Dynamics of Fracture

The behavior of materials and constructions under high-speed loading has a number of peculiarities, and its examination is far from complete. This is due to the deficiency of experimental research data on controlled loading in the micro- and nanosecond ranges and by unsuccessful attempts to elucidate the results of these experiments on the basis of traditional static mechanics concepts.

Among the experimental methods of research on dynamic crack-growth resistance and fast fracture, the dynamic photoelastic and caustic methods are the most effective. These methods have been developed in the last two decades. The most important feature of these methods is the ability to directly track behavior possibilitis for quantitative characteristics of the material stress state during fracture. This is attained by a combination of classical methods of optical image processing with high-speed photography techniques. In this chapter we will examine principles and peculiarities of both methods as they are applied to fast-start and crack-propagation problems in brittle solids.

One of the main problems of testing the characteristics of resistant materials in dynamics is the dependence of dynamic strength on the way that the exterior action is applied. This difficulty typically appears under conditions of high-rate loading. In this case, the strength can be interpreted as a critical value of the stress-intensity factor which corresponds to microcracking near the crack tip. The strength can also be interpreted as a dynamic local stress leading to rupture continuum. Both are intensity limits of a local stress field and the fracture occurs when these limits are reached. The dependence of dynamic strength on the method of loading is manifested as critical values during variations of action duration, of amplitude, and of rate of rise of the exterior force. In the case of macrocrack motion initiation, such values will be critical as regards the stress-intensity factor of growth of the macrocrack. During fracture of ‘intact’ solids (i. e., not containing the given macroscopic defects) the local cleavage stress is not determined by a material’s characteristics but as a complex function of loading history.

Many modeling methods of dynamic fracture effects are associated with nonelastic rheology and macrocrack development. In many cases this association is an inevitable physical necessity. However, for practical aims it is very important to provide a direct mechanical approach, permitting the reduction of the dynamic fracture analysis to a simple ‘industrial’ procedure. That is why the rejection from the engineering mode of energy and power balance traditional schemes of fracture mechanics would be unjustified. Even in the framework of linear elasticity and brittle fracture these schemes are not complete. Their development, as will be shown below, can give sufficiently simple explanations of many peculiarities of high rate-fracture [23, 25, 26, 30, 31, 45, 47, 99].

Let us examine some nonclassical modeling methods of brittle-material fracture, especially efficient in situations where the classical approaches and the Griffith—Irwin criterion do not ensure success.

We will consider materials without artificially made defects and concentrators, like cracks or sharp notches, to be ‘intact’ materials. Let us examine the specific features of these materials’ fracture and the possible methods of its modeling. In this chapter the works [30, 31, 45, 47, 94, 95, 98, 116] are used.

In dynamics, the stress field behavior has a number of specific features. These important peculiarities obtain a principal character in the case of high-rate loading and fast rupture of solids [23, 24, 28, 29, 46, 50, 96]. In this chapter we will consider for fracture mechanics some of the simplest and traditional initial boundary value problems, present their solutions and notice some peculiarities of stress field behavior in dynamics.

It is well known that when formulating the macrorupture criterion, complementing the solid-medium mechanics equations, one has to take into account the most important peculiarity of dynamic fracture — the existence of not only a spatial but also a temporal structure of the process. This circumstance must be reflected while choosing criterion-determining parameters and test methods of dynamic strength properties of a material. Structural—temporal criteria, already considered in the previous chapters, permit taking this dynamic fracture peculiarity into account and modeling the process of crack-growth initiation under the action of impact pulses.

In this chapter we examine some principal peculiarities, and present calculation methods and an interpretation of the well-known high-rate fracture effects of elastic bodies with cracks [23-29, 31, 49, 99].

The problem, studied in this chapter, is connected wich the fracture ‘mode change’ effect. It was discovered experimentally by J. F. Kalthoff and S. Winkler [81], and then it was investigated by J. F. Kalthoff [76, 77], A. J. Rosakis et al. [107] and K. Ravi-Chandar [101].

In this chapter the incubation-time notion is used to construct criterion relations, describing the dynamic yield of materials. A similar approach was proposed by J. R. Klepaczko [122].