770

* Equivalent to 1% in 10,000 hours. t Equivalent to 1% in 100,000 hours. Not recommended for use where temperatures exceed 800°F.

* Equivalent to 1% in 10,000 hours. t Equivalent to 1% in 100,000 hours. Not recommended for use where temperatures exceed 800°F.

A shear fracture is indicated by a dull or fibrous appearance. A shiny or crystalline appearance is associated with a cleavage fracture.

The data obtained from a Charpy test are used to plot curves, such as those in Fig. 1.11, of energy or percentage of shear fracture as a function of temperature. The temperature near the bottom of the energy-temperature curve, at which a selected low value of energy is absorbed, often 15 ft • lb, is called the ductility transition temperature or the 15-ft • lb

FIGURE 1.11 Transition curves from Charpy-V notch impact tests. (a) Variation of percent shear fracture with temperature. (b) Variation of absorbed energy with temperature.

FIGURE 1.11 Transition curves from Charpy-V notch impact tests. (a) Variation of percent shear fracture with temperature. (b) Variation of absorbed energy with temperature.

transition temperature. The temperature at which the percentage of shear fracture decreases to 50% is often called the fracture-appearance transition temperature. These transition temperatures serve as a rating of the resistance of different steels to brittle fracture. The lower the transition temperature, the greater is the notch toughness.

Of the steels in Table 1.1, A36 steel generally has about the highest transition temperature. Since this steel has an excellent service record in a variety of structural applications, it appears likely that any of the structural steels, when designed and fabricated in an appropriate manner, could be used for similar applications with little likelihood of brittle fracture. Nevertheless, it is important to avoid unusual temperature, notch, and stress conditions to minimize susceptibility to brittle fracture.

In applications where notch toughness is considered important, the minimum Charpy V-notch value and test temperature should be specified, because there may be considerable variation in toughness within any given product designation unless specifically produced to minimum requirements. The test temperature may be specified higher than the lowest operating temperature to compensate for a lower rate of loading in the anticipated application. (SeeArt. 1.1.5.)

It should be noted that as the thickness of members increases, the inherent restraint increases and tends to inhibit ductile behavior. Thus special precautions or greater toughness, or both, is required for tension or flexural members comprised of thick material. (See Art. 1.17.)

Fracture-Mechanics Analysis. Fracture mechanics offers a more direct approach for prediction of crack propagation. For this analysis, it is assumed that a crack, which may be defined as a flat, internal defect, is always present in a stressed body. By linear-elastic stress analysis and laboratory tests on a precracked specimen, the defect size is related to the applied stress that will cause crack propagation and brittle fracture, as outlined below.

Near the tip of a crack, the stress component / perpendicular to the plane of the crack (Fig. 1.12a) can be expressed as

V2^r where r is distance from tip of crack and K, is a stress-intensity factor related to geometry

FIGURE 1.12 Fracture mechanics analysis for brittle fracture. (a) Sharp crack in a stressed infinite plate. (b) Disk-shaped crack in an infinite body. (c) Relation of fracture toughness to thickness.

FIGURE 1.12 Fracture mechanics analysis for brittle fracture. (a) Sharp crack in a stressed infinite plate. (b) Disk-shaped crack in an infinite body. (c) Relation of fracture toughness to thickness.

of crack and to applied loading. The factor K, can be determined from elastic theory for given crack geometries and loading conditions. For example, for a through-thickness crack of length 2a in an infinite plate under uniform stress (Fig. 1.12a), where fa is the nominal applied stress. For a disk-shaped crack of diameter 2a embedded in an infinite body (Fig. 1.12b), the relationship is

If a specimen with a crack of known geometry is loaded until the crack propagates rapidly and causes failure, the value of KI at that stress level can be calculated from the derived expression. This value is termed the fracture toughness Kc.

A precracked tension or bend-type specimen is usually used for such tests. As the thickness of the specimen increases and the stress condition changes from plane stress to plane strain, the fracture toughness decreases to a minimum value, as illustrated in Fig. 1.12c. This value of plane-strain fracture toughness designated KIc, may be regarded as a fundamental material property.

Thus, if KIc is substituted for K„ for example, in Eq. (1.15) or (1.16) a numerical relationship is obtained between the crack geometry and the applied stress that will cause fracture. With this relationship established, brittle fracture may be avoided by determining the maximum-size crack present in the body and maintaining the applied stress below the corresponding level. The tests must be conducted at or correlated with temperatures and strain rates appropriate for the application, because fracture toughness decreases with temperature and loading rate. Correlations have been made to enable fracture toughness values to be estimated from the results of Charpy V-notch tests.

Fracture-mechanics analysis has proven quite useful, particularly in critical applications. Fracture-control plans can be established with suitable inspection intervals to ensure that imperfections, such as fatigue cracks do not grow to critical size.

(J. M. Barsom and S. T. Rolfe, Fracture and Fatigue Control in Structures; Applications of Fracture Mechanics, Prentice-Hall, Inc. Englewood Cliffs, N.J.)

Stresses that remain in structural members after rolling or fabrication are known as residual stresses. The magnitude of the stresses is usually determined by removing longitudinal sections and measuring the strain that results. Only the longitudinal stresses are usually measured. To meet equilibrium conditions, the axial force and moment obtained by integrating these residual stresses over any cross section of the member must be zero.

In a hot-rolled structural shape, the residual stresses result from unequal cooling rates after rolling. For example, in a wide-flange beam, the center of the flange cools more slowly and develops tensile residual stresses that are balanced by compressive stresses elsewhere on the cross section (Fig. 1.13a). In a welded member, tensile residual stresses develop near the weld and compressive stresses elsewhere provide equilibrium, as shown for the welded box section in Fig. 1.13b.

For plates with rolled edges (UM plates), the plate edges have compressive residual stresses (Fig. 1.13c). However, the edges of flame-cut plates have tensile residual stresses (Fig. 1.13d). In a welded I-shaped member, the stress condition in the edges of flanges before welding is reflected in the final residual stresses (Fig. 1.13e). Although not shown in Fig. 1.13, the residual stresses at the edges of sheared-edge plates vary through the plate

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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