Lesson Plan Review New Words and Phrases Reading and Translating—Unit Two Classroom Exercises

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Unit Two Stress-Strain Relationship of Materials 单 元 2 材料的应力－应变关系

The primary objective of a course in mechanics of materials is the development of relationships between the loads applied to a nonrigid body and the internal forces and deformations induced in the body.

材料力学课程的主要目的，是展示施加在 非刚性物体上的载荷与物体中由此而引起的内 力和变形之间的关系。

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.

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，如灰色铸铁 和混凝土的应力－应变图，即使在很小的应力下 也表现为微弯的曲线，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。

Thomas Young, in 1807, suggested what amounts to using the ratio of stress to strain measure the stiffness of a material. This ratio is called Young’s modulus or the modulus of elasticity and is the slope of the straight-line portion of the stress-strain diagram.

托马斯 · 杨在 1807 年建议采用应力与应变之 比来度量材料的刚度。这个比值称为杨氏模量 或弹性模量，它是应力－应变图直线部分的斜 率。

Young's modulus is written as or Where E is used for normal stress and strain and G (sometimes called the modulus of rigidity) is used for shearing stress and strain. The maximum stress for which stress and strain are proportional is called the proportional limit.

Young's modulus is written as or Where E is used for normal stress and strain and G (sometimes called the modulus of rigidity) is used for shearing stress and strain. The maximum stress for which stress and strain are proportional is called the proportional limit. 杨氏模量的表达式为： 或 式中 E 用于正应力和正应变， G ( 有时称为刚性模量 ) 用于剪应力和剪应变。应力－应变比例的峰值应力，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.

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.

当应力超过弹性极限 ( 或实际上的比例极限 ) 时，可以发现在载荷卸除后仍保留部分变形。 这种载荷卸除后仍然存在的变形，称为塑性变 形。

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.

与加载持续时间无关的塑性变形，称为滑 移。蠕变（徐变）是在恒定应力下继续增长的 塑性变形。

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.

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 1imit 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.

比例极限的精确值是很难得到的，特别在 应力－应变图是由直线渐渐过渡成曲线的情况 下。因此，需要另外的方法度量可以用作实际 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 to 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 － 。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.

材料在断裂前，按其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 变更（拓展）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。

Classroom Exercises 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 decrease. Thus, the stress based on the original area decrease beyond the ultimate strength of the material, although the true stress continues to increase until rupture.