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Statistical investigation of the behaviour of microcracks in carbon steels
I n v e s t i g a t i o n o f t h e n o n - p r o p o r t i o n s i m u l t i a x l a l strain d e f o r m a t i o n o f
1045 steal. Sherwood, J.A., Fay, E.M. and Jayaraman, N. Scri. Metall. Mater. M a y 1991 25, (5), 1075-1080 The capabilities of an automated procedure for finding physically reasonable material constants for the Ramaswamy-Stouffar model are demonstrated for proportional and non-proportional Ioadings of 1045 steel. The goal is to show that the automated material constant determination procedure yields constants that are consistent with muitiaxial test results. The model and constants can capture the change in the shape of the hysteresis loop as the phase angle changes. Thus, the multiaxial mechanical response of field service components can be investigated with a complex but extremely powerful constitutive model. Graphs. 6 refs.
Assessment
o f t h e r e m a i n i n g f a t i g u e life o f w r o u g h t - i r o n
bridges.
Tanner, P. and Hirt, M.A. Stahlbau J u l y 1991 60, (7), 2 1 1 - 2 1 9 (in G e r m a n ) An increasing number of bridges are not replaced at the end of their design lives for reasons of economy. To prescribe rational maintenance and inspection strategies for such structures, bases for the evaluation of the remaining fatigue life need to be established. The remaining fatigue life of a bridge depends on its geometry and on the service stress ranges. The relevant parameters affecting crack growth in wrought-iron bridge members are discussed, in relation to test results using Fe 510 and possible crack detection, by applying fracture mechanics methods. For an existing bridge the effect of the failure of individual members on structural safety is estimated. Graphs. 12 refs.
Estimate by fracture mechanics theory for rolling contact fatigue life end s t r e n g t h o f case-hardened gear m a t e r i a l s using a computer. Jiang, B., Zheng, X. and Wu, L. Eng. Fract. Mech. 1991 39, (5), 8 6 7 - 8 7 4 The stress intensity range ~IK and equation for crack growth da/dN = c (~K) n in linear elastic fracture mechanics was put forward to calculate the contact fatigue life and strength of case-hardenad gear materials. It was found that the ratio of maximum shearing stress Smaxand hardness Hv of the material multiplied by Srnax, S2max/Hv, can be regarded as the crack growth driving force; the value of the index n is nine for this kind of material The calculated results are in good agreement with the experimental data. Graphs, 8 refs. A cohesive m i c r o m e c h a n i c f a t i g u e model. II, F a t i g u e - c r e e p interaction and the Goodman d i a g r a m . Altus, E. Mech. Mater. J u l y 1991 11, (4), 2 8 1 - 2 9 3 A cohesive micromechanical fatigue model (CMFM), which identifies a chemical reaction between a broken chain and its neighbour as the main microscale source of fatigue failure has been developed recently. The successive chain breakages that control the damage evolution were characterized by the statistical strength distribution of the chains and the probability that the neighbour breaks. The model explained the power law of the S - N curve for high-cycle fatigue and the endurance limit phenomenon. The basic concept is expanded by defining two kinds of breakage sources for the neighbours. A dynamic type, associated with the local transient disturbance, occurring during breakage, and a static type, related to the relative motion between adjacent chains. The first is dominated by the strain at the breaking point and leads to a creep-like macroresponse. The second is a function of the maximum strain difference experienced during unloading, which causes fatigue failure. The interaction between the two mechanisms gives a total macroresponse that depends on both the mean and the alternate stress. Results provide a theoretical explanation for the empirical 'Goodman diagram' and for the low-cycle fatigue behaviour. The effect of different probability functions for the chemical reaction was studied. An activation type was found most suitable for predicting the macroresponse, and a Weibull distribution has been used. All the material parameters that were introduced on the microscale have a direct, uncoupled outcome on the macroresponse. The materials discussed are 1208; 1208b, 1219 and 4130 steels, and 7075 Ai. Graphs. 34 refs. A cohesive m i c r o m e c h a n i c a f a t i g u e model. I. Basic mechanisms. Altus, E. Mech. Mater. J u l y 1991 11, (4), 2 7 1 - 2 8 0 A model that identifies a cohesive (bonding) reaction between a broken element (molecule or chain) and its neighbour as the main microscale source of fatigue failure is proposed. By applying statistical laws, the macroresponse is revealed. Three types of rnacrodamege accumulation functions emerge, in agreement with known experimental evidence, as a direct result of different values for the micromaterial parameters. The reference type shows secondary and tertiary stages, the second type includes an additional primary stage, and the third type, exhibiting an endurance limit, has a primary stage only. A very well known empirical power law relationship between the fatigue stress and the number of cycles to failure is obtained analytically for the reference type, when a Weibull strength distribution function for the microelements is used. The microscale roots of the model enable the use of physical internal variables for the damage evolution equations. Thus, a clear insight into the macroresponse, including the existence of an endurance limit, is achieved through the basic mechanism on the microscale. Experimental correlations with available fatigue data for different materials, including metals (eg, 1208, 1208b, 4130, 1219 and 7075) plastics and composites (eg, PC, PP, nylons, graphite-epoxy composite, and acrylic resins) show the general validity of the model in spite of the diversity of their microstructures. It may be proposed that, in each material type, the physical 'element' is different (ie molecules for plastics, grains for metals, etc), but their response towards fatigue is similar: a non-reversible bonding beWveen a broken element and its neighbour. Graphs. 35 refs. A comparison of f a t i g u e failure m o r p h o l o g y b e t w e e n t i t a n i u m - n i t r i d e coated end uncoated lubricated rollers. Chang, T.P., Cheng, H.S., Chiou,
W.A. and Sproul, W.D. Tribol. Trans. J u l y 1991 34, (3), 4 0 8 - 4 1 6
Two series of morphological fatigue tests were conducted with a two-disc machine for titanium-nitride-coated rollers (4118) and uncoated rollers. Surface examinations showed that 1 /~m titanium-nitride-coated surfaces principally underwent elastic deformation without coating debonding. However, uncoated surfaces were heavily
Int J Fatigue May 1992
deformed even after a shorter contact cycle. For the uncoated rollers, cross-sectional micrographs revealed the presence of many near-surface microcrecks at an asperity scale nearly parallel to the surface. It is believed that these microcracks are initiated by asperity interactions. Metaliographic examinations of the unCOated subsurface revealed a thin layer of dark etching region corresponding to the microcreck failure region. For the coated roller, few cracks were found and the dark etching region was absent. The hard coating minimizes the surface distress and suppresses the initiation of microcracks. This explains why the fatigue life is enhanced with a thin hard coating. A cross-sectional transmission electron microscopy (XTEM) study showed a coherent interface structure for the coated specimens. The interface after rolling and sliding contact exhibited no clear boundary compared with that of the as-deposited coating. This may indicate that a good coating adhesion can be maintained during the current concentrated contact tests. Graphs, photomicrographs. 18 refs.
T h e o v e r l o a d r e t a r d a t i o n effect in f a t i g u e crack propagation of wormlike g r a p h i t e cast iron. Zhang, A., Thang, S.-Q. and Sun, X. J. Eng. Mater. Technol. (Trans. ASME) J u l y 1991 113, (3), 3 0 7 - 3 1 3 Single and multiple overloading tests under cyclic-controlled stress were carried out on specimens of worm-like graphite cast iron (WGCI), a brittle material. The results showed that the overloading had a strong retardation effect on this material when the overload ratio r (the ratio between the overload range and the baseline load range) is more than 1.2. For example, the number of cycles of retardation due to overloading, N', may be as high as ten times the number of cycles, N, required for the same crack length under baseline loading conditions. In addition, for the test conditions examined, there is no significant difference in the retardation effect under single or multiple overloading for this materiel. An analytical model based on the concept of crack closure and the effective stress intensity range was developed for evaluating the effect of the retardation. The development lad to a correlation between the number of applied cycles and the crack size after overloading, and permits one to calculate the number of retardation cycles N'. Finally, the mechanisms attributed to the retardation effect for WGCI are discussed. Graphs, photomicrographs, 13 refs.
Fatigue crack g r o w t h behaviour of alloy 800H at elevated temperatures.
Hour, K.Y. and Stubbins, J,F. J. Eng. Mater. Technol. (Trans. ASME) J u l y 1991 113, (3), 2 7 1 - 2 7 9 The high-tsmperature crack growth behaviour is investigated over a wide range of R-ratios, frequencies and temperatures in Alloy 800H. It is found that a high R-ratio, low frequency or high temperature can enhance creep damage and thus induce an intergranular crack growth mode. At low frequencies, the non-linear fracture mechanics parameter, C', is found to correlate the time-dependent fatigue crack growth rate well if the applied mean stress is used in calculating C'. On the other hand, the Paris crack growth law using Keff is proven to be an adequate expression to use when fatigue (time-independent) damage dominates. These conclusions correlate well with the damage mechanisms observed from sample fracture surfaces. Graphs, photomicrographs. 26 refs.
Statistical i n v e s t i g a t i o n steals. Goto, M.
o f t h e bahaviour of microcracks in carbon
Fatigue Fract. Eng. Mater. Struct. 1991 14, (8), 8 3 3 - 8 4 5 To clarify the statistical behaviour of microcracks, rotating-bending fatigue tests of plain specimens were carried out using two kinds of carbon steel with different microstructures; normalized 0.21% C steel and hest-treatad 0.45% C steel. The emphasis is to investigate separately the statistical properties of the initiation and propagation of microcracks through successive observations of the specimen surface. Results show that the microcrack initiation life distributions of normalized and heattreated steels are expressed by a two-parameter Weibull distribution and a Weibull distribution of the mixed type, respectively. On the other hand, the microcrack propagation life distributions of these steels are represented by three- and two-paramater Weibull distributions, respectively. The three-peramater Weibull distribution is well fitted to the crack length distribution for both steels. Graphs, photomicrographs. 16 refs.
Evaluation o f f a t i g u e crack propagation properties under random loading avoiding crack closure. Suzuki, N., Takeda, H., Ohta, A. and Ohuchida, H. Fatigue Fract. Eng. Mater. Struct. 1991 14, (8), 815-821 Fatigue crack propagation rates and the fatigue threshold of HT80 steel were measured by maintaining the maximum load during the whole period of random loading to prevent fatigue crack closure. The random loading pattern involved 62 level block Ioadings in which the waveform was approximated to the Rayleigh distribution of peaks. The fatigue crack propagation rates under random loading were well predicted from those obtained from constant-amplitude loading and assuming a linear cumulative damage law. That is, da/dn = C ( A I ~ - AK~th)where the equivalent stress intensity factor, ~,Keq = (Zni~K~i/Zni) ljm, where ni ~ 0 for /tKi AKth, or ni = nl for &Ki > t'Kth. Graphs. 14 refs. Prediction o f f a t i g u e crack g r o w t h u n d e r single-overload application in Ti-6AI-4V
Ghonem, H. and Zeng, M. Fatigue Fract. Eng. Mater. Struct. 1991 14, (8), 8 0 5 - 8 1 4 The use of a Markovian stochastic crack growth model to predict crack growth beheviour in zones affected by a single-overload application is considered. The model introduces an effective stress intensity factor in the definition of the transition intensity of the stochastic process. This, in turn, generates a unified probability growth law that was used to predict scatter in the single overload history. An experimental program was carried out on compact-tension specimens of Ti-6AI-4V material to generate sample crack growth curves, each of which contains three single-overload zones. The sample curves were then manipulated into experimental constant probability growth curves. These curves were compared with those theoretically generated using the proposed model. A good ag reement was established between these two data sets. Graphs. 22 refs.
201
1045 steal. Sherwood, J.A., Fay, E.M. and Jayaraman, N. Scri. Metall. Mater. M a y 1991 25, (5), 1075-1080 The capabilities of an automated procedure for finding physically reasonable material constants for the Ramaswamy-Stouffar model are demonstrated for proportional and non-proportional Ioadings of 1045 steel. The goal is to show that the automated material constant determination procedure yields constants that are consistent with muitiaxial test results. The model and constants can capture the change in the shape of the hysteresis loop as the phase angle changes. Thus, the multiaxial mechanical response of field service components can be investigated with a complex but extremely powerful constitutive model. Graphs. 6 refs.
Assessment
o f t h e r e m a i n i n g f a t i g u e life o f w r o u g h t - i r o n
bridges.
Tanner, P. and Hirt, M.A. Stahlbau J u l y 1991 60, (7), 2 1 1 - 2 1 9 (in G e r m a n ) An increasing number of bridges are not replaced at the end of their design lives for reasons of economy. To prescribe rational maintenance and inspection strategies for such structures, bases for the evaluation of the remaining fatigue life need to be established. The remaining fatigue life of a bridge depends on its geometry and on the service stress ranges. The relevant parameters affecting crack growth in wrought-iron bridge members are discussed, in relation to test results using Fe 510 and possible crack detection, by applying fracture mechanics methods. For an existing bridge the effect of the failure of individual members on structural safety is estimated. Graphs. 12 refs.
Estimate by fracture mechanics theory for rolling contact fatigue life end s t r e n g t h o f case-hardened gear m a t e r i a l s using a computer. Jiang, B., Zheng, X. and Wu, L. Eng. Fract. Mech. 1991 39, (5), 8 6 7 - 8 7 4 The stress intensity range ~IK and equation for crack growth da/dN = c (~K) n in linear elastic fracture mechanics was put forward to calculate the contact fatigue life and strength of case-hardenad gear materials. It was found that the ratio of maximum shearing stress Smaxand hardness Hv of the material multiplied by Srnax, S2max/Hv, can be regarded as the crack growth driving force; the value of the index n is nine for this kind of material The calculated results are in good agreement with the experimental data. Graphs, 8 refs. A cohesive m i c r o m e c h a n i c f a t i g u e model. II, F a t i g u e - c r e e p interaction and the Goodman d i a g r a m . Altus, E. Mech. Mater. J u l y 1991 11, (4), 2 8 1 - 2 9 3 A cohesive micromechanical fatigue model (CMFM), which identifies a chemical reaction between a broken chain and its neighbour as the main microscale source of fatigue failure has been developed recently. The successive chain breakages that control the damage evolution were characterized by the statistical strength distribution of the chains and the probability that the neighbour breaks. The model explained the power law of the S - N curve for high-cycle fatigue and the endurance limit phenomenon. The basic concept is expanded by defining two kinds of breakage sources for the neighbours. A dynamic type, associated with the local transient disturbance, occurring during breakage, and a static type, related to the relative motion between adjacent chains. The first is dominated by the strain at the breaking point and leads to a creep-like macroresponse. The second is a function of the maximum strain difference experienced during unloading, which causes fatigue failure. The interaction between the two mechanisms gives a total macroresponse that depends on both the mean and the alternate stress. Results provide a theoretical explanation for the empirical 'Goodman diagram' and for the low-cycle fatigue behaviour. The effect of different probability functions for the chemical reaction was studied. An activation type was found most suitable for predicting the macroresponse, and a Weibull distribution has been used. All the material parameters that were introduced on the microscale have a direct, uncoupled outcome on the macroresponse. The materials discussed are 1208; 1208b, 1219 and 4130 steels, and 7075 Ai. Graphs. 34 refs. A cohesive m i c r o m e c h a n i c a f a t i g u e model. I. Basic mechanisms. Altus, E. Mech. Mater. J u l y 1991 11, (4), 2 7 1 - 2 8 0 A model that identifies a cohesive (bonding) reaction between a broken element (molecule or chain) and its neighbour as the main microscale source of fatigue failure is proposed. By applying statistical laws, the macroresponse is revealed. Three types of rnacrodamege accumulation functions emerge, in agreement with known experimental evidence, as a direct result of different values for the micromaterial parameters. The reference type shows secondary and tertiary stages, the second type includes an additional primary stage, and the third type, exhibiting an endurance limit, has a primary stage only. A very well known empirical power law relationship between the fatigue stress and the number of cycles to failure is obtained analytically for the reference type, when a Weibull strength distribution function for the microelements is used. The microscale roots of the model enable the use of physical internal variables for the damage evolution equations. Thus, a clear insight into the macroresponse, including the existence of an endurance limit, is achieved through the basic mechanism on the microscale. Experimental correlations with available fatigue data for different materials, including metals (eg, 1208, 1208b, 4130, 1219 and 7075) plastics and composites (eg, PC, PP, nylons, graphite-epoxy composite, and acrylic resins) show the general validity of the model in spite of the diversity of their microstructures. It may be proposed that, in each material type, the physical 'element' is different (ie molecules for plastics, grains for metals, etc), but their response towards fatigue is similar: a non-reversible bonding beWveen a broken element and its neighbour. Graphs. 35 refs. A comparison of f a t i g u e failure m o r p h o l o g y b e t w e e n t i t a n i u m - n i t r i d e coated end uncoated lubricated rollers. Chang, T.P., Cheng, H.S., Chiou,
W.A. and Sproul, W.D. Tribol. Trans. J u l y 1991 34, (3), 4 0 8 - 4 1 6
Two series of morphological fatigue tests were conducted with a two-disc machine for titanium-nitride-coated rollers (4118) and uncoated rollers. Surface examinations showed that 1 /~m titanium-nitride-coated surfaces principally underwent elastic deformation without coating debonding. However, uncoated surfaces were heavily
Int J Fatigue May 1992
deformed even after a shorter contact cycle. For the uncoated rollers, cross-sectional micrographs revealed the presence of many near-surface microcrecks at an asperity scale nearly parallel to the surface. It is believed that these microcracks are initiated by asperity interactions. Metaliographic examinations of the unCOated subsurface revealed a thin layer of dark etching region corresponding to the microcreck failure region. For the coated roller, few cracks were found and the dark etching region was absent. The hard coating minimizes the surface distress and suppresses the initiation of microcracks. This explains why the fatigue life is enhanced with a thin hard coating. A cross-sectional transmission electron microscopy (XTEM) study showed a coherent interface structure for the coated specimens. The interface after rolling and sliding contact exhibited no clear boundary compared with that of the as-deposited coating. This may indicate that a good coating adhesion can be maintained during the current concentrated contact tests. Graphs, photomicrographs. 18 refs.
T h e o v e r l o a d r e t a r d a t i o n effect in f a t i g u e crack propagation of wormlike g r a p h i t e cast iron. Zhang, A., Thang, S.-Q. and Sun, X. J. Eng. Mater. Technol. (Trans. ASME) J u l y 1991 113, (3), 3 0 7 - 3 1 3 Single and multiple overloading tests under cyclic-controlled stress were carried out on specimens of worm-like graphite cast iron (WGCI), a brittle material. The results showed that the overloading had a strong retardation effect on this material when the overload ratio r (the ratio between the overload range and the baseline load range) is more than 1.2. For example, the number of cycles of retardation due to overloading, N', may be as high as ten times the number of cycles, N, required for the same crack length under baseline loading conditions. In addition, for the test conditions examined, there is no significant difference in the retardation effect under single or multiple overloading for this materiel. An analytical model based on the concept of crack closure and the effective stress intensity range was developed for evaluating the effect of the retardation. The development lad to a correlation between the number of applied cycles and the crack size after overloading, and permits one to calculate the number of retardation cycles N'. Finally, the mechanisms attributed to the retardation effect for WGCI are discussed. Graphs, photomicrographs, 13 refs.
Fatigue crack g r o w t h behaviour of alloy 800H at elevated temperatures.
Hour, K.Y. and Stubbins, J,F. J. Eng. Mater. Technol. (Trans. ASME) J u l y 1991 113, (3), 2 7 1 - 2 7 9 The high-tsmperature crack growth behaviour is investigated over a wide range of R-ratios, frequencies and temperatures in Alloy 800H. It is found that a high R-ratio, low frequency or high temperature can enhance creep damage and thus induce an intergranular crack growth mode. At low frequencies, the non-linear fracture mechanics parameter, C', is found to correlate the time-dependent fatigue crack growth rate well if the applied mean stress is used in calculating C'. On the other hand, the Paris crack growth law using Keff is proven to be an adequate expression to use when fatigue (time-independent) damage dominates. These conclusions correlate well with the damage mechanisms observed from sample fracture surfaces. Graphs, photomicrographs. 26 refs.
Statistical i n v e s t i g a t i o n steals. Goto, M.
o f t h e bahaviour of microcracks in carbon
Fatigue Fract. Eng. Mater. Struct. 1991 14, (8), 8 3 3 - 8 4 5 To clarify the statistical behaviour of microcracks, rotating-bending fatigue tests of plain specimens were carried out using two kinds of carbon steel with different microstructures; normalized 0.21% C steel and hest-treatad 0.45% C steel. The emphasis is to investigate separately the statistical properties of the initiation and propagation of microcracks through successive observations of the specimen surface. Results show that the microcrack initiation life distributions of normalized and heattreated steels are expressed by a two-parameter Weibull distribution and a Weibull distribution of the mixed type, respectively. On the other hand, the microcrack propagation life distributions of these steels are represented by three- and two-paramater Weibull distributions, respectively. The three-peramater Weibull distribution is well fitted to the crack length distribution for both steels. Graphs, photomicrographs. 16 refs.
Evaluation o f f a t i g u e crack propagation properties under random loading avoiding crack closure. Suzuki, N., Takeda, H., Ohta, A. and Ohuchida, H. Fatigue Fract. Eng. Mater. Struct. 1991 14, (8), 815-821 Fatigue crack propagation rates and the fatigue threshold of HT80 steel were measured by maintaining the maximum load during the whole period of random loading to prevent fatigue crack closure. The random loading pattern involved 62 level block Ioadings in which the waveform was approximated to the Rayleigh distribution of peaks. The fatigue crack propagation rates under random loading were well predicted from those obtained from constant-amplitude loading and assuming a linear cumulative damage law. That is, da/dn = C ( A I ~ - AK~th)where the equivalent stress intensity factor, ~,Keq = (Zni~K~i/Zni) ljm, where ni ~ 0 for /tKi AKth, or ni = nl for &Ki > t'Kth. Graphs. 14 refs. Prediction o f f a t i g u e crack g r o w t h u n d e r single-overload application in Ti-6AI-4V
Ghonem, H. and Zeng, M. Fatigue Fract. Eng. Mater. Struct. 1991 14, (8), 8 0 5 - 8 1 4 The use of a Markovian stochastic crack growth model to predict crack growth beheviour in zones affected by a single-overload application is considered. The model introduces an effective stress intensity factor in the definition of the transition intensity of the stochastic process. This, in turn, generates a unified probability growth law that was used to predict scatter in the single overload history. An experimental program was carried out on compact-tension specimens of Ti-6AI-4V material to generate sample crack growth curves, each of which contains three single-overload zones. The sample curves were then manipulated into experimental constant probability growth curves. These curves were compared with those theoretically generated using the proposed model. A good ag reement was established between these two data sets. Graphs. 22 refs.
201