Keywords: driving force, fracture mechanisms, structural integrity.
Fracture mechanics is considered as mechanics of fracture mechanisms and not as a theory of a crack in a plate. The thesis of R.W. Hamming 'Purpose of computing is insight, not numbers' is highly important for the approach.
Perceiving information a designer is apt to prefer drawings and graphs to formulas, text and long explanations. In addition, such obligatory principal notions as fracture mechanisms, driving force, critical state equation are necessarily involved in teaching each section of fracture mechanics. The well-structured presentation of every section (Table) is efficient for examination of arising problems. The principal topics of fracture mechanics are: 1) brittle fracture; 2) mixed mode fracture; 3) elasto-plastic fracture; 4) fatigue. The key notions are presented in the following order : 1) macroscopic fracture mechanism; 2) definition of driving force appropriate to the mechanism; 3) engineering approaches for practical use of fracture criteria. Thus, in the classic problem of a crack under tension the failure takes place when the stress intensity factor (SIF) reaches its critical value. The factor determines stress state in the crack tip vicinity. Diagrams 'critical stress - defect size' make possible to solve several kinds of engineering problems. For the 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 (mode I, II, III) and fracture mechanisms (breaking (A), shear (B),). Direction of propagation and the moment of fracture initiation depend on stress distribution in the crack tip (radial direction). The distribution can be expressed by equivalent stress intensity factors KA and KB. The engineering approach considers several possible fracture mechanisms. Shear is the basic macromechanism of plastic deformation and fracture. Forms of the plastic zones may be sufficiently different. Strain energy release rate or J-integral characterize the stress-strain state. The engineering approach considers two cases: full-scale plasticity and breaking from the crack tip. Fatigue crack growth rate depends on the range of the (equivalent) stress intensity factor, the propagation has different stages and the diagram has different characteristic parts. The engineering approach is to use s-N curves.
|
FRACTURE |
LOADING |
DEFORMATION |
FATIGUE |
|
| MACRO-
MECHANISM |
breaking |
A breaking B shear |
 |
microshears |
| DRIVING
FORCE |
|
|
strain energy release rate G, J-integral |
 |
| ENGINEERING
APPROACH |
|
|
|
|
The next stage is to consider the influence of different factors on static and cyclic crack resistance characteristics (Fig. 2). Varying thickness or sizes of specimens, temperature, loading rate we show qualitative modifications (different mechanisms) and quantitative changes of crack resistance characteristics.
size (thickness) |
temperature |
loading rate, lg |
SIF K, lg |
Multiplicity and complexity of fracture of these materials greatly complicate application of the fracture mechanics methods. Nevertheless, some useful generalizations can be made. The order of sections is the following: description of macro mechanism, definition of damage parameters, driving force and analysis of engineering approaches. For fiber composites the damage parameters are fractions of fiber breaking, delamination and volume eliminated from the carrying system. The mechanism of fracture is 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 like for the foregoing. The governing parameters are nominal stresses (interlaminar, interply, fiber). The engineering approach answers the question how optimal fiber placement produces desired properties of composite structures. Damages of components in particulate reinforced composites are sufficiently different. 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 make reduce rigidity over certain zone, enlarge further the area and 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 principal features peculiar to many composites. Analysis of the critical strain allows to point out three classes of materials: 'reinforced matrix', 'composite', 'bundle of fibers'. The scale effect gives the following: there are qualitative distinctions between fiber and composite because of strength reservation. Consideration of probability makes this difference even more pronounced. For fatigue the stress-strain state parameters determine the rates of damage growth only for some characteristics of the damaged state. Since we work with complex unhomogenous microsystems - the composite materials it is efficient to demonstrate the structure of the materials, especially during the fracture process, the pictures of non-destructive control methods, computer films with results of structure imitation modeling. Analysis of real structures and failure causes takes a lot of teaching time.
volume fraction |
total length of fibres, lg |
fracture probability, lg |
driving force, lg |
