This article describes how NDT, FTE, and FTP are used in engineering design through the fracture analysis diagram (FAD). The temperature dependence of yield strength, tensile strength, and fracture strength is explained, along with the influence of various initial flaw sizes and the dynamic tear test (DT), which serves as a highly versatile test for both low-strength ductile materials and high-strength low-toughness materials. The fracture analysis diagram provides engineers with a comprehensive tool for understanding the relationship between flaw size, stress, and temperature in structural steel design.
The first part of this article introduced several terms dealing with brittle fracture, including NDT, FTE, and FTP. The tests for determining these transition temperatures have been described. Before examining how these parameters are used in engineering design through the fracture analysis diagram, we must redefine these transition points by referencing the basic properties of the tension test.
The subambient temperature dependence of yield strength σo (Rp0.2) and ultimate tensile strength σu in a body-centered cubic (bcc) metal demonstrates critical behavior patterns for fracture analysis.For an unnotched specimen without flaws, the material remains ductile until reaching a very low temperature at point A, where σo equals σu. Point A represents the NDT temperature for a flaw-free material. The curve BCD represents the fracture strength of a specimen containing a small flaw (a < 0.1). The temperature corresponding to point C is the highest temperature at which the fracture strength σf approximately equals σo. Point C represents the NDT for a specimen with a small crack or flaw.
Figure 1: Temperature dependence of yield strength (σo), tensile strength (σu), and fracture strength for a steel containing flaws of different sizes
The presence of a small flaw raises the NDT of steel by approximately 200°F (110°C). Increasing the flaw size decreases the fracture stress curve, as shown in curve EF, until a limiting curve of fracture stress HJKL is reached with increasing flaw size. Below the NDT, the limiting safe stress ranges from 5,000 to 8,000 psi (approximately 35 to 55 MPa).
Above the NDT, the stress required for unstable propagation of a long flaw (JKL) rises sharply with increasing temperature. This phenomenon defines the crack-arrest temperature curve (CAT). The CAT establishes the highest temperature at which unstable crack propagation can occur at any stress level. Fracture will not occur for any point to the right of the CAT curve.The fracture transition elastic (FTE) represents the temperature above which elastic stresses cannot propagate a crack. This is defined by the temperature when the CAT curve intersects the yield-strength curve at point K. The fracture transition plastic (FTP) occurs at the temperature where the CAT curve crosses the tensile-strength curve at point L. Above this temperature, the material behaves as if it is flaw-free, since any crack, regardless of size, cannot propagate as an unstable fracture.
Data obtained from the Drop Weight Test (DWT) and other large-scale fracture tests have been assembled by Pellini and coworkers into a useful design procedure called the fracture analysis diagram. The NDT as determined by the DWT provides a key data point for constructing the fracture analysis diagram. For mild steel below the NDT, the CAT curve remains flat.A stress level exceeding 5,000 to 8,000 psi (35 to 55 MPa) causes brittle fracture regardless of the initial flaw size. Extensive correlation between the NDT and Robertson CAT tests for various structural steels has demonstrated that the CAT curve maintains a fixed relationship to the NDT temperature. Therefore, NDT+30°F provides a conservative estimate of the CAT curve at stress of σo/2. NDT+60°F provides an estimate of the CAT at σ = σo (the FTE), and NDT+120°F provides an estimate of the FTP. Consequently, for structural steels, once the NDT has been determined, the entire scope of the CAT curve can be established sufficiently for engineering design.
The curve traced in Figure 2 represents the worst possible case for large flaws exceeding 24 inches. Engineers can envision a spectrum of curves translated upward and to the left for smaller, less severe flaws. Correlation with service failures and other tests has enabled the approximate determination of curves for various initial flaw sizes. Thus, the FAD provides a generalized relationship of flaw size, stress, and temperature for low-carbon structural steels typically used in ship construction.
Figure 2: Fracture-analysis diagram showing influence of various initial flaw sizes
The fracture analysis diagram can be utilized in several ways during the design process. One straightforward approach involves using the FAD to select steel with an FTE lower than the lowest expected service temperature. With this criterion, the worst expected flaw would not propagate as long as the stress remained elastic.However, this procedure may prove too expensive and overconservative. A slightly less conservative design against brittle fracture, while still maintaining a practical approach, would involve designing based on an allowable stress level not exceeding σo/2. From Figure 2, we observe that any crack will not propagate under this stress provided the temperature does not fall below NDT+30°F. For example, if the service temperature is not expected to drop below 10°F, we would select steel whose NDT is 10° - 30°, which equals -20°F.
The dynamic tear test (DT) can be used to construct the FAD effectively. Below the NDT, fracture is brittle and exhibits a flat, featureless surface devoid of tiny shear lips. At temperatures above the NDT, there is a sharp rise in energy for fracture, and the fracture surfaces begin to develop shear lips. The shear lips become progressively more prominent as temperature increases toward the FTE.Above the FTE, fracture becomes ductile, exhibiting void coalescence-type fracture characteristics. The fracture surface displays a fibrous slant fracture pattern. The upper shelf of energy represents the FTP. The lower half of the DT energy curve traces the temperature course of the CAT curve from NDT to FTE.The DT test serves as a highly versatile testing method because it proves equally useful with low-strength ductile materials that show a high upper energy shelf and with high-strength low-toughness materials that have low upper shelf energy values. The large size of the DT specimen provides a high degree of triaxial constraint and results in minimal scatter. Extensive correlations are being developed between DT results and fracture toughness and Charpy V-notch test data.
The fracture analysis diagram represents a comprehensive tool for understanding the complex relationships between temperature, stress, and flaw size in structural steel applications. By utilizing NDT, FTE, FTP, and dynamic tear test data, engineers can make informed decisions about material selection and design parameters to prevent brittle fracture in critical applications. The systematic approach provided by the FAD ensures both safety and economic efficiency in structural design.
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