Effects of the creep deformation on the fractal dimension of the grain boundaries in an austenite steel

The change in the fractal dimension of the grain boundaries during creep was investigated using an austenitic SUS304 steel at 973 K. The fractal dimension of the grain-boundary surface profile (the fractal dimension of the grain boundaries, D, 1 < D < 2) in the plane parallel to the tensile direction (in the parallel direction) and in the transverse direction, was examined on specimens deformed up to rupture (about 0.30 creep strain). Grain boundaries became serrated and the fractal dimension of the grain boundaries increased with increasing creep strain, because the density of slip lines which formed ledges and steps on grain boundaries increased as the creep strain increased. The increase in the fractal dimension due to creep deformation was slightly larger under the higher stress (118 MPa) than under the lower stress (98 MPa), while the increase of the fractal dimension with strain was a little larger in the specimens tensile-strained at room temperature (293 K) than in the crept specimens. These results were explained by the grain-boundary sliding and the diffusional recovery near grain boundaries, which lowered the increase of the fractal dimension with the creep strain. The fractal dimension of the grain boundaries in the parallel direction was slightly larger than that in the transverse direction in both creep at 973 K and tensile deformation at room temperature, especially at the large strains. This could be correlated with the shape change of the grains by creep or plastic deformation. Grain-boundary cracks were principally initiated at grain-boundary triple junctions in creep, but ledges, steps and carbide precipitates on serrated grain boundaries were not preferential nucleation sites for the cracks.     

Forming and fracture limits of aluminium alloy

Abstract

Forming and fracture limits of an AA 3104-H19 aluminium alloy sheet were studied by hydraulic bulging and Marciniak type deep drawing and tensile tests. The alloy appeared to be highly anisotropic, exhibiting distinctly different fracture patterns in the rolling and transverse directions. The preferred fracture direction was transverse to the rolling direction. In the tensile test, samples loaded in the rolling direction failed transverse to the rolling direction, but in the transverse direction, the fracture was inclined at ～55° to the tensile axis. In some cases, two such competing fractures in the characteristic directions could be observed. Scanning electron microscopy studies revealed a typical ductile fracture pattern. The fracture occurred by shearing in the through thickness direction, and typical alternating shear lips in a direction inclined at ～45° to the through thickness direction could be observed. Forming limit diagrams for both rolling and transverse directions were determined from the experiments. The measured limit strains in uniaxial tension were predicted well by the modified Rice–Tracey theory, but in equibiaxial tension, the theory overestimated the fracture limit strains.     

In situ high resolution transmission electron microscopy investigation of deformation mechanism in sub-10-nm Au crystals

Abstract

In situ high resolution transmission electron microscopy investigations were performed on sub-10-nm Au crystals. The effects of tensile loading direction and crystal size on the deformation mechanism of Au crystals were analysed. For the Au crystals with a width below 2 nm, the surface atom diffusion with a phenomenon of layer by layer peeling is the main deformation mechanism and the tensile loading direction plays negligible effect. For the Au crystals with a width over 7 nm, the dislocations generated form surface and gliding into crystal dominate the plastic deformation and the tensile loading direction plays important role. Lomer dislocations are produced and destructed by dislocation reaction during tensile strain process in <001> oriented Au crystal. The Schmid law is the key intrinsic issue controlling the deformation mechanism for the nanowires with a size larger than 7 nm.     

Study on dislocation slips in ferrite and deformation of cementite in cold drawn pearlitic steel wires from medium to high strain

Abstract

The deformation of cementite was studied via optical microscopy and SEM in the longitudinal sections of pearlitic steel wires from medium to high strain. The cementite shows good deformability, the angle between the deformation direction of cementite and drawing direction decreases with increasing strain, and finally the deformation directions of cementite turn to the drawing axis at high strains. The deformation of the cementite is strongly related to plastic deformation in the ferrite, with coarse slip steps, S-bands and cracks across cementite observed parallel to either {110}_α-Fe or {112}_α-Fe plane traces determined by the largest Schmid factors.     

Effect of anisotropy in commercial purity titanium on deep drawability at elevated temperatures

Abstract

Commercial purity Ti sheets (0.88 mm thick) were deep drawn by a complex working process at two temperatures using a hot die and a cool punch. The working temperature ranged from 25 to 400°C. Generally, the limiting drawing ratios (LDRs) along both the rolling direction (RD) and transverse direction (TD) increased with increasing operating temperature, while the optimal blank holding force decreased with temperature. The LDR(RD) is larger than the LDR(TD) at all temperatures in the range tested and the difference (ΔLDR) is largest at 200°C or higher. The deep drawn cups failed at the cup wall near the die throat along the TD. The thickness strain along the TD was consistently smaller than that along the RD. The anisotropy index δ _011¯1 increased significantly at 100°C and the largest δ _hkil values were found in δ ₀₀₀₂ along the RD and δ _112¯0 along the TD. The reorientation bands that appeared when drawn at 25°C are a result of work hardening, but the microshear bands that occurred in the 400°C specimen are a result of large deformation. The difference in microstructures along the TD and RD may explain the anisotropy in deep drawing properties.     

The crack surface anomalous scaling and its connection with the size-scale effects

The size-scale effects is one of the most important research topics in solid mechanics. Several theories have been proposed in order to describe the scaling of mechanical properties in fracture mechanics of quasi-brittle materials such as concrete, rock, wood and a broad class of fibrous or particulate composites. In the last two decades they were investigated by means of several techniques, including renormalisation group theory, intermediate asymptotics, dimensional analysis, statistics of extremes among the others. One of the most successful approaches is the fractal one. It is based on the assumption of a fractal-like damage localization at the mesostructural level and on the linking of mechanical properties to the fractal dimensions of the damage domains. In particular, the fractal dimension of fracture surface an be linked to the scaling properties of toughness. On the other side, recent experimental researches have shown that fracture surfaces present an anisotropic propagation in the longitudinal and transverse directions. To describe such anisotropy, it does not appear sufficient to characterize the fracture surface by a single fractal dimension, but the anomalous scaling (Morel et al., Physical Review E 58, 6999–7005 [1998]) should be introduced. This approach has proved to be very effective in describing the R-curve behaviour (Morel et al., International Journal of Fracture 114, 307–325 [2002]). Dealing with the size-scaling effects, a scaling law for both fracture toughness and tensile strength has been recently proposed. In this work, we point out some inconsistencies of the proposed approach, suggesting a more consistent way to derive the scaling laws and a correction on the scaling exponent at the larger scales. The phenomenon of scaling in notched and un-notched structures is summarized in a unified framework and the anomalous scaling is applied to the case of unnotched specimens, showing how it captures correctly only the convexity of the scaling law in a bilogarithmic plane and not the real asymptotes, thus indicating that the anomalous scaling can not be considered as a satisfactory explanation to the size-scale effects.     

Effect of cold work on anodic polarization of low carbon steel

Carbon steel nails prepared by deep drawing exhibit grains elongated in the direction of swaging. They are also characterized by high corrosion rates, as measured potentiodynamically in 0.1 M H₂SO₄. Normalization of grain dimensions and reduction in the corrosion rate are achieved through annealing. Treatment at 750? C for 2 h is effective in producing strain-free specimens with rounded grains. Extended heat treatment at this temperature causes the development of larger grains and the improvement in the corrosion behaviour of the alloy. “As-received” and strain-free specimens are subjected to controlled tensile or torsional cold work. In all cases deformation results in an increase in the susceptibility of the alloy to undergo attack. The rate of corrosion increases greatly when the deformed steel corrodes in Cl^? ion containing media. Both general and pitting corrosion are operative.     

Fractal characteristics of the deformation surfaces of a composite material and their correlation with the structure

An investigation was made of the deformation relief formed at the surface of a solid under active deformation, and its fractal properties were determined. A correlation was established between the fractal dimension of the surface profile and the parameters of the fine crystalline structure of the material. Pis’ma Zh. Tekh. Fiz. 25, 34–38 (January 26, 1999)     

Size effect on deformation behavior and ductile fracture in microforming of pure copper sheets considering free surface roughening

In meso/micro-scaled plastic deformation, material deformation and ductile fracture are quite different from those in macro-scale. The roughness of the free surfaces of workpiece increases with deformation and the decrease of grain number in the sample thickness direction, leading to the nonuniformity of specimen thickness. The so-called size effect and free surface roughening may in turn affect the deformation behavior, ductility and fracture morphology of the samples. To explore the coupled effect of workpiece geometry and grain size on material flow behavior in meso/micro-scaled plastic deformation, uniaxial tensile test of pure copper sheets with different thicknesses and comparable microstructure was performed. The experimental results reveal that the material flow stress, fracture stress and strain, and the number of microvoids on fracture surface are getting smaller with the decreasing ratio of specimen thickness to grain size. In addition, the modified Swift’s equation and the corrected uniform strain are closer to the experimental ones considering the thickness nonuniform coefficient induced by the free surface roughening. Furthermore, the observation of fracture morphologies confirms that the local deformation caused by the free surface roughening leads to strain localization and a decreased fracture strain when there are only a few grains involved in plastic deformation.     

Modeling and Experimental Studies on 3D-Magnetic Flux Leakage Testing for Enhanced Flaw Detection in Carbon Steel Plates

ABSTRACT

For enhanced detection of flaws in engineering components using magnetic flux leakage (MFL) technique, measurement of the leakage magnetic field components along the three perpendicular directions is beneficial. This article presents the three dimensional-magnetic flux leakage (3D-MFL) modeling and experimental studies carried out on carbon steel plates. Magnetic dipole model has been used for the prediction of MFL signals and images. Sensitivity of the MFL signals peak amplitudes of tangential (H_X), circumferential (H_Y), and normal (H_Z) components with respect to flaw length, width, depth and lift-off have been studied. A 3D-GMR sensor has been used for simultaneous measurement of all the three components of leakage magnetic fields from surface flaws in 12 mm thick carbon steel plates. The experimental MFL images have been compared with the model predicted MFL images. The sensor has shown the capability to detect and image 0.9 mm deep surface flaws with a signal to noise ratio of 8 dB. Principal component analysis (PCA)-based image fusion has been performed for fusion of the 3D-MFL images to obtain a geometrical profile of the flaws. Study reveals that 3D-GMR enhances the capability for detection of flaws having irregular geometries.     

Modelling surface ridging in ferritic stainless steel

Abstract

A new model is proposed to account for the occurrence of surface ridging (parallel corrugations) in ferritic stainless steel. In the absence of notable texture component clustering, it is shown that local anisotropy in plastic behaviour can still occur on a scale considerably larger than the grain size. The construction of a simple finite element model incorporating plasticity data from microtexture measurements demonstrates that parallel surface corrugations can be simulated during uniaxial tensile straining. It is shown that the corrugation profile is the result of the superimposition of a number of differential transverse strains that contribute to the overall deformation induced bending.     

Deformation and fracture of cork in tension

Various properties related to the deformation and fracture of cork in tension were experimentally determined, including the Young's modulus, the stress and strain at fracture and the fracture toughnessK _Ic. The transverse isotropy of cork implies that there are three independent systems of mode I crack propagation andK _Ic was measured for each. The mechanisms of deformation and fracture were identified by SEM microscope observation ofin situ deformation and of the fracture surfaces and crack paths. Two fundamental mechanisms of fracture occur: crack propagation along the lateral cell walls in non-radial tension, withK _Ic = 94±16 kPam^1/2 and crack propagation by breaking the cell walls in radial tension withK _Ic=125±14 kPam^1/2. In radial tension, local fractures that do not propagate due to crack stopping were observed which lead to serrations in the tensile curves for that direction. The strain to fracture in this direction is considerably larger than in the perpendicular (non-radial) directions.     

Evaluation of Tablet Formation of Different Lactoses by 3D Modeling and Fractal Analysis

ABSTRACT

The aim of this study was to use 3D modeling to differentiate not only among the four different types of lactose α-lactose monohydrate, spray-dried lactose, agglomerated lactose and lactose anhydrous but also between products from different manufacturers. Further “box-counting” fractal analysis of SEM images was done to gain additional information on tableting characteristics and tablet properties which can be found in the fractal structure. Twelve different materials from different manufacturers were analyzed for their powder-technological and physicochemical properties. They were tableted on an eccentric tableting machine at graded maximum relative densities and the recorded data, namely force, time, and displacement were analyzed by the 3D modeling technique. Tablet properties such as, elastic recovery, crushing force and morphology were analyzed. The results show that 3D modeling can precisely distinguish deformation behavior for different types of lactose and also for the same type of material produced with a slightly different technique. Furthermore, the results showed that the amorphous content of the lactose determined the compactibility of the material, which is due to a reversible exceeding of the glass transition temperature of the material. The three fractal dimensions D_BW (box surface dimension), D_WBW (pore/void box mass dimension), and D_BBW (box solid mass dimension) are capable of describing morphological differences in lactose materials. Multivariate regression analysis showed that the fractal surface structure of the lactose-based materials is strongly correlated to tableting characteristics and tablet properties. Especially with regards to 3D modeling, it was found that the fractal indices can describe the parameters time plasticity d, pressure plasticity e, and fast elastic decompression, which is the inverse of ω. In addition, the 3D parameters are able to describe the powder and tablet fractal indices. In conclusion, the 3D modeling is not only able to characterize the compression process but it can also provide information on the final tablet morphology.     

R-curve behavior and roughness development of fracture surfaces

We investigate the idea that the fractal geometry of fracture surfaces in quasibrittle materials such as concrete, rock, wood and various composites can be linked to the toughening mechanisms. Recently, the complete scaling analysis of fracture surfaces in quasibrittle materials has shown the anisotropy of the crack developments in longitudinal and transverse directions. The anomalous scaling law needed to describe accurately these particular crack developments emphasizes the insufficiency of the fractal dimension, usually used to characterize the morphology of fracture surfaces. It is shown that a fracture surface initiating from a straight notch, exhibits a first region where the amplitude of roughness increases as a function of the distance to the notch, and a second one where the roughness saturates at a value depending on the specimen size. Such a morphology is shown to be related to an R-curve behavior in the zone where the roughness develops. The post R-curve regime, associated with the saturation of the roughness, is characterized by a propagation at constant fracture resistance. Moreover, we show that the main consequence of this connection between anomalous roughening at the microscale and fracture characteristics at the macroscale is a material-dependent scaling law relative to the critical energy release rate. These results are confirmed by fracture experiments in Wood (Spruce and Pine).     

Fractal dimension of metallic fracture surface

In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is performed. For calculation of the same fractal dimension, the fd3 program has been used, which is available through the Internet. The essential element of the method is optimisation concerning microscopic magnification (scale of a length), resolution of the recorded image and selection of the grey level threshold at binarization. The tests for the stability of discretization, which enable minimization of the error of the measurement, have also been carried out. These tests consist in checking the difference in fractal dimensions for the same profile obtained in two different methods of contouring as well as the difference between capacitive, informative and correlative dimensions. In both cases, too big difference suggests that the determined dimension is not reliable. This method allows determination of the fractal dimension with an absolute accuracy of 0.05 in non-dimensional units. The method has been employed in many studies. In this paper the following tests have been presented: a “fractal map” of the fracture surface was made, an influence of the mechanical notch radius in a compact specimen on the fractal dimension of the fracture surface, an influence of the distortion rate on the fractal dimension, an effect of fatigue crack propagation rate on the fractal dimension and influence of the stress-intensity factor on the fractal dimension of the fracture surface. The following materials were examined: Armco iron, P355N steel and 41Cr4 steel in different states after the heat treatment. The measurements have been made for the specimens of the compact type. There was considered an influence of location of the place of measurement on the fractal dimension being determined. The dimension was determined on the profiles lying longwise and crosswise the crack propagation direction. It has been found that the fractal dimension of the fracture surface does not depend on a place of measurement. This suggests, among other things, that a distinction between the places, which were created under conditions of the plane stress, and the places, which were created under conditions of the plane strain state, cannot be made with the help of the fractal dimension. When testing an influence of the radius of the mechanical tip notch on the fractal dimension of a fracture surface, this dimension was determined in the places located at different distances from the tip of the mechanical notch. With respect to the radii up to 1.0 mm, no significant differences in fractal dimensions have been found. The fractal dimensions of the fracture surface for all examined materials were practically the same and they ranged from 2.02 to 2.10. However in some ranges of da/dN rate the dimension was changing inversely proportional to da/dN. Obtained results confirm that fractal dimension do not depend on the investigated material.     

玻璃纤维/聚丙烯复合材料层合板拉深成型性

为研究纤维增强树脂复合材料零部件快速成型,加速复合材料零部件大规模产业化量产,以玻璃纤维/聚丙烯复合材料层合板为实验对象,首先利用设计加工的拉深成型模具,进行了玻璃纤维增强热塑性树脂复合材料（Glass fiber reinforced thermoplastic resin composite,GFRTP）板材外表面纤维方向和模具长轴方向为0°和90°的试件在不同温度和不同拉深深度条件下的深拉深成型实验,将成型件制备金相试件在光学显微镜下进行微观组织观察,并对试件的成型情况和不同拉深力-行程曲线进行分析。其后进行了GFRTP板材外表面纤维方向和模具长轴方向为0°、45°和90°的试件的不同温度下的浅拉深成型实验,并对成型后的试验件进行了室温条件下的拉伸性能测试,对其拉伸失效情况及具体力学性能进行了对比分析。试验结果表明,在室温25℃到基体树脂的熔融温度165℃之间,随着温度的升高,板材的极限拉深深度增大,最大拉深力呈下降趋势。在选取的试验温度范围内,85℃时试件成型性能较好且0°试件优于90°试件,温度对拉深成型试件的皱曲改善不明显。浅拉深成型试件拉伸力学特性受试件铺层纤维方向的影响较大,防止皱曲等缺陷的发生对GFRTP板材拉深成型十分重要。     

Three-dimensional Computer Reconstruction of Random Rough Surface

Abstract

The two-dimensional function f(x y) with slow variation in the y direction and describing a random rough surface in the x direction is expanded in a Fourier series i.e. considered as a sum of sinusoidal harmonic grating in the x direction. The scattered optical field by each line of this surface in the x direction is considered as a sum of the diffracted optical fields from the sinusoidal gratings. The diffracted fields are registered by consecutive scanning of the surface in the y direction, and the surface profile of each line is reconstructed using the theory developed in [1,2]. The studied surface is visualized by the reconstructed profiles in ten lines using a program visualizing a function depending on two variables. The calculated mean roughness Ra is averaged along all lines and is found to be in satisfactory agreement with that averaged by the Hobson type profilometer within the laser spot.     

Anisotropy of Gum Metal analysed by ultrasonic measurement and digital image correlation

ABSTRACT

The mechanical anisotropy of a multifunctional titanium alloy, Gum Metal, is investigated in this paper. The structural characterisation showed a strong <110> texture for Gum Metal, that is a result of the cold-swaging process applied during its manufacture. Gum Metal was treated as a transversally isotropic solid because of this texture. A significant difference from Young’s moduli of the alloy was detected from the ultrasonic measurement of parallel and perpendicular directions to the alloy swaging direction. Samples of Gum Metal cubes were compressed in two different orientations. During the deformation process, two perpendicular walls of each sample were monitored by two visible range cameras for further two-dimensional digital image correlation analysis, this confirmed a strong plastic anisotropy in Gum Metal.

This paper is part of a Thematic Issue on The Crystallographic Aspects of Metallic Alloys.     

Acoustic emissions during tensile test of DC06 and HCT600X

In this paper the acoustic emission behaviour during tensile tests of the materials DC06 and HCT600X is studied. Two steels with different characteristics (mild deep‐drawing steel DC06 and high‐strength steel HCT600X) are consciously chosen to show the influence of the material properties on the generated acoustic emissions. The acoustic emission behaviour and the corresponding signals differ clearly from each other. In addition, the effect of the strain rate as well as the rolling direction (0°, 90°) on the acoustic emission behaviour is investigated. Both parameters have a significant influence on the resulting acoustic emissions during tensile deformation. Furthermore, a new criterion based on the acoustic emission parameter FCOG (centroid frequency) for detection of damage beginning in dual‐phase steels is developed. The criterion supports the assumption that during tensile deformation of dual‐phase steels two failure mechanisms, ferrite/martensite interface decohesion and martensite phase fracture, exist.     

Size effect in the low-field Hall coefficient of single-crystal copper films

Measurements of the low-field Hall coefficientR _H of single-crystal copper films were made at 4.2 K by the use of a SQUID. The surface normaln of the samples was directed in the [100], [110], and [111] directions and the ratio of the thickness to the mean free path ranged from 0.1 to 0.7. It is found that the effect of surface scattering causesR _H to decrease whenn [100], whereas it causesR _H to increase whenn [110] and [111]. This behavior is interpreted in terms of the geometrical characteristics of the Fermi surface.