Edexcel A-Level Physics: Materials | 爱德思 A-Level 物理：材料

📚 Edexcel A-Level Physics: Materials | 爱德思 A-Level 物理：材料

Materials is a core topic in Edexcel A-Level Physics. It links everyday stretching and breaking of objects to quantitative ideas of stress, strain and the Young modulus. You need to know how to interpret force-extension and stress-strain graphs, perform calculations and describe experimental procedures.

材料是爱德思 A-Level 物理的核心章节之一。它把日常生活中物体的拉伸和断裂与应力、应变和杨氏模量等定量概念联系起来。你需要掌握如何解释力-伸长图和应力-应变图、进行计算，并能描述实验步骤。

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1. Hooke’s Law and the Spring Constant | 胡克定律与弹簧劲度系数

Hooke’s law states that the extension x is directly proportional to the applied force F, provided the elastic limit is not exceeded. The relationship is written as F = kx, where k is the spring constant, also called stiffness.

胡克定律指出，在不超过弹性极限的前提下，伸长量 x 与施加的力 F 成正比。该关系写作 F = kx，其中 k 为弹簧劲度系数，也称为刚度。

F = kx

The spring constant k is measured in N m⁻¹. A stiff spring has a large k, meaning a large force is needed to produce a given extension.

弹簧劲度系数 k 的单位是 N m⁻¹。较硬的弹簧 k 值较大，意味着产生相同伸长量需要更大的力。

The elastic limit is the point beyond which the wire or spring no longer returns to its original length when the load is removed.

弹性极限是超过该点后，金属丝或弹簧在撤去负载时不再恢复原长的临界点。

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2. Stress: Force per Unit Area | 应力：单位面积上的力

To compare materials fairly, we use stress rather than force alone. Stress is defined as the force applied per unit cross-sectional area.

为了公平地比较不同材料，我们使用应力而不是单独的力。应力定义为施加在单位横截面积上的力。

σ = F / A

Here σ is the tensile stress, F is the applied force, and A is the original cross-sectional area. The SI unit is the pascal, Pa, where 1 Pa = 1 N m⁻².

其中 σ 为拉伸应力，F 为施加的力，A 为原始横截面积。国际单位是帕斯卡 Pa，1 Pa = 1 N m⁻²。

Because stress is normalised by area, a thick wire and a thin wire made of the same material can be compared directly. A thin wire carrying the same force experiences a larger stress than a thick wire.

由于应力除以了面积，相同材料制成的粗丝和细丝可以直接比较。承载相同力的细丝比粗丝承受更大的应力。

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3. Strain: Extension per Unit Length | 应变：单位长度的伸长量

Strain measures the fractional extension of a material. It is defined as the extension ΔL divided by the original length L.

应变衡量材料伸长量相对于原始长度的比例。它定义为伸长量 ΔL 除以原始长度 L。

ε = ΔL / L

Strain has no units because it is a ratio of two lengths. It can be quoted as a decimal or as a percentage, for example 0.002 or 0.2%.

应变没有单位，因为它是两个长度的比值。它可以用小数或百分数表示，例如 0.002 或 0.2%。

Using strain avoids the problem that a 2 m wire and a 0.5 m wire are expected to extend by different amounts under the same tension. The strain is the same if the material is the same and stress is the same.

使用应变可以避免这样的问题：2 m 长的金属丝和 0.5 m 长的金属丝在相同拉力下伸长量不同。如果材料相同且应力相同，应变就相同。

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4. Young Modulus E | 杨氏模量 E

The Young modulus E is a measure of the stiffness of a material in tension. It is the ratio of tensile stress to tensile strain within the limit of proportionality.

杨氏模量 E 是衡量材料拉伸刚度的量。在比例极限内，它等于拉伸应力与拉伸应变之比。

E = σ / ε = (F / A) ÷ (ΔL / L) = FL / (A ΔL)

The unit of E is the pascal, Pa. Since E is a property of the material, it does not depend on the dimensions of a particular wire or rod.

E 的单位是帕斯卡 Pa。由于 E 是材料本身的属性，它不取决于某根金属丝或杆的尺寸。

A high Young modulus means the material is difficult to stretch. For example, steel has a much larger E than rubber, so steel produces a much smaller strain for the same stress.

杨氏模量大意味着材料难以被拉伸。例如，钢的 E 远大于橡胶，因此在相同应力下，钢产生的应变要小得多。

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5. Stress-Strain Graphs | 应力-应变图

A stress-strain graph is a powerful way to summarise the behaviour of a material. Key points on the curve include the limit of proportionality, elastic limit, yield point, ultimate tensile stress and breaking stress.

应力-应变图是总结材料行为的有效方法。曲线上的关键点包括比例极限、弹性极限、屈服点、极限拉伸应力和断裂应力。

• Limit of proportionality: the point where the graph stops being a straight line.
• Elastic limit: the maximum stress for which the material returns to its original shape.
• Yield point: the stress at which plastic deformation becomes significant.
• Ultimate tensile stress: the maximum stress the material can withstand.
• Breaking stress: the stress at which the material fractures.

• 比例极限：图像不再为直线的点。
• 弹性极限：材料仍能恢复原始形状的最大应力。
• 屈服点：塑性形变开始明显时的应力。
• 极限拉伸应力：材料能承受的最大应力。
• 断裂应力：材料断裂时的应力。

For a ductile material such as copper or mild steel, the graph shows an initial straight line, then a curved region, a yield point, a region of plastic flow, and finally fracture.

对于铜或低碳钢等延性材料，图像先是一段直线，然后是弯曲区域、屈服点、塑性流动区域，最后发生断裂。

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6. Elastic and Plastic Deformation | 弹性形变与塑性形变

Elastic deformation is reversible. When the stress is removed, the material returns to its original length and the work done is released as elastic strain energy.

弹性形变是可逆的。撤去应力后，材料恢复原始长度，所做的功以弹性应变能的形式释放。

Plastic deformation is permanent. Beyond the elastic limit, atoms in the material slip past one another and do not return to their original positions. The material remains stretched after unloading.

塑性形变是永久的。超过弹性极限后，材料中的原子相互滑移，不再回到原来的位置。卸载后材料仍保持伸长状态。

On a force-extension graph, elastic deformation is represented by the straight line through the origin. Plastic deformation is shown by the graph deviating from this straight line and by permanent extension after the force is removed.

在力-伸长图上，弹性形变表现为过原点的直线。塑性形变则表现为图像偏离这条直线，并且在撤去力后仍然存在永久伸长。

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7. Elastic Strain Energy | 弹性应变能

The work done in stretching a spring or wire is stored as elastic strain energy, provided the deformation is elastic. For a force-extension graph, the energy is equal to the area under the curve.

在弹性形变范围内，拉伸弹簧或金属丝所做的功以弹性应变能的形式储存

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