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.

Jérôme Molimard is Professor at the Ecole des Mines de Saint-Etienne, France. His current research interests concern the use in mechanical engineering of optical field methods, which he has applied to lubrication, composite materials and the biomechanics of soft tissues.

Foreword ix

Introduction xi

Chapter 1. Mechanical Tests 1

1.1. Introduction 1

1.2. Measurable quantities 2

1.3. Tensile test 3

1.3.1. Optimal testing conditions 5

1.3.2. Result of a standard tensile test 7

1.3.3. Stiffness of a tensile testing machine 9

1.4. Bending test 10

1.4.1. Test principle 10

1.4.2. Optimal realization conditions 10

1.4.3. Determination of flexural modulus 11

1.4.4. Damage to the structure 13

Chapter 2. A Few Sensors Used in Mechanics 15

2.1. Introduction 15

2.2. Strain measurement 15

2.2.1. Principle 15

2.2.2. Gauge factor 16

2.2.3. Description of a gauge 17

2.2.4. Conditioning 19

2.2.5. Multi-gauge assemblies 20

2.2.6. Compensation of bending effects 21

2.2.7. Effect of temperature 22

2.2.8. Measurement of a surface-strain tensor of an object 23

2.2.9. “Measurement” considerations 25

2.3. Displacement measurement 27

2.3.1. Principle 27

2.3.2. Key characteristics 27

2.4. Force measurement 28

2.4.1. Strain gauge load cell 28

2.4.2. Piezoelectric gauge load cell 29

2.5. Acceleration measurement 33

2.5.1. Principle 33

2.5.2. Selection criteria 37

Chapter 3. Optical Full-Field Methods 39

3.1. Overview 39

3.2. Selection of a field optical method 40

3.2.1. Factors governing selection 40

3.2.2. Fringe projection 41

3.2.3. Grid method 45

3.2.4. Digital image correlation 49

3.2.5. Speckle interferometry (ESPI) 53

3.3. Main processing methods of photomechanical results 60

3.3.1. Metrological aspects 60

3.3.2. Correction of target distorsions 62

3.3.3. Denoising in mapping 63

3.3.4. Phase unwrapping 65

3.3.5. Derivation of a displacement map 66

Chapter 4. Basic Tools for Measurement Methods 71

4.1. Introduction 71

4.2. Measurement and precision 72

4.2.1. Calibration 72

4.2.2. Tests 75

4.2.3. Evaluating uncertainties 78

4.3. Experimental test plans 88

4.3.1. Preparation 90

4.3.2. Approach 91

4.3.3. Adjusting polynomial models by least squares 92

4.3.4. Linear factorial design without interaction 94

4.3.5. Linear factorial design with interactions 100

4.3.6. Quadratic design with interactions 104

4.3.7. Variance analysis 107

4.4. Hypothesis tests 109

4.4.1. General principle 109

4.4.2. 1st and 2nd order error: a test’s power 110

4.4.3. Choosing a statistical law 112

4.4.4. Examples 113

4.4.5. Test for model adjustment: a return to ANOVA analysis 114

Chapter 5. Exercises 117

5.1. Multiple-choice questions 117

5.2. Problem: designing a torque meter 118

5.2.1. Mechanical analysis 118

5.2.2. Electrical installation 119

5.2.3. Analyzing uncertainty 120

5.3. Problem: traction test on a composite 121

5.3.1. Sizing a traction test 121

5.3.2. Measuring 121

5.3.3. Photomechanics 122

5.4. Problem: optic fiber Bragg gratings 122

5.4.1. What happens when there is traction on the fiber? 123

5.4.2. What will the effective index become depending on the temperature and strain parameters? 124

5.4.3. Separating temperature and mechanics 124

5.4.4. Analyzing uncertainty 124

5.5. Problem: bending a MEMS micro-sensor 124

5.5.1. Suggesting a mechanical model for this problem 125

5.6. Problem: studying a 4-point bending system 126

5.6.1. Analyzing the device 126

5.6.2. Mechanical analysis 127

5.6.3. Analyzing uncertainties 127

5.6.4. Optical full field methods 127

5.7. Digital pressure tester: statistical tests 128

5.7.1. Discovering the statistical functions library 128

5.7.2. Estimating a confidence interval 128

5.7.3. Calculating a test’s power 128

Conclusion 131

Bibliography 133

Index 141

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