《材料力學(xué)性能》大三教學(xué)PPT課件,材料力學(xué)性能,材料,力學(xué)性能,大三,教學(xué),PPT,課件 Stressed and Strained StatesLi ChenhuiStress Stress is the load applied to a body and related per unit area of the bodys section.A relative quantity;The dimension of stress is determined as the force active per unit area of the body section to which the force is applied.Usually measured as newtons per square metre(N/m2)or kgf/mm2;The units of stress express the principal mechanical properties(ultimate strength,resistance to plastic flow,resistance to indentation,fatigue strength,creep strength,etc.)The case of axial tension of a cylindrical rod)if S=constant (uniform distribution of the stress over the cross section)P=SF or S=P/FIn a more general case The normal stress(正應(yīng)力)The shear stress(剪應(yīng)力Thus,if we know the tensile force P applied to the rod and the cross-sectional area F.we can determine the normal and shear stresses in any plane making an arbitrary angle with the rod axis.The distribution of normal and shear stresses in variously oriented planes of a tensioned specimen are illustrated in Fig.4.Engineering/Actual(True)StressF:forceapplied;A0:areabeforedeformation The engineering stress is often employed for elastic stresses or stresses for components deformed to small plastic strains.At large strains,the change in cross-sectional area significantly alters the actual stresses.The true stress is:where A is the instantaneous area.Strain Strain is the ratio of the change in dimension to its initial value.Axial tension of a cylindrical rod as;Load applied;Rod deformed,the length increased from l0 to ln;engineering strainThe engineering strain should be used only if the deformation strains are small in magnitude(e.g.,eeng E for a tensile test,a result intuitively deduced previously.In contrast,if the material were compressed so that the cross-sectional area increased during deformation(with E 0),we would find T E.Which shows that T E in a tension test(i.e.,ln(l+x)a0 and u is positive.In compression,a a0 and u 0.The equilibrium condition can be written,as follows:where (u)is the bond energy on displacement u.By analysing the system of two atoms,it is also possible to derive Hookes law which establishes the relationship between the external force applied and the resulting displacement.For Hookes law to be valid,the following three conditions must be satisfied:(1)the function(u)must be continuous;(2)the function(u)must have a minimum d/du=0 at u=0;and(3)the displacement u must be much less than a0.The first condition makes it possible to expand the interaction energy function into a Taylor series:In this equation,0 is the interaction energy at u=0 and,all the derivatives are obtained for the point u=0.Since d/du is equal to zero at u=0,and,the terms with the third and higher powers of u can be neglected(as u is small),we obtain:The second derivative(d2/du2)o is the curvature of the function(u)in point u=0,and,therefore,it does not depend on u and is a constant.Thus,weobtainf=constu,i.e.the force is proportional to displacement(Hookes law).It should be recalled that the region of a direct proportionality between the force and displacement is limited to slight deformations.With an appreciable magnitude of displacement u,the terms of higher powers of u cannot be neglected and,therefore,the f(u)curve deviates from the straight line.This phenomenon is never encountered in practice,since an irreversible plastic deformation begins in metal even at lower stresses.The law of direct proportionality is then disturbed but for different reasons.Perfect thread-shaped metal crystals of a diameter of around 2 um(called whiskers),in which plastic flow is impeded,can,however,be deformed elastically by a few per cent and,at high elastic deformations,a deviation from Hookes law can be observed experimentally InshearstressTheshearstressisrelatedwithacorrespondingsheardeformationbysimilarexpression:whereGistheshearmodulus(orthemodulusofelasticityinshear)(1-3)Inhydrostaticcompression(ortension)Hookeslawexpressesadrectproportionalitybetween the hydrostaticpressurePandthevolumechangex:where K is the modulusofbulkdeformation.(1-4)Hookes law(3)Formulae(1-2),(1-3)and(1-4)expresswhatiscalledHookslaw.DeterminestherelationshipbetweenstressandstrainactinginthesamedirectionWhen deformation appear in a directiondifferentfromthatofthestressaction,itdoesnotwork.Elementaryform nomenclature(1)Poissons ratioIsotropicAnisotropicModuliCoefficientPolymorphous transformationPhase transformation術(shù)語（1）泊松比各向同性的各向異性的modulus的復(fù)數(shù)系數(shù)多形態(tài)轉(zhuǎn)變相變nomenclature （2）RecrystallizationSubstantiallyPreferable orientationTextureRadiographicHeterophaseAnomaly,（anomalies,anomalous）PeculiarMagnetic effectElinvar術(shù)語（2）重結(jié)晶充分地?fù)駜?yōu)取向織構(gòu)輻射照相的異質(zhì)相（名）不規(guī)則，異常的人或物罕見的、特殊的；特權(quán)磁效應(yīng)恒彈性鎳鉻鋼P(yáng)oissons ratioA rod subjected to uniaxial tension not only increases in length(a change in the size along the axis X)but also diminishes in diameter(compression along the two other axes).Thus,a uniaxial stressed state results in a tridimensional deformation.The ratio of the sizes change in the lateral direction to their change in the longitudinal direction is called Poissons ratio:v is Poissons ratio and is a material elastic property;the negative sign in Eq.indicates that the sample dimensions normal to the primary extension decrease(increase)as the axial length of the sample increases(decreases).For metals,the value of v is often on the order of 1/3.The change in volume associated with the small strains of linear elastic deformation can be obtained by differentiating the expression for the volume(V=l1l2l3)and keeping terms only to first order.The result is For uniaxial deformation,V/V=(l-2).Given that =1/3,an elastic uniaxial strain of 0.5%would produce a volume change of ca.0.2%.Since linear elastic strains are typically smaller than this,the volume change during this type of deformation is usually quite small.The elastic volume change decreases as increases.For an incompressible material,such as a plastically deforming metal for which the volume change is zero,the ratio of lateral to uniaxial strain is 1/2.Such a value does not imply that,an elastic property,has a value of 0.5 for a metal during plastic deformation.long-chain polymers typically have values of v greater than metals.Hence,and as noted in the previous section,these materials differ substantially from other linear elastic materials.Four elastic constants of an isotropic bodyEffect of various factors on elastic moduliTemperatureWork hardeningAlloyingAnomalousTemperature effectSince elastic moduli are associated with interatomic forces and the latter depend on the distances between atoms in the crystal lattice,elastic constants depend on temperature.The temperature dependence of elastic moduli is very weak;As may be seen,the magnitude of modulus decreases with increasing temperature,with the E(T)relationship being almost linear.On the average,the elastic modulus decreases by 2-4 per cent by every 100C.The temperature coefficient of the elastic modulus of a metal depends on the melting point of that metal.For that reason it is sometimes convenient to consider the dependence of the modulus on homologous temperature.In this presentation,the temperature relationship of the modulus is nearly linear.Empirical correlation indicates that the appropriate scaling constant is about 100(when SI units are used;i.e.,kTm in J and in m3).Thus,K=Boltzmann constant,Tm=absolute melting temperature,=volume per atom The modulus decreases concurrent with the increased atomic separation.This decrease is essentially linear with temperature,and an approximate equation describing the modulus-temperature relationship iswhere E is the modulus at temperature T and E0 the modulus at 0 K.The proportionality constant a for most crystalline solids is on the order of 0.5.Thus,for such a typical material,the modulus decreases by about 50%as the temperature increases from 0 K to the materials melting point.Alloying(1)Alloying(2)in AlThe effect of alloying on elastic constants,like the effect of temperature,can be associated with variations in the interatomic distances and interatomic forces in the crystal lattice.As has been demonstrated in radiographic studies,the lattice parameter of a solvent varies almost linearly with the concentration of an alloying element.The dependence of the elastic modulus of an alloy on the concentration of an alloying element is also close to linear.As may be seen from the figure,alloying can increase the elastic modulus in some cases and decrease it in others,depending on the relationship between the bond forces of atoms of the solute and solvent,on the one hand,and the forces of atomic interaction in the solvent lattice,on the other.If the former are greater than the latter,alloying will increase the elastic moduli.Apart from the variations of the interatomic forces in the lattice of the base component,alloying can also cause certain structural changes which can influence appreciably the magnitude of the elastic constants.For instance,if alloying above a definite limit results in the formation of a second phase,the elastic modulus may change additionally compared with its value in a single-phase solid solution.If the second phase has a higher modulus than that of the base metal,its presence will increase the modulus of the heterophase alloy.Work hardeningWork hardening has no essential effect on elastic moduli.A slight decrease of elastic moduli(usually below 1 percent)on work hardening is usually associated with distortions of the crystal lattice of a metal or alloy.Work hardening can result in the formation of preferable orientations,or textures,which make the material anisotropic and can change substantially the elastic moduli.Recrystallization during heating of a deformed metal also forms textures and changes appreciably the elastic moduli.Variations in elastic moduli and due to the formation and destruction of preferable orientations may reach a few tens per cent.In textured polycrystalline materials,the magnitude of an elastic modulus depends on the direction of measurement.AnomalousElinvar Magnetic effects compensate the normal drop of moduli with temperature.The range of climatic variations of temperature.Review Stress(relative/engineeringoractual/true)Strain(relative/engineeringoractual/true)HookeslawYoungsmodulus（Stiffness)ShearmodulusBulkmodulusShearstrainBulkStrainelasticmoduli nomenclature(1）Anelasticity Hysteresis Microscopic Macroscopic CoordinatesThermodynamicLinearityQuasi-術(shù)語（1）n.滯彈性 n.滯后現(xiàn)象 微觀的宏觀的坐標(biāo)熱力學(xué)的線性準(zhǔn)、偽，類似nomenclature （2）InstantaneouslyReciprocityMicroplasticallyMacroplasticallyHysteresis loopElastic aftereffectsStress relaxationInternal frictionDissipate術(shù)語（2）即時地，瞬時地互惠微觀塑性（地）宏觀塑性（地）滯后環(huán)彈性后效應(yīng)力松弛內(nèi)摩擦、內(nèi)耗消耗Ideal elastic bodiesA unique relationship between stress and strain in the elastic regionAssumption:the load is increased infinitely slow so that the state of the system has the time to follow load variations.Or:a change in the state of a system occurs instantaneously with a change in the load.The process of loading and unloading can be regarded energetically reversible.AnelasticityIn real bodies,the direct relationship between stress an strain is disturbed and a hysteresis loop appears on the Stress-Strain diagramStress-strain diagram in cyclic loading and unloading AnelasticityAn irreversible dissipation of energy during the processes of loading and unloading;The energy dissipated in one cycle is determined as the area of the hysteresis loop in the-coordinates and is the measure of internal friction in the material.在彈性極限內(nèi)應(yīng)變落后于應(yīng)力的現(xiàn)象稱為滯彈性。Three different meanings of anelastic deformation:Anelastic deformation is possible without participation of dislocations;(below microscopic elastic limit)Anelastic deformation can be due to energetically irreversible movement of dislocation;(between microscopic elastic limit and macroscopic elastic limit)At still higher stresses,movement of dislocations ceased to be mechanically reversible.Elastic aftereffects and stress relaxation(t)=M(t)where M is the static modulus of elasticity.Relaxation at constant stress(a)and constant strain(b)Elastic aftereffects and stress relaxation(2)The gradual rise of strain in loading and gradual disappearance upon unloading are called respectively the direct and the reverse elastic aftereffect.The gradual variation of the stress to the value corresponding to Hookes law is called stress relaxationElastic and plastic strain in stress relaxation nomenclature （1）Bauschinger effect InhomogeneuosDamping PrecipitationDissolutionAmplitudeResonanceAcoustic術(shù)語（1）包申格效應(yīng)不均勻的阻尼、衰減沉淀、析出分解、溶解振幅共振聲學(xué)的nomenclature （2）Pseudo-PseudoelasticityThermoelasticMartensiteTubularAnnealingDeviateSuccessive術(shù)語（2）偽、假、虛偽彈性熱彈性的馬氏體管狀的退火偏離繼承的、連續(xù)的Internal frictionInternal friction is the ability of materials to dissipate the mechanical energy obtained on load application;The area of the hysteresis loop in the-coordinates is the measure of internal friction in the material.Types of hysteresisWhy internal friction?應(yīng)力感生有序產(chǎn)生內(nèi)耗；位錯內(nèi)耗；熱流產(chǎn)生內(nèi)耗；磁致伸縮內(nèi)耗；非共格晶界內(nèi)耗應(yīng)力感生有序產(chǎn)生內(nèi)耗應(yīng)力感生有序產(chǎn)生內(nèi)耗Successive stages of deflection of a locked dislocation line at increasing stressStress-dislocation strain relationship for the model The Bauschinger effect金屬材料經(jīng)過預(yù)先加載產(chǎn)生少量塑性變形（殘余應(yīng)變小于4%），而后再同向加載，規(guī)定殘余伸長應(yīng)力增加；反向加載，規(guī)定殘余伸長應(yīng)力減少的現(xiàn)象叫做包申格效應(yīng)；包申格應(yīng)變：在給定應(yīng)力條件下，拉伸卸載后第二次拉伸與拉伸卸載后第二次壓縮兩曲線之間的應(yīng)變差。Bauschinger effect in twisted tubular steel specimen Anisotropy of slip barriers causing Bauschinger effectSignificance of anelastic phenomenaInstrument-making,elastic element,bells or musical instrumentsHigh damping capacity:diminish noise,avoid failures due to resonanceInhomogeneity,local microplastic deformation,internal transformation,superplastic alloys etc for High-damping application.Psudoelasticity and shape memory effectAnomalous mechanical behaviour:thermoelastic martensitic transformation;Psudoelasticity(or superelasticity)and“shape memory”Martensitic transformation at an external stress;Reverse transformation by heating;Ni-Ti,Cu-Al-Ti,etc.