Plastic Deformation Of Materials Research Articles

Study on the nano-cutting mechanism of monocrystalline silicon material with an amorphous layer by molecular dynamics simulations

Monocrystalline silicon is prone to brittle fracture during the nano-cutting process. Surface modification through ion implantation to create an amorphous layer on monocrystalline silicon significantly enhances its processability. This paper conducted molecular dynamics simulations to deeply reveal the nanometric cutting mechanism for monocrystalline silicon with an amorphous layer. The influence of the amorphous layer on material removal, subsurface damage, cutting forces, stress distribution, and temperature profiles was analyzed and thoroughly discussed. The calculating results reveal that primary material removal mode transitions from shearing to extrusion under the influence of the amorphous layer. The presence of an amorphous layer can efficiently reduce stress concentration and defects in the nanometric machining process. When the thickness of the amorphous layer equals the cutting depth of the tool, subsurface damage is reduced to approximately 2 nm, indicating that an optimal surface quality is achieved. When the thickness of the amorphous layer reaches more than cutting depth, the hydrostatic stress of the monocrystalline silicon part is significantly lower than the phase transition threshold of 12 GPa, which greatly reduces the occurrence of phase transition. Furthermore, the formation and evolution of shear bands are the primary reasons for the fluctuations in cutting force. The cutting temperature is closely related to structural transformations. The heat generated by shear slip in monocrystalline silicon material is higher than the heat generated by plastic deformation of material in the amorphous layer. Moreover, the heat energy produced by plastic deformation of amorphous layer atoms exceeds that generated by structural transformation of monocrystalline silicon atoms. This work reveals the nanometric cutting behavior of the monocrystalline silicon material with amorphous layer surfaces based on phase transformation. It can provide effective references for the preparation of amorphous layer thickness and selection of cutting parameters in nanometric cutting process of the monocrystalline silicon with amorphous layer surfaces.

Energetics of Point Defects in D0a Ag3Sn: First‐Principles Calculations

The Ag3Sn intermetallic compound is commonly found and acts as a strengthening factor in the key lead‐free solders based on Sn‐Ag‐Cu. The Ag3Sn phase exhibits also an asymmetric off‐stoichiometry, which necessitates the existence of constitutional point defects. The presence of point defects can, in general, sensitively affect the plastic deformation of materials and the strengthening role of Ag3Sn in particular. To understand the nature of the point defects and the compositional stability of Ag3Sn, the relaxed structures and the energies of single point defects (vacancies and antisite defects) in all three sublattices of Ag3Sn are calculated at 0 K using ab initio density functional theory (DFT) and the supercell method. The first‐principles‐based calculations predict that the AgSn antisite defect (Ag substitution for Sn) has the smallest enthalpy of formation, thus indicating that the AgSn antisite defect is the dominant point defect in Ag3Sn. The point defect concentrations as a function of Sn content are estimated using the DFT defect energies and the Wagner–Schottky model. The compositional dependence of the point defect concentrations gives new insights on the atomistic mechanisms of formation of nonstoichiometric Ag3Sn.

Characterization and simulation of AlSi10Mg reinforcement structures by direct energy deposition by means of laser beam and powder

Among metal additive manufacturing technologies, direct energy deposition (DED) processes have the advantage to be easily integrable in a manufacturing chain with other conventional technologies. This characteristic can be exploited by designing reinforcement structures to be added by DED onto pre-existing subcomponents to tailor the part’s mechanical properties while keeping the part lightweight. This study focuses on DED by means of laser beam and powder process optimization to improve material quality and geometrical accuracy of AlSi10Mg reinforcement structures while preventing excessive thermal deformations and material dilution into the substrate. These results are compared with finite elements numerical simulations of the deposition process, comprising thermo-elastic deformation and material deposition, to predict the bending and reinforcement of the processed substrate. In particular, the model includes the deterministic prediction of the deposition profile as a function of the process parameters and a few condition-specific coefficients: once calibrated, the model was used to compare the numerical and experimental residual deformation of the reinforced sample, obtaining promising agreement. The reinforcement provided to a 1.5 mm thick substrate by a single wall of deposited materials, with cross-sectional dimensions of 2 mm in width and 2.5 mm in height, was evaluated by three points bending. With the reinforcement on the tensile side of the stresses, the energy absorbed by the material plastic deformation increased by 2.4% as compared to the substrate alone, while with the reinforcement on the compression side of the stresses the energy absorption increased by 75.8% on average.

Grain rotation mechanisms in nanocrystalline materials: Multiscale observations in Pt thin films.

Near-rigid-body grain rotation is commonly observed during grain growth, recrystallization, and plastic deformation in nanocrystalline materials. Despite decades of research, the dominant mechanisms underlying grain rotation remain enigmatic. We present direct evidence that grain rotation occurs through the motion of disconnections (line defects with step and dislocation character) along grain boundaries in platinum thin films. State-of-the-art in situ four-dimensional scanning transmission electron microscopy (4D-STEM) observations reveal the statistical correlation between grain rotation and grain growth or shrinkage. This correlation arises from shear-coupled grain boundary migration, which occurs through the motion of disconnections, as demonstrated by in situ high-angle annular dark-field STEM observations and the atomistic simulation-aided analysis. These findings provide quantitative insights into the structural dynamics of nanocrystalline materials.

Uncovering all possible dislocation locks in face-centered cubic materials

Dislocation reactions and locks play an important role in the plastic deformation and mechanical behavior of crystalline materials. Various types of dislocation locks in face-centered cubic (FCC) materials have been reported in the literature pertaining to material-specific molecular-dynamic simulations and high-resolution transmission electron microscopy observations. However, it is unknown how many dislocation locks are possible, and how immobile all the dislocation locks are, with respect to each other. Here we present a discrete mathematics-based approach to reveal all possible dislocation locks in the FCC crystal structure. Totally eight types of dislocation locks are uncovered, resulting from all possible reactions of mobile/glissile (namely, perfect and Shockley partial) dislocations with (a) non-coplanar Burgers vectors which reside on two slip planes intersecting at both obtuse and acute angles and (b) coplanar Burgers vectors. We redefine the degree of dislocation lock immobility based on misorientations between non-close-packed lock planes and close-packed {111} slip planes. The subsequently derived sequences for the dislocation lock immobility and formation tendency are rationalized by the reported experimental and dislocation-dynamics simulation results.

Modeling Strain Hardening of Metallic Materials with Sigmoidal Function Considering Temperature and Strain Rate Effects.

This study uses a sigmoidal function to describe the plastic strain hardening of metallic materials, considering temperature and strain rate effects. The effectiveness of this approach is evaluated and systematically compared with other hardening laws. Incorporating temperature and strain rate effects into the parameters of this sigmoidal-type hardening law enables a more precise description and prediction of the plastic deformation of materials under different combinations of temperature and strain rate. The temperature effect is coupled using a simplified Arrhenius model, and the strain rate effect is coupled with a modified Johnson-Cook model. The sigmoidal-type hardening law is integrated with an asymmetric yield criterion to address complex behavior, such as anisotropy and strength differential effects. The calibration and validation of the constitutive model involve examining uniaxial tensile/compressive flow curves in various directions and biaxial tensile/compressive flow curves for diverse metallic alloys, proving the proposed model's broad applicability.

Clustering of negative topological charges precedes plastic failure in 3D glasses.

The deformation mechanism in amorphous solids subjected to external shear remains poorly understood because of the absence of well-defined topological defects mediating the plastic deformation. The notion of soft spots has emerged as a useful tool to characterize the onset of irreversible rearrangements and plastic flow, but these entities are not clearly defined in terms of geometry and topology. In this study, we unveil the phenomenology of recently discovered, precisely defined topological defects governing the microscopic mechanical and yielding behavior of a model 3D glass under shear deformation. We identify the existence of vortex-like and antivortex-like topological defects within the 3D nonaffine displacement field. The number density of these defects exhibits a significant anticorrelation with the plastic events, with defect proliferation-annihilation cycles matching the alternation of elastic-like segments and catastrophic plastic drops, respectively. Furthermore, we observe collective annihilation of these point-like defects via plastic events, with large local topological charge fluctuations in the vicinity of regions that feature strong nonaffine displacements. We reveal that plastic yielding is driven by several large sized clusters of net negative topological charge, the massive annihilation of which triggers the onset of plastic flow. These findings suggest a geometric and topological characterization of soft spots and pave the way for the mechanistic understanding of topological defects as mediators of plastic deformation in glassy materials.

Investigating grain-resolved evolution of lattice strains during plasticity and creep using 3DXRD and crystal plasticity modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

Microstructural and fatigue characterization of 316L stainless steel subjected to flow drilling and tapping: comparison with machined threads

Despite extensive research on the plastic deformation of materials to enhance their fatigue resistance, the influence of the flow tapping process on the fatigue resistance of drilled and tapped bars remains poorly understood. Herein, the fatigue performance of flow-drilled (friction-drilled) and flow-tapped 316L stainless steel bars was experimentally analyzed and compared with that of conventional material-shearing-based drilling and tapping operations. The effect of flow processes on the material properties was evaluated via microhardness tests and microstructural analyses. The results indicated that the hardness near the holes produced via flow forming was 62 % higher than that of the base metal. Moreover, grain refinement and plastic deformation were observed beneath the thread surfaces. Metallographic observations revealed the occurrence of craters and folds at the crest of the flow-formed threads. Following the ASTM F382-17 standard, four-point bending fatigue tests were performed at three stress amplitudes with a stress ratio of 0.1. No noteworthy differences were observed when the maximum bending moments applied were at 75 % and 60 % of the bending moment at yield. However, when the maximum bending moment applied was limited to 50 % of the bending moment at yield, the average fatigue life of the specimens with machined threads was longer than that of their flow-formed counterparts. Fractographic observations were used to identify the crack initiation regions and elucidate the underlying fracture mechanisms. For both types of specimens, failure originated at the crest of the first thread, beneath the surface of the maximum tensile stress. The flow-processed specimens exhibited secondary cracks at the root of the threads, where grain refinement also occurred. This study provides robust empirical evidence that using flow-forming processes to thread 316L stainless steel does not systematically improve the fatigue resistance of the material surrounding the holes. Furthermore, by optimizing the flow process and eliminating discontinuities, the threading process proposed herein could help improve the fatigue resistance of orthopedic implants.

Surface Interaction and Wear Due to Sliding Electrical Contact of Materials

This article reports a research study on sliding electrical contacts of copper–diamond materials, involving modeling and validation, contact status simulations, and parametric studies. The simulation model includes the analyses of both mechanical and electrical heat sources, evaluations of heat partition and temperature, and the capture of material thermal softening, plastic deformation, and material removal. The simulation model is validated through result comparison with experimental average temperature and measured wear. With this model, temperature variation and surface wear accumulation were numerically predicted under the influences of material property variations. Factors influencing wear of the copper surfaces were explored, and parameter sensitivity was investigated by means of the Taguchi L18 matrix. The results reveal that thermally related parameters of the contact interface strongly affect the wear of the copper pin, and thermal conductivity of its mating surface material is of critical importance. The research also suggests that the electromagnetic field change due to switching the polarity of the power supply does not affect the friction and wear results; however, the polarity change influences material electrochemistry, which results in a difference in friction and wear.

Finite Element Analysis of Plastic Deformation in Ultrasonic Vibration Superimposed Face Milling of Steel X46Cr13.

Ultrasonic vibration superimposed face milling enables the generation of predefined surface microstructures by an appropriate setting of the process parameters. The geometrical reproducibility of the surface characteristics depends strongly on the plastic material deformation. Thus, the precise prediction of the emerging surface microstructures using kinematic simulation models is limited, because they ignore the influence of material flow. Consequently, the effects of plastic as well as elastic deformation are investigated in depth by finite element analysis. Microstructured surfaces resulting from these numerical models are characterized quantitatively by areal surface parameters and compared to those from a kinematical simulation and a real machined surface. A high degree of conformity between the values of the simulated surfaces and the measured values is achieved, particularly with regard to material distribution. Deficits in predictability exist primarily due to deviations in plastic deformation. Future research can address this, either by implementing a temperature consideration or adapting specific modeling aspects like an adjusted depth of cut or experimental validated material parameters.

Effect of Al Content on Microstructure and Properties of AlxCr0.2NbTiV Refractory High-Entropy Alloys.

High-temperature creep refers to the slow and continuous plastic deformation of materials under the effects of high temperatures and mechanical stress over extended periods, which can lead to the degradation or even failure of the components' functionality. AlxCr0.2NbTiV (x = 0.2, 0.5, or 0.8) refractory high-entropy alloys were fabricated by arc melting. The effects of Al content on the microstructure of AlxCr0.2NbTiV alloys were studied using X-ray diffraction, scanning electron microscopy, and electron backscatter diffraction. The microhardness, compression properties, and nanoindentation creep properties of AlxCr0.2NbTiV alloys were also tested. The results show that the AlxCr0.2NbTiV series exhibits a BCC single-phase structure. As the Al content increases, the lattice constant of the alloys gradually decreases, and the intensity of the (110) crystal plane diffraction peak increases. Adding aluminum enhances the effect of solution strengthening; however, due to grain coarsening, the microhardness and room temperature compressive strength of the alloy are only slightly improved. Additionally, because the effect of solution strengthening is diminished at high temperatures, the compressive strength of the alloy at 1000 °C is significantly reduced. The creep mechanism of the alloys is predominantly governed by dislocation creep. Moreover, increasing the Al content helps to reduce the sensitivity of the alloy to the loading rate during the creep process. At a loading rate of 2.5 mN/s, the Al0.8Cr0.2NbTiV alloy exhibits the lowest creep strain rate sensitivity index (m), which is 0.0758.

Nanoscale speckle patterning for combined high‐resolution strain and orientation mapping of environmentally sensitive materials

AbstractScanning electron microscopy‐based high‐resolution digital image correlation (HRDIC) is now an established technique, providing full‐field strain and displacement measurement at the microscale. Techniques for generating speckle patterns for sub‐micron strain mapping can often be either substrate dependent or rely on applying aggressive conditions which may alter the microstructure of interest or damage the substrate in highly sensitive materials. We detail a modification of a methodology successfully applied in the literature to allow its use with metallic materials that are particularly sensitive to the corrosive media, such as copper‐base alloys. Nanometre‐thick silver films, applied with physical vapour deposition, are remodelled using NaBr in non‐aqueous isopropanol, replacing the aqueous solution of NaCl in the original method, forming a uniform dispersion of silver islands highly suitable for digital image correlation (DIC) measurement. The entire procedure is performed at ambient temperature. We find that the DIC pattern is suitably electron transparent to allow electron backscatter diffraction (EBSD) measurements without pattern removal, producing diffraction patterns of sufficient quality for cross‐correlation based high‐angular resolution EBSD. This property facilitates simultaneous EBSD and DIC mapping experiments, providing deeper insights into the kinematics of plastic deformation in crystalline materials. Sub‐100 nm islands are achieved through control of the sputter coating parameters, resulting in DIC cross‐correlation subwindows of 140 nm with a 50% overlap. This resolution is sufficient to capture the fine detail of strain localisation phenomena during plastic deformation, demonstrated here with a case study in CuCrZr, a precipitation‐hardened heat sink material for application in nuclear fusion components. Here, we extract full‐field displacement data with DIC and corresponding orientation information using EBSD without the need for pattern removal.

Study of the mechanism of the strength-ductility synergy of α-Ti at cryogenic temperature via experiment and atomistic simulation

Alpha titanium (α-Ti) is a promising material for making high-performance components for applications in aerospace, marine, energy and healthcare fields. The excellent strength-ductility synergy has been observed for α-Ti at cryogenic temperature. Twinning is generally considered a key mechanism of outstanding cryogenic ductility. The dislocation-grain boundaries (GBs) interaction and void nucleation usually play crucial roles in the plastic deformation of polycrystalline materials, but their effects on the cryogenic ductility of α-Ti are rarely considered. To eliminate this confusion and gain an in-depth insight into the mechanism of the cryogenic strength-ductility synergy of α-Ti, in this work, a series of characterization experiments and molecular dynamics (MD) simulations were designed and carried out. 1) From uniaxial tension tests of the coarse-grained α-Ti sheets at the temperature from 25 to -180 °C, the uniform elongation and post-necking elongation were increased by 92 % and 20 %, respectively. The material maintained a larger strain hardening rate within a greater range of strain at cryogenic temperature compared with room temperature. 2) Via microstructure and fractography observations and the analysis of slip and geometrically necessary dislocation (GND) activities, the uniform plastic deformation was mainly accomplished by prismatic slip, whether at room temperature or at cryogenic temperature. The significantly increased uniform elongation is mainly attributed to the more uniform distribution of GND pile-ups at cryogenic temperature. 3) The MD simulations revealed that cryogenic temperatures made the GBs present a stronger barrier effect on dislocation transmission compared with that at room temperature, contributing to the more uniform distribution of GNDs and lower densities of GND pile-ups. The GBs at cryogenic temperature show a greater ability to resist void nucleation due to the decreased accumulation rate of excess potential energy and increased energy required to void nucleation. The larger strains were thus required to increase the densities of GND pile-ups to induce large stress concentrations for driving void nucleation. This made the uniform elongation of α-Ti increase significantly at cryogenic temperature. This study revealed that the enhanced barrier effect of GBs on dislocation transmission and the improved ability of GBs to resist void nucleation are key mechanisms besides twinning governing the cryogenic strength-ductility synergy of α-Ti. The understanding developed in this work can be useful for the development of new high-performance materials and the precise forming of complex components with high quality.

МАТЕМАТИЧНА МОДЕЛЬ ВПЛИВУ ПОВОРОТУ ВИДОВЖЕНИХ ЗЕРЕН НА ПРОЦЕС ВИСОКОТЕМПЕРАТУРНОГО ДЕФОРМУВАННЯ КЕРАМІКИ НА ОСНОВІ НІТРИДУ КРЕМНІЮ

The speed of direct high-temperature extrusion of ceramics based on silicon nitride was analyzed. The influence of rotation of elongated grains on mass transfer processes and deformation rate is established. The influence of the parameters of the high-temperature deformation process on the deformation rate is shown. An equation is proposed that describes the effect of rotation of elongated grains on the strain rate. The described equation of strain rate can be used to create technological processes of plastic deformation of ceramic materials.

МАТЕМАТИЧНА МОДЕЛЬ ВПЛИВУ ЗЕРНОГРАНИЧНОГО КОВЗАННЯ НА ПРОЦЕС ВИСОКОТЕМПЕРАТУРНОГО ДЕФОРМУВАННЯ КЕРАМІКИ НА ОСНОВІ НІТРИДУ КРЕМНІЮ

The speed of direct high-temperature extrusion of ceramics based on silicon nitride was analyzed. The influence of grain boundary slip and viscous flow of the intergrain phase on mass transfer processes and deformation rate is established. The influence of the parameters of the high-temperature deformation process on the deformation rate is shown. An equation is proposed that describes the effect of grain boundary slip and viscous flow of the intergranular phase on the strain rate. The described equation of strain rate can be used to create technological processes of plastic deformation of ceramic materials.

Investigating micro-cutting mechanism of glow discharge polymer based on material properties and removal behaviors analysis

Glow discharge polymer (GDP) is the unique artificial material for the target balls in Inertial Confinement Fusion tests, while its practical micromachining such as the fabrication of microstructure on material surfaces keeps challenging due to its unclear micro-cutting mechanism. Hence, this paper seeks to investigate the micro-cutting mechanism of GDP from the perspective of the material flow and cutting energy. To achieve it, the energy conservation equation of three cutting modes triggered by different ratios of uncut chip thickness to the tool cutting edge radius (RTS) was established based on cutting deformation behaviors. Meanwhile, the diamond cutting tests and the FEM simulation at different RTS were developed. The experimental observation of cutting forces and specific cutting forces verified the evolution of three cutting modes, including shearing, shearing-ploughing and ploughing in the micro-cutting of GDP with the decrease of RTS. Next, from the change of the node displacement vector observed from the simulated results, it can be seen that the real-time material flow behavior during micro-cutting of GDP varies obviously with the evolution of cutting modes. Besides, the fracture toughness Gc, and the energy dissipation of different cutting modes were analyzed. The proportion of the energy spent on material fracture (Gc=9.95 N/mm) is the largest one in shearing and shearing-ploughing modes, while in ploughing mode, the material plastic deformation consumed the most energy. The above results reveal the specific material properties and removal behaviors of GDP and contribute to optimizing the machining strategies for the practical micromachining of microstructures on material surfaces.

Enhancing the Structural and Mechanical Properties of Ti-Zr Alloy through Boron Doping

This study aims to improve the structural strength of the commonly used Ti-15Zr alloy in dental applications by investigating the effects of low boron additions. Ti-15Zr alloys containing 1-4% boron have been produced by vacuum arc melting. The phase ratios in the microstructure of the produced alloys vary according to the boron content. With increasing boron content, the ratio of TiB compound in the phase structure increases. The hardness of Ti-Zr-B alloys exhibited a notable increase in correlation with rising boron content. Measured hardness values of 36.31, 39.50, 44.14, and 53.40 displayed a clear upward trend with higher boron percentages. The tensile strength of the Ti-Zr-B alloys exhibits a trend of initially increasing with boron content, reaching its highest value of 888 MPa at 1% boron. The yield strength follows a similar with tensile strengh, with an initial rise from 449 MPa at 0% boron to a peak of 562 MPa at 1% boron content. Beyond this point, the yield strength slightly decreases to 469 MPa at 2% boron but sharply drops to 186 MPa at 4% boron content. As boron content increases in the Ti-Zr-B alloys, the percentage elongation, indicating the material's plastic deformation capacity before fracture, consistently decreases from 17.03% at 0% boron to 0.70% at 4% boron content.

Modeling of shock wave propagation in porous magnesium based on artificial neural network

Data transfer from the level of atomistic simulations to the level of continuum modeling is one of the urgent problems in the mechanics of materials. In this work, we perform multiple molecular dynamics (MD) simulations of the uniaxial (along different crystallographic directions) and volumetric (isotropic) compression of porous HCP magnesium single crystals in order to study the atomistic processes of the plastic deformation of anisotropic porous material and to create a reference dataset (strain dependencies of stresses, porosity and dislocation density at different temperatures and initial porosities). The MD data are used to train two artificial neural networks (ANNs): the first ANN is a surrogate of the constitutive equation of porous magnesium, while the second ANN describes the dislocation nucleation/emission as the onset of plastic flow. In contrast to the previously considered case of porous FCC aluminum, the present approach takes into account the anisotropy of the matrix material. The ANN-based constitutive equation is successfully used within the continuum mechanics model for numerical study on the shock wave structure in porous magnesium in comparison with direct MD simulation of the shock wave problem.

Effects of moisture content and soil suction on the permanent deformation of tropical subgrade soils: experimental investigations and modelling

This study presents the effects of moisture variation and the influence of matric suction on the permanent deformation (PD) of three tropical soils with different geological-geotechnical characteristics used in road subgrades in southern Brazil. The experimental programme consisted in determining the soil-water characteristic curves and in dynamic triaxial tests to obtain the PD in different compaction and post-compaction moisture contents. The variation of compaction moisture content caused microstructural changes, influencing the plastic behaviour of soils: the higher the initial moisture content, the greater their accumulated permanent deformations. As expected, the post-compaction moisture variation (wetting process) tended to increase the plastic deformation of materials, evidencing the influence of the suction variation on the performance of the soils studied. In addition, matric suction proved to be the best variable to represent the effects of moisture variation on the plastic behaviour of soils subjected to cyclic loading. Thus, a PD prediction model for tropical soils with the inclusion of this parameter was proposed. The model proved to be highly predictive and may become an important tool to be incorporated into current mechanistic-empirical design methods.