Experimental Mechanics of Solids and Structures

Jérôme Molimard

• Publisher: Wiley-ISTE
• Year: 2016
• Print ISBN: 9781848219960
• eBook ISBN: 9781119292326
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

From the characterization of materials to accelerated life testing, experimentation with solids and structures is present in all stages of the design of mechanical devices. Sometimes only an experimental model can bring the necessary elements for understanding, the physics under study just being too complex for an efficient numerical model.

This book presents the classical tools in the experimental approach to mechanical engineering, as well as the methods that have revolutionized the field over the past 20 years: photomechanics, signal processing, statistical data analysis, design of experiments, uncertainty analysis, etc.

Experimental Mechanics of Solids and Structures also replaces mechanical testing in a larger context: firstly, that of the experimental model, with its own hypotheses; then that of the knowledge acquisition process, which is structured and robust; finally, that of a reliable analysis of the results obtained, in a context where uncertainty could be important.

1
Mechanical Tests

1.1. Introduction

The mechanical tests performed in solid and structural mechanics have different objectives, depending on the level of knowledge sought through these tests:

• – primarily, the characterization tests allow understanding of undefined mechanisms. They are particularly useful when the level of knowledge of a problem is low, such as in biomechanics and tribology. They are, therefore, essential elements of modeling and enable the development of analytical, numerical, and experimental models;
• – reference tests can quantify intrinsic values (Young’s modulus) and classify technical solutions according to extrinsic parameters (e.g. coefficient of friction). These tests should be finely described and reproduced by the scientific community in order to enable valid comparisons. This description, which increases the reliability of a test, is the standard. Various tests performed under sufficiently near operating conditions can be compared and stored in databases;
• – the result of reference tests cannot be considered “as is” without verification. In particular, the actual geometry, size, or production conditions require validation tests scaled to a structure.

The diversity of the available standardized tests as well as tests related to a product (for example, the maximum deflection of a ski, the elasticity of a support stocking, etc.) render a comprehensive approach quite impossible. Moreover, it is more interesting to draw from certain examples how to design a mechanical testing device and how to establish the test-calculation dialogue. The examples selected below are conventional tests of solid mechanics, allowing analysis using a mechanical model of beams. The approach developed for these simple cases is absolutely transposable to more complex cases, where calculation-test dialogue involves high-level tools (optical full field methods, finite element modeling).

The selected tests correspond to the simple loading of a beam: traction, bending, and shear. Fields of stress and strain in the area of analysis must be higher than in other areas so the desired phenomena (e.g. occurrence of cracking or plasticity) appear in this area. For a quantitative analysis, the fields must be described by few parameters, and they must ideally be uniform.

NOTE.– Why use all these test categories? A numerical model, however powerful, cannot describe the complexity of a real object; as it is limited by the computing capacity, imagination of designers, and especially the various assumptions. The most debatable points in any modeling are often the boundary conditions: the rigid (welding, bonding, etc.) or mobile links.

1.2. Measurable quantities

A designer may require various mechanical quantities to design a test, depending on the material and the loading mode. Here are a few examples.

Most materials are linear, elastic, and isotropic. Two parameters are required for their characterization: Young’s modulus, which represents the proportionality of stress to strain (σ = E∈) and Poisson’s ratio, which describes the cross-sectional reduction during unidirectional loading

Other representations commonly used include Lamé coefficients.

In the case of an anisotropic material, the modules are dependent on the direction considered, which considerably increases the experimental protocol. Sometimes, the linear elastic model is set to default; the material may be elastic and nonlinear. In this case, the law of behavior is described by a higher number of parameters.

In most cases, elasticity is a convenient approximation of a material behavior. However, we must remember that more often, even for metals or glasses, the materials are viscoelastic, which results in a deferred deformation over time, which can be illustrated during a relaxation or creep test. The first step is to observe the variation of force over time to a fixed deformation level, and the second is to observe the variation of deformation for fixed force. In both cases, the elastic behavior is coupled with viscous behavior, characterized by a viscosity μ reflecting the proportionality between shear stress and shear rate

In order to ensure the behavior of a mechanical part over the short time, the designer uses the elastic limit of the material under traction and/or compression, or sometimes resistance to traction. Over the long term, however, there was fracture for light loads, due of the repetition of load. An endurance test is performed to determine the endurance limit.

Further, during the shaping of metal parts, permanent deformation is obtained by subjecting the material to plastic deformation. The perfect elasto-plastic model is often too limited. In particular, the more the material is deformed, the greater is the yield strength. The strain hardening rate characterising this phenomenon can be described by the power law or Hollomon law σ = K ∈ⁿ , where n is the strain hardening coefficient.

These quantities are probably the most important however there are many others that could be added to the list. Similarly, different types of tests may sometimes lead to identical values. Thus, a static tensile or bending test, a dynamic ultrasonic test or an indentation test all enable us to determine Young’s modulus. Therefore, it ...

Table of contents

• Cover
• Table of Contents
• Title
• Copyright
• Foreword
• Introduction
• 1 Mechanical Tests
• 2 A Few Sensors Used in Mechanics
• 3 Optical Full-Field Methods
• 4 Basic Tools for Measurement Methods
• 5 Exercises
• Conclusion
• Bibliography
• Index
• End User License Agreement