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Designing reliably for fatigue crack growth under random loading
Fatigue cracking in damaged cylinders subjected to cyclic compressive loading. Walker, A.C. and Kwok, M.K. Thin-Walled Struct. 1990 9 ( 1 - 4 ) , 3 5 1 - 3 7 6 This paper presents the results of analytical and experimental investigations of the occurrence of cracking in thin-walled structures that are damaged and subjected to axial compressive loading with cyclically varying magnitudes. The experimental investigation comprised ninesheetsteeltest specimens, namely three plain cylinders, three plain-ring-stiffened and three T-ring-stiffened cylinders. The paper describes the method whereby damage was inflicted on the cylinders and describes test results, including strain gauge data. The analysis was performed using a commercial finite-element program that incorporated non-linearities in the strain-displacement and stress-strain relationships. The results of the analysis were found to be in good agreement with the test results, and the occurrence of cracking was noted to be dependent on the combined levels of tensile residual stresses resulting from the damage and to the levels of compressive stresses arising from the imposed loading. Graphs. 9 refs.
Low-cycle fatigue crack initiation: modelling the effect of porosity. Gerard, D.A. and Koss, D.A. Int. J. Powder Metall. Oct. 1990 26 (4), 3 3 7 - 3 4 3 The effect of porosity on crack initiation during low-cycle fatigue has been modelled, assuming that porosity located at a surface can be simulated as a through-thickness hole under plane-stress conditions. Utilizing existing theory to predict plastic strain distributions near a hole, adapting a Manson-Coffin law as a failure criterion, and applying cumulative damage theory, a theoretical analysis is presented that predicts the number of cycles for microcrack initiation in the presence of porosity. The predictions, which rely on pore shapes and the low-cycle fatigue response of the fully dense matrix, compare favourably with those measured experimentally for the number of cycles necessary to initiate a 15 p.m crack adjacent to both isolated and interconnected pores during the low-cycle fatigue of powder-pressed Ti. Graphs, photomicrographs. 31 refs.
Durability assessment based on initial material quality. Magnusen, P.E., Hinkle, A.J. Kaiser, W.T., Bucci, R.J. and Rolf, R.L.
with Whee~er's retardation model and reliability analysis provides an important tool for designing structures for a fatigue crack growth model of failure under random loads. It is also seen that Wheeler's retardation model improves the simulation results produced using the probabilistic model. These results compare well with the experimental findings on three steels. The shape exponent of Wheeler's model is found to vary for different materials and yield strengths. It is also found to be dependent on the load histories following the same probability distribution family and parameter for any given material. Simulated results are found to be generally conservative in estimating the fatigue life when the retardation effect is not considered, in other words when the shape exponent is set equal to zero. The materials mentioned are 1018, 4340 and 17-7PH steels. Graphs. 12 refs.
Influence of loading history of fatigue threshold behaviour in a titanium alloy. Mall, S., Perez, J.A. and Nicholas, T. Eng. Fract. Mech. 1990 37 (1), 1 5 - 2 6 The effects of loading history on the fatigue threshold behaviour in Ti-6AI-2Sn-4Zr-6Mo were studied. Two types of loading profiles were employed, The first type involved a history of gradually decreasing -~K to reach the threshold condition. In this type of test, two kinds of loading history were used; one was the standard ASTM decreasing ~,K test, while the other one maintained constant Kmax while Kmin was gradually increased. The second type of loading involved a sudden step decrease in .~K while maintaining the same stress ratio to achieve a nonpropagating condition. The crack opening displacement near the crack tip was measured using a laser interferometric displacement gauge. This allowed the crack closure levels to be accurately determined from which the threshold stress intensity range ~Kefi" th was determined. The value of &Keff.thwas found to be constant for all tests in which the loading history involved a gradual change, that is ASTM decreasing ~K and constant Kmax with increasing Kmin. However, the J,Keff.th determined from the non-propagating condition in the tests involving a sudden change in loading did not coincide with the values from the tests involving a gradual change in loading. Thus, the near-tip crack closure measurements and the use of an effective stress intensity range are unable to provide a unique value of the threshold in tests when sudden changes in load history are compared with gradually decreasing load histories. Graphs. 21 refs.
ASTM J. Test. Eva/. Nov. 1990 18 (6), 4 3 9 - 4 4 5 New US Air Force durability design philosophies are aimed at minimizing the evolution and growth of structural cracks to sizes affecting the state of readiness and the life cycle repair costs. Durability design requires attention to material quality and manufacturing quality, since both can be sources of in-service cracking problems. Improvement in the quality of AI-Zn-Cu-Mg, 7050 alloy, thick plate through reductions in microporosity has been correlated with increased smooth-coupon fatigue lives. Consequently, in commercial production, the smooth fatigue test is now employed as a lot release test to warrant initial metal quality. This work is aimed at translating the results of smooth fatigue quality-screening tests to aircraft component performance in the context of new durability methodologies. For this purpose, a fracture mechanics analysis is used to convert the smooth-coupon lifetimes to an equivalent initial flaw size (EIFS) distribution, which then becomes the starting point for probabilistic crack growth assessment in a component. The EIFS distribution extrapolated back from life data is shown to be in good agreement with the distribution of crack-initiating mieroflaws determined by more labourintensive post-test fractography. Consequently, the fracture mechanics calculation enables cost-effective conversion of coupon lifetimes (a simple measurement) into a material characteristic, the initial flaw size population, which can then be utilized analytically for durability design trade studies. A hypothetical component study performed in this manner for materials of varying initial quality is used to demonstrate how material quality differentiated at the coupon level can be translated into a performance advantage under representative in-service loading conditions. Graphs. 44 refs.
Modelling plasticity-induced fatigue crack closure. Llorca, J. and Galvez, V.A.
Eng. Fract. Mech. 1990 37 (1), 1 8 5 - 1 9 6 A numerical analysis of plasticity-induced fatigue crack closure based upon the finite-difference method is presented. This new method permits easy modelling of fatigue crack growth and contacts between fracture faces, without requiring sophisticated algorithms. The model is applied to a wide analysis of the influence of the mechanical properties of the material (yield stress, strain hardening capacity) and testing conditions (plane stress strain, stress ratio, maximum load) on plasticityinduced fatigue crack closure. The agreement with other numerical or experimental results when possible is excellent. It is concluded that plasticity-induced crack closure is determined by compressive residual stresses induced behind the crack tip. These residual stresses depend on the plastic strains produced in the material and on its strain hardening capacity. The material mentioned is 2024-T3 At, Graphs. 28 refs.
Stress intensity factor for a crack passing through a thickness step. Nishimura, T., U c h i m o t o , T. and Hiraoka, K. Eng. Fract. Mech. 1990 37 (1), 1 7 5 - 1 8 3 Stress intensity factors for a crack passing through a step in a plate where the thickness discontinuously decreases were derived from crack propagation tests and two-dimensional finite-element analysis. Finite-element analysis was used to generalize the effect of geometric parameters (plate width, thickness) on the stress intensity factor, and these relations were combined with the results of actual crack propagation tests to establish applicable design charts for the stress intensity correction factor. To verify the proposed design charts, crack propagation tests of plates with a reinforced square cut-out were conducted. It was found that the proposed charts gave good agreement with the stress intensity factors derived from the crack propagation tests. The test material was 2024-T351 AI. Graphs. 12 refs.
Designing reliably for fatigue crack growth under random loading. Alawi, H.
Eng. Fract. Mech. 1990 37 (1), 7 5 - 8 5 Fatigue crack growth is simulated on a personal computer using a probabilistic model developed earlier, under stationary narrow-band Rayleigh-distributed peak loads. The retardation effect is taken into consideration in the simulation using Wheeler's model. Results are then compared with experimental findings for three steels. It is clearly shown that the probabilistic model developed earlier coupled
Int J Fatigue July 1991
Dependence of stress frequency on fatigue crack initiation in orthotropic material. Sakamoto, H. and Takezono, S. Eng. Fract. Mech. 1990 36 (3), 4 9 5 - 5 0 6 The effect of stress frequency on fatigue crack initiation in 99.5% pure Ti plate, which has a remarkable strain rate dependence on the plastic region and a notable orthotropism, was studied. Fatigue crack initiation tests were carried out under three kinds of stress frequencies (0.2, 1 and 20 Hz). The test specimens were cut out from the rolling direction and the transverse to rolling direction of the plate. An anisotropic elasto/viscoplastic analysis was performed by the use of the orthotropic elasto/viscoplastic overlay model, and the comparison between the cycles to crack initiation and the viscoplastic strain range at notch root obtained by the analysis was made. The results obtained are summarized as follows. (1) It was found from the experiment that the cycles to fatigue crack initiation depended on the cut-out direction of the specimen because of the anisotropy of the Ti plate, and were approximately in proportion to fn (n>O), where f is the stress frequency. (2) A parameter closely related to the fatigue crack initiation in the orthotropic material is the viscoplastic strain range at the notch root, and the number of cycles to fatigue crack initiation is approximately in inverse proportion to the nth power of the viscoplastic strain range at the notch root. (3) The effect of stress frequency on fatigue crack initiation may be explained by the variation of viscoplastic strain range at the notch root based on the strain rate dependence and the anisotropy of the material. Graphs. 13 refs.
Fatigue crack propagation through residual stress fields with closure phenomena. Beghini, M. and Bertini, L. Eng. Fract. Mech. 1990 36 (3), 3 7 9 - 3 8 7 The effects produced by residual stress fields on fatigue crack propagation are evaluated, After a short discussion of general phenomenological aspects, the results of fatigue crack growth tests on compact tension specimens (e.g., C-Mn microalloyed steel) containing residual stresses arising from welding are summarized, Two numerical methods, that is the finite-element method and the weight function method, are then applied to model the effects produced by the residual stress field, allowing a detailed analysis of the experimental data to be obtained. Graphs. 9 refs.
Study on the fatigue embrittlement fracture limit, An, Z, Eng. Fract. Mech. 1990 36 (3), 3 7 3 - 3 7 7 The embrittlement of metals (e.g., No 45 steel) in fatigue was studied. Two new parameters, the fatigue brittle fracture limit, Nc, and the degree, psi, of fatigue embrittlement, were defined. The method of measurement of these two parameters was given also. Graphs, photomicrographs. 3 refs.
An experimental and numerical study of the factors governing crack growth under cyclic compression. Li, Z., Zhang, J., Luo, J. and Feng, Z. Eng. Fract. Mech. 1990 36 (6), 1029-1035 Cyclic compressive fatigue tests were performed on double-edge-notched specimens of a medium-carbon low-alloy steel for different stress amplitudes under constant mean stress and different mean stresses under constant stress amplitude. The crack growth rate, the length of the arrested crack and the shape of the crack front were examined, based on the characteristics of the tensile stress field obtained from finite-element analysis. A plot to show the characteristics of the tensile field is proposed and the influence of some key factors, such as stress state, stress ratio and the compressive plastic zone (i.e, minimum compressive stress), on the behaviour of the cyclic compressive fatigue is discussed. Graphs. 15 refs. A parameter for the local cyclic strain distribution. Shimada, H., Park, Y.-C., Furuya, Y. and Kawasaki, A. Eng. Fract. Mech. 1990 36 (6), 1021-1028 The local cyclic strain distribution near the crack tip was investigated by the computer-aided fine-grid method. This method makes it possible to measure continuously every in-plane component of the local cyclic strain distribution. It was
359
Low-cycle fatigue crack initiation: modelling the effect of porosity. Gerard, D.A. and Koss, D.A. Int. J. Powder Metall. Oct. 1990 26 (4), 3 3 7 - 3 4 3 The effect of porosity on crack initiation during low-cycle fatigue has been modelled, assuming that porosity located at a surface can be simulated as a through-thickness hole under plane-stress conditions. Utilizing existing theory to predict plastic strain distributions near a hole, adapting a Manson-Coffin law as a failure criterion, and applying cumulative damage theory, a theoretical analysis is presented that predicts the number of cycles for microcrack initiation in the presence of porosity. The predictions, which rely on pore shapes and the low-cycle fatigue response of the fully dense matrix, compare favourably with those measured experimentally for the number of cycles necessary to initiate a 15 p.m crack adjacent to both isolated and interconnected pores during the low-cycle fatigue of powder-pressed Ti. Graphs, photomicrographs. 31 refs.
Durability assessment based on initial material quality. Magnusen, P.E., Hinkle, A.J. Kaiser, W.T., Bucci, R.J. and Rolf, R.L.
with Whee~er's retardation model and reliability analysis provides an important tool for designing structures for a fatigue crack growth model of failure under random loads. It is also seen that Wheeler's retardation model improves the simulation results produced using the probabilistic model. These results compare well with the experimental findings on three steels. The shape exponent of Wheeler's model is found to vary for different materials and yield strengths. It is also found to be dependent on the load histories following the same probability distribution family and parameter for any given material. Simulated results are found to be generally conservative in estimating the fatigue life when the retardation effect is not considered, in other words when the shape exponent is set equal to zero. The materials mentioned are 1018, 4340 and 17-7PH steels. Graphs. 12 refs.
Influence of loading history of fatigue threshold behaviour in a titanium alloy. Mall, S., Perez, J.A. and Nicholas, T. Eng. Fract. Mech. 1990 37 (1), 1 5 - 2 6 The effects of loading history on the fatigue threshold behaviour in Ti-6AI-2Sn-4Zr-6Mo were studied. Two types of loading profiles were employed, The first type involved a history of gradually decreasing -~K to reach the threshold condition. In this type of test, two kinds of loading history were used; one was the standard ASTM decreasing ~,K test, while the other one maintained constant Kmax while Kmin was gradually increased. The second type of loading involved a sudden step decrease in .~K while maintaining the same stress ratio to achieve a nonpropagating condition. The crack opening displacement near the crack tip was measured using a laser interferometric displacement gauge. This allowed the crack closure levels to be accurately determined from which the threshold stress intensity range ~Kefi" th was determined. The value of &Keff.thwas found to be constant for all tests in which the loading history involved a gradual change, that is ASTM decreasing ~K and constant Kmax with increasing Kmin. However, the J,Keff.th determined from the non-propagating condition in the tests involving a sudden change in loading did not coincide with the values from the tests involving a gradual change in loading. Thus, the near-tip crack closure measurements and the use of an effective stress intensity range are unable to provide a unique value of the threshold in tests when sudden changes in load history are compared with gradually decreasing load histories. Graphs. 21 refs.
ASTM J. Test. Eva/. Nov. 1990 18 (6), 4 3 9 - 4 4 5 New US Air Force durability design philosophies are aimed at minimizing the evolution and growth of structural cracks to sizes affecting the state of readiness and the life cycle repair costs. Durability design requires attention to material quality and manufacturing quality, since both can be sources of in-service cracking problems. Improvement in the quality of AI-Zn-Cu-Mg, 7050 alloy, thick plate through reductions in microporosity has been correlated with increased smooth-coupon fatigue lives. Consequently, in commercial production, the smooth fatigue test is now employed as a lot release test to warrant initial metal quality. This work is aimed at translating the results of smooth fatigue quality-screening tests to aircraft component performance in the context of new durability methodologies. For this purpose, a fracture mechanics analysis is used to convert the smooth-coupon lifetimes to an equivalent initial flaw size (EIFS) distribution, which then becomes the starting point for probabilistic crack growth assessment in a component. The EIFS distribution extrapolated back from life data is shown to be in good agreement with the distribution of crack-initiating mieroflaws determined by more labourintensive post-test fractography. Consequently, the fracture mechanics calculation enables cost-effective conversion of coupon lifetimes (a simple measurement) into a material characteristic, the initial flaw size population, which can then be utilized analytically for durability design trade studies. A hypothetical component study performed in this manner for materials of varying initial quality is used to demonstrate how material quality differentiated at the coupon level can be translated into a performance advantage under representative in-service loading conditions. Graphs. 44 refs.
Modelling plasticity-induced fatigue crack closure. Llorca, J. and Galvez, V.A.
Eng. Fract. Mech. 1990 37 (1), 1 8 5 - 1 9 6 A numerical analysis of plasticity-induced fatigue crack closure based upon the finite-difference method is presented. This new method permits easy modelling of fatigue crack growth and contacts between fracture faces, without requiring sophisticated algorithms. The model is applied to a wide analysis of the influence of the mechanical properties of the material (yield stress, strain hardening capacity) and testing conditions (plane stress strain, stress ratio, maximum load) on plasticityinduced fatigue crack closure. The agreement with other numerical or experimental results when possible is excellent. It is concluded that plasticity-induced crack closure is determined by compressive residual stresses induced behind the crack tip. These residual stresses depend on the plastic strains produced in the material and on its strain hardening capacity. The material mentioned is 2024-T3 At, Graphs. 28 refs.
Stress intensity factor for a crack passing through a thickness step. Nishimura, T., U c h i m o t o , T. and Hiraoka, K. Eng. Fract. Mech. 1990 37 (1), 1 7 5 - 1 8 3 Stress intensity factors for a crack passing through a step in a plate where the thickness discontinuously decreases were derived from crack propagation tests and two-dimensional finite-element analysis. Finite-element analysis was used to generalize the effect of geometric parameters (plate width, thickness) on the stress intensity factor, and these relations were combined with the results of actual crack propagation tests to establish applicable design charts for the stress intensity correction factor. To verify the proposed design charts, crack propagation tests of plates with a reinforced square cut-out were conducted. It was found that the proposed charts gave good agreement with the stress intensity factors derived from the crack propagation tests. The test material was 2024-T351 AI. Graphs. 12 refs.
Designing reliably for fatigue crack growth under random loading. Alawi, H.
Eng. Fract. Mech. 1990 37 (1), 7 5 - 8 5 Fatigue crack growth is simulated on a personal computer using a probabilistic model developed earlier, under stationary narrow-band Rayleigh-distributed peak loads. The retardation effect is taken into consideration in the simulation using Wheeler's model. Results are then compared with experimental findings for three steels. It is clearly shown that the probabilistic model developed earlier coupled
Int J Fatigue July 1991
Dependence of stress frequency on fatigue crack initiation in orthotropic material. Sakamoto, H. and Takezono, S. Eng. Fract. Mech. 1990 36 (3), 4 9 5 - 5 0 6 The effect of stress frequency on fatigue crack initiation in 99.5% pure Ti plate, which has a remarkable strain rate dependence on the plastic region and a notable orthotropism, was studied. Fatigue crack initiation tests were carried out under three kinds of stress frequencies (0.2, 1 and 20 Hz). The test specimens were cut out from the rolling direction and the transverse to rolling direction of the plate. An anisotropic elasto/viscoplastic analysis was performed by the use of the orthotropic elasto/viscoplastic overlay model, and the comparison between the cycles to crack initiation and the viscoplastic strain range at notch root obtained by the analysis was made. The results obtained are summarized as follows. (1) It was found from the experiment that the cycles to fatigue crack initiation depended on the cut-out direction of the specimen because of the anisotropy of the Ti plate, and were approximately in proportion to fn (n>O), where f is the stress frequency. (2) A parameter closely related to the fatigue crack initiation in the orthotropic material is the viscoplastic strain range at the notch root, and the number of cycles to fatigue crack initiation is approximately in inverse proportion to the nth power of the viscoplastic strain range at the notch root. (3) The effect of stress frequency on fatigue crack initiation may be explained by the variation of viscoplastic strain range at the notch root based on the strain rate dependence and the anisotropy of the material. Graphs. 13 refs.
Fatigue crack propagation through residual stress fields with closure phenomena. Beghini, M. and Bertini, L. Eng. Fract. Mech. 1990 36 (3), 3 7 9 - 3 8 7 The effects produced by residual stress fields on fatigue crack propagation are evaluated, After a short discussion of general phenomenological aspects, the results of fatigue crack growth tests on compact tension specimens (e.g., C-Mn microalloyed steel) containing residual stresses arising from welding are summarized, Two numerical methods, that is the finite-element method and the weight function method, are then applied to model the effects produced by the residual stress field, allowing a detailed analysis of the experimental data to be obtained. Graphs. 9 refs.
Study on the fatigue embrittlement fracture limit, An, Z, Eng. Fract. Mech. 1990 36 (3), 3 7 3 - 3 7 7 The embrittlement of metals (e.g., No 45 steel) in fatigue was studied. Two new parameters, the fatigue brittle fracture limit, Nc, and the degree, psi, of fatigue embrittlement, were defined. The method of measurement of these two parameters was given also. Graphs, photomicrographs. 3 refs.
An experimental and numerical study of the factors governing crack growth under cyclic compression. Li, Z., Zhang, J., Luo, J. and Feng, Z. Eng. Fract. Mech. 1990 36 (6), 1029-1035 Cyclic compressive fatigue tests were performed on double-edge-notched specimens of a medium-carbon low-alloy steel for different stress amplitudes under constant mean stress and different mean stresses under constant stress amplitude. The crack growth rate, the length of the arrested crack and the shape of the crack front were examined, based on the characteristics of the tensile stress field obtained from finite-element analysis. A plot to show the characteristics of the tensile field is proposed and the influence of some key factors, such as stress state, stress ratio and the compressive plastic zone (i.e, minimum compressive stress), on the behaviour of the cyclic compressive fatigue is discussed. Graphs. 15 refs. A parameter for the local cyclic strain distribution. Shimada, H., Park, Y.-C., Furuya, Y. and Kawasaki, A. Eng. Fract. Mech. 1990 36 (6), 1021-1028 The local cyclic strain distribution near the crack tip was investigated by the computer-aided fine-grid method. This method makes it possible to measure continuously every in-plane component of the local cyclic strain distribution. It was
359