At the initial rolling temperature of 250 to 400 ℃, AZ31B magnesium alloy sheets were hot rolled by four different rolling routes. Microstructures and mechanical properties of the hot-rolled magnesium alloy sheets we...At the initial rolling temperature of 250 to 400 ℃, AZ31B magnesium alloy sheets were hot rolled by four different rolling routes. Microstructures and mechanical properties of the hot-rolled magnesium alloy sheets were analyzed by optical microscope and tensile tests respectively. Based on the Hall-Petch relation, considering the average grain size and grain size distribution, the nonlinear fitting analysis between the tensile strength and average grain size was carried on, and then the prediction model of tensile strength of hot-rolled AZ31B magnesium alloy sheet was established. The results indicate that, by rolling with multi-pass cross rolling, uniform, fine and equiaxial grain microstructures can be produced, the anisotropy of hot-rolled magnesium sheet can also be effectively weakened. Strong correlation was observed between the average grain size and tensile property of the hot-rolled magnesium alloy sheet. Grain size distribution coefficient d(CV) was introduced to reflect the dispersion degree about a set of grain size data, and then the Hall-Petch relation was perfected. Ultimately, the prediction accuracy of tensile strength of multi-pass hot-rolled AZ31B magnesium alloy was improved, and the prediction of tensile property can be performed by the model.展开更多
This paper discusses the single-machine rescheduling problem with efficiency and stability as criteria, where more than one disruption arises in large-scale dynamic circumstances. Partial rescheduling (PR) strategy is...This paper discusses the single-machine rescheduling problem with efficiency and stability as criteria, where more than one disruption arises in large-scale dynamic circumstances. Partial rescheduling (PR) strategy is adopted after each disruption and a rolling mechanism is driven by events in response to disruptions. Two kinds of objective functions are designed respectively for PR sub-problem involving in the interim and the terminal of unfinished jobs. The analytical result demonstrates that each local objective is consistent with the global one. Extensive computational experiment was performed and the computational results show that the rolling PR strategy with dual objectives can greatly improve schedule stability with little sacrifice in efficiency and provide a reasonable trade-off between solution quality and computational efforts.展开更多
Deep rolling is one of the most widely used surface mechanical treatments among several methods used to generate compressive residual stress. This process is usually used for axisymmetric components and can lead to im...Deep rolling is one of the most widely used surface mechanical treatments among several methods used to generate compressive residual stress. This process is usually used for axisymmetric components and can lead to improvements of the surface quality, dimensional accuracy, and mechanical properties. In this study, we deduced the appropriate deep rolling parameters for Al-3vol%Si C nanocomposite samples using roughness and microhardness measurements. The nanocomposite samples were fabricated using a combination of mechanical milling, cold pressing, and hot extrusion techniques. Density measurements indicated acceptable densification of the samples, with no porosity. The results of tensile tests showed that the samples are sufficiently strong for the deep rolling process and also indicated near 50% improvement of tensile strength after incorporating Si C nanoparticle reinforcements. The effects of some important rolling parameters, including the penetration depth, rotation speed, feed rate, and the number of passes, on the surface quality and microhardness were also investigated. The results demonstrated that decreasing the feed rate and increasing the number of passes can lead to greater surface hardness and lower surface roughness.展开更多
Lithium(Li)is a promising candidate for nextgeneration battery anode due to its high theoretical specific capacity and low reduction potential.However,safety issues derived from the uncontrolled growth of Li dendrite ...Lithium(Li)is a promising candidate for nextgeneration battery anode due to its high theoretical specific capacity and low reduction potential.However,safety issues derived from the uncontrolled growth of Li dendrite and huge volume change of Li hinder its practical application.C onstructing dendrite-free composite Li anodes can significantly alleviate the above problems.Copper(Cu)-based materials have bee n widely used as substrates of the composite electrodes due to their chemical stability,excellent conductivity,and good mechanical strength.Copper/lithium(Cu/Li)composite anodes significantly regulate the local current density and decrease Li nucleation overp otential,realizing the uniform and dendrite-free Li deposition.In this review,Cu/Li composite methods including electrodeposition,melting infusion,and mechanical rolling are systematically summarized and discussed.Additionally,design strategies of Cu-based current collectors for high performance Cu/Li composite anodes are illustrated.General challenges and future development for Cu/Li composite anodes are presented and postulated.We hope that this review can provide a comprehensive understanding of Cu/Li composite methods of the latest development of Li metal anode and stimulate more research in the future.展开更多
Synthesis of tubular nanomaterials has become a prolific area of investigation due to their wide range of applications.A facile solution-based method has been designed to fabricate uniform Bi_(2)S_(3)nanotubes with av...Synthesis of tubular nanomaterials has become a prolific area of investigation due to their wide range of applications.A facile solution-based method has been designed to fabricate uniform Bi_(2)S_(3)nanotubes with average size of 20 nm×160 nm using only bismuth nitrate(Bi(NO_(3))_(3)·5H_(2)O)and sulfur powder(S)as the reactants and octadecylamine(ODA)as the solvent.Powder X-ray diffraction(XRD),transmission electron microscopy(TEM),high-resolution TEM(HRTEM),and energy dispersive spectroscopy(EDX)experiments were employed to characterize the resulting Bi_(2)S_(3)nanotubes and the classic rolling mechanism was applied to explain their formation process.展开更多
Rolling contact fatigue is the main failure mechanism of tapered roller bearings. This study investigated the fatigue mechanism of rollers in a tapered roller bearing that failed in a run-to-failure test. Roller micro...Rolling contact fatigue is the main failure mechanism of tapered roller bearings. This study investigated the fatigue mechanism of rollers in a tapered roller bearing that failed in a run-to-failure test. Roller microstructure and crack morphology were investigated through scanning electron microscopy. A microhardness test was performed to investigate the strain hardening of the roller material induced by rolling contact fatigue. Results showed that microcavities and holes are important influential factors of crack initiation and propagation. Crack propagation angle affects crack morphology and propagation mode. Material strain hardening accelerates crack growth. Furthermore, roller misalignment causes uneven hardenability and severe damage to roller ends.展开更多
With recent relevant publications on stochastic motion robots in Nature, Science, and other journals, research on such robots has gained increasing attention. However, theoretical and applied research on stochastic mo...With recent relevant publications on stochastic motion robots in Nature, Science, and other journals, research on such robots has gained increasing attention. However, theoretical and applied research on stochastic motion in the field of robotics and mechanisms face many challenges due to the uncertainty of stochastic motion. Currently, a large gap remains in the research of stochastic motion mechanism. In this study, a novel mechanism that can conduct probabilistic rolling is proposed to reach a designated position and achieve overlying movement over a particular area. The mechanism consists of a regular tetrahedron frame, a central node, and four connecting linear actuators. According to mobility and kinematic analyses, the mechanism can implement probabilistic rolling. Each rolling gait has three probable rolling directions, and the mechanism rolls in one of the three directions in probability. A kinematic simulation is conducted, and a control method is proposed on the basis of the moving path analysis. Furthermore, the mathematical principle of probabilistic rolling is revealed in terms of probability theory and statistics. Lastly, a prototype is fabricated. To achieve the rolling function, the design of the linear actuators is improved, and the extension ratio is increased from 0.58 to 1.13. Then, tests are conducted. In a 4 m2 test site, the mechanism makes 11 moves to reach the target position and covers 29.25% of the site.展开更多
Ultrafine-grain and high-strength Mg-SLi-1Al sheets were prepared by accumulative roll bonding (ARB) process. Evolution of microstructure and mechanical properties of ARB-processed Mg-5Li-1Al sheets was investigated...Ultrafine-grain and high-strength Mg-SLi-1Al sheets were prepared by accumulative roll bonding (ARB) process. Evolution of microstructure and mechanical properties of ARB-processed Mg-5Li-1Al sheets was investigated. Results show that, during ARB process, the evolution of deformation mechanism oft Mg-5Li-1Al alloy is as follows: twinning deformation, shear deformation, forming macro shear zone, and finally dynamic recrystallization (DRX). The grain refining mechanism changes from twin DRX to rotation DRX. With the increase in ARB cycles, strength of the Mg-5Li-1Al sheets is enhanced, whilst elongation varies slightly. With the increase in rolling cycles, anisotropy of mechanical properties decreases. It is conclusive that strain hardening and grain refinement dominate the strengthening mechanism of Mg-5Li-1Al alloy.展开更多
In the present work, an ultrahigh strength bearing steel(AISI 52100) was subjected to surface mechanical rolling treatment(SMRT) at room temperature. Microstructural observations showed that martensitic laths, twi...In the present work, an ultrahigh strength bearing steel(AISI 52100) was subjected to surface mechanical rolling treatment(SMRT) at room temperature. Microstructural observations showed that martensitic laths, twins and cementite particles in the initial microstructure underwent distinct plastic strains and were gradually refined into nanostructures. Consequently, a gradient nanostructured(GNS) surface layer with a mean grain size of -24 nm at the top surface was obtained on the bearing steel, resulting in an increment of -20% in the surface hardness. Analyses based on microstructural evolution, phase constitution and in-depth hardness distribution revealed a mechanically induced formation mechanism of the GNS surface layer. The multiple surface severe plastic deformation under fine lubrication and cooling during SMRT contributed to the formation of a thick hardened surface layer on the bearing steel.展开更多
Welded joints are usually characterized by microstructural and compositional inhomogeneities, which may significantly degrade their fatigue properties and result in unpredictable failures. The present work demonstrate...Welded joints are usually characterized by microstructural and compositional inhomogeneities, which may significantly degrade their fatigue properties and result in unpredictable failures. The present work demonstrates a novel and simple method to effectively optimize the microstructure in the surface layer and promote the fatigue properties of welded specimens. By a recently developed approach—surface mechanical rolling treatment(SMRT), a gradient nanostructured surface layer is formed on welded S355 J2 W steel specimens. The mean grain size is refined to nanometer scale, and the hardness is significantly enhanced in the SMRT surface layer. Independent of the initially inhomogeneous microstructure and hardness distributions, the microstructure and hardness distributions in the surface layers are comparable on different zones of a welded specimen after SMRT with the same procedure. Consequently, fatigue property of the SMRT specimens is significantly enhanced relative to that of the as-welded specimens within the high cycle fatigue regime.展开更多
Sheet samples of Mg-8Li,Mg-8Li-3Al,Mg-8Li-3AlSi and Mg-8Li-5AlSi alloys were obtained by hot rolling.Optical microscope,microhardness tester,nanoindentor,X-ray diffractometer and electrochemical analyzer were adopted ...Sheet samples of Mg-8Li,Mg-8Li-3Al,Mg-8Li-3AlSi and Mg-8Li-5AlSi alloys were obtained by hot rolling.Optical microscope,microhardness tester,nanoindentor,X-ray diffractometer and electrochemical analyzer were adopted to investigate the microstructures,micro-mechanical properties and corrosion resistance.Roller was preheated to 150°C before rolling process,and rolling reduction designed was about20% per pass with a total rolling reduction of 84%.The rolled plates were annealed at 200°C for 120 min.The tensile tests were performed at room temperature.Experimental results showed that both the strength and corrosion resistance of theα+βdual-phase of Mg-Li alloy were significantly improved with adding Al-Si elements.The strength enhancement was attributed to the solid solution of Al into theα-Mg matrix and into theβ-Li matrix as well as to the precipitation strengthening of Mg2 Si particles.Besides,the dendrite grains ofα-Mg transformed to equiaxed ones with addition of Al into alloy Mg-Li.展开更多
Different samples of TRIP (transformation induced plasticity) steel obtained by two different hot rolling schedules are investigated by using a SEM (scanning electron microscope). The microstructure is characteriz...Different samples of TRIP (transformation induced plasticity) steel obtained by two different hot rolling schedules are investigated by using a SEM (scanning electron microscope). The microstructure is characterized by using an OM (optical microscope) for phase distribution and by EBSD (electron backscatter diffraction) for texture and phase mapping. ODF (orientation distribution function) graphs are used to investigate the effect of recrystallization behavior of the hot-deformed austenite on phase transformation during the controlled cooling process. The mechanical behavior is interpreted in terms of the strength of both hard and soft phases, in combination with the quantity, loca- tion and transformation kinetics of the mechanically induced martensite (TRIP effect). The results show that more austenite grains exist in the steels obtained at finishing rolling temperature (FRT) of 750 ℃, which inherited the de- formation structure after the hot-rolling process. The instantaneous n value (ni) of those steels is kept high during a large range of strain before failure, while the tensile strength and total elongation of the steels with respect to the dif- ferent finishing rolling temperatures do not show any significant differences.展开更多
基金Funded by the National Natural Science Foundation of China(No.U1510131)the Key Research and Development Projects of Shanxi Province(No.201603D121010)+1 种基金the Science and Technology Project of Jincheng City(No.20155010)the Project of Young Scholar of Shanxi Province and the Leading Talent Project of Innovative Entrepreneurial Team of Jiangsu Province and the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi(TYAL)
文摘At the initial rolling temperature of 250 to 400 ℃, AZ31B magnesium alloy sheets were hot rolled by four different rolling routes. Microstructures and mechanical properties of the hot-rolled magnesium alloy sheets were analyzed by optical microscope and tensile tests respectively. Based on the Hall-Petch relation, considering the average grain size and grain size distribution, the nonlinear fitting analysis between the tensile strength and average grain size was carried on, and then the prediction model of tensile strength of hot-rolled AZ31B magnesium alloy sheet was established. The results indicate that, by rolling with multi-pass cross rolling, uniform, fine and equiaxial grain microstructures can be produced, the anisotropy of hot-rolled magnesium sheet can also be effectively weakened. Strong correlation was observed between the average grain size and tensile property of the hot-rolled magnesium alloy sheet. Grain size distribution coefficient d(CV) was introduced to reflect the dispersion degree about a set of grain size data, and then the Hall-Petch relation was perfected. Ultimately, the prediction accuracy of tensile strength of multi-pass hot-rolled AZ31B magnesium alloy was improved, and the prediction of tensile property can be performed by the model.
基金Supported by National Natural Science Foundation of China (60274013, 60474002)Science Research Foundation of Shandong University at Weihai (XZ2005001)
文摘This paper discusses the single-machine rescheduling problem with efficiency and stability as criteria, where more than one disruption arises in large-scale dynamic circumstances. Partial rescheduling (PR) strategy is adopted after each disruption and a rolling mechanism is driven by events in response to disruptions. Two kinds of objective functions are designed respectively for PR sub-problem involving in the interim and the terminal of unfinished jobs. The analytical result demonstrates that each local objective is consistent with the global one. Extensive computational experiment was performed and the computational results show that the rolling PR strategy with dual objectives can greatly improve schedule stability with little sacrifice in efficiency and provide a reasonable trade-off between solution quality and computational efforts.
文摘Deep rolling is one of the most widely used surface mechanical treatments among several methods used to generate compressive residual stress. This process is usually used for axisymmetric components and can lead to improvements of the surface quality, dimensional accuracy, and mechanical properties. In this study, we deduced the appropriate deep rolling parameters for Al-3vol%Si C nanocomposite samples using roughness and microhardness measurements. The nanocomposite samples were fabricated using a combination of mechanical milling, cold pressing, and hot extrusion techniques. Density measurements indicated acceptable densification of the samples, with no porosity. The results of tensile tests showed that the samples are sufficiently strong for the deep rolling process and also indicated near 50% improvement of tensile strength after incorporating Si C nanoparticle reinforcements. The effects of some important rolling parameters, including the penetration depth, rotation speed, feed rate, and the number of passes, on the surface quality and microhardness were also investigated. The results demonstrated that decreasing the feed rate and increasing the number of passes can lead to greater surface hardness and lower surface roughness.
基金supported by the National Key Research and Development Program of China(No.2021YFB2500200)the National Natural Science Foundation of China(No.52302243)China Postdoctoral Science Foundation(Nos.2022M721029 and 2022M721030)。
文摘Lithium(Li)is a promising candidate for nextgeneration battery anode due to its high theoretical specific capacity and low reduction potential.However,safety issues derived from the uncontrolled growth of Li dendrite and huge volume change of Li hinder its practical application.C onstructing dendrite-free composite Li anodes can significantly alleviate the above problems.Copper(Cu)-based materials have bee n widely used as substrates of the composite electrodes due to their chemical stability,excellent conductivity,and good mechanical strength.Copper/lithium(Cu/Li)composite anodes significantly regulate the local current density and decrease Li nucleation overp otential,realizing the uniform and dendrite-free Li deposition.In this review,Cu/Li composite methods including electrodeposition,melting infusion,and mechanical rolling are systematically summarized and discussed.Additionally,design strategies of Cu-based current collectors for high performance Cu/Li composite anodes are illustrated.General challenges and future development for Cu/Li composite anodes are presented and postulated.We hope that this review can provide a comprehensive understanding of Cu/Li composite methods of the latest development of Li metal anode and stimulate more research in the future.
基金National Science Foundation of China(NSFC)(90606006)the State Key Project of Fundamental Research for Nanoscience and Nanotechnology(2006CB932300)the Key Grant Project of Chinese Ministry of Education(No.306020)and the National Undergraduate Innovation Training Project.
文摘Synthesis of tubular nanomaterials has become a prolific area of investigation due to their wide range of applications.A facile solution-based method has been designed to fabricate uniform Bi_(2)S_(3)nanotubes with average size of 20 nm×160 nm using only bismuth nitrate(Bi(NO_(3))_(3)·5H_(2)O)and sulfur powder(S)as the reactants and octadecylamine(ODA)as the solvent.Powder X-ray diffraction(XRD),transmission electron microscopy(TEM),high-resolution TEM(HRTEM),and energy dispersive spectroscopy(EDX)experiments were employed to characterize the resulting Bi_(2)S_(3)nanotubes and the classic rolling mechanism was applied to explain their formation process.
基金supported by National Natural Science Foundation of China(Grant No.51421004)Key Project supported by National Natural Science Foundation of China(Grant No.61633001)
文摘Rolling contact fatigue is the main failure mechanism of tapered roller bearings. This study investigated the fatigue mechanism of rollers in a tapered roller bearing that failed in a run-to-failure test. Roller microstructure and crack morphology were investigated through scanning electron microscopy. A microhardness test was performed to investigate the strain hardening of the roller material induced by rolling contact fatigue. Results showed that microcavities and holes are important influential factors of crack initiation and propagation. Crack propagation angle affects crack morphology and propagation mode. Material strain hardening accelerates crack growth. Furthermore, roller misalignment causes uneven hardenability and severe damage to roller ends.
基金This work was supported by the Fundamental Research Funds for the Central Universities,China(Grant No.2019JBM046).
文摘With recent relevant publications on stochastic motion robots in Nature, Science, and other journals, research on such robots has gained increasing attention. However, theoretical and applied research on stochastic motion in the field of robotics and mechanisms face many challenges due to the uncertainty of stochastic motion. Currently, a large gap remains in the research of stochastic motion mechanism. In this study, a novel mechanism that can conduct probabilistic rolling is proposed to reach a designated position and achieve overlying movement over a particular area. The mechanism consists of a regular tetrahedron frame, a central node, and four connecting linear actuators. According to mobility and kinematic analyses, the mechanism can implement probabilistic rolling. Each rolling gait has three probable rolling directions, and the mechanism rolls in one of the three directions in probability. A kinematic simulation is conducted, and a control method is proposed on the basis of the moving path analysis. Furthermore, the mathematical principle of probabilistic rolling is revealed in terms of probability theory and statistics. Lastly, a prototype is fabricated. To achieve the rolling function, the design of the linear actuators is improved, and the extension ratio is increased from 0.58 to 1.13. Then, tests are conducted. In a 4 m2 test site, the mechanism makes 11 moves to reach the target position and covers 29.25% of the site.
基金supported by the National Natural Science Foundation of China (51671063)Research Fund for the Doctoral Program of Higher Education (20132304110006)+1 种基金the Fundamental Research Funds for the Central Universities (HEUCF20161016)Harbin City Application Technology Research and Development Project (2015AE4AE005, 2015RQXXJ001, 2016AB2AG013)
文摘Ultrafine-grain and high-strength Mg-SLi-1Al sheets were prepared by accumulative roll bonding (ARB) process. Evolution of microstructure and mechanical properties of ARB-processed Mg-5Li-1Al sheets was investigated. Results show that, during ARB process, the evolution of deformation mechanism oft Mg-5Li-1Al alloy is as follows: twinning deformation, shear deformation, forming macro shear zone, and finally dynamic recrystallization (DRX). The grain refining mechanism changes from twin DRX to rotation DRX. With the increase in ARB cycles, strength of the Mg-5Li-1Al sheets is enhanced, whilst elongation varies slightly. With the increase in rolling cycles, anisotropy of mechanical properties decreases. It is conclusive that strain hardening and grain refinement dominate the strengthening mechanism of Mg-5Li-1Al alloy.
基金supported financially by the National Key Research and Development Program of China (No.2017YFA0204400)Shenyang National Laboratory for Materials Science(No. 2015RP04)
文摘In the present work, an ultrahigh strength bearing steel(AISI 52100) was subjected to surface mechanical rolling treatment(SMRT) at room temperature. Microstructural observations showed that martensitic laths, twins and cementite particles in the initial microstructure underwent distinct plastic strains and were gradually refined into nanostructures. Consequently, a gradient nanostructured(GNS) surface layer with a mean grain size of -24 nm at the top surface was obtained on the bearing steel, resulting in an increment of -20% in the surface hardness. Analyses based on microstructural evolution, phase constitution and in-depth hardness distribution revealed a mechanically induced formation mechanism of the GNS surface layer. The multiple surface severe plastic deformation under fine lubrication and cooling during SMRT contributed to the formation of a thick hardened surface layer on the bearing steel.
基金the National Key Research and Development Program of China(Nos.2017YFA0204401 and 2017YFA0204403)the Liaoning Revitalization Talents Program(No.XLYC1808008)the Shenyang National Laboratory for Materials Science。
文摘Welded joints are usually characterized by microstructural and compositional inhomogeneities, which may significantly degrade their fatigue properties and result in unpredictable failures. The present work demonstrates a novel and simple method to effectively optimize the microstructure in the surface layer and promote the fatigue properties of welded specimens. By a recently developed approach—surface mechanical rolling treatment(SMRT), a gradient nanostructured surface layer is formed on welded S355 J2 W steel specimens. The mean grain size is refined to nanometer scale, and the hardness is significantly enhanced in the SMRT surface layer. Independent of the initially inhomogeneous microstructure and hardness distributions, the microstructure and hardness distributions in the surface layers are comparable on different zones of a welded specimen after SMRT with the same procedure. Consequently, fatigue property of the SMRT specimens is significantly enhanced relative to that of the as-welded specimens within the high cycle fatigue regime.
基金supported by National Natural Science Foundation of China(51274149,51401143)Shanxi Scholarship Council of China(No.2014-029)
文摘Sheet samples of Mg-8Li,Mg-8Li-3Al,Mg-8Li-3AlSi and Mg-8Li-5AlSi alloys were obtained by hot rolling.Optical microscope,microhardness tester,nanoindentor,X-ray diffractometer and electrochemical analyzer were adopted to investigate the microstructures,micro-mechanical properties and corrosion resistance.Roller was preheated to 150°C before rolling process,and rolling reduction designed was about20% per pass with a total rolling reduction of 84%.The rolled plates were annealed at 200°C for 120 min.The tensile tests were performed at room temperature.Experimental results showed that both the strength and corrosion resistance of theα+βdual-phase of Mg-Li alloy were significantly improved with adding Al-Si elements.The strength enhancement was attributed to the solid solution of Al into theα-Mg matrix and into theβ-Li matrix as well as to the precipitation strengthening of Mg2 Si particles.Besides,the dendrite grains ofα-Mg transformed to equiaxed ones with addition of Al into alloy Mg-Li.
基金Foundation Item:Item Sponsored by National Natural Science Foundation of China(50804005)Central Collegiate Basic Scientific Research Bursary of China(FRF-TP-11-005B)
文摘Different samples of TRIP (transformation induced plasticity) steel obtained by two different hot rolling schedules are investigated by using a SEM (scanning electron microscope). The microstructure is characterized by using an OM (optical microscope) for phase distribution and by EBSD (electron backscatter diffraction) for texture and phase mapping. ODF (orientation distribution function) graphs are used to investigate the effect of recrystallization behavior of the hot-deformed austenite on phase transformation during the controlled cooling process. The mechanical behavior is interpreted in terms of the strength of both hard and soft phases, in combination with the quantity, loca- tion and transformation kinetics of the mechanically induced martensite (TRIP effect). The results show that more austenite grains exist in the steels obtained at finishing rolling temperature (FRT) of 750 ℃, which inherited the de- formation structure after the hot-rolling process. The instantaneous n value (ni) of those steels is kept high during a large range of strain before failure, while the tensile strength and total elongation of the steels with respect to the dif- ferent finishing rolling temperatures do not show any significant differences.