Name: brittle material failure under tension
Uploaded: 2025-05-22T09:06:17.000Z
Duration: 1 min 24 s
Channel: JoVE

脆性材料在拉伸应力作用下，断裂前不会显著伸长，这意味着其极限强度与断裂强度相同。与延性材料相比，脆性材料在断裂时的应变较小。
它沿垂直于载荷的表面发生，表明失效主要由正应力引起。
脆性材料在应力作用下不会发生明显的颈缩现象。
大多数脆性材料在压缩状态下的极限强度高于拉伸状态，这主要是由于微观缺陷（如裂纹或孔洞）在拉伸状态下会削弱材料的性能。
考虑混凝土板的应力-应变图，这是脆性材料的一个示例。
在受力状态下，材料表现出线性弹性范围，直至屈服点，随后应变的增长速度超过应力，直至试件断裂。
在受压情况下，混凝土表现出更大的线弹性范围，当应力达到峰值时并不会立即发生断裂。相反，应力开始下降，而应变继续增加，直至最终发生断裂。
弹性模量由线性区域的斜率表示，对于大多数脆性材料而言，其在压缩和拉伸状态下的数值相等。

应力应变图 - 脆性材料

Stress-Strain Diagram - Brittle Materials

脆性材料，其中包括玻璃、铸铁和石材，这些材料能够表现出其独特的特性。它们在发生断裂时其伸长率没有发生显著的变化，这表明了它们的断裂强度和极限强度是相当的。此类材料在断裂点处还表现出了较低的应变水平。脆性材料的失效主要是由正应力所引起的，沿着垂直于其施加载荷的表面所产生的破裂就证明了这一点。这些材料没有表现出明显的颈缩。颈缩是指在应力作用下，其横截面积的局部逐渐减小。在大多数脆性材料中，一个有趣的方面是它们在压缩时的极限强度高于在拉伸时的极限强度，这主要是由于裂纹或空洞等微观缺陷会在拉伸应力的状态下来削弱材料的强度，但对其压缩强度的影响却很小。

混凝土是一种常见的脆性材料，在拉伸和压缩下的表现是不同的。拉伸下的应力-应变图显示了直至屈服点的线性弹性范围，随后应变迅速增加直至其发生破裂。相比之下，混凝土在压缩下能够表现出较大的线性弹性范围，即使在峰值的应力下也不会发生破裂。相反的，应力随着应变的增加而逐渐减小，直至其发生破裂。重要的是，对于大多数脆性材料，弹性模量（在应力-应变曲线中通过线性部分的斜率进行表示）在拉伸和压缩方面是保持一致的。

脆性材料（如玻璃、铸铁和石材）具有独特的特性，其在断裂前不会发生明显的伸长变化……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Stress and Strain - Axial Loading

应力与应变 - 轴向加载

KEY TERMS AND CONCEPTS

关键术语与概念

brittle material failure under tension

Brittle materials such as glass, cast iron, and stone fail with very little change in elongation. Their breaking strength and ultimate strength are nearly the same, and the strain at rupture is low. In these materials, failure is usually driven by normal stress, so the break surface is typically perpendicular to the applied load.

Brittle materials also show little or no necking. Necking is the local narrowing of a material’s cross section under stress. Another important feature is that many brittle materials are stronger in compression than in tension. Small cracks or cavities can weaken them in tension, but these defects have much less effect when the material is compressed.

Concrete is a common example of a brittle material. Under tension, its stress-strain curve has a linear elastic region up to the yield point, followed by a rapid rise in strain until rupture. Under compression, concrete has a longer linear elastic range, and rupture does not happen at the peak stress. Instead, stress drops as strain keeps increasing until failure.

For most brittle materials, the modulus of elasticity is the same in tension and compression. The modulus of elasticity is the slope of the linear part of the stress-strain curve. This slope shows how stiff the material is in both loading modes.

Brittle Material Failure Under Tension

normal strain under axial loading

Axial Stress and Strain in a Rod

Axial stress and strain in a rod describe how a material changes length when a force is applied along its axis. The force may stretch the rod or compress it. In mechanics of materials, this deformation is called normal strain. Normal strain is found by dividing the change in length by the original length. This gives a unitless ratio that shows how much the material deforms under load. A load-deformation diagram can show elongation, but it cannot predict how another rod will deform. When a...

stress-strain diagram

Tensile Test Data and Material Behavior

A stress-strain diagram shows how a material responds during a tensile test. It records the mechanical behavior of a cylindrical specimen as it is pulled by an increasing centric load. The specimen is carefully prepared before testing. Two gauge marks are inscribed on the central part of the specimen. The distance between these marks is the gauge length. As the load increases, the gauge length also increases. This change in length is called elongation. The elongation is measured for each load...

stress-strain diagram - ductile materials

Ductile Material Stress-Strain Stages

Ductile materials such as structural steel and aluminium show a multi-stage stress-strain response. When a specimen is loaded, its length first increases linearly at a slow rate. This produces a steep straight line on the stress-strain diagram. That initial part shows elastic deformation, which means the material returns to its original shape after unloading. When the stress reaches a critical value, plastic deformation begins. In this stage, the material changes shape a lot while the applied...

stress-strain diagram - brittle materials

Brittle materials such as glass, cast iron, and stone fail with very little change in elongation. Their breaking strength and ultimate strength are nearly the same, and the strain at rupture is low. In these materials, failure is usually driven by normal stress, so the break surface is typically perpendicular to the applied load. Brittle materials also show little or no necking. Necking is the local narrowing of a material’s cross section under stress. Another important feature is that many...

true stress and true strain

Stress-Strain Curves Beyond Yield

Stress-strain curves beyond yield show how ductile materials behave after they start to deform permanently. Engineering stress is found by dividing the load by the original, undeformed cross-sectional area. It is a useful approximation, but it can lose accuracy when strain becomes large. True stress gives a more exact picture of the same specimen under load. It is calculated by dividing the applied load by the instantaneous cross-sectional area during deformation. As the specimen stretches,...

hooke's law

Stress-Strain Limits in Materials

Stress-strain limits in materials explain how solids respond when force is applied. Stress is the applied force per area, and strain is the change in shape or size that results. In the elastic range, strain stays directly proportional to stress. The constant that connects them is called the modulus of elasticity, or Young's modulus. This linear behavior continues only up to the proportional limit. After that point, the stress-strain relationship becomes nonlinear. For ductile materials, this...

plastic behavior

Yielding and Strain-Hardening in Metals

Yielding and strain-hardening describe how a material changes when stress goes beyond the elastic range. Under elastic behavior, the stress disappears when the load is removed, and the material returns to its original shape. Once stress exceeds the yield point, yielding begins and permanent deformation, or plastic set, starts. The switch from elastic to plastic behavior depends on the peak stress and on how long the load stays in place before removal. A specimen that is loaded, unloaded, and...

fatigue

Fatigue Failure in Repeated Loading

Fatigue failure happens when materials rupture after repeated or fluctuating loads. The stress can be far below the material’s static breaking strength. Even ductile materials can fail in a brittle way under fatigue. This behavior matters in machines and structural parts that face repetitive or changing loads. One example is an unbalanced pump impeller that creates vibrations. Another is a thin steel rod or wire bent back and forth in the same spot until it breaks. The number of loading...

deformation of member under multiple loadings

deformation-of-member-under-multiple-loadings

Calculating Rod Stretch from Mixed Loads

Calculating rod stretch from mixed loads starts with breaking the rod into parts. This step is needed when the rod is made of different materials or has changes in cross-section. Each part has its own internal force, cross-sectional area, length, and modulus of elasticity. These values are used to find the deformation of the full rod. For a member with a variable cross-section, the strain is not constant. Instead, it changes with position along the rod. The deformation of a small element is...

statically indeterminate problem solving

Axial Rod Reactions with Redundant Support

Axial rod reactions with a redundant support are found by combining equilibrium with deformation. The structure here uses two cylindrical rods, one steel and one brass, joined at point B and held by rigid supports at points A and C. The goal is to determine the reactions at A and C and the deflection at B. This setup is statically indeterminate because the supports create more unknown reactions than the equilibrium equations can solve. Statics alone is not enough to find every internal force...

thermal strain

Thermal Expansion of a Free Rod

Thermal strain describes how a structure changes length when temperature changes. It is important in real-world design because structures do not always stay at one temperature. Temperature shifts can affect how they behave and how long they last. A simple example is a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. When the rod is heated, it elongates. The amount of elongation depends on the temperature change and the rod’s original length. This...

temperature dependent deformation

Thermal Stress in a Composite Rod

A steel-and-brass composite rod can build stress when temperature changes while both ends are restrained. The rod is nonhomogeneous, so its two sections respond differently. To find the compressive load, the problem is treated as statically indeterminate, which means the force cannot be found from equilibrium alone. The analysis begins by disconnecting one support so the rod can expand or contract freely under the temperature change. An unknown force is then applied at the free end. That force...

poisson's ratio

Material Strain Under Axial Loading

Poisson's ratio describes how a material changes shape when it is pulled or compressed along one direction. It links the strain in the direction of the force to the strain that happens sideways. When a slender bar is loaded axially, it stretches along the load and contracts laterally. Poisson's ratio is defined as the negative ratio of lateral contraction to axial elongation. The negative sign is used because the two strains usually have opposite signs. This keeps the ratio positive and makes...

generalized hooke's law

Multiaxial Stress and Strain Relation

Multiaxial stress and strain describe how an isotropic material responds when forces act along more than one direction. A cube-shaped sample under normal stresses on the three coordinate axes can change into a rectangular parallelepiped. Even after this deformation, the sides remain equal, and normal strain appears along the coordinate axes. The strain components are found from the stress components by studying each stress effect one at a time. The separate effects are then combined using the...

bulk modulus

Volume Change Under Hydrostatic Pressure

Bulk modulus describes how much a material resists a uniform squeeze. It links a change in pressure to the relative change in volume. For high school students, it is easiest to think of it as a measure of how hard it is to compress a material evenly from all sides. The idea becomes clearer when an isotropic material element is treated as a cube with unit volume. When normal stresses act on the cube, it deforms into a rectangular parallelepiped and its volume changes. The difference between the...

shearing strain

Shear Modulus and Angular Change

Shearing strain is the angular change that happens in a cubic element when it is loaded by shearing stress. Under this stress, the cube can change into an oblique parallelepiped without creating normal strains. If the cube is acted on only by shearing stress, its shape can shift strongly into a rhomboid. The amount of shearing strain is considered positive when the angle between the axes becomes smaller. This change in angle shows the direct effect of shear on the material. The deformation can...

relation between poisson's ratio, modulus of elasticity and modulus of rigidity

relation-between-poisson-s-ratio-modulus-elasticity-modulus

Axial Load Effects on Shear Strain

Axial load effects on shear strain are shown by how a slender bar deforms under tension or compression. When the bar is loaded along its axis, it changes in both the axial direction and the transverse direction. A small cubic element inside the bar can turn into a rectangular parallelepiped or a rhombus, depending on how it is oriented. This change in shape creates shearing strain, which is the distortion caused when angles in a material change. Axial loading produces both normal strain and...

saint-venant's principle

Load Effects Away from the Ends

Saint-Venant's principle describes how stress changes in a structural member when a load is applied. It shows that the exact way a load is placed matters most near the point of application. Farther away from that point, the stress pattern becomes much less dependent on how the load was applied. A simple example uses a member with plates on both ends. When the loads are applied at the center of the plates, the plates move toward each other without rotating. The member shortens in length and...

stress concentrations

Stress at Holes and Fillets

Stress can become much higher near holes and abrupt changes in shape within a structural member. These discontinuities create localized stress that may exceed the average stress in the part. For flat bars, the stress distribution can be measured experimentally with a photoelastic method. This approach is used for bars with a circular hole or with changing widths joined by fillets. The results depend on geometric ratios, such as the hole radius to the smaller width for a circular hole. For...

residual stresses

Residual Stresses After Welding and Cooling

Residual stresses are stresses that remain in a structure after the original load or heat source is removed. They often form when different parts of a material undergo uneven plastic deformation, which means permanent shape change. A rod stretched past its yield point is one example. It will not return to its original length, and some stress stays inside even after the load is gone. These stresses can also develop during welding. Heat changes the material during the weld and can cause plastic...

key terms and concepts

Explore how brittle materials like glass, cast iron, stone, and concrete behave under tension and compression, including rupture, necking, and elasticity.

Brittle Material Failure Under Tension | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Brittle Material Failure Under Tension

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