《材料力學性能》中英文全套PPT課件,材料力學性能,材料,力學性能,中英文,全套,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.應力應力是和物體單位表面單位表面上受到的載荷載荷。A relative quantity;相對量The dimension of stress is determined as the force active per unit area of the body section to which the force is applied.其大小由受力物體單位表面載荷大小決定。Usually measured as newtons per square metre(N/m2)or kgf/mm2;通常單位 注：kgf/mm2表示的是每平方毫米的面積上施加1kg力的壓力，這個壓強大約相當于10Mpa。The units of stress express the principal mechanical properties(ultimate strength強度極限,resistance to plastic flow塑性變形抗力,resistance to indentation壓痕阻力,fatigue strength強度疲勞,creep strength蠕變強度,etc.)應力的單位反映了它的力學性質The case of axialtension of a cylindricalrod)圓柱體受軸向載荷的情況if S=constant (uniform distribution of the stress over the cross section)應力在橫截面上均勻分布。P=SF or S=P/FIn a more general case The normal stress(正應力)The shear stress(剪應力)單軸拉伸的莫爾圓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)Stress工程應力和真實應力F:forceapplied作用力;A0:areabeforedeformation 變形前的面積The engineering stress is often employed for elastic stresses or stresses for componentsdeformed to small plastic strains.工程應力通常應用于彈性應力或者適用于微小塑性應變下的應力At large strains,the change in cross-sectional area significantly alters the actual stresses.在大的應變下，橫截面的改變會顯著改變真實應力The true stress is:where A is the instantaneous 瞬時的area.Strain Strainis the ratio of the change in dimension to its initial value.應變是材料尺寸的變化量和它初始尺寸的比值。Axial tension of a cylindrical rod as;圓柱體受到的軸向拉力Load applied;拉力加載Rod deformed,the length increased from l0 to ln;桿開始變形，長度由l0伸長到lnengineering strain工程應變=桿長度改變量/桿的原始長度The 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相應，對于擠壓時，截面積增加：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 a0，u 0；受壓時a a0，u 0。The equilibrium condition 等效計算式can be written,as follows:where (u)is the bond（結合）energy on displacement（位移）u.其中(u)是距離為u時原子間的作用能。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.研究兩個原子間的作用機制，可以從本質上來探尋Hookes law，來研究外作用力和它所造成的位移的關系。For Hookes law to be valid（有效）,the following three conditions must be satisfied:胡克定律的應用有三個條件：(1)the function（函數(shù)）(u)must be continuous;作用能(u)必須是連續(xù)的(2)the function(u)must have a minimum d/du=0 at u=0;and 當u=0時，d/du=0，(u)必須具有最小值(3)the displacement u must be much less than a0.變形量u必須遠小于原子間的初始距離a0。The first condition makes it possible to expand the interaction energy function into a Taylor series:第一個條件允許把方程展開成Taylor式In this equation,0 is the interaction energy at u=0 and,all the derivatives are obtained for the point u=0.在等式中，0是位移量u=0處的原子間初始能量，該等式是在u=0處展開的。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:因為在u=0處d/du，并且由于u很小，所以三次微分和更高次可以被忽略，得到：The second derivative(d2/du2)o is the curvature（曲率）of the function(u)in point u=0,and,therefore,it does not depend on u and is a constant.二次微分項是函數(shù)(u)在u=0處的變化率，因此它不依賴于U，它是一個常數(shù)。Thus,weobtainf=constu,i.e.the force is proportional to displacement(Hookes law).力與形變量成比例。這就解釋了為什么應力和應變對應成比例關系。It should be recalled that the region of a direct proportionality between the force and displacement is limited to slight deformations.應當提醒的是：應力應變線性關系只適用于微量變形中。With an appreciable magnitude of displacement u,the terms of higher powers of u cannot be neglected and,therefore,the(u)curve deviates from the straight line.當位移量u很大時，u的高階冪不能忽略，那(u)就不是直線了。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.在實際中，這個理想情況不可能遇到，因為塑性變形在極小應力下就發(fā)生了。因為這個原因（這里面有位錯的原因），胡克定律就不適用了。Perfect thread-shaped metal crystals of a diameter of around 2 um(called whiskers（晶須）),in which plastic flow is impeded（阻礙）,can,however,be deformed elastically by a few per cent and,at high elastic deformations,a deviation from Hookes law can be observed experimentally 直徑為2 um的針狀金屬，加載載荷，當變形為百分之幾的時候盡管里面已經(jīng)發(fā)生了塑性變形但仍符合為彈性變形規(guī)律。如果再超過一定的變形量，就不符合胡克定律。在實驗中可能觀測到右圖：InshearstressTheshearstressisrelatedwithacorrespondingsheardeformationbysimilarexpression:切應力對應一個切變 量，有相同的表達式：whereGistheshearmodulus(orthemodulusofelasticityinshear)G 是切變模量。(1-3)Inhydrostaticcompression(ortension)在流體拉（壓）中Hookeslawexpressesadrec直直接接proportionalitybetween the hydrostaticpressurePandthevolumechangex:胡克定律揭示了流體壓力P和體積變化量x間的關系where K is the modulusof bulk（體體積積）deformation.K稱為體彈模量(1-4)Hookes law(3)Formulae(1-2),(1-3)and(1-4)expresswhatiscalledHookslaw.(1-2),(1-3)和(1-4)公式是胡克定律。Determinestherelationshipbetweenstressandstrainactinginthesamedirection用來決定同方向上的應力應變間的關系。Whendeformationappearinadirectiondifferentfromthatofthestressaction,itdoesnotwork.不適用于不同方向上的應力應變。Elementaryform基本形式 nomenclature(1)Poissons ratioIsotropicAnisotropicModuliCoefficientPolymorphous transformationPhase transformation術語（1）泊松比各向同性的各向異性的modulus的復數(shù)系數(shù)多形態(tài)轉變相變nomenclature （2）RecrystallizationSubstantiallyPreferable orientationTextureRadiographicHeterophaseAnomaly,（anomalies,anomalous）PeculiarMagnetic effectElinvar術語（2）重結晶充分地擇優(yōu)取向織構輻射照相的異質相（名）不規(guī)則，異常的人或物罕見的、特殊的；特權磁效應恒彈性鎳鉻鋼Poissons 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.一個桿受到軸向拉伸后，長度增加，同時直徑減小，因此一個軸向載荷造成的是一個三維的變形。The ratio of the sizes change in the lateral(橫向的)direction to their change in the longitudinal direction is called Poissons ratio:截面方向尺寸的變化和長度方向尺寸的變化比為泊松比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).v是泊松比，是一材料的彈性性能參數(shù)。上式中的負號(正號)表明當桿受拉(壓)時，其截面積減小(增加)。For metals,the value of v is often on the order of 1/3.對金屬來說，v大約在1/3左右。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 應變造成的體積方面的變化，可以由體積計算公式V=l1l2l3得到，如下：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.對于軸向變形而言V/V=(l-2)，當=1/3時，一個0.5%的軸向變形在體積方面造成的變形為0.2%。因彈性變形體軸向變形明顯小于0.5%，因此其體積的變形往往很小。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.當v增加，體積變形減小。對于一個不可壓縮的材料，例如體積變化量為0的塑性變形的金屬，截面應變對軸向應變的比為-0.5，但它并不表示塑性變形中泊松比為0.5long-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.長鏈聚合物泊松比明顯大于金屬因此，這些材料的材質和線性彈性材料有明顯的區(qū)別。Four elastic constants of an isotropic body基本上與價位、熔點呈線性關系Refractory metal 難熔金屬Strong carbide forming metal 強碳化物形成金屬Effect of various factors on elastic moduli對彈性模量的幾種影響因素Temperature溫度Work hardening加工硬化Alloying合金化Anomalous異?，F(xiàn)象Temperature 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.由于彈性模量和原子間的作用力有關，而原子間的作用力依靠晶體點陣中原子間的作用距離，所以彈性模量和溫度有關。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.彈性模量對溫度的依賴是非常微弱的，由上圖可以看出，彈性常數(shù)隨溫度的增加而減小，E(T)曲線幾乎成線性關系。平均來說，溫度每增加100度，彈性常數(shù)減小24個百分點。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.一塊金屬的彈性模量的溫度因數(shù)取決于該金屬的熔點。因此可明確相同溫度下彈性模量的變化規(guī)律。表述之，溫度和彈性模量呈近似線性關系。Empirical（經(jīng)驗主義的）correlation indicates that the appropriate scaling constant is about 100(when SI units are used;i.e.,kTm in J and in m3).Thus,經(jīng)驗公式表明近似比例常數(shù)是大約100.K=Boltzmann constant,波爾茲曼常數(shù)Tm=absolute melting temperature,熔點溫度=volume per atom 單個原子的體積The modulus decreases concurrent（一致的）with the increased atomic separation.This decrease is essentially linear with temperature,and an approximate equation describing the modulus-temperature relationship is當原子間距離增加時，彈性系數(shù)減小，這個減小和溫度成線性關系。相應彈性系數(shù)和溫度間的關系式為：where E is the modulus at temperature T and E0 the modulus at 0 K.The proportionality constant a for most crystalline（透明的，水晶般的）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.上式中E是溫度T時的彈性模量，E0是溫度為0K時的彈性模量，比例常數(shù)a對多數(shù)晶體而言大約是0.5，因此對于一個典型材料，當溫度由0K增加到材料的熔點時彈性模量減小50%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.合金對彈性系數(shù)的影響，就像溫度的影響一樣，和晶體點陣內的內部原子間隔距離和作用力有關。As has been demonstrated in radiographic studies,the lattice parameter（參數(shù)）of a solvent（溶劑）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.在多項晶體的研究中已經(jīng)證實：溶劑點陣常數(shù)因合金成分濃度的不同而近乎成線性變化。合金彈性系數(shù)和合金成分的濃度也接近線性關系。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（溶質）and solvent（溶劑）.從上面的數(shù)據(jù)可以看出，合金有時增加彈性模量，有時減小彈性模量，是取決于溶劑、溶質原子間的相互作用力。on the one hand,and the forces of atomic interaction in the solvent lattice.1.如果溶質溶劑原子間的作用力小于溶劑點陣中溶劑原子間的相互作用力，那么合金將減小彈性模量。on the other,If the former are greater than the latter,alloying will increase the elastic moduli.2.如果溶質溶劑原子間的作用力大于溶劑點陣中溶劑原子間的相互作用力，那么合金將增加彈性模量。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.除了改變基底點陣中原子間的作用力外，合金也可以引起其結構的改變，這將顯著改變彈性模量常數(shù)的大小。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.例如如果合金超過一個有限的度就可以形成第二相，那么其彈性系數(shù)和單相時相比會發(fā)生顯著變化。If the second phase has a higher modulus than that of the base metal,its presence will increase the modulus of the heterophase（異相質）alloy.如果第二相的彈性系數(shù)比基底金屬大，它的出現(xiàn)將增加此異相合金的彈性系數(shù)。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.加工硬化自身（冷塑性加工）對彈性模量沒有什么本質影響。冷塑性加工導致彈性模量輕微減小，常伴隨著金屬或合金晶體點陣的畸變。Plastic deformation can also cause some other structural change in the material.Work hardening can result in the formation of preferable orientations（擇優(yōu)取向）,or textures（織構）,which make the material anisotropic（各向異性）and can change substantially（充分地）the elastic moduli.塑性變形會導致金屬結構的改變。加工硬化能使晶體的形成晶面的擇優(yōu)取向或織構，從而導致材料內部晶體結構各向異向，從而大大改變彈性模量。Recrystallization during heating of a deformed metal also forms textures and changes appreciably the elastic moduli.變形金屬在加熱過程中的重結晶也能形成織構，從而明顯改變材料的彈性模量。Variations in elastic moduli and due to the formation and destruction of preferable orientations may reach a few tens per cent.擇優(yōu)取向的形成或減小，導致部分彈性系數(shù)的改變可能達到幾十個百分點。In textured polycrystalline materials,the magnitude of an elastic modulus depends on the direction of measurement.在已形成織構的多晶體材料中，彈性系數(shù)的大小和測量的方向有關。Anomalous異常現(xiàn)象Elinvar（）鎳鉻鋼 Magnetic（有磁性的）effects compensate（補償）the normal drop of moduli with temperature.磁效應補償了由于溫度而減小的彈性模量。The range of climatic variations of temperature.氣溫（-50 50）變化范圍下的異?，F(xiàn)象。Review Stress(relative/engineeringoractual/true)Strain(relative/engineeringoractual/true)HookeslawYoungsmodulus（Stiffness)ShearmodulusBulkmodulusShearstrainBulkStrainelasticmoduli nomenclature(1）Anelasticity（）Hysteresis（）Microscopic Macroscopic CoordinatesThermodynamicLinearityQuasi-術語（1）n.滯彈性 n.滯后現(xiàn)象 微觀的宏觀的坐標熱力學的線性準、偽，類似nomenclature （2）InstantaneouslyReciprocityMicroplasticallyMacroplasticallyHysteresis loopElastic aftereffectsStress relaxationInternal frictionDissipate術語（2）即時地，瞬時地互惠微觀塑性（地）宏觀塑性（地）滯后環(huán)彈性后效應力松弛內摩擦、內耗消耗Ideal elastic bodies理想彈性體A unique relationship between stress and strain in the elastic region 彈性范圍內應力和應變有精確關系。Assumption:the load is increased infinitely slow so that the state of the system has the time to follow load variations.假定：載荷無限慢地加載，體系狀態(tài)能有足夠的時間來產(chǎn)生應變。Or:a change in the state of a system occurs instantaneously with a change in the load.或者：載荷每一個點變化系統(tǒng)中都有一個實時的應變和它對應。The process of loading and unloading can be regarded energetically reversible.加載和卸載過程在能量上可認為是可逆的。Anelasticity滯彈體In real bodies,the direct relationship between stress an strain is disturbed and a hysteresis loop appears on the Stress-Strain diagram 在實際受力體中，應力和應變間的直接關系被破壞了，應力應變圖中出現(xiàn)了一個滯后環(huán)。Stress-strain diagram in cyclic loading and unloading循環(huán)加載卸載中應力應變圖 AnelasticityAn irreversible dissipation of energy during the processes of loading and unloading;在加載和卸載中產(chǎn)生一個不可回復的能量損失。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.在一個循環(huán)中損失的能量由應力應變圖中后滯環(huán)的面積來確定。其面積也是材料內耗的一個度量。在彈性極限內應變落后于應力的現(xiàn)象稱為滯彈性。Three different meanings of anelastic deformation:滯彈性變形的三種情況Anelastic deformation is possible without participation of dislocations;(below microscopic elastic limit)1.滯彈性可能沒有位錯的參與。例如：它能在彈性極限下的應力發(fā)生。它的大小不符合胡克定律，滯彈性變形需要一段時間間隔才發(fā)生，并不是及時發(fā)生的。就這而言滯彈性現(xiàn)象和塑性變形有一點相似性。例如，剛卸載時，材料的直徑和初始直徑有一定的差別。但和塑性變形不同的是，過一段時間后，這種不同便會逐漸消失，最終沒有任何殘余變形被觀察到。這種變形應該稱作“偽滯彈性”。Anelastic deformation can be due to mechanically irreversible movement of dislocation;(between microscopic elastic limit and macroscopic elastic limit)2.彈性后滯也可以解釋為位錯不可回復的運動而造成的。例如，當應力沒有達到彈性極限時，有些位錯就開始運動，但在到達晶體表面之前，就在晶體內被阻塞了。當卸載時，阻礙位錯運動的力消失，它們就可以回到原來的位置，所以沒有殘余變形發(fā)生。但任何位錯的運動都會消耗能量，所以滯彈性現(xiàn)象在能量上是不可回復的。就這種解釋而言，滯彈性變形可以理解為可以回復的塑性變形。At still higher stresses,movement of dislocations ceased（中止）to be mechanically reversible.3.當應力增大到一定程度時，位錯就不可回復，卸載后位錯就不回到它原來的位置，一個可測量的變形出現(xiàn)了。無論經(jīng)過多長時間彈性滯后環(huán)都不會在=0，=0處合攏。這種情況，滯彈性變形在變形機制和卸載體積殘余變化上都類似于塑性變形。我們應該知道的是在實際中，幾種不同的滯彈性效應是同時發(fā)生的。在應力超過彈性極限時，偽滯彈性變形可以忽略，因為它和總的滯彈性變形相比來說很小。Elastic aftereffects and stress relaxation彈性后效和應力松弛 把應力和應變的時效差異考慮在內的話，應描述為：(t)=M(t)where M is the static modulus of elasticity 其中M是彈性模量的狀態(tài)參數(shù).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.加載時逐漸增加，卸載時逐漸減小的應變，稱為直接可回復的彈性后效The gradual variation of the stress to the value corresponding to Hookes law is called stress relaxation 應力逐漸變化到依胡克定律理論計算的應力大小稱為應力松弛。Elastic and plastic strain in stress relaxation開始時，殘余塑性變形為0，所以0=e1。塑性變形隨時間而增加，而彈性變形隨時間而減小。因為應力和彈性變形相伴出現(xiàn)，彈性減小時，應力減小，因此應力松弛出現(xiàn)了。nomenclature （1）Bauschinger effect InhomogeneuosDamping PrecipitationDissolutionAmplitudeResonanceAcoustic術語（1）包申格效應不均勻的阻尼、衰減沉淀、析出分解、溶解振幅共振聲學的nomenclature （2）Pseudo-PseudoelasticityThermoelasticMartensite()TubularAnnealing()DeviateSuccessive術語（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 friction內耗Internal friction is the ability of materials to dissipate the mechanical energy obtained on load application;內耗是材料在加載時消耗機械能的能力。The area of the hysteresis loop in the-coordinates is the measure of internal friction in the material.應力應變圖中彈性后滯環(huán)的面積是材料內耗的量度。Types of hysteresis幾種彈性滯環(huán)Why internal friction?應力感生有序產(chǎn)生內耗；位錯內耗；熱流產(chǎn)生內耗；磁致伸縮內耗；非共格晶界內耗應力感生有序產(chǎn)生內耗應力感生有序產(chǎn)生內耗Successive stages of deflection of a locked dislocation line at increasing stress應力增加，一個被鎖住的位錯連續(xù)的彎曲變形Stress-dislocation strain relationship for the model 模型中應力位錯應變關系The Bauschinger effect包申格效應金屬材料經(jīng)過預先加載產(chǎn)生少量塑性變形（殘余應變小于4%），而后再同向加載，規(guī)定殘余伸長應力增加；反向加載，規(guī)定殘余伸長應力減少的現(xiàn)象叫做包申格效應；包申格應變：在給定應力條件下，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變差。Bauschinger effect in twisted tubular steel specimen管狀鋼扭轉時發(fā)生的包申格效應 Anisotropy of slip barriers causing Bauschinger effect各向異性導致的滑移障礙造成的包申格效應Significance of anelastic phenomena滯彈性現(xiàn)象的重要性Instrument-making,elastic element,bells or musical instruments 常用來制造樂器、彈性器件、鈴和其它樂器。High damping capacity:diminish noise,avoid failures due to resonance 高的阻尼衰減能力，能消除噪音，減小由于共振而造成的失真。Inhomogeneity,local microplastic deformation,internal transformation,superplastic alloys etc for High-damping application.結構不均，局部微觀塑性變形，內部變形，高塑性合金等可應用高阻尼衰減場合。Psudoelasticity and shape memory effect偽彈體和形狀記憶效應Anomalous mechanical behaviour:thermoelastic martensitic transformation;異常變化機制：馬氏體熱彈性轉變Psudoelasticity(or superelasticity)and“shape memory”偽彈體和形狀記憶Martensitic transformation at an external stress;在外力作用下的馬氏體相變Reverse transformation by heating;由于加熱而造成的可逆變形。Ni-Ti,Cu-Al-Ti,etc.在一定的溫度下，發(fā)現(xiàn)多種合金中應力達到一定水平后會發(fā)生馬氏體相變，即所謂的馬氏體相變，伴隨應力誘導相變，產(chǎn)生偽彈性現(xiàn)象，偽彈性變形的量級大約在6%左右，大大超過正常彈性變形，形狀記憶合金即是利用此做成的。