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# ASM Metals HandBook Volume 12 - Fractography

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whose effect on the fatigue crack growth rate will be presented in more detail below. From a technical standpoint, cyclic frequency (the rate at which the fatigue load is applied) and the wave form (the shape of the load versus time curve) are two independent variables. They are unrelated because the same frequency can exhibit different wave forms, such as sinusoidal or triangular. However, from a practical standpoint, the frequency and the wave form are the only two fatigue parameters that are not load related and are similar enough to be discussed in the same section. In addition to discussing \u2206K, frequency, and wave form, the effect of these parameters on the fatigue crack growth rate and the fracture appearance will be illustrated by using the results of fatigue tests conducted on different materials under different testing conditions. Each example will contain such data as a description of the material, the testing conditions, and the results of the tests. Effect of the Stress Intensity Range, \u2206K. The stress intensity factor, K, is a fracture mechanics parameter that expresses the stress condition in the material adjacent to the tip of a crack and is a function of the applied load and the crack shape factor, which for a partial thickness crack is expressed as a function of the depth and length of the crack (Ref 15, 31, 32). A numerically larger K represents a more severe state of stress. In fatigue, \u2206K represents the range of the cyclic stress intensity factor; however, it is generally referred to as the stress intensity range. The stress intensity range, \u2206K, is defined as: \u2206K = Kmax - Kmin (Eq 2) where Kmax is the maximum stress intensity factor, and Kmin is the minimum stress intensity factor. The values Kmax and Kmin are calculated by using the maximum and minimum stress (load) associated with each fatigue load cycle. For an actual fatigue test using an edge-cracked specimen, \u2206K can be calculated directly from (Ref 244): P aK BW w g D D = (Eq 3) where \u2206P is load amplitude (Pmax - Pmin), B is specimen thickness, W is specimen width (distance from point where load is applied and the uncracked edge of specimen), a is crack length, and \u3b3(a/W) is the K calibration function. The fatigue crack growth rate always increases with the value of \u2206K because a numerically larger \u2206K represents a greater mechanical driving force to propagate the crack. The relationship between the fatigue crack growth rate, da/dN and \u2206K can be expressed as (Ref 31, 32): ( )mda C K dN = D (Eq 4) where a is the distance of crack growth (advance), N is the number of cycles applied to advance the crack a distance (a), da/dN is the fatigue crack growth rate, and C and m are constants. If the fatigue crack propagates exclusively by a striation-forming mechanism, da/dN represents the average striation spacing, which increases with the value of \u2206K. The fatigue parameters Kmean and R are defined as: min max( ) 2mean k kK += (Eq 5) and max minKR K = (Eq 6) By using Eq 2, 5, and 6, it can be shown that Kmean and R are related to \u2206K as follows: min 2mean kK k D= + (Eq 7) and max 1 KR K D = - (Eq 8) Because Kmean and R are both directly related to \u2206K, by determining the effect of \u2206K on the fatigue crack growth rate, the effect of Kmean and R can be deduced from Eq 7 and 8. In the examples given later in this section, the fatigue crack growth rate in a material is sometimes given at low and high numerical values of \u2206K for moist air as well as the inert environment. As discussed previously, at low fatigue crack growth rates (low values of \u2206K), the corrosive effects of moist air can result in an increase in the fatigue crack growth rate above that in the inert environments, but at high fatigue crack growth rates (high values of \u2206K), the moist air environment has little effect and all environments exhibit similar fatigue growth rates, for these reasons, the span of the fatigue crack growth rates between the low and high values of \u2206K is generally smaller for the fatigue cracks propagating in the moist air than an inert environments. The effect of \u2206K on the fatigue crack growth rate, da/dN, in various materials is summarized below. Unless specified, the cyclic wave form is sinusoidal and the gas pressures are at or slightly above atmospheric. Example 1. An API-5LX Grade X42 carbon-manganese pipeline steel with an ultimate tensile strength of 490 to 511 MPa (71 to 74 ksi) was tested under the following conditions: R = 0.1, f = 5 Hz, dry nitrogen gas at a pressure of 69 atm, at room temperature (Ref 218). The results are listed below: \u2206K MPa m ksi in da/dN, mm/cycle 7 6.5 1 × 10-6 40 36.5 6 × 10-4 The fatigue crack growth rate at \u2206K = 40 MPa m (36.5 ksi in .) was 600 times greater than at 7 MPa m (6.5 ksi in .). Example 2. A nickel-chromium-molybdenum-vanadium rotor steel (Fe-0.24C-0.28Mn-3.51Ni-1.64Cr-0.11V-0.39Mo) with an ultimate tensile strength of 882 MPa (128 ksi) was tested under the following conditions: R = 0.5, f = 120 Hz, air (30 to 40% relative humidity), at room temperature (Ref 220). The results are listed below: \u2206K MPa m ksi in da/dN, mm/cycle 4 3.5 6 × 10-7 20 18 8 × 10-5 The fatigue crack growth rate at \u3b4K = 20 MPa m (18 ksi in ) was about 130 times greater than at 4 MPa m (3.5 ksi in ). Example 3. An AISI 4130 steel with an ultimate tensile strength of 1330 MPa (193 ksi) and a hardness of 43 HRC was tested under the following conditions: R = 0.1, f = 1 to 50 Hz, moist air (relative humidity not specified), at room temperature (Ref 251). The results are listed below: \u2206K MPa m ksi in da/dN, mm/cycle 10 9 7 × 10-6 40 36.5 2 × 10-4 The fatigue crack growth rate at \u2206K = 40 MPa m (36.5 ksi in ) was about 30 times greater than at 10 MPa m (9 ksi in ). Example 4. An AISI 4340 steel with an ultimate tensile strength of 2082 MPa (302 ksi) was tested under the following conditions: R = 0.1, f = 20 Hz, dry argon gas, at room temperature (Ref 253). the results are listed below: \u2206K MPa m ksi in da/dN, mm/cycle 15 13.5 7 × 10-5 30 27.5 1.2 × 10-4 The fatigue crack growth rate at \u2206K = 30 MPa m (27.5 ksi in ) was less than twice as great as that at 15 MPa m (13.5 ksi in ). Example 5. An SUS 410J1 martensitic stainless steel (Japanese equivalent of type 410 stainless steel), which was tempered at 600 °C (1110 °F) for 3 h, was tested under the following conditions: R = 0, f = 30 Hz, laboratory air (relative humidity not specified), at room temperature (Ref 233). The results are listed below: \u2206K MPa m ksi in da/dN, mm/cycle 4 3.5 2 × 10-7 15 13.5 2 × 10-5 The fatigue crack growth rate at \u2206K = 15 MPa m (13.5 ksi in ) was 100 times greater than at 4 MPa m (3.5 ksi in ). Example 6. An annealed type 316 stainless steel was tested under the following conditions: R = 0.05, f = 0.17 Hz, vacuum (better than 10-6 torr), at 25 °C (75 °F) Ref 242). The results are listed below: \u2206K MPa m ksi in da/dN, mm/cycle 35 32 2 × 10-4 70 63.5 7 × 10-3 The fatigue crack growth rate at \u2206K = 70 MPa m (63.5 ksi in ) was 35 times greater than at 35 MPa m (32 ksi in ). Example 7. Annealed type 301 and 302 stainless steel specimens were tested under the following conditions: R = 0.05, f = 0.6 Hz, dry argon gas, at room temperature (Ref 217). The results are listed below: \u2206K Specimen MPa m ksi in da/dN, mm/cycle 50 45.5 4 × 10-4 Type 301 100 90 3 × 10-3 Type 302 50 45.5 6 × 10-4 The fatigue crack growth rate at \u2206K = 100 MPa m (90 ksi in ) was about eight times greater than at