Measuring fracture parameters

In the previous sections, we introduced several important material parameters The fracture toughness Ki., the critical energy release rate t/j, and the crack-growth resistance curve. We now want to see how these quantities are measured. 

A common feature of all experiments is that the test specimens are precracked. To achieve this, a notched sample is used and a crack is propagated from this notch by cyclic loading (see chapter 10) as shown in figure 5.13. Creating the initial crack in this way is necessary because the notch tip is usually not sharp enough to behave like a true crack. Cyclic loading allows to produce the initial crack at a load that is much smaller than that needed for static experiments (see chapter 10). 

For the compact tension specimen, the stress intensity factor can be calculated from the external load F by 

A special case is shown in figure 5.16(c). On reaching a load Fq, the crack propagates unstably for a certain distance and then becomes arrested. This is called pop-in. 

To determine the fracture toughness Kic, the following procedure has been agreed upon (see e.g., standards astme399 and ISO 12737)  

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The literature contains many references to the use of notched, as opposed to pre-cracked or plain, specimens in laboratory studies of stress corrosion, for reasons of improved reproducibility, inability to crack plain specimens under otherwise identical conditions or ease of measuring some parameter such as crack growth rate when the crack location is predetermined. However, the developments in fracture mechanics (see Section 8.9), have resulted in a whole new field of stress-corrosion testing involving the use of specimens... 

High rate fracture parameters are important in the assessment of structural integrity, particularly in applications where there is a risk of rapid crack propagation. Linear elastic fracture mechanics provide a method for assessing fracture parameters under quasi-static conditions but under impact conditions various dynamic effects make both experimental measurement and analysis difficult. 

There are no standard test methods specific for discontinuous fiber (or short fiber) reinforced thermoplastics. It is also not clear whether a geometry-independent fracture parameter can be measured for these nonuniformly inhomogeneous materials. However in spite of these reservations there has been considerable work conducted towards characterizing short fiber composites for fracture toughness using the standard and other procedures outlined in the previous sections. The investigators have recognized that fracture mechanics data provide much more reliable information than the customary alternative tests for material selection and also a service performance indicator for components. 

A comprehensive account of the fracture toughness of cellular materials including foams, honeycombs, woods, and cancellous bone is presented by Gibson and Ashby [198], They have put emphasis on establishing and verifying relationships between the fracture parameters and the density of the material rather than the microstructural parameters such as the cell wall thickness. This is a practical approach since the density data for these materials are readily available or can be easily measured. 

Some of the important fracture parameters that are determined from the stress-strain curves are also illustrated in Figure 6, and include the initial modulus, proportional limit stress, ultimate strength and strain to failure. It is often very difficult to determine unambiguously the stress at which the first matrix crack occurs, so the proportional limit stress, i.e. the stress at which the strain deviates by 0.005% from linear loading, is more commonly used to characterize this important stress level. All of the in-plane fracture data reported here was measured at initial strain rates (prior to matrix cracking) between 3 x 10 and 10 " s unless otherwise noted. 

A brief review of microfracture processes and the energy absorption mechanics of fiber reinforced composites is given by Miyajima et al [239]. Fiber pullout is considered to be the most important toughening mechanism. They describe an experimental technique to determine fiber pullout energy, using a 3-point bend specimen. From measurements of fundamental fracture parameters, fracture mechanisms for the fiber pullout processes of carbon fiber reinforced carbon composites are discussed. 

With the reference toughness curve approach, the RT m index first came into use as the reference nil-ductility temperature which is determined in accordance with the ASME Code, Section III, Subsection NB-2331. The reference toughness Km curve and the Ki curve for static crack initiation later came into use as part of Section XI where the Km curve was called the crack arrest Xia curve. Thus, the RTndt reference temperature index has become the key material parameter in determining the allowable (P-T) limits for plant operation and for evaluating RPV integrity as the result of extreme transients such as PTS. Note that several years ago, the concept of a different, directly measured fracture toughness Master Curve approach was accepted in the ASME Code based on the index parameter RTjq. This development is covered in detail in Chapter 10. 

To conclude the above information on spinel, an SCG assessment and strength-probability-time prediction for long-term rehability assessment were based on the loading-rate effect of fracture-strength measurements. The parameter characterizing the slow crack-growth sensitivity suggests that FG materials are less affected. The maximum stress for a lifetime of 40 years (failure probability of 1 %) was... 

The ideal linear elastic fracture mechanics gives rise to the Eq. (1.1) discussed in Chapter 1, which is expressed theoretically by critical stress intensity factors Kq or These parameters must be measured by experiment before they can be used for engineering design purposes. The ideal conditions in all theories discussed in fracture mechanics do not exist. Therefore, it is necessary to have a general theory/equation that can be used to measure fracture mechanics parameters in terms of critical stress intensity factors Kq or Kic for engineering applications (Zhang and Cresswell, 2015). 

A second fracture parameter is also provided by linear elastic theory, namely, the energy G required to create unit area of fracture surface. Again there is a critical value, of G at which the crack begins to propagate, and a configuration-dependent formula which gives G in terms of measurable quantities. For the center crack mentioned above, the formula for G is... 

This method involves critical load evaluation and crack depth measurement, and has been used in recent years to define fracture parameters in several ceramics, for example, UO2, SiC, and TiC. ° ... 

R. K. Govila, Indentation Precracking and Double Torsion Methods for Measuring Fracture Mechanics Parameters in Hot pressed SisN4, J. Am. Ceram. Soc., 63 (5 6) 319 326 (1980). 

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