How to Calculate fatigue life using the following informationmore details of the problem in the screen shots
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How to Calculate fatigue life using the following informationmore details of the problem in the screen shots below:
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N No R Sa Saz S(T) a(R) Sf(-1) Si Sm m(R) dunetk m(-1) DESIGNATIONS - number of cycles (fatigue life), - base number of cycles (No= 106 cycles), - stress ratio (R = Smin/Smax), - sinusoidal cycle stress amplitude in MPa, - sinusoidal cycle equivalent amplitude with Sm i Sa parameters in MPa, - sinusoidal cycle stress amplitude with the given value of a stress ratio R determining a line of constant fatigue life (N=const.) in MPa, - sinusoidal cycles fatigue limit with stress ratio (R=-1) for number of cycles No in MPa, - local stress value at the i-th load level in MPa - sinusoidal cycle average value of stress in MPa - sinusoidal cycle average value of stress with given value of stress ratio R determining a line of constant fatigue life (N=const.) in MPa, - stress maximum value in a sinusoidal cycle in MPa, - material tensile strength in MPa, - yield point of material in MPa, - exponent in the equation VN = N* (log k = 1.973 - log Rm), -exponent in the formula describing fatigue (Wöhler) graph for the stress ratio R=-1, - material sensitivity coefficient for the asymmetry of the cycle for N# No, - number of repetitions of a program to fatigue fracture. The value of the yield point of material Re determined in the tensile test is taken as the criterion for separated into the low cycles fatigue (LCF) and high cycle fatigue (HCF) for the hybrid method. From the load run shown in Figure 2 it is evaluated that cycles marked as 1-2 and 5-6 are characterized by an amplitude lower than the yield point Re. However cycles 3-4 and 7-8 have an amplitude with a higher value than the yield point. Therefore cycles 1-2 and 5-6 have been classified to the high-cycle range, and fatigue life calculations are made on the basis of the Wöhler chart. Cycles 3-4 and 7-8 according to the adopted method were assigned to the low-cycle range by calculations based on the Manson-Coffin diagram. Calculation of fatigue life was performed for S355J0 steel. This material is a low-alloy steel with increased strength, with a pearlitic-ferritic structure. The S355J0 steel has the following static properties [7], tensile strength Rm at 678 MPa and the yield stress R₂ of 499 MPa, as well as Young s modulus E = 208159 MPa. Cyclic properties of S355J0 steel on the basis of calculations were made [7]: m (-1) = 12.33, C (-1) = 1.145-1036, Sf (-1) = 243.1 MPa, k = 0.1386, WN=0.1205. Figure 3 presents the fragment of the stresses changes run in the structural element registered under operational loads, which became the basis for determining fatigue life. The course is shown in a relative Si / Smax form, where Smax is the maximum value occurring in the course of loads. Ramberg-Osgood cyclic deformation diagram. The number of cycles for the low-cycle fatigue was determined using the Manson-Coffin chart. For the low cycle fatigue and high cycle fatigue, calculation was performed using the Palmgren-Miner rule [2, 8, 11, 12], which is expressed by the formula: D= n₁ N₁ =1.0 (1) According to the hybrid method, the low-cycle and high-cycle fatigue damage is added separately. The results of fatigue life for the total damage are presented in the form of the number of completed load blocks, which were calculated from the following equation: λ== D The fatigue life expressed in the number of cycles Ne was estimated from the equation: Nς = λ ·no (3) The calculations made it possible to determine the graphs of fatigue life Smax = f(2). The fatigue life chart compares the results of calculations for the IM model and the II model with experimental tests. N No R Sa Saz S(T) a(R) Sf(-1) Si Sm m(R) dunetk m(-1) DESIGNATIONS - number of cycles (fatigue life), - base number of cycles (No= 106 cycles), - stress ratio (R = Smin/Smax), - sinusoidal cycle stress amplitude in MPa, - sinusoidal cycle equivalent amplitude with Sm i Sa parameters in MPa, - sinusoidal cycle stress amplitude with the given value of a stress ratio R determining a line of constant fatigue life (N=const.) in MPa, - sinusoidal cycles fatigue limit with stress ratio (R=-1) for number of cycles No in MPa, - local stress value at the i-th load level in MPa - sinusoidal cycle average value of stress in MPa - sinusoidal cycle average value of stress with given value of stress ratio R determining a line of constant fatigue life (N=const.) in MPa, - stress maximum value in a sinusoidal cycle in MPa, - material tensile strength in MPa, - yield point of material in MPa, - exponent in the equation VN = N* (log k = 1.973 - log Rm), -exponent in the formula describing fatigue (Wöhler) graph for the stress ratio R=-1, - material sensitivity coefficient for the asymmetry of the cycle for N# No, - number of repetitions of a program to fatigue fracture. The value of the yield point of material Re determined in the tensile test is taken as the criterion for separated into the low cycles fatigue (LCF) and high cycle fatigue (HCF) for the hybrid method. From the load run shown in Figure 2 it is evaluated that cycles marked as 1-2 and 5-6 are characterized by an amplitude lower than the yield point Re. However cycles 3-4 and 7-8 have an amplitude with a higher value than the yield point. Therefore cycles 1-2 and 5-6 have been classified to the high-cycle range, and fatigue life calculations are made on the basis of the Wöhler chart. Cycles 3-4 and 7-8 according to the adopted method were assigned to the low-cycle range by calculations based on the Manson-Coffin diagram. Calculation of fatigue life was performed for S355J0 steel. This material is a low-alloy steel with increased strength, with a pearlitic-ferritic structure. The S355J0 steel has the following static properties [7], tensile strength Rm at 678 MPa and the yield stress R₂ of 499 MPa, as well as Young s modulus E = 208159 MPa. Cyclic properties of S355J0 steel on the basis of calculations were made [7]: m (-1) = 12.33, C (-1) = 1.145-1036, Sf (-1) = 243.1 MPa, k = 0.1386, WN=0.1205. Figure 3 presents the fragment of the stresses changes run in the structural element registered under operational loads, which became the basis for determining fatigue life. The course is shown in a relative Si / Smax form, where Smax is the maximum value occurring in the course of loads. Ramberg-Osgood cyclic deformation diagram. The number of cycles for the low-cycle fatigue was determined using the Manson-Coffin chart. For the low cycle fatigue and high cycle fatigue, calculation was performed using the Palmgren-Miner rule [2, 8, 11, 12], which is expressed by the formula: D= n₁ N₁ =1.0 (1) According to the hybrid method, the low-cycle and high-cycle fatigue damage is added separately. The results of fatigue life for the total damage are presented in the form of the number of completed load blocks, which were calculated from the following equation: λ== D The fatigue life expressed in the number of cycles Ne was estimated from the equation: Nς = λ ·no (3) The calculations made it possible to determine the graphs of fatigue life Smax = f(2). The fatigue life chart compares the results of calculations for the IM model and the II model with experimental tests.
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Income Tax Fundamentals 2013
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31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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