Stress-Strain Relationship of Materials

The satisfactory performance of a structure frequently is determined by the amount of deformation or distortion that can be permitted. A deflection of a few thousandths of an inch might make a boring machine useless, whereas the boom on a dragline might deflect several inches without impairing its usefulness. It is often necessary to relate the loads on a structure, or on a member in a structure, to the deflection the loads will produce. Such information can be obtained by plotting diagrams showing loads and deflections for each member and type of loading in a structure, but such diagrams will vary with the dimensions of the members, and it would be necessary to draw new diagrams each time the dimensions were varied. A more useful diagram is one showing the relation between the stress and strain.Such diagrams are called stress-strain diagrams ( see Fig. 3.1).

结构正常的工作性能通常可以由允许的变形量或扭曲量来确定。镗床如果产生了千分之几英寸的挠度就不能正常工作，而挖掘机的悬臂即使产生几英寸的挠度也不妨碍其使用。经常需要建立结构或每个结构构件上载荷与由于载荷作用所产生的挠度之间的关系。这种数据可通过画出表示结构中的每一个构件所承受的荷载及其挠度以及载荷种类的图而得到，但这种图将随构件的尺寸而变化，而且每当尺寸发生变化时就要画出新的图。更有用的图是表示应力与应变关系的图。这样的图称为应力－应变图。

Figure 3.1 Stress-strain curve for a typical low-carbon steel in tension

Data for stress-strain diagrams are usually obtained by applying an axial load to a test specimen and measuring the load and deformation simultaneously. A testing machine is used to strain the specimen and to measure the load required to produce the strain. The stress is obtained by dividing the load by the initial cross-sectional area of the specimen. The area will change somewhat during the loading, and the stress obtained using the initial area is obviously not the exact stress occurring at higher loads. It is the stress most commonly used, however, in designing structures. The stress obtained by dividing the load by the actual area is frequently called the true stress and is useful in explaining the fundamental behavior of materials. Strains are usually relatively small in materials used in engineering structures, often less than 0.001, and their accurate determination requires special measuring equipment.

应力－应变图的数据通常由在试件上加轴向载荷，并通过同时测量载荷和变形而得到。试验机用来使试件产生应变，并测量产生应变时所施加的载荷。把载荷除以试件原有的横截面面积就得到应力。在加载时横截面面积会有些变化，在载荷较大时用原有的横截面面积算得的应力显然不是精确的应力。然而，在结构设计中，这是最常采用的应力。用载荷除以实际的横截面面积而求得的应力，通常称之为真实应力，在解释材料的基本性能时应用真实应力。工程结构中材料的应变通常是很小的，一般小于 0.001,需要采用专门的测量仪器才能进行精确测量。

True strain, like true stress, is computed on the basis of the actual length of the test specimen during the test and is used primarily to study the fundamental properties of materials. The difference between nominal stress and strain, computed from initial dimensions of the specimen, and true stress and strain is negligible for stresses usually encountered in engineering structures, but sometimes the difference becomes important with larger stresses and strains.

真实应变同真实应力一样，是在试验中试件实际长度的基础上计算得来的，主要是用来研究材料的基本性质。对于工程结构中通常承受的应力来说，用试件原来尺寸算得的名义应力和应变与真实应力和应变之间的差别可以忽略不计，但是对于较大的应力和应变，有时这种差别是重要的。

The initial portion of the stress-strain diagram for most materials used in engineering structures is a straight line. The stress-strain diagrams for some materials, such as gray cast iron and concrete, show a slight curve even at very small stresses, but it is common practice to draw a straight line to average the data for the first part of the diagram and neglect the curvature. The maximum stress for which stress and strain are proportional is called the proportional limit.

在工程结构中使用的大多数材料的应力－应变图的初始部分是直线。有些材料，如灰铸铁和混凝土的应力－应变图，即使在很小的应力下也表现为微李的曲线，但在实际中通常把图的开始部分按平均值画成直线，略去其曲率。应力与应变成比例的最大应力，称为比例极限。

The action is said to be elastic if the strain resulting from loading disappears when the load is removed. The elastic limit is the maximum stress for which the material acts elastically.

由加载所产生的应变在卸除载荷后消失的现象，称为弹性。材料产生弹性作用时所对应的最大应力，称为弹性极限。

When the stress exceeds the elastic limit (or proportional limit for practical purposes) , it is found that a portion of the deformation remains after the load is removed. The deformation remaining after an applied load is removed is called plastic deformation. Plastic deformation independent of the time duration of the applied load is known as slip. Creep is plastic deformation that continues to increase under a constant stress. In many instances creep continues until fracture occurs; however, in other instances the rate of creep decreases and approaches zero as a limit. Some materials are much more susceptible to creep than are others, but most materials used in engineering exhibit creep at elevated temperatures. The total strain is thus made up of elastic strain, possibly combined with plastic strain that results from slip, creep, or both. When the load is removed, the elastic portion of the strain is recovered, but the plastic part (slip and creep) remains as permanent set.

可以发现当应力超过弹性极限（或实际上的比例极限）时，在载荷卸除后仍会保留部分变形。这种载荷卸除后仍然存在的变形，称为塑性变形。与加载持续时间无关的塑性变形，称为滑移。蠕变是在恒定应力下继续增长的塑性变形。在许多情况下，蠕变持续作用直至断裂；然而，在另一些情况下，蠕变率减小并趋近于为零的极限。某些材料对蠕变比另外一些材料要敏感得多，但是大部分工程材料在高温下呈现蠕交现象。因此，总应变是由弹性应变以及可能出现的塑性应变组成的，而塑性应变是由滑移，蠕变或者两者共同组成的。当载荷卸除时，应变的弹性部分消失，但塑性部分（滑移和蠕变）保留下来，成为永久性应变。

A precise value for the proportional limit is difficult to obtain, particularly when the transition of the stress-strain diagram from a straight line to a curve is gradual. For this reason, other measures of stress that can be used as a practical elastic limit are required. The yield point and the yield strength for a specified offset are frequently used for this purpose.

要想得到比例极限的精确值，特别在应力－应变图是由直线渐渐过渡成曲线的情况下是很困难的。因此，需要另外的度量方法来确定可以用作实际弹性极限的应力。某一特定变形的屈服点和屈服强度常常用于这一目的。

The yield point is the stress at which there is an appreciable increase in strain with no increase in stress, with the limitation that, if straining is continued, the stress will again increase.

屈服点就是应力不增加而应变明显增加时的应力，而且有这样的限制，即如果应变继续增加，应力将再增加。

The yield strength is defined as the stress that will induce a specified permanent set, usually 0.05 to 0.3 percent, which is equivalent to a strain of 0. 0005 to 0.003. The yield strength is particularly useful for materials with no yield point. 

屈服强度被定义为产生某一特定永久变形的应力，其永久变形通常为0.05% ~0.3%，等于应变为 0.0005~0.003。屈服强度对于没有屈服点的材料特别有用。

The maximum stress, based on the original area, developed in a material before rupture is called the ultimate strength of the material, and the term may be modified as the ultimate tensile, compressive, or shearing strength of the material. Ductile materials undergo considerable plastic tensile or shearing deformation before rupture.

When the ultimate strength of a ductile material is reached, the cross-sectional area of the test specimen starts to decrease or neck down, and the resultant load that can be carried by the specimen decreases. Thus, the stress based on the original area decreases beyond the ultimate strength of the material, although the true stress continues to increase until rupture.

按照材料在断裂前，原来的面积求得的最大应力，称为材料的极限强度，这一名词可以被改称为材料的极限拉伸强度，极限压缩强度或极限剪切强度。延性材料在断裂前能承受相当大的塑性拉伸变形 或剪切变形。当延性材料达到极限强度时，试件横截面开始变小或产生颈缩，试件所能承受的总载荷减小。因此，材料达到极限强度以后，虽然实际应力继续增大直至断裂，但是按原来截面算的的应力却是在减少。