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The Eigen equation of crack growth to metals
A new resistance-curve method was proposed for predicting the growth threshold of short fatigue cracks near the notch root. The wistance curve was constructed in terms of the experimentally determined threshold value of the maximum stress intensity factor which was the sum of the threshold effective stress intensin, range A& ti and the opening stress intensity factor /bp tti The A&,, ,,, value was constant. irrespective of crack length or notch geometry. The relation between. f& m and crack length was independent of notch geometry. The predicted effects of the notch-root radius and the notch depth on the propagation threshold of shon fatigue cracks were compaed with the experimental date obtained using centre-notched specimens (JIS SM41B steel) with various notch-root radii and single-edge notched specimens with various notch depths Excellent agreement was obtained between predictions and experiments 17 refs.
The Eigen equation of crack growth to metab. Zhao. X. Eng. Fracf.me&. 1988.30, (6). xl-757 There IS an assumption that crack growth is controlled by the high strain area at the very tip of a crack. Based upon the theory of the interaction energy between the inclusion and the applied stress. and the theon/ of the force acting on elastic singularity. the Eigen equation of crack growth is proposed According to the Eigen equation, the relation between fracture toughness K,, and tensile propenies is researched A general analytical expression for calculation of fatigue threshold values of common metals and alloys (eg Al. Ni. Cu. low alloy steels, 18/8 stainless steel, AI-45Cu. Cw4OZn. Monel. and Inconel) is also dewed The fracture toughness and fatigue threshold values for some materials are calculated It is found that the theoretical values are in good agreement with the experimental results A new method for predicting the Eigen value is also proposed. 13 refs.
On the ohvsical woeas in the deformation and fracture of ukrastrengtli s&l. F&i, If. Eng. Fract. Mech. 1988,30, (6). 747-751 The uniexial stretch process of ultra-strength steel, which was made by means of sound emission and fracture surface observation, is summarized. A new idea for ttw sectionarmed power hardening and the division of the specimen fracture surface is suggested. To confirm this new idea. a theoretical explanation is given. Also included is a physical graph of the deformation and fracture during the uniaxial stretch. 5 refs.
The effect of near crystal orientation on intermediate temperature mechanical behsviour of single crystal nickel-base superalloys. (Dissertation). Richards, R.J. l&s. Abstr. htt. Sept. 1988.49, (3) Creep and stress rupture dependencies on pr~marv and secondaw CWtSl Orientation at !ntermedlate temperatures and stresses have been reported for single crwtal Ni-base superalloy MAR-M200 and MAR-M247 at crystal onentatlons near . These orientation dependencies were rationalized in terms of < 112 > slip system activltv during Primaw
{l 11)
creep and subsequent work hardening as the crystals rotated Into orientations allowing duplex and multiple slip. This research was ntiated to tnvestlgate the elevated temperature deformation behawour of a high-volume fraction y’ strengthened single crystal NI-base superalloy NASAIR 100. under high mean stress fatigue and creep loading to determine whether or not high mean stress fatigue behaviour IS also crystal orientation sensitive near co01 > High mean stress fatigue tests results were obtalned at two test frequencies and creep test results were obtalned at the high mean fatigue stress and the mawmum fatigue stress Results showed no significant effect of crystal orientation on either high mean stress fatigue behaviour or creep behaviour Lack of significant near ~001 z crystal orientation affected creep behaviour led to the re-evaluation of single cn/stal Ni-base superalloy creep behavlour because of the inconslstencles in the orientation affected behaviour among stmllar single cwstal superalloys. MAR-MZOO creep test results, repeated for this research at orientations tested for NASAIR 100. show primav creep strains and primary c reep rates that vary with crystal orientation in the same manner as previous MAR-M200 work Comparison of primary creep results for the alloys tested here and those in the literature shows that there is. as yet. no consistent description for the effect of orientation on near ~001 > single crystal NI-base superalloy behavlour The Inconsistencies in crystal orientation affected behaviour are rationaltzed in terms of pr~man/ creep behaviour LImIted primary creep strain results I” the absence of signtficant orientation effects. Consequently. those parameters that limit primary creep response near ~001 > also llmlt significant orlenration effects
A study of fatigue microcrack growth in aluminium alloy 707S-T551. (Dissertation). Chung, J.S. D&s. Absh: Int. Sept. 1988.48, (3). Small crack growth was investigated experimentally in a commonly used IrwXUral Al alloy. 7075T651, for different strain amplitudes. Two types of specimen were used: rotating bending and a wide plate in cantilevered bending. The rotating bending specimen had close to uniaxial stress while the plate had biaxial tension near its centre, where data on crack growth were taken. Tests of plate specimens were also conducted for several different R-ratios at a lower strain amplitude. Cracks started slightly sooner in plate specimens than in rotating bending specimens for a given strain amplitude. Cracks initiated sooner in plate specimens at R = 0 than R = -1 for tests with a strain amplitude of 0 35% In these tests. small crack growth rates were significantly higher than large crack growth rates foi a gwen AK. Small crack growth rates do not fall along one line when plotted vs and when the R-ratid or the amphtude of applied cyclic strains are different. For a given AK., the higher’the amplitude or the ‘higher the R-ratlo. the faster the growth rate When growth rate IS plotted vs AK it was found that cracks grew faster I” plate
Int J Fatigue May 1999
specimens than in rotating bending specimens for a given strain amplitude. When microcrack growth rate in plate skimens at R = - 1, divided by crack length. is plotted on lowlog coordinates vs ranae of maximum shear strain. or range of octahedral shear strain. the data tend to follow&e line. In other words, crack growth rate was found to be proportional to the product. of one of these strain range parameters with an exponent and crack length. For maximum shear strain range. the data from plate specimens and those from rotating bending specimens correlated well.
Ths mlm of pbaia Mrmnbn FJ.M.andMujidsmrsh J. Tribohqy (Tram.
in mr
of thin films.
7kngmu A.G., bt+“~,
EA. ASME)
Oct.
1963.110. (4). W2-W
The correlation between mechanical stresses and tribological behaviour for thin films was studied. A noble metal layer (Au) was applied on different substrates (Co and glass). Depending on the thickness of the film and the mechanicalproperties of the substrate. thewearof the film in a pin-on-plate (steel/Au) configuration changed. Using finiteelement calculations It was shown that the geometw of the system. the mechanical properties of the substrate and the contact load determined the mechanical deformations of the top layer. The calculated van Mises stress averaged over the contact ema end the depth of the thin film correlated well with the year measured. If this average van Miws stress was above the yield stress of the thin film. the wear increased enormously. indicafing the importance of plastic deformation in the film. A relatively simple low cycle fatigue model using the CoffirwManson relation gave a good description of the wear beheviour as a function of the avenge van M&es stress 17 refs.
Testingand contraI for prediotlng fmt@ue damage in W va. Nma; CK. Dim. Ahur. Int. Apr. 1988, Q, (10)
structures.
The onset and growth of fatigue cracks in metal structures can lead to catastrophic consequences if left unchecked A frequent nondestructive inspection and evluation programme may avert an impending disaster and considerably extend the useful selvvze life of a structure. However. due to the time and expense involved in thorough inspection programmes. a simple and Inexpensive method that provides a visual warning of potential fatigue damage would be quite useful. The use of notched crack gauges to provide a clear indication of the onset of fatigue crack grmvth in structural steel details is examined. The crack gauge consists of a thin steel coupon which can be bonded to a structural member in the vicinity of a known stress raiser. such as et the end of a cover plate or near a stiffener. The crack gauge concept has traditionally been used to correlate fatigue crack growth in the gauge to crack growth in the structure. The present emphasis. however. is to use the crack gauge to detect the onsat of fatigue crack growth. The geometry of the crack gauge is designed such that either initiation or significant crack propagation in the gauge provides a direct indication that the structural element has developed a detectable fatigue crack. The structure element studied is a transverse welded butt joint member containing a full-length lack of penetration (LOP) discontinuity. The effect of the LOP discontinuity on the fatigue behaviour of transverse welded butt joints is funher investigated, with emphasis on the fraction of the cyclic life spent in fatigue crack initiation. The crack gauge fatigue test results are compared with analytical predictions of the fraction of cyclic life spent in crack initiation and crack propagation. The results of the LOP and the control fatigue tests are compared with those from other studies Finally. the suitability of the crack gauge for actual use is evaluated with practical examples. and recommendations for design are made
New apparatus for studying fatigue deformation at high rnagnifications. St&en& R.R. and Hoeppner,D. W Rev. Sci. Instrum. Aug. 1s8e, 59, (8-l ), 1412-l 419 One of the steps taken to enhance accurate fatigue life estimations and material mcdelling is the development of an electrohydraulic. servo-controlled feedback fatigue apparatus that has been joined to a scanning electron microscope. This apparatus allcws in situ observations of cyclically loaded specimens undergoing fatigue deformation. Using thts apparatus, recordings can be made of the events related to the surface response of materials under different loading conditions. showing how microstruclural features influence crack nucleation and propagation beheviour. With the development of this apparatus. existing mathematical models describing the fatigue process can be enhanoed or improved. and more accurate fatigue life estimation methods can be obtained. The apparatus developed and a few selected results on 7076T6 Al alloy. lMl685 Ti alloy and pure Ni are described 9 refs.
Analyticel and anal ue techniques for determini potential distribution around crocks. Omen, D.A., Kendall. J.% a&Knott J.F. lnt. J. Fact. May ?!I!? 1 ,37, (1). M-R12 The potential distribution around short cracks which lie at an angle to the testpiece surface is addressed, relating to the fact that small fatigue cracks usually grow at an angle of approx 45’ to the applied tensile stress axis. It is then imponant to know whether the fact that the cracks are at 45’ rather than 9r. to the surface so affects the potential calibration that the inferred crack growth rate is significantly in error The impwtance of growth is increased in materials which exhibit planar slip characteristics. 12 refs.
211
The Eigen equation of crack growth to metab. Zhao. X. Eng. Fracf.me&. 1988.30, (6). xl-757 There IS an assumption that crack growth is controlled by the high strain area at the very tip of a crack. Based upon the theory of the interaction energy between the inclusion and the applied stress. and the theon/ of the force acting on elastic singularity. the Eigen equation of crack growth is proposed According to the Eigen equation, the relation between fracture toughness K,, and tensile propenies is researched A general analytical expression for calculation of fatigue threshold values of common metals and alloys (eg Al. Ni. Cu. low alloy steels, 18/8 stainless steel, AI-45Cu. Cw4OZn. Monel. and Inconel) is also dewed The fracture toughness and fatigue threshold values for some materials are calculated It is found that the theoretical values are in good agreement with the experimental results A new method for predicting the Eigen value is also proposed. 13 refs.
On the ohvsical woeas in the deformation and fracture of ukrastrengtli s&l. F&i, If. Eng. Fract. Mech. 1988,30, (6). 747-751 The uniexial stretch process of ultra-strength steel, which was made by means of sound emission and fracture surface observation, is summarized. A new idea for ttw sectionarmed power hardening and the division of the specimen fracture surface is suggested. To confirm this new idea. a theoretical explanation is given. Also included is a physical graph of the deformation and fracture during the uniaxial stretch. 5 refs.
The effect of near
{l 11)
creep and subsequent work hardening as the crystals rotated Into orientations allowing duplex and multiple slip. This research was ntiated to tnvestlgate the elevated temperature deformation behawour of a high-volume fraction y’ strengthened single crystal NI-base superalloy NASAIR 100. under high mean stress fatigue and creep loading to determine whether or not high mean stress fatigue behaviour IS also crystal orientation sensitive near co01 > High mean stress fatigue tests results were obtalned at two test frequencies and creep test results were obtalned at the high mean fatigue stress and the mawmum fatigue stress Results showed no significant effect of crystal orientation on either high mean stress fatigue behaviour or creep behaviour Lack of significant near ~001 z crystal orientation affected creep behaviour led to the re-evaluation of single cn/stal Ni-base superalloy creep behavlour because of the inconslstencles in the orientation affected behaviour among stmllar single cwstal superalloys. MAR-MZOO creep test results, repeated for this research at orientations tested for NASAIR 100. show primav creep strains and primary c reep rates that vary with crystal orientation in the same manner as previous MAR-M200 work Comparison of primary creep results for the alloys tested here and those in the literature shows that there is. as yet. no consistent description for the effect of orientation on near ~001 > single crystal NI-base superalloy behavlour The Inconsistencies in crystal orientation affected behaviour are rationaltzed in terms of pr~man/ creep behaviour LImIted primary creep strain results I” the absence of signtficant orientation effects. Consequently. those parameters that limit primary creep response near ~001 > also llmlt significant orlenration effects
A study of fatigue microcrack growth in aluminium alloy 707S-T551. (Dissertation). Chung, J.S. D&s. Absh: Int. Sept. 1988.48, (3). Small crack growth was investigated experimentally in a commonly used IrwXUral Al alloy. 7075T651, for different strain amplitudes. Two types of specimen were used: rotating bending and a wide plate in cantilevered bending. The rotating bending specimen had close to uniaxial stress while the plate had biaxial tension near its centre, where data on crack growth were taken. Tests of plate specimens were also conducted for several different R-ratios at a lower strain amplitude. Cracks started slightly sooner in plate specimens than in rotating bending specimens for a given strain amplitude. Cracks initiated sooner in plate specimens at R = 0 than R = -1 for tests with a strain amplitude of 0 35% In these tests. small crack growth rates were significantly higher than large crack growth rates foi a gwen AK. Small crack growth rates do not fall along one line when plotted vs and when the R-ratid or the amphtude of applied cyclic strains are different. For a given AK., the higher’the amplitude or the ‘higher the R-ratlo. the faster the growth rate When growth rate IS plotted vs AK it was found that cracks grew faster I” plate
Int J Fatigue May 1999
specimens than in rotating bending specimens for a given strain amplitude. When microcrack growth rate in plate skimens at R = - 1, divided by crack length. is plotted on lowlog coordinates vs ranae of maximum shear strain. or range of octahedral shear strain. the data tend to follow&e line. In other words, crack growth rate was found to be proportional to the product. of one of these strain range parameters with an exponent and crack length. For maximum shear strain range. the data from plate specimens and those from rotating bending specimens correlated well.
Ths mlm of pbaia Mrmnbn FJ.M.andMujidsmrsh J. Tribohqy (Tram.
in mr
of thin films.
7kngmu A.G., bt+“~,
EA. ASME)
Oct.
1963.110. (4). W2-W
The correlation between mechanical stresses and tribological behaviour for thin films was studied. A noble metal layer (Au) was applied on different substrates (Co and glass). Depending on the thickness of the film and the mechanicalproperties of the substrate. thewearof the film in a pin-on-plate (steel/Au) configuration changed. Using finiteelement calculations It was shown that the geometw of the system. the mechanical properties of the substrate and the contact load determined the mechanical deformations of the top layer. The calculated van Mises stress averaged over the contact ema end the depth of the thin film correlated well with the year measured. If this average van Miws stress was above the yield stress of the thin film. the wear increased enormously. indicafing the importance of plastic deformation in the film. A relatively simple low cycle fatigue model using the CoffirwManson relation gave a good description of the wear beheviour as a function of the avenge van M&es stress 17 refs.
Testingand contraI for prediotlng fmt@ue damage in W va. Nma; CK. Dim. Ahur. Int. Apr. 1988, Q, (10)
structures.
The onset and growth of fatigue cracks in metal structures can lead to catastrophic consequences if left unchecked A frequent nondestructive inspection and evluation programme may avert an impending disaster and considerably extend the useful selvvze life of a structure. However. due to the time and expense involved in thorough inspection programmes. a simple and Inexpensive method that provides a visual warning of potential fatigue damage would be quite useful. The use of notched crack gauges to provide a clear indication of the onset of fatigue crack grmvth in structural steel details is examined. The crack gauge consists of a thin steel coupon which can be bonded to a structural member in the vicinity of a known stress raiser. such as et the end of a cover plate or near a stiffener. The crack gauge concept has traditionally been used to correlate fatigue crack growth in the gauge to crack growth in the structure. The present emphasis. however. is to use the crack gauge to detect the onsat of fatigue crack growth. The geometry of the crack gauge is designed such that either initiation or significant crack propagation in the gauge provides a direct indication that the structural element has developed a detectable fatigue crack. The structure element studied is a transverse welded butt joint member containing a full-length lack of penetration (LOP) discontinuity. The effect of the LOP discontinuity on the fatigue behaviour of transverse welded butt joints is funher investigated, with emphasis on the fraction of the cyclic life spent in fatigue crack initiation. The crack gauge fatigue test results are compared with analytical predictions of the fraction of cyclic life spent in crack initiation and crack propagation. The results of the LOP and the control fatigue tests are compared with those from other studies Finally. the suitability of the crack gauge for actual use is evaluated with practical examples. and recommendations for design are made
New apparatus for studying fatigue deformation at high rnagnifications. St&en& R.R. and Hoeppner,D. W Rev. Sci. Instrum. Aug. 1s8e, 59, (8-l ), 1412-l 419 One of the steps taken to enhance accurate fatigue life estimations and material mcdelling is the development of an electrohydraulic. servo-controlled feedback fatigue apparatus that has been joined to a scanning electron microscope. This apparatus allcws in situ observations of cyclically loaded specimens undergoing fatigue deformation. Using thts apparatus, recordings can be made of the events related to the surface response of materials under different loading conditions. showing how microstruclural features influence crack nucleation and propagation beheviour. With the development of this apparatus. existing mathematical models describing the fatigue process can be enhanoed or improved. and more accurate fatigue life estimation methods can be obtained. The apparatus developed and a few selected results on 7076T6 Al alloy. lMl685 Ti alloy and pure Ni are described 9 refs.
Analyticel and anal ue techniques for determini potential distribution around crocks. Omen, D.A., Kendall. J.% a&Knott J.F. lnt. J. Fact. May ?!I!? 1 ,37, (1). M-R12 The potential distribution around short cracks which lie at an angle to the testpiece surface is addressed, relating to the fact that small fatigue cracks usually grow at an angle of approx 45’ to the applied tensile stress axis. It is then imponant to know whether the fact that the cracks are at 45’ rather than 9r. to the surface so affects the potential calibration that the inferred crack growth rate is significantly in error The impwtance of growth is increased in materials which exhibit planar slip characteristics. 12 refs.
211