應力應變的關系和行為外文文獻翻譯@中英文翻譯@外文翻譯

1、<p><b>　　原文：</b></p><p>　　Stress-Strain Relationships and Behavior</p><p>　　5.1 INRODUCTION</p><p>　　5.2 MODELS FOR DEFORMATION BEHAVIOR</p><p>　　5.3 E

2、LASTIC DEFORMATION</p><p>　　5.4 ANISOTROPIC MATERIALS</p><p>　　5.5 SUMMARY</p><p>　　OBJECTIVES</p><p>　　Become familiar with the elastic, plastic, steady creep, and tra

3、nsient creep types of strain, as well as simple rheological models for representing the stress-strain-time behavior for each.</p><p>　　Explore three-dimensional stress-strain relationships for linear-elastic

4、 deformation in isotropic materials, analyzing the interdependence of stresses or strains imposed in more than one direction.</p><p>　　Extend the knowledge of elastic behavior to basic cases of anisotropy, i

5、ncluding sheets of matrix-and –fiber composite material.</p><p>　　5.1 INRODUCTION</p><p>　　The three major types of deformation that occur in engineering materials are elastic, plastic, and cree

6、p deformation. These have already been discussed in Chapter 2 from the viewpoint of physical mechanisms and general trends in behavior for metals, polymers, and ceramics. Recall that elastic deformation is associated wit

7、h the stretching, but not breaking, of chemical bonds. In contrast, the two types of inelastic deformation involve processes where atoms change their relative positions, such as</p><p>　　In engineering desig

8、n and analysis, equations describing stress-strain behavior, called stress-strain relationships, or constitutive equations, are frequently needed. For example, in elementary mechanics of materials, elastic behavior with

9、a linear stress-strain relationship is assumed and used in calculating stresses and deflections in simple components such as beams and shafts. More complex situations of geometry and loading can be analyzed by employing

10、the same basic assumptions in the form o</p><p>　　Stress-strain relationships need to consider behavior in three dimensions. In addition to elastic strains, the equations may also need to include plastic str

11、ains and creep strains. Treatment of creep strain requires the introduction of time as an additional variable. Regardless of the method used, analysis to determine stresses and deflections always requires appropriate str

12、ess-strain relationships for the particular material involved.</p><p>　　For calculations involving stress and strain, we express strain as a dimensionless quantity, as derived from length change, ε=ΔL/L. Hen

13、ce, strains given as percentages need to be converted to the dimensionless form, ε=ε%/100, as do strains given as microstrain, ε=εμ/106.</p><p>　　In the chapter, we will first consider one-dimensional stress

14、-strain behavior and some corresponding simple physical models for elastic, plastic, and creep deformation. The discussion of elastic deformation will then be extended to three dimensions, starting with isotropic behavio

15、r, where the elastic properties are the same in all directions. We will also consider simple cases of anisotropy, where the elastic properties vary with direction, as in composite materials. However, discussion of three&

16、lt;/p><p>　　5.2 MODELS FOR DEFORMATION BEHAVIOR</p><p>　　Simple mechanical devices, such as linear springs, frictional sliders, and viscous dashpots, can be used as an aid to understanding the vari

17、ous types of deformation. Four such models and their responses to an applied force are illustrated in Fig.5.1. Such devices and combinations of them are called rheological models.</p><p>　　Elastic deformatio

18、n, Fig.5.1(a), is similar to the behavior of a simple linear spring characterized by its constant k. The deformation is always proportional to force, x=P/k, and it is recovered instantly upon unloading. Plastic deformati

19、on, Fig.5.1(b), is similar to the movement of a block of mass m on a horizontal plane. The static and kinetic coefficients of friction μ are assumed to be equal, so that there is a critical force for motion P0=μmg, where

20、 g is the acceleration of gravity. If a co</p><p>　　a =(P’-P0)/m (5.1)</p><p>　　When the force is removed at time t, the block has moved a distance a=at2/2, and it remai

21、ns at this new location. Hence, the model behavior produces a permanent deformation, xp.</p><p>　　Creep deformation can be subdivided into two types. Steady-state creep, Fig.5.1(c), proceeds at a constant ra

22、te under constant force. Such behavior occurs in a linear dashpot, which is an element where the velocity, , is proportional to the force. The constant of proportionality is the dashpot constant c, so that a constant val

23、ue of force P’ gives a constant velocity, , resulting in a linear displacement versus time behavior. When the force is removed, the motion stops, so that the deformation i</p><p>　　The second type of creep,

24、is called transient creep, Fig.5.1(d), slows down as time passes. Such behavior occurs in a spring mounted parallel to a dashpot. If a constant force P’ is applied, the deformation increases with time. But an increasing

25、fraction of the applied force is needed to pull against the spring as x increases, so that less force is available to the dashpot, and the rate of deformation decreases. The deformation approaches the value P’/k if the f

26、orce is maintained for a long peri</p><p>　　Rheological models may be used to represent stress and strain in a bar of material under axial loading, as shown in Fig. 5.2. The model constants are related to ma

27、terial constants that are independent of the bar length L or area A. For elastic deformation, the constant of proportionality between stress and strain is the elastic modulus, also called Young’s modulus, given by </p

28、><p>　　E=σ/ε (5.2)</p><p>　　Substituting the definitions of stress and strain, and also employing P = k x, yields the relationship between E and k:</p><p>　

29、　E=kL/A (5.3)</p><p>　　For the plastic deformation model, the yield strength of the material is simply </p><p>　　σ0=P0/A (5.4)</p><p&g

30、t;　　For the steady-state creep model, the material constant analogous to the dashpot constant c is called the coefficient of tensile viscosity1 and is given by</p><p><b>　　(5.5)</b></p>&l

31、t;p>　　Where is the strain rate. Substitution from Fig. 5.2 and P= cx. Yields the relationship between η and c:</p><p><b>　　(5.6)</b></p><p>　　Equations 5.3 and 5.6 also apply to

32、the spring and dashpot elements in the transient creep model. </p><p>　　Before proceeding to the detailed discussion of elastic deformation, it is useful to further to discuss plastic and creep deformation m

33、odels.</p><p>　　5.2.1 Plastic Deformation Models</p><p>　　As discussed in Chapter 2, the principal physical mechanism causing plastic deformation in metals and ceramics is sliding (slip) between

34、 planes of atoms in the crystal grains of the material, occurring in an incremental manner due to dislocation motion. The material’s resistance to plastic deformation is roughly analogous to the friction of a block on a

35、plane, as in the rheological model of Fig. 5.1(b).</p><p>　　For modeling stress-strain behavior, the block of mass m can be replaced by a massless frictional slider, which is similar to a spring clip, as sho

36、wn in Fig. 5.3(a). Tow additional models, which are combinations of linear springs and frictional sliders, are shown in (b) and (c). These give improved representation of the behavior of real materials, by including a sp

37、ring in series with the slider, so that they exhibit elastic behavior prior to yielding at the slider yield strength σo. In addition,</p><p>　　Figure 5.3 gives each model’s response to three different strain

38、 inputs. The first of these is simple monotonic straining—that is, straining in a single direction. For this situation, for models (a) and (b), the stress remains at σo beyond yielding.</p><p>　　For monotoni

39、c loading of model (c), the strain ε is the sum of strainε1 in spring E1 and strainε2 in the (E2, σo) parallel combination:</p><p>　　, (5.7)</p><p>　　The vertical bar is ass

40、umed not to rotate, so that both spring E2 and sliderσo have the same strain. Prior to yielding, the slider prevents motion, so that strainε2 is zero:</p><p>　　,(σσo) (5.8)</p><p

41、>　　Since there is no deflection in spring E2, its stress is zero, and all of the stress is carried by the slider. Beyond yielding, the slider has a constant stressσo, so that the stress in spring E2 is (σ-σo). Hence,

42、the strainε2 and the overall strainε are</p><p>　　, (5.9)</p><p>　　From the second equation,the slope of the stress-strain curain curve is seen to be </p><p><b>

43、　　(5.10)</b></p><p>　　Which is the equivalent stiffness Ee, lower than both E1 and E2, corresponding to E1 and E2 in series.</p><p>　　Figure 5.3 also gives the model responses where strain

44、 is increased beyond yielding and then decreased to zero. In all three cases, there is no additional motion in the slider until the stress has changed by an amount 2σ0 in the negative direction . For models (b) and (c) ,

45、 this gives an elastic unloading of same slope E1 as the initial loading. Consider the point during unloading where the stress passes through zero, as shown in Fig. 5.4. The elastic strain, εe, that is recovered correspo

46、nds to</p><p>　　Now consider the response of each model to the situation of the last column in Fig. 5.3, where the model is reloaded after elastic unloading to σ = 0. In all cases, yielding occurs a second t

47、ime when the strain again reaches the value ε1 from which unloading occurred. It is obvious that the two perfectly plastic models will again yield at σ = σ0. But the linear-hardening model now yields at a value σ = σ1, w

48、hich is higher than the initial yield stress. Furthermore, σ1 is the same value of stress</p><p>　　We will return to spring and slider models of plastic deformation in Chapter 12, where they will be consider

49、ed in more detail and extended to nonlinear hardening cases.</p><p><b>　　譯文：</b></p><p>　　應力應變的關系和行為</p><p><b>　　5.1 概述</b></p><p>　　5.2 變形的典型模式

50、</p><p><b>　　5.3 彈性變形</b></p><p>　　5.4 各向異性材料</p><p><b>　　5.5總結(jié)</b></p><p><b>　　目標</b></p><p>　　熟悉彈性應變，塑性應變，穩(wěn)態(tài)蠕變和瞬態(tài)蠕變等應

51、變類型，以及每個用來表示應力——應變與時間相關的簡單的流變類型。</p><p>　　探討在各向同性材料中線性彈性變形的三維的應力應變關系，分析應力應變在多個方向上施加的相互作用力</p><p>　　擴展在各向異性材料中以及一些基體纖維復合材料中彈性形變的基本情況的知識。</p><p><b>　　5.1概述</b></p>

52、<p>　　工程材料發(fā)生變形的三種主要類型是彈性變形，塑性變形，蠕變變形。這些已經(jīng)在金屬聚合物和陶瓷行為的物理機制和一般趨勢的觀點的第2章中被討論過了，記得彈性變形與拉伸相關，但是不打破化學鍵。相比之下，這兩種涉及原子的相對位置變化的過程類型的非彈性變形，比如晶面滑移和鏈分子滑動。如果非彈性變形取決于時間，它被歸類為蠕變，區(qū)別于不取決于時間的的塑性變形。</p><p>　　在工程設計和分析中，應力應變

53、行為的方程描述，稱為應力應變的關系或本構方程是很必要的。比如，在基礎材料力學中，與線性應力-應變相關的彈性行為是被假定和用來計算簡單的構件如梁和軸的應力和變形的。在更復雜的幾何和加載情況下，可以由彈性理論的形式使用相同的基本假設分析。現(xiàn)在經(jīng)常利用被稱為與數(shù)字計算機相關的有限元分析的數(shù)字科技來完成。</p><p>　　應力應變關系需要考慮在三維中的行為，除了彈性應變外，這個方程可能還需要包括塑性應變和蠕變應變。處

54、理蠕變應變要引入時間作為一個額外的變量。不管用什么方法，對于特定的材料分析確定應力和變形總是需要適當?shù)膽?應變關系。對于應力和應變的計算，我們把應變作為一個無量綱的量表達，來自于長度的變化，ε=ΔL/L。因此，應變給定的百分比需要被轉(zhuǎn)換成無量綱形式，ε=ε%/100，也可以把應變百分比做為微應變ε=εμ/106。</p><p>　　在本章中，我們將首先考慮一維應力應變行為和一些相應的彈性，塑性，蠕變變形的簡單

55、的物理模型。彈性變形的探討將擴展到三個維度，從各向同性行為開始，在所有的方向中的彈性性質(zhì)是相同的。我們也會考慮在復合材料中各向異性的簡單情況，其中的彈性性質(zhì)隨方向而變化。但是，三維塑性變形和蠕變變形行為探討將分別推遲到第12章和15章。</p><p>　　5.2變形的典型模式</p><p>　　簡單的機械裝置，如線性彈簧、摩擦滑塊和粘滯阻尼器，可以用于幫助理解變形的各種類型。四個這樣的

56、模型對于一個施加力的反應展示在圖5.1。這樣的裝置和它們的組合被稱為流變模型。</p><p>　　彈性變形，圖.5.1(a)，類似于一個簡單的線性彈簧的行為，用常數(shù)K表示，這種變形都是成比例的力，x=P/k,，并且當它的力卸載時變形會恢復。塑性變形，圖5.1(b),類似于一個質(zhì)量為m的塊在一個水平面上的運動，動、靜摩擦系數(shù)被認為是相等的，所以有一個臨界動摩擦力P0=μmg，其中g是重力加速度。如果施加一個恒定的

57、力P小于臨界值，P’<P0，沒有運動的發(fā)生。但是，如果這個力再大點，P’>P0，這個塊做加速度運動，</p><p>　　a =(P’-P0)/m (5.1)</p><p>　　當這個力作用時間為t，這個塊移動的距離a= at2/2，它仍然是在這個新的位置。因此，該類型的行為產(chǎn)生永久變形，Xp。蠕變變形可分為兩種類型，穩(wěn)態(tài)蠕變，圖5.1（

58、c），在恒力作用下進行恒速運動，這種行為發(fā)生在一個線性阻尼情況下，一個恒定的速度單元，與力成正比。比例常數(shù)是阻尼常數(shù)C，因此，一個恒定的力P’值給出了一個恒定的速度，，導致了一個線性位移與時間的關系。當這個力撤去時，運動停止，所以這個變形是永久性的，不可恢復的。一個阻尼器可以通過將一個活塞放在一個充滿粘性液體（如重油）的圓筒中構造出來，當施加一個力時，少量的油漏過活塞，使活塞移動。運動的速度將與力的大小近似成比例，當所有的力撤去時位移將

59、會保持。</p><p>　　第二種蠕變類型，被稱為瞬態(tài)蠕變，圖5.1（d），隨著時間的推移減慢。這樣的情況是發(fā)生在一個裝有平行的阻尼和彈簧上，如果有一個恒定的力P作用，變形會隨時間增加。但隨著x的增加需要越來越多的一部分施加的力來拉彈簧，因此，這些小部分的力可以通過阻尼器獲得，并且變形速率降低。如果力是維持很長一段時間變形值近似于p / k，如果施加的力撤去，已經(jīng)被延伸的彈簧，現(xiàn)在拉回阻尼器。這導致所有的變形是

60、在極長的時間恢復。</p><p>　　流變模型可以用來表示軸向載荷下一塊材料的應力和應變，如圖5.2所示，該模型常數(shù)與材料常數(shù)有關，與材料的長度或面積無關。對彈性形變來說，應力應變之間的常數(shù)是彈性模量，也稱為楊氏模量，由E=σ/ε （5.2） 得出，用應力和應變的定義，并采用P = K X，可得出E和K之間的關系 </p><p>　　E=k L/A

61、 (5.3)</p><p>　　對于塑性變形模型，材料的屈服強度很簡單，</p><p>　　σ0=P0/A (5.4)</p><p>　　對于穩(wěn)態(tài)蠕變模型，類似于阻尼常數(shù)C的材料常數(shù)稱為拉伸粘度系數(shù)，由下式得出</p><p><b>　　(5.5)<

62、/b></p><p>　　當應變速率由得出時，從圖5.2和P = CX替代，可得出η和C之間的關系</p><p><b>　　(5.6)</b></p><p>　　在瞬態(tài)蠕變模型中，方程5.3和5.6也適用于彈簧和阻尼器的元素。</p><p>　　在詳細討論彈性形變之前，對于進一步討論塑性和蠕變變形的模型也

63、是有用的。</p><p>　　5.2.1塑性變形模型</p><p>　　如同在2章中討論的，在金屬和陶瓷中產(chǎn)生塑性變形的主要的物理機制是材料晶粒和原子平面的滑移（滑動），由于位錯運動以漸進的方式發(fā)生。材料的塑性變形大致類似于一個塊在平面上的摩擦，如同圖5.1（b）的流變模型。</p><p>　　為了建立應力應變模型，質(zhì)量為m的塊可以用一個無質(zhì)量的摩擦滑塊替代，

64、類似于一個彈簧夾，如圖5.3(a)所示。兩個額外的模型，即線性彈簧和摩擦滑塊組合，如圖（b）和（c）。通過滑塊與彈簧相連，使實際材料的行為描述得到了改善，所以，他們用屈服強度σo表現(xiàn)滑塊的彈性屈服。另外，模型（C）有第二個線性彈簧與滑塊并聯(lián)，所以它的阻力隨著變形增大而增加。模型（a）是剛性的，完全的塑性變形，模型（b）有彈性，是完全的塑性變形，模型（c）也有彈性，是線性硬化變形。</p><p>　　圖5.3給出

65、了三種不同的應變輸入時每個模型的響應，第一個是簡單的單調(diào)的應變，是一個單方向的應變。在這種情況下，對于模型（a）和（b）來說，應力保持在σo 并不超過。</p><p>　　對于單調(diào)加載的模型（c），總應變ε是彈簧E1的應變ε1與E2和σo并聯(lián)應變ε2 的和。</p><p><b>　　(5.7）</b></p><p>　　垂直桿不轉(zhuǎn)動，所

66、以，彈簧E2和滑塊σo有相同的應變。在屈服之前，滑塊阻止運動，所以ε2是0。</p><p>　　(σσo) （5.8）</p><p>　　既然有彈簧E2無偏轉(zhuǎn)，其應力為零，所有的應力是由滑塊產(chǎn)生。除了屈服，滑塊具有一個恒定應力σo ，所以，彈簧E2的應力為(σ-σo)，因此，應變ε2和總應變ε是</p><p><b>　　(5.9)&l

67、t;/b></p><p>　　從第二個方程，應力-應變曲線斜率被看作是</p><p><b>　　(5.10)</b></p><p>　　是等效剛度Ee，小于E1、E2，相當于E1E2并聯(lián)。</p><p>　　圖5.3也給出了應變增加超過屈服極限后下降到零模型的響應，在所有的三種情況中，滑塊沒有額外的運動直

68、到應力變成負方向的2σ0 。對于模型（b）和（c），給出了一個相同斜率的彈性卸載E1作為初始加載?？紤]在卸載過程中的應力通過零點，如圖5.4。彈性應變，εe,，對應于彈簧E1的松弛而恢復。永久性或塑性應變εP對應滑塊滑動到最高點的最大應變，實際的材料一般具有非線性硬化的應力-應變曲線如圖（C），但隨著彈性卸載類似于流變模型。</p><p>　　現(xiàn)在考慮各模型在圖5.3中的最后一列的情況下的響應，模型的彈性卸載至

69、0后重新加載。在所有的情況中，當卸載時應變值達到ε1，屈服再次發(fā)生。很明顯這兩個完全的塑性變形在σ = σ0時會再次發(fā)生。但線性硬化模型現(xiàn)在的屈服值σ = σ1，高于初始屈服應力值。而且，當卸載第一次開始時，σ1與應力ε=ε1的值相同。在所有的3個模型中，可以這樣解釋，模型具有記憶先前的卸載點的能力。特別地，卸載發(fā)生時，屈服在同一點σ-ε再次發(fā)生，并且隨后的反應與沒有卸載時相同。真實材料的塑性變形表現(xiàn)出類似的記憶效應。</p>