2002 Vol. 19, No. 6

ADVANCES IN STUDY OF CONSTITUTIVE RELATIONS OF BLENDED/FILLED POLYMERIC COMPOSITES CONSIDERING DAMAGE EVOLUTION
WANG Jianxiang, CHEN Jiankang, BAI Shulin
2002, 19(6): 1-7.
Abstract:
Constitutive relations are the basis for design of composite materials. This paper summarizes the damage evolution laws, the research methodology and the major results in the study of constitutive relations of blended/filled polymeric composite materials. It is pointed out that more studies are needed to understand some important mechanisms in the damage process of the composite materials such as the nucleation and coalescence of voids, effects of the void interaction and non-linearity of the matrix on the damage evolution, effects of the strain rate and temperature on the damage process, etc.
POST-IMPACT COMPRESSIVE STRENGTH OF SMALL COMPOSITE LAMINATE SPECIMENS
CHENG Xiaoquan, ZHANG Zilong, WU Xueren
2002, 19(6): 8-12.
Abstract:
A miniature post impact compression test was used to study the technique for composite testing with a view to reducing the cost of testing materials. This test method can be used in a material developing phase. Based on experimental studies, a reduced stiffness inclusion model was developed to predict the residual compressive strength of composite laminates after the low velocity impact. In this model the damage was considered as a soft zone of the material. The damage zone was assumed to be circular. A finite element code with the 8-node 2D isoparametric element was programmed to compute the stress distributions. The point stress criterion was used to determine whether the post-impact laminates are compressed to failure or not. Good agreement between predicted residual compressive strengths and experimental results is obtained.
DYNAMICS RESPONSE CONTROL MODEL OF THE PIEZOELASTIC LAMINATED CYLINDRICAL SHELL UNDER HYDROSTATIC PRESSURE
LI Hongyun, LIU Zhengxing
2002, 19(6): 13-19.
Abstract:
Based on the classical laminated plate theory and Navier solutions, the control of the piezoelastic laminated cylindrical shell's dynamic response under hydrostatic pressure was discussed in this paper. Considering the direct and inverse piezoelectric effects of piezoelectric materials and using Hamilton's principle, the nonlinear dynamic equations of the piezoelastic laminated cylindrical shell were derived first. Using the close circuit method, the charge enclosed in the piezoelectric sensor layer was measured. Furthermore, the voltage applied on the actuator layer was obtained based on the closed-circuit charge signal of the sensor and velocity negative feedback control algorithm. An active dynamic response control model of simply supported laminated cylindrical shells with piezoelectric sensor/actuator under various dynamic loads was established at last. Three types of loading conditions, namely, sinusoidally distributed load, line load and moving point load, were considered in numerical examples to investigate the performance of the control model. The numerical results show that the active control model can suppress the vibration of the structure under dynamic loading effectively.
MICROSTRUCTURE AND MECHANICAL PROPERTIES OF Ti3SiC2 CERAMICS
LI Shibo, CHENG Laifei, WANG Dong, ZHANG Litong
2002, 19(6): 20-24.
Abstract:
Dense layered material Ti3SiC2 was fabricated by hot-pressed TiH2, Si and C powders. The Vickers indentations were made at loads of 0.5~30 kg to measure hardness. The results show that the hardness decreased with the increasing of loads. At the load of 30 kg, the hardness value was stable to 4 GPa. Most importantly, no indentation cracks were observed even at 30 kg load. This property should be due to the multiply energy absorbing-grain delamination, crack deflection, grain deformation, et al. The flexural strength and fracture toughness were 270 MPa and 6.8 MPa·m1/2, respectively, by means of the three point bending test and single edge notched beam test. The fracture surfaces show the obvious layered nature in the observation of scanning electron microscope (SEM). Larger Ti3SiC2 grains are prone to delamination and intragranular fracture, but smaller grains are more easily pulled out. Crack propagation is parallel to the basal plane of Ti3SiC2 resulting in the grain delamination. Crack propagation will be deflected inner of grains when it is normal to the basal plane, and the crack propagation path was prolonged and the spreading energy was dissipated. The morphology of the crack propagation path is similar to that of synthetic multilayered composites. The main mechanisms of improving fracture toughness are crack deflection, crack pinning, grain pull out, and grain delamination. Moreover, the authors found the samples for the single edge notched beam (SENB) test without breaking pieces after unloading. The feature indicates that Ti3SiC2 is a damage tolerance material and has plastic property like as the ductile metals at the room temperature.
INFILTRATION OF MOLTEN ALUMINUM AND HEAT TRANSFER IN CENTRIFUGAL CASTING PROCESSES
HU Guoxin, TIAN Qinwei, WANG Minglei, WANG Guoxiang
2002, 19(6): 25-30.
Abstract:
In this paper, molten aluminum flow with heat transfer through SiC porous media in a centrifugal force field was described with a mathematical and physical model. The implicit TDMA Algorithm and the first kind of first-order upwind difference were employed to solve the conservation equation associated with appropiate boundary conditions. The distribution of molten aluminum velocity and its pressure, the temperature profiles of fluid and porous media in a centrifugal force field were examined for different conditions. The results show that the local temperature of the fluid phase is different from that of the solid phase in the front edge of the infiltrated region. The temperature difference between the fluid and solid phases increases with the SiC volume fraction and angular velocity, and decreases with the time of infiltration. The infiltration of the molten aluminum through SiC porous media depends mainly on the angular velocity of the centrifugal force field. SiC volume fraction has a strong effect on the velocity and pressure distribution of the molten aluminum.
CHARACTERISTICS OF MICROMECHANICAL DAMAGE EVOLUTION AND WEAKEST CHAIN MODEL FOR PARTICULATE REINFORCED ALUMINUM MATRIX COMPOSITES
CHENG Guangxu, LI Feng, LI Zhijun
2002, 19(6): 31-36.
Abstract:
Micromechanical damage evolution characteristics for a variety of particulate reinforced metal matrix composites(PRMMC) were investigated in ductile fracture. A weakest chain model of micro-damage was proposed, and the relationship between the global damage variable and micro-damage mechanism was established. The influence of the reinforcement size and the volume fraction on damage evolution was investigated for commercially pure aluminum and aluminum matrices reinforced with SiC particles. The effects of matrix heat treatment on the damage evolution were analyzed as well. It is concluded that the damage evolution could be expressed in a power-law form and the weakest chain model of micro-mechanical damage is able to investigate the damage mechanism. A very good agreement is obtained between the calculated values and experimental data for ductile damage evolution.
APPLICATION OF ACTIVE FILLER IN PREPARATION OF FIBER REINFORCED CERAMIC MATRIX COMPOSITES BY POLYMER-INFILTRATION-PYROLYSISⅠ.DENSIFICATION MODELS
XIE Zhengfang, CHEN Zhaohui, XIAO Jiayu
2002, 19(6): 37-42.
Abstract:
In the preparation of fiber reinforced ceramic matrix composites (FRCMCs) by polymer-infiltration-pyrolysis (PIP), the volume of the composites would change during the conversion of the preceramic polymer into a ceramic matrix in the first pyrolysis process. The repetition cycle-density densification model is revised by introducing the volume shrinkage percentage of the composites. The densification models for the FRCMCs preparation by active filler and/or inert filler-containing preceramic polymer-infiltration-pyrolysis are also developed. The relationships between the theoretical density and porosity of the composites and the repetition cycle are discovered. For the active filler-containing system, the theoretical density not only relates with the ceramic yield of the polymer and the density ratio between the pyrolysis product and polymer, but also relates with the reaction yield and density ratio of the active filler after reaction, and the volume shrinkage of the composite. It is proved that the addition of the active filler is more effective than that of the inert filler for the composite densification.
DYNAMIC ANTI-OXIDATION BEHAVIOUR OF MoSi2/SiC COATING SYSTEM FOR CARBON-CARBON COMPOSITES
ZENG Xierong, LI Hejun, LI Long, LI Ailan
2002, 19(6): 43-46.
Abstract:
In the present work, the dynamic anti-oxidation behavior and damage mechanism of MoSi2-SiC multilayer ceramic coating for carbon-carbon composites were investigated experimentally at various temperatures of 1100~1500℃ under the test for gas jet washout. Experimental data of dynamic oxidation show that the mass loss of MoSi2/SiC coated carbon-carbon composites decreases, and the ability of oxidation resistance is enhanced with raising the gas temperature up to 1500℃. The mechanism of dynamic oxidation and the concept of the integrity of the coating layer are explained from the theory of mass transportation and the damage of gas jet washout. In this respect, the dynamic oxidation behaviour differs from the static oxidation. The results show that the MoSi2/SiC ceramic coating for carbon-carbon composites can provide dynamic oxidation protection to C/C composites at temperatures up to 1500℃ in a gas jet environment.
IN SITU OBSERVATION ON FRACTURE PROCESS OF SiCf/Al METAL MATRIX COMPOSITES
YANG Shengliang, YANG Deming, QUAN Gaofeng, HE Jiawen
2002, 19(6): 47-51.
Abstract:
The fracture process in the fatigue and tensile test of SiC fiber reinforced aluminum composites was observed in situ with a scanning electron microscope. It is found there exist three stages of damage. The first stage is that the cracks initiate at the stress-concentrated sites caused by fiber fracturing, which increases as the load cycles increase. The second stage is characterized by multi-cracks in each fiber and extension of cracks. The last stage indicates the coalescence of cracks and the formation of a main cracked plane. No fiber-matrix interface debonding was observed during the fracture process. The apparent interfacial bonding strength evaluated in terms of a shear lag model indicates a strong interfacial bonding.
MICROSTRUCTURE AND CHARACTER OF FRICTION AND WEAR OF WCP/Ni BASED ALLOY GRADIENT COMPOSITE COATING BY WIDE-BAND LASER CLADDING
LIU Qibin, ZHU Weidong, ZOU Longjiang, WANG Cunshan, XIA Yuan-liang
2002, 19(6): 52-56.
Abstract:
In order to eliminate cracks produced in the process of laser cladding, a new kind of gradient composite coating is designed. The experimental results indicate that the excellent metallurgical bonding is formed between the gradient composite coating and substrate. There are γ-Ni dendrite structure, γ-Ni+M23C6 eutectic structure and M6C,M7C3,M23C6 in the composite coating. With increment of cast WCP volume fraction,the friction coefficient of the composite coating decreases,but the wear resistance of the coating increases.The wear resistance value of 19-4 sample is 4.61,and is increased by three times on an average as compared with that of the substrate.The wear mechanism of coatings results from a composite action of abrasive wear and adhesive wear.
BENDING MECHANICAL PROPERTIES AND ITS EVALUATION OF ALUMINIUM ALLOY MATRIX GRADIENT COMPOSITES REINFORCED WITH SiC PARTICLES
GUO Cheng, GUO Shengwu, CHENG Yu, ZHANG Xingong, SHI Dongcai
2002, 19(6): 57-60.
Abstract:
The bending mechanical properties of aluminium alloy matrix gradient composites reinforced with SiC particles were studied using a bending test under three-point loading. The bending strength ratios R1 and R2 of the composites were put forward. The results show that the bending mechanical properties of the Metal Matrix Gradient Composites (MMGC) do not obey the Role of Mixture (ROM) law. The bending strength is remarkably influenced by the distribution way of SiC particles and bending direction.The MMGC can develop their full potential in bending properties when the matrix component is laid at the tensile side and the component with high SiC volume fraction at the compressive side. The potential of mechanical properties and the oriented features of the MMGC by the action of gradient stress are influenced by many factors such as the state, the macro-uniformity and the micro-continuity of materials. The bending strength ratios R1 and R2 can be used to justify the bending properties and the orientation of the composites.
GRAFTING POLYMERIZATION ONTO NANOSILICA AND ITS EFFECT ON MECHANICAL PROPERTIES OF PP COMPOSITES
WU Chunlei, ZHANG Mingqiu, RONG Minzhi
2002, 19(6): 61-67.
Abstract:
To modify the surface of nano-SiO2, polytyrene and polyethylacrylate were grafted onto the particles through irradiation grafting polymerization, respectively. Mechanical testing of the modified nanosilica filled polypropylene (PP) composites reveals the significant strengthening and toughening effects of the treated nanoparticles on the matrix resin. It is believed that the extensive shear deformation of PP induced by the modified nanosilica is responsible for the improvement of the composites toughness. Microscopic observation further demonstrates that the modified nanoparticle aggregates become more compact due to the grafting polymer chains, which in turn provides an enhanced interfacial adhesion between the fillers and the matrix.
RESEARCH ON BTDE/PMDE COPOLYMER PMR POLYIMIDE RESIN
YUAN Zijun, ZHANG Zuoguang, LI Min, PAN Yishan
2002, 19(6): 68-71.
Abstract:
A series of BTDE/PMDE copolymer PMR resin was synthesized by introducing a second monomer to PMR-15 system on the principle that material properties depend on its molecular structure. The relations between properties such as resin viscosity, impact strength and thermo-oxidative stability and molecular structure were discussed. Simultaneously, the optimal resin system was characterized by TGA, DSC and DMTA. Experiment shows that with increasing of the molecular weight, the resin viscosity and thermo-oxidative stability increase, while the impact strength decreases after increasing. With increasing of PMDE content, the resin viscosity and impact strength decrease, while the thermo-oxidative stability increases.
NUMERICAL SIMULATION OF CRACK GROWTH PROCESS BETWEEN LAYERS IN TIRE STRUCTURE
FENG Xijin, YAN Xiangqiao, WEI Yintao, DU Xingwen
2002, 19(6): 72-81.
Abstract:
A tire is a very complex structure made from rubber and fiber-rubber composite materials. During its use, a delamination crack growth often occurs, which obviously affects its durability and life. A new crack growth model between layers in composite structures is presented in the paper. The crack growth model, Irwin's virtual crack close technique and finite element analysis method were together used in simulating numerically the growth process of the delamination crack between layers in a tire structure. The results show that the crack growth model proposed in the present paper can more really reveal the complexity of the growth process of the delamination crack between layers in a complex composite structure.
TWO KINDS OF KAOLIN FILLED UHMWPE COMPOSITES AND THEIR TRIBOLOGICAL BEHAVIORS
GONG Guofang, QI Zongneng, YANG Huayong
2002, 19(6): 82-86.
Abstract:
Kaolin filled UHMWPE composites were prepared by melt mixing and polymerization respectively. Their thermal properties, crystallizability, aggregate structure and tribological behaviors sliding against 45 steel were tested and studied thoroughly, and the relationship between the tribological behavior and the structure was analyzed. It was found that the polymerization-filled composites have much better tribological properties than the mixing-filled ones with the same components, and the relevant properties are closely related to the reinforcement of kaolin particles dispersed evenly, the combining strength of the interface and the crystal patterns.
IN-SITU MONITORING OF COMPOSITE CURE PROCESS WITH FIBER OPTIC REFRACTIVE SENSORS
WU Zhanjun, ZHANG Boming, WANG Dianfu, LI Qingkun, YU Jiayin
2002, 19(6): 87-91.
Abstract:
Till now the processing of advanced composite is still empirical due to its complicated physical and chemical change. In order to transform the processing technique from an empirical state to a transparent, scientific and intelligent approach, the idea of monitoring the cure process of the composite products with fiber optic sensing technique is put forth. A fiber optic refractive sensor was developed and a portable instrument for the optic emission, signal receiving and interogation was integrated to meet the requirement of on-site application. With it the cure process of resin and fiber reinforced prepregs can be monitored. Tests of resin cure process monitoring are carried out with both the resin that should be cured under room temperature and the resin that should be cured under high temperature. The results of tests with resin cure under temperature were compared with the results of Michelson interferometer tests under similar circumstances, which are in good consistency. Tests were also carried out in composite manufacture, in which the fiber optic refractive sensors were embedded in the prepreg during the cure process. It is proved that with this method the key information of the cure process can be extracted out during the process and can be used in on-line intelligent control. In conclusion, this technique can be used not only in the establishment of the cure routine but also in the in-situ monitoring and control of the composite manufacture process.
ANALYTICAL MODELING OF WOVEN FABRIC UNDER BALLISTIC PERFORATION
GU Bohong
2002, 19(6): 92-96.
Abstract:
Composite materials have become a key element in designing structural components subjected to impact loading, for example, in personal or vehicle armors. But it is difficult to model the behavior of composite materials under ballistic impact because of the complexity of damage mechanism. The first way to solve this problem is to model the primary part of composite materials before explanation of the behavior of the entire composite. An analytical model of multi-layered fabrics based on the strain rate effect of the fiber property is developed in this paper. Rate-dependent tensile property of Twaron filaments is also discussed. Application of the high strain rate property to ballistic perforation of multi-layered fabrics conforms to the actual situation better than that of the quasi-static property. The analytical model proposed in this paper can be used to calculate the process of ballistic penetration and perforation on soft armours, such as fabric target plate, at intuitive approach and simple algorithm with a little computer process time. Predictions of the residual velocities and energy absorbed by the multi-layered fabric show good agreement with experimental data.
CPP/PLLA COMPOSITES OF SCAFFOLDS FOR TISSUE ENGINEERING
SHI Zongli, WANG Yanping, DAI Gang, LI Chongan
2002, 19(6): 97-100.
Abstract:
The CPP/PLLA composites of the scaffold for cartilage tissue engineering were fabricated with a solvent-casting, particulate-leaching method. Their properties of physical mechanics and degradation rates in vitro (in hank's at 37℃) were measured. The experimental results show that the composites have high porosity(ε=90%), good biodegradability and compressive modulus (8.6 GPa) as well as the 3-D ,connectivity network microstructures. Therefore, this composites might be one of cartilage scaffold materials for tissue engineering with potentially broad applicability.
MOISTURE ABSORPTION BEHAVIOR OF 3-D CARBON-FIBER-EPOXY COMPOSITES AND EFFECT OF EXTERNAL STRESS
WANG Yulin, WAN Yizao, CHEN Guicai, ZHOU Fugang, CHENG Guoxiang
2002, 19(6): 101-105.
Abstract:
Three-dimensionally (3-D) braided carbon fiber reinforced epoxy resin (C3D/ER) composites were produced by vacuum impregnation technique. The present study is carried out in order to determine the water absorption characteristics of the 3D composites. In addition, the influences of the external load on the water uptake and changes in the flexural, shear and impact strengths were also determined as a result of moisture absorption. The kinetics of moisture absorption by the stressed and unstressed composites, as well as the unreinforced epoxy resin, was determined for the absorption at 37 ℃±0.5 ℃. The results show that the C3D/ER composites exhibited a complicated absorption behavior. In contrast to the epoxy resin, the absorption behavior of the C3D/ER composite could not be described by using Fick's law of diffusion. The results clearly demonstrate the contribution of the external stress to the water absorption behavior and changes in mechanical properties. The external stress was found to increase the moisture content and mechanical properties reduction at earlier stages. At later stages, a contrary trend was observed. It is concluded that the mechanical properties are proportional to their moisture content for the C3D/ER composites. Mechanisms were proposed to interpret these experimental phenomena.
EFFECT OF PEROXIDE ON THE CURING PROCESS OF QY8911-Ⅲ RESIN
YANG Dean, ZHAO Wei, LU Yan, XU Tingxian
2002, 19(6): 106-110.
Abstract:
Differential scanning calorimetry was used to study the effect of the peroxide on the cure reaction of BMI. The effect of peroxide content on the properties of the cured BMI was investigated. The results show that the peroxide reduced the initial reaction temperature and prompted the reaction speed, increased the bending strength and decreases the impacting strength. So the peroxide content should be less than 0.6%. CF/SiO2/BMI composites are fabricated from the BMI containing peroxide and its microstructure and properties are better than those of the composites free of peroxide. According to the injection molding experiment the spilling problem is overcome and the forming time is reduced from two hours to fifteen minutes when peroxide was added.
FRICTION AND WEAR PROPERTIES OF PTFE COMPOSITES FILLED WITH DIFFERENT MIX MATERIALS MADE OF NANOCRYSTALLINE AND GRAPHITE
HE Chunxia
2002, 19(6): 111-115.
Abstract:
It is discussed that the friction and wear properties of polytetrafluoroethylene (PTFE) composites filled with different mix materials made of nanocrystalline and graphite. The friction and wear tests were carried out using MM-200 wear tester. The worn surfaces of PTFE composites were examined by the scanning electric microscopy (SEM). It is found that the addition of nanocrystalline and graphite not only increases the wear resistance of PTFE, but also results in changing the friction coefficient of the material. The three materials have different properties of anti-wear.The SiO2-graphite-PTFE has excellent tribology property. The raising of the wear load increases the wear mass loss of PTFE composites.
PTC CHARACTERISTIC OF Sn-Pb ALLOY-LOADED POLYMER COMPOSITES
LIU Jing, PAN Yi, ZHANG Xiangwu
2002, 19(6): 116-119.
Abstract:
PTC characteristics of PS and HDPE composites incorporated with Sn-Pb alloy particles were studied. The composites were made by mixing in a satellite ball mill and hot-pressed in a matched metal die. The results show that the low melting point of Sn-Pb alloy results in the excellent PTC characteristics. The electrical resistivity of the Sn-Pb alloy filled PS exhibits PTC characteristic with high density and abrupt transition. The electrical resistivity of the Sn-Pb alloy-loaded HDPE composite exhibits two PTC transitions near the melting points of Sn-Pb alloy and HDPE, respectively.
PROPERTIES OF CRACKING RESISTANCE OF CEMFIBER REINFORCED CONCRETE
XING Feng, LENG Faguang, FENG Naiqian, LI Weiwen
2002, 19(6): 120-124.
Abstract:
Polypropylene fiber is a new measure to prevent plastic cracks of concrete. Effects of the parameters, such as dosage and types of fibers, on the plastic cracks were studied systematically. The properties of cracking resistance of mortar, ordinary concrete and high performance concrete were investigated using samples of two types in shape. The results show that: (1) Polypropylene fibers may increase the cracking resistance of concrete significantly and increasing the dosage of fibers may increase cracking resistance of concrete further; (2) As smaller quantity of cement and higher quantity of aggregate as possible should be used to prevent concrete from cracking; (3) The main causes why polypropylene fibers increase cracking resistance of concrete are increasing strain capacity of concrete at an early age, decreasing shrinkage strain, improving plastic tensile strength and decreasing tensile stress of the capillary.
A NOVEL FIBER OPTIC PRESSURE SENSOR USED IN COMPOSITE CURE PROCESS MONITORING
WU Zhanjun, ZHANG Boming, WANG Dianfu, DU Shanyi
2002, 19(6): 125-129.
Abstract:
Fiber optic sensor has been proved a very promising monitoring method in many fields such as arms and aerospace industry. One of its most popular applications is the cure process monitoring of advanced fiber reinforced resin matrix composite. The main obstacle of wide utilization of this technique is the high cost and complex modulation technology. A novel fiber optic sensor was developed, which has the feature of high sensitivity and low cost and is easy to handle, to do the job. The fiber optic sensor is developed based on fiber optic microbend losses and aimed to monitor the pressure variation, through which key information to the cure can be obtained through computation directly or indirectly, on the reinforced fiber network during the cure process. In this presentation, the design and preparation of the sensor is given. The dynamic and static response of the fiber optic pressure sensor under pressure is tested. The influence of the temperature and refractive index variation around the sensor on the response of the sensor's signal attenuation is dicussed. On the basis of the fiber optic pressure sensor, a portable instrument is integarted, which includes laser diode, detector, A/D, etc. With it in-situ monitoring of the cure process of fiber reinforced composite laminates is carried out and good result is obtained.
EFFECT OF ALKALINE TREATMENT ON RAMIE/CELLULOSE ACETATE COMPOSITES
WANG Junbo, ZHENG Shuirong, ZHAO Chuan, YANG Minge, SUN Manling
2002, 19(6): 130-133.
Abstract:
By an optimization processing of alkaline treatment to improve the structure and properties of ramie fibers, and by introducing some additives into the cellulose acetate to improve its processability, a new kind of composite, ramie fiber reinforced cellulose acetate,was fabricated. The results show that the tensile strength,tensile modulus,toughness and surface adsorption ability of the ramie fiber can be improved when the ramie fiber is treated with NaOH,and that the shear strength and bend strength of ramie fiber reinforced cellulose acetate composites are modified.
DYNAMIC ANALYSIS OF THE CARBON FIBER HONEYCOMB SANDWICH STRUCTURE
WANG Pingping, LUO Wenbo, ZHOU Jinxiang, KONG Xianren
2002, 19(6): 134-136.
Abstract:
In this paper,the dynamic analysis of the carbon fiber honeycomb sandwich structure was deeply investigated. The carbon fiber net plate was equivalent to an orthotropic plate, and the honeycomb core was equivalent to a three-dimensional orthotropic solid based on the principle of work equivalence. In order to prevent some buckling of the structure, it is important to thicken the part of the carbon fiber plate and densify the core of the honeycomb. Using complex structure finite element analysis, the theoretical prediction conforms with the experimental results very well, the equivalent model is reasonable, and the method is correct.