Experimental Observations and Computational Modeling of Fracturing in an Anisotropic Brittle Crystal (Sapphire)

The commonly used fracture criteria-maximum K_I, zero K_II, maximum hoop-stress, and maximum energy-release rate-predict similar fracture paths in isotropic materials, but not in anisotropic materials. In the general anisotropic case, the fracture path depends on the material-symmetry properties, the nature of the applied loads, and the overall geometry of the specimen. In addition, anisotropy in the material's resistance to fracturing plays a key role in defining crack initiation and its propagation path. Experiments are performed on notched specimens made from sapphire, a microscopically homogeneous and brittle single-crystal solid. The force required for fracture initiation is measured. The experimental measurements/observations are compared with the numerical results of the FEM simulations. A stress-based fracture parameter, is shown to be a good measure of the fracture criterion, where σ and E, respectively, are the tensile stress and Young's modulus in the direction normal to the cleavage plane, with surface energy γ , and R is a characteristic length, e.g., the notch radius. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. More than two-thirds of the notched specimens fractured at the point and along a cleavage plane where A is maximum. The measurements of the applied force made it possible to quantitatively obtain a critical value for parameter A. Finally, experiments show that for the notched sapphire specimens the weakest family of cleavage planes, , are the fracture planes, although a few specimens fractured along non-cleavage planes. This revised version was published online in July 2006 with corrections to the Cover Date.     

An experimental study on the dynamic fracture of extruded AA6xxx and AA7xxx aluminium alloys

The dynamic fracture behaviour of extruded AA6xxx and AA7xxx aluminium alloys is investigated using an instrumented Charpy test machine and V-notch specimens. The specimens are made from extruded flat profiles with a rectangular cross-section of 10 mm thickness and 83 mm width. The material is in T6 temper, i.e. the peak hardness condition. The alloys have either recrystallized or fibrous grain structure. For each alloy six different Charpy impact tests are carried out in two series. In Series 1, the notch is parallel to the thickness direction of the profile (i.e. through the thickness), while the notch is perpendicular to the thickness direction in Series 2 (i.e. lying in the plane of the flat profile). In each series, the longitudinal direction of the specimen is parallel, 45° or 90° to the extrusion direction. Comprehensive fractographic investigations are carried out for the different tests and alloys. It is found that the dissipated energy is practically invariant to specimen orientation and notch direction for the recrystallized alloy. For the fibrous alloys the dissipated energy is lower when the longitudinal direction of the specimen is 90° to the extrusion direction, i.e. when the notch is parallel with the fibrous grain structure. Further, the energy dissipation is higher for Series 2 than for Series 1 due to substantial delamination and secondary cracking in Series 2. The precipitate-free zones (PFZs) formed adjacent to the grain boundary are weak areas, preferable for crack initiation and growth. This is seen in the fracture surface as facets with high density of small dimples and is more pronounced for specimens with the notch parallel to the fibre direction.     

High temperature,high strain rate embrittlement of Al-Mg-Mn alloy: evidence of cleavage of an fcc alloy

Abstract

The fracture behaviour in tension of an Al-Mg -Mn alloy has been investigated. At high temperatures and strain rates, intergranular brittle fracture is observed along with cleavage fracture. Intergranular fracture is related to local melting at the grain boundaries. Cleavage occurs in equal proportions on the {100} and {110} crystallographic planes. The area fraction of cleavage facets on the fracture surface has been quantified. Their initiation is shown to be related both to the liquid metal embrittlement of the grain boundaries and to the presence of brittle Mn containing particles at the grain boundaries. Cleavage fracture in an aluminium alloy also requires an inhibition of plastic flow which prevents plastic blunting at the crack tip. It is proposed that this modification of the plastic behaviour is provided by the decrease in stacking fault energy at high temperatures in Al-Mg alloys.     

Influence of microstructure and texture on mechanical properties of aluminium alloy 2124 + 5%SiC particulate composites

Abstract

A study of texture, microstructure, mechanical properties, and crack propagation mechanisms was carried out on aluminium alloy 2124 reinforced with 5 vol.-%SiC particles (3 μm). Three fabrication techniques have been used to produce the composites. composite I wasfabricated by blending followed by hot isostatic pressing. composite II was fabricated by mechanical alloying followed by hot isostatic pressing. composite III wasfabricated by agglomeration of aluminium powder by mechanical alloying followed by blending with SiC and hot isostatic pressing. All three composites were hot rolled to nominally 12.5 mm thick plate. Similar textures were observed for all composites. A model of the observed texture is {001} (211), {111} (211), and {211} (111) for rolling, side, and transverse planes respectively. Composite I showed a homogeneous distribution of SiC particles. Transmission electron micrographs of composite I showed good interface bonding, stacking faults present in SiC particles, and segregation of aluminium, oxygen, copper, and magnesium to the interface. composites II and III showed an inhomogeneous distribution of SiC particles. The elastic modulus was slightly higher in the (211) direction than in the (111) direction. The fracture toughness of composite I was higher in the (211) crack direction whereas that for composite II and composite III was higher in the (111) crack direction. Secondary crack propagation modes follow the crystallographic orientations of {100} and {111} planes.     

Fracture of Gd2 (MoO4)3 single crystals

Fracture behaviour of Gd2 (MoO4)3 single crystal, which is improper ferroelectric–ferroelastic, has been examined by means of point loading. There are three fracture planes in gadolinium molybdat (GMO): ;100} – main cleavage plane, {210} and {110} – secondary cleavage ones. It is shown that cracks have a tendency to transit from secondary planes up to cubic plane and vice versa. This would be considered as the main cause of river pattern appearance on fracture surfaces of samples. Mechanical twinning and crack growth are independent channels for relaxation of elastic energy in GMO, which do not connected between themselves, so excluding of twinning leads to increase of crack length.     

Mechanical anisotropy in Ca-treated and ultra-low sulphur HSLA-100 steel

A few elongated MnS inclusions were observed in ultra-low sulphur HSLA-100 steel which significantly decreased the yield strength (YS), ultimate tensile strength and notch toughness of short transverse direction. The slight anisotropies of YS (≈5?MPa) and notch toughness (≈15?J) between longitudinal and transverse directions are correlated to the presence of texture components in the vicinity of {113}<110> and {554}<225>. In the case of anisotropy between longitudinal and short transverse directions, it is found that recognising the contribution of each effective factor in the creation of strength anisotropy is not possible. However, the most primary effective factor in the creation of remarkable notch toughness anisotropy (≈70?Pct), especially at ?85°C, is related to the existence of elongated MnS inclusions.     

Orientation dependence of fracture toughness measured by indentation methods and its relation to surface energy in single crystal silicon

Fracture toughness of silicon crystals has been investigated using indentation methods, and their surface energies have been calculated by molecular dynamics (MD). In order to determine the most preferential fracture plane at room temperature among the crystallographic planes containing the 〈001〉, 〈110〉 and 〈111〉 directions, a conical indenter was forced into (001), (110) and (111) silicon wafers at room temperature. Dominant {110}, {111} and {110} cracks were introduced from the indents on (001), (011) and (111) wafers, respectively. Fracture occurs most easily along {110}, {111} and {110} planes among the crystallographic planes containing the 〈001〉, 〈011〉 and 〈111〉 directions, respectively. A series of surface energies of those planes were calculated by MD to confirm the orientation dependence of fracture toughness. The surface energy of the {110} plane is the minimum of 1.50 Jm⁻² among planes containing the 〈001〉 and 〈111〉 directions, respectively, and that of the {111} plane is the minimum of 1.19 Jm⁻² among the planes containing the 〈011〉 direction. Fracture toughness of those planes was also derived from the calculated surface energies. It was shown that the K _IC value of the {110} crack plane was the minimum among those for the planes containing the 〈001〉 and 〈111〉 directions, respectively, and that K _IC value of the {111} crack plane was the minimum among those for the planes containing the 〈011〉 direction. These results are in good agreement with that obtained conical indentation.     

Microstructural and crystallographic features of hydrogen-related fracture in lath martensitic steels

ABSTRACT

This paper summarised the microstructural and crystallographic features of hydrogen-related fracture under tensile deformation in martensitic steels. The specimens with relatively low strength exhibited quasi-cleavage fracture. Crystallographic orientation analysis demonstrated that the quasi-cleavage fracture occurred on {011} planes. On the other hand, the macroscopic fracture surface morphologies of the specimens with relatively high strength appeared to be intergranular-like. However, nature of the fracture was somewhat different from a typical intergranular fracture, and the fracture surfaces consisted of facets parallel to {011} planes on a microscopic level. Based on the experimental results, we concluded that the crystallographic feature of {011} plane itself had an important role on the hydrogen-related fracture.

This paper is part of a thematic issue on Hydrogen in Metallic Alloys     

Fracture of precipitated NiTi shape memory alloys

The fracture mechanisms in single crystal and polycrystalline Ti-50.8at%Ni shape memory alloys containing Ti₃Ni₄ precipitates are studied using the scanning electron microscope (SEM). Aged materials with three different precipitate sizes (50 nm, 150 nm, and 400 nm), which have interfaces ranging from semi-coherent to incoherent, are considered. The mechanisms of material fracture identified in the single crystal NiTi are: 1. Nucleation, growth, and coalescence of voids from the Ti₃Ni₄ precipitates, 2. Cleavage fracture on {100} and {110} crystallographic planes, 3. Nucleation, growth, and coalescence of voids from fractured Ti-C inclusions. Cleavage and ductile tearing mechanisms also operate in polycrystalline NiTi, however, since the Ti-C inclusions are an artifact of single crystal growth processes, mechanism 3 was not discovered in the polycrystalline materials. Cleavage fracture and ductile tearing are found to act in conjunction, with the relative dominance of one over the other depending on the local precipitate size and concentration. As the Ti₃Ni₄ precipitate size increases to about 400 nm, the overall fracture is dominated by failure mechanism 1, and the cleavage markings become diffuse. Finally, we assert that the high tensile ductility of drawn NiTi polycrystals is due partially to the fact that drawn bar and wire stock usually have a strong {111} fiber texture. Such a texture promotes the initiation of the transformation at low stresses and concurrently prevents primary cleavage on the {100} or {110} planes.     

Fractography and structure of the subsurface cleavage zone in molybdenum

Transmission electron microscopy of thin foils was used to examine the structure of fracture surfaces of single crystals of molybdenum failed by cleavage along different crystallographic planes, and the dislocation structure of the zone adjacent to the fracture surface was also studied. The results show that cleavage steps are the main characteristic element in failure along any plane in the group of the examined planes ({100}, {110}, {211}, {123}). The number, dimensions, and crystal geometry of the cleavage steps depend on the cleavage plane. The primary cleavage elements are steps of the minimum size (height 8–17 nm). The results also show that with an increase of the work used in failure in transition from one cleavage of macroplane to another the thickness of the zone with high (in comparison with the initial value) dislocation density increases together with the dislocation density directly on the fracture surface.Translated from Problemy Prochnosti, No. 1, pp. 58–63, January, 1991.     

Twinning characteristics in textured AZ31 alloy under impact loading along specified direction

A plate of hot extruded AZ31 alloy with some large grains was selected for impact tests. The occurrence of twinning was investigated. It was found that when impacted along the normal direction (ND) of the plate, {10-11}-{10-12} double twinning is commonly observed in large grains, and {10-12} tension twinning can also be activated although their c-axis is close to the compression direction. In small grains, {10-12} tension twins are favored in which case the extension strain component is parallel to the c-axis. In addition, twins with < 11-20> 75° misorientation to the parent matrix were also observed.     

砷化镓晶体力学特性的各向异性计算

砷化镓因其良好的光电特性被广泛应用于电子与半导体领域, 为推动砷化镓解理加工技术, 对砷化镓材料力学特性的各向异性进行计算并分析。本研究对砷化镓各个晶面之间的夹角、面间距、原子的密度等结构参数进行计算, 基于广义胡克定律结合压痕实验, 分析砷化镓材料表层弹性模量、泊松比、剪切模量、硬度、断裂韧性等力学特性在{100}晶面沿不同晶向力学性能的变化规律。结果表明: 砷化镓不同晶面间结构参数的不同是导致砷化镓力学特性呈现各向异性的主要原因; 砷化镓在{100}晶面上弹性模量、泊松比、剪切模量的各向异性均呈现出周期性变化, 且{100}晶面的剪切模量为恒值59.4 GPa; 砷化镓{100}晶面硬度的各向异性变化幅度较小, 断裂韧性变化幅度较大, 最小值为0.304 MPa·m^1/2, 位于<110>晶向, 确定<110>晶向是裂纹最容易扩展的晶向。     

Modified twinning behaviour induced by texture evolution in hot rolled Mg–3Al–1Zn alloy

Abstract

Compressive deformation along the rolling direction (RD) of a hot rolled Mg–3Al–1Zn alloy is applied to investigate the texture evolution and the recompressive yield strength (RYST) along the transverse direction (TD). Preferential orientation of the basal and prismatic planes is generated by the plastic deformation. Precompression along RD results in one plane of {10–10} aligned nearly perpendicular to the normal direction to the rolling plane. As the compressive strain along RD increases, the RYST shows an earlier raised and later decreased trend. The modified twinning mechanism is investigated using X-ray diffraction and electron backscattered diffraction observations. The results reveal that {10–12} twinning in the matrix dominates the recompression along TD, while the formation of {10–12}–{10–12} twins becomes comparatively easier to occur in the previous {10–12} twins for large precompressed samples.     

Deformation bands in Inconel 718

Abstract

The deformation bands formed under monotonic loading in the homogenised and the aged Inconel 718 have been investigated using transmission electron microscopy. The crystallographic behaviour of the deformation bands is discussed. The orientations of the deformation bands were observed in tranmission electron micrographs as follows: two orientations of <112> bands and one orientation of <110> bands on the {O 11} plane; two orientations of <110> bands on the {DOl} plane, and three orientations of <110> bands on the {111} plane. Deformation bands were classified into <112> and <110> bands, theformer corresponding to the projections of edge traces of {111} planes, and the latter corresponding to the projections of inclined deformation {111} planes. Both twins and dislocations were observed in the deformation bands.

MST/2002     

Crystallography of brittle fracture and deformation twinning in ferritic steels

Abstract

The crystallography of brittle fracture and deformation twinning in ferritic steels is difficult to study experimentally, because of its three-dimensional aspects. The present paper reports the development of methodologies to study the phenomenon via customisation of various electron backscatter diffraction and SEM routes. It is shown that both direct (from the fracture surface) and indirect (from an adjacent polished side) measurements yield valuable information on crystallographic aspects of the fracture processes. Specifically, brittle fracture in three ferritic steels is studied: a C–Mn weld metal, a low alloy Mn–Mo–Ni steel similar to grade A533 and an ultralow carbon (0·002 wt-%C, 0·058 wt-%P) steel plate. The main conclusions resulting from development of the experimental techniques are that cleavage fracture occurs only on {001} planes, and that intergranular accommodation is present at the fracture surface. Further observations suggest that a cleavage side crack, initially deflected by a deformation twin, eventually blunts at the intersection of two deformation twins. This provides a mechanism for limiting the mean length of microcracks during brittle fracture.     

Effect of initial notch orientation on fracture toughness in fail-safe steel

A 0.4C–2Si–1Cr–1Mo steel bar with an ultrafine-elongated grain (UFEG) structures was produced by multi-pass warm caliber rolling. The test sample was machined from the rolled bar with 0°, 45°, and 90° rotation along the rolling direction, and a static three-point bending test was conducted at ambient temperature. The toughness anisotropy on the steel with UFEG structures were studied, including the crack propagation on the basis of the microstructural features. The strength and toughness decreased with an increase in the rotation angle along the rolling direction. The toughness decreased drastically, compared to the strength. The notch orientation dependence on toughness is due to differences in the spatial distribution of weak sites such as {100} cleavage planes and boundaries of elongated grains. For the toughness design in ultrafine-grained materials, it is essential to understand the spatial distribution of these weak sites as well as the grain size.     

Influence of nanometre-sized notch and water on the fracture behaviour of single crystal silicon microelements

The influence of a notch and a water environment on the quasi‐static and fatigue fracture behaviour was investigated in single crystal silicon microelements. The tests were conducted in smooth and notched microcantilever beam samples. Smooth specimens were prepared by micromachining (photo‐etching) of (110) silicon wafers. For some specimens, a nanometre‐sized notch was machined 100 μm away from the sample root by using a focused ion beam system. A machining condition was optimized, and the V‐shaped notch was successfully introduced. The radius of curvature of the notch, measured by an atomic force microscope (AFM), decreased with an increase in notch depth, and ranged from about 20 to 100 nm. Single‐crystal Si microelements deformed elastically until final failure, which was of a brittle nature. The maximum fracture strength of a smooth microcantilever specimen reached about 7.7 GPa, which was higher than that obtained in millimetre‐sized single crystal Si samples. However, the fracture strength decreased with an increase in notch depth, even though the notch depth was of the order of a nanometre. This means that a nanometre deep notch, which is often regarded as surface roughness in ordinary‐sized mechanical components, caused a decrease in the fracture strength of Si microelements. The fracture initiated at the notch, and then the {111} crack propagated in the direction normal to the sample surface. Fatigue tests were also conducted in laboratory air and in pure water at a stress cycle frequency of 0.1 Hz and a stress ratio of 0.1. In laboratory air, no fatigue damage was observed even though the surface was nanoscopically examined by an AFM. However, when the fatigue tests were conducted in pure water, the fatigue lives in water were decreased. Crack formation on the {111} plane was promoted by a synergistic effect of the dynamic loading and the water environment. Atomic force microscopy was capable of imaging the nanoscopic cracks, which caused failure in water.     

Crack growth process in Ni-Single crystal with hydrogen cathodic charging

Notched tensile tests {orientation tensile axis [001] and ${[\bar{1}\bar{1}1]}$ , direction of notching: [010], [011], [112]} were performed to investigate the crack growth process in Ni-single crystal with hydrogen cathodic charging. It was investigated that the crack growth direction tends to be <011> on {001} with any tensile direction. Y-shaped hillocks and striation-like pattern were observed on the fracture surfaces of hydrogen embrittled specimens using a scanning electron microscope (SEM) and an atomic force microscope (AFM). The striation-like patterns were not matched on both fracture surfaces of specimens, though the Y-shaped hillocks were exactly matched. Moreover, it was indicated that the striation-like pattern is perpendicularly formed to the crack growth direction on the fracture surface behind the crack tip and its shape results in an obtuse angle with respect to the fracture surface. The Y-shaped hillock was formed between micro-cracks located at crack tip by shear fracture. Furthermore, we proposed a crack growth model in Ni-single crystal at hydrogen atmosphere from the observation of the fracture surfaces.     

316不锈钢应力腐蚀断裂扫描电镜研究

应用扫描电镜和Ｘ射线能量色散谱仪对３１６不锈钢应力腐蚀断口形貌、腐蚀产物及裂纹扩展的晶体学特征进行研究。结果表明,断裂为穿晶断裂,断口形貌为台阶条纹和河流花样,并有腐蚀产物和腐蚀坑等。通过对腐蚀坑形貌的研究,提出了腐蚀坑形态与晶面之间的关系,证明了３１６不锈钢在氯离子环境下的应力腐蚀开裂主要沿｛１００｝、｛１１１｝、｛１１０｝晶面扩展的机制。     

FRACTURE AND DEFECT ASSESSMENT OF CERAMIC COMPOSITES

Abstract— Industrial ceramic crucibles manufactured by hot-pressing a mixture of ceramic powders sometimes fail by delamination when operated under extreme conditions. Results of laboratory tests under similar conditions suggest that failure may be caused by the constrained evaporation of a water rich liquid absorbed by relative large aggregate particles. Fracture mechanics test results, from specimens cut parallel and transverse to the direction of hot pressing, revealed a clear anisotropic behaviour and a large sensitivity to notch size for notches smaller than a millimetre in depth. A model based on the existence of a notch-tip damage zone is proposed and used to present fracture curves that can be employed for failure assessment of industrial crucibles.