📚 Matter and Materials | 物质与材料
In CIE A-Level Physics, the topic “Matter and Materials” connects measurable quantities such as density, pressure, force, extension, stress and strain to the behaviour of real solids, fluids and wires. Mastering these ideas allows you to predict whether a spring obeys Hooke’s law, calculate the pressure at a depth in a liquid, and explain why a steel cable stretches elastically before it fails.
在 CIE A-Level 物理中，”物质与材料”这一主题将密度、压强、力、伸长量、应力和应变等可测量量与真实固体、流体和金属丝的行为联系起来。掌握这些概念，你就能判断弹簧是否遵循胡克定律，计算液体中某一深度的压强，并解释钢缆为何先发生弹性拉伸然后才失效。
1. Density and Pressure | 密度与压强
Density is defined as mass per unit volume. Its SI unit is kg m⁻³. The density of a material is a characteristic property that does not depend on the size of the sample, provided the material is uniform.
密度定义为单位体积的质量。其 SI 单位是 kg m⁻³。材料的密度是一种特征属性，只要材料均匀，就与样品大小无关。
ρ = m / V
Pressure is the normal force acting per unit area. The SI unit of pressure is the pascal, Pa, where 1 Pa = 1 N m⁻². Pressure is a scalar quantity because it acts in all directions at a point in a fluid.
压强是垂直作用在单位面积上的力。压强的 SI 单位是帕斯卡 Pa，1 Pa = 1 N m⁻²。压强是标量，因为它在流体中某一点向所有方向作用。
P = F / A
2. Pressure in Fluids | 流体中的压强
For a liquid of density ρ at depth h below the surface, the pressure due to the liquid is given by the expression below, where g is the gravitational field strength. The total pressure at that depth is this liquid pressure plus the atmospheric pressure acting on the surface.
对于密度为 ρ 的液体，在液面下深度 h 处，由液体产生的压强由下式给出，其中 g 是重力场强度。该深度处的总压强等于此液体压强加上作用在液面上的大气压强。
P = hρg
Pressure in a fluid is transmitted equally in all directions, which is the principle behind hydraulic systems. A small force applied to a small piston can produce a large force on a larger piston because the pressure is the same throughout the enclosed fluid.
流体中的压强向各个方向等量传递，这是液压系统背后的原理。施加在小活塞上的小力可以在大活塞上产生大力，因为在封闭流体中各处的压强相同。
3. Hooke’s Law | 胡克定律
Hooke’s law states that the extension x of a spring or wire is directly proportional to the applied force F, provided the elastic limit is not exceeded. The constant k is the spring constant or stiffness, measured in N m⁻¹.
胡克定律指出，只要不超过弹性极限，弹簧或金属丝的伸长量 x 与施加的力 F 成正比。常数 k 是弹簧常量或劲度系数，单位为 N m⁻¹。
F = kx
The spring constant k depends on the material, the length, the cross-sectional area and the number of coils. A stiffer spring has a larger k, so a greater force is needed to produce the same extension.
弹簧常量 k 取决于材料、长度、横截面积和圈数。较硬的弹簧具有较大的 k，因此产生相同的伸长量需要更大的力。
A force-extension graph for a spring obeying Hooke’s law is a straight line through the origin. The gradient of this line is equal to the spring constant k.
遵循胡克定律的弹簧的力-伸长量图是一条通过原点的直线。该直线的斜率等于弹簧常量 k。
4. Stress and Strain | 应力与应变
Stress is defined as the force applied per unit cross-sectional area of a material. Its SI unit is Pa or N m⁻². Stress measures how concentrated the load is over the material’s cross-section.
应力定义为单位横截面积上施加的力。其 SI 单位是 Pa 或 N m⁻²。应力衡量载荷在材料横截面上的集中程度。
σ = F / A
Strain is the fractional extension produced in a material. It has no units because it is a ratio of two lengths, but it may be quoted as a decimal or percentage.
应变是材料产生的伸长比例。它没有单位，因为它是两个长度之比，但可以用小数或百分数表示。
ε = ΔL / L₀
Using stress and strain allows the behaviour of different materials or different shapes to be compared fairly. Unlike force and extension, stress and strain are independent of the sample dimensions.
使用应力和应变可以公平地比较不同材料或不同形状的行为。与力和伸长量不同，应力和应变与样品尺寸无关。
5. Young Modulus | 杨氏模量
The Young modulus E of a material is the ratio of tensile stress to tensile strain within the linear elastic region. It has the same unit as stress, Pa, and is a measure of the stiffness of a material itself.
材料的杨氏模量 E 在线性弹性区域内等于拉伸应力与拉伸应变之比。它与应力具有相同的单位 Pa，是材料本身刚度的一种量度。
E = σ / ε = FL₀ / AΔL
A high Young modulus means the material is stiff and shows only a small strain for a large stress. For example, steel has a much larger Young modulus than rubber, so a steel wire stretches far less than a rubber band under the same load.
杨氏模量高表示材料刚硬，在较大应力下只产生较小的应变。例如，钢的杨氏模量远大于橡胶，因此在相同载荷下钢丝的伸长远小于橡皮筋。
To determine the Young modulus experimentally, a long thin wire is loaded, and the extension is measured with a vernier scale or travelling microscope. The original length and cross-sectional area are also measured, then E is calculated from the gradient of a stress-strain graph or directly from the formula.
实验测定杨氏模量时，通常对一根细长金属丝加载，并用游标尺或移测显微镜测量伸长量。同时测量原始长度和横截面积，然后根据应力-应变图的斜率或直接利用公式计算出 E。
6. Elastic and Plastic Deformation | 弹性与塑性形变
An object undergoes elastic deformation when it returns to its original shape and size after the load is removed. In this region, atoms or molecular chains are displaced slightly but return to their original positions when the stress is released.
当物体在卸去载荷后恢复到原来的形状和尺寸时，它发生的是弹性形变。在此区域，原子或分子链发生轻微位移，但应力释放后会回到原始位置。
Plastic deformation occurs when the material is stretched beyond its elastic limit and does not return to its original length after the load is removed. The material has been permanently stretched, and the force-extension graph no longer retraces the loading line.
当材料被拉伸超过弹性极限，卸去载荷后不能恢复到原始长度时，就发生了塑性形变。材料被永久拉长，力-伸长量图不再沿加载线返回。
The elastic limit is the maximum stress or force that can be applied without permanent deformation. Beyond this point, Hooke’s law may no longer hold, and permanent atomic rearrangement begins.
弹性极限是材料不发生永久形变所能承受的最大应力或力。超过该点后，胡克定律可能不再成立，并开始发生永久性的原子重排。
7. Energy Stored in Deformation | 形变中储存的能量
Work is done when a spring or wire is stretched, and this work is stored as elastic potential energy. For a spring obeying Hooke’s law, the energy stored is the area under the force-extension graph.
拉伸弹簧或金属丝时做了功，这些功以弹性势能的形式储存起来。对于遵循胡克定律的弹簧，储存的能量等于力-伸长量图下方的面积。
E = ½Fx = ½kx²
If the material is stretched beyond the elastic limit, not all of the work done is recovered when the load is removed. The area between the loading and unloading curves represents the energy dissipated as heat due to plastic deformation.
如果材料被拉伸超过弹性极限，卸去载荷时并不能全部回收所做的功。加载曲线与卸载曲线之间的面积代表塑性形变过程中以热量形式耗散的能量。
Elastic potential energy per unit volume is a useful quantity for comparing materials. For a linear material within its elastic limit, this energy density is given by the expression below.
单位体积的弹性势能是比较材料时有用的量。对于处于弹性极限内的线性材料，此能量密度由下式给出。
Energy per unit volume = ½σε
8. Stress-Strain Graphs | 应力-应变图
A stress-strain graph shows the behaviour of a material from loading to fracture. For a ductile metal such as copper, the graph initially shows a straight line through the origin, representing the linear elastic region where stress is proportional to strain and the Young modulus is constant.
应力-应变图显示了材料从加载到断裂的行为。对于铜等韧性金属，图线最初是一条通过原点的直线，代表线性弹性区域，在该区域应力与应变成正比，杨氏模量恒定。
Beyond the elastic limit, the graph curves and the material begins to deform plastically. For a ductile metal, a noticeable region of large strain with little increase in stress may appear before the material necks and finally fractures.
超过弹性极限后，图线弯曲，材料开始发生塑性形变。对于韧性金属，在材料颈缩并最终断裂之前，可能出现应变大幅增加而应力几乎不增加的明显区域。
Brittle materials such as glass or cast iron show a steep, nearly linear graph and fracture at small strain without significant plastic deformation. Rubber and many polymers show a very curved graph with a much larger strain before breaking, because their molecular chains can uncoil and straighten.
玻璃或铸铁等脆性材料表现出陡峭且近乎线性的图线，在小应变时即断裂，没有明显的塑性形变。橡胶和许多聚合物则表现出非常弯曲的图线，断裂前应变大得多，因为它们的分子链可以解卷并伸直。
Comparing stress-strain graphs is therefore a direct way to identify whether a material is stiff, ductile, brittle or tough. The gradient gives stiffness, the area gives energy absorbed per unit volume, and the maximum stress gives strength.
因此，比较应力-应变图是直接判断材料是刚硬、韧性、脆性还是强韧的方法。斜率表示刚度，面积表示单位体积吸收的能量，最大应力表示强度。
9. Ultimate Tensile Strength and Breaking Stress | 极限抗拉强度与断裂应力
The ultimate tensile strength, UTS, is the maximum stress a material can withstand while being stretched before fracture. It is read from the highest point of a stress-strain graph and is measured in Pa.
极限抗拉强度 UTS 是材料在拉伸至断裂前能承受的最大应力。它从应力-应变图的最高点读取，单位为 Pa。
Breaking stress is the stress at which the material actually fractures. For a brittle material, the breaking stress is usually close to the ultimate tensile strength, while for a ductile material the breaking stress may be lower than the UTS because necking reduces the effective cross-sectional area.
断裂应力是材料实际发生断裂时的应力。对于脆性材料，断裂应力通常接近极限抗拉强度；而对于韧性材料，由于颈缩使有效横截面积减小，断裂应力可能低于 UTS。
These quantities are important when selecting materials for load-bearing structures. A steel cable for a crane must have a UTS far greater than the working stress to provide a safety margin.
这些量在为承重结构选择材料时非常重要。起重机用钢缆的 UTS 必须远大于工作应力，以提供安全裕度。
10. Material Selection and Practical Examples | 材料选择与实例
Engineers choose materials by matching their mechanical properties to the application. A car body may use steel because of its high stiffness and strength,
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