Linear elastic fracture mechanics, principles

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

The term fracture toughness or toughness with a symbol, R or Gc, used throughout this chapter refers to the work dissipated in creating new fracture surfaces of a unit nominal cross-sectional area, or the critical potential energy release rate, of a composite specimen with a unit kJ/m. Fracture toughness is also often measured in terms of the critical stress intensity factor, with a unit MPay/m, based on linear elastic fracture mechanics (LEFM) principle. The various micro-failure mechanisms that make up the total specific work of fracture or fracture toughness are discussed in this section. 

The application of linear elastic fracture mechanics is in principle straightforward, albeit at times very complicated in application. Say, for example, a structural element is to be constructed of a given material. The value of (or Kj ) can be determined from tests on standard specimens or perhaps obtained from handbooks of materials properties. If the designer can now perform a stress analysis for the part under the loads in question for its... 

FRACOD is a two dimensional BEM/DDM code for fracturing analysis in rocks, (see Part 11 in Rinne, 2003). The code is based on the principles of linear elastic fracture mechanics and has been developed to track both fracture initiation and propagation. The initiation of fracturing can be specified using any criterion, but once initiated fracture growth is controlled by the fracture toughness. 

The fundamental principle on which fracture mechanics is based is that cracklike defects exist in all materials and that when critical conditions are attained at the crack tip, the crack will begin to propagate and the material will fracture. In linear elastic fracture mechanics (LEFM) the assumption is made that the material deforms elastically (i.e. is Hookean) at all times, thereby greatly simplifying definition of the elastic energy stored in the material prior to fracture. The most... 

Soutis, Fleck, and Smith [22], proposed the use of linear elastic fracture mechanics and the principle of superposition to determine the failure strength of composites with holes, in particular, under compression. This approach essentially models the damage developing at the edge of the hole as a crack with loaded surfaces. This is a one-parameter model as the crack surface stress must be determined by tests. 

Rates of CF crack propagation are uniquely defined by the linear elastic fracture mechanics stress intensity factor range that combines the effects of applied load, crack size, and geometry 17,40. The similitude principle states that fatigue and CF cracks grow at equal rates when subjected to equal values of AK [6-S]. The dal N versus AK relationship may be complex however, an effective approach is based on a power (or Paris) relationship of the form [4/]... 

Principles of linear elastic fracture mechanics (LEFM)... 

The model Is based on elastic-plastic fracture mechanics principles, and Incorporates effects associated with thermal expansion mismatch and modulus mismatch of various constituents, as well as non-linear material behavior as a function of load and temperature. Key properties of the constituents, such as those of the interlayer, reaction zone, and base material are provided as a data base these data were measured in this program by using bulk samples, The model then uses the processing history, specimen geometry and loading conditions to evaluate the performance of the joint, The results of finite element analysis of cracked specimens have been consolidated In arriving at the engineering model, JADM,... 

A notable feature of this experimental arrangement is the non-linear relationship that holds between force P and angle 0, a measure of deformation, Eq. (24). Provided that the system is elastic, the principles of fracture mechanics can be applied to systems that follow nonlinear relations between load and deflection. Another example is given in the next section. 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

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