Pressure stimulated current in progressive failure process of combined coal-rock under uniaxial compression:Response and mechanism

Effective monitoring of the structural health of combined coal-rock under complex geological conditions by pressure stimulated currents(PSCs)has great potential for the understanding of dynamic disasters in underground engineering.To reveal the effect of this way,the uniaxial compression experiments with PSC monitoring were conducted on three types of coal-rock combination samples with different strength combinations.The mechanism explanation of PSCs are investigated by resistivity test,atomic force microscopy(AFM)and computed tomography(CT)methods,and a PSC flow model based on progressive failure process is proposed.The influence of strength combinations on PSCs in the progressive failure process are emphasized.The results show the PSC responses between rock part,coal part and the two components are different,which are affected by multi-scale fracture characteristics and electrical properties.As the rock strength decreases,the progressive failure process changes obviously with the influence range of interface constraint effect decreasing,resulting in the different responses of PSC strength and direction in different parts to fracture behaviors.The PSC flow model is initially validated by the relationship between the accumulated charges of different parts.The results are expected to provide a new reference and method for mining design and roadway quality assessment.

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

Rational manipulation of electrolyte to induce homogeneous SEI on hard carbon anode for sodium-ion battery

Sodium-ion batteries (SIBs) have great potential to be the next major energy storage devices due to their obvious advantages and developing advanced electrodes and electrolytes is urgently necessary to promote its future industrialization.However,hard carbon as a state-of-the-art anode of SIBs still suffers from the low initial Coulomb efficiency and unsatisfactory rate capability,which could be improved by forming desirable solid electrolyte interphases (SEI) to some extent.Indeed,the chemistry and morphology of these interfacial layers are fundamental parameters affecting the overall battery operation,and optimizing the electrolyte to dictate the quality of SEI on hard carbon is a key strategy.Hence,this review summarizes the recent research on SEI design by electrolyte manipulation from solvents,salts,and additives.It also presents some potential mechanisms of SEI formation in various electrolyte systems.Besides,the current advanced characterization techniques for electrolyte and SEI structure analyses have been comprehensively discussed.Lastly,current challenges and future perspectives of SEI formation on hard carbon anode for SIBs are provided from the viewpoints of its compositions,evolution processes,structures,and characterization techniques,which will promote SEI efficient manipulation and improve the performance of hard carbon,and further contribute to the development of SIBs.

Gravel hardness effect on compaction characteristics of gravelly soil

The compaction characteristics of gravelly soil are affected by gravel hardness.To investigate the evolution and influencing mechanism of different gravel hardness on the compaction characteristics of gravelly soil,heavy compaction tests and crushing tests were conducted on gravelly soils with gravels originated from hard,soft and extremely soft rocks.According to orthogonal experiments and variance analysis,it was found that hardness has a significant impact on the maximum dry density of gravelly soil,followed by gravel content,and lastly,moisture content.For gravel compositions with an average saturated uniaxial compressive strength less than 60 MPa,the order of compacted maximum dry density is soft gravels>hard gravels>extremely soft gravels.Each type of gravelly soil has a threshold for gravel content,with 60%for hard and soft gravels and 50%for extremely soft gravels.Beyond these thresholds,the compacted dry density decreases significantly.There is a certain interaction between hardness,gravel content,and moisture content.Higher hardness increases the influence of gravel content,whereas lower hardness increases the influence of moisture content.Gravelly soils with the coarse aggregate(CA)between 0.7 and 0.8 typically achieve higher dry densities after compaction.In addition,the prediction equations for the particle breakage rate and CA ratio in the Bailey method were proposed to estimate the compaction performance of gravelly soil preliminarily.The results further revealed the compaction mechanism of different gravelly soils and can provide reference for subgrade filling construction.

Failure mechanism and infrared radiation characteristic of hard siltstone induced by stratification effect

The deformation in sedimentary rock induced by train loads has potential threat to the safe operation of tunnels. This study investigated the influence of stratification structure on the infrared radiation and temporal damage mechanism of hard siltstone. The uniaxial compression tests, coupled with acoustic emission(AE) and infrared radiation temperature(IRT) were conducted on siltstones with different stratification effects. The results revealed that the stratigraphic structure significantly affects the stress-strain response and strength degradation characteristics. The mechanical parameters exhibit anisotropy characteristics, and the stratification effect exhibits a negative correlation with the cracking stress and peak stress. The failure modes caused by the stratification effect show remarkable anisotropic features, including splitting failure(Ⅰ: 0°-22.50°, Ⅱ: 90°), composite failure(45°), and shearing failure(67.50°). The AE temporal sequences demonstrate a stepwise response characteristic to the loading stress level. The AE intensity indicates that the stress sensitivity of shearing failure and composite failure is generally greater than that of splitting failure. The IRT field has spatiotemporal migration and progressive dissimilation with stress loading and its dissimilation degree increases under higher stress levels. The stronger the stratification effect, the greater the dissimilation degree of the IRT field. The abnormal characteristic points of average infrared radiation temperature(AIRT) variance at local stress drop and peak stress can be used as early and late precursors to identify fracture instability. Theoretical analysis shows that the competitive relationship between compaction strengthening and fracturing damage intensifies the dissimilation of the infrared thermal field for an increasing stress level. The present study provides a theoretical reference for disaster warnings in hard sedimentary rock mass.

Free radicals trigger the closure of open pores in lignin-derived hard carbons toward improved sodium-storage capacity

The chemical activation of various precursors is effective for creating additional closed pores in hard carbons for sodium storage.However,the formation mechanism of closed pores under the influence of pore-forming agents is not well understood.Herein,an effective chemical activation followed by a high-temperature self-healing strategy is employed to generate interconnected closed pores in lignin-derived hard carbon(HCs).By systematic experimental design combined with electron paramagnetic res-onance spectroscopy,it can be found that the content of free radicals in the carbon matrix influences the closure of open pores at high temperatures.Excessively high activation temperature(>700 C)leads to a low free radical concentration,making it difficult to achieve self-healing of open pores at high tempera-tures.By activation at 700°C,a balance between pore making and self-healing is achieved in the final hard carbon.A large number of free radicals triggers rapid growth and aggregation of carbon microcrys-tals,blocking pre-formed open micropores and creating additional interconnected closed pores in as-obtained hard carbons.As a result,the optimized carbon anode(LK-700-1300)delivers a high reversible capacity of 330.8 mA h g^(-1) at 0.03 A g^(-1),which is an increase of 86 mA h g^(-1) compared to the pristine lignin-derived carbon anode(L-700-1300),and exhibits a good rate performance(202.1 mA h g^(-1) at 1 A g^(-1)).This work provides a universal and effective guidance for tuning closed pores of hard carbons from otherprecursors.

Influence of heat input on microhardness and microstructure across the welding interface between stainless steel and low alloy steel

The welding interface is crucial to the service safety of dissimilar metal weld(DMW)joints between stainless steel(SS)and low alloy(LA)steel.Different status of welding interfaces was prepared by cladding SS consumables to LA steel substrates with different heat inputs via tungsten inert gas arc welding(TIG),followed by a series of microstructural characterizations and hardness tests.Results showed that a hardening and transition layer(TL)would be generated along the welding interface,and the width and hardening degree of the TL would increase with the heat input.Meanwhile,heavy load hardness tests showed that highly severe inhomogeneous plastic deformation and the microcrack would be generated in the interfacial region and the welding interface respectively in the highest heat input sample(1.03 kJ/mm).These results indicate that the increase in heat input would deteriorate the bonding performance of DMW joints.Further microstructural observations showed that the higher hardening degree of the highest heat input sample was mainly attributed to the stronger grain boundary,solution,and dislocation strengthening effects.

Physical and numerical investigations of target stratum selection for ground hydraulic fracturing of multiple hard roofs

Ground hydraulic fracturing plays a crucial role in controlling the far-field hard roof,making it imperative to identify the most suitable target stratum for effective control.Physical experiments are conducted based on engineering properties to simulate the gradual collapse of the roof during longwall top coal caving(LTCC).A numerical model is established using the material point method(MPM)and the strain-softening damage constitutive model according to the structure of the physical model.Numerical simulations are conducted to analyze the LTCC process under different hard roofs for ground hydraulic fracturing.The results show that ground hydraulic fracturing releases the energy and stress of the target stratum,resulting in a substantial lag in the fracturing of the overburden before collapse occurs in the hydraulic fracturing stratum.Ground hydraulic fracturing of a low hard roof reduces the lag effect of hydraulic fractures,dissipates the energy consumed by the fracture of the hard roof,and reduces the abutment stress.Therefore,it is advisable to prioritize the selection of the lower hard roof as the target stratum.

Sulfur doped iron-nitrogen-hard carbon nanosheets as efficient and robust noble metal-free catalysts for oxygen reduction reaction in PEMFC

Transition metal-nitrogen-carbon(M-N-C)as a promising substitute for the conventional noble metalbased catalyst still suffers from low activity and durability for oxygen reduction reaction(ORR)in proton exchange membrane fuel cells(PEMFCs).To tackle the issue,herein,a new type of sulfur-doped ironnitrogen-hard carbon(S-Fe-N-HC)nanosheets with high activity and durability in acid media were developed by using a newly synthesized precursor of amide-based polymer with Fe ions based on copolymerizing two monomers of 2,5-thiophene dicarboxylic acid(TDA)as S source and 1,8-diaminonaphthalene(DAN)as N source via an amination reaction.The as-synthesized S-Fe-N-HC features highly dispersed atomic Fe Nxmoieties embedded into rich thiophene-S doped hard carbon nanosheets filled with highly twisted graphite-like microcrystals,which is distinguished from the majority of M-N-C with soft or graphitic carbon structures.These unique characteristics endow S-Fe-N-HC with high ORR activity and outstanding durability in 0.5 M H_(2)SO_(4).Its initial half-wave potential is 0.80 V and the corresponding loss is only 21 m V after 30,000 cycles.Meanwhile,its practical PEMFC performance is a maximum power output of 628.0 mW cm^(-2)and a slight power density loss is 83.0 m W cm^(-2)after 200-cycle practical operation.Additionally,theoretical calculation shows that the activity of Fe Nxmoieties on ORR can be further enhanced by sulfur doping at meta-site near FeN_(4)C.These results evidently demonstrate that the dual effect of hard carbon substrate and S doping derived from the precursor platform of amid-polymers can effectively enhance the activity and durability of Fe-N-C catalysts,providing a new guidance for developing advanced M-N-C catalysts for ORR.

A novel nano-grade organosilicon polymer:Improving airtightness of compressed air energy storage in hard rock formations

Enhancing cavern sealing is crucial for improving the efficiency of compressed air energy storage(CAES)in hard rock formations.This study introduced a novel approach using a nano-grade organosilicon polymer(NOSP)as a sealant,coupled with an air seepage evaluation model that incorporates Knudsen diffusion.Moreover,the initial coating application methods were outlined,and the advantages of using NOSP compared to other sealing materials,particularly regarding cost and construction techniques,were also examined and discussed.Experimental results indicated a significant reduction in permeability of rock specimens coated with a 7–10μm thick NOSP layer.Specifically,under a 0.5 MPa pulse pressure,the permeability decreased to less than 1 n D,and under a 4 MPa pulse pressure,it ranged between4.5×10^(-6)–5.5×10^(-6)m D,marking a 75%–80%decrease in granite permeability.The sealing efficacy of NOSP surpasses concrete and is comparable to rubber materials.The optimal viscosity for application lies between 95 and 105 KU,and the coating thickness should ideally range from 7 to 10μm,applied to substrates with less than 3%porosity.This study provides new insights into air transport and sealing mechanisms at the pore level,proposing NOSP as a cost-effective and simplified solution for CAES applications.

Hard-carbon hybrid Li-ion/metal anode enabled by preferred mesoporous uniform lithium growth mechanism

To achieve high energy density in lithium batteries,the construction of lithium-ion/metal hybrid anodes is a promising strategy.In particular,because of the anisotropy of graphite,hybrid anode formed by graphite/Li metal has low transport kinetics and is easy to causes the growth of lithium dendrites and accumulation of dead Li,which seriously affects the cycle life of batteries and even causes safety problems.Here,by comparing graphite with two types of hard carbon,it was found that hybrid anode formed by hard carbon and lithium metal,possessing more disordered mesoporous structure and lithophilic groups,presents better performance.Results indicate that the mesoporous structure provides abundant active site and storage space for dead lithium.With the synergistic effect of this structure and lithophilic functional groups(–COOH),the reversibility of hard carbon/lithium metal hybrid anode is maintained,promoting uniform deposition of lithium metal and alleviating formation of lithium dendrites.The hybrid anode maintains a 99.5%Coulombic efficiency(CE)after 260 cycles at a specific capacity of 500 m Ah/g.This work provides new insights into the hybrid anodes formed by carbon-based materials and lithium metal with high specific energy and fast charging ability.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.

The Violent Redemption Theme in A Good Man is Hard to Find

Flannery O’Connor is one of the representative figures of American Southern writers.Being recognized as the most outstanding writer of the American South after Faulkner,she has great influence in the literary world.Her works are always shrouded in a strange and grotesque atmosphere and full of death as well as religious metaphors.The protagonists are a series of American Southern freaks struggling with the crisis of spiritual belief.The protagonists of her novel A Good Man is Hard to Find are a hypocritical believer in the world of sinners and a lost man suffering in the midst of real sin,thus O’Connor uses the highest form of violence-death to bring ultimate redemption to them.In people’s conception,violence and redemption are often opposite to each other,but O’Connor uses bloody and violent plots to explore the theme of religious salvation,integrating and unifying the two contrary concepts to form her unique and profound violent redemption writing.

Stability prediction of hard rock pillar using support vector machine optimized by three metaheuristic algorithms

Hard rock pillar is one of the important structures in engineering design and excavation in underground mines.Accurate and convenient prediction of pillar stability is of great significance for underground space safety.This paper aims to develop hybrid support vector machine(SVM)models improved by three metaheuristic algorithms known as grey wolf optimizer(GWO),whale optimization algorithm(WOA)and sparrow search algorithm(SSA)for predicting the hard rock pillar stability.An integrated dataset containing 306 hard rock pillars was established to generate hybrid SVM models.Five parameters including pillar height,pillar width,ratio of pillar width to height,uniaxial compressive strength and pillar stress were set as input parameters.Two global indices,three local indices and the receiver operating characteristic(ROC)curve with the area under the ROC curve(AUC)were utilized to evaluate all hybrid models’performance.The results confirmed that the SSA-SVM model is the best prediction model with the highest values of all global indices and local indices.Nevertheless,the performance of the SSASVM model for predicting the unstable pillar(AUC:0.899)is not as good as those for stable(AUC:0.975)and failed pillars(AUC:0.990).To verify the effectiveness of the proposed models,5 field cases were investigated in a metal mine and other 5 cases were collected from several published works.The validation results indicated that the SSA-SVM model obtained a considerable accuracy,which means that the combination of SVM and metaheuristic algorithms is a feasible approach to predict the pillar stability.

Low-Temperature Carbonized Nitrogen-Doped Hard Carbon Nanofiber Toward High-Performance Sodium-Ion Capacitors

Carbon nanofiber(CNF)was widely utilized in the field of electrochemical energy storage due to its superiority of conductivity and mechanics.However,CNF was generally prepared at relatively high temperature.Herein,nitrogen-doped hard carbon nanofibers(NHCNFs)were prepared by a lowtemperature carbonization treatment assisted with electrospinning technology.Density functional theory analysis elucidates the incorporation of nitrogen heteroatoms with various chemical states into carbon matrix would significantly alter the total electronic configurations,leading to the robust adsorption and efficient diffusion of Na atoms on electrode interface.The obtained material carbonized at 600°C(NHCNF-600)presented a reversible specific capacity of 191.0 mAh g^(−1)and no capacity decay after 200 cycles at 1 A g^(−1).It was found that the sodium-intercalated degree had a correlation with the electrochemical impedance.A sodium-intercalated potential of 0.2 V was adopted to lower the electrochemical impedance.The constructed sodium-ion capacitor with activated carbon cathode and presodiated NHCNF-600 anode can present an energy power density of 82.1 Wh kg^(−1)and a power density of 7.0 kW kg^(−1).

Vanadium-modified hard carbon spheres with sufficient pseudographitic domains as high-performance anode for sodium-ion batteries

Hard carbons are promising anode materials for sodium-ion batteries.To meet practical requirements,searching for durable and conductive carbon with a stable interface is of great importance.Here,we prepare a series of vanadiummodified hard carbon submicrospheres by using hydrothermal carbonization followed by high-temperature pyrolysis.Significantly,the introduction of vanadium can facilitate the nucleation and uniform growth of carbon spheres and generate abundant V-O-C interface bonds,thus optimizing the reaction kinetic.Meanwhile,the optimized hard carbon spheres modified by vanadium carbide,with sufficient pseudographitic domains,provide more active sites for Na ion migration and storage.As a result,the HC/VC-1300 electrode exhibits excellent Na storage performance,including a high capacity of 420 mAh g^(-1) at 50mA g^(-1) and good rate capability at 1 A g^(-1).This study proposes a new strategy for the synthesis of hard carbon spheres with high tap density and emphasizes the key role of pseudographitic structure for Na storage and interface stabilization.

Multiple omics datasets reveal significant physical and physiological dormancy in alfalfa hard seeds identified by multispectral imaging analysis

Physical dormancy(PY) commonly present in the seeds of higher plants is believed to be responsible for the germination failure by impermeable seed coat in hard seeds of legume species, instead of physiological dormancy(PD). In this study, a non-destructive approach involving multispectral imaging was used to successfully identify hard seeds from non-hard seeds in Medicago sativa, with accuracy as high as96.8%–99.0%. We further adopted multiple-omics strategies to investigate the differences of physiology,metabolomics, methylomics, and transcriptomics in alfalfa hard seeds, with non-hard seeds as control.The hard seeds showed dramatically increased antioxidants and 125 metabolites of significant differences in non-targeted metabolomics analysis, which are enriched in the biosynthesis pathways of flavonoids, lipids and hormones, especially with significantly higher ABA, a hormone known to induce dormancy. In our transcriptomics results, the enrichment pathway of “response to abscisic acid” of differential expressed genes(DEG) supported the key role of ABA in metabolomics results. The methylome analysis identified 54,899, 46,216 and 54,452 differential methylation regions for contexts of CpG, CHG and CHH, and 344 DEGs might be regulated by hypermethylation and hypomethylation of promoter and exon regions, including four ABA-and JA-responsive genes. Among 8% hard seeds in seed lots,24.5% still did not germinate after scarifying seed coat, and were named as non-PY hard seeds.Compared to hard seeds, significantly higher contents of ABA/IAA and ABA/JA were identified in nonPY hard seeds, which indicated the potential presence of PD. In summary, the significantly changed metabolites, gene expressions, and methylations all suggested involvement of ABA responses in hard seeds, and germination failure of alfalfa hard seeds was caused by combinational dormancy(PY + PD),rather than PY alone.

Engineering homotype heterojunctions in hard carbon to induce stable solid electrolyte interfaces for sodium-ion batteries

Developing effective strategies to improve the initial Coulombic efficiency(ICE)and cycling stability of hard carbon(HC)anodes for sodium-ion batteries is the key to promoting the commercial application of HC.In this paper,homotype heterojunctions are designed on HC to induce the generation of stable solid electrolyte interfaces,which can effectively increase the ICE of HC from 64.7%to 81.1%.The results show that using a simple surface engineering strategy to construct a homotypic amorphous Al_(2)O_(3) layer on the HC could shield the active sites,and further inhibit electrolyte decomposition and side effects occurrence.Particularly,due to the suppression of continuous decomposition of NaPF 6 in ester-based electrolytes,the accumulation of NaF could be reduced,leading to the formation of thinner and denser solid electrolyte interface films and a decrease in the interface resistance.The HC anode can not only improve the ICE but elevate its sodium storage performance based on this homotype heterojunction composed of HC and Al_(2)O_(3).The optimized HC anode exhibits an outstanding reversible capacity of 321.5mAhg^(−1) at 50mAg^(−1).The cycling stability is also improved effectively,and the capacity retention rate is 86.9%after 2000 cycles at 1Ag^(−1) while that of the untreated HC is only 52.6%.More importantly,the improved sodium storage behaviors are explained by electrochemical kinetic analysis.

Spalling failure of deep hard rock caverns

Spalling is a typical brittle failure phenomenon of hard rock in deep caverns under high geostress.In this study,key issues are systematically studied concerning the spalling failure of deep hard rock caverns.First,the prismatic rock specimens with small thicknesses(i.e.width×thickness×height:20 mm×50 mm×100 mm)are employed in our tests which not only successfully simulate the spalling failure of hard rock in the laboratory but also obtain a reasonable spalling strength similar to that of the rock mass.Then,a series of spalling experiments is carried out to investigate the mechanism of spalling failure of deep hard rock caverns.Our results show that the intermediate principal stress,weak dynamic disturbances,and rock microstructure have significant effects on the spalling failure.The spalling strength is approximately(0.3–0.8)UCS,where UCS is the uniaxial compressive strength of the cylindrical rock sample with a diameter of around 50 mm.The spalling strength increases first and then decreases with increasing intermediate principal stress.Moreover,an empirical spalling strength criterion and a numerical method of spalling failure are proposed.This numerical method can not only simulate the spalling failure zone formed by tangential compressive stress concentration after excavation under different intermediate principal stresses,but also successfully simulate the failure transition from tensile mode to shear mode associated with confinement change in deep hard rock caverns.Furthermore,an acoustic emission-based early warning method using neural network is proposed to predict the spalling failure.Finally,a technical roadmap for preventing and controlling spalling failure of deep hard rock caverns is presented after summarizing the successful experiences in a typical engineering case.

Relationship between Hardness and Deformation during Cold Rolling Process of Complex Profles

The hardening on surface of complex profles such as thread and spline manufactured by cold rolling can efectively improve the mechanical properties and surface quality of rolled parts. The distribution of hardness in superfcial layer is closely related to the deformation by rolling. To establish the suitable correlation model for describing the relationship between strain and hardness during cold rolling forming process of complex profles is helpful to the optimization of rolling parameters and improvement of rolling process. In this study, a physical analog experiment refecting the uneven deformation during complex-profle rolling process has been extracted and designed, and then the large date set (more than 400 data points) of training samples refecting the local deformation characteristics of complexprofle rolling have been obtained. Several types of polynomials and power functions were adopted in regression analysis, and the regression correlation models of 45# steel were evaluated by the single-pass and multi-pass physical analog experiments and the complex-profle rolling experiment. The results indicated that the predicting accuracy of polynomial regression model is better in the strain range (i.e., ε < 1.2) of training samples, and the correlation relationship between strain and hardness out strain range (i.e., ε > 1.2) of training samples can be well described by power regression model;so the correlation relationship between strain and hardness during complex-profle rolling process of 45# steel can be characterized by a segmented function such as third-order polynomial in the range ε < 1.2 and power function with a ftting constant in the range ε > 1.2;and the predicting error of the regression model by segmented function is less than 10%.