1、Stressed and Strained StatesLi ChenhuiStress Stress is the load applied to a body and related per unit area of the bodys section. 應(yīng)力應(yīng)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(duì)量The dimension of stress is determined as the force active per unit area of the body section to which the force is applied

2、. 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(gè)壓強(qiáng)大約相當(dāng)于10Mpa。The units of stress express the principal mechanical properties (ultimate strength強(qiáng)度極限, resistance to plastic flow塑性變形抗力, resistance to indentation壓痕阻力, fatigue s

3、trength強(qiáng)度疲勞, creep strength蠕變強(qiáng)度, etc.) 應(yīng)力的單位反映了它的力學(xué)性質(zhì)The case of axial tension of a cylindrical rod) 圓柱體受軸向載荷的情況SdFPif S= constant (uniform distribution of the stress over the cross section)應(yīng)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(yīng)力)The shear stress(剪應(yīng)力)單軸拉伸的莫爾圓 Thus, if

4、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 i

5、n Fig. 4. Engineering/Actual (True) Stress工程應(yīng)力和真實(shí)應(yīng)力F :force applied作用力;A0: area before deformation 變形前的面積 The engineering stress is often employed for elastic stresses or stresses for components deformed to small plastic strains. 工程應(yīng)力通常應(yīng)用于彈性應(yīng)力或者適用于微小塑性應(yīng)變下的應(yīng)力 At large strains, the change in cross-sec

6、tional area significantly alters the actual stresses. 在大的應(yīng)變下，橫截面的改變會(huì)顯著改變真實(shí)應(yīng)力 The true stress is :where A is the instantaneous 瞬時(shí)的area. Strain Strain is the ratio of the change in dimension to its initial value. 應(yīng)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Ro

7、d deformed, the length increased from l0 to ln; 桿開始變形，長度由l0伸長到lnengineering strain00 n工程應(yīng)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 materia

8、l were compressed so that the cross-sectional area increased during deformation (with E 0), we would find T E相應(yīng)，對(duì)于擠壓時(shí)，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(shí)a a0 ， u 0。 The equilibrium condition 等效計(jì)算式can be wri

9、tten, as follows: where (u) is the bond（結(jié)合） energy on displacement（位移） u. 其中 (u)是距離為u時(shí)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(gè)原子間的作用機(jī)制，可以從本質(zhì)上來探尋Ho

10、okes law，來研究外作用力和它所造成的位移的關(guān)系。For Hookes law to be valid（有效）, the following three conditions must be satisfied:胡克定律的應(yīng)用有三個(gè)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(dāng)u = 0時(shí)， d/du = 0， (u)必須具有最小值 (3) the displacement u mu

11、st be much less than a0. 變形量u必須遠(yuǎn)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(gè)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

12、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?yàn)樵趗 = 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, ther

13、efore, it does not depend on u and is a constant.二次微分項(xiàng)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(gè)常數(shù)。Thus, we obtainf = const u, 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(yīng)力和應(yīng)變對(duì)應(yīng)成比例關(guān)系。 It should be recalled that the region of a direct proportionality between the force and dis

14、placement is limited to slight deformations. 應(yīng)當(dāng)提醒的是：應(yīng)力應(yīng)變線性關(guān)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(dāng)位移量u很大時(shí)， u的高階冪不能忽略，那(u)就不是直線了。 This phenomenon is never encounte

15、red 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(shí)際中，這個(gè)理想情況不可能遇到，因?yàn)樗苄宰冃卧跇O小應(yīng)力下就發(fā)生了。因?yàn)檫@個(gè)原因（這里面有位錯(cuò)的原因）， 胡克定律就不適用了。Perfect thread-shaped metal crystals of a diameter of around

16、 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(dāng)變形為百分之幾的時(shí)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(shí)驗(yàn)中可能觀測

17、到右圖：In shear stress The shear stress is related with a corresponding shear deformation by similar expression: 切應(yīng)力對(duì)應(yīng)一個(gè)切變 量，有相同的表達(dá)式： where G is the shear modulus (or the modulus of elasticity in shear) G 是切變模量。 (1-3)gtG In hydrostatic compression (or tension) 在流體拉（壓）中 Hookes law expresses a drec直接直接 p

18、roportionality between the hydrostatic pressure P and the volume change x : 胡克定律揭示了流體壓力P和體積變化量x間的關(guān)系 where K is the modulus o f b u l k （ 體 積 ）（ 體 積 ） deformation. K稱為體彈模量vv (1-4)PK Hookes law (3) Formulae (1-2), (1-3) and (1-4) express what is called Hooks law. (1-2), (1-3) 和(1-4)公式是胡克定律。 Determines

19、 the relationship between stress and strain acting in the same direction 用來決定同方向上的應(yīng)力應(yīng)變間的關(guān)系。 When deformation appear in a direction different from that of the stress action, it does not work. 不適用于不同方向上的應(yīng)力應(yīng)變。 Elementary form 基本形式 nomenclature (1) Poissons ratio Isotropic Anisotropic Moduli Coefficient

20、 Polymorphous transformation Phase 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） Recrystallization Substantially Preferable orientation Texture Radiographic Heterophase Anomaly, （ anomalies, anomalous） Peculiar Magnetic effect Elinvar術(shù)語（2） 重結(jié)晶 充分地 擇優(yōu)取向 織構(gòu) 輻射照相的 異質(zhì)相 （名）不規(guī)

21、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.一個(gè)桿受到軸

22、向拉伸后，長度增加，同時(shí)直徑減小，因此一個(gè)軸向載荷造成的是一個(gè)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 sampl

23、e 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(fù)號(hào)(正號(hào))表明當(dāng)桿受拉(壓)時(shí)，其截面積減小(增加)。 For metals, the value of v is often on the order of 1/3. 對(duì)金屬來說，v大約在1/3左右。 The change in volume associated with the small strain

24、s 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(yīng)變?cè)斐傻捏w積方面的變化，可以由體積計(jì)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

25、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(duì)于軸向變形而言V/V = (l - 2 )，當(dāng) = 1/3時(shí)，一個(gè)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

26、 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(dāng)v增加，體積變形減小。對(duì)于一

27、個(gè)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(yīng)變對(duì)軸向應(yīng)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 m a t e r i a l s d i f f e r 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(zhì)和線性彈性材料有明顯的區(qū)別。F

28、our elastic constants of an isotropic body基本上與價(jià)位、熔點(diǎn)呈線性關(guān)系Refractory metal 難熔金屬Strong carbide forming metal 強(qiáng)碳化物形成金屬Effect of various factors on elastic moduli對(duì)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 effect Since elastic moduli are associated with interatomic

29、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(guān)，而原子間的作用力依靠晶體點(diǎn)陣中原子間的作用距離，所以彈性模量和溫度有關(guān)。 The temperature dependence of elastic moduli is very weak; As may be seen, the magnitude of modulus decreases with increa

30、sing 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(duì)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(guān)系。平均來說，溫度每增加100度，彈性常數(shù)減小24個(gè)百分點(diǎn)。 The temperature coefficient of the elastic modulus of a metal depends on

31、 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(diǎn)。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(guān)系。 Empi

32、rical（經(jīng)驗(yàn)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(yàn)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(diǎn)溫度 =volume per atom 單個(gè)原子的體積 The modulus decreases concurrent（一致的） with the

33、increased atomic separation. This decrease is essentially linear with temperature, and an approximate equation describing the modulus-temperature relationship is當(dāng)原子間距離增加時(shí)，彈性系數(shù)減小，這個(gè)減小和溫度成線性關(guān)系。相應(yīng)彈性系數(shù)和溫度間的關(guān)系式為：where E is the modulus at temperature T and E0 the modulus at 0 K. The proportionality consta

34、nt 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(shí)的彈性模量，E0是溫度為0K時(shí)的彈性模量，比例常數(shù)a對(duì)多數(shù)晶體而言大約是0.5，因此對(duì)于一個(gè)典型材料，當(dāng)溫度由0K增加到材料的熔點(diǎn)時(shí)彈性模量減小50%Alloying (

35、1)Alloying (2) in Al The 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(duì)彈性系數(shù)的影響，就像溫度的影響一樣，和晶體點(diǎn)陣內(nèi)的內(nèi)部原子間隔距離和作用力有關(guān)。 As has been demonstrated in radiographic studies

36、, 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(xiàng)晶體的研究中已經(jīng)證實(shí)：溶劑點(diǎn)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(guān)系。 As m

37、ay 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(zhì)） and solvent（溶劑）. 從上面的數(shù)據(jù)可以看出，合金有時(shí)增加彈性模量，有時(shí)減小彈性模量，是取決于溶劑、溶質(zhì)原子間的相互作用力。 on the one hand, and the forces of atomi

38、c interaction in the solvent lattice. 1.如果溶質(zhì)溶劑原子間的作用力小于溶劑點(diǎn)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(zhì)溶劑原子間的作用力大于溶劑點(diǎn)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 o

39、f 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(diǎn)陣中原子間的作用力外，合金也可以引起其結(jié)構(gòu)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 m

40、odulus may change additionally compared with its value in a single-phase solid solution. 例如如果合金超過一個(gè)有限的度就可以形成第二相，那么其彈性系數(shù)和單相時(shí)相比會(huì)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(zhì)） 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

41、相合金的彈性系數(shù)。Work hardening Work 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(duì)彈性模量沒有什么本質(zhì)影響。冷塑性加工導(dǎo)致彈性模量輕微減小，常伴隨著金屬或合金晶體點(diǎn)

42、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(gòu)）, which make the material anisotropic （各向異性）and can change substantially（充分地） the elastic moduli. 塑性變形會(huì)導(dǎo)致金屬結(jié)構(gòu)的改變。加工硬化能使晶體的

43、形成晶面的擇優(yōu)取向或織構(gòu)，從而導(dǎo)致材料內(nèi)部晶體結(jié)構(gòu)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(jié)晶也能形成織構(gòu)，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 reac

44、h a few tens per cent. 擇優(yōu)取向的形成或減小，導(dǎo)致部分彈性系數(shù)的改變可能達(dá)到幾十個(gè)百分點(diǎn)。 In textured polycrystalline materials, the magnitude of an elastic modulus depends on the direction of measurement. 在已形成織構(gòu)的多晶體材料中，彈性系數(shù)的大小和測量的方向有關(guān)。Anomalous異?，F(xiàn)象 Elinvar（） 鎳鉻鋼 Magnetic（有磁性的） effects compensate（補(bǔ)償） the normal drop of moduli with

45、temperature. 磁效應(yīng)補(bǔ)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 / engineering or actual /true) Strain (relative / engineering or actual /true) Hookes law Youngs modulus （Stiffness) Shear modulus Bulk modulus Shear strain Bulk Strain elas

46、tic moduli nomenclature (1） Anelasticity（） Hysteresis （） Microscopic Macroscopic Coordinates Thermodynamic Linearity Quasi-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） Instantaneously Reciprocity Microplastically Macroplastically Hysteresis loop Elastic aftereffects Stress relaxation

47、 Internal friction Dissipate術(shù)語（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 bodies理想彈性體 A unique relationship between stress and strain in the elastic region 彈性范圍內(nèi)應(yīng)力和應(yīng)變有精確關(guān)系。 Assumption: the load is increased infinitely slow so that the state of the system has the time to follo

48、w load variations. 假定：載荷無限慢地加載，體系狀態(tài)能有足夠的時(shí)間來產(chǎn)生應(yīng)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(gè)點(diǎn)變化系統(tǒng)中都有一個(gè)實(shí)時(shí)的應(yīng)變和它對(duì)應(yīng)。 The process of loading and unloading can be regarded energetically reversible. 加載和卸載過程在能量上可認(rèn)為是可逆的。Anelasticity滯彈體 In real bodies, the

49、direct relationship between stress an strain is disturbed and a hysteresis loop appears on the Stress-Strain diagram 在實(shí)際受力體中，應(yīng)力和應(yīng)變間的直接關(guān)系被破壞了，應(yīng)力應(yīng)變圖中出現(xiàn)了一個(gè)滯后環(huán)。Stress-strain diagram in cyclic loading and unloading循環(huán)加載卸載中應(yīng)力應(yīng)變圖 Anelasticity An irreversible dissipation of energy during the processes of loa

50、ding and unloading; 在加載和卸載中產(chǎn)生一個(gè)不可回復(fù)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(gè)循環(huán)中損失的能量由應(yīng)力應(yīng)變圖中后滯環(huán)的面積來確定。其面積也是材料內(nèi)耗的一個(gè)度量。 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 an

51、elastic 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(cuò)的參與。例如：它能在彈性極限下的應(yīng)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(shí)間間隔才發(fā)生，并不是及時(shí)發(fā)生的。就這而言滯彈性現(xiàn)象和塑性變形有一點(diǎn)相似性。例如，剛卸載時(shí)，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(shí)間后，這種不同便會(huì)逐漸消失，最終沒有任何殘余變形被觀察到。這種變

52、形應(yīng)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(cuò)不可回復(fù)的運(yùn)動(dòng)而造成的。例如，當(dāng)應(yīng)力沒有達(dá)到彈性極限時(shí)，有些位錯(cuò)就開始運(yùn)動(dòng)，但在到達(dá)晶體表面之前，就在晶體內(nèi)被阻塞了。當(dāng)卸載時(shí)，阻礙位錯(cuò)運(yùn)動(dòng)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(cuò)的運(yùn)動(dòng)都會(huì)消耗能量，所以滯彈性現(xiàn)

53、象在能量上是不可回復(fù)的。就這種解釋而言，滯彈性變形可以理解為可以回復(fù)的塑性變形。 At still higher stresses, movement of dislocations ceased（中止） to be mechanically reversible. 3.當(dāng)應(yīng)力增大到一定程度時(shí)，位錯(cuò)就不可回復(fù)，卸載后位錯(cuò)就不回到它原來的位置，一個(gè)可測量的變形出現(xiàn)了。無論經(jīng)過多長時(shí)間彈性滯后環(huán)都不會(huì)在 =0，=0處合攏。這種情況，滯彈性變形在變形機(jī)制和卸載體積殘余變化上都類似于塑性變形。我們應(yīng)該知道的是在實(shí)際中，幾種不同的滯彈性效應(yīng)是同時(shí)發(fā)生的。在應(yīng)力超過彈性極限時(shí)，偽滯彈性變形可以忽略，因?yàn)樗?/p>

54、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(yīng)力松弛 把應(yīng)力和應(yīng)變的時(shí)效差異考慮在內(nèi)的話，應(yīng)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 a

55、nd gradual disappearance upon unloading are called respectively the direct and the reverse elastic aftereffect. 加載時(shí)逐漸增加，卸載時(shí)逐漸減小的應(yīng)變，稱為直接可回復(fù)的彈性后效 The gradual variation of the stress to the value corresponding to Hookes law is called stress relaxation 應(yīng)力逐漸變化到依胡克定律理論計(jì)算的應(yīng)力大小稱為應(yīng)力松弛。Elastic and plastic strain in stress relaxation開始時(shí)，殘余塑性變形為0，所以0=e1。塑性變形隨時(shí)間而增加，而彈性變形隨時(shí)間而減小。因?yàn)閼?yīng)力和彈性變形相伴出現(xiàn)，彈性減小時(shí)，應(yīng)力減小，因此應(yīng)力松弛出現(xiàn)了。 nomenclature （1） Bauschinger effect Inhomogeneuos Damping Precipitation Dissolution Amplitude Resonance Acoustic術(shù)語（1） 包申格效應(yīng)