part 2 Plastic deation and Strain hardening.ppt

1、Plastic deformation and Strain hardening塑性变形和应变硬化,Nomenclature,Plastic deformation Strain hardening Slip Resolved shear stress Critical resolved shear stress Austenitic () Intersect Lacquer,塑性变形 应变硬化 滑移 分切应力 临界分切应力 奥氏体的 相交、交叉、横断 漆、涂漆于使表面光滑,术语,Nomenclature 术语,Peculiarity Polycrystalline Periodically

2、Isothermal Crystallography Hexagonal Syngony,特性 多晶的 周期性地 等温的 结晶学、晶体学 六角形的，六边形的 晶系,The mechanical behaviour of metals and alloys金属和合金的力学特性,The mechanical behaviour of metals and alloys is described by the following laws of their resistance to elastic and plastic deformation and fracture . 金属和合金的力学行为由

3、它们对弹性和塑性的变形以及断裂的抵抗性来描述。 The isothermal (等温的)mechanical behaviour of a metal is determined by four factors: Stress, time, shape, and structure. 金属的等温力学行为由四个因素描述：压力，时间，形状和结构。,Peculiarities of Mechanical(力学的) behaviour金属力学特性的特征,(i) how high can be periodically or constantly applied loads so that an obj

4、ect could restore its shape and size upon their removal; 在金属发生形变前最大可以加载多大的周期性或恒定的载荷。 (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 particula

5、r conditions of load application determine the course of plastic flow at a desired rate; 多大的短期或长期的力能使物体发生塑性变形，物体形状或体积发生多大的变形。为了达到某种想要的形变，需要什么样的条件和载荷。 (iii) how large is the force to cause fracture（断裂） of the object to pieces. 多大的力使物体断裂。,More deep analysis of the mechanical behaviour of metals and al

6、loys 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 mec

7、hanical behaviour of materials seems to be fruitful. 在过去二三十年间，依靠位错理论，原子级结构的观察，连续体研究的发展。金属和合金力学特性的分析也得到了发展。这些力学特性方面的研究很有成果。 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. 金属宏观力学机制在其它课程中已经讨论了。我们这

8、里只研究位错级的金属塑性变形机制。,Carbon steel in the elastic region碳素钢在弹性区的变化,Linear elasticity and subsequent plasticity比例弹性变形和紧接的塑性变形,Unstable creep in annealed copper铜退火后的蠕变,Plastic deformation塑性变形,The deformation which is independent of time and is retained upon stress release is called plastic deformation. 塑性

9、变形是不随时间而变化，应力去除后仍然保留的形变。,Effect of deformation rate on stress-strain curve 变形效应对应力应变曲线的影响,Slip of metal crystalsa Zn, b Cd, c-Sn, d-Bi金属晶体的滑移,Variation of slip orientation in deformed tungsten single crystal at a different direction of external shear stress 钨单晶受到不同方向外部切应力作用时滑移方向的变化。,Slip of low-carb

10、on steel (polycrystalline )低碳钢（多晶）的滑移,Slip,Slip is the displacement of a portion of a crystal relative to another portion with the crystal structure of both portions remaining unchanged. 滑移是晶体的一部分移动到另一部分的位置，并且在移动过程两部分晶体的结构保持不变。,a-undeformed 未变形 b-elastically deformed 弹性变形 c-elastically and plastical

11、ly deformed, 弹性和塑性变形 d-plastically deformation in which slip has taken place 塑性变形滑移发生 AB slip plane 滑移面,Slip planes in three typical lattice of metal crystals (Slip plains usually have the closest packing of atoms)三种典型金属晶体结构的滑移面（滑移面通常也是原子密排面）,Three possible slip directions in -Fe; the shortest direc

12、tion is preferable 在 -Fe中三个可能的滑移方向， 是其中最优滑移方向。,Microstructure of austenitic Cr-Ni-Mo steel deformed 25% (a.) and 50% (b. )奥氏体Cr-Ni-Mo钢变形25%或50%时的微观结构,Strain bands of low-carbon steel低碳钢的应变带,Stretched grains in low-carbon steel低碳钢中的被拉伸晶粒,Crystallography of slip in single crystals单晶的晶体滑移体系,Fracture of

13、 zinc single crystal锌单晶体的断裂,In cubic syngony crystals this situation is impossible, i.e. the ultimate strength in tension cannot be attained earlier than plastic flow begins. 在立方晶系晶体中，这种情况（上图中的脆性断裂）是不可能的。例如：只有当晶体发生塑性变形时才可能达到最大的拉应力。 For instance, in f.c.c. crystals where the four systems of 111 plane

14、s 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, si

15、lver) subjected to tension or compression, fracture is always preceded by a plastic deformation. 例如：在面心立方晶体中， 111 四个滑移体系相互作用，所以它不可能使晶体转到一个方向使其只受拉应力和压应力，使这些面上的剪切应力为0；但其中至少有一个滑移体系会成为最优滑移体系。对fcc金属晶体（铝铜铅金银）而言受拉应力、或压应力，在断裂之前通常已经发生塑性变形。,B.c.c. crystals have no planes with such a dense packing of atoms as

16、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. 体心立方晶体没有像六方晶体的底面和面心晶体那样的院

17、子密排面（这里的密排面指的是和其它晶面有显著区别的面）。例如：体心立方晶体中的111 面。尽管它们称为最密面，但只和晶体中其它的滑移面有微量区别。,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（对角线）. These directions play even a greater part in slip

18、than the close-packed directions in hexagonal or face-centered cubic crystals. 体心立方晶体最基本的特征，对滑移有影响的是，其有一系列密排方向， 体对角线。在滑移时其起到的作用比六方和面心立方晶体中的密排方向更大。,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, 11

19、2 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

20、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. 在体心立方晶体中， 方向对应于几种不同的滑移面相互构成不同的滑移系。例如在a钢中有， 110, 112 和 123晶面。在这种情况下滑移在这几个滑移面上同时发生。通常情况下，不可能预言具体那个晶面会发生滑移。在另一方面，这些金属比六方晶系具有更多的滑移体系，所以它们比其它晶体结构的金属有更好的塑性。,As comp

21、ared 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 b

22、ut they offer a lower resistance to the development of plastic deformation before fracture. 和面心立方晶体相比，体心立方晶体滑移面上的原子排列密度和其它晶面并没有太大的差距，也小于面心立方晶体的原子密排面的密度。因这个原因，体心立方晶体滑移开动需要一个更大的剪切应力，但体心立方晶体开始变形后在断裂前对塑性变形的阻碍较小。,Slip systems in metallic crystal structures 金属晶体结构的滑移体系,In general, the ductility of b.c.c.

23、metals, such as a-iron, tungsten, molybdenum, or |-brass has intermediate values between those of f.c.c. and c.p.h. metals. 总体来说，体心立方晶体金属，像钢、钨、钼或 |-brass 等的延展性介于面心立方晶体和六方晶体之间。,nomenclature 术语,Schmid-Boas law Resolved shear stress Critical resolved shear stress Twinning Octahedral Indeterminacy Incoh

24、erent boundaries,分切应力 临界分切应力 孪生 八面体的 不确定 不连贯界面,Partial coherent boundaries部分连贯界面,Incoherent boundary不连贯界面,Resolved shear stress 分剪切应力,Schmid-Boas law临界切应力定律，这方面有经典著作“晶体范性学”,Orientation factor 角度因素(Schmid factor),EXAMPLE PROBLEM 1. Hexagonal close-packed zinc slips by basal plane slip. A zinc single

25、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 deforma

26、tion commences. 六方密排晶体锌，以底面为滑移面。一锌单晶的滑 移面的法线和拉力成60，如果三个滑移方向和拉 力分别成30、45、84，并且锌的临界切应力 为2.3MN/m2，请确定锌开动滑移的拉应力。,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

27、 of the slip systems in this crystal and calculate the Schmid factor for this loading geometry. 一个单晶体为简单立方晶体结构（滑移面为100，滑移方向为），它受到的拉力和晶向平行，请写出此晶体的所有滑移体系，并且为它们分别计算Schmid几何因子。,T.A.,Consider this problem for a situation where the tensile axis is parallel to the 011 crystal axis. 当其受到的拉应力平行于晶向011 时，再考虑到这

28、个问题。,Effect of orientation factor on slip stress角度因素对滑移应力的影响,Effect of temperature on in Mg镁中温度对的影响,Effect of temperature on and in Mg镁中温度对 和 的影响,Effect of temperature on in Cu and Cu alloys在Cu-Cu合金中温度对的影响,The relationship between and composition of f.c.c. single crystals 和面心单晶体结构的关系,Effect of conce

29、ntration of alloying elements on in Mg alloysMg合金的成分浓度对的影响,1-Mg 2-Mg-In 3-Mg-Cd 4-Mg-Ti 5-Mg-Al 6-Mg-Zn,Effect of alloying elements on depending on the difference in atomic diameters合金元素对的影响取决于原子直径的不同。,The relationship between and composition of f.c.c. single crystals,Crystallographic diagram of twi

30、nning孪晶的晶体学图示,Twinning 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. 像滑移一样，当剪切力达到临界值时即可发生孪晶现象。它遵行一定的晶体学规律。对

31、称镜面称为孪晶面，其滑移方向称为孪生方向。 The twinning direction is polar; 孪晶方向是相反的。 Twinning shear can occur in only direction only; 孪晶剪切只能发生在一个方向。 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 t

32、he surface of a twin band. 孪晶中的原子面由相同的非常小的间隔（其小于原子间距）移动，所以没有可见的应变痕迹留在孪晶带的表面上。,The role of the twinning process usually increases with decreasing temperature of deformation and /or increasing rate of deformation. 孪晶通常降低了变形时的温度，或增加了变形量。 Since the stress needed for propagation（增值） of a twin is much hig

33、her than the slip stress, it is clear that twinning is possible under particular conditions when the resolved shear stress turns out to be high. 孪晶形成时需要的临界剪切应力远大于滑移应力，因此在分剪切应力很高时才形成孪晶。,Twinning in b.c.c. and f.c.c. crystals is usually observed at low temperatures and high deformation rates and in c.

34、p.h. crystals, when the available orientations are unfavourable for basal slip. 在面心立方和体心立方中，只有当温度很低，或变形量很大时才形成孪晶。 在六方晶体中，只有在滑移方向不利于基面滑移时，才形成孪晶。,Effect of the grain size d on the critical stresses of twinning t ans slip s 晶粒大小对孪晶临界应力t和滑移临界应力s的影响。,The supressing effect of fine grain on twinning can be

35、 attributed three reasons:晶粒细化对孪晶形成的张力效果可以归结为三个原因：,A higher dislocation density; 更高的位错密度。 A lower stress concentration;(nucleation) 更低的应力集中（形核）。 Grain boundaries are barriers for the growth of twins.(critical-size twins) 晶界是形成孪晶的障碍。（孪晶的临界大小）。,Twinning deformation of Cr-20% Fe孪晶变形,nomenclature 术语,Sin

36、usoidal Conditioned Multiplication Proportional Luders-Chernov bands Configuration Avalanche Interstitial Convex Schematic,正弦曲线 有条件的 增殖、乘法 比例的、均衡的 吕德斯带、拉伸应变带、滑移线痕 构造、结构、配置、外形 雪崩 空隙的 凸起的 示意性的,Luders-Chernov bands,Shear in an ideal crystal (a); Variations of force and 理想晶体中的剪切 energy in shear (b); 剪切下

37、力和能量的变化。 Variations of energy in shear of two adjacent atomic planes with account of energy variations in the source of deformation (c). 两相邻剪切面间的能量随变形量的变化。,Successive stages of unit shear剪切时原子连续变化步骤,Movement of an edge dislocation in simple cubic lattice简单立方晶体中一个刃型为错的运动。,Yield Stress Peak应力屈服极限,Crys

38、tals with impurities杂质晶体,In crystals with impurities, especially in b.c.c. crystals, the plastic flow starts at a certain drop of the deforming stress. 杂质晶体，特别是体心立方晶体中，塑性变形在变形应力下降的时候发生。 After that one can observe a continuous deformation with almost constant stress, which is accompanied with the pro

39、pagation of the Luders-Chernov bands. 可观察到一个在恒定应力作用下连续的变形，并且伴随着拉伸应变带的增殖。 This type of variation of flow stress is often attributed to locking of dislocations by impurity atoms. 这种塑性变形应归因于杂质原子对位错运动的阻碍作用。,Especially strong interaction can be observed between dislocations and interstitial impurities in

40、 b.c.c.metals. 通常能在体心立方晶体中观察到位错和间隙杂质原子之间的强相互作用。 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. 通常认为较大的屈服极限时让被

41、杂质原子锁住的位错运动的应力，而较小的屈服应力极限则是在点阵中移动自由位错所需的应力。,Variations of the critical resolved shear stress with deformation in (a) Ge and (b) LiF single crystals (a) Ge和(b) LiF单晶变形所需剪切应力的变化,In rather pure crystals在较纯晶体中,The concentration of impurities is very low or at least insufficient for dislocation locking;

42、杂质原子的浓度非常小，或者对位错运动的阻碍非常小。 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. 这种晶体在塑性范围变化时屈服极限的下降是有条件的： 1.较低的位错密度； 2.位错的运动速率有强烈的应力敏感性。,A

43、 distinct（明显的） yield stress exhibits in such b.c.c. crystals:体心立方晶体中的应力屈服极限,(i)in the original state, the density of unlocked (mobile) dislocations decreases down to 102-104 cm-2; 初始时，自由为错的密度下降到102-104 cm-2 (ii) in subsequent（后来的） deformation, the density of dislocations increases with strain roughl

44、y by a factor of 1010; 在接下来的变形中，位错的密度以1010的比值增加 (iii) the rate of movement of dislocations is strongly stress-sensitive. 位错的运动速率有强烈的应力敏感性。,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

45、and, to a less extent, with unpinning of dislocations from impurities. 许多研究者认为：在体心立方金属中屈服应力极限主要是位错运动速率对应力的敏感性，其次才是杂质原子阻碍位错的运动。,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 b

46、eginning of plastic flow. 塑性变形被打断的一般理论把屈服极限的出现归因于在塑性变形开始阶段大量增加的移动位错。 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. 另一方面，一个屈服极限开始出现时通常可移动位错的密度很低，但开始塑性变形后，位错的密度快速增殖。,

47、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. 上屈服极限应力的下降是由形核和位错的大量增殖所决定，位错增殖在应力集中时即开始，在Luders拉伸应变带中继续。 In real crystals, the intens

48、ity 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. 在实际晶体中，被钉扎的可移动位错的强度也许不同。如果它们被少量阻挡时，塑性变形的开始是由

49、于它们没有被锁住。如果位错被强力阻挡时，塑性变形的开始时由于应力集中时产生的新位错。,In polycrystals, grain boundaries inhibit（抑制，禁止） 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（邻近的） grain either by dislocation unlocking (with we

50、ak locking) or by creation of new dislocations in volumes at the other side of of the grain boundary (with strong locking). 在多晶体中，晶界阻碍了晶粒间的塑性变形（主要指滑移）。当滑移带（孪晶带）末端应力集中时，相邻晶粒由于可活动位错（当其未被锁住时），或是由于体积中形成了新位错（位错被锁严重时）而产生塑性变形。,In f.c.c. metals,The mechanism described is in principle poorly applicable to f.

51、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 dislo

52、cation 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. 这个机制对面心立方晶体并不太适用。因为位错只能和杂质原子极其微弱地作用。事实上，在这些晶体中，没有观察到由于位错没被阻挡而导致屈服极限下降的形象，除了合金浓度很高的单晶体外。另一个重要的事实是面心立方晶体中位错的移动速度对应力的依赖度也很

53、小。例如：这种关系大约对铜成200 的比例，对银成300 的比例。,Schematic stress-strain curves at two different temperatures (T2T1)两个不同温度下应力应变曲线简图,Diagram of the Cottrell-Stokes experiment for determining the effect of test temperature on deforming stress Cottrell-Stokes实验图像中表现出来的温度和变形应力间的关系,Effect of the amount of deformation o

54、n the ration of the deforming stresses at variations of test temperature (of Al)Al在不同测试温度下变形量对变形应力的影响,Appearance 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) 当温度由低到高时，有效屈服点和屈服加长区出现。,Stress-strain curv

55、es of an aluminium crystal铝晶体应力应变曲线,ABCtensioning in liquid air; the specimen at point C was held at room temperature (recovery （回复）or age-harding（时效硬化）); DEfurther tensioning in liquid air. ABC在液态空气中拉长，在C点试样保持在室温（回复或时效硬化），DE在空中继续拉长。,The mechanical state of a crystal cannot be described by a single

56、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. 晶体的力学机制不能简单的仅仅由一个结构参数决定。例如，用位错的密度描述时，至少要加一个额外的参数，如位错的分布，因为它间接地描

57、述了所形成的位错结构的稳定性。,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 deforma

58、tion 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. 低温和高温下同样的变形，高温下的滑移线看起来粗一些。一般认为滑移带附近的材料好像是被“退火”了：就像它在某个特定的温度（在变形的最低温度上面，且靠近最高温度）。因这个原因，高温变形时形成的新滑移带靠近已经存在的滑移带，所以看起来粗一

59、些。,With the same elongation in the low- and high-temperature deformation, dislocations in the former case will be arranged less uniformly （一致地）on the account of the greater inhomogeneity (gradient梯度) 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 c