X-ray Microbeam Diffraction Technique Research Articles

Microscopic stress characterisation of functional iron-based alloys by white X-ray microbeam diffraction

Microscopic residual stress evolution in an austenite (γ) grain during a shape-memory process in an Fe-Mn-Si-Cr alloy was investigated using the white X-ray microbeam diffraction technique. The stresses were measured on a coarse grain, which had an orientation near <144>, parallel to the tensile loading direction with a high Schmid factor for a martensitic transformation. The magnitude of the residual stresses in a grain of the sample, which was subjected to a 23 % tensile strain and subsequent shape-recovery heating, was found to be very small and comparable to that prior to tensile deformation. Measurements of the recovery strain and microstructural analyses using electron backscatter diffraction suggested that the low residual stresses could be attributed to the significant shape recovery caused by a highly reversible martensitic transformation in the grain with a particular orientation.

Microscopic residual stress evolution during deformation process of an FeMnSiCr shape memory alloy investigated using white X-ray microbeam diffraction

Microscopic residual stress evolution in different austenite (γ) grains during shape memory process in an FeMnSiCr alloy was investigated using the white X-ray microbeam diffraction technique. The use of high-energy white X-ray microbeam with small beam size allowed us to measure the microscopic residual stress in coarse γ grains with specific orientation. After tensile deformation large compressive residual stress was evolved in γ grains due to the formation of stress-induced ε martensite, but upon recovery heating it almost disappeared as a result of reverse transformation of martensite. The magnitude of compressive residual stress was higher in grains with orientations close to 〈144〉 and 〈233〉 orientations than in a grain with near 〈001〉 orientation. Analysis of the microstructure of each grain using electron backscattering diffraction suggested that the difference in the magnitude of compressive residual stress could be attributed to different martensitic transformation characteristics in the grains.

X-ray characterisation of local molecular orientation in the electroclinic effect of surface-stabilised SmA liquid crystals

The local molecular orientation in the electroclinic effect of the chiral smectic A phase in a surface-stabilised cell has been determined using a time-resolved synchrotron X-ray microbeam diffraction technique. Space- and time-resolved X-ray wide-angle halo scattering under an electric field reveals the static and dynamic intralayer molecular orientation. The molecular orientation varies spatially in accordance with the stripe texture and is dependent on the applied voltage. It has been found that the deviation of the molecular orientation from the rubbing direction depends strongly on the sample history. The relation between the apparent molecular orientation and the layer structure is discussed.

Counter Method as X-Ray Microbeam Diffraction Technique and Its Application to Stress Concentration Problems

In the present paper, the applicability of the counter method for stress measurement as one of the X-ray microbeam diffraction techniques is discussed. The stress can be measured at a local area of 330μ in diameter for Cr powder and 450μ for HT60 steel by using the crystal oscillation X-ray microbeam diffraction technique. The stress measured by this method agrees with the applied stress, and therefore, this method is suitable for both residual and applied stresses.As an example of the application of the method, internally notched plates were stretched and the stress distributions in the vicinity of notch tips were measured. The stress distributions obtained experimentally at the notch tips were similar to those calculated by the finite element method in the elastic regime. In the plastic regime, however, there was a slight discrepancy between them because of the influence of the yielding conditions of specimens.It is concluded that the counter method is a very effective mean for the studies of stress concentration problems and its application to the field of strength of materials is promissing.

細束Ｘ線応力測定の一方法とその疲労き裂伝ぱ問題への応用

A new method for measuring stress at local area of about 100μ in an diameter by the X-ray microbeam diffraction technique was proposed. The method can be regarded as an improvement of the single incident angle method and uses information on lattice strain along the whole Debye ring in order to determine the stress value. The accuracy of the stress value measured by this method was found to be nearly the same as that of the sin2ψ method. As an example of the application of the method to fatigue crack growth problems, the residual stress field near the fatigue crack tip was measured after the application of several cycles of overloads. The compressive residual stress became higher as the number of overload cycle increased. The higher compressive residual stress may be responsible for the greater amount of growth retardation of a fatigue crack due to increasing number of overload cycles.

Correlation of X-Ray Microbeam Diffraction Pattern and Substructure by Transmission Electron Microscopy

The X-ray microbeam diffraction technique is a powerful method for observation of substructures in metallic materials, because of its ability to measure the microstructural changes in a localized region quantitatively and non-destructively. In recent years, the microstructure in the vicinity of fatigue crack tip has been investigated by using this technique and the mechanism of crack propagation has been discussed based on the results obtained. However, the correlation of the X-ray microbeam diffraction patterns and the microstructures observed by the other methods has not been made sufficiently clear.In the present study, the X-ray microbeam diffraction patterns from deformed specimens were compared with the substructures photographed by means of transmission electron microscopy.The material used was 0.12% carbon steel, and the low cycle fatigue test, the high cycle fatigue test and the impact test were performed to form substructures in the specimens.A good correlation was obtained qualitatively between the X-ray microbeam patterns and substructures in both the low cycle fatigued and impacted specimens. It was possible to distinguish the mode of substructure through X-ray microbeam diffraction patterns.A disagreement existed, however, between the values of subgrain size obtained by different analytical methods. It is considered that getting agreement between these values is difficult in the present stage, because of the assumptions on analyses. But the subgrain size should be a good parameter representing the plastic deformation, if an analytical method suitable for the mode of diffraction pattern is adopted.

Local Plastic Strain Measurement by X-Ray Microbeam Diffraction Technique

Local Plastic Strain Measurement by X-Ray Microbeam Diffraction Technique

The Effect of Stress Amplitude on Fatigue Processes of Annealed and Cold-Rolled Low-Carbon Steels

The specimens of 0.01%C annealed and 15% cold-rolled steels were fatigued under completely reversed plane bending. The effect of stress amplitude on fatigue process of these materials was investigated by using the X-ray microbeam diffraction technique, optical microscopy and electron microscopy. The results are summarized as follows:(1) The stress cycles at slip band formation Ns and the crack initiation Nc were measured of both the materials by means of an optical microscope. The ratios of Ns and of Nc to the number of stress cycles at fracture Nf were obtained of the annealed material asNs:Nc:Nf=0.02∼0.04:0.40:1, and of the cold-rolled material they are expressed asNs:Nc:Nf=0.002∼0.003:0.26:1.The critical stress amplitude of slip band formation during fatigue in annealed materials is nearly equal to the frictional stress.(2) The amount of crystal deformation during fatigue was dependent on the applied stress amplitude. In the case of the annealed material, the micro-lattice-strain Δd/d at the half of the total fatigue life was related to the stress amplitude σn in the following equation, α·σn=9.3+2.0×104(Δd/d), where α is the stress concentration factor of the specimens 1.03.The excess dislocation density D is also a function of stress amplitude. The function is approximated as follows:α·σn=11.0+5.8×10-4√D, when σn is less than 22kg/mm2.(3) For the cold-rolled material, total misoriention β at the half of the total fatigue life increased when stress amplitude was higher than the yield stress. Subgrain size decreased during fatigue and the amount of its decrease was larger when σn was higher.(4) Fatigue cracks were nucleated through the linking of pores formed along the subboundaries in the annealed material. A similar mechanism of fatigue crack initiation by pore linking was verified for low stress amplitude fatigue in the case of the cold-rolled material. On the other hand, the formation of pores was not observed in high stress amplitude fatigue.

Investigation of Stress State at Fatigue Crack Tip by Means of X-Ray Microbeam

The stress-strain relation at the vicinity of fatigue crack tip is one of the most demanded points in the study of fatigue crack propagation. Recently, the oscillating crystal X-ray microbeam diffraction technique which enables to measure the stress in such a minute domain as the vicinity of fatigue crack tip has been devised by K. Honda and T. Konaga.In the present study, the stress condition at the crack tip was studied by this technique. An alternating tension-compression load was applied to the annealed and recovered plate specimens of 0.05%C low carbon steel with notches at the both sides. The stresses at the vicinity of fatigue crack tip in the area of 180μ in diameter were measured under several loading conditions. The results obtained are summarized as follows;(1) The stress concentration factor, which is the ratio of the stress at the maximum load or the minimum load to the applied nominal stress, is approximately the same for both annealed and recovered specimens: it's value is nearly unit for compression load, nearly 2.5 for tension load in the case of annealed specimens and nearly 2.2 in the case of recovered specimens.(2) The mean value of cyclic stress at the vicinity of fatigue crack tip is an almost zero as a consequence of compressive residual stress when the applied mean stress is zero.(3) No remarkable distribution of residual stress is measured in the vicinity of crack tip.(4) The result mentioned in (1) suggests that the cyclic stress-strain relation at the tip of crack having a relatively low propagation rate is similar to the relation obtainable after the saturation of cyclic hardening or softening.(5) The residual stress at the crack tip tends to change in reverse direction to the applied mean stress so that the cyclic stress at crack tip is almost in a fully reversed stress condition almost irrespective of the mean applied stress.

Fatigue Crack Propagation in Low-Carbon Steel under Doubly-Repeated Stress

A new method of the X-ray microbeam diffraction technique was used to measure the local residual stress near the fatigue crack tip. The residual stress was compressive at the crack tip and changed to tensile away from the crack tip. The shape of the residual stress distribution ahead of the crack tip was found to agree with the analytical result derived by using Rice's rigid plastic strip model, although the maximum compression at the crack tip was lower than that expected from the analysis. The calculated distance from the crack tip to the point where the residual stress changed from compression to tension was 1.5∼2 times as long as the distance measured by the X-ray method.Three kinds of plastic regions were observed ahead of the fatigue crack tip, i.e., (1) the region calculable from Dugdale's equation (ζ-region), (2) the slip band region (ξ-region), and (3) the substructure-formed region where the formation of substructure was evidently observed by the X-ray microbeam method (η-region).Fatigue crack propagation under doubly-repeated stress was discussed on the basis of the results of microscopic observations mentioned above. The influence of stress cycling at the first stress level on the propagation rate under the second stress level was quantified with a parameter κ asκ=Kp/K, where K is the applied stress intensity factor and Kp is the value of the stress intensity factor obtained by substituting the measured value of dl/dN into the K vs. dl/dN relation for the constant stress amplitude fatigue. Five components were first considered to affect the κ value asκ=1+Δκr+Δκd+Δκs+Δκb+Δκpwhere Δκr, Δκd, Δκs, Δκb and Δκp represent the contributions of residual stress, fatigue damage, strain hardening, the blunting of the crack tip and the profile of the crack front within the specimen thickness, respectively.Several examples of the variation of κ with the increment λ of the crack length after the time of stress change were measured for fatigue with a high-low drop of the stress amplitude. These variations were explained with three values: a negative value of Δκr in the region with the compressive residual stress, a positive value of Δκd in ηv-and ξv-regions, and a negative value of Δκs in the region of ξv<λ<ζv. As λ approached to ζv, the κ value became unity.In the case of stress-raise fatigue, the variation of κ with λ was explained by a negative value of Δκd in ηv-region and a positive value of Δκs in the region of ξv<λ<ζv.

Microscopic Observation of Fatigue Crack Initiation Process in Low-Carbon Steel Notched Specimens

Sharply notched specimens of 0.03%C annealed steel were fatigued under completely reversed in-plane bending. Microstructural change in the vicinity of the notch root during fatigue process preceding crack initiation was examined by means of the X-ray microbeam diffraction technique and optical microscopy. The following are the summary of the results obtained.(1) The distribution of the excess dislocation density near the notch root just before crack initiation was measured with the X-ray microbeam technique and was used to evaluate the stress amplitude at the notch root, termed as the effective stress amplitude σeff. The relation between σeff and the number of stress cycles at crack initiation near the notch root Nnc was equal to that between the stress amplitude σ and the number of stress cycles at crack initiation Nc for plain specimens. A method of estimating Nnc of notched specimens from σ-Nc relation for plain specimens was proposed.(2) The formation of slip bands for notched specimens took place when the average value of elastic stress amplitude over one grain at the notch root was higher than the lower yield stress of the test material.(3) The initiation of fatigue cracks for notched specimens was thought to occur when the stress amplitude was high enough for the linked micro cracks to grow beyond the grain boundary, which were formed along the slip bands within a grain at the notch root. The critical stress amplitude can be correlated to the threshold value of the stress intensity factor in fatigue crack propagation laws proposed by Paris et al.

Microscopic Observations of Fatigue Crack Initiation Process in 18-8 Austenitic Steel

It is suggested that fatigue failure mechanisms in the face-centered cubic metals are greatly affected by stacking fault energy. It was from this viewpoint that the fatigue crack initiation and stage I type crack propagation in 18-8 austenitic steel which had the lowest stacking fault energy among the face-centered cubic metals on the market, were discussed by the X-ray microbeam diffraction technique and the replica electron microscopic method.The fatigue slip line at room temperature tests has fine and straight configurations which are characteristic of low stacking fault energy materials, while the wavy and coarse slip line is typical of fatigue tests at 200°C where screw dislocation is more easily prone to cross slip. In both of these cases very complicated deformation configurations are caused by double slip and cross slip near the grain boundaries, and frequent extrusion and intrusion are observed in these areas. Fatigue crack nucleation might be caused by stress concentration at the notch and peak topography. The stage I type fatigue crack propagates immediately after the initiation, mainly along and frequently across the intense slip lines. Its growth in the area neighbouring the grain boundary runs in the direction that depends on both the crystal orientations of the grain containing the crack and the grains adjacent to it.Total misorientation and micro lattice strain measured by X-ray micro-beam diffraction technique increase abruptly at early fatigue stressing, then equilibrium values are attained and finally increase rapidly. These three periods during the fatigue deformation might be corresponding to those of the fine slip line initiation, the intensification of each slip line without new slip line formation and of final initiation of micro crack, respectively. Furthermore it will be noticed that the equilibrium value of total misorientation of 18-8 austenitic steel during the fatigue process is about one-tenth of that of carbon steel.The area of substructural zone near the fatigue crack of 18-8 austenitic steel is smaller than that of aluminum of high stacking fault energy and body-centered cubic iron. Therefore, the formations of subgrain and martensite could not be detected by X-ray micro-beam diffraction technique when irradiated by Cr-Kα of 200μφ beam size. In order to clarify these points the detailed observation at the fatigue crack tip must be made by using transmission electron microscopy. These results will be reported elsewhere.

Substructure Formed in the Vicinity of the Fatigue Crack in 18-8 Austenitic Steel

The Stage II type fatigue crack propagation processes in 18-8 austenitic steel were studied upon observation of the substructure formed in the vicinity of its fatigue crack, by the X-ray microbeam diffraction technique and by the replica electron microscopic method. The main results obtained are as follows.(1) Although 18-8 austenitic steel has very low stacking fault energy, it breeds subgrains in the vicintiy of the fatigue crack, characteristically indistinct and indefinable in observation by microbeam X-ray diffraction technique.(2) The area of the substructural zone thus formed in the vicinity of the fatigue crack is small as compared with that formed in the metals where screw dislocation cross slips easily and is nearly limited within the grain that contains the fatigue crack. The fatigue deformation in the grain is remarkably uneven. In this way the X-ray Laue method is considered to be suitable for the detailed investigation of substructure formed in the fatigue deformation area, and various information can be obtained from each grain by its application.(3) An α-martensite has been detected in the vicinity of fatigue crack and fatigue crack tip. Fatigue crack can be grown by the repeated cleavage-like fracture of the martensitic structure, and therefore, the fatigue fracture mechanism in 18-8 austenitic steel is considerably different from other metals.(4) Well defined cross slip lines are observed in the fatigued 18-8 austenitic steel, but the region in which this cross slip occurs is limited to the spot near the grain boundary. This will suggest that the grain boundary acts as the strong obstruction to dislocation motin.

結晶振動細束X線回折法による微小領域の応力測定と二, 三の応用

結晶振動細束X線回折法による微小領域の応力測定と二, 三の応用

Influence of Matrix Micro-Structure on the Relation between the Applied Stress and the Crack Propagating Rate

Three kinds of low carbon steel were examined to study the relation between the applied stress condition and the crack propagating rate. The respectively chosen specimens were those initially annealed, those stretched and those recovered. These were all subjected to alternating push-pull load.The study was made from the view point of micro-structural change at the crack tip observed by the X-ray microbeam diffraction technique.

On the Crack Propagating Mechanism and the Micro-Structural Change at the Crack Tip Observed by X-Ray Micro-Beam Diffraction Technique

The mechanism of fatigue crack propagation has been investigated from the point of view of micro-structural change at the crack tip. The relation between the crack propagating mechanism and the developed sub-structure is discussed.

The X-Ray Investigation of Microstructural Change Caused by Low-Cycle Fatigue in Low Carbon Steel

The authors have applied X-ray diffraction techniques to the study of low-cycle fatigue in order to discuss its macroscopic behavior from the microscopic point of view. In a previous paper, it was reported that a good correlation was obtained between the particle size measured by the profile analysis of the X-ray diffraction peaks and the damage fraction in 0.16% C steel under low-cycle fatigue of constant strain amplitude for some range of the strain range. It is found that the nondestructive measurement of the remaining life might be possible using this correlation. However, the above finding was not successfully used for the discussion of the mechanism of deformation and fracture in low-cycle fatigue, because the publications dealing with the analytical method and the application of this X-ray technique gave little available information for relating the data obtained by the authors to the microstructural changes reported by various investigators.In these circumstances, the authors applied the X-ray microbeam diffraction technique to a further study of the microstructural changes which occurred during the low-cycle fatigue. The behavior of the subgrain was observed by this technique, and was made to bear on the measurements of the X-ray profile analysis.The following was obtained as the results of this investigation:(1) Low-cycle fatigue before visible cracks occurred had two stages in its process, each of them having its own particular X-ray phenomenon. The first stage was the stage of subgrain formation indicated clearly by the changes in the subgrain size and the interaction function of dislocations. The subgrain size was reduced rapidly and was inclined to saturate. The interaction function, which was defined as the ratio of the dislocation density obtained from the value of microstrain to that from the particle size, was reduced considerably. On the other hand, the excess dislocation density at the subgrain walls increased remarkably in the second stage, which was termed the stage of the subgrain development. The number of cycles at which the first stage was completed was around 270 in the case of the strain amplitude of 2.0%.(2) The observation of surface patterns by electron microscopy showed a clear development of surface irregularities like extrusion and intrusion after the first stage was completed. This development may be related to that of the subgrain.(3) The particle size had a linear relation with the subgrain size, and the interaction function indicated well the state of the subgrain. However, for the practical use of these measurements of X-ray profile analysis for closer examination of the substructure which appears in plastically deformed metals, it is necessary that further investigation will be made along this line.

Effect of the Mean Stress Applied to Specimens on the Fatigue Crack Propagating Rate and Observation of the Micro-Structure at the Crack Tip by the X-Ray Microbeam Diffraction Technique

When the mean stress is applied to the notched low-carbon steel specimens subjected to alternating push-pull load, the effect on the crack propagating rate is discussed from the view point of the microstructural change at the crack tip observed by the X-ray microbeam diffraction technique.

Observation of Fatigue Crack Propagation Process in Cold-Rolled Low-Carbon Steel by X-Ray Microbeam Technique

The microstructural change around a fatigue crack in 15% cold-rolled low-carbon steel specimens was investigated by using the back-reflection X-ray microbeam diffraction technique. The results obtained are summarized as follows:(1) Dislocations introduced by predeformation rearrange themselves in the vicinity of a fatigue crack. The excess dislocation density in a subgrain, the subgrain size and the micro lattice strain in a grain are decreased by this rearrangement of dislocations while the excess dislocation density at subboundaries increases. In this way the preformed substructure developes near a fatigue crack. Micro cracks are expected to exist at subboundaries of fatigue-induced substructure and a main crack will propagate along subboundaries, joining these micro cracks.(2) The crack propagation rate has a great deal to do with the degree of development in substructure at crack tips, that is, the amount of decrement in micro lattice strain and subgrain size become larger as the propagation rate increases. It is considered that by using this relation, the estimation of the propagation rate of a crack whose rate is unknown will be possible, if the information about substructure at the crack tip is given in the observation by the X-ray microbeam.

X-ray Investigation on Fatigue Fracture of Notched Steel Specimen : Observation of Deformation near the Grain Tip of Fatigue Crack Generated in Annealed Low-Carbon Steel by Means of X-ray Microbeam Diffraction Technique

X-ray Investigation on Fatigue Fracture of Notched Steel Specimen : Observation of Deformation near the Grain Tip of Fatigue Crack Generated in Annealed Low-Carbon Steel by Means of X-ray Microbeam Diffraction Technique