Dynamic testing of materials: Selected topics
Dynamic testing of materials is a vast subject involving a large variety of techniques according to the investigated properties. Consequently, one cannot cover it extensively and the present chapter will address three selected topics that were discussed d
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ynamic fracture testing
Dynamic fracture mechanics addresses the evolution of cracks in structures subjected to transient loadings. It can be broadly divided into two main domains, namely stationary and propagating cracks. The interested reader
T. àodygowski, A. Rusinek (Eds.), Constitutive Relations under Impact Loadings, CISM International Centre for Mechanical Sciences, DOI 10.1007/978-3-7091-1768-2_2, © CISM, Udine 2014
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D. Rittel
can refer to Freund’s book on the subject to get familiar with the analytical aspects of the subject (1990). We will focus here on stationary cracks only, since from an engineering point of view, the designer needs to have a criterion and the matching material property to predict whether the crack will propagate or not (Cox et al., 2005). The simplest (one parameter) way to analyze the dynamic stationary crack problem is analogous to the quasi-static case. Namely, the crack-tip stress field can be described by: Kα (t) σij (t) = √ fij (θ) . 2πr
(1)
Where (r,θ) are the coordinates of a point from the crack-tip located at the origin, σ is the stress tensor, f is a tabulated geometric function and t stands for time. The indices i and j vary from 1 to 3. K has the usual meaning of the stress intensity factor (SIF), with a=I, II or III according to the loading mode. Note that the only difference with the quasi-static case lies in the fact that both the stress tensor and the stress intensity factor are now functions of time. Eqn. (1) is valid as long as the crack remains stationary. Consequently, a fracture criterion can be written as: KI (t) = KId .
(2)
Where KI is the stress intensity factor assuming mode I for the sake of simplicity, and its critical value KId is called the dynamic initiation (fracture) toughness. This section deals with the measurement of the dynamic fracture toughness, leaving aside considerations as to whether this is a true material property, a point on which there is no wide agreement yet. To measure the dynamic fracture toughness, one needs to select an appropriate specimen and the corresponding experimental setup. While several variations can be found in the literature (see e.g. (Jiang and Vecchio, 2009)), it seems like the simplest configuration that can be used for testing materials of a limited ductility is the one-point impact technique (Giovanola, 1986). From a practical point of view, the specimen is a rectangular beam into which a sharp crack has been introduced. Belenky et al. (2010) investigated the dynamic fracture of transparent nanograined alumina, using the one-point impact technique. To produce sharp cracks, these authors used micro-indentation (Vickers) to obtain initially 4 cracks at each corner of the pyramidal indentation. Subsequent careful controlled bending allowed a pair of cracks to grow through the thickness of the specimen to a controlled depth, as shown in Fig. 1.
Dynamic Testing of Materials: Selected Topics
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Fig.1. Left: Pyramidal indentation with cracks at each corner (arrowed). Right: The fully grown sharp crack. In the ex
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