Toughness, fracture

Fracture toughness is determined by the flaw sensitivity of the material. 

Creep data for a number of ceramics at high stress values. (From W. R. Cannon and T. G. Langdon, /. Mater. Sci., 18,1-50,1983.) 

The fracture toughness of PEEK has been studied via fatigue tests of notched and unnotched samples and three-point bend tests using single-notched specimens. Typical fatigue behaviors of 

For these reasons, attention has been paid to energy criteria as a measure of toughness. The following points need to be noted. Materials do not reach their theoretical strength (that is of their primary chemical bonds), because of the presence of minute flaws. Stress is concentrated at these flaws and so is enhanced. In effect this amounts to a weakening of the material. Under load, cracks propagate from these flaws and lead to failure. 

Fracture toughness is the resistance to propagation of cracks through a material and is usually quantified by the stress intensity factor, K, defined as 

There are a number of methods of determining fracture toughness, but the one used so far for AB cements is the double torsion method introduced 

Double torsion test specimens take the form of rectangular plates with a sharp groove cut down the centre to eliminate crack shape corrections. An initiating notch is cut into one end of each specimen (Hill Wilson, 1988) and the specimen is then tested on two parallel rollers. A load is applied at a constant rate across the slot by two small balls. In essence the test piece is subjected to a four-point bend test and the crack is propagated along the groove. The crack front is found to be curved. 

The double torsion test specimen has many advantages over other fracture toughness specimen geometries. Since it is a linear compliance test piece, the crack length is not required in the calculation. The crack propagates at constant velocity which is determined by the crosshead displacement rate. Several readings of the critical load required for crack propagation can be made on each specimen. 

Of course, the ability to dissipate energy is only one of the characteristics concerned in toughness, or the ability to resist fracture (see Section 3.2). Thus the modulus itself contributes to the total energy and the stress required for fracture a particulate filler may, by raising the modulus of a very low-modulus polymer, increase the toughness. 

Typical manifestations of embrittlement are obvious in a number of measurements, such as impact strength more detailed studies tend to confirm frequent adverse effects on ductility. For example, in the investigation of filled epoxy resins by Moehlenpah et ai (1970, 1971) cited previously, it was foui)d that, for both compressive and tensile loading, filling raised the temperature for the brittle-ductile transition at a given strain rate. In other words, the filled material was brittle at higher temperatures and lower strain rates than the unfilled polymer. The effect of filler on the ductile to ductile-rubbery transition was, on the other hand, much less. 

The fracture toughness, a term defined by Irwin (1956, 1960) to characterize brittleness, provides a measure of the conditions required for catastrophic crack propagation in a material (see Section 1.6). One fracture toughness parameter is the surface fracture energy y, defined as one-half G, the critical strain energy release rate above which catastrophic failure occurs. In turn G is related to another convenient toughness parameter, the critical stress intensity factor a measure of the stress field at the crack tip. For fracture of an isotropic material in a plane strain modet (Baer, 1964, p. 946)  

Studies of this type are important in any consideration of toughening mechanisms. The fracture toughness may be expressed explicitly in terms of Ty, Gy, and for a typical polymer having a value for Poisson s ratio of 0.35, y becomes [from equations (12.27) and (12.29)] 

The trend toward the lowering of fracture toughness by particulate fillers is consistent with considerable experience [see property tables in, e.g.. Modern Plastics Encyclopedia (1974-1975)] and with results of several other studies of the effects of filler on the area under a stress-strain curve 

their shape, and their propagation are the central themes of this chapter. The various aspects of brittle failure are discussed from several viewpoints. The concepts of fracture toughness and flaw sensitivity are discussed first. The factors influencing the strengths of ceramics are dealt with in Sec. 11.3. Toughening mechanisms are dealt with in Sec. 11.4. Section 11.5 introduces the statistics of brittle failure and a methodology for design. 

To illustrate what is meant by flaw or notch sensitivity, consider the schematic of what occurs at the base of an atomically sharp crack upon the application of a load F pp. For a crack-free sample (Fig. 11.3fl), each chain of atoms will carry its share of the load F/w, where n is the number of chains, i.e., the applied stress cxapp is said to be uniformly distributed. The introduction of a surface crack results in a stress redistribution such that the load that was supported by the severed bonds is now being carried by only a few bonds at the crack tip (Fig. 11.2 b). Said otherwise, the presence of a flaw will locally amplify the applied stress at the crack tip Oup. As o app is increased, a p increases accordingly and moves up the stress versus interatomic distance curve, as shown in Fig. 11.3c. As long as T,jp (Tmax-the situation is stable and the flaw will not propagate. However, if at any time (7,ip exceeds cTmax- the situation becomes catastrophically unstable (not 

The time-dependent mechanical properties such as creep and subcritical crack growth are dealt with separately in the next chapter. 

To be a little more quantitative in predicting the applied stress that would lead to failure, atip would have to be calculated and equated to 

as noted above, fracture can be reasonably assumed to occur y/10, it follows that 

The mechanical strength of hard materials is critical for load-bearing, structural applications. These brittle materials only deform plastically at high temperatures, or under severe hydrostatic constraint, since the Peierls stress for dislocation movement is high. Failure is usually by unstable crack propagation under a tensile stress that exceeds the tensile strength of the material. In terms of fracture mechanics, brittle failure occurs when the Mode I stress intensity factor Kj reaches the fracture toughness of the material, Kic (see below). 

An experimental uniaxial stress-strain relationship, determined in tension, would provide the necessary design information for ceramics and hard materials Young s modulus, Poisson s ratio and the tensile fracture strength. However, tensUe data for brittle materials are often unreliable, due to parasitic bending stresses associated with dimensional inaccuracy in machining tensile dog-bone specimens and misalignment of the specimen grips. 

Several issues need to be addressed when a bend test is used to evaluate the strength The sources of errors that are responsible for statistical scatter in the results the statistical nature of the strength of a brittle material the relationship between the measured flexural strength and the strength derived from a valid uniaxial tensile test, together with the effect of sample size on the strength and 

Brittle materials fail by unstable crack propagation from a pre-existing flaw. The size, orientation, and shapes of the flaws in a given flaw population determine the variability of the failure stress the statistical failure probability, F, first formulated by Weibull [34] and described by the Weibull function  

If a 3PB test piece is loaded, the volume element subjected to the maximum tensile stress is very small. This volume is much larger for a 4PB specimen, but a unidirectional tensile specimen will have the largest volume under maximum stress. It follows that the median strength of a 3PB specimen may exceed that of a 4PB specimen, which in turn should have a higher average strength than a tensile specimen. The measured strength ratio between specimens of identical size subjected to 3PB and to pure tension is predicted to be [34,37]  

Delamination represents the weakest failure mode in laminated eomposites, and is considered to be the most prevalent life-limiting crack growth mode in most composite structures. As such, ever-increasing attention has been directed toward the understanding and characterization of delaminations of various natures, and at 

Composite structures in service are often subjected to complex 3-D load paths. In general, a delamination will be subjected to a crack driving force with a mode I opening, a mode II forward shear and a mode III anti-plane shear, as illustrated in Fig 3.29. Because delamination is constrained to grow between individual plies, both interlaminar tension and shear stresses are commonly present at the 

Impact testing data for pearlitic steels as a function of temperature for various wt% carbon content. High carbon steels are stronger but become brittle at ambient temperatures, whereas low carbon steels are ductile until 50°C, when they suddenly become brittle. (From Reinbolt, 1j. and Harris, W.J., Trans. ASM, 43,1951. Reprinted with permission of ASM International. All rights reserved.) 

FIGURE 5.9 Plot showing product of impact strength and stiffness that is important in dynamic loading of a cantilever beam. 

Assume the length L and depth h are constant, but the width b needs to be selected to satisfy a certain factor of safety given by Equation 5.4. Thus, select 

Whereas the impact strength is the measure of a ductile polymer to absorb energy, the fracture toughness is a measure of a more brittle polymer to resist crack propagation. Polymers can contain flaws from processing, such as cracks, voids, and inclusions. These flaws act as stress concentrations. Often these flaws are microscopic. 

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Panasyuk V.V., Andreikiv A.V., Kovchik S.E. (1977) Methods of estimating the fracture toughness of structural materials. Kiev (in Russian). 

Fig. 6. Fracture toughness test specimens (a) single-edge notch (b) center notch (c) compact tension and (d) three-point bend. Terms are defined in text.

ASTM E399-90, "Plane Strain Fracture Toughness of Metallic Materials," MnnualBook ofMSTM Standards, ASTM PubHcations, Philadelphia, 1993. 

ASTM D5045-91, "Plane Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials," A.nnualBook ofyiSTM Standards, ASTM Puhhcations, Philadelphia, 1993. 

Finally, the nature of the crystalline microstmcture, ie, crystal size and morphology and the textural relationship among the crystals and glass, is the key to many mechanical and optical properties, including transparency/opacity, strength and fracture toughness, and machinabiUty. These microstmctures can be quite complex and often are distinct from conventional ceramic microstmctures (6). 

One of the most important appHcations of LEFM is to estimate the critical crack or defect size which causes fast fracture to occur. This occurs when the value of iCin a stmcture becomes equal to the plain strain fracture toughness, of the material the critical crack size, for a given stress and fracture toughness, is then given by equation 31. 

This behef is supported by the results of burst tests on tubular specimens made of AISI 4335 tempered to various fracture toughness levels from... 

Eor an impact strength of 34 J (25 ft-lbf) the equivalent fracture toughness (150) is approximately 120 MPay. The fracture toughness dictates the critical size of crack above which fast fracture intervenes, so the smaller its value the smaller the critical crack and hence the greater significance of the transverse impact requirement specified by Manning. 

A proposed mechanism for toughening of mbber-modifted epoxies based on the microstmcture and fracture characteristics (310—312) involves mbber cavitation and matrix shear-yielding. A quantitative expression describes the fracture toughness values over a wide range of temperatures and rates. 

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