材料力学专业英语1.ppt

Chapter1 Tension and Compression 第一章 拉伸与压缩 Axially Loaded Bar The simplest case to consider at the start is that of an initially straight metal bar of constant cross section, loaded at its ends by a pair of oppositely directed collinear forces coinciding with the longitudinal axis of the bar and acting through the centroid of each cross section. For static equilibrium the magnitudes of the forces must be equal. If the forces are directed away from the bar, the bar is said to be in tension; if they are directed toward the bar, a state of compression exists. These two conditions are illustrated in Fig. 1-1. 轴向受载杆件 同线的 质心 平衡大小 不变的 首先我们研究最简单情况：一等截面金属直杆在其两 端承受一对共线、反向力的作用。这两个力的作用线与各截 面形心组成的纵向轴线重合，为了满足静力学平衡条件，这 两个力的数值必须相等。如果这两个力的方向是离开此杆的 ，杆将承受拉伸；如果这两个力是指向此杆的，杆将承受压 缩，如图1-1所示。 Fig. 1-1 图1-1 Under the action of this pair of applied forces, internal resisting forces are set up within the bar and their characteristics may be studied by imagining a plane to be passed through the bar anywhere along its length and oriented perpendicular to the longitudinal axis of the bar. Such a plane is designated as a-a in Fig. 1-2(a). Fig.1-2 图1-2 垂直的， 正交的 在这样这样 两个力的作用之下，杆的内部将产产生抗力。我 们们可以用位于杆轴轴某处处、且与杆轴轴垂直的假想截面来研究 杆的内部抗力，这样这样 的截面如图图1-2（a）中的a-a所示。 If for purposes of analysis the portion of the bar to the right of this plane is considered to be removed, as in Fig. 1-2(b), then it must be replaced by whatever effect it exerts upon the left portion. By this technique of introducing a cutting plane, the originally internal forces now become external with respect to the remaining portion of the body. For equilibrium of the portion to the left this “effect” must be a horizontal force of magnitude P. However, this force P acting normal to the cross-section a-a is actually the resultant of distributed forces acting over this cross section in a direction normal to it. 施加（力 ） 水平的 法线 合力分布式的 为为了分析计计算，可考虑虑将此截面右侧侧的杆段除去，如图图1-2（ b）所示。因而，必须补充右侧杆段对左侧杆段的作用。用此 处引入的截面法，初始的内力便成为保留杆段的外力。为使左 侧杆段平衡，这种效应在数值上等于水平力P。然而，沿截面 a-a法向作用的力P实际上是截面上法向分布力合成的结果。 Fig.1-2 图1-2 Instead of speaking of the internal force acting on some small element of area, it is better for comparative purposes to treat the normal force acting over a unit area of the cross section. The intensity of normal force per unit area is termed the normal stress and is expressed in units of force per unit area, e,g., 1N/m2. Normal Stress 法应力 把称作 比较的 应力 替代讨论讨论 作用在某处处小面积积上内力，最好转为转为 处处理单单位面积积上法向力。单单位面积积上法向力的 强度称为为法应应力，它是用单单位面积积上的作用力 单单位表示的，亦即1 If the forces applied to the ends of the bar are such that the bar is in tension, then tensile stresses are set up in the bar; if the bar is in compression we have compressive stresses. It is essential that the line of action of the applied end forces pass through the centroid of each cross section of the bar. 如果杆端的力使杆拉伸，杆内就产生拉应力，如果杆是受压 缩的，杆内产生压应力。施加在杆端的力作用线必须通过每 一个截面形心。 The axial loading shown in Fig. 1-2(a) occurs frequently in structural and machine design problems. To simulate this loading in the laboratory, a test specimen is held in the grips of either an electrically driven gear-type testing machine or a hydraulic machine. Both of these machines are commonly used in materials testing laboratories for applying axial tension. Test Specimens 试样 样品 夹具 电力地 液压的 应用，施加 图1-2（ a）所示的轴轴向载载荷经经常出现现在结结构 和机械设计设计 中，为为了在实验实验 室中模拟这拟这 种轴轴向 载载荷，试试件应夹应夹 持在电电子或液压压万能试验试验 机的 夹头夹头 中。这这两种试验试验 机通常在材料实验实验 室用做施 加轴轴向载载荷。 In an effort to standardize materials testing techniques the American Society for Testing Materials (ASTM) has issued specifications that are in common use. Only two of these will be mentioned here, one for metal plates thicker than in (4.76mm) and appearing as in Fig.1-3, the other for metals over 1.5in (38mm) thick and having the appearance shown in Fig.1-4. 在材料实验技术规范标准中，美国材料实验协会颁布 了详细的使用说明。此处只讲其中两种试件。一种厚度超 过3/16in（4.76mm）的金属板试件如图1-3所示，另外一 种直径为1.5in（38mm）的金属圆棒状试件如图1-4所示。 标准化 As may be seen from these figures, the central portion of the specimen is somewhat smaller than the end regions so that failure will not take place in the gripped portion. The rounded fillets shown are provided so that no stress concentrations will arise at the transition between the two lateral dimensions. The standard gage length over which elongations are measured is 8in (203mm) for the specimen shown in Fig.1-3 and 2in (57mm) for that shown in Fig.1-4. 正如图中所看到的，试件的中部区域尺寸略小于两端尺寸。 因而，破环不会发生在两端的夹持段，过度圆角保证试件两 种尺寸的过渡部位不会发生应力集中。供测量伸长的标距长 度为8in（203mm，图1-3试件）和2in（51mm，图1-4试 件）。 稍微，有些 失效，破坏 过渡区 伸长标距 The elongations are measured by either mechanical or optical extensometers or by cementing an electric resistance-type strain gage to the surface of the material. This resistance strain gage consists of a number of very fine wires oriented in the axial direction of the bar. As the bar elongates, the electrical resistance of the wires changes and this change of resistance is detected on a Wheatstone bridge and interpreted as elongation. 伸长计 粘贴 电阻应变片 细的 转换 试件的伸长既可以使用机械的、光学的伸长计 ，也可以使用粘贴在试件表面的电阻应变片来测 量，这种电阻应变片由若干个沿试件轴向的、很 细的电阻丝组成。当试件伸长时，电阻丝的电阻 就会发生改变，电阻的改变由惠斯通电桥测量并 转换为伸长量。 Let us suppose that one of these tension specimens has been placed in a tension-compression testing machine and tensile forces gradually applied to the ends. The elongation over the gage length may be The elongation over the gage length may be measured as indicated above for any predetermined measured as indicated above for any predetermined increments of the axial load. From these values the increments of the axial load. From these values the elongation per unit length, which is termed elongation per unit length, which is termed normal strain normal strain and denoted by and denoted by , may be found by dividing the total , may be found by dividing the total elongation elongation by the gage length L, that is,by the gage length L, that is, = = / L. / L. The strain is usually expressed in units of inches per inch or meters per meter and consequently is dimensionless. Normal Strain 法应变 应变 增量 对对于每一个事先指定的轴轴向载载荷增量都要测测 量相应应的标标距的伸长长。由这这些数值值得到单单位长长度 的伸长长，并将之定义为义为 法应变应变 ，用来表示，可 以用标距长度L去除总伸长来得到法应变。 As the axial load is gradually increased in increments, the total elongation over the gage length is measured at each increment of load and this is continued until fracture of the specimen takes place. Knowing the original cross-sectional area of the test specimen the normal stress, denoted by , may be obtained for any value of axial load by the use of the relation Stress-Strain Curve 应力应变曲线 where P denotes the axial load in pounds or Newtons and A the original cross-sectional area. Having obtained numerous pairs of values of normal stress and normal strain,the experimental data may be plotted with these quantities considered as ordinate and abscissa, respectively. This is the stress-strain curve or diagram of the material for this type of loading. Stress-strain diagrams assume widely differing forms for various materials. Figure 1-5 is the stress-strain diagram for a medium-carbon structural steel, Fig.1-6 is for an alloy steel, and Fig.1-7 is for hard steels and certain nonferrous alloys. For nonferrous alloys and cast iron the diagram has the form indicated in Fig.1-8, while for rubber the plot of Fig.1-9 is typical. 量，数量 纵坐标 横坐标 碳素结构钢 有色金属合金 铸铁 P是轴轴向载载荷，A是初始截面积。于是，得到由法应 力和法应变组成的很对数据对，然后分别以法应 力为纵轴，法应变为横轴，用上述实验数据作图， 这就是材料的应力应变曲线或拉伸图。图1-5是碳 素结构钢的应力应变图，图1-6是合金钢，图1-7是 硬质刚或某些有色金属合金的应力应变图，有色 金属合金或铸铁的应力应变图如图1-8所示，而对 于橡胶，图1-9是典型的应力应变图。 1. The concepts of stress and strain can be illustrated in an elementary way by considering the extens