1、 Stress:Stress:load per unit Area 单位面积的载荷AF F:load applied in N 载荷 牛A:cross sectional area in m截面积 m :stress in Pa 应力 帕FFAStrainStrain-Ratio of elongation of a material to the original length 材料的伸长量与原始长度的比率 oLe LLoee :elongation(m)伸长量Lo:unloaded(original)length of a material(m):strain(m/m)原始长度Elonga
2、tion oLLeL:loaded length of a material(m)受力伸长后的长度S Ee应力应变图Stress-Strain Diagram The diagram gives us the behavior of The diagram gives us the behavior of the material and material properties.the material and material properties.Each material produces a different Each material produces a different st
3、ress-strain diagram.stress-strain diagram.Stress Stress Strain Behavior(I)Strain Behavior(I)Stress-strain behavior can be brittle(A),plastic(B),and highly elastic(C)Curve C is totally elastic(rubber-like elasticity).典型陶瓷的应力应变图 材料在外力去除后仍能保持部分应变的特性称为塑性（Plasticity)。材料发生塑性形变而不开裂的能力称为延展性（Ductility)。利用延展性
4、进行冷加工：锻造、冲压等；主要是金属材料；陶瓷材料由于具有很少的塑性形变而不能用于这些工序。晶体中的塑性形变有两种基本的形式：滑移与挛晶 位错运动 在单晶材料中，塑性形变主要由滑移引起；挛晶的贡献很小。滑移是晶体在受到外力时，一部分相对于另一部分的平滑移动。它是在剪切应力作用下在一定的滑移系统上进行的。实际晶体中存在位错缺陷，当受到剪切应力作用时，并不是晶体内两部分整体相对错动，而是位错在滑移面上沿滑移方向运动。使位错运动所需要的力要比使晶体两部分的整体滑动所需要的力小得多。It is important to understand the mechanisms for failure,spe
5、cially to prevent in-service failures via design.1.2.1材料的断裂现象Stress-Strain Behavior versus TemperatureDuctility is reduced with temperature reduction.IronFailure(Fracture)Brittle fractureDuctile fracturemoderately ductile fractureTwo steps:Crack formation Crack propagation断口形貌Cup-and-cone fracture i
6、n AlBrittle fracture in mild SteelMicrostructureOrigin of crackBrittle fractureMicrostructureDuctile fractureTensile loadingShear loadingBrittle FractureTransgranular fractureCracking through grainsIntergranular fractureCracking along the GBMicrostructure 无机材料的抗压强度是抗拉强度的近10倍，所以抗拉强度是最值得研究的环节。无机材料的强度随
7、材料尺寸的增大而下降，原因是什么？无机材料的强度数据的离散性特别大，对于它的安全使用构成了极大的威胁！这是急待解决的问题！1.3.1原子间约束力与原子间距的关系曲线-0.40.00.40.30.40.50.60.7-4-2024Lennard-Jones potential (KJ/mol)Distance(nm)Force(1012N/mol)l/2maxlXth2sinOrowan将上述精确曲线简化为下面的正弦曲线，得出：th为理论结合强度；l为正弦曲线的波长将材料拉断时，产生两个新的表面，因此使单位面积的原子平面分开所做的功应等于产生两个单位面积的新表面所需的表面能，这样材料才能断裂。假
8、设分开单位面积原子平面所做的功为v，则llllllthththxdxxv20202cos22sinll22thth在接近平衡位置的区域，曲线可以用直线代替，服从Hookes law，即EaxEa 为原子间距。x很小时，llxx22sinaEth于是就有：tip tipactip21 ac2ctip21 is the applied stress,c is the half length of the crack,is the radius of curvature of the crack tip,a is the distance between two atoms如果a ,即为扁平的锐裂纹
9、，则a/将很大，上式中的1将被省略；从而可得：ctip2Orowan 认为很小，与原子间距a相当，可以将上式改写成下面的形式：actip2当tip等于材料的理论强度时，裂纹就会被拉开；即裂纹就会迅速扩展（propagation）。c 随之变大，tip又进一步增加。如此恶性循环，导致材料迅速断裂。因此，裂纹扩展的临界条件是：thtipaEac 2cEc4这是Inglis 考虑了（而且只考虑了）裂纹尖端的应力集中而得到的结果；实际上，裂纹尖端的应力状态是非常复杂的。Griffith 借鉴上述理论结果，又从能量的角度研究了裂纹扩展的条件。由弹性理论可以算出，当人为割开长度为2c的裂纹时，平面应力状态
10、（无限薄板）下系统应变能的降低为：平面应变状态（厚板）下系统应变能的降低为：EcWe22EcWe2221 is Poissons ratio 泊松比cWe4为单位面积上的断裂表面能裂纹进一步扩展2dc，单位面积所释放的能量为：dcdwe2形成新的单位表面积所需的表面能为：dcdws2dcdwdcdwse22时，为临界状态。EcEcdcddcdwe222222422cdcddcdws22Ecc由此可推出临界应力为：cEc2 如果是平面应变状态，临界应力则表示为：cEc212这就是Griffith 从能量观点分析得出的结果。如果能够控制裂纹的尺寸在原子间距的数量级上，就可以使材料的临界断裂强度达到
11、理论强度。但实际上，人类目前是很难达到的；不过，这一结果至少可以告诉人们：制备高强度材料的基本方向-材料的模量E和断裂表面能要大，裂纹尺寸c要小。Griffiths experiments with glass fibers(1921)Strength of bulk glass:170 MPa Extrapolates to 11 GPa123TENSILE STRENGTH(GPa)020406080 100 1200 应力场强度因子和平面应变断裂韧性 Griffith 微裂纹理论在上个世纪初期形成，在随后的近百年时间里得到了广泛的应用。上个世纪前半期，人们一直认为这一理论只适用于玻璃陶瓷
12、等的脆性材料领域。The hulls of Liberty Ships fractured without warning,mainly in the North Atlantic.There were 2,751 Liberty Ships manufactured between 1941-1945.Cracks propagated in 400 of these ships including 145 catastrophic failures;only 2 exist today which are sea-worthy.On April 28,1988,part of the fu
13、selagefuselage机身 of a Boeing 737 failed after 19 years of service.The failure was caused by fatigue(multi-site damage).Modes of Fracture which Operate on CracksMode IMode IIMode IIIa Tensile 掰开型Mode I is most often encountered.b Sliding错开型c Tearing撕开型21 Kcc这是实验规律，但能够说明断裂应力受材料中微裂纹的控制。crackxycrackCrac
14、k tip stressxZryyxxxyyy23sin2sin12cos21rKxx23sin2sin12cos21rKyy23cos2sin2cos21rKxyK1为与外加应力、裂纹长度c、裂纹种类和受力状态有关的系数，应力场强度因子，其下标I表示裂纹扩展类型为I型；单位为21mPa ijijfrK210,cr rKyyxx21式中r为半径向量，为角坐标。当时，即为裂纹尖端处的一点，则：使裂纹扩展的主要动力是yycYcrrKA2221K1是反映裂纹尖端应力场强度的强度因子；Y为几何形状因子，它与裂纹类型、试件的几何形状有关。求K1的关键在于求几何形状因子Y。求不同条件下的Y就是断裂力学的内
15、容，几何形状因子Y也可以通过实验得到。现在已经有几何形状因子数据手册可供检索。对于三点弯曲试样，当S/W=4时，几何形状因子的计算式为：2/5.14/07.393.1WcWcY43/8.25/07.25WcWcA critical value of K exists,similar to the value c,known as fracture toughness given by:cYcrrKA2221cKcYK11这就表明应力场强度因子小于或等于材料的平面应变断裂韧性时，材料的使用才是安全的。Irwin将裂纹扩展单位面积所降低的弹性应变能定义为应变能释放率或裂纹扩展动力，对于有内裂纹（长
16、2c）的薄板，有（2-16）式：EcdcdWGe22EcGcc2cK1此为裂纹扩展的动力。如为临界状态，则有：对于有内裂纹的薄板，221cccKEKGcc21EKGcc2121将代入上式可得：（平面应力状态）（平面应变状态）2cGEKc212112EKc（平面应力状态）（平面应变状态）K1c与材料本征参数E,等物理量有直接关系，也是材料的本征物理量。反映具有裂纹的材料对于外界作用的一种抵抗能力，即阻止裂纹扩展的能力；K1c是材料的固有性质。WBP,SP/2P/2c3-Point Bend SpecimenSingle edge notched bend(SENB)specimen with t
17、hrough thickness cracks 3-Point Bend Specimen 试样尺寸的比例及要求试样尺寸的比例及要求 c/w=0.4-0.6;w/s=1/4;B 0.5 w 三点弯曲受力时，三点弯曲受力时，K1c 值的计算公式可沿用美国值的计算公式可沿用美国ASTME399-74中所列公式：中所列公式：wcfWSBPYaKccc/2/31MPam1/22/92/72/52/32/1/7.38/6.37/8.21/6.4/9.2/wcwcwcwcwcwcf其中Pc为临界载荷 VfPs exp mocfomocsVVPexpIf the material is under cons
18、tant stressThus using the Weibull distribution in the case of uniform stressomocsfVVPPexp11omocsfVVPPexp11It is just a mathematical description of dataIt has no physical meaningIt can be used to explain any set of experimental data and is not exclusive to failure of ceramicsAlso important in describ
19、ing fatigue failure times in metalsomosfVVPPexp11ReasonsThere is no physical evidence for there being such a critical stressIf we set it to zero it makes manipulation of the expression a little easier!Note that for other applications of the distribution there may be a valid reason(e.g.threshold stre
20、ss in fatigueomosfVVPPexp11o and Vo are normalising constants introduced to make the expression within the brackets dimensionless.They are related to average values of the data set.m is the Weibull modulus it characterises the width of the distributionomocsVVPexpmocosVVPlnocosmVVPlnlnlnln-3-2-101B B
21、r ri it tt tl le e F Fr ra ac ct tu ur re e D Da at ta aln(stress)ln(-ln(1-Pf)200MPa300MPam=4.8RankStrength EstimatedValue(MPa)Probability(n)of Failure Pf=n/(N+1)11780.122100.232350.342480.452620.562760.672960.783180.893450.9REAL DATAIn general Weibull diagrams give a good representation of behaviou
22、r even at the important low strength limitTypical Weibull modulus of an as-finished ceramic is about 10Thus a designer can predict failure without an intimate knowledge of the flaw distribution The ability to resist indentation,abrasion,and wear-for metals,this is determined with the Rockwell Hardne
23、ss or Brinell tests that measure ndentation/penetration under a loadSTRENGTH and HARDNESS are related!A high-strength material is typically resistant to wear and abrasion.A comparison of hardness of some typical materials:MaterialBrinell HardnessPure Aluminum15Pure Copper35Mild Steel120304 Stainless
24、 Steel250Hardened Tool Steel650/700Hard Chromium Plate1000Chromium Carbide1200Tungsten Carbide1400Titanium Carbide2400Diamond8000Sand10001)Talc 滑石2)Gypsum 石膏3)Calcite方解石4)Flourite 萤石5)Apatite 磷灰石6)Feldspar 长石7)Quartz 石英8)Topaz 黄玉9)Corundum 刚玉10)Diamond金刚石SoftestHardest12345678910 氧化铝陶瓷目前分为高纯型与普通型两种。
25、高纯型氧化铝陶瓷系含量在以上的陶瓷材料，由于其烧结温度高达，透射波长为，一般制成熔融玻璃以取代铂坩埚：利用其透光性及可耐碱金属腐蚀性用作钠灯管；在电子工业中可用作集成电路基板与高频绝缘材料。普通型氧化铝陶瓷系按含量不同分为瓷、瓷、瓷、瓷等品种，有时含量在或者也划为普通氧化铝陶瓷系列。其中氧化铝瓷材料用于制作高温坩埚、耐火炉管及特殊耐磨材料，如陶瓷轴承、陶瓷密封件及水阀片等；氧化铝瓷主要用作耐腐蚀、耐磨部件；瓷中由于常掺入部分滑石，提高了电性能与机械强度，可与、铌、钽等金属封接，有的用作电真空装置器件。Rotor(Alumina)Gears(Alumina)Ceramic RotorCerami
26、csMetalsCeramic MaterialsGlassesClay ProductsRefractoriesAbrasivesCementsAdvanced CeramicsGlass Ceramics(Amorphous,silica based)(polycrystalline,eg.Pyroceram)Alumina,Silica high purity oxides GraphiteDiamond SiC Silica Sand AluminaCalcium SiliconSi N34SiC,BC,WCZrO2Ceramic-Matrix Composites(fibre and
27、 whisker reinfored)nFound in igneous rocks nIs responsible for the beautiful gemstones known as sapphires,and rubies This is the alumina structure.As you can see it is hexagonal close packed.2.3.1 Slip CastingFillingMouldCompactionGreen partejected-then sinteredlDeveloped at the Oak Ridge National L
28、aboratorylColloidal ceramic forming processlIn-situ polymerization of a monomer solutionlPolymer holds together the“green”ceramic partlDeveloped with Alumina,can be used with all engineering ceramics原料粉石蜡、油酸加热搅拌快搅拌慢搅拌热压注成型排蜡高温烧成 体积密度3.65(g/cm3）抗折强度 280（MPa）线膨胀系数（106mm/）20500(6.57)20800(6.58)介电常 1MH2
29、20 910 10GH220 910 击穿强度（Kv/mm）15 化学稳定性（mg/cm2）1:9Hcl 7 10%NaOH 0.2 介质损耗角正切值（10-4）1MH220 4 10GH220 10 体积电阻率（.cm）25 81014Fibre99%Al2O3Su=3000 MPaE=400 Gpa=3.95 g/cm3ProjectileOuter hard skinCeramic-DiscontinuousInnerductileskinPersonnelandEquipmentCeramic Armor System Ceramic armor systems are used to
30、 protect military personnel and equipment.Advantage:low density of the material can lead to weight efficient armor systems.Typical ceramic materials used in armor systems include alumina,boron carbide,silicon carbide,and titanium diboride.The ceramic material is discontinuous and is sandwiched betwe
31、en a more ductile outer and inner skin.The outer skin must be hard enough to shatter the projectile.Most of the impact energy is absorbed by the fracturing of the ceramic and any remaining kinetic energy is absorbed by the inner skin,that also serves to contain the fragments of the ceramic and the p
32、rojectile preventing severe impact with the personnel/equipment being protected.CF uses alumina ceramic/Kevlar composite system in sheets about 20mm thick and having a bulk density of about 2.5 g/cm3 to protect key areas of Hercules aircraft(cockpit crew/instruments and loadmaster station).This ligh
33、tweight solution provided an efficient and removable/replaceable armor system.Similar systems used on APCs 3.1Introduction to zirconia zirconium;named from the Arabic,zargun=gold color Fabrication:Obtained from the mineral zircon Addition of MgO,CaO,CeO,or Y2O3 stabilize tetragonal crystal structure
34、(e.g.97 mol%ZrO2 and 3 mol%Y2O3)Usually hot-pressed or hot isostatically pressed Zirconia offers chemical and corrosion resistance to temperatures well above the melting point of Alumina.In its pure form crystal structure changes limit mechanical applications,however stabilised Zirconias produced by
35、 addition of Calcium,Magnesium or Ytrium Oxides can produce very high strength,hardness and particularly toughness.In addition the material has low thermal conductivity and is an ionic conductor above 600C.This has lead to applications in oxygen sensors and high temperature fuel cells.High temperatu
36、re capabilty up to 2400C High density High strength and fracture toughness High hardness and wear resistance Low thermal conductivity(20%that of Alumina)Good chemical resistance Ionic conductivity Precision ball valve(balls and seats)High density grinding media Threadguides 导丝器 Cutting blades Medica
37、l prostheses Pump seals,valves and impellors Oxygen sensors Fuel cell membranes Radio frequency heating susceptors Metrology components partially stabilised zirconia(PSZ)higher flexural strength fracture toughness better reliability lower Youngs modulus ability to be polished to a superior surface f
38、inish lower hardness下图为三种晶型的单位晶胞结构：0ZrO2结构特征纯ZrO2 在不同温度下具有单斜（m）、四方（t）、立方(c)三种不同晶型，晶型转化式为：11700C23700C27150C单斜相四方相立方相液相Stabilized zirconia FSZ fully stabilized zirconia PSZ partially stabilized zirconia TZP tetragonal zirconia polycrystalline stabilizer CaO MgO Y2O3 CeO2To produce colored cubic zirco
39、nia,the following oxides can be added to achieve the following colors.Oxide Colors Produced Cerium oxide red,orange,yellow Copper oxide yellow,amber,brownIron oxide yellow,amber,brownNickel oxide yellow,amber,brownPraseodymium oxide yellow,amber,brownTitanium oxide yellow,amber,brownErbium oxide pin
40、kEuropium oxide pinkHolmium oxide pinkChromium oxide greenManganese oxide greenVanadium oxide greenCobalt oxide lilac,violetManganese oxide lilac,violetNeodymium oxide lilac,violetExcess yttrium oxide blue,greenCubic Zirconia-history Cubic Zirconia was discovered in its natural state in 1937 by two
41、German mineralogists,von Stackelberg and Chudoba.It was in a highly metamict zircon given to them by B.W.Anderson.The zircon contained tiny crystals that were determined to be the cubic form of zirconium oxide by x-ray diffraction.The two mineralogists thought so little of their discovery that they
42、did not even give it a name;which is why it is still known by its scientific name,cubic zirconia.It wasnt until the 1970s,however,that Soviet scientists learned how to grow the crystals in the laboratory.In 1977,it was first marketed under the trade name Djevalite.But CZ really took off in the 1980s
43、 when Swarovski&Co.,a world-renowned Australian producer of leaded crystal,began producing cubic zirconia for mass consumption.Cubic ZirconiaCubic Zirconia is well known as a substitute for diamond,due to its high hardness and great fire.But in recent years,it has established itself as a gorgeous ge
44、m in its own right.CZ is a beautiful synthetic gemstone that is durable and inexpensive and now even comes in any color of the rainbow,making it even more desirable.Cubic ZirconiaFully Stabilized Zirconias adopt the Fluorite structure CaF2,which is the structure of pure zirconia at high temperature.
45、The lattice is face-centered cubic(fcc)and the space group is Fm3m.Zirconium cations occupy the positions(0,0,0)of the lattice and oxygen anions occupy the positions(1/4,1/4,1/4).Each Zr cation is surrounded by eight O ions which are contained in tetrahedrons formed by zirconium ions.The oxygen ions
46、 form a cubic sublattice of half the lattice parameter of the fcc cell.In a 3-dimensional view,every alternate cube of oxygen ions has a zirconium ion in his center and one cube has only one edge in common with another.Cubic Zirconia Cubic Zirconia is a cubic form of zirconium oxide that is created
47、in a laboratory,thus it is not a mineral.However,it was found naturally occurring once at one site in the 1930s,but has yet to be discovered since then.The mineral with the same chemical composition as CZ,but in the monoclinic crystal system,is baddeleyite.Cubic Zirconia Cubic zirconia has a hardnes
48、s of 8.5 on Mohs Scale of Hardness and a white streak.It has a specific gravity between 5.65 and 5.95,and a density between 5.5 and 5.9.It is in the isometric crystal system with a 4/mbar32/m crystal class and a Fm3m space group.The refractive index of CZ is between 2.088 and 2.176,which is very hig
49、h.It has dispersion in the C-F area of the visible light spectrum of 0.060.Since CZ is transparent,it is often faceted.It can be made in nearly any color and can be faceted into many cuts.Stabilized zirconia(continued)The PSZ is the more common commercial material and is made as a MgO partially stab
50、ilized zirconia.The second variety,TZP,is a pure tetragonal very fine grain material.This material,which is challenging to produce,has found uses in cutting and wear resistant applications due to its reliable and outstanding hardness and toughness.TZP properties degrade rapidly when the material is
