicroSim-SM® software and studying the alloy through physical simulations to obtain critical temperatures and determine the CCT diagram. Four ranges of coiling temperatures (525–550 °C/550–600 °C/600–650 ° C/650–700 °C) were applied to evaluate their impact on microstructure, precipitation hardening, and mechanical properties, with the results showing a very refined microstructure, with the highest yield strength observed at coiling temperatures of 600–650 °C. This scenario is explained by the maximum precipitation of titanium carbide observed at this temperature, leading to a greater contribution of precipitation hardening provided by the presence of a large volume of small-sized precipitates. This paper shows that the combination of optimized industrial parameters based on metallurgical mechanisms and advanced modeling techniques opens up new possibilities for a robust production of high-strength steels using a Steckel mill. The microstructural base for a stable production of high-strength hot-rolled products relies on a consistent grain size refinement provided mainly by the effect of Nb together with appropriate rolling parameters, and the fine precipitation of TiC during cooling provides the additional increase to reach the requested yield strength values.