Fracture toughness, definition

There are two principal theories, or models, that attempt to describe what happens during brittle fracture, the Griffith fracture theory and the Irwin model. Both assume that fracture takes place through the presence of preexisting cracks or flaws in the polymer and are concerned with what happens near such a crack when a load is applied. Each leads to the definition of a fracture-toughness parameter and the two parameters are closely related to each other. The Griffith theory is concerned with the elastically stored energy near the crack, whereas the Irwin model is concerned with the distribution of stresses near the crack. Both theories apply strictly only for materials that are perfectly elastic for small strains and are therefore said to describe linear fracture mechanics. 

The interphase is a three-dimensional (3-D) layer in the immediate vicinity of filler surface, possessing physical properties different from the two main phases or components in a composite (i.e., matrix and filler). For the purpose of this chapter, the term interphase is limited to the layers introduced on the filler surface intentionally in a controlled maimer—engineered interphase layers (EIL). In these layers, a gradient of chemical composition can also exist as well as a gradient of physical properties. The pivotal problem is therefore a definition and an evaluation of an interphase thickness and its properties, namely, stiffness and fracture toughness. Interphase behavior plays a paramount role in the ability to transfer loads from the matrix to the reinforcements, hydrolytic stability of the material, and fracture behavior of a particulate composite. 

Fracture mechanics studies the effect of stress concentrations that occur when a load is applied to a body containing a void, independent of the geometry or material of the body. By this definition it would seem logical that the fracture toughness of a material, as determined by specific fracture mechanics techniques, would be an appropriate design criterion. 

The plastic-zone work is Up = P p, where Mp is the displacement. The general definition of fracture toughness R, analogous to G for stable growth, may he used ... 

Another important quantity in interface fracture mechanics is mode mixity. The crack tip field of an interface crack is intrinsically mixed mode [8] due to the asymmetric elastic properties across the interface. Hence, mode mixity is required to fully characterize the loading conditions at the crack tip. Furthermore, the fracture toughness of an interface is known to depend on the mixed mode condition, typically observed to rise with increasing mixed mode. The degree of the mode mixity can be characterized using the definition of the complex interface stress intensity factor K = iK + after He and Hutchinson [5] ... 

It is assumed that the use of such a nanocomposite as a matrix in continuous fiber-reinforced composites will definitely improve the matrix-related properties, such as interlaminar fracture toughness, transverse tensile strength and modulus, as well as interlaminar shear strength. The same should be true for polymer-based tribomaterials, in which such a nanoparticle-modifled resin is used in combination with friction and wear improving fillers, such as short carbon fibers, PTFE particles, and graphite flakes. 

The picture further complicates moving to carbon steel type A 533 B, already seen in Fig. 10.27. Figure 10.36 shows the experimental data obtained at several temperatures, from —18 to 300 °C [48]. Now it is not possible at aU to identify a trend common to all temperatures. At 120 °C the FCGR, da/dN, reaches its minimum whilst the maximum is at 25 °C. Between these two temperatures all other FCGR lay, but in a rather random order not certainly sequential. It is definitely necessary a reading key and this key is precisely the fracture toughness Kjc already discussed in Sect. 10.8 and used in Fig. 10.33 to compact aU FCGR curves. To this purpose, Fig. 10.37 presents the same results of Fig. 10.36 [63], but in a different fashion. Fig. 10.37a [48], in fact, is a summary of the effect of... 

Modem fracture mechanics was pioneered by A.A. Griffith who showed that brittle materials could fail catastrophically by cracks that become self-propagating even at stresses much lower than their tensile strength. Griffith s theory was expanded to include ductile materials and has led to the definition of a material property called fracture toughness that allows the prediction of critical crack lengths. 

Ceramics and glasses are generally multicomponent sohds that are chemically bonded by ionic or covalent bonding such that there are no free electrons. Therefore, the electrical conductivity and the thermal conductivity are low and the material is brittle. If there is crystallinity the material is called a ceramic and if there is no crystallinity (i.e. the material is amorphous) the material is called a glass. Ceramics and glasses are characterized by low ductility and low fracture toughness. Some elemental materials, such as boron, carbon, and silicon, can be formed as amorphous materials, so the definitions must be taken with some exceptions. 

The protocol considers the determination of fracture toughness at fracture initiation, and the initiation point is to be determined from the load record. The definition of initiation is as problematic here as in metals and the same rules as in E 399 ( pop-in , maximum load and load at 5% offset) are adopted. 

The main conclusion of that work was that the toughness of the adhesive joint could be defined thermodynamically as the work of adhesion W. Of course, this definition was only applicable in certain special equilibrium circumstances, when the materials were elastic and when the fracture occurred very slowly. The toughness W was measurable in a T peel test shown in Fig. 15.4. This idea explained the force F required to peel two sheets apart, depending only on W and the width of the strips b (see Section 7.7). 

Unlike rubber-toughened epoxy polymers, the relationship between the microstructure and toughness of thermoplastic-toughened epoxy polymers is not fully understood. Several studies have been initiated the focusing on fracture properties and fractrography of thermoplastic-toughened epoxy systems to establish the definitive relationships between microstructure and fracture properties. However, as discussed in detail next, the complex nature of materials precludes straightforward interpretations. 

Answer by author It has been shown that for type 301 stainless steel that notched/unnotched tensile ratios of unity or higher indicate sufficient resistance to brittle fracture for structural applications. Definite correlations between notched/unnotched tensile ratios, axial fatigue data of complex welded joints and fatigue data of actual tanks have been obtained on the 300 series stainless steels. It is felt, however, that sufficient information is not presently available to quantitatively state the notched/unnotched tensile ratio required to insure sufficient toughness in other alloy systems such as the aluminum base alloys. 

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