Experimental Mechanics of Solids and Structures

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 ixIntroduction xiChapter 1 Mechanical Tests 11.1 Introduction 11.2 Measurable quantities 21.3 Tensile test 31.3.1 Optimal testing conditions 51.3.2 Result of a standard tensile test 71.3.3 Stiffness of a tensile testing machine 91.4 Bending test 101.4.1 Test principle 101.4.2 Optimal realization conditions 101.4.3 Determination of flexural modulus 111.4.4 Damage to the structure 13Chapter 2 A Few Sensors Used in Mechanics 152.1 Introduction 152.2 Strain measurement 152.2.1 Principle 152.2.2 Gauge factor 162.2.3 Description of a gauge 172.2.4 Conditioning 192.2.5 Multi-gauge assemblies 202.2.6 Compensation of bending effects 212.2.7 Effect of temperature 222.2.8 Measurement of a surface-strain tensor of an object 232.2.9 “Measurement” considerations 252.3 Displacement measurement 272.3.1 Principle 272.3.2 Key characteristics 272.4 Force measurement 282.4.1 Strain gauge load cell 282.4.2 Piezoelectric gauge load cell 292.5 Acceleration measurement 332.5.1 Principle 332.5.2 Selection criteria 37Chapter 3 Optical Full-Field Methods 393.1 Overview 393.2 Selection of a field optical method 403.2.1 Factors governing selection 403.2.2 Fringe projection 413.2.3 Grid method 453.2.4 Digital image correlation 493.2.5 Speckle interferometry (ESPI) 533.3 Main processing methods of photomechanical results 603.3.1 Metrological aspects 603.3.2 Correction of target distorsions 623.3.3 Denoising in mapping 633.3.4 Phase unwrapping 653.3.5 Derivation of a displacement map 66Chapter 4 Basic Tools for Measurement Methods 714.1 Introduction 714.2 Measurement and precision 724.2.1 Calibration 724.2.2 Tests 754.2.3 Evaluating uncertainties 784.3 Experimental test plans 884.3.1 Preparation 904.3.2 Approach 914.3.3 Adjusting polynomial models by least squares 924.3.4 Linear factorial design without interaction 944.3.5 Linear factorial design with interactions 100w4.3.6 Quadratic design with interactions 1044.3.7 Variance analysis 1074.4 Hypothesis tests 1094.4.1 General principle 1094.4.2 1st and 2nd order error: a test’s power 1104.4.3 Choosing a statistical law 112w4.4.4 Examples 1134.4.5 Test for model adjustment: a return to ANOVA analysis 114Chapter 5 Exercises 1175.1 Multiple-choice questions 1175.2 Problem: designing a torque meter 1185.2.1 Mechanical analysis 1185.2.2 Electrical installation 1195.2.3 Analyzing uncertainty 1205.3 Problem: traction test on a composite 1215.3.1 Sizing a traction test 1215.3.2 Measuring 1215.3.3 Photomechanics 1225.4 Problem: optic fiber Bragg gratings 1225.4.1 What happens when there is traction on the fiber? 1235.4.2 What will the effective index become depending on the temperature and strain parameters? 1245.4.3 Separating temperature and mechanics 1245.4.4 Analyzing uncertainty 1245.5 Problem: bending a MEMS micro-sensor 1245.5.1 Suggesting a mechanical model for this problem 1255.6 Problem: studying a 4-point bending system 1265.6.1 Analyzing the device 1265.6.2 Mechanical analysis 1275.6.3 Analyzing uncertainties 1275.6.4 Optical full field methods 1275.7 Digital pressure tester: statistical tests 1285.7.1 Discovering the statistical functions library 1285.7.2 Estimating a confidence interval 1285.7.3 Calculating a test’s power 128Conclusion 131Bibliography 133Index 141