Experimental Mechanics

An electrical resistance strain gage is a resistor used to measure strain. In its basic form, it is a wire adhered onto the surface of a component so that strains of the component are transmitted to the wire. Its operation is based on the discovery made by Lord Kelvin in 1856 that the electrical resistance of a wire increases with increasing strain and decreases with decreasing strain. By measuring the change of the resistance of the strain gage the strain is inferred. Strain gages constitute the most widely used method of measuring strain at a point.

Optical methods of stress analysis, including geometric, coherent, and interferometric moiré, photoelasticity, interferometry, speckle photography and interferometry, holography, optical fibers, digital image correlation, are of great importance in experimental mechanics.

Geometric moiré is an optical method of experimental mechanics for measurement of displacements and slopes. It is based on the phenomenon of obstruction of light when it passes through two superposed gratings. The moiré effect can be explained by geometric optics and there is no need to invoke the wave theory of light. Moiré is the French name of textile with wavy (watered) appearance produced mainly from silk, but also wool, cotton, and rayon.

Geometric moiré is a well-established full-field method for measuring displacements. A serious drawback of the method is its low sensitivity. The density of the gratings cannot exceed 40 lines/mm or the pitch cannot be smaller than 2.5 × 10^–2 mm. The displacement difference between two successive fringes is equal to the pitch of the grating and this limits the sensitivity of the method. For higher density gratings diffraction effects enter which alter the nature of the geometric moiré effect. For measuring small displacements moiré methods with much higher sensitivity than geometric moiré have been developed. They use coherent illumination as opposed to geometric moiré which uses ordinary light.

In this chapter, we present two moiré methods that use remote gratings for the determination of the gradients of the out-of-plane displacements or the sum of the two in-plane principal stresses for plane stress conditions. The moiré patterns are created by projecting the rulings of one grating onto the rulings of a second grating after interacting with the specimen. The first method developed by Theocaris (Moiré fringes in strain analysis. Pergamon Press, pp 178–218, 1969 [1]), Theocaris and Koutsambessis (J Sci Instr 42:607–610, 1965 [2]), Theocaris and Koutsambessis (Exp Mech 8:82–87, 1968 [3]), Theocaris and Koutsambessis (Strain 4:10–15, 1968 [4]) is based on geometric moiré and uses while light. The second method termed “Coherent Gradient Censor (CGS)” was developed by Tippur et al. (Int J Fract 48:193–204, 1991 [5]), Tippur et al. (Int J Fract 52:91–117, 1991 [6]), Tippur and Rosakis (J Exp Mech 31:243–251, 1991 [7]), Krishnaswamy et al. (J Mech Phys Sol 40:339–372, 1992 [8]), Tippur (Appl Opt 31:4428–4439, 1992 [9]), Bruck and Rosakis (Opt Lasers Eng 17:83–101, 1992 [10]), Mason et al. (J Mech Phys Solids 40:641–661, 1992 [11]), Rosakis (VCH Publishers, pp 327–425, 1993 [12]), Bruck and Rosakis (Opt Lasers Eng 18:25–51, 1993 [13]), Rosakis (Special issue of optics and lasers in engineering devoted to photomechanics applied to dynamic response of materials, pp 19, 3–41, 1993 [14]), Lee et al. (Opt Lasers Eng 25:25–53, 1996 [15]), Rosakis et al. (Thin Solid Films 325:42–54, 1998 [16]), Mello et al. (Exp Mech 49:277–289, 2009 [17]). It is based on the diffraction of light by two gratings and uses coherent light. Both methods involve simple optical setups.

The method of caustics is a simple optical method mainly used for the determination of stress intensity factors in crack problems under static and dynamic loading. Together with the method of geometric moiré, they are the only two optical methods of experimental mechanics included in this book that are based on geometric optics and not on the phenomena of interference or diffraction of light, as the other optical methods. Besides crack problems, the method can also be used to obtain optical patterns from reflecting surfaces.

Photoelasticity is a simple full-field optical method of experimental mechanics. Its name comes from the Greek words “photo” which means light and “elasticity” which refers to the ability of an object or material to resume its normal shape after being stretched or compressed. It is based on the phenomenon of temporary or artificial double refraction or birefringence effect, first discovered by Sir David Brewster in 1816, according to which transparent materials that are optically isotropic when unstressed become optically anisotropic and behave like birefringent crystals when they are stressed. The birefringence of the material is proportional to the difference of the principal stresses and is retained only during the application of loads. It disappears when the loads are removed.

Interferometric methods of stress analysis are based on the phenomenon of interference of light. They use interferometers to measure the optical retardations of bodies due to loading, which are directly related to the stresses. When combined with the difference of the principal stresses obtained from isochromatic patterns of photoelasticity the individual principal stresses are determined.

Holography is an optical method for recording both the amplitude and the phase of a wavefront. Its name comes from the Greek words “holo” which means “whole” and “graphy” which means “recording”. The term “wavefront reconstruction” is also used. Before holography the only method of recording and retaining as a permanent record the picture of an object was photography. In photography, the wavefront emitted by an object is transformed by a lens and impinges on a photosensitive plate that responds to the intensity of light. Thus, only the amplitude, not the phase, of the wave can be recorded. Holography is based on the phenomena of interference and diffraction of light.

Fiber optic sensor (FOS) technology uses optical fibers. FOSs offers important advantages over conventional sensors, such as immunity to electromagnetic radiation, multiplexing, small size, high sensitivity, high accuracy, remote sensing, and are chemically and biologically inert. They have been employed for measurement of temperature, strain, index of refraction, humidity. Their development has been stimulated by the technological progress of fiber optic communication by providing higher performance, more reliable telecommunication links with decreasing bandwidth cost.

Speckle methods are high-sensitivity non-contact optical methods for measuring displacements. They are based on the speckle effect. Speckles are granular dots that result from the illumination of a diffusively reflecting rough surface with coherent light. The reflected or scattered wavelets interfere to create a random speckle pattern with statistical properties. The laser speckle is due to the coherence of the light and the roughness of the surface of the order of the wavelength of light.

Digital image correlation (DIC) is a full-field non-contacting optical method that can capture the shape, motion, and deformation of solid objects. The basis of the method is the matching of the gray values of points from an image of the surface of an object before and after deformation. The gray values of points of images of an object are acquired, stored, digitized, and correlated (matched) to compute shape and surface displacements. A matching process based on gray intensity levels is performed, hence the name of the method digital image correlation. DIC techniques can be applied to macro-, micro-, and nano-scale mechanical testing under static and dynamic loading. The development of DIC is due to the advances in computer technology and digital cameras.

The indentation test is a simple commonly used technique to measure the hardness and related mechanical properties of materials in an easy and speedy way. The method consists of touching the material of interest with another material whose properties are known. In a typical test, a hard indenter of known geometry is driven into a soft material by applying a preset load and the dimensions of the resulting imprint are measured and related to the hardness index number.

Nondestructive testing (NDT) refers to the science and technology of non-invasive methods of testing, evaluation, and characterization of materials, components, or systems without impairing their performance and serviceability. It provides techniques to detect and characterize flaws in materials and structures and plays an important role in the prevention of failure. The terms nondestructive examination (NDE), nondestructive inspection (NDI), and nondestructive evaluation (NDE) are also commonly used to describe this technology. NDT is important for the in-service inspection of load-bearing structures whose failure could have catastrophic consequences. In most NDT methods some form of energy, such as optical, electromagnetic, radiation, acoustic, etc. is sent through the material and the response of the material is analyzed by sensors. Sensor development played an important role and led to increased sensitivity and reliability of NDT methods.

Residual stresses are locked-in, self-equilibrating stresses that remain in a material after the external loads are removed. They result from any mechanisms that cause misfits among different parts of a material or structure, such as processing operations, non-uniform plastic deformation, temperature gradients, surface treatments, material forming, and shaping procedures, phase transformations, etc. Residual stresses are developed in composite materials, welds, quenched components, semiconductor fabrication, thin films, etc. They can be tensile or compressive. They are algebraically summed with applied stresses. In some cases, beneficial compressive residual stresses are introduced intentionally, as in pre-stressed concrete, in brittle materials which can be toughened, in shot peening, quenching, tempered glass. Generally speaking, residual stresses are undesirable.