Force Fracture

The fracture energy for influxes with a maximum fracture force F is determined by... 

This is a very important relationship in that it permits the fundamental material property Gc to be calculated from the fracture force, Fc, and the variation of compliance with crack length. 

AB cements tend to be essentially brittle materials. This means that when subjected to mechanical loading, they tend to rupture suddenly with minimal deformation. There are a number of different types of strength which have been identified and have been determined for AB cements. These include compressive, tensile and flexural strengths. Which one is determined depends on the direction in which the fracturing force is applied. For full characterization, it is necessary to evaluate all of these parameters for a given material no one of them can be regarded as the sole criterion of strength. 

The manner in which a particle fractures depends on (i) the nature of the particle and (ii) the manner in which the fracture force is applied. A number of terms have been used to describe the different mechanisms of single particle fracture. The different terms considered here are abrasion, cleavage, shatter, and chipping. It may be pointed out that in practice these events do not occur in isolation. Real breakage involves a combination of these processes, with the proportions changing, depending on the equipment, and on the manner each particle is stressed within it. 

Davis, S.P., et al. 2004. Insertion of microneedles into skin Measurement and prediction of insertion force and needle fracture force. J Biomech 37 1155. 

Typical examples of load-time traces of pre-cracked Charpy specimens at impact rates from 0.1 up to 3.3 m/s are shown in Fig. 4a for PVC. While the recorded non-damped signal up to about 0.5 m/s is of sufficient quality to directly determine the fracture force, Fp, significant force oscillations are visible on the signals for higher loading rates. 

The value of 2 can be used to find a chain scission force//, = arraZ(,/2 if the crazing stress ocraze is known, using reasoning similar to that used for the transition from chain pullout to crazing considered in the previous section. This fracture force should be characteristic of the fracture of a C-C bond and therefore not only independent of N, but also independent of the detailed molecular structure of the polymer. This appears to be indeed the case and the results obtained for several experimental systems [22,37,39,40,46] all yield a very similar value of/, -2x10 N. 

Figure 2. Bending fracture force versus rubber content for U-notched specimens.

This theory relates the force needed to separate the two surfaces to the mucoadhesive strength and is widely applied in research, where force of detachment versus distance is normally measured. In general, the fracture stress (considered to be equivalent to the mucoadhesion stress) is calculated by dividing the fracture force by the area of contact in the mucoadhesive bond. In the same study, fracture energy (or work of mucoadhesion) can be obtained as the area under the curve in the force versus distance plot. Nowadays, instruments measure directly the force of mucoadhesion between two surfaces in contact as a function of distance and time. 

Equatimi (14) perfectly explains the degradatimi behavior ((7) and (9)) of polymer chains in QSSF observed by Odell and Keller [27,28,97-99,101,102,129]. Moreover, the fracture force obtained from (13) corresponds to the strength of C-C bond calculated using Morse potential [27, 28,129]. Additionally, the above equation is... 

Fig. 41 (a) Model of a ladder-like polymer formed by interpolymer associations (highlighted by red dashed lines) [279]. The flow direction is horizontal, (b) Increase of the maximnm Icmgth permissible Wiad/Min in the ease of a ladder-like polymer as compared to a linear polymer, for the same fracture force. The legend indicates different normalized bead size ajh. (Adopted with permission from Agarwal et al. [279]. Copyright 1994 American Institute of Physics)... 

In the course of analysing the fracture force was determined and the fracture pattern was judged. 

Of course, the deflection is also influenced greatly by the way in which the forces are applied to the composite body in order to stimulate fracture. Forces can... 

Because the fracture force P is, in principle, constant, it will only fluctuate if the bond strength itself is variable. Thus variations in the fracture force can he directly associated with variations in the strength of adhesion. 

The mechanics of microneedle insertion are fundamentally important to practical applications. Only microneedles with the correct geometry and physical properties can be inserted into tissues. When the force required for insertion is too large compared with needle strength, microneedles can break or bend before insertion occurs. Two mechanical events play a critical role in microneedle insertion the force required to insert microneedles and the force needles can withstand before fracturing. The fracture force must be larger than the insertion force for the microneedles to be functional. 

For constant strength of the solid bridges. Fig. 7 shows the ratio of the median fracture force and the CToss-section area of the aggregates as a function of the structure characteristics according to the Rumpf formula (Eqs. 2 and 3). As... 

Fig. 7 Median fracture force of the silica model aggregates with various primary particle sizes as function of the elementary breaking stress according to Rumpf (simplified strength of the solid bridge, CTsb> is assumed constant)...

---