ASM Metals Handbook - Desk Edition (ASM_ 1998) Episode 13 pdf

Fig. 37 Typical fatigue life test sp ecimens. (a) Torsional specimen. (b) Rotating cantilever beam specimen. (c) Rotating beam specimen. (d) Plate specimen for cantilever reverse bending. (e) Axial loading specimen. The design and type of specimen used depend on the fatigue testing machine us ed and the objective of the fatigue study. The test section in the specimen is reduced in cross section to prevent failure in the grip ends and should be proportioned to use the upper ranges of the load capacity of the fatigue machine (i.e., avoiding very low load amplitudes where sensitivity and response of the system are decreased). Test Methods Testing machines are defined by several classifications: the controlled test parameter (load, deflection, strain, twist, torque, etc.); the design characteristics of the machine (direct stress, plane bending, rotating beam, etc.) used to conduct the specimen test; or the operating characteristics of the machine (electromechanical, servohydraulic, electromagnetic, etc.). Machines range from simple devices that consist of a cam run against a plane cantilever beam specimen in constant- deflection bending to complex servohydraulic machines that conduct computer-controlled spectrum load tests. Axial and rotating-bending machines are most commonly used for fatigue tests. Surface preparation of specimens is critical in all fatigue life tests. Axial Fatigue Life Tests. ASTM E 466 specifies specimens to be used in axial fatigue tests. The specific dimensions of specimens depend on the objective of the experimental program, machine to be used, and available material. ASTM does not specify dimensions but details preparation techniques and reporting techniques. In reporting, a sketch of the specimen, with dimensions, should be given. The surface-roughness and out-of-flatness dimensions should be included. Specimens should not be subjected to any surface treatment. For axial loading, ASTM E 466 states that regardless of the machining, grinding, or polishing method used, the final metal removal should be in a direction approximately parallel to the longitudinal axis of the specimen. Improper preparation methods can greatly bias the results. Hence, preparation techniques should be carefully developed; if a change in the preparation technique is made, it has to be demonstrated that it does not introduce any bias in the results. Rotating-bending fatigue tests of the simple beam type are performed in testing machines such as that shown in Fig. 38, sometimes called the R.R. Moore testing machine. In operation, an electric motor rotates a cylindrical specimen, usually at 1800 rpm or higher, while a simple mechanical counter records the number of cycles. Loads are applied to the center of the specimen by a system of bearings and dead weights. A limit switch stops the test when the specimen breaks and the weights descend. Fig. 38 Loading arrangement for a rotating-beam fatigue-testing machine. S, specimen; P, load The weights produce a moment that causes the specimen to bend. A strain gage placed on the specimen shows compressive stresses on the top and tensile stresses when the gage is rotated to the bottom. Stresses range from maximum tension to maximum compression during each revolution of the testing machine. Bending moments can be converted to stress by assuming that they are elastic and by employing the flexure formula: = MC/I For circular specimens, I = C 4 /4, where C is the specimen radius. The maximum stress at the outer fiber, , is proportional to the bending moment, M. This moment is the product of the moment arm and the force. The specimen is machined from the material to be tested and is fastened into the bearing housing with special cap screws. The effective dead weight of the R.R. Moore machine and weighing apparatus is 4.54 kg (10 lb), which is deducted from the total weight required and added to the weight pan (Fig. 38) to provide the desired stress: 18.22 kg - 4.54 kg = 13.68 kg (40.13 lb - 10 lb = 30.13 lb) When the drive motor is actuated, a counter records the number of revolutions. If the specimen breaks, the bearing housing descends and actuates a switch that shuts off the drive motor. If the specimen does not break (carbon and low- alloy steels may achieve a million or more cycles), the stress is at or below the endurance limit. Next, the machine is shut off and another specimen is run at a higher stress level. A series of tests is performed to provide sufficient data at varying stress levels. For cantilever-beam rotating-bending machines of the White-Souther type (Fig. 39), a different bending moment is used in stress calculation. A weight, P, is supported by fixture to a ball-bearing housing at the free end of the specimen. This produces a bending moment, M, that equals P × L, which is the distance of the specimen from the center of the applied load, 75 mm (3 in.). The stress in the outer fiber is The weight added to the weight pan is the calculated weight minus the weight of the weighing apparatus. Fig. 39 Loading arrangement for a cantilever-beam fatigue machine for rotating-bending testing. S, specimen; P, load Plate-Bending Machines. In rotating-bending tests, the mean or average stress is always zero. The effect of mean stress, which is very important in fatigue, is evaluated by cantilever bending machines that are used to test plate materials. In these machines, sometimes called Kraus plate-bending machines, specimens are loaded with constant deflection by means of an eccentric crank (Fig. 40). Stresses can be calculated by assuming that they are elastic. In many cases this is not a good assumption, because, when tested, some soft materials may involve small amounts of plastic stress. Fig. 40 Reciprocating-bending fatigue-testing machine, and typical specimen (at lower left) for testing of sheet Specimens are usually tapered to provide a constant-stress test area. The approximate stress, S, is given by: where y is the specimen deflection, t is the thickness of the specimen, E is the elastic modulus, and l is the distance from load application to the back of the specimen. Constant-deflection beam-type machines are used to test both strip and plate. A typical specimen is shown at lower left in Fig. 40. Resonant-Testing Machines. Machines for resonant testing are basically spring-mass, vibrating systems. The frame design is based on a resonant, spring-mass system that consists of two masses linked by the specimen and grip string and that oscillates as a dipole. The system is excited by an electromagnet housed in the machine base. The masses and load string are positioned in the vertical frame, which is suspended and guided on leaf springs. The eight springs are arranged in a special configuration to make a unique and compact design without the need for a heavy seismic block. Mean load is applied by a motor located in the base of the system. The motor drives the four comer gearboxes through two shafts and applies mean loads in both tension and compression. The mean-load force is carried by the box-type structure of springs, and the level either is adjusted by a hand-held controller or is maintained at a level preset by the controller. The magnet air gap is maintained automatically by the action of the gap servomotor driving a wedge beneath the electromagnet. A linear variable displacement transformer (LVDT) constantly monitors the air gap, and control is maintained even when the mean load is changed while the machine is running. A manually operated drive located in the upper mass permits major adjustment of specimen spacing. The electromagnet excites the dual-mass system at its natural frequency by means of pulse excitation. This feature enables a simple switch to replace the conventional power amplifier, thus providing high reliability at low cost and, in addition, eliminating the need to tune an oscillator to the natural frequency of the system. Closed-loop amplitude control is achieved by controlling the pulse power to the magnet from the error between the actual and demanded load amplitudes, thereby providing fast response to changing load demands. A strain-gaged load cell provides accurate load monitoring and digital indication of peak dynamic load, mean load, and frequency. Ultrasonic fatigue testing involves cyclic stressing of material at frequencies typically in the range of 15 to 25 kHz. The major advantage of using ultrasonic fatigue is its ability to provide near-threshold data within a reasonable length of time. High-frequency testing also provides rapid evaluation of the high-cycle fatigue limit of engineering materials as described in the article "Ultrasonic Fatigue Testing" in Mechanical Testing, Volume 8, Metals Handbook, 9th edition. Corrosion Fatigue Life Testing. High-cycle corrosion fatigue tests (performed in the range of 10 5 to 10 9 cycles to failure) are typically done at a relatively high frequency of 25 to 100 Hz to conserve time. Multiple, inexpensive rotating- bend machines are often dedicated to these experiments. Low-cycle corrosion fatigue tests (in the regime where plastic strain, p , dominates) follow from the ASTM standard for low-cycle fatigue testing in air (ASTM E 606). For aqueous media, the typical cell for corrosion fatigue life testing includes an environmental chamber of glass or plastic that contains the electrolyte. The specimen is gripped outside of the test solution to preclude galvanic effects. The chamber is sealed to the specimen, and solution can be circulated through the environmental cell. The setup should include reference electrodes and counter electrodes to enable specimen (working electrode) polarization with standard potentiostatic procedures. Care should be taken to uniformly polarize the specimen, to account for voltage drop effects, and to isolate counter electrode reaction products. If potential is controlled, control of the oxygen content of the solution may not be necessary, although highly deaerated solutions are considered prudent. Environmental containment for high-cycle and low-cycle corrosion fatigue life testing is similar, but the overall setup for low-cycle (strain-controlled) testing is more complicated because gage displacement must be measured. For strain- controlled fatigue life, testing in simple aqueous environments, diametral or axial displacement is measured by a contacting but galvanically insulated extensometer, perhaps employing pointed glass or ceramic arms extending from an extensometer body located outside of the solution. Hermetically sealed extensometers or linear-variable-differential transducers can be submerged in many electrolytes over a range of temperatures and pressures. Alternately, the specimen can be gripped in a horizontally mounted test machine and be half submerged in the electrolyte with the extensometer contacting the dry side of the gage. For simple and aggressive environments, grip displacement can be measured external to the cell-contained solution, such as for high-temperature water in a pressurized autoclave. It is necessary to conduct low-cycle fatigue tests in air (at temperature), with an extensometer mounted directly on the specimen gauge, to relate grip displacement and specimen strain. Fatigue Life Data It has long been recognized that fatigue data, when resolved into elastic and plastic terms, can be represented as linear functions of life on a logarithmic scale. Figure 41 schematically shows this representation of elastic and plastic components, which together define the total fatigue life curve of a material. The general fatigue-life relation, expressed in terms of the strain range ( , where is the strain change from cyclic loading), is as follows: = e + p (Eq 27) where e is the elastic strain range, p is the plastic strain range, and where: (Eq 28) (Eq 29) Therefore, the total strain amplitude (or half the total strain range, /2) can be expressed as the sum of Eq 28 and 29: (Eq 30) where ' f is the fatigue ductility coefficient, ' f is the fatigue strength coefficient, b is the fatigue strength exponent, c is the fatigue ductility exponent, and N f is the number of cycles to failure. Fig. 41 Schematic of fatigue life curve with the Manson four- point criteria for the elastic and plastic strain lines. D is the tensile ductility, f is the fracture stress (load at fracture divided by cross- sectional area after fracture), and UTS is conventional ultimate tensile strength. These four empirical constants (b, c, ' f , ' f ) form the basis of modeling strain-life behavior for many alloys, although it must be noted that some materials (such as some high-strength aluminum alloys and titanium alloys) cannot be represented by Eq 30. For many steels and other structural alloys, substantial data have been collected for the four parameters in Eq 30. In many cases, the four fatigue constants have been defined by curve fitting of existing fatigue life data. A collection of this data is tabulated in Fatigue and Fracture, Volume 19, ASM Handbook. The four fatigue constants can also be estimated from monotonic tensile properties. With the availability of extensive data, however, these techniques are not widely used. Nonetheless, the "four-point method" is a method to estimate fatigue life behavior from tensile properties. This method can be used to compare fatigue and tensile properties. In addition, it should also be mentioned that the four fatigue constants are also related to the following parameters: (Eq 31) n' = b/c (Eq 32) where K' is the cyclic strength coefficient and n' is the cyclic strain hardening exponent in the power-law relation for a log-log plot of the completely reversed stabilized cyclic true stress ( ) versus true plastic strain ( p ), such that = K'( p ) n' . The use of power-law relationship is not based on physical principles, although the relationships in Eq 31 and 32 may be convenient for mathematical purposes. The parameters K' and n' are usually obtained from a curve fit of cyclic stress- strain data. Four-Point Method Numerous studies have been devoted to the development of techniques for estimating strain-controlled fatigue characteristics (per Eq 30). For the most part, these studies dealt with data generated under completely reversed strain cycling (i.e., R = -1, or A = ) and usually attempted to relate fatigue properties with tensile properties. Extensions of these studies have carried the estimating procedures a step further, addressing the correlation of fatigue data obtained at various strain ratios (R). Two common methods for approximating the shape of a fatigue curve are the "method of universal slopes" and the "four- point correlation" method. These two methods have been known for many years. The method of universal slopes, first proposed by Manson, is based on the relation: (Eq 33) where UTS is ultimate strength, E is modulus of elasticity, and f is true fracture ductility, or ln [1/(1 - RA)]. This approximation thus requires only tensile strength, modulus, and reduction in area (RA). However, note that it is based on strain range ( ) rather than strain amplitude ( /2). The four-point method also allows construction of fatigue life curves from more readily available handbook data (i.e., monotonic tensile data). This method can be compared with the traditional strain-based approach (Fig. 41) or a stress- based approach. In both cases, the four-point method is based on the premise that total fatigue life per Eq 30 can be estimated as the sum of elastic strain (Eq 28) and plastic strain (Eq 29) components. The step-by-step process for locating points on the plastic- and elastic-strain-life lines is described below for both strain-based and stress-based data. Strain-Based Four-Point Method. The four-point method initially was developed in terms of strain range by Manson (Fig. 41). The four points in Fig. 41 are determined as follows: • Point P 1 on the elastic strain line is positioned at N f = 0.25 cycles (where a monotonic test is of one fatigue cycle) and at an elastic strain range of 2.5 f /E (where f is the fracture stress in a tensile test and E is the elastic modulus). • Point P 2 on the elastic strain line is positioned at N f = 10 cycles and at an elastic strain range of 0.9 UTS/E, where UTS is the conventional ultimate tensile strength. • Point P 3 on the plastic strain line is positioned at N f = 10 cycles, where the plastic strain range is 0.25D 3/4 and D is the conventional logarithmic ductility (also known as f ). • Point P 4 on the plastic strain line is positioned at N f = 10 4 cycles, where the plastic strain range is given by p (at 10 4 cycles) = 0.0069 - 0.525 e (at 10 4 cycles), where the elastic strain-range line at N f = 10 4 cycles; ( e at 10 4 ) is shown as * e in Fig. 41. Point P 1 depends on fracture stress, which is not readily available in literature. However, fracture stress (which is the load at fracture divided by the area as measured after fracture) can be estimated by means of the following approximate relationship among fracture stress, ultimate tensile stress, and fracture ductility, thus, f = UTS(1 + D) (Eq 34) This relation follows from Fig. 42, where each point is fixed by the data for one material. Fig. 42 Fracture stress versus tensile ductility On the basis of the approximate equality in Eq 34, Manson noted that when E is known, only two tensile properties ultimate tensile strength (UTS) and the reduction in area (to give D) are needed to position the lines in Fig. 41 and thus obtain a prediction of fatigue behavior. Figure 43 shows a convenient graphical solution by Manson for locating the four points. For example, if UTS/E is 0.01 and the reduction in area is 50% (D = 0.694), the value of P 2 from the right-hand scale is 0.009 and that of P 3 from the top scale is 0.18. Locating the point with the coordinates UTS/E = 0.01 and reduction in area equal to 50% gives values for P 1 and P 4 of 0.042 and 0.0009, respectively. These points will locate the two strain-range lines, and the total strain-range curve can then be positioned to relate and N f for the material in question. Fig. 43 Graphical solution to obtain the four points (P 1 , P 2 , P 3 , and P 4 , in Fig. 41 ) to position the elastic and plastic strain-range lines. Stress-Based Four-Point Method. The four-point also applies to the construction of a stress-based S-N fatigue curve, as shown in Fig. 44. The four points A, B, C, and D in Fig. 44 can be defined in terms of either stress or strain. In terms of strain, the points are identical to points P 1 , P 2 , P 3 , and P 4 in Fig. 41. For construction of an S-N fatigue curve, the points are determined as described below. Fig. 44 Schematic summary of four-point method for estimating fatigue strength or strain life Point A (in terms of stress) is simply the ultimate tensile strength of the metal, plotted on the vertical axis of the graph at N = . As in the strain-based approach, this assumes that the simple tensile test represents one-fourth of a single, completely reversed fatigue cycle the peak positive value of the applied stress. Point B, the right-hand locator of the elastic curve, is defined as the fatigue-endurance limit, if the metal has one; otherwise, point B is the endurance strength. Some ferrous alloys have an endurance limit, that is, a stress level below which fatigue failure will never occur, regardless of number of cycles. This is generally around 10 7 or 10 6 cycles, at which point the fatigue curve approaches zero-slope, or a horizontal line. Many metals, particularly those that do not work harden, have no detectable endurance limit. Their long-life fatigue curves never become truly horizontal. For these metals, a pseudo-endurance limit, called endurance strength, is reported. Usually, this value is defined as the failure stress at some large number of cycles, for example, 10 7 to 10 10 . Point B can also be obtained from tensile-test data a virtue of this technique, as handbook values for fatigue-endurance strengths or limits are often not available. Figure 45 is used to find the fatigue-endurance value from yield strength and true ultimate tensile strength for the material. The "ductility parameter" is simply calculated from handbook tensile data using the equation on the horizontal axis of the graph. Then find the "endurance-to-yield" strength ratio for the appropriate material. Multiply this ratio by "yield strength" to find the endurance value, which is point B. Fig. 45 Plot for estimating fatigue-endurance limits (point B in Fig. 44) for common structural alloy groups Beyond point B, the ratio of ultimate tensile strength to yield strength can be used to approximate the slopes of the long- life portion of the fatigue curve. According to many researchers, a ratio greater than 1.2 suggests that the material strain hardens sufficiently to produce a pronounced endurance limit value, and the curve assumes a zero slope. For ratios less than 1.2, however, the curve will continue to drop beyond point B. The lower the ratio below 1.2, the further the fatigue curve deviates from a horizontal, zero-slope line beyond point B. Because both endurance strength and endurance limit are reported in terms of stress, this value must be divided by Young's modulus for the metal if the fatigue curve is being constructed in terms of strain. Point C is a value known as "fracture ductility." If natural, or true, strain at fracture for a simple tension test is known (which would be the distance between gage points at fracture divided by initial gage length), fracture ductility is the natural log of this value. In most cases, however, reduction of area for a simple tensile test is given in handbooks. As before in the discussion on the universal slopes method, fracture ductility, f , is estimated. (Eq 35) where RA is percentage reduction of area. [...]... M · , various quantities based on erosion-time curves (see ASTM test method G 32 for description) M · t-1 L10 tind, Nf M, V, D M, V, D V, SR M, V, D, SR M, V, D, SR M, V, D, SR M · t-1, D · t-1, M · ,V· M · P-1 · X-1, V · t-1, M · t-1, V · X-1, M · X-1, M · M · P-1 · X-1, M · P-1 · N-1, V · t-1, M · t-1 ,V· M · t-1, D · t-1 V · t-1, M · t-1, V · N-1, M · N-1, D = length or dimenional change, L10... specimen K that Fig 47 Fatigue-crack-growth behavior of ASTM A 533 B1 steel with a yield strength of 470 MPa (70 ksi) Test conditions: R = 0.10; ambient room air; 24 °C (75 °F) Test Methods Testing procedures for measuring fatigue-crack-growth rates are described in ASTM method E 647 This method applies to medium-to-high crack-growth rates that is, above 1 0-8 m/cycle (3.9 × 1 0-7 in./cycle) For applications... 18, ASM Handbook) is also a method to measure wear, as is surface layer activation by radionulcides Table 1 Common units for reporting wear and wear rates Wear category Sliding Impact Rolling Subcategory Abrasive, two-body Wear quantities M, V, D Wear rate quantities M · P-1 · X-1, V · t-1, M · t-1, M · ,V· Abrasive, threebody Sliding, unidirectional Sliding, reciprocating Fretting Polishing wear Two-body... Fatigue and Fracture, Volume 19, ASM Handbook) It is extremely expensive to obtain a true definition of Kth, and in some materials a true threshold may be nonexistent Generally, designers are more interested in the fatigue crack growth rates in the near-threshold regime, such as the K that corresponds to a fatigue crack growth rate of 1 0-8 to 1 0-1 0 m/cycle (3.9 × 1 0-7 to 1 0-9 in./cycle) Because the duration... to determine the effect of corrosion or other chemical reaction on cyclic loading Cyclic loading may involve various wave forms for constant-amplitude loading, spectrum loading, or random loading For constant-amplitude loading, a set of crack-length-versus-elapsed-cycle data (a versus N) is collected, with the specimen loading, Pmax and Pmin, generally held constant The minimum crack length increment... cyclic load range The general nature of fatigue-crack growth and its description using fracture mechanics can be briefly summarized by the example data shown in Fig 47 This figure shows a logarithmic plot of the crack growth per cycle, da/dN, versus the stress-intensity-factor range, K, corresponding to the load cycle applied to a specimen The da/dN-versus- K plot shown is from five specimens of ASTM... on the material Results of fatigue-crackgrowth-rate tests for nearly all metallic structural materials have shown that the da/dN-versus- K curves have the following characteristics: a region at low values of da/dN and K in which fatigue cracks grow extremely slowly or not at all below a lower limit of K called the threshold of K, Kth; an intermediate region of power-law behavior described by the Paris... shear-test data are in the designing of structures that are riveted, pinned, or bolted together and where service stresses are actually in shear Notable examples of such structures are found in the aerospace industry The required standardization is given by ASTM B 565 Single- and Double-Shear Testing In the many tests that have been devised for evaluating shear strength, both single- and double-shear... steady-state wear rate of the material system and will not be affected so greatly by running-in phenomena In other cases, it is important to know the total amount of wear of the material, including the pre-steady-state wear Testing results should indicate whether the total wear or the steady-state postrunning-in wear was used in computing the wear rates Table 1 lists common units for reporting the quantities... curves approximated from handbook data (P Weihsmann, Mater Eng., March 1980, p 53) In addition, a more recent analysis by J.H Ong (Int J Fatigue, Vol 15, 1993, p 1 3-1 9) on 49 steels demonstrates that the predicted values by the four-point correlation method and the universal slopes method give satisfactory agreement with experimental data The analysis by Ong shows that the four-point method gives the . step-by-step process for locating points on the plastic- and elastic-strain-life lines is described below for both strain-based and stress-based data. Strain-Based Four-Point Method. The four-point. for measuring fatigue-crack-growth rates are described in ASTM method E 647. This method applies to medium-to-high crack-growth rates that is, above 10 -8 m/cycle (3.9 × 10 -7 in./cycle). For. position the elastic and plastic strain-range lines. Stress-Based Four-Point Method. The four-point also applies to the construction of a stress-based S-N fatigue curve, as shown in Fig. 44.