Fracture mechanic

Fracture mechanics is now quite weU estabHshed for metals, and a number of ASTM standards have been defined (4—6). For other materials, standardization efforts are underway (7,8). The techniques and procedures are being adapted from the metals Hterature. The concepts are appHcable to any material, provided the stmcture of the material can be treated as a continuum relative to the size-scale of the primary crack. There are many textbooks on the subject covering the appHcation of fracture mechanics to metals, polymers, and composites (9—15) (see Composite materials). 

Crack Tip Stresses. The simplest case for fracture mechanics analysis is a linear elastic material where stress. O, is proportional to strain, S, 

Kirk-Othmer Encyclopedia of Chemical Technology (4th Edition) 

Therefore, the magnitude of the stress at small distances from the crack tip is a function of the crack length, a, and the remotely appHed stress. O. Close to the crack tip (r ft) the stress can be scaled usiag a parameter called the stress intensity factor, K (9—11)  

Because the material is assumed to be linear elastic, the local displacements around the crack tip can also be expressed ia terms of K 

The strength under stress and the fracture properties of materials make up an extensive branch of engineering science. A vast literature on the subject exists and the reader is encouraged to consult relevant textbooks (e.g., Moore, Pavan, and Williams 2001). Here, only a few brief remarks will be made to serve as an introduction. 

At a molecular level, polymeric materials fail by a combination of two mechanisms bond breakage and chain slippage. When a stress is applied, the initial deformation usually involves shear flow of polymer chains past one another because breaking noncovalent bonds requires much lower stresses than those required to break covalent bonds (by one to two orders of magnitude). The balance between the two mechanisms determines the fracture behavior. If breakage of bonds is the predominant mechanism, brittle fracture is observed. If slippage of chains is the main process, more ductile fracture occurs. Of course, failure usually 

Fracture is caused by higher stresses around flaws or cracks than in the surrounding material. However, fracture mechanics is much more than the study of stress concentration factors. Such factors are useful in determining the influence of relatively large holes in bodies (see Section 6.3, Holes in Laminates), but are not particularly helpful when the body has sharp notches or crack-like flaws. For composite materials, fracture has a new dimension as opposed to homogeneous isotropic materials because of the presence of two or more constituents. Fracture can be a fracture of the individual constituents or a separation of the interface between the constituents. 

The discussion of fracture mechanics will be divided in two parts. First, basic principles of fracture mechanics will be described. Second, the application of fracture mechanics concepts to composite materials will be discussed. In both parts, the basic approach is that of Wu [6-12], 

From the engineering standpoint, crazing itself is of minor importance. There are a few applications in which a certain level of craze formation renders the component unserviceable e.g. PMMA helicopter cabins, where visibility is reduced, and ABS pipes in which porosity can be a problem. However, the main reason for the continuing interest in crazing is that it is the precursor to fracture in a large number of polymers. 

Brittle solids fracture because the applied stress is amplified by minute cracks—of order I //m in size—which occur naturally, as a result of fabrication, solidification, fatigue damage, etc. These cracks are frequently termed Griffith cracks, after the originator of the theory we are about to describe. 

Consider a stress a applied to a wide sheet which contains a throughthickness elliptic crack, oriented as shown in Fig. 5.9. The axes of the ellipse are of length 2a and 2b. Let the sheet be of width IV and thickness B. The description wide (or infinite ) is to be taken to mean that IV 2a. A force F applied to the end surfaces of the sheet develops the stress a 

The presence of the crack modifies the elastic stress distribution in its vicinity. 

From the fracture viewpoint, the stress distribution along the indicated line Oxi is particularly significant. In the Xa-direction, the stress r22 reaches a maximum value at the ellipse surface 722 falls as X] increases, and ultimately obtains the value a at a distance from the crack (as expected). In the Xi-direction, ji, is zero at the ellipse surface and rises to a value of order of a before falling again to zero with increasing Xi (as expected). The amplification of the applied stress a is greatest at the crack surface (Xi — 0) and is 

The general equation to describe the applied stress field around a crack tip is [15]  

The equations cited above are for an ideal semi-infinite plate, with no boundary effects. Application to real specimens requires calibration factors, so that the fracture toughness of Eq. (11-51), at the critical point is given by  

The total work of crack formation equals Gc x the crack area. Catastrophic failure is predicted to occur when C7[ ra] / = or when = IKGJ /.  

Kc and Gc are the parameters used in linear elastic fracture mechanics (LEFM). Both factors are implicitly defined to this point for plane stress conditions. To understand the term plane stress, imagine that the applied stress is resolved into three components along Cartesian coordinates plane stress occurs when one component is = 0. Such conditions are most likely to occur when the specimen is thin. 

The parameters which apply to plane strain fracture are G c and Ki, where the subscript 1 indicates that the crack opening is due to tensile forces. K]c is measured by applying Eq. (11-52) to data obtained with thick specimens. To illustrate the differences between plane stress and plane strain fracture modes, thin polycarbonate specimens, with thicknesses 3 mm reported to have G values of 10 kJ/m, while the Gic of thick specimens is 1.5 kJ/m.  

Mechanisms of toughening in ceramic matrix composites are discussed by Rice [236,237] and Marshall [238] deals with failure mechanisms in ceramic matrix composites. 

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. 

Rand B, Zeng RJ, Fibre reinforced ceramic matrix composites, Figueiredo, Bernardo CA, Baker 

Hiittinger KJ eds., Carbon Fibers Filaments and Composites, Kluwer, Dordrecht, 367-398, 

Chung DDL, Carbon Fiber Composites, Boston, Butterworth-Heinemann, 177 200, 1994. 

Sankar and Dn Ke i kar attended Twenty-Seventh Automotive lechnology Development Sontlactors Coordination Meeting on October 22-2G, 1989 at 

M Wiederhorn, D. Cranmer, D. Kauffman and D. E, Roberts (The National Institute of Standards and Technology) 

The long transient behavior, noted above, suggests that the microstructure of the material is slowly modified by exposure to elevated temperatures. Similar observations were made earlier on AY6 (made by GTE), in which case the increase in creep resistance of the material was attributed to devitrification of the glass phase at Si3N,j grain interfaces. The devitrification process was slow, and only effected the creep rate when the narrowest boundaries between the grains became devitrified. TEM studies on the material will be completed 

Extended creep curve for NT154. Note that transient creep occurs over the entire 1100 hr creep period. The minimum creep rate was determined by a least squares fit over the last 200 hr of the creep curve. 

Materials received by Dr. K. Liu at Oak Ridge National Laboratories (ORNL) exhibits the same high creep resistance as the ones that have been exposed for 1500 hr in the current tests. Also, the specimens tested by ORNL do not exhibit extensive transient creep, which suggests that the creep measurements are being affected either by minor differences in the microstructure of the two batches of materials, or by some difference in test procedure. To further study the creep process, a set of specimens are being annealed at 1350°C before being crept at high temperatures. Also, set of specimens prepared from the same billet will be tested both at ORNL and at NIST to determine if some difference in test procedure can account for the differences in creep behavior, 

For a plate containing an elliptical hole and stressed at right angles to the major axis a, he obtained the stability criterion 

If a crack travels at the interface of an adhesive joint one observes an adhesive debonding rather than cohesive failure. Except for minor differences in boundary condition the analgy to the fracture mechanical treatment of cohesive failure is complete [38-40] and the normal debonding stress a is obtained as  

The interpretation of and E is rather involved. These quantities not only depend on the static surface free energies and elastic moduli of the interacting (polymeric) materials but also on the work of deformation which the adhesive layer 

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Using flaw visuahzation system data the strength and fracture mechanics estimations are carried out in accordance with defect assessment regulatory procedure M-02-91 [5]. Recently, the additions had been included in the procedure, concerning interpretation of expert flaw visualization sysf em data, computer modelling, residual stresses, in-site properties of metal, methods of fracture analysis. 

The sensitivity tests are carried out on artificial defects (nickel-chromium specimens of NFA 09.520,see figure 3 of annex 1) and natural defects (one part in "light" alloy, one part in stellite grade 1 containing micropores, 2 specimens of fracture mechanical type CT20 in Z2 CN 12.10 (NFA 03.180). 

In an ideal situation we would like to have a balanced combination between evaluation of the welder s performance on one hand, and a fracture mechanics basis on the other hand in tenns of "being certain that a defect with dimensions exceeding a certain critical value is not present". The second aspect could be regarded as a safety net with a balanced conservatism. 

The Institute has many-year experience of investigations and developments in the field of NDT. These are, mainly, developments which allowed creation of a series of eddy current flaw detectors for various applications. The Institute has traditionally studied the physico-mechanical properties of materials, their stressed-strained state, fracture mechanics and developed on this basis the procedures and instruments which measure the properties and predict the behaviour of materials. Quite important are also developments of technologies and equipment for control of thickness and adhesion of thin protective coatings on various bases, corrosion control of underground pipelines by indirect method, acoustic emission control of hydrogen and corrosion cracking in structural materials, etc. 

Ghassemieli, E. and Nassehi, V., 2001b. rediction of failure and fracture mechanisms of polymeric composites using finite clement analysis. Part 1 particulate filled composites. Poly- Compos. 22, 528-541. 

Bui H.D., Ehrlacher A. (1997) Developments of fracture mechanics in France in the last decades. In Fracture Research in Retrospect. H.P. Rossmanith (Ed.), A.A.Balkema, Rotterdam, 369-387. 

Cherepanov G.P. (1983) Fracture mechanics of composite materials. Nauka, Moscow (in Russian). 

Ohtsuka K. (1986) Generalized G-integral and three-dimensional fracture mechanics. Surface crack problems. Hirosima Math. J. 16 (2), 327-352. 

Ohtsuka K. (1994) Mathematical aspects of fracture mechanics. Lect. Notes in Num. Appl. Anal. 13, 39-59. 

Fracture mechanics (qv) tests are typically used for stmctural adhesives. Thus, tests such as the double cantilever beam test (Fig. 2c), in which two thick adherends joined by an adhesive are broken by cleavage, provide information relating to stmctural flaws. Results can be reported in a number of ways. The most typical uses a quantity known as the strain energy release rate, given in energy per unit area. 

In moie ductile materials the assumptions of linear elastic fracture mechanics (LEFM) are not vahd because the material yields more at the crack tip, so that... 

The use of fatigue data and crack length measurements to predict the remaining service life of a stmcture under cyclic loading is possibly the most common application of fracture mechanics for performance prediction. In complex stmctures the growth of cracks is routinely monitored at intervals, and from data about crack growth rates and the applied loadings at that point in the stmcture, a decision is made about whether the stmcmre can continue to operate safely until the next scheduled inspection. 

J. F. Knott, fundamentals of fracture Mechanics, Butterworths, London, 1979. 

D. Broek, E/ementa Engineering fracture Mechanics, Martinus Nijhoff, Dordrecht, the Netherlands, 1987. 

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