Name: how strain gauges measure deformation
Uploaded: 2024-05-23T12:59:55.000Z
Duration: 1 min 27 s
Channel: JoVE

La déformation mesure la déformation ou le déplacement d’un matériau. La déformation normale est calculée en comparant les longueurs avant et après l’application d’une charge.
Une méthode plus précise pour mesurer les déformations normales consiste à utiliser des jauges de contrainte électriques constituées d’un fil mince cimenté à deux feuilles de papier.
Lorsque le matériau s'allonge, la longueur du fil augmente et son diamètre diminue, ce qui entraîne une augmentation de la résistance électrique. La mesure de ce changement de courant détermine la déformation précise.
Les composantes de déformation en un point donné peuvent être déterminées en mesurant la déformation normale sur les axes tracés à travers ce point. Une troisième mesure le long de la médiatrice de l’angle formé par les axes détermine la déformation de cisaillement.
Les mesures de déformation sont effectuées le long de trois lignes tracées à travers un point, formant des angles respectifs avec l’axe horizontal.
Les mesures de déformation correspondantes sont substituées dans l’équation de déformation normale pour former trois équations de mesure de déformation.
La disposition des jauges de contrainte utilisée pour mesurer les déformations est appelée rosette de contrainte, généralement dans des configurations à 45° ou 60°.

mesures de déformation

Measurements of Strain

La déformation quantifie la déformation d'un matériau soumis à une force, généralement mesurée comme une déformation normale, qui représente le changement de longueur par rapport à la longueur d'origine. Des jauges de contrainte électriques sont utilisées pour une précision accrue. Ces dispositifs sont constitués d'un fil conducteur monté sur un support papier qui adhère à la surface du matériau. Ces jauges fonctionnent par effet piézorésistif, où la résistance électrique du fil change en réponse à une déformation mécanique. La jauge de contrainte s'ajuste à mesure que le matériau s'allonge ou se comprime, modifiant la résistance du fil proportionnellement à la contrainte subie.

Pour comprendre globalement la déformation en un point matériel spécifique, considérez les déformations normales et de cisaillement, qui tiennent compte des changements de forme à volume constant. Cette analyse nécessite plusieurs jauges de contrainte disposées selon différentes orientations. Les mesures de déformation sont généralement effectuées le long de lignes définies à des angles définis par rapport à un axe horizontal, ces lectures étant utilisées pour calculer les composantes globales de la déformation.

Une rosette de jauge de contrainte, qui positionne plusieurs jauges dans des configurations telles que 0°, 45° et 90°, ou 0°, 60° et 120°, permet des mesures de déformation multidirectionnelles simultanées. Un tel agencement est essentiel pour l'analyse détaillée des déformations en un point et est largement utilisé dans l'analyse structurelle, les tests de matériaux et la validation de pièces. Ces méthodologies sont essentielles aux ingénieurs pour évaluer le comportement des matériaux, améliorant ainsi la conception et la sécurité des structures techniques.

Mesures de déformation

La déformation mesure la déformation ou le déplacement d’un matériau. La déformation normale est calculée en comparant les longueurs avant et après l’application d’une charge.
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Education

Enseignement

JoVE Core

Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Transformations of Stress and Strain

Transformations des contraintes et des déformations

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

how strain gauges measure deformation

Strain describes how a material deforms when a force is applied. Normal strain compares the change in length with the original length. Engineers use this measure to track stretching or compression in materials.

For higher accuracy, they often use electrical strain gauges. A strain gauge has a conductive wire on a paper backing that sticks to the surface of the material. It works through the piezoresistive effect, which means the wire’s electrical resistance changes when the material is bent, stretched, or compressed.

As the material elongates or shortens, the strain gauge changes with it. That change alters the wire’s resistance in proportion to the strain. To understand strain at one point more fully, engineers also consider normal strain and shearing strain, which describe shape change at constant volume.

This more detailed analysis needs several strain gauges placed at different angles. Strain is often measured along lines set at defined angles to a horizontal axis. The readings are then used to calculate the overall strain components.

A strain gauge rosette makes this process easier by arranging multiple gauges together. Common layouts include 0°, 45°, and 90°, or 0°, 60°, and 120°. These setups allow simultaneous measurements in multiple directions and are widely used in structural analysis, materials testing, and part validation. Engineers use the results to study material behavior and improve the design and safety of engineered structures.

How Strain Gauges Measure Deformation

transformation of plane stress

Plane Stress Changes with Rotation

Plane stress changes with rotation in a material element. The analysis looks at a prismatic element inside a cube under plane stress. As the element turns, the normal stress and shearing stress on its faces change in both size and direction. These changes are described with trigonometric functions of the rotation angle. The forces on the rotated faces are compared with the forces on the original faces that are perpendicular to each principal axis. The equilibrium equations use only the forces...

principal stresses

Stress Circle for Principal and Shear Stress

The stress circle shows how normal stress and shearing stress change with angle on a transformed plane. Its center, C, lies on the vertical axis and represents the average normal stress. The radius shows the amount of stress variation as the plane rotates. Points A and B, where the circle crosses the horizontal axis, mark the maximum and minimum normal stresses. At these points, shearing stress is zero. These points define the principal stress planes, where only normal stress, called principal...

principal stresses: problem solving

Finding Principal Planes and Stress Limits

Principal planes and principal stresses are found by analyzing two planes that meet at right angles under shearing, tensile, and compressive stresses. The goal is to use the given stress values to describe how the material is loaded and to locate the planes where the stress state changes. To find the principal planes, use the formula that relates the plane angle to twice the shearing stress divided by the difference between tensile and compressive stresses. After substituting the known stress...

mohr&#39;s circle for plane stress

Reading Stress Components with Mohr's Circle

Mohr's circle is a graphical way to read the stress state at a point in a material under plane stress. It turns normal stress and shearing stress into a two-dimensional picture. This makes stress transformation easier to analyze. The method uses Cartesian coordinates. The horizontal axis shows normal stress, written as σ, and the vertical axis shows shearing stress, written as τ. Two points, A and B, are plotted from the stresses on the element. Point A is at (σx, -τxy), and point B is at (σx,...

general state of stress

Stress Tensor and Principal Stresses

The stress tensor describes the internal forces inside a material. It is used when a material is under external force or deformation. At a point such as O, the tensor can show the stress components on any plane through that point. A tetrahedral element helps show how these forces act. One face, XYZ, is perpendicular to the line OA. The other faces line up with the coordinate axes, and point O is the origin. The stress on the tetrahedron is split into normal and shear components on each face. <br...

yield criteria for ductile materials under plane stress

yield-criteria-for-ductile-materials-under-plane-stress

Tresca and Von Mises Yield Criteria

Ductile materials can yield when they are loaded beyond a safe stress level. Engineers use yield criteria to check whether structural elements and machine parts can handle the expected load without permanent deformation. The yield point is first found with a tensile test, which measures how the material responds to uniaxial stress. A tensile test is not enough when a part faces biaxial or plane stress conditions. In those cases, more advanced criteria are needed to predict failure. One common...

transformation of plane strain

Plane Strain Under Rotated Axes

Plane strain changes when the coordinate axes are rotated. This matters for long bars and similar elongated structures that are loaded uniformly on their sides. In these members, one dimension is much larger than the others, so deformation is mainly studied in a single plane. At a point such as O, the key strain components lie along the x and y axes. The strain along the z-axis is negligible in plane strain. Together, the x and y strain components describe the deformation state in the xy-plane.

mohr&#39;s circle for plane strain

Principal and Shear Strains on Mohr’s Circle

Mohr’s circle for plane strain shows how normal strain and shear strain change on a graph. The horizontal axis is normal strain, written as ε, and the vertical axis is shear strain, written as γ. It uses two plotted points, X and Y, to represent the strain state. Point X has coordinates (εx, -γXY), and point Y has coordinates (εY, γXY). The center of the circle, O, gives the average normal strain. The radius comes from the relationship between normal strain and shear strain, so the circle...

three-dimensional analysis of strain

Principal Strain Directions in 3D

Three-dimensional strain analysis shows how a material changes shape when it is loaded. It is especially useful for elastic, homogeneous materials. A small cubic element inside the material can expand or contract along principal stress axes. That change turns the cube into a rectangular parallelepiped, which makes the deformation easier to picture. The principal stress axes are orthogonal, or at right angles to each other. Along these directions, the stress does not create shear inside the...

measurements of strain

Strain describes how a material deforms when a force is applied. Normal strain compares the change in length with the original length. Engineers use this measure to track stretching or compression in materials. For higher accuracy, they often use electrical strain gauges. A strain gauge has a conductive wire on a paper backing that sticks to the surface of the material. It works through the piezoresistive effect, which means the wire’s electrical resistance changes when the material is bent,...

key terms and concepts

Learn how strain gauges measure deformation, from normal and shearing strain to rosette layouts used in structural analysis and materials testing.

How Strain Gauges Measure Deformation | JoVE K12

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mechanical engineering

How Strain Gauges Measure Deformation

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