📚 IB OCR Physics: Material Physics Key Points Review | IB OCR 物理：材料物理 考点精讲
Material physics is a fascinating and highly practical topic in both IB and OCR specifications. It explores how materials respond to forces, temperature changes, and electric fields, and provides the foundation for understanding everything from bridge design to semiconductor technology. Mastering the key definitions, diagrams, and calculations is essential for exam success.
材料物理是 IB 和 OCR 物理课程中既迷人又高度实用的主题。它探索材料如何响应力、温度变化和电场，并为从桥梁设计到半导体技术的一切提供基础。掌握关键定义、图表和计算对于考试成功至关重要。
1. Introduction to Material Physics | 材料物理导论
Material physics investigates the macroscopic and microscopic properties of solids. In exams, you will be asked to classify materials, interpret stress-strain graphs, calculate elastic moduli, and explain thermal and electrical behaviour.
材料物理研究固体的宏观和微观性质。在考试中，你会被要求对材料进行分类、解释应力-应变图、计算弹性模量，并解释热学和电学行为。
It bridges mechanics, thermodynamics, and electromagnetism. Whether you are dealing with a steel cable under tension or a thermistor in a circuit, material physics provides the quantitative models.
它连接了力学、热力学和电磁学。无论你处理的是受拉的钢缆还是电路中的热敏电阻，材料物理都提供了定量模型。
2. Stress and Strain | 应力与应变
Stress (σ) is defined as the force applied per unit cross-sectional area. It is measured in pascals (Pa) or N m⁻². The formula is σ = F / A, where F is the force normal to the area A.
应力 (σ) 定义为单位横截面积上所施加的力。它以帕斯卡 (Pa) 或 N m⁻² 为单位。公式为 σ = F / A，其中 F 是垂直于面积 A 的力。
Tensile stress stretches the material, while compressive stress squeezes it. Shear stress acts parallel to the surface. For most exam questions, we focus on tensile and compressive stress.
拉伸应力会拉伸材料，而压缩应力会挤压材料。剪切应力平行于表面作用。大多数考题中，我们重点关注拉伸和压缩应力。
Strain (ε) is the extension per unit original length, a dimensionless ratio. ε = ΔL / L₀, where ΔL is the change in length and L₀ is the original length. It can also be expressed as a percentage.
应变 (ε) 是每单位原始长度的伸长量，是一个无量纲比值。ε = ΔL / L₀，其中 ΔL 是长度变化量，L₀ 是原始长度。它也可以用百分比表示。
Stress causes strain; the relationship between them depends on the material and the loading conditions. Understanding this link is the heart of elasticity.
应力导致应变；它们之间的关系取决于材料和加载条件。理解这种联系是弹性力学的核心。
3. Young’s Modulus | 杨氏模量
Young’s modulus (E) quantifies a material’s stiffness in the linear elastic region. It is defined as the ratio of tensile stress to tensile strain: E = σ / ε. Since strain has no units, E has the same unit as stress, the pascal.
杨氏模量 (E) 量化了材料在线性弹性区域的刚度。它定义为拉伸应力与拉伸应变之比：E = σ / ε。由于应变没有单位，E 的单位与应力相同，为帕斯卡。
A high Young’s modulus means the material is stiff and resists deformation. For example, steel (E ≈ 200 GPa) is much stiffer than rubber (E ≈ 0.01 GPa).
高杨氏模量意味着材料坚硬、不易变形。例如，钢 (E ≈ 200 GPa) 比橡胶 (E ≈ 0.01 GPa) 坚硬得多。
Young’s modulus is determined experimentally by measuring the extension of a wire under known loads. The gradient of a stress-strain graph in the linear portion yields E.
杨氏模量可通过测量已知载荷下金属丝的伸长量的实验来确定。应力-应变图中线性部分的斜率即为 E。
| Material | Young’s Modulus (GPa) | 材料 |
| Steel | 200 | 钢 |
| Aluminium | 70 | 铝 |
| Copper | 130 | 铜 |
| Glass | 70 | 玻璃 |
| Rubber | 0.01–0.1 | 橡胶 |
4. Stress-Strain Curves | 应力-应变曲线
A stress-strain curve is the most powerful graph in material physics. It typically starts with a straight line through the origin, representing Hooke’s law: stress is proportional to strain. The slope of this line is Young’s modulus.
应力-应变曲线是材料物理中最强大的图表。它通常从一条通过原点的直线开始，代表胡克定律：应力与应变成正比。这条线的斜率就是杨氏模量。
After the proportional limit, the graph curves. For a ductile material like mild steel, there is an elastic limit, a yield point, and a region of plastic flow before necking and fracture.
在比例极限之后，曲线弯曲。对于像软钢这样的延性材料，在颈缩和断裂之前存在弹性极限、屈服点和塑性流动区域。
Key points to label on a stress-strain curve include: proportional limit, elastic limit, yield point, ultimate tensile strength (UTS), and fracture point.
应力-应变曲线上需要标注的关键点包括：比例极限、弹性极限、屈服点、极限抗拉强度 (UTS) 和断裂点。
The area under the curve represents the work done per unit volume to deform or break the material, which is related to the material’s toughness.
曲线下的面积代表使材料变形或断裂所做的单位体积功，这与材料的韧性相关。
5. Elastic and Plastic Deformation | 弹性形变与塑性形变
Elastic deformation is reversible: when the load is removed, the material returns to its original shape. Hooke’s law applies only in the elastic region, where the extension is directly proportional to the force.
弹性形变是可逆的：当载荷移除时，材料恢复其原始形状。胡克定律仅适用于弹性区域，在此区域伸长量与力成正比。
The elastic limit is the maximum stress a material can withstand without permanent deformation. Beyond this point, plastic deformation begins.
弹性极限是材料在不发生永久形变的情况下所能承受的最大应力。超过此点，塑性形变开始。
Plastic deformation is irreversible. Atoms slip past each other and do not return to their original positions. This property is used in metal forming and forging.
塑性形变是不可逆的。原子相互滑过并且不会回到原来的位置。这一特性被用于金属成型和锻造。
On the stress-strain curve, unloading within the plastic region leaves a permanent strain. The slope of the unloading line is still equal to Young’s modulus.
在应力-应变曲线上，在塑性区域内卸载会留下永久应变。卸载线的斜率仍等于杨氏模量。
6. Brittle and Ductile Materials | 脆性与延性材料
Ductile materials, like copper and mild steel, exhibit significant plastic deformation before fracture. Their stress-strain curves show a large area under the curve, indicating high toughness.
延性材料，如铜和软钢，在断裂前表现出显著的塑性形变。它们的应力-应变曲线显示出较大的曲线下面积，表明高韧性。
Brittle materials, such as glass, cast iron, and most ceramics, fracture with little or no plastic deformation. Their stress-strain curve is essentially a straight line ending suddenly at fracture.
脆性材料，如玻璃、铸铁和大多数陶瓷，在几乎没有或完全没有塑性形变的情况下断裂。它们的应力-应变曲线基本上是一条直线，在断裂时突然结束。
Both material types have the same Young’s modulus interpretation for the initial linear part, but their behaviour under excessive load is completely different. Engineers must choose accordingly.
两种材料类型在初始线性部分的杨氏模量解释是相同的，但它们在过度载荷下的行为完全不同。工程师必须据此进行选择。
A common exam question is to compare the stress-strain curves of a brittle and a ductile material and identify each from the graph’s shape.
常见的考题是比较脆性材料和延性材料的应力-应变曲线，并根据曲线形状识别每种材料。
7. Energy Stored in Deformation | 形变储能
When a material is deformed elastically, it stores elastic potential energy. The elastic strain energy per unit volume, often called strain energy density, is given by the area under the stress-strain curve up to the elastic limit.
当材料发生弹性形变时，它会储存弹性势能。单位体积的弹性应变能，常称为应变能密度，由应力-应变曲线在弹性极限以下部分的面积给出。
For a material obeying Hooke’s law, this area is a triangle. Therefore, strain energy density = ½ × stress × strain = ½ σ ε. Substituting σ = E ε gives ½ E ε².
对于遵循胡克定律的材料，这个区域是一个三角形。因此，应变能密度 = ½ × 应力 × 应变 = ½ σ ε。代入 σ = E ε 得到 ½ E ε²。
This concept is crucial when designing springs, shock absorbers, and safety components. The total energy stored can be found by multiplying the energy density by the volume of the material.
该概念在设计弹簧、减震器和安全部件时至关重要。总储存能量可通过能量密度乘以材料体积求得。
You should be able to derive the formula and calculate energy stored using the force–extension graph or the stress–strain graph.
你应该能够推导公式，并利用力–伸长量图或应力–应变图计算储存的能量。
8. Other Mechanical Properties | 其他力学性质
Beyond stiffness and strength, materials are described by hardness, toughness, and malleability. Hardness measures resistance to surface indentation or scratching. Toughness is the ability to absorb energy before fracturing – the total area under the stress-strain curve.
除了刚度和强度之外，材料还可以用硬度、韧性和延展性来描述。硬度衡量抵抗表面压痕或划擦的能力。韧性是在断裂前吸收能量的能力——即应力-应变曲线下的总面积。
Malleability refers to the ability to be hammered or rolled into thin sheets, a subset of plastic behaviour typical of metals. Ductility is specifically the ability to be drawn into a wire.
延展性是指被锤击或轧制成薄板的能力，这是金属典型塑性行为的一部分。韧性特指被拉制成丝的能力。
Understanding these terms helps in selecting materials for specific applications: hard materials for cutting tools, tough materials for safety helmets, ductile materials for wiring.
理解这些术语有助于为特定应用选择材料：切削工具用硬材料，安全帽用韧性材料，电线用延性材料。
9. Thermal Properties | 热学性质
Material physics also includes thermal properties such as specific heat capacity and thermal conductivity. Specific heat capacity (c) is the energy required to raise the temperature of 1 kg of the material by 1 K, measured in J kg⁻¹ K⁻¹.
材料物理还包括热学性质，如比热容和热导率。比热容 (c) 是使 1 kg 材料温度升高 1 K 所需的能量，单位为 J kg⁻¹ K⁻¹。
The equation Q = m c Δθ is used to calculate energy transfer during heating or cooling. Materials with high specific heat capacity, like water, store large amounts of thermal energy.
方程 Q = m c Δθ 用于计算加热或冷却过程中的能量转移。具有高比热容的材料，如水，能储存大量热能。
Thermal conductivity (κ) describes how quickly heat flows through a material. Good conductors like copper have high κ; insulators like polystyrene have low κ. The rate of heat transfer is given by ΔQ/Δt = κ A ΔT / d.
热导率 (κ) 描述热量通过材料的快慢程度。良导热体如铜具有高 κ 值；绝缘体如聚苯乙烯具有低 κ 值。热传递速率由 ΔQ/Δt = κ A ΔT / d 给出。
In exams, you may be asked to interpret an experiment on thermal conduction or to compare different materials using a cooling curve.
在考试中，你可能会被要求解释热传导实验，或利用冷却曲线比较不同材料。
10. Electrical Properties | 电学性质
Resistivity (ρ) is an intrinsic property that determines how strongly a material opposes electric current. It is related to resistance by R = ρ L / A, where L is length and A is cross-sectional area.
电阻率 (ρ) 是一种固有属性，决定材料阻碍电流的强弱。它与电阻的关系为 R = ρ L / A，其中 L 为长度，A 为横截面积。
Conductivity (σ) is the reciprocal of resistivity: σ = 1 / ρ. Metals have high conductivity and low resistivity; insulators have very high resistivity.
电导率 (σ) 是电阻率的倒数：σ = 1 / ρ。金属具有高电导率和低电阻率；绝缘体具有非常高的电阻率。
Semiconductors lie between conductors and insulators and their resistivity changes dramatically with temperature and impurities. This behaviour is exploited in thermistors and LDRs.
半导体介于导体和绝缘体之间，其电阻率随温度和杂质显著变化。这一行为被用于热敏电阻和光敏电阻中。
Understanding resistivity is vital for designing electrical components, choosing wiring materials, and analysing the effect of dimensions on resistance.
理解电阻率对于设计电子元件、选择电线材料以及分析尺寸对电阻的影响至关重要。
11. Applications & Safety Factors | 应用与安全系数
In real-world engineering, materials are not used right up to their yield stress. A safety factor is introduced: working stress = yield stress / factor of safety. This ensures the structure remains well within the elastic limit.
在实际工程中，材料的使用并不会达到其屈服应力。会引入一个安全系数：工作应力 = 屈服应力 / 安全系数。这确保结构远处于弹性极限之内。
Examples include crane cables, suspension bridge wires, and aircraft components. The safety factor accounts for uncertainties in loading, material defects, and environmental effects.
例子包括起重机缆绳、悬索桥钢丝和飞机部件。安全系数考虑了载荷不确定性、材料缺陷和环境影响。
When selecting materials, engineers also consider density for lightweight structures, corrosion resistance, cost, and sustainability. Composite materials are often tailored to combine properties.
在选择材料时，工程师还会考虑密度以制作轻质结构、耐腐蚀性、成本和可持续性。复合材料通常经过定制以结合多种性能。
You should be able to justify material choices using quantitative data like Young’s modulus, UTS, density, and cost per kilogram.
你应该能够使用杨氏模量、极限抗拉强度、密度和每公斤成本等定量数据来证明材料选择的合理性。
12. Summary of Key Formulas | 关键公式总结
Here is a concise list of the most important formulas you need to memorise for the Material Physics topic.
以下是你需要熟记的材料物理主题最重要公式的简明列表。
σ = F / A
ε = ΔL / L₀
E = σ / ε
Strain energy density = ½ σ ε = ½ E ε²
R = ρ L / A
Q = m c Δθ
ΔQ/Δt = κ A ΔT / d
Be careful with units: length in metres, area in m², force in newtons, stress in Pa, and energy in joules. With these equations, you can solve the vast majority of quantitative problems.
注意单位：长度用米，面积用平方米，力用牛顿，应力用帕斯卡，能量用焦耳。有了这些方程，你就能解决绝大多数定量问题。
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