📚 Compressive and Tensile Forces | 压缩力与拉伸力
In everyday structures, from bridges to bones, two basic types of mechanical force determine safety and performance: tension and compression. A-Level Physics requires a clear understanding of how these forces create stress and strain, how materials obey Hooke's law, and how the Young modulus links elastic stress to strain.
在从桥梁到骨骼的日常结构中，两种基本机械力——拉伸和压缩——决定了安全与性能。A-Level物理要求清楚地理解这些力如何产生应力和应变、材料如何遵循胡克定律，以及杨氏模量如何把弹性应力与应变联系起来。
1. What Are Tensile and Compressive Forces? | 什么是拉伸力和压缩力？
A tensile force pulls atoms apart along the line of action, tending to stretch or extend an object. A compressive force pushes atoms together along the line of action, tending to shorten or squash an object.
拉伸力沿作用线把原子拉开，使物体有伸长或延展趋势；压缩力沿作用线把原子压近，使物体有缩短或被压扁趋势。
Tension examples include a crane cable lifting a load, a rope in tug-of-war, a tightened guitar string, and the lower surface of a loaded beam. Compression examples include a concrete column under a building, a table leg, a soda can being crushed, and the upper surface of a loaded beam.
拉伸的例子包括吊起货物的起重机缆绳、拔河用的绳子、拉紧的吉他弦，以及承受载荷的梁的下表面。压缩的例子包括建筑物下方的混凝土柱、桌腿、被压扁的易拉罐，以及承受载荷的梁的上表面。
Long, slender members under compression can also fail by buckling before the material itself is crushed. This is a stability effect rather than a simple strength effect, and it is very important for columns and struts.
细长构件在压缩下也可能在材料本身被压碎前发生屈曲失效。这是一种稳定性效应，而不是简单的强度效应，对柱和撑杆非常重要。
2. Internal Forces and Equilibrium | 内力与平衡
When external tensile or compressive forces act on a body, internal forces arise between neighbouring layers or particles. If the object is in equilibrium, the internal force at a section balances the applied load.
当外部拉伸或压缩力作用在物体上时，相邻层或粒子之间会产生内力。物体平衡时，某一截面上的内力与外加载荷平衡。
In tension, each cross-section experiences equal and opposite pulls. In compression, each cross-section experiences equal and opposite pushes. These internal effects are distributed over the cross-sectional area, which is why a thick rod resists better than a thin rod.
拉伸时每个横截面承受大小相等、方向相反的拉力；压缩时承受大小相等、方向相反的压力。这些内部作用分布在横截面积上，所以粗杆比细杆更能抵抗变形。
| Feature / 特征 | Tension / 拉伸 | Compression / 压缩 |
|---|---|---|
| Direction / 方向 | Pulls apart / 拉开 | Pushes together / 压拢 |
| Length change / 长度变化 | Increases / 增加 | Decreases / 减小 |
| Typical sign / 常用符号 | Positive / 正 | Negative / 负 |
| Common failure / 常见失效 | Fracture after necking / 颈缩后断裂 | Crushing or buckling / 压碎或屈曲 |
3. Stress: Force per Unit Area | 应力：单位面积上的力
Stress measures how concentrated an internal force is. For a force F acting perpendicular to a cross-sectional area A, the tensile or compressive stress is:
应力衡量内力的集中程度。若力 F 垂直作用于横截面积 A，则拉伸或压缩应力为：
σ = F ÷ A
es a much larger stress on a thin wire than on a thick column, which is why nominal area matters.
应力的单位是帕斯卡 Pa，1 Pa = 1 N m⁻²。同样的力作用在细线上产生的应力远大于作用在粗柱上，因此标称横截面积非常重要。
gives a cross-sectional area of about 7.85 × 10⁻⁷ m² and a stress of about 1.27 × 10⁸ Pa.
例如，100 N 的力作用在直径 1.0 mm 的金属丝上，横截面积约为 7.85 × 10⁻⁷ m²，应力约为 1.27 × 10⁸ Pa。
4. Strain: Extension or Compression per Unit Length | 应变：单位长度的伸长或压缩
Strain describes the relative change in length. For an original length L₀ and a change in length ΔL, the tensile or compressive strain is:
应变描述长度的相对变化。设原长为 L₀，长度变化为 ΔL，则拉伸或压缩应变为：
ε = ΔL ÷ L₀
Strain has no units because it is a ratio of two lengths. In tension ΔL is positive; in compression ΔL is often treated as negative, giving a negative strain.
应变没有单位，因为它是两个长度之比。拉伸时 ΔL 为正；压缩时 ΔL 常视为负，因此应变为负。
m ÷ 2.0 m = 5.0 × 10⁻⁴. This small value is typical for metals within the elastic region.
如果一根 2.0 m 的钢丝伸长 1.0 mm，则拉伸应变为 0.001 m ÷ 2.0 m = 5.0 × 10⁻⁴。这个很小的数值在金属弹性区内是典型的。
5. Hooke's Law and the Elastic Limit | 胡克定律与弹性极限
Hooke' o the applied force: F = kx, where k is the spring constant and x is the change in length.
胡克定律指出，在小变形下，伸长或压缩与外力成正比：F = kx，其中 k 是劲度系数，x 是长度变化。
The limit of proportionality is the point beyond which the graph of force against extension stops being a straight line. The elastic limit is the greatest stress or force that a material can withstand and still return to its original shape when unloaded.
比例极限是力–伸长图不再为直线的点。弹性极限是材料卸载后仍能恢复原状的最大应力或力。
In compression, a spring obeys Hooke's law until its coils touch, after which it becomes much stiffer. In tension, it obeys until the elastic limit is passed, after which unloading leaves a permanent extension.
压缩时，弹簧在簧圈接触前遵循胡克定律，之后显著变硬；拉伸时，弹簧在超过弹性极限后卸载会留下永久伸长。
6. Young Modulus as a Material Property | 杨氏模量作为材料属性
Young modulus E compares stress and strain in the linear elastic region. It is defined by:
杨氏模量 E 反映线弹性区内应力与应变的关系。其定义为：
E = σ ÷ ε = (F ÷ A) ÷ (ΔL ÷ L₀)
tress to produce a given strain. Steel has a typical Young modulus of about 2.0 × 10¹¹ Pa.
它的单位与应力相同，为 Pa。杨氏模量高表示材料刚硬，需要较大应力才能产生一定应变。钢的典型杨氏模量约为 2.0 × 10¹¹ Pa。
For many engineering metals, the Young modulus is similar in tension and compression within the elastic range. However, concrete, polymers and biological materials can show different stiffness in tension and compression.
许多工程金属在弹性范围内拉伸和压缩的杨氏模量相近。但混凝土、聚合物和生物材料在拉伸和压缩下可能表现出不同的刚度。
7. Force–Extension and Stress–Strain Curves | 力–伸长曲线与应力–应变曲线
A force–extension graph for a wire under tension initially shows a straight line through the origin, obeying Hooke's law. The gradient of this straight line equals the spring constant k.
金属丝受拉伸时的力–伸长图起初是一条过原点的直线，遵循胡克定律。该直线的斜率等于劲度系数 k。
After the elastic limit, the graph curves and the material may yield. A ductile metal such as copper undergoes a large extension before fracture, while a brittle material such as glass fractures soon after the elastic limit.
超过弹性极限后曲线弯曲，材料可能屈服。铜等延性金属断裂前产生较大伸长，而玻璃等脆性材料在弹性极限后很快断裂。
Compression curves for brittle materials such as concrete show a fracture stress in compression much greater than in tension. Concrete can be strong in compression but weak in tension, which is why it is often reinforced with steel.
混凝土等脆性材料的压缩曲线显示其抗压断裂应力远高于抗拉断裂应力。混凝土抗压能力强但抗拉能力弱，因此常用钢筋增强。
8. Elastic and Plastic Deformation | 弹性变形与塑性变形
Elastic deformation is recoverable: when the load is removed, atoms return to their original equilibrium spacing. Plastic deformation is permanent: layers of atoms slide past one another and do not return to their original positions.
弹性变形是可恢复的：卸载后原子回到原来的平衡间距。塑性变形是永久的：原子层相互滑移，不会回到原来位置。
The work done during elastic deformation is stored as strain energy and can be released. The work done during plastic deformation is mostly dissipated as heat, so it is not recoverable.
弹性变形过程中所做的功以应变能形式储存并可释放。塑性变形过程中所做的功主要耗散为热，因此不可恢复。
On a force–extension graph, the area under the curve equals the work done. For a material obeying Hooke's law, the elastic strain energy stored is:
在力–伸长图上，曲线下的面积等于所做的功。对于遵循胡克定律的材料，储存的弹性应变能为：
Eₑ = ½ FΔL = ½ k(ΔL)²
9. Brittle, Ductile and Malleable Behaviour | 脆性、延性与展性行为
Brittle materials, such as glass and cast iron, fracture with little or no plastic deformation. Ductile materials, such as copper and aluminium, can be drawn into wires under tension because they undergo large plastic strain before breaking.
玻璃、铸铁等脆性材料断裂时几乎没有塑性变形。铜和铝等延性材料在拉伸下可拉成丝，因为它们在
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