应力应变的关系和行为外文文献翻译@中英文翻译@外文翻译

原文： Stress-Strain Relationships and Behavior 5.1 INRODUCTION 5.2 MODELS FOR DEFORMATION BEHAVIOR 5.3 ELASTIC DEFORMATION 5.4 ANISOTROPIC MATERIALS 5.5 SUMMARY OBJECTIVES Become familiar with the elastic, plastic, steady creep, and transient creep types of strain, as well as simple rheological models for representing the stress-strain-time behavior for each. Explore three-dimensional stress-strain relationships for linear-elastic deformation in isotropic materials, analyzing the interdependence of stresses or strains imposed in more than one direction. Extend the knowledge of elastic behavior to basic cases of anisotropy, including sheets of matrix-and fiber composite material. 5.1 INRODUCTION The three major types of deformation that occur in engineering materials are elastic, plastic, and creep 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 with 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 slip of crystal planes or sliding if chain molecules. If the inelastic deformation is time dependent, it is classed as creep, as distinguished from plastic deformation, which is not time dependent. In engineering design 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 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 the same basic assumptions in the form of theory of elasticity. This is now often accomplished by using the numerical technique called finite element analysis with a digital computer. Stress-strain relationships need to consider behavior in three dimensions. In addition to elastic strains, the equations may also need to include plastic strains 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 stress-strain relationships for the particular material involved. For calculations involving stress and strain, we express strain as a dimensionless quantity, as derived from length change, = L/L. Hence, strains given as percentages need to be converted to the dimensionless form, = %/100, as do strains given as microstrain, = /106. In the chapter, we will first consider one-dimensional stress-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 behavior, 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-dimensional plastic and creep deformation behavior will be postponed to Chapters 12 and 15, respectively. 5.2 MODELS FOR DEFORMATION BEHAVIOR Simple mechanical devices, such as linear springs, frictional sliders, and viscous dashpots, can be used as an aid to understanding the various 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. Elastic deformation, 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 deformation, 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 are assumed to be equal, so that there is a critical force for motion P0= mg, where g is the acceleration of gravity. If a constant applied force P is less than the critical value, PP0, the block moves with an acceleration a =(P-P0)/m (5.1) When the force is removed at time t, the block has moved a distance a=at2/2, and it remains at this new location. Hence, the model behavior produces a permanent deformation, xp. Creep deformation can be subdivided into two types. Steady-state creep, Fig.5.1(c), proceeds at a constant rate under constant force. Such behavior occurs in a linear dashpot, which is an element where the velocity, dtdx/x 。 , is proportional to the force. The constant of proportionality is the dashpot constant c, so that a constant value of force P gives a constant velocity, cPx /。 , resulting in a linear displacement versus time behavior. When the force is removed, the motion stops, so that the deformation is permanent-that is, not recovered. A dashpot could be physically constructed by placing a piston in a cylinder filled with a viscous liquid, such as a heavy oil. When a force is applied, small amounts of oil leak past the piston, allowing the piston to move. The velocity of motion will be approximately proportional to the magnitude of the force, and the displacement will remain after all force is removed. The second type of creep, 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 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 force is maintained for a long period of time. If the applied force is removed, the spring, having been extended, now pulls against the dashpot. This results in all of the deformation being recovered at infinite time. 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 material 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 Youngs modulus, given by E= / (5.2) Substituting the definitions of stress and strain, and also employing P = k x, yields the relationship between E and k: E=kL/A (5.3) For the plastic deformation model, the yield strength of the material is simply 0=P0/A (5.4) 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 . (5.5) Where dtd /. is the strain rate. Substitution from Fig. 5.2 and P= cx. Yields the relationship between and c: AcL (5.6) Equations 5.3 and 5.6 also apply to the spring and dashpot elements in the transient creep model. Before proceeding to the detailed discussion of elastic deformation, it is useful to further to discuss plastic and creep deformation models. 5.2.1 Plastic Deformation Models As discussed in Chapter 2, the principal physical mechanism causing plastic deformation in metals and ceramics is sliding (slip) between planes of atoms in the crystal grains of the material, occurring in an incremental manner due to dislocation motion. The materials resistance to plastic deformation is roughly analogous to the friction of a block on a plane, as in the rheological model of Fig. 5.1(b). 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 shown 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 spring in series with the slider, so that they exhibit elastic behavior prior to yielding at the slider yield strength o. In addition, model (c) has a second linear spring connected parallel to the slider, so that its resistance increases as deformation proceeds. Model (a) is said to have rigid, perfectly plastic behavior； model (b) elastic, perfectly plastic behavior； and model (c) elastic, linear-hardening behavior. Figure 5.3 gives each models response to three different strain 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 o beyond yielding. For monotonic loading of model (c), the strain is the sum of strain 1 in spring E1 and strain 2 in the (E2, o) parallel combination: 21 , E11 (5.7) The vertical bar is assumed not to rotate, so that both spring E2 and slider o have the same strain. Prior to yielding, the slider prevents motion, so that strain 2 is zero: 02 , E1 ( o) (5.8) 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 stress o, so that the stress in spring E2 is ( - o). Hence, the strain 2 and the overall strain are E 2 02 , EE 2 01 (5.9) From the second equation,the slope of the stress-strain curain curve is seen to be EE EEE edd 21 21 (5.10) Which is the equivalent stiffness Ee, lower than both E1 and E2, corresponding to E1 and E2 in series. Figure 5.3 also gives the model responses where strain 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 20 in the negative direction . For models (b) and (c) , 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, e, that is recovered corresponds to the relaxation of spring E1. The permanent or plastic strain p corresponds to the motion of the slider up to the point of maximum strain. Real materials generally have nonlinear hardening stress-strain curves as in (c), but with elastic unloading behavior similar to that of the rheological models. 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 = 0. In all cases, yielding occurs a second time when the strain again reaches the value 1 from which unloading occurred. It is obvious that the two perfectly plastic models will again yield at = 0. But the linear-hardening model now yields at a value = 1, which is higher than the initial yield stress. Furthermore, 1 is the same value of stress that was present at =1, when the unloading first began. For all three models, the interpretation may be made that the model possesses a memory of the point of previous unloading. In particular, yielding again occurs at the same - point from which unloading occurred, and the subsequent response is the same as if there had never been any unloading. Real materials that deform plastically exhibit a similar memory effect. We will return to spring and slider models of plastic deformation in Chapter 12, where they will be considered in more detail and extended to nonlinear hardening cases. 译文： 应力应变的关系和行为 5.1 概述 5.2 变形的典型模式 5.3 弹性变形 5.4 各向异性材料 5.5 总结 目标 熟悉弹性应变，塑性应变，稳态蠕变和瞬态蠕变等应变类型，以及每个用来表示应力 应变与时间相关的简单的流变类型。 探讨在各向同性材料中线性弹性变形的三维的应力应变关系，分析应力应变在多个方向上施加的相互作用力 扩展在各向异性材料中以及一些基体纤维复合材料中弹性形变的基本情况的知识。 5.1 概述 工程材料发生变形的三种主要类型是弹性变形，塑性变形，蠕变变形。这些已经在金属聚合物和陶瓷行 为的物理机制和一般趋势的观点的第 2 章中被讨论过了，记得弹性变形与拉伸相关，但是不打破化学键。相比之下，这两种涉及原子的相对位置变化的过程类型的非弹性变形，比如晶面滑移和链分子滑动。如果非弹性变形取决于时间，它被归类为蠕变，区别于不取决于时间的的塑性变形。 在工程设计和分析中，应力应变行为的方程描述，称为应力应变的关系或本构方程是很必要的。比如，在基础材料力学中，与线性应力 -应变相关的弹性行为是被假定和用来计算简单的构件如梁和轴的应力和变形的。在更复杂的几何和加载情况下，可以由弹性理论的形式使用相同的基本假设 分析。现在经常利用被称为与数字计算机相关的有限元分析的数字科技来完成。 应力应变关系需要考虑在三维中的行为，除了弹性应变外，这个方程可能还需要包括塑性应变和蠕变应变。处理蠕变应变要引入时间作为一个额外的变量。不管用什么方法，对于特定的材料分析确定应力和变形总是需要适当的应力 -应变关系。对于应力和应变的计算，我们把应变作为一个无量纲的量表达，来自于长度的变化， = L/L。因此，应变给定的百分比需要被转换成无量纲形式， = %/100，也可以把应变百分比做为微应变 = /106。 在本章中，我们将首先考虑一 维应力应变行为和一些相应的弹性，塑性，蠕变变形的简单的物理模型。弹性变形的探讨将扩展到三个维度，从各向同性行为开始，在所有的方向中的弹性性质是相同的。我们也会考虑在复合材料中各向异性的简单情况，其中的弹性性质随方向而变化。但是，三维塑性变形和蠕变变形行为探讨将分别推迟到第 12 章和 15 章。 5.2 变形的典型模式 简单的机械装置，如线性弹簧、摩擦滑块和粘滞阻尼器，可以用于帮助理解变形的各种类型。四个这样的模型对于一个施加力的反应展示在图 5.1。这样的装置和它们的组合被称为流变模型。 弹性变形，图 .5.1(a)， 类似于一个简单的线性弹簧的行为，用常数 K 表示，这种变形都是成比例的力， x=P/k,，并且当它的力卸载时变形会恢复。塑性变形，图 5.1(b),类似于一个质量为 m 的块在一个水平面上的运动，动、静摩擦系数被认为是相等的，所以有一个临界动摩擦力 P0= mg，其中 g 是重力加速度。如果施加一个恒定的力 P 小于临界值， P P0，这个块做加速度运动， a =(P -P0)/m (5.1) 当这个力作用时间为 t，这个块移动的距离 a= at2/2，它仍然是在这个新的位置。因此，该类型的行为产生永久变形， Xp。蠕变变形可分为两种类型，稳态蠕变，图 5.1（ c），在恒力作用下进行恒速运动，这种行为发生在一个线性阻尼情况下，一个恒定的速度单元dtdx/x 。 ，与力成正比。比例常数是阻尼常数 C，因此，一个恒定的力 P值给出了一个恒定的速度， cPx /。 ，导致了一个线性位移与时间的关系。当这个力撤去时，运动停止，所以这个变形是永久性的，不可恢复 的。一个阻尼器可以通过将一个活塞放在一个充满粘性液体（如重油）的圆筒中构造出来，当施加一个力时，少量的油漏过活塞，使活塞移动。运动的速度将与力的大小近似成比例，当所有的力撤去时位移将会保持。 第二种蠕变类型，被称为瞬态蠕变，图 5.1（ d），随着时间的推移减慢。这样的情况是发生在一个装有平行的阻尼和弹簧上，如果有一个恒定的力 P 作用，变形会随时间增加。但随着 x 的增加需要越来越多的一部分施加的力来拉弹簧，因此，这些小部分的力可以通过阻尼器获得，并且变形速率降低。如果力是维持很长一段时间变形值近似于 p / k，如果施加的力撤去，已经被延伸的弹簧，现在拉回阻尼器。这导致所有的变形是在极长的时间恢复。 流变模型可以用来表示轴向载荷下一块材料的应力和应变，如图 5.2 所示，该模型常数与材料常数有关，与材料的长度或面积无关。对弹性形变来说，应力应变之间的常数是弹性模量，也称为杨氏模量，由 E= / （ 5.2） 得出，用应力和应变的定义，并采用 P = K X，可得出 E 和 K 之间的关系 E=k L/A (5.3) 对于塑性变形模 型，材料的