Direction Of Maximum Tensile Stress Research Articles

Sensitivity of material failure to surface roughness: A study on titanium alloys Ti64 and Ti407

The relationship between material failure and surface roughness has been investigated using two titanium alloys: Ti64 and the more ductile Ti407. Three surface types were created (polished, sandblasted and scratched) with instances spanning a wide range of average roughness. The surfaces were tested in three-point bending with the imparted roughness on the tensile under-surface of a rectangular beam specimen. Results showed failure of Ti64 to be highly sensitive to both magnitude and orientation of roughness. High roughness in the maximum tensile stress direction (and scratch like features perpendicular to this direction) were most detrimental. Thus, strain-to-failure (and work-to-failure) in Ti64 dropped off significantly with increasing surface roughness in the tensile direction. Finite element modelling of the test indicated that cracks initiate at zones of high plastic strain at the tips of roughness valleys due to high local surface curvature. Thus, roughness can be considered as a series of blunt crack-like features where larger crack tip curvature induces greater likelihood of crack propagation. Contrastingly, the mechanical response of Ti407 was insensitive to surface roughness owing to its significantly greater ductility. Thus, designers need to be aware of the sensitivity of failure of particular materials to surface roughness. The insensitivity of Ti407 is advantageous, but the sensitivity of failure to surface roughness in a material like Ti64 is potentially serious if not properly accounted for.

Numerical modeling of the nucleation of facets ahead of a primary crack under mode I + III loading

A numerical study of crack front segmentation under mode I + III loading is proposed. Facets initiation ahead of a parent crack is predicted through a tridimensional application of the coupled criterion. Crack initiation shape, orientation and spacing are determined for any mode mixity ratio by coupling a stress and an energy criterion using matched asymptotic expansions. The stress and the energy conditions are computed through a 3D finite element modeling of a periodic network of facets ahead of the parent crack. The initiation shape, loading and spacing of facets depend on the blunted parent crack tip radius. A good estimate of facet orientations is obtained based on the direction of maximum tensile stress. The facet shapes, determined using the stress isocontours, are qualitatively similar to those observed experimentally. The order of magnitude of numerical predictions of facets spacing is very close to experimental measurements.

Tensile stress-strain response of metallic glass matrix composites reinforced with crystalline dendrites: Role of dendrite morphology

Bulk metallic glass composites (BMGCs) consisting of soft crystalline phases (commonly referred to as dendrites) in a metallic glass matrix have shown enhanced tensile ductility compared to conventional bulk metallic glasses (BMGs). Experiments and atomistic simulations suggest that a large number of geometrical parameters such as aspect ratio, spacing and orientation of dendrites as well as their spatial distribution can affect the mechanical response of BMGCs. However, the precise mechanism by which these parameters influence shear band initiation and propagation is not well understood. Therefore, continuum simulations of tensile loading on BMGCs with different morphologies are performed in this work. The results show that aspect ratio of dendrites has weak effect on the mechanical response up to the peak stress stage. However, it influences ductility considerably, albeit in a different manner for BMGCs with high and low hardening dendrites. The present analysis suggests that a BMGC capable of displaying mildly strain hardening response with large strain to failure can be designed by using closely spaced dendrites of high aspect ratio, and aligning them parallel to the maximum tensile stress direction.

An Improved Projection Method for Determination of Fatigue Parameters of Metal Structures Based on Spherical Direction Cosine Group Construction

The key components of railway rolling stock are almost constantly in the multiaxial stress state in service. To evaluate the fatigue strength of the structure, stress parameters should be obtained beforehand. The traditional projection method assumes that the maximum principal stress is the maximum tensile stress, and then the projection process is performed without taking the tension/compression states of principal stresses into account. To address these inadequacies, a method for fatigue parameter determination was proposed based on principal stress projection toward a spherical direction cosine group. This method can determine the direction of maximum tensile stress and preserve the tension/compression attribute of stress during calculating the maximum stress and the minimum stress. Therefore, the physical meaning of present improved method is more apparent than the traditional projection method, and its algorithm is simple and effective. The fatigue strength assessments of a welded bogie frame were performed utilizing the traditional projection method and present method, respectively. Results obtained show that maximum stresses calculated by the improved method can be 19.4% higher than those obtained by the traditional one at some nodes, while the minimum stresses and the stress ratios derived by these two methods can even be of opposite sign. The present method, which takes the tension/compression properties of principal stresses into consideration, is more reasonable, as compared with the traditional projection method, and thus, its fatigue strength assessment results are more credible.

Multi-scale Curvature Analysis and Correlations with the Fatigue Limit on Steel Surfaces after Milling

A strong correlation (R2 >0.96) is found between machined surfaces and their fatigue limits. In a larger study, the four- point bending fatigue limit was determined on steel specimens milled with two different conditions, in two directions, with and without residual stresses relieved. Curvature analysis is shown here, based on Heron's formula, as a function of scale and position, on profiles extracted parallel to the direction of maximum tensile stress, from areal texture measurements. Several combinations of parameters are regressed linearly with the fatigue limits over a range of scales. The strongest correlations are found with the mean curvature plus two standard deviations, at a scale of 610μm. The correlation varies smoothly, although not monotonously, with respect to decreasing scale, with R2 falling to zero at 100μm.

Chemically induced fracturing in alkali feldspar

Fracturing in alkali feldspar during Na+–K+ cation exchange with a NaCl–KCl salt melt was studied experimentally. Due to a marked composition dependence of the lattice parameters of alkali feldspar, any composition gradient arising from cation exchange causes coherency stress. If this stress exceeds a critical level fracturing occurs. Experiments were performed on potassium-rich gem-quality alkali feldspars with polished (010) and (001) surfaces. When the feldspar was shifted toward more sodium-rich compositions over more than about 10 mole %, a system of parallel cracks with regular crack spacing formed. The cracks have a general (h0l) orientation and do not correspond to any of the feldspar cleavages. The cracks are rather oriented (sub)-perpendicular to the direction of maximum tensile stress. The critical stress needed to initiate fracturing is about 325 MPa. The critical stress intensity factor for the propagation of mode I cracks, K Ic, is estimated as 2.30–2.72 MPa m1/2 (73–86 MPa mm1/2) from a systematic relation between characteristic crack spacing and coherency stress. An orientation mismatch of 18° between the crack normal and the direction of maximum tensile stress is ascribed to the anisotropy of the longitudinal elastic stiffness which has pronounced maxima in the crack plane and a minimum in the direction of the crack normal.

Experimental Na/K exchange between alkali feldspar and an NaCl–KCl salt melt: chemically induced fracturing and element partitioning

The exchange of Na+ and K+ between alkali feldspar and a NaCl–KCl salt melt has been investigated experimentally. Run conditions were at ambient pressure and 850 °C as well as 1,000 °C. Cation exchange occurred by interdiffusion of Na+ and K+ on the feldspar sub-lattice, while the Si–Al framework remained unaffected. Due to the compositional dependence of the lattice parameters compositional heterogeneities resulting from Na+/K+ interdiffusion induced coherency stress and associated fracturing. Depending on the sense of chemical shift, different crack patterns developed. For the geometrically most regular case that developed when potassic alkali feldspar was shifted toward more sodium-rich compositions, a prominent set of cracks corresponding to tension cracks opened perpendicular to the direction of maximum tensile stress and did not follow any of the feldspar cleavage planes. The critical stress needed to initiate fracturing in a general direction of the feldspar lattice was estimated at ≤0.35 GPa. Fracturing provided fast pathways for penetration of salt melt or vapor into grain interiors enhancing overall cation exchange. The Na/K partitioning between feldspar and the salt melt attained equilibrium values in the exchanged portions of the grains allowing for extraction of the alkali feldspar mixing properties.

Helical crack-front instability in mixed-mode fracture

Planar crack propagation under pure tension loading (mode I) is generally stable. However, it becomes universally unstable with the superposition of a shear stress parallel to the crack front (mode III). Under this mixed-mode (I + III) loading configuration, an initially flat parent crack segments into an array of daughter cracks that rotate towards a direction of maximum tensile stress. This segmentation produces stepped fracture surfaces with characteristic 'lance-shaped' markings observed in a wide range of engineering and geological materials. The origin of this instability remains poorly understood and a theory with which to predict the surface roughness scale is lacking. Here we perform large-scale simulations of mixed-mode I + III brittle fracture using a continuum phase-field method that describes the complete three-dimensional crack-front evolution. The simulations reveal that planar crack propagation is linearly unstable against helical deformations of the crack front, which evolve nonlinearly into a segmented array of finger-shaped daughter cracks. Furthermore, during their evolution, facets gradually coarsen owing to the growth competition of daughter cracks in striking analogy with the coarsening of finger patterns observed in nonequilibrium growth phenomena. We show that the dynamically preferred unstable wavelength is governed by the balance of the destabilizing effect of far-field stresses and the stabilizing effect of cohesive forces on the process zone scale, and we derive a theoretical estimate for this scale using a new propagation law for curved cracks in three dimensions. The rotation angles of coarsened facets are also compared to theoretical predictions and available experimental data.

Fracture initiation/propagation parameters for duplex TiAl grain boundaries based on twinning, slip, crystal orientation, and boundary misorientation

The role of mechanical twinning in microcrack nucleation and crack propagation in a near-γ TiAl alloy was characterized using 4-point bend tests and analyzed with advanced electron microscopy techniques. Smooth bend specimens were used to examine microcrack nucleation prior to fracture, and notched bend specimens were used to examine crack propagation. A combination of selected area channeling patterns and electron backscattered diffraction pattern maps were used to identify grain orientations in regions of microstructure surrounding microcracks or growing cracks. Microcracks were observed, where twins on highly stressed twinning systems intersected certain grain boundaries. An anisotropic elastic analysis of a tri-crystal showed that local stresses near boundaries can vary by as much as 45%, which may enhance microcracking in the presence of deformation defects. To determine why some twin boundary intersections resulted in cracking, but not others, a fracture initiation parameter was developed to identify how efficiently slip can be transferred across the boundary. Cracks were found to be more prevalent when this parameter is large, which occurs when the twin Burgers vector is closely aligned with the direction of maximum tensile stress and when the twin Burgers vector is somewhat aligned with other slip systems that could accommodate the twin strain in the neighboring grain. The orientation of the grain boundary plane has little effect. On the basis of a fracture initiation parameter, it is possible to predict the path of cracks knowing only the primary tensile stress axis and spatially resolved grain orientations.

Novel Kinematics for Cylindrical Grinding of Brittle Materials

Brittle materials are characterised by grinding direction related strength anisotropy attributed to the dual population of grinding induced microcracks. Surface grinding operations are therefore implemented such that the grinding lay is along the direction of maximum tensile stress in the component, which corresponds to minimal strength degradation. The kinematic configuration of conventional machine tools inherently precludes such an approach in cylindrical traverse grinding. To this end, the paper presents aspects of an innovative material-adapted kinematic variant, which corresponds to an enhancement of characteristic flexural strength of about 30% in comparison to conventionally ground quartz samples.

Fatigue Crack Growth Thresholds of Deflected Mixed-Mode Cracks in PWA1484

The fatigue crack growth (FCG) behavior of PWA1484 single crystals was characterized in air under mixed-mode loading at 593°C as a function of crystallographic orientation using an asymmetric four-point bend test technique. Most mixed-mode fatigue cracks deflected from the symmetry plane and propagated as transprecipitate, noncrystallographic cracks, while self-similar fatigue crack growth occurred on the (111) planes in (111)/[011] and 111/[112]¯ oriented crystals. The local stress intensity factors and the crack paths of the deflected mixed-mode cracks were analyzed using the finite-element fracture mechanics code, FRANC2D/L. The results indicated that the deflected crack path was close to being normal to the maximum tensile stress direction where the Mode II component diminishes. Crystallographic analysis of the deflected crack paths revealed that the Mode I and the deflected mixed-mode cracks were usually of different crystallographic orientations and could exhibit different Mode I FCG thresholds when the crystallography of the crack paths differed substantially. These results were used to identify the driving force and conditions for cracking mode transition.

Patterns of Vertical Root Fracture: Factors Affecting Stress Distribution in the Root Canal

Previous studies have indicated that vertical root fracture tends to occur in a buccolingual direction, where dentin thickness is greatest. Factors potentially influencing the location and direction of root fracture include root canal shape, external root morphology, and dentin thickness. In this finite-element study, simulated root sections were varied systematically with respect to canal size and shape, external root morphology, and dentin thickness to determine their relative contribution to vertical root fracture. Similar models were constructed based on cross-sections of human tooth roots that had been fractured clinically or experimentally. Finite-element models demonstrated that canal curvature seems more important than external root morphology, in terms of stress concentration, and that reduced dentin thickness increases the magnitude but not the direction of maximum tensile stress. Models based on actual root fractures showed a strong similarity between tensile-stress distribution and fracture patterns.

Evidence for diffuse extension of the Pacific Plate from Pukapuka ridges and cross‐grain gravity lineations

Satellite altimeter measurements of marine gravity reveal 100 to 200‐km wavelength lineations over a wide area of the Pacific plate oriented roughly in the direction of absolute plate motion. At least three mechanisms have been proposed for their origin: small‐scale convective rolls aligned in the direction of absolute plate motion by shear in the asthenosphere; diffuse N‐S extension of the lithosphere resulting in lineated zones of extension (boudins); and minihotspots that move slowly with respect to major hotspots and produce intermittent volcanism. Recently, several chains of linear volcanic ridges have been found to be associated with the gravity lineations. Following ridgelike gravity signatures apparent in high‐resolution Geosat gravity measurements, we surveyed a series of volcanic ridges that extend northwest from the East Pacific Rise flank for 2600 km onto 40 Ma seafloor. Our survey data, as well as radiometric dates on samples we collected from the ridges, provide tight constraints on their origin: (1) Individual ridge segments and sets of ridges are highly elongate in the direction of present absolute plate motion. (2) The ridges formed along a band 50 to 70‐km‐wide in the trough of one of the more prominent gravity lineations. (3) Radiometric dates of the largest ridges show no hotspot age progression. Moreover, the directions predicted for minihotspot traces older than 24 Ma do not match observed directions of either the gravity lineations or the ridges. Based on this last observation, we reject the minihotspot model. The occurrence of the ridges in the trough of the gravity lineation is incompatible with the small‐scale convection model which would predict increased volcanism above the convective upwelling. We favor the diffuse extension model because it is consistent with the occurrence of ridges in the trough above the more highly extended lithosphere. However, the multibeam data show no evidence for widespread normal faulting of the crust as predicted by the model. Perhaps the fault scarps are buried under more than 30 m of sediments and/or covered by the elongated ridges. Finally, we note that if ridge‐push force is much smaller than trench‐pull force, then near the ridge axis the direction of maximum tensile stress must be perpendicular to the direction of absolute plate motion.

Rolling-sliding behavior of rail steels

A twin disk-rolling-sliding contact machine has been used to investigate the deformation, wear and cracking that occur during rolling-sliding of high-carbon rail and wheel steels. A martensitic wheel steel with initial hardness of 360 HV contacted pearlitic or martensitic rail steels of different initial hardness, 280–360 HV. Other variables included test time, test environment and slip ratio (0%, 5%, 10% and 26%). Tests were run in air, but with different lubrication conditions, e.g. dry, with water, water with inhibitor, silicone oil, and various combinations. Wear was measured by weight loss. Wear surfaces, sample cross-sections and wear debris were observed by optical and scanning electron microscopy. Principal conclusions are as follows. The thickness of the highly deformed layer was very small for pure rolling compared with cases involving slip. Wear debris was generated from near-surface material in which the cementite phase had broken into small particles. Cracks initiated at the surface and propagated along lines of earlier plastic flow, rather than normal to the local direction of maximum tensile stress. The results of rolling-sliding in water or other liquids after dry rolling-sliding indicate that extensive deformation from sliding during the dry stage prepares the material for extensive cracking during subsequent operation with a lubricant.

The early stage of fatigue crack propagation

It is observed that an early stage fatigue crack propagates along the maximum shear direction rather than perpendicular to the maximum tensile stress direction. In the present paper, an analytical consideration is given concerning the effects of localized plastic deformation on the early stage of fatigue crack propagation. It is seen that the localized plastic deformation shields the local mode II stress intensity factor and leads the micro-crack to propagate along the maximum shear stress direction. In this analytical modeling, the localized plastic zone is modeled as an elliptical inclusion with eigenstrains where the Eshelby inclusion solution [ Proc. R. Soc. A241, 376–396 (1957)] is employed.

Fracture behavior of a laminated steel-brass composite in bend tests

A 35-layer laminated metal composite, consisting of alternating ultrahigh carbon steel (UHCS) and brass layers, was evaluated for its plasticity and fracture characteristics in bending. The unnotched composite achieved remarkable ductility exhibiting a 0T bend ( i.e. bent upon itself) without failure. Voids were formed in the tension and compression regions of the UHCS layers and were associated with elongated carbide particles. Even with initial notches on the surface, the composite can be bent without failure. Delamination and crack tip blunting in the brass layer inhibited crack propagation and prevented total failure. Propagation of cracks occurs at about 45° to the maximum tensile stress direction. In contrast, laminated polymer-base composites fracture at 90° to the maximum tensile stress direction.

Fault offsets and lateral crustal movement on Europa: Evidence for a mobile ice shell

Right-lateral structural offsets of ∼25 km have been identified on the icy Galilean satellite Europa. These occur along dark lineaments oriented orthogonally to wedge-shaped bands, which are also ∼25 km wide. Wedge-shaped bands are interpreted as dilated tension fractures, which formed as crustal blocks (or plates) 50–100 km across separated and slipped past each other along flanking strike-slip faults. This style of deformation does not appear to be characteristic of other lineament types, and with the exception of Earth appears to be unique to Europa. Together, the subparallel wedge-shaped b bands form a broad NW-SE trending belt, ∼1500 km long and less than 500 km across, near the anti-Jovian point. This belt is interpreted as a major crustal fracture (or rift) zone, with a pole of rotation (determined by the strike-slip faults) near 47°S, 144°W, and an approximate NE-SW direction of maximum tensile stress. Extension may have been areally compensated at Agenor Linea, a bright band of possible compressional origin. Global expansion, tidal distortion, and nonsynchronous rotation do not explain the inferred minimum principal (i.e., least compressive) stress directions. Alternatively, fracturing near the anti-Jovian point may be a result of (i) solid-state convection in the lower ice crust (possibly triggered by uneven heat flow from the silicate interior), (ii) rotation of the icy shell about the sub- and anti-Jovian points induced by latitudinal lithospheric thickness variations, or (iii) preferential strain accumulation from the rest of the icy shell. No significant distortion of the crustal blocks occurred during fracturing and rotation, indicating that the icy crust was probably mechanically decoupled from the silicate interior in this region over the time scale of fracturing. Decoupling on a global scale is also likely the simple geometry of lineaments argues for formation in an icy lithosphere, not a silicate one, and other evidence for fracturing caused by nonsynchronous rotation stress is not compatible with a tidally locked silicate interior (which we show is likely) unless the ice shell rotates independently. Decoupling could have been due to either warm ice or liquid water near the base of the icy crust. Mechanical bounds on lithospheric thickness (a few to ∼10 km) lead to heat flow estimates that admit both possibilities but favor decoupling by liquid water.

The micromechanisms of fatigue crack growth in a commercial Al-Zn-Mg-Cu alloy

A detailed fractographic and microstructural study, using combined scanning and transmission electron microscopy has been made of the fracture surfaces produced by fatigue of a commercial aluminium alloy 7010:T76 in moist air, dry argon and dry oxygen. In the dry environments fracture is entirely ductile: the fracture surface is non-crystallographic and essentially striation free. In moist air fracture occurs by cleavage on {110} coupled with plastic deformation during the blunting and closing of the crack: this results in the formation of well defined surface striations. Striation topography is controlled by the local orientation of the cleavage plane to the direction of maximum tensile stress and to the slip systems of highest local shear stress. In consequence a range of striation profiles are developed. It is suggested that the cleavage component of growth is the result of hydrogen embrittlement of the matrix ahead of the crack and that dislocation transport is necessary to introduce this hydrogen.