Behavioural problems failure

Often in stress analysis we may be required to make simplified assumptions, and as a result, uneertainties or loss of aeeuraey are introdueed (Bury, 1975). The aeeuraey of ealeulation deereases as the eomplexity inereases from the simple ease, but ultimately the eomponent part will still break at its weakest seetion. Theoretieal failure formulae are devised under assumptions of ideal material homogeneity and isotropie behaviour. Homogeneous means that the materials properties are uniform throughout isotropie means that the material properties are independent of orientation or direetion. Only in the simplest of eases ean they furnish us with the eomplete solution of the stress distribution problem. In the majority of eases, engineers have to use approximate solutions and any of the real situations that arise are so eomplieated that they eannot be fully represented by a single mathematieal model (Gordon, 1991). 

It may be seen from Fig. 2.80 that some plastics experience the change from ductile to brittle behaviour over a relatively narrow temperature range. This permits a tough/brittle transition temperature to be quoted. In other plastics this transition is much more gradual so that it is not possible to attribute it to a single value of temperature. In these circumstances it is common to quote a Brittleness Temperature, rg(l/4). This temperature is defined as the value at which the impact strength of the material with a sharp notch (1/4 mm tip radius) equals 10 kJ/m. This temperature, when quoted, gives an indication of the temperature above which there should be no problems with impact failures. It does not mean that the material should never be used below Tb(1/4) because by definition it refers only to the sharp notch case. When the material has a blunt notch or is un-notched its behaviour may still be satisfactory well below Tb(1/4). 

Failures are modeled as deviations from the normal behaviour of a component (observed on the component s interface). The modeling is achieved by altering the specification of a component and its interaction with other components. To provide for completeness of failure modes we follow a systematic procedure of failure mode identification. The problem is to formulate hypotheses about potential failure modes of a component X and to decide which of them are included in further analyses (by accepting or rejecting the failure hypotheses). In order to control the completeness of failure hypotheses we apply the following criteria. 

Specimens are loaded under drained conditions. Pore pressure is measured in order to check possible excess pore water pressure. Several times before failure, loading is stopped. Axial force is kept constant and when pressure equilibrium is installed through the specimen, permeability measurement is performed using a transient method the pulse technique. This method has been introduced by Brace et at. (1968) to measure very low permeability (less than 10 m"). The more classical steady state method is inadequate because of the very low flow induced. In addition the time to reach steady state can be very large, indicating stability problems in time (long term behaviour of the specimen, chemical effects). Theoretical data analysis of pulse method is based on the diffusion equation of pressure wave. The specimen is surrounded by two reservoirs and the system is under equilibrium (at the same water pressure). A pulse of pressure is created at one end of the specimen and the propagating wave induced is recorded at the other end. Pore pressure then reaches a new equilibrium. The shape of the wave... 

But it is not only the number of the solutions which matters their character assumes predominant importance in some problems, and this in various peculiar ways which, however, it is only expedient to introduce as the interpretation of experimental facts demands. One concrete example arises from certain of the facts already considered. The necessity for the quantum theory itself emerges clearly from the failure of the kinetic theory to provide without it an adequate description of the energy content of matter. The need for further postulates is shown by the failure of the ideas so far introduced to account adequately for the detailed behaviour of the specific heat of hydrogen. 

A future trend in composite bolted joint design is the use of more advanced continuum damage mechanics approaches to model joint failure, so that non-linear shear behaviour and gradual stiffness degradation can be implemented. An important element of joint failure is delamination, and many efforts are being undertaken to implement delamination in finite element models. However, for bolted joints analysis this poses many problems due to the large number of delamination interfaces in thick laminates. 

We have just found that, for large molecules, the predicted behaviour is the same whether we use the separable or the non-separable model. Clearly, then, many situations where randomisation failure is thought to be a factor can be examined quite adequately by using the separable approach. One can envisage three such possible situations. Of obvious contemporary interest is the problem of multiphoton dissociation of large... 

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