Critical specimen size

If one applies tensile stress on a solid, the solid elongates and gets strained. The stress (a) - strain (e) relation is linear for small stresses (Hooke s law) after which nonlinearity appears, in some cases. Finally at a critical stress CTf, depending on the material, amount of disorder and the specimen size etc., the solid breaks into pieces fracture occurs. In the case of brittle solids, the fracture occurs immediately after the Hookean linear region, and consequently the linear elastic theory can be applied to study the essentially nonlinear and irreversible static fracture properties of brittle solids (Lawn and Wilshaw 1975, Thomson 1986, Evans and Zok 1986). 

Bazant formulated a statistical theory of fracture for quasibrittle materials [5, 23, 24]. He assumed that there exist several hierarchical orders which each can be described by parallel and serial linking of so-called representative volume elements (RVEs). For large specimens (and low probability of failures) the fracture statistics is equal to the Weibull statistics, i.e. if the specimens size is larger than 500 to 1000 times of the size of one RVE. In the actual case this is similar to the diameter of the critical flaw. For smaller specimens the volume effect disappears and the fracture... 

Fig. 2 Diameter of the critical flaw size (d = 2a, ) versus the volume of the specimen (full line) in a double logarithmic plot. The edge length of a cube having the effective volume is also shown (bold, dashed line).

Strength test results on ceramic specimens show, in general, a large scatter. This follows from the fact, that in each individual specimen, the size of the critical crack is a little different. Rearranging Eq. (8) provides a relationship for the critical crack size (Griffith crack size) in a specimen ... 

We have also received and ultrasonically examined 21 silicon nitride tensile specimens. These samples are cylindrical and have a diameter of 6.4 mm in the gage section, which was the only region inspected. The evaluation was conducted using a 75-MHz. spherically focused transducer. As we have mentioned in previous reports, the sharply curved entry surface of small-diameter cylindrical specimens introduces both severe astigmatism and spherical aberration in the ultrasonic beam distribution inside the solid and limits the depth at which critical flaw sizes can be detected to a few hundred microns. Our work has indicated that this limitation could be greatly reduced by aspherical shaping of the transducer lens, but the cost of such a transducer has thus far proved prohibitive. No indications were observed in any of the specimens although we could not perform a 100% inspection on any of the rods because of equipment limitations. 

The selection of the specimen size is critically important in preparing polished sections. Relatively small specimens with a section surface area of 100 mm are preferable. These are considerably easier and quicker to prepare than very small or very large specimens. 

Fracture mechanics is a systems approach to estimate the relationship between the stresses, the flaw geometry, and the material properties as it relates to the structural integrity of the component under consideration. The primary objectives are to prevent failures, promote effective design, and make efficient use of materials. The modern approach seeks a parameter that is a measure of the material s toughness that is independent of the geometry, and can be used with stress analysis to predict fracture loads and critical crack sizes. Using this toughness value from a test specimen in the laboratory, the flaw sizes at which fracture will occur for the structural component used in service can be predicted. The reverse scenario is also... 

ASTM E132 was developed as an improvement on the apparatus in ASTM E162 [38]. The specimen size for flame spread studies is 155 by 800 mm by a maximum thickness of 50 mm. This test method determines the critical flux for flame spread, the surface temperature needed for flame spread and the thermal inertia or thermal heating property (product of the thermal conductivity) test. These properties are used mainly for assessment of fire hazard and for input into fire models. A flame spread parameter is also determined, and this can be used as a direct way of comparing the responses of the specimens. It has been used for predictions of full-scale flame performance [39]. 

Winzer et al. [69] compared the LIST and the CERT in the evaluation of TGSCC of AZ91 in distilled water and 5g/L NaCl. The LIST apparatus [82], illustrated in Fig. 8.18, is based on the lever principle. The specimen is attached to one end of the lever arm. A known mass is attached to the other end. The tensile load applied to the specimen increases linearly as the distance between the fulcrum and the mass is increased by means of a screw thread and synchronous motor. LIST is load controlled whereas CERT is extension controlled. They are essentially identical until SCC initiation. Thereafter, LIST ends as soon as a critical crack size is reached whereas CERT can take much longer as typically CERT only ends when the final ligament suffers ductile rapture. 

Specimens that were water quenched from a temperature difference of 400 °C had a strength distribution (504 46 MPa) that was above the threshold thermal shock value (70% of 525 MPa = 368 MPa). In contrast, specimens quenched at a temperature difference of 500 °C had a strength distribution (230 145 MPa) that fell below the thermal shock threshold value. Thus, the flexural strength after thermal shock was affected by both the critical crack size and the location of the flaw in the test bar. 

Traditionally, turbidity or opacity has been used for detecting the cloud-point curve (CPC), which approximated the bimodal of the phase diagram. Evolution of this approach involved application of laser light scattering, which combined with small specimen size and precise temperature control led to the pulse-induced critical scattering (PICS) for spinodal determination. Unfortunately, the method is limited to the size of heterogeneity > 100 nm and the difference in refractive index of the two phases > 0.01. ° i... 

In numerous applications of polymeric materials multilayers of films are used. This practice is found in microelectronic, aeronautical, and biomedical applications to name a few. Developing good adhesion between these layers requires interdiffusion of the molecules at the interfaces between the layers over size scales comparable to the molecular diameter (tens of nm). In addition, these interfaces are buried within the specimen. Aside from this practical aspect, interdififlision over short distances holds the key for critically evaluating current theories of polymer difllision. Theories of polymer interdiffusion predict specific shapes for the concentration profile of segments across the interface as a function of time. Interdiffiision studies on bilayered specimen comprised of a layer of polystyrene (PS) on a layer of perdeuterated (PS) d-PS, can be used as a model system that will capture the fundamental physics of the problem. Initially, the bilayer will have a sharp interface, which upon annealing will broaden with time. 

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