FRACTURE MECHANICS

Keywords: driving force, fracture mechanisms, structural integrity.

Fracture mechanics is considered the mechanics of fracture mechanisms rather than a theory of a crack in a plate, and R.W. Hamming's 'Purpose of computing is insight, not numbers' is highly important for the approach.


Fracture mechanics models for isotropic materials

Designers ted to prefer drawings and graphs to formulas, text, and long explanations. In addition, such obligatory principal notions as fracture mechanism, driving force, and critical state equation are necessarily involved in the teaching of each section of fracture mechanics. The well-structured presentation of every section (see the table) is efficient for the examination of arising problems. The principal topics of fracture mechanics are: 1) brittle fracture; 2) mixed mode fracture; 3) elasto-plastic fracture; and 4) fatigue. The key notions are presented in the following order : 1) the macroscopic fracture mechanism; 2) the definition of driving force appropriate to the mechanism; and 3) the engineering approaches for the practical use of fracture criteria. Thus, in the classic problem of a crack under tension, failure ocurs when the stress intensity factor (SIF) reaches its critical value. The factor determines the stress state in the crack tip vicinity. Diagrams of 'critical stress and defect size' make it possible to solve several kinds of engineering problems. For mixed mode loading there are two principal macroscopic fracture mechanisms initiating new cracks in two different directions: breaking and shear. It is necessary to distinguish the loading mode (modes I, II, and III) and fracture mechanisms (breaking (A), shear (B)). The direction of propagation and the moment of fracture initiation depend on the stress distribution in the crack tip (radial direction). The distribution can be expressed by equivalent SIF KA and KB. The engineering approach considers several possible fracture mechanisms. Shear is the basic macromechanism of plastic deformation and fracture. The forms of the plastic zones can be sufficiently different. The strain energy release rate, or J-integral, characterizes the stress-strain state. The engineering approach considers two cases: full-scale plasticity and breaking from the crack tip. The fatigue crack growth rate depends on the range of the (equivalent) SIF, and the propagation has different stages and the diagram different characteristic parts. The engineering approach is to use s-N curves.

BRITTLE
FRACTURE
MIXED MODE
LOADING
ELASTO-PLASTIC
DEFORMATION

FATIGUE

MACRO-

MECHANISM

breaking


A breaking
B shear

microshears
DRIVING

FORCE


stress intensity
factor SIF


Equivalent SIF:
KA KB


strain energy
release rate G,
J-integral
ENGINEERING

APPROACH


crack length




The next stage is to consider the influence of different factors on static and cyclic crack resistance characteristics (Fig. 2). Using varying thicknesses or sizes of specimens, temperature, and loading rates we can show qualitative modifications (different mechanisms) and quantitative changes of crack resistance characteristics.


size (thickness)

temperature

loading rate, lg

SIF K, lg
Crack resistance characteristics


Fracture mechanics of composite materials.

The multiplicity and complexity of the fracture of these materials greatly complicate the application of the fracture mechanics methods. Nevertheless, some useful generalizations can be made. The order of sections is as follow: the description of the macro-mechanism, the definition of damage parameters, and the driving force and analysis of engineering approaches. For fiber composites the damage parameters are the fractions of fiber breaking, delamination, and volume eliminated from the carrying system. The mechanism of fracture is a step-by-step enlargement of the damaged zone. The governing parameter of the stress-strain-damage state of the composite is one of energy characteristics and/or nominal strain. The engineering approach can yield the critical strain value and, consequently, the critical stress value. Damage parameters for laminate composites are defined as for the foregoing. The governing parameters are nominal stresses (e.g. interlaminar, interply, and fiber). The engineering approach answers the question of how optimal fiber placement produces the desired properties of composite structures. Damaged of components in particulate reinforced composites are sufficiently different. The brittleness and plasticity of the components affect the fracture mechanisms and strength parameters of the composites. The engineering approach can yield the critical stress value. In large-scale composite structures, microdamages can reduce rigidity over a certain zone, enlarge further the area, or grow a macrocrack grow. Energy parameters for the damaged zone define the moment of full-scale fracture initiation. The engineering approaches use s-N curves.

After this, we focus our attention on the principal features peculiar to many composites. The analysis of the critical strain allows us to point out three classes of materials: 'reinforced matrix', 'composite', and 'bundle of fibers'. The scale effect suggests there are qualitative distinctions between fiber and composite because of strength reservation. The consideration of probability makes this difference even more pronounced. For fatigue the stress-strain state parameters determine the rates of damage growth for only some characteristics of the damaged state. Since we work with complex heterogeneous microsystems, the composite materials, it is efficient to demonstrate the structure of the materials, especially during the fracture process, as well as the pictures of non-destructive control methods and computer films with the results of structure imitation modeling. The analysis of real structures and reasons for failure causes take a lot of teaching time.


volume fraction

total length of fibres, lg

fracture probability, lg

driving force, lg
Mechanical properties of composite materials

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