Karl Hoffmann An Introduction to Stress Analysis and Transducer Design using Strain Gauges The definitive work on strain gauge measurement www.hbm.com Contents IX Contents Page 1. Introduction ...................................................................................................... 1 1.0.1 Metal strain gages............................................................................................... 2 1.0.2 Semiconductor strain gages ................................................................................ 7 1.0.3 Vapor-deposited (thin-film) strain gages............................................................ 8 1.0.4 Capacitive strain gages ....................................................................................... 9 1.0.5 Piezoelectric strain gages.................................................................................. 10 1.0.6 Photoelastic strain gages................................................................................... 11 1.0.7 Mechanical strain gages.................................................................................... 11 1.0.8 Other systems ................................................................................................... 11 1.1 The operating principle of the strain gage ........................................................ 12 1.1.1 Metal strain gages............................................................................................. 12 1.1.2 Semiconductor strain gages .............................................................................. 14 1.2 The measurement system.................................................................................. 15 2 Terms and units of measurement used in strain gage technology ............. 17 2.1 Strain: Definition and unit of measurement ..................................................... 17 2.1.1 Absolute change of length ................................................................................ 17 2.1.2 Relative change of length or strain ................................................................... 18 2.1.3 Unit of measurement for strain [2-1]................................................................ 19 2.2 Mechanical stress: Definition and unit of measurement................................... 21 2.2.1 Normal stress.................................................................................................... 21 2.2.2 Shear stress....................................................................................................... 22 2.2.3 Residual stress, thermal stress .......................................................................... 24 2.2.4 Stress states....................................................................................................... 25 2.3 Material parameters .......................................................................................... 26 2.3.1 Modulus of elasticity, definition and units ....................................................... 26 2.3.2 Shear modulus .................................................................................................. 28 2.3.3 Poisson's ratio................................................................................................... 29 2.3.4 Thermal expansion........................................................................................... 31 2.4 Strain gage loading ........................................................................................... 32 2.4.1 Static measurements (zero referenced)............................................................. 32 2.4.2 Quasi-static measurements ............................................................................... 33 2.4.3 Dynamic measurements (non-zero referenced)................................................ 33 3 Selection criteria for strain gages.................................................................. 34 3.1 Range of application......................................................................................... 36 3.1.1 Stress analysis, model measurement techniques, biomechanics ...................... 36 3.1.2 Transducer construction................................................................................... 36 3.2 Types of strain gages ........................................................................................ 37 3.2.1 Length of measuring grid ................................................................................. 37 3.2.1.1 Homogeneous field of strain............................................................................. 38 3.2.1.2 Inhomogeneous strain field .............................................................................. 40 3.2.1.3 Dynamic strain conditions ................................................................................ 42 3.2.2 Multiple strain gages, their advantages and fields of application..................... 42 3.2.2.1 Strain gage chains for the determination of stress gradients ............................ 42 3.2.2.2 Strain gage rosettes for the determination of stress conditions ........................ 44 3.2.2.3 Strain gage rosettes for the investigation of residual stress.............................. 46 3.2.3 Special strain gages.......................................................................................... 48 HBM Test and Measurement www.hbm.com X Contents 3.2.3.1 Weldable strain gages....................................................................................... 49 3.2.3.2 Free-grid strain gages, high-temperature strain gages...................................... 49 3.2.3.3 Weldable high-temperature strain gages .......................................................... 50 3.2.4 Electrical resistance.......................................................................................... 50 3.2.5 Useful temperature range ................................................................................. 51 3.3 Technical data................................................................................................... 52 3.3.1 Strain gage sensitivity (gage factor) for metal strain gages ............................. 53 3.3.2 Gage factor for semiconductor strain gages..................................................... 54 3.3.3 Transverse sensitivity....................................................................................... 56 3.3.4 Temperature response of a mounted strain gage.............................................. 59 3.3.4.1 Temperature compensated strain gages............................................................ 61 3.3.4.2 Thermal drift..................................................................................................... 67 3.3.5 The dependence of sensitivity on temperature................................................. 67 3.3.6 Static elongation............................................................................................... 69 3.3.7 Dynamic strain measurement ........................................................................... 70 3.3.7.1 Continuous vibration characteristics................................................................ 71 3.3.7.2 The cut-off frequency....................................................................................... 74 3.3.8 Electrical loading.............................................................................................. 79 3.3.9 Creep ................................................................................................................ 80 3.3.10 Mechanical hysteresis.......................................................................................87 3.4 Environmental influences................................................................................. 90 3.4.1 Temperature...................................................................................................... 90 3.4.2 Humidity........................................................................................................... 90 3.4.3 Hydrostatic pressure......................................................................................... 91 3.4.4 Vacuum ............................................................................................................ 96 3.4.5 Ionizing radiation............................................................................................. 99 3.4.5.1 The effects of ionizing radiation on strain gage measuring points................. 100 3.4.6 Magnetic flelds............................................................................................... 104 3.4.7 Storage............................................................................................................ 107 4 Materials used for mounting strain gages.................................................. 108 4.1 Strain gage bonding materials ........................................................................ 108 4.2 Mounting materials......................................................................................... 112 4.2.1 Cleaning agents.............................................................................................. 112 4.2.2 Soldering agents............................................................................................. 113 4.2.2.1 Soldering devices........................................................................................... 113 4.2.2.2 Solders and fluxing agents ............................................................................. 114 4.2.3 Connection methods......................................................................................