《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(yǔ)（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(yǔ)（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(jiàn)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(yǔ)（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(yǔ)（2）即時(shí)地，瞬時(shí)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(yǔ)（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(yǔ)（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(cuò)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(guò)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(zhǎng)應(yīng)力增加；反向加載，規(guī)定殘余伸長(zhǎng)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.Plastic deformation and Strain hardeningNomenclaturePlastic deformation Strain hardeningSlip Resolved shear stressCritical resolved shear stress Austenitic IntersectLacquer塑性變形應(yīng)變硬化滑移分切應(yīng)力臨界分切應(yīng)力奧氏體的相交、交叉、橫斷漆、涂漆于使表面光滑術(shù)語(yǔ)Nomenclature 術(shù)語(yǔ)Peculiarity Polycrystalline Periodically Isothermal CrystallographyHexagonal Syngony 特性多晶的周期性地等溫的結(jié)晶學(xué)、晶體學(xué)六角形的，六邊形的晶系The mechanical behaviour of metals and alloys The mechanical behaviour of metals and alloys is described by the following laws of their resistance to elastic and plastic deformation and fracture.The isothermal mechanical behaviour of a metal is determined by four factors:Stress,time,shape,and structure.Peculiarities of Mechanical behaviour(i)how high can be periodically or constantly applied loads so that an object could restore its shape and size upon their removal;(ii)how high is the resistance of an object to plastic flow at a short-term or long-term load applied,what is the rate of variation of the shape and dimensions of the object,and what characteristics and particular conditions of load application determine the course of plastic flow at a desired rate;(iii)how large is the force to cause fracture of the object to pieces.More deep analysis of the mechanical behaviour of metals and alloys in the last two or three decades is associated with the development of the theory of dislocations and the description of the phenomena observed on the atomic level and also with improvements in the methods of continuum mechanics.This association between various levels of description of the mechanical behaviour of materials seems to be fruitful.The mechanical behaviour at the macroscopic level is studied in other courses;we shall deal with the mechanism of plastic flow at the dislocation level.Carbon steel in the elastic region Linear elasticity and subsequent plasticity Unstable creep in annealed copper Plastic deformation The deformation which is independent of time and is retained upon stress release is called plastic deformation.Effect of deformation rate on stress-strain curve Slip of metal crystalsa Zn,b Cd,c-Sn,d-Bi Variation of slip orientation in deformed tungsten single crystal at a different direction of external shear stress Slip of low-carbon steel (polycrystalline)Slip Slip is the displacement of a portion of a crystal relative to another portion with the crystal structure of both portions remaining unchanged.a-undeformed,b-elastically deformed,c-elastically and plastically deformed,d-plastically deformation in which slip has taken place;AB slip plane Slip planes in three typical lattice of metal crystals(Slip plains usually have the closest packing of atoms)Three possible slip directions in-Fe;the shortest direction is preferable Microstructure of austenitic Cr-Ni-Mo steel deformed 25%(a.)and 50%(b.)Strain bands of low-carbon steel Stretched grains in low-carbon steelCrystallography of slip in single crystals Fracture of zinc single crystal In cubic syngony crystals this situation is impossible,i.e.the ultimate strength in tension cannot be attained earlier than plastic flow begins.For instance,in f.c.c.crystals where the four systems of 111 planes intersect one another,it is impossible to orientate the crystal relative to the tensile or compressive axis so that the shear stress be zero in all these planes.At least one of the plane systems turns out to be orientated for favourable slip.With f.c.c.metals(aluminium,copper,lead,gold,silver)subjected to tension or compression,fracture is always preceded by a plastic deformation.B.c.c.crystals have no planes with such a dense packing of atoms as the basal planes in c.p.h.crystals or octahedral planes in f.c.c.crystals.For instance,the 110 planes in b.c.c.crystals,though they are characterized by the closest packing of atoms,differ in this parameter only slightly from other families of planes in that lattice.The most essential structural feature of b.c.c.crystals,which can influence the course of slip,is the existence of a family of close-packed directions,cube diagonals.These directions play even a greater part in slip than the close-packed directions in hexagonal or face-centered cubic crystals.In b.c.c.crystals,however,the direction of preferable slip can be found in several families of planes:in a-iron,for instance,it is found in 110,112 and 123.In that case,slip occurs simultaneously in a number of families of planes,in the example discussed,in two or even three families;in the general case,it is impossible to predict reliably which of the slip planes in b.c.c.metals will be operative.On the other hand,these metals have a larger number of intersecting systems of probable slip planes than c.p.h.metals and for that reason they are more plastic than the latter.As compared with f.c.c.metals,the slip planes in b.c.c.metals differ less appreciably from the other planes of the b.c.c.lattice and have a lower density of atoms packing than the slip planes in the f.c.c.lattice.For that reason,a higher shear stress is required to initiate slip in b.c.c.crystals but they offer a lower resistance to the development of plastic deformation before fracture.Slip systems in metallic crystal structuresIn general,the ductility of b.c.c.metals,such as a-iron,tungsten,molybdenum,or|-brass has intermediate values between those of f.c.c.and c.p.h.metals.nomenclature 術(shù)語(yǔ)Schmid-Boas law Resolved shear stress Critical resolved shear stress TwinningOctahedral Indeterminacy Incoherent boundaries分切應(yīng)力臨界分切應(yīng)力孿生八面體的不確定不連貫界面Partial coherent boundariesIncoherent boundaryResolved shear stressSchmid-Boas lawOrientation factor(Schmid factor)EXAMPLE PROBLEM 1.Hexagonal close-packed zinc slips by basal plane slip.A zinc single crystal is oriented so that the normal to its slip plane makes an angle of 60 with the tensile axis.If the three slip directions have angles of 38,45,and 84 with respect to this axis,and the critical resolved shear stress for Zn is 2.3 MN/m2,determine the tensile stress at which plastic deformation commences.EXAMPLE PROBLEM 2.A single crystal having a simple cubic structure(slip planes 100,slip directions)is oriented such that the tensile axis is parallel to the 010 crystal axis.Make a list of the slip systems in this crystal and calculate the Schmid factor for this loading geometry.T.A.010001Consider this problem for a situation where the tensile axis is parallel to the 011 crystal axis.Effect of orientation factor on slip stressEffect of temperature on in Mg single crystal1、Burke and Hibbard2、Schmid and SiebelEffect of temperature on and in iron single crystals1、upper yield limit2、lower yield limit3、critical resolved shear stressEffect of temperature on in Cu and Cu alloys1、pure Cu2、Cu-Ag(0.1%)3、Cu-Ge(0.33%)4、Cu-Ag(0.2%)The relationship between and composition of f.c.c.single crystals Effect of concentration of alloying elements on in Mg alloys1-Mg2-Mg-In3-Mg-Cd4-Mg-Ti5-Mg-Al6-Mg-ZnEffect of alloying elements on depending on the difference in atomic diametersThe relationship between and composition of f.c.c.single crystalsCrystallographic diagram of twinningTwinning takes place where the shear stress attains the critical value and,like slip,obeys certain crystallographic relationships.The mirror image plane is called the twinning plane and the direction of displace is called the twinning direction.The twinning direction is polar;Twinning shear can occur in one direction only;Atomic planes are displaced in twinning through the same very small distance(smaller than the interatomic distance),so that no individual visible strain traces form on the surface of a twin band.The role of the twinning process usually increases with decreasing temperature of deformation and/or increasing rate of deformation.Since the stress needed for propagation of a twin is much higher than the slip stress,it is clear that twinning is possible under particular conditions when the resolved shear stress turns out to be high.Twinning in b.c.c.and f.c.c.crystals is usually observed at low temperatures and high deformation rates and in c.p.h.crystals,when the available orientations are unfavourable for basal slip.Effect of the grain size d on the critical stresses of twinning t ans slip s-Fe,-105The supressing effect of fine grain on twinning can be attributed three reasons:A higher dislocation density;A lower stress concentration;(nucleation)Grain boundaries are barriers for the growth of twins.(critical-size twins)Twinning deformation of Cr-20%Fe nomenclature 術(shù)語(yǔ)SinusoidalConditioned MultiplicationProportional Luders-Chernov bands Configuration Avalanche Interstitial ConvexSchematic正弦曲線有條件的增殖、乘法比例的、均衡的呂德斯帶、拉伸應(yīng)變帶、滑移線痕構(gòu)造、結(jié)構(gòu)、配置、外形雪崩空隙的凸起的示意性的Luders-Chernov bandsShear in an ideal crystal(a);Variations of force and energy in shear(b);Variations of energy in shear of two adjacent atomic planes with account of energy variations in the source of deformation(c).Successive stages of unit shearMovement of an edge dislocation in simple cubic latticeYield Stress PeakCrystals with impuritiesIn crystals with impurities,especially in b.c.c.crystals,the plastic flow starts at a certain drop of the deforming stress.After that one can observe a continuous deformation with almost constant stress,which is accompanied with the propagation of the Luders-Chernov bands.This type of variation of flow stress is often attributed to locking of dislocations by impurity atoms.Especially strong interaction can be observed between dislocations and interstitial impurities in b.c.c.metals.It is assumed that the upper yield limit corresponds to stress required to“tear off”dislocations from the atmosphere of impurities and the low yield limit is the stress required to move free(unlocked)dislocations through the lattice.Variations of the critical resolved shear stress with deformation in(a)Ge and(b)LiF single crystalsIn rather pure crystalsThe concentration of impurities is very low or at least insufficient for dislocation locking;The drop of the yield stress in such crystals on passage into plastic region is conditioned,first,by a low density of dislocations and,second,by a strong stress sensitivity of the speed of dislocations movement.A distinct yield stress exhibits in such b.c.c.crystals:(i)in the original state,the density of unlocked(mobile)dislocations decreases down to 102-104 cm-2;(ii)in subsequent deformation,the density of dislocations increases with strain roughly by a factor of 1010;(iii)the rate of movement of dislocations is strongly stress-sensitive.Many researchers suppose that the yield stress peak in b.c.c.metals is associated mainly with the strong stress sensitivity of the rate of dislocation movement and,to a less extent,with unpinning of dislocations from impurities.General theory The general theory of interrupted plastic flow attributes the appearance of a sharp yield peak to rapid increase of the number of mobile dislocations at the beginning of plastic flow.In other words,a sharp yield peak appears always when the initial density of mobile dislocations is low,but dislocations can multiply rapidly in the course of plastic deformation.The drop of the stress at the upper yield limit yu is determined by nucleation and multiplication of mobile dislocations.The latter usually starts at stress concentrators and continues in the Luders-Chernov bands.In real crystals,the intensity of pinning of mobile dislocations may be different.If the are pinned only weakly,plastic flow begins owing to their unpinning;with strong blocking of dislocations,plastic flow starts due to the creation of new dislocations at stress concentrators.In polycrystals,grain boundaries inhibit the propagation of plastic flow from grain to grain until the stress concentration at the ends of a slip band(or twinning band)causes flow in an adjacent grain either by dislocation unlocking(with weak locking)or by creation of new dislocations in volumes at the other side of of the grain boundary(with strong locking).In f.c.c.metalsThe mechanism described is in principle poorly applicable to f.c.c.metals crystals since dislocations in them can only weakly interact with impurity atoms.Indeed,no yield drop due to dislocation unpinning is practically observed in these crystals,except for singles crystals of heavily alloyed metals.An important circumstance is also that the speed of dislocation movement in f.c.c.crystals is only weakly depend on stress;for instance,this relationship is estimated to be proportional to roughly 200 for copper and to 300 for silver.Schematic stress-strain curves at two different temperatures(T2T1)Diagram of the Cottrell-Stokes experiment for determining the effect of test temperature on deforming stressEffect of the amount of deformation on the ration of the deforming stresses at variations of test temperature(of Al)1、from 293 to 90 K;2、from 90 to 293KAppearance of the valid yield point and yield elongation zone on the stress-strain curve on a change from a low temperature(1)to a higher temperature(2)Stress-strain curves of an aluminium crystalABCtensioning in liquid air;the specimen at point C was held at room temperature(recovery or age-harding);DEfurther tensioning in liquid air.The mechanical state of a crystal cannot be described by a single fine-structure parameter,for instance,by dislocation density,and that at least one additional parameter is needed,such as the distribution of dislocations which describes indirectly the stability of the dislocation structure formed.With the same amount of low-temperature and high-temperature deformation,slip lines in the later case are positioned thicker.It has been supposed that the material near an operative slip band is“annealed”,as it were at a certain temperature:above the lower temperature of deformation and near the higher temperature.For this reason,new slip lines in the high-temperature deformation are formed preferably close to the existing ones,thus forming a thicker set.With the same elongation in the low-and high-temperature deformation,dislocations in the former case will be arranged less uniformly on the account of the greater inhomogeneity(gradient)of deformation in the bulk of a crystal.A low-temperature deformation produces more local pile-ups of dislocations at barriers and local fields of internal stress.This highly distorted state of a crystal results in that the strain hardening obtained by low-temperature deformation is unstable.In subsequent high-temperature deformation,the unstable component of strain hardening disappears quickly owing to the simultaneous effect of temperature and stress.This occurs either by destruction of barriers(at tips of pile-up),after which the freed avalanche of unpinned dislocations moves in a crystal and produces slip at a lower stress or by liberation of dislocations in pile-ups due to activation of cross-slip.Variations of the conditional yield limit with temperature in(I)single-phase and(II)two-phase alloys1-carbonyl nickel;2-Ni+13%Al,alloy with precipitates;3-Ni+13%Al,supersaturated solid solution;4-Ni+10%Al,single phase alloyWork HardeningSchematic of the shear stress-shear strain curve of a single crystal Stage I:The crystal work-hardening rate after yielding is initially low(has a low value of d/d).This easy glide is associated with single slip on the slip system having the maximum value of ;The strong work hardening resulting from interactions of dislocations does not occur.The work hardening observed during easy glide results from the overlap of dislocation stress fields among dislocations gliding on parallel planes;Stage II:the linear hardening region,the slope of the curve is large,on the order of G/300.The transition from Stage I to Stage II behavior is almost invariably associated with the onset of multiple slip,and the strong work hardening resulting from interactions among dislocations on nonparallel planes.Stage III,“exhaustion”or“saturation”hardening,is characterized by a reduction in the work-hardening rate in comparison to Stage II.The above description is in accord with many experiments.For example,the strain extent of Stage I decreases with temperature,and this is consistent with the easier onset of multiple slip at higher temperatures.Likewise,the extent of Stage II is reduced as temperature is raised and this is consistent with recovery processes operating more effectively at higher temperatures.Constraints on sample deformation during tensile testing(a)If the sample grips did not geometrically restrain a single crystal,it would assume the shape shown.(b)The grips prove for axial alignment of the crystal and tensile.This is accomplished by a rotation such that angles between the tensile axis and slip plans normal and the slip direction are changed from their original values.Concurrently,other slip systems are having their values of these angles changed.When the Schmid factor on a secondary system equals that on the primary one duplex slip initiates.Near the specimen grip some bending of the crystal may take place.Change in crystal orientation during compression(a)The initial orientation of the slip plane and direction with respect to the compression axis,(b)During compression the slip direction rotates away from the compression axis,while the slip plane normal rotates toward it.Even though the respective rotations are different for compression and tension,the resultthat other slip systems eventually become active during single crystal plastic deformationis the same for both situations.Although the basic slip mechanisms are the same in polycrystals as single crystals,their stress-strain behavior differs substantially.In polycrystals,the displacements across grain boundaries must be matched,so as to permit the grains to deform in concert.In the absence of such cooperative displacements,voids or cracks would appear at the grain boundaries.PLASTIC FLOW IN POLYCRYSTALS In a physical sense,therefore,neighboring grains restrain the plastic flow of each other and,in so doing,provide a polycrystal with an intrinsically greater resistance to plastic flow than that of a single crystal.Tensile deformation of a bicrystalThe crystals A and B are of the same material,but oriented differently with respect to the tensile axis.Dilational and shear strains must be matched along the interface(the xz plane)between the crystals.This constraint increases the flow stress of a bicrystal in comparison to that of a single crystal.The following conditions must be satisfied at the grain boundary in order to provide material continuity Since one grain has a higher value of cos cos than the other,the constraints described by former equations restrict the deformation of this more favorably oriented grain and result in a higher yield stress(and a greater work-hardening response)of the bicrystal.In a polycrystalline aggregate,the grain boundary constraints are more restrictive than those for a bicrystal and,thus,the level of the stress-strain curve for a polycrystal is correspondingly higher.Room-temperature tensile force-strain curves of single crystals,bicrystals,and polycrystals of niobium Room-temperature tensile stress-strain curves of single crystals,bicrystals,and polycrystals of NaCl Surface slip traces on a Fe-3%Si bicrystal Primary slip traces in each of the crystals run from lower left to upper right and are found in grain interiors as well as near the grain boundary.Traces of secondary slip(running from upper left to lower right),which maintains strain compatibility across the boundary,are restricted to the boundary region.The tensile yield strength(y)relates to crss where m is a suitable average for the polycrystal.In evaluating m,care must be taken that it reflects the greater constraints provided by the least-favorably oriented grains;that is,m is not a geometrical average of the m values of all of the randomly oriented crystals but is,rather,somewhat higher than this.m is found to be 3.06 for the fcc structure and 2.75 for the bcc structure.An additional strengthening effect associated with polycrystals c