Stress and Strain / 应力与应变

When a force (or load) is applied to a material, it produces a stress in the material. The stress acting on the material is the force exerted per unit area:
当一个力(或载荷)作用于一材料上时,这个力就对这个材料产生一个应力。作用在材料上的应力是单位面积上所受的力:
Stress = Force / Area
应力 = 力 / 面积

Stresses may be tensile, compressive or shear in nature. Figure 1 shows a metal block in tension, i.e. the force F is a stretching force which thus increases the length of the block and reduces its cross-section. If the metal block has a cross-section A, then the tensile stress is F/A.
从性质上来说,应力可能是拉应力、压应力或剪切力,图1为一受拉金属块,即力F是使金属块在长度方向上变长,横截面积缩小的拉力。若这个金属块的横截面积为A,那么拉应力为F/A。

The dimensional change caused by a stress is called strain. In tension (or compression), the strain is the ratio of the change in length to the original length.
由应力引起的尺寸变化叫做应变。在拉伸(压缩)时,应变是长度变化量与原始长度之比。
Thus in fig. 1
图1所示
Tensile strain = Extension in length / Original length = l / L
拉应变 = 轴向伸长量 / 原始长度

Being a ratio, strain is a number without units, but change both in length and original length must be expressed in the same units. Strain may also be expressed as a percentage.
作为一个比值,应变是一个无单位的数,长度变化量的单位必须与原长度的单位相同。用百分数也可以表示应变。

In fig. 2, the force F compresses the metal, thus reducing its length and increasing its cross-section. In this case, the compressive stress is F/A and
在图2中,压力F作用于金属块上,所以长度减少,横截面积增加,这时,压应力是F/A,即
Compressive strain = Reduction in length / Original length = l / L
压应力 = 轴向缩短量 / 原始长度

In elastic behavior, the strain produced in a stressed material is completely removed as soon as the stress is removed, so that the material returns to its original dimensions. Some metallic materials show elastic properties up to fairly high stresses, while others have little, if any, elasticity. When an elastic material is loaded progressively in tension, the elastic strain produced is directly proportional to the stress causing it. This relationship is known as Hooke’s law. The graph of stress against strain (Fig. 3) will be a straight line passing through the origin. The slope of this straight line (stress/strain) is a constant for a given material. This constant is known as Young’s modulus, or the modulus of elasticity, and is denoted by E, so that
在弹性阶段,当作用在材料上的应力被解除时,应变也完全消失,材料又恢复到原始尺寸。一些金属材料能承受相当高的应力来显示弹性性能,而另一些金属材料几乎没有,即使有也是很小的弹性。当弹性材料被逐渐施加拉力时,所产生的弹性应变与相应的应力成正比,这就是胡克定律,应力与应变曲线图是一通过原点的直线(图3),这个直线的斜率(F/A)对所给的材料是个常数,这个常数叫做杨氏模量,或弹性模量,用E表示,所以
Modulus of elasticity E = Stress / Strain
弹性模量E = 应力 / 应变

Since strain is a dimensionless quantity, E has the same units as stress. The value of E is governed by the nature of the material; for steel it is about 2×105N/mm2 and is not much affected by composition or heat treatment, but decreases with increase in temperature. The higher the value of E the more springy a material is.
因为应变是一个无量纲的数,所以E的单位与应力的单位相同。E的值取决于材料的性质,钢的弹性模量大约是2×105N/mm2,而材料的成分或热处理对E的值影响不大,但随着温度的升高而降低,E值越高,材料的弹性越好。

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