Classical fracture mechanics

Interestingly, the ductile-brittle transition observed for the MIM system provided an opportunity to assess the material fracture toughness, which was not possible using classical fracture mechanics tests due to the intrinsic brittleness of the MIM system. The measurement of the critical crack length, Lc, in the contact plane at the onset of brittle propagation allows estimation of a fracture toughness K C = a x+JnLc in the order of 0.85 MPa m1/2, i.e. much less than that of a poly(methylmethacrylate) homopolymer (1.20 MPa m1/2). 

A quantitative approach to the reinforcement of interfaces with block copolymers is necessary. Such an approach requires a way to evaluate the strength of the interface separately from any change in the morphology or microstructure of the blend. While classic fracture mechanics tests such as compact tension and double torsion could be used, the asymmetric double cantilever beam (ADCB) test used in the first such study [17] has been adopted by all successive workers to date. In this experimental geometry, shown schematically in Fig. 3, a wedge (usually a razor blade) is inserted at the interface. In some versions of the test the... 

The application of classical fracture mechanics in the case of pastes means that the strength is not controlled by total porosity but by a size of largest pores, playing the role of cracks . This idea was proposed by several authors, for example by Mindess [95] and Wittmarm [96]. 

Classical fracture mechanics presumes the presence of a single crack whose propagation proceeds in notch direction and thus can be described by only one parameter. This condition is not fulfilled in multidirectional laminates with their complex damage patterns. More recent fracture mechanic models adopt the concept of damage zones. 

Groth (1988) used a fracture mechanics approach without considering a preexisting crack. He formulated a fracture criterion based on an equivalent generalized stress intensity factor similar to that in classical fracture mechanics. Comparing it to a critical value, joint fi-acture may be predicted. However, the critical stress intensity factor needs first to be tuned with an experimental test which makes this approach questionable. 

For equilibrium systems with no contact hysteresis G = W, which is the classical Griffith criterion in fracture mechanics. For such a system, Eqs. 12 and 37 are the same. That is, the strain energy release rate is given by... 

Eisele et al24 describe the so called tear analyzer using a strip test piece with a cut in one edge cycled in tension, which can be considered the classic geometry for obtaining fracture mechanics data on rubbers. This sophisticated instrument introduces nothing new in concept but has a temperature controlled chamber and can operate at different frequencies, pre-strains and strain amplitudes, with automatic compensation for set. 

A clearer understanding of the relationship between foam structure and mechanical properties of solid foams has been developed by Gibson and Ashby (1988). They related the mechanical properties (e.g., strength, modulus, yield stress, fracture toughness) of idealised cellular solids to their relative density. This work considered the cell walls of solid foams as a three-dimensional network of beams (Figure 20.18) and treated their deformation in terms of classical solid mechanics, with strength and modulus related to beam thickness and length by the equations ... 

Barsom, J. M. (editor). Fracture Mechanics Retrospective Early Classic Papers (1913-1965), ASTM, Philadelphi Pennsylvania, 1987. 

Finally, it will be demonstrated that fracture mechanics provides insight into the preferred path of crack growth, A perplexing problem that, despite considerable speculation over the last 50 years, has remained unsolved is why do cracks follow a particular path For example, for many practical joints, it has been observed that cracks typically proceed in the adhesive rather than along the interface. This phenomenon is so common that, in his classical text on adhesives, Kinloch states [11] ... 

Griffith, Alan Arnold (1893-1963), was known as The Father of Fracture Mechanics and Bubble Griffith, the first for his classic work in fracture mechanics and the role of flaws and the second for his work on soap films. He was a British aeronautical engineer who worked at RoUs-Royce from 1939 to 1960 designing turbojet engines. 

The cracked plate model is a classical example in Fracture Mechanics and its relative simplicity allows a detailed and complete study of different simulation techniques. A thorough description of this model can be found in (Ardillon Venturini 1995). 

Johnson et al. (3) have shown how the elastic energy can be computed in the case of a spherical punch by adding a rigid body displacement to the classical elastic solution. In fact, this method is quite general for punches of any shape and can be proved by the general theory of elasticity (4) stresses and discontinuities of displacement are those of fracture mechanics ... 

Theoretical investigations into phenomenon of the notch sensitivity of composites have tended to rely on classical fracture concepts. ITiese efforts have taken two forms micro-and macro-mechanical representations. In die micro-mechanics format, local... 

As an example [30] of current research based on questionable assumptions we now consider the application of linear-elastic fracture mechanics (LEFM) [31-32] and classical yield criteria (von Mises, etc. [8]) to unoriented glassy polymers. That there actually is a basic problem needs some clarification ... 

The model of the thermoplastie matrix reinforeed with short fibres, in its different forms, was widely exploited, in the elaboration of the theory eoneerning the eomposite materials fracture. A first approach belongs to the material resistanee field, which uses the classical criterion of fracture of the ideal material, without faults the fracture mechanic studies the initiation and propagation of a fault, preexistent or artificially created, and, finally, the failure mechanic investigates the material behaviour until to the apparition of a microscopic fault, which corresponds to the catastrophic fracture initiation. 

Application The authors applied this methodology to the investigation of Si. In particular, they studied brittle fracture mechanisms (crack propagation, determination of the stress-strain curve, and so on), vacancy diffusion, and gliding of a pair of partial dislocations at finite temperature. In all of these applications, the authors used a tight-binding (TB) scheme to perform the quantum calculations, and the Stillinger-Weber potential (SW) for the classical ones. 

A hybrid atomistie/eontinuum mechanics method is established in the Feng et al. [70] study the deformation and fracture behaviors of CNTs in composites. The unit eell eontaining a CNT embedded in a matrix is divided in three regions, whieh are simulated by the atomic-potential method, the continumn method based on the modified Cauchy-Bom rule, and the classical continuum mechanics, respectively. The effect of CNT interaction is taken into account via the Mori-Tanaka effective field method of micromechanics. This method not only can predict the formation of Stone-Wales (5-7-7-5) defects, but also simulate the subsequent deformation and fracture process of CNTs. It is found that the critical strain of defect nucleation in a CNT is sensitive to its chiral angle but not to its diameter. The critical strain of Stone-Wales defect formation of zigzag CNTs is nearly twice that of armchair CNTs. Due to the constraint effect of matrix, the CNTs embedded in a composite are easier to fracture in comparison with those not embedded. With the increase in the Young s modulus of the matrix, the critical breaking strain of CNTs decreases. 

Fracture mechanical methods evaluate the propagation of cracks and damage in materials under dynamic load (crack or damage propagation tests). However, there are several objections to applying classic - linear elastic - fracture mechanical methods to long fiber-reinforced composites due to the heterogeneity and anisotropy of fiber composites [125] ... 

Cracking occurs when the stress in the network exceeds its strength. Since the classic work of Griffith [70], it has been understood that fracture of brittle materials depends on the presence of flaws that amplify the stress applied to the body. That is, if a uniform stress is applied to a body containing a crack with a length of c, the stress at the tip of the crack is proportional to ct,Vc, and failure occurs when that stress exceeds the strength of the material. The theory of linear elastic fracture mechanics (LEFM), which is discussed in several excellent textbooks [71-73], indicates that catastrophic crack propagation occurs when... 

---