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Application of minimum energy formalism in a multiple slip band model for fatigue. I. Calculation of slip band spacings
abeefption in low-cycle fatigue in 9Cr-IMo and 304 Upadhyaya, K.R. • and Shetty, •Mater.• ScL s Eng. tA Oct. / M.N.s y
stainless
1991 A147 (1) 6 7 - 7 5
Energy-absorption characteristics in slow tensile cyclic deformation within the flow stress are examined as functions of temperature and previous plastic strain. The energy absorption is analysed in terms of thermal activation, and the activation energy is determined by separately determining the activation volume from stress relaxation at stress values below the flow stress. The required internal stress and the dislocation velocity-stress exponent are obtained from instantaneous strain rate change experiments. Some possible mechanisms are considered based on the energy absorption and the activation energy, which have different temperature dependences in the two steels.
The influence o f air humidity on neer-threshold fatigue crack growth of 2024-'r3 e l u m i n i u m alloy. Stanzl, S.F., Mayer, H.R. and Tschegg, E.K. Mater. Sci. Eng. A Oct. 1991 A147 (1) 4 5 - 5 4 The environmental influence of humid air, dried air, and vacuum on the fatigue crack growth behaviour of the AI alloy 2024-T3 was measured in the very low threshold regime (down to approx 10-13 m/cycle), using the high-frequency (20000 Hz) technique of ultrasonic resonance fatigue. The crack growth curves, (~a/~N vs. Km=xrelationship) obtained in humid air were characterized by a plateau-like regime (regime with reduced slope of crack growth curve) between 10-9 and 10-1° m/cycle and a threshold value of 2.1 MPa m °'5, The threshold in vacuum was 3.3 MPa m°-s and no plateau-like regime occurred. In dried air, the curve was very close to that in vacuum, when the Kmaxvalues were high enough; at the very lowest Kmaxvalues, however, the curve approached that for humid air, and an almost identical threshold stress intensity value (2.3 MPa m°'s) was found. The fracture morphology reflected the changing cracking mechanisms: ductile fracture with more plastic deformation and some crystallographic and intercrystalline features were observed for 'high'/(max values, whereas less plastic deformation and no crystallographic or intercrystalline features were characteristic of the threshold regime. Hydrogen embrittlement is assumed to be the main mechanism responsible for the observed corrosion fatigue bahaviour of alloy 2024-T3 in humid air.
The effect of N= and CO= environments on t h e f a t i g u e failure of MARM200 + hafnium superalloy at 975 °C. Aghion, E., Bamberger, M. and Berkovits, A. Mater. Sci. Eng. A Nov. 1991 A147 (2) 181-189 High-temperature, low-cycle fatigue (HTLCF) failure mechanisms were studied in unidirectionally solidified MAR-M200 + Hf Ni-based superalloy in pure N2 and C02 environments at 975 °C. The loading conditions were constant and consisted of creep tension and plastic compression according to the cp mode of the strain-rangepartitioning method. The crack initiation and propagation were investigated using scanning electron microscopy, X-ray diffraction and Auger electron spectroscopy. The results obtained indicated that N2 and CO2 atmospheres cannot be treated as passive gaseous environments. On the contrary, these environments have a significant influence on the HTLCF crack growth behaviour. In an N2 environment, the fracture was transgranular. This was a result of an intensive chemical interaction between nitrogen and the main alloying elements making up the ~/' phase Ni3 (AI, Ti) located inside the dendritic grain regions. In a C02 atmosphere, a partial catalytic decomposition of this environment into its basic components oxygen and carbon was obtained. The fracture was intergranular owing to the preferential chemical interaction of O with elements of the interdendritic microsegregation zones. In both C02 and N2 environments, a uniphase layer was formed ahead of the propagating crack tip. This layer was produced via internal oxidation or nitridation caused by interstitial penetration of O or N respectively. It was evident that the nature of formation and the properties of the uniphase layer exert a decisive effect on the HTLCF crack growth characteristics, which enables identification of the mechanism of failure under the various tested environments.
Changes of elastic constants associated with fatigue damage in an aluminium alloy. Ranganathan, N, and Mazot, P. Mater. Sci. Eng. A Nov. 1991 A147 (2) 161-166 Dynamic modulus and contraction ratio changes have been measured following fatigue cycling using a resonance technique on a high-strength AI alloy (2024). It is shown that the classical hardening behaviour is accompanied by a decrease in dynamic modulus. The contraction ratio increases in the beginning followed by a sharp decrease. The consequences of the measured changes in the elastic constants are evaluated for the elastic strain field near a crack tip. It is shown here that the size of the isodeformation profiles can be significantly modified in plane strain conditions, if the altered values of the elastic constants are taken into account.
The influence of nitriding on t h e finite fatigue life of steels. Spies, H.-
J., Scharf, M. and Nguyen, D.T. Harterei-Tech. Mitt. Sept.-Oct. 1991 46 (5) 288-293 (in German)
The distribution of hardness and residual stress of nitrided layers was varied via the content of nitride-forming elements and the nitriding conditions. Statistically ascertained rotating bending investigations on smooth samples have demonstrated that the finite life increases with increasing nitrided case depth, strengthening, core hardness and toughness of the nitrided layer. The endurance behaviour can be interpreted by the dependence of the location of the initial cracking.
Enhanced fatigue crack growth rate at elevated temperatures. Tang, N.-Y., Niessen, P. and Plumtree, A. Z. Metallkd. Sept. 1991 82 (9) 721-726 Fatigue crack propagation (FCP) rates in air for AISI type H13 hot work tool steel were measured over the temperature range 300-600 °C. The frequency-dependent apparent activation energy for thermally activated crack growth was found to be lower than that for oxygen diffusion in ferrite. It is shown that this is the consequence of stress gradients at the crack tip which cause diffusion processes to be position dependent.
Int J Fatigue September 1992
Fatigue crack growth process of steels at the near-threshold region in air and vacuum. Zhu, W. Xi'an Jiaotong Daxue Xuebao (J. Xi'an Jiaotong Univ.) 1991 25 (2) 127-134, 142 (in Chinese) A comparison is made of the crack opening and fatigue crack growth characteristics of three tempered martensitic steels, 2.25Cr-1Mo, SAE 4135, and modified 9Cr-lMo, in ambient air and vacuum (3 x 10-s torr). In vacuum, roughness-induced and plasticity-induced closures are both responsible for crack closure formation in the near-threshold region and the level of the closure is independent of K. tn ambient air, oxidation can further increase the overall closure level by as much as 50% in 2.25Cr-1Mo and SAE 4135 steels, but no detective increment in modified 9Cr-lMo steel. The environment affects crack growth mode: the mixture of intergranular and transgranular in air; and the pure transgranular in vacuum. The da/dNvs. K curves of load decreasing and successive load increasing tests in air do not coincide with each other simply due to the presence of a severe oxide layer.
Limitations of g r o w t h regimes for cracks initiated in s m o o t h fatigue specimens. Kwon, D., Lahodny, H. and Bruckner-Foit, A. Theor. Appl. Fract. Mech. Oct. 1991 16 (1) 63-71 The stages of the growth of small cracks initiating at natural flaws in smooth specimens (e.g. Ni base superalloy) subjected to fatigue loading are characterized, and the dominant propagation mechanisms and corresponding fracture paths are described. Characteristic crack lengths are introduced to assess the transition between the regimes of microstructurally small cracks, physicalty small cracks and long cracks. A log ~o--Iog a diagram is used to derive estimates of these crack lengths. It is shown that simple formulae can be found which relate these characteristic crack lengths to mechanical and material parameters that can be measured using standard fracture mechanics specimens and fatigue tests.
An application of incremental plasticity t h e o r y t o f a t i g u e life prediction of steels. Chen, W.R. and Keer, L.M. J. Eng. Mater. Techno/. (Trans. ASME) Oct. 1991 113 (4) 404-410 An incremental plasticity model is proposed based on the von Mises yield condition, associated flow rule, and nonlinear kinematic hardening rule. In the present model, fatigue life prediction requires only the uniaxial cycle stress-strain curve and uniaxial fatigue test results on smooth specimens. Experimental data on 304 stainless steel and 1045 carbon steel were used to validate this analytical model. It is shown that a reasonable description of steady-state hysteresis stress-strain loops and prediction of fatigue lives under various combined axial-torsional ioadings are given by this model.
Application of minimum energy formalism in a multiple slip bend model for fatigue. II. Crack nucleation and derivation of a generalized C o f f i n - M a n s o n law. Venkataraman, G., Chung, Y.W. and Mura, T. Acta Metal/. Mater. Nov. 1991 39 (11) 2631-2638 A situation of multiple parallel slip bands is considered. Each slip band is modelled as an accumulation of edge dipoles. The dislocation dipole density within the slip bands continually increases with fatigue cycling. The strain energy density within the slip bands consequently builds up with cycling until a critical cycle number when it becomes energetically favourable to nucleate a microcreck within one of the slip bands. This is proposed to be the crack nucleation cycle number. The above criterion based on the strain energy density is used to derive an explicit expression for the number of cycles for crack nucleation. It is shown that there is a parallel between the criterion for crack nucleation and other criteria that are based on the accumulation of a certain critical amount of damage. A generalized Coffin-Manson law for crack initiation is also derived. Copper is used for comparison purposes. The size and most likely site of the just-nucleated crack are discussed.
Application of minimum energy formalism in a multiple slip band model for fatigue. I. Calculation o f slip band spacings. Venkataraman, G.,
Chung, Y.W. and Mura, 7". Acta Metal/. Mater. Nov. 1991 39 ( 1 1 ) 2 6 2 1 - 2 6 2 9
A theory of slip band spacing in fatigued materials has been developed based on a criterion of minimum strain energy accumulation within slip bands. A twodimensional, quasi-monotonic, dipole pile-up model is employed for this purpose. Multiple parallel, equally spaced, mutually interacting slip bands are considered. Each slip band is modelled as an accumulation of dipoles. Partially irreversible slip processes with stochastic fluctuations are allowed in the model. It is shown that for a given imposed plastic work. there exists a unique configuration (number and spacing) of the bands that has the minimum internal energy stored within all bands. An expression for the optimum slip band spacing in polycrystalline materials has been derived based on all experimentally determinable parameters. The effects of plastic strain amplitude, temperature and environment on this optimum slip band spacing are assessed. There is reasonably good agreement between theory and experiment.
Application of the cyclic J-integral t o fatigue crack propagation of AI 2024-T351. Banks-Sills, L. and Volpert, Y. Eng, Fract. Mech. 1991 40 (2) 355-370 An experimental/numerical study of the cyclic J-integral, AJ, is carried out to explain more clearly the meaning of this parameter for fatigue crack growth studies. Constant amplitude fatigue tests with two R ratios (R approx - 0.05 and R approx - 0.5) are performed on compact tension specimens fabricated from AI 2024-T351. A simulation of tests is carried out numerically by means of the finite element method with the material modelled to be elasto-plastic. From the numerical results, values of •J are calculated from both a path-independent integral and load vs. loadline displacement data. Comparisons between these values and those determined from experimental data are seen to be reasonable. The parameter A j is seen to correlate properly the crack growth rate under elastic and small-scale yielding conditions.
345
stainless
1991 A147 (1) 6 7 - 7 5
Energy-absorption characteristics in slow tensile cyclic deformation within the flow stress are examined as functions of temperature and previous plastic strain. The energy absorption is analysed in terms of thermal activation, and the activation energy is determined by separately determining the activation volume from stress relaxation at stress values below the flow stress. The required internal stress and the dislocation velocity-stress exponent are obtained from instantaneous strain rate change experiments. Some possible mechanisms are considered based on the energy absorption and the activation energy, which have different temperature dependences in the two steels.
The influence o f air humidity on neer-threshold fatigue crack growth of 2024-'r3 e l u m i n i u m alloy. Stanzl, S.F., Mayer, H.R. and Tschegg, E.K. Mater. Sci. Eng. A Oct. 1991 A147 (1) 4 5 - 5 4 The environmental influence of humid air, dried air, and vacuum on the fatigue crack growth behaviour of the AI alloy 2024-T3 was measured in the very low threshold regime (down to approx 10-13 m/cycle), using the high-frequency (20000 Hz) technique of ultrasonic resonance fatigue. The crack growth curves, (~a/~N vs. Km=xrelationship) obtained in humid air were characterized by a plateau-like regime (regime with reduced slope of crack growth curve) between 10-9 and 10-1° m/cycle and a threshold value of 2.1 MPa m °'5, The threshold in vacuum was 3.3 MPa m°-s and no plateau-like regime occurred. In dried air, the curve was very close to that in vacuum, when the Kmaxvalues were high enough; at the very lowest Kmaxvalues, however, the curve approached that for humid air, and an almost identical threshold stress intensity value (2.3 MPa m°'s) was found. The fracture morphology reflected the changing cracking mechanisms: ductile fracture with more plastic deformation and some crystallographic and intercrystalline features were observed for 'high'/(max values, whereas less plastic deformation and no crystallographic or intercrystalline features were characteristic of the threshold regime. Hydrogen embrittlement is assumed to be the main mechanism responsible for the observed corrosion fatigue bahaviour of alloy 2024-T3 in humid air.
The effect of N= and CO= environments on t h e f a t i g u e failure of MARM200 + hafnium superalloy at 975 °C. Aghion, E., Bamberger, M. and Berkovits, A. Mater. Sci. Eng. A Nov. 1991 A147 (2) 181-189 High-temperature, low-cycle fatigue (HTLCF) failure mechanisms were studied in unidirectionally solidified MAR-M200 + Hf Ni-based superalloy in pure N2 and C02 environments at 975 °C. The loading conditions were constant and consisted of creep tension and plastic compression according to the cp mode of the strain-rangepartitioning method. The crack initiation and propagation were investigated using scanning electron microscopy, X-ray diffraction and Auger electron spectroscopy. The results obtained indicated that N2 and CO2 atmospheres cannot be treated as passive gaseous environments. On the contrary, these environments have a significant influence on the HTLCF crack growth behaviour. In an N2 environment, the fracture was transgranular. This was a result of an intensive chemical interaction between nitrogen and the main alloying elements making up the ~/' phase Ni3 (AI, Ti) located inside the dendritic grain regions. In a C02 atmosphere, a partial catalytic decomposition of this environment into its basic components oxygen and carbon was obtained. The fracture was intergranular owing to the preferential chemical interaction of O with elements of the interdendritic microsegregation zones. In both C02 and N2 environments, a uniphase layer was formed ahead of the propagating crack tip. This layer was produced via internal oxidation or nitridation caused by interstitial penetration of O or N respectively. It was evident that the nature of formation and the properties of the uniphase layer exert a decisive effect on the HTLCF crack growth characteristics, which enables identification of the mechanism of failure under the various tested environments.
Changes of elastic constants associated with fatigue damage in an aluminium alloy. Ranganathan, N, and Mazot, P. Mater. Sci. Eng. A Nov. 1991 A147 (2) 161-166 Dynamic modulus and contraction ratio changes have been measured following fatigue cycling using a resonance technique on a high-strength AI alloy (2024). It is shown that the classical hardening behaviour is accompanied by a decrease in dynamic modulus. The contraction ratio increases in the beginning followed by a sharp decrease. The consequences of the measured changes in the elastic constants are evaluated for the elastic strain field near a crack tip. It is shown here that the size of the isodeformation profiles can be significantly modified in plane strain conditions, if the altered values of the elastic constants are taken into account.
The influence of nitriding on t h e finite fatigue life of steels. Spies, H.-
J., Scharf, M. and Nguyen, D.T. Harterei-Tech. Mitt. Sept.-Oct. 1991 46 (5) 288-293 (in German)
The distribution of hardness and residual stress of nitrided layers was varied via the content of nitride-forming elements and the nitriding conditions. Statistically ascertained rotating bending investigations on smooth samples have demonstrated that the finite life increases with increasing nitrided case depth, strengthening, core hardness and toughness of the nitrided layer. The endurance behaviour can be interpreted by the dependence of the location of the initial cracking.
Enhanced fatigue crack growth rate at elevated temperatures. Tang, N.-Y., Niessen, P. and Plumtree, A. Z. Metallkd. Sept. 1991 82 (9) 721-726 Fatigue crack propagation (FCP) rates in air for AISI type H13 hot work tool steel were measured over the temperature range 300-600 °C. The frequency-dependent apparent activation energy for thermally activated crack growth was found to be lower than that for oxygen diffusion in ferrite. It is shown that this is the consequence of stress gradients at the crack tip which cause diffusion processes to be position dependent.
Int J Fatigue September 1992
Fatigue crack growth process of steels at the near-threshold region in air and vacuum. Zhu, W. Xi'an Jiaotong Daxue Xuebao (J. Xi'an Jiaotong Univ.) 1991 25 (2) 127-134, 142 (in Chinese) A comparison is made of the crack opening and fatigue crack growth characteristics of three tempered martensitic steels, 2.25Cr-1Mo, SAE 4135, and modified 9Cr-lMo, in ambient air and vacuum (3 x 10-s torr). In vacuum, roughness-induced and plasticity-induced closures are both responsible for crack closure formation in the near-threshold region and the level of the closure is independent of K. tn ambient air, oxidation can further increase the overall closure level by as much as 50% in 2.25Cr-1Mo and SAE 4135 steels, but no detective increment in modified 9Cr-lMo steel. The environment affects crack growth mode: the mixture of intergranular and transgranular in air; and the pure transgranular in vacuum. The da/dNvs. K curves of load decreasing and successive load increasing tests in air do not coincide with each other simply due to the presence of a severe oxide layer.
Limitations of g r o w t h regimes for cracks initiated in s m o o t h fatigue specimens. Kwon, D., Lahodny, H. and Bruckner-Foit, A. Theor. Appl. Fract. Mech. Oct. 1991 16 (1) 63-71 The stages of the growth of small cracks initiating at natural flaws in smooth specimens (e.g. Ni base superalloy) subjected to fatigue loading are characterized, and the dominant propagation mechanisms and corresponding fracture paths are described. Characteristic crack lengths are introduced to assess the transition between the regimes of microstructurally small cracks, physicalty small cracks and long cracks. A log ~o--Iog a diagram is used to derive estimates of these crack lengths. It is shown that simple formulae can be found which relate these characteristic crack lengths to mechanical and material parameters that can be measured using standard fracture mechanics specimens and fatigue tests.
An application of incremental plasticity t h e o r y t o f a t i g u e life prediction of steels. Chen, W.R. and Keer, L.M. J. Eng. Mater. Techno/. (Trans. ASME) Oct. 1991 113 (4) 404-410 An incremental plasticity model is proposed based on the von Mises yield condition, associated flow rule, and nonlinear kinematic hardening rule. In the present model, fatigue life prediction requires only the uniaxial cycle stress-strain curve and uniaxial fatigue test results on smooth specimens. Experimental data on 304 stainless steel and 1045 carbon steel were used to validate this analytical model. It is shown that a reasonable description of steady-state hysteresis stress-strain loops and prediction of fatigue lives under various combined axial-torsional ioadings are given by this model.
Application of minimum energy formalism in a multiple slip bend model for fatigue. II. Crack nucleation and derivation of a generalized C o f f i n - M a n s o n law. Venkataraman, G., Chung, Y.W. and Mura, T. Acta Metal/. Mater. Nov. 1991 39 (11) 2631-2638 A situation of multiple parallel slip bands is considered. Each slip band is modelled as an accumulation of edge dipoles. The dislocation dipole density within the slip bands continually increases with fatigue cycling. The strain energy density within the slip bands consequently builds up with cycling until a critical cycle number when it becomes energetically favourable to nucleate a microcreck within one of the slip bands. This is proposed to be the crack nucleation cycle number. The above criterion based on the strain energy density is used to derive an explicit expression for the number of cycles for crack nucleation. It is shown that there is a parallel between the criterion for crack nucleation and other criteria that are based on the accumulation of a certain critical amount of damage. A generalized Coffin-Manson law for crack initiation is also derived. Copper is used for comparison purposes. The size and most likely site of the just-nucleated crack are discussed.
Application of minimum energy formalism in a multiple slip band model for fatigue. I. Calculation o f slip band spacings. Venkataraman, G.,
Chung, Y.W. and Mura, 7". Acta Metal/. Mater. Nov. 1991 39 ( 1 1 ) 2 6 2 1 - 2 6 2 9
A theory of slip band spacing in fatigued materials has been developed based on a criterion of minimum strain energy accumulation within slip bands. A twodimensional, quasi-monotonic, dipole pile-up model is employed for this purpose. Multiple parallel, equally spaced, mutually interacting slip bands are considered. Each slip band is modelled as an accumulation of dipoles. Partially irreversible slip processes with stochastic fluctuations are allowed in the model. It is shown that for a given imposed plastic work. there exists a unique configuration (number and spacing) of the bands that has the minimum internal energy stored within all bands. An expression for the optimum slip band spacing in polycrystalline materials has been derived based on all experimentally determinable parameters. The effects of plastic strain amplitude, temperature and environment on this optimum slip band spacing are assessed. There is reasonably good agreement between theory and experiment.
Application of the cyclic J-integral t o fatigue crack propagation of AI 2024-T351. Banks-Sills, L. and Volpert, Y. Eng, Fract. Mech. 1991 40 (2) 355-370 An experimental/numerical study of the cyclic J-integral, AJ, is carried out to explain more clearly the meaning of this parameter for fatigue crack growth studies. Constant amplitude fatigue tests with two R ratios (R approx - 0.05 and R approx - 0.5) are performed on compact tension specimens fabricated from AI 2024-T351. A simulation of tests is carried out numerically by means of the finite element method with the material modelled to be elasto-plastic. From the numerical results, values of •J are calculated from both a path-independent integral and load vs. loadline displacement data. Comparisons between these values and those determined from experimental data are seen to be reasonable. The parameter A j is seen to correlate properly the crack growth rate under elastic and small-scale yielding conditions.
345