Fracture probability

A glass drying trap on a hydrochloric acid storage tank was filled with silica gel instead of the calcium sulfate specified. The glass trap fractured, probably owing to thermal shock from the much higher heat of adsorption of water and hydrogen chloride on silica gel. 

Kanis JA, Johnell O, De Laet C et al. (2002) International variations in hip fracture probabilities implications for risk assessment. J Bone Miner Res 17(7) 1237-1244 Kemppainen H, Raiha I, Sourander L (1997) Clinical presentation of peptic ulcer in the elderly. Gerontology 43(5) 283-288... 

This method was used in the examination of an Eskimo who died 1600 years ago. The body was discovered in a frozen state on St. Lawrence Island, Alaska in 1972 and remained frozen until it was brought to Fairbanks in 1973. Examination of the female individual revealed that she had a skull fracture, probably resulting from instant bunal caused by a landslide. Aspaitic acid laceiuization analysis of a tooth from the mummy yielded an age at death of 53 5 years, which correlated well with earlier estimates based upon morphological features. This method is an example of the need to preserve mummies (Alaskan. Egyptian, and Peruvian, among others) for application of new dating techniques as they develop. 

Judging by the composition of water encountered in the shallow aquifers, which resemble the deep water of the Botucatu, it is possible that great fractures exist in the Basalto with a vertical extension of 400—500 m. These fractures probably permit a vertical ascending circulation of water from the Botucatu into the Bauru aquifer. The ascending warm water may become enriched with constituents in the Basalto and cause secondary mineralization. 

Figure 15. Weibull plot of biaxial flexural strength data, Op tor LIST dental porcelain with and without ion exchange. Dotted lines are 95% confidence interval m is Weibull modulus, Uq is characteristic strength, and 05% is fracture stress at 5% fracture probability. Data from [71]...

It s a must to apply a material suitable module- and joining technique for the complex stress collective. For the ceramic components it s necessary to detect the in use mechanical, thermal and chemical loads. To analyze the stress field the FEA (Finite-Element-Analysis) is a suitable tool to calculate the particular stress distributions. In the next step the stress distributions (axial and torque loads) will be superposed to get an idea of the whole stress field. Furthermore with the FEA it s possible to calculate the tension stressed volume (VefO for these geometric complex components and offers the possibihty to calculate fracture probabilities according to the WeibuU-Theory. 

The pressure-difference over the thread was estimated with Ap=80 bars. This assumption contains an approximate security loading of about 40% to the realistic case of operation. The torque at the torque transmission point was estimated with Mt=1100 Nm. The midsection auger segment shows a fracture probability of Fb=7,5-10 % and that for the end auger segment of Fb=6,23-10 %, both made of SSiC. These positive results admit the application of ceramic segments for extrusion process. 

According to the Weibull distribution, the fracture probability Pf is expressed by... 

Determine the fracture probability of structures and components. This is rather conventionally undertaken using fragility curves which relate the conditioned probability of fracture with the maximum acceleration of the component/struc-ture. The simplification introduced by the fragility curves consists in the fact that they are supposed to depend on three parameters only a median rupture acceleration, /, and two logarithmic standard deviations (log-normal distribution), Par and Pav, related to the intrinsic variability of the component behaviour and to the variability... 

Table 14-1 shows a summary of some available statistics for both destructive events and nondestructive breaks, the latter include all the cases of fractures discovered in time or which could become destructive and all those minor fractures, probably not potentially destructive, that required intervention because of their size. The principal causes of the reported fractures are fatigue (mechanical, thermal or corrosion assisted) associated with pre-existing fabrication defects, generally corresponding to structural discontinuities such as appendages, penetrations, etc. 

A statistical definition of brittleness can be formulated in terms of the Weibull distribution of fracture probability for a material (Derby et al., 1992). The Weibull modulus m (see Eq. 2) can range from zero (totally random fracture behaviour, where the failure probability is the same at all stresses, equivalent to an ideally brittle material) to infinity (representing a precisely unique, reproducible fracture stress, equivalent to an ideally non-brittle material). 

Fig. 7.73 Fracture probability of polished and shot peened samples (N3208), respectively, determined in static and cyclic ball-on-plate tests. Note that in case of the static tests of the shot peened samples the capacity of the test equipment was exceeded [23], With kind permission of Elsevier...

Observe in Fig. 7.73 that the static-load capacity of the polished reference samples is 4 kN at a 50 % fracture probability, whereas the cyclic-load capacity of the SP silicon nitride samples is 10.4 kN. The SP treatment increased the static-load capacity to more than 16 kN. Thus, the static load capacity is about 4 times higher. The capacity of the testing device was not high enough to introduce any cracks into the SP surfaces. From the no failure results of the static load up to... 

A maximum compressive-residual stress of 300 MPa is observed on the surface of the SP specimen, decreasing in the depth direction. In the case of the SP + CH specimen, the residual stress also decreased, but still exhibited a compressive-residual stress of 200 MPa. However, the induction of compressive-residual stress was accompanied by simultaneous CH. SP, in combination with CH, is a useful technique for improving the strength of ceramics, as may be seen in Fig. 7.82, which compares plots of the fracture probability against the crack-initiation load. 

The proposed failure theory for slow crack growth Is a probabilistic methodology based on the principles of fracture mechanics. Component failure probability starts at the fast fracture probability and deteriorates with time. In addition to the fast fracture material constants, two additional constants representing the deterioration of mean strength with time are determined from testing. The approach considers both area and volume reliabilities. The software for this task Is completed and incorporated Into the CARES code. 

Table 11.1.8 shows the influence of the shaft types on silicon nitride ring fracture. The tests were conducted 15 times for each type of shafts. If fracture interference values at a cumulative fracture probability of 50% are compared for the three types of shafts, it can be seen that the interference values of the hollow and spline shafts are approximately 1.3 times greater than that of the solid shaft. Consequently, it can be said that compared with a solid shaft, a hollow or a spline shaft contributes to the relief of the circumferential stress generating in the bore surface of the silicon nitride ring, and makes the fracture... 

Numerous studies have been undertaken to identify metastatic lesions in tubular bones, which are at risk of fracture. However, most of these studies lack a well-performed statistical basis. One of the most reliable risk analyses for fractures of the tubular bones was performed by Mirels, who proposed a classification system (Mirels 2003 Damron et al. 2003). It includes four risk factors (1) location, (2) lesion type, (3) pain, and (4) lesion size. To every risk factor, 1-3 points are allotted. Scores range from 4 to 12 points. The fracture risk increases exponentially when a sum score more than 8 points is obtained (Table 35.1). A score of 8 is suggestive of an impending fracture (probabihty of a fracture 15%), while a score of 9 is found to be diagnostic for a fracture (probability of a fracture 33% no false positives in this group). When a score of 7 or less is obtained, the probability of a fracture is low (5%). Such a lesion can be treated conservatively. In patients with a score of at least 9, prophylactic surgery is reconunended. If the sum is 8, then an individual decisions should be made. 

The Hertz method of determining Kc involves the use of an optically flat surface and a blunt— i.e., spherical— indenter. The sphere is pressed with a series of loads P until a critical load P ris found that gives a 50% chance of Hertz ring crack formation. In practice this is found by plotting the fracture probability against applied load for any given indenter radius a typical plot would look like Figure 5.18. 

The total componors fracture probability p in mechanical tests is obviously equal to one. Further this value is divided at the conditionp =p +P2 follows. In Fig. 14.10, the dependence of fracture stress a on extrusion draw ratio X for componor UHMPE-Al is shown. As one can see, the growth is ceased and changes to drop(compare with the plot of Fig. 14.6). Such the dependence Oj( l) type is due to interfacial boundaries pol5mier-filler fracture at > 5 [44]. Hence, at < 5 the fracture of pol5mier matrix and interfacial boundary is equally probable (p =p = 0.5) and at A, > 5 the second fracture probability is higher (p >P2)- In addition it is assumed, that at A 5 is... 

At the (P = 0.1) line, 10% of the test specimens are fractured, at the middle line 50%, at the (P= 0.9) line 90% failed. It is obvious that the width of fracture probability (number of stress cycles) increases with decreasing load. 

Figure 1.65 S-Nlines fracture probability as fatigue criterion scatter width increases with...

Tlexural strength value at 50% fracture probability. Sources ASM Handbooks, Volumes 1 and 2, Engineered Materials Handbooks, Volumes 1 and 4, Metals Handbook Properties and Selection Nonferrous Alloys and Pure Metals, Vol. 2, 9th edition, Advanced Materials Processes, Vol. 146, No. 4, and Materials Processing Databook (1985), ASM International, Materials Park, OH Modern Plastics Encyclopedia The McGraw-Hill Companies, New York, NY R. F. Floral and S. T. Peters, Composite Structures and Technologies, tutorial notes, 1989 and manufacturers technical data sheets. ... 

P(AilAkii ) represents the non-fracture probability of the k-th element under the condition of non-fracture of the k-l-th element. 

Substitute the negative experiential distribution in (11) and let AV is sufficient small the fracture probability can be written as follows... 

In Figure 3.12 a computer simulation by Dobrodumov et al. of the fracture development within a regular model lattice is shown [58]. The authors have taken the ratio of the elastic constants in and perpendicular to the direction of orientation as 10 1 and an element fracture probability as given by Eq. (3.23). The distribution of local stresses was determined by a numerical iteration procedure. It is readily observed that for small loads (P q/RT = 5) a large number of isolated defects appear before (from the accidental accumulation of a few defect points) a crack starts growing. At higher loads ( 3>Fo/RT = 20) a smaller number of defect points initiate... 

If the fracture probability P is associated with a breaking stress a of a specimen of volume V, then a breaking stress L corresponds to the same probability value, for a volume stracture V made up of the same material, processed and treated in strictly identical conditions, with ... 

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