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:
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.
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.
Thus in fig. 1
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.
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
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
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.