Severe Necking Research Articles

A strain components-based Mohr–Coulomb fracture criterion for proportional loading

Ductile fracture criteria are crucial in the application of elastoplastic materials like advanced high-strength steels, particularly due to their tendency to fail without significant localized necking. It is aimed to figure out the unified mechanism for ductile fracture and accurately describe it with phenomenological criteria. In this study, the effect of the stress triaxiality and the Lode parameter is analyzed mathematically. The maximum shear strain and the normal strain to fracture are emphasized in the proposed strain components-based Mohr–Coulomb fracture criterion particularly designed for plane stress states, and it is assumed that fracture occurs when the combination of the maximum shear strain and the normal strain reaches the critical value. It is then extended to describe fracture with the equivalent plastic strain and the normal strain to fracture. The experimental fracture data of AA 2024-T351 and the additively manufactured Ti-6Al-4V titanium alloy are used to verify the proposed models. A fracture forming limit diagram comprising forming limit curves calibrated from stress states under different stress triaxialities is proposed based on the proposed fracture criteria for plane stress states. This study shows that a strong correlation between the maximum shear strain and the normal strain to fracture has been observed, and it can be described piecewise-linearly. Besides, the orientation of the fracture surface under both tension (including plane strain tension) and compression (including plane strain compression) can be qualitatively explained by the Mohr’s strain circles. The results provide a new insight into the intrinsic deformation and fracture mechanism of materials that fail without severe localized necking.

Tension-Induced Cavitation in Li-Metal Stripping.

Designing stable Li metal and supporting solid structures (SSS) is of fundamental importance in rechargeable Li-metal batteries. Yet, the stripping kinetics of Li metal and its mechanical effect on the supporting solids (including solid electrolyte interface) remain mysterious to date. Here, through nanoscale in situ observations of a solid-state Li-metal battery in an electron microscope, two distinct cavitation-mediated Li stripping modes controlled by the ratio of the SSS thickness (t) to the Li deposit's radius (r) are discovered. A quantitative criterion is established to understand the damage tolerance of SSS on the Li-metal stripping pathways. For mechanically unstable SSS (t/r< 0.21), the stripping proceeds via tension-induced multisite cavitation accompanied by severe SSS buckling and necking, ultimately leading to Li "trapping" or "dead Li" formation; for mechanically stable SSS (t/r> 0.21), the Li metal undergoes nearly planar stripping from the root via single cavitation, showing negligible buckling. This work proves the existence of an electronically conductive precursor film coated on the interior of solid electrolytes that however can be mechanically damaged, and it is of potential importance to the design of delicate Li-metal supporting structures to high-performance solid-state Li-metal batteries.

Effect of heating rate during solution treatment on the bendability of Al–Mg–Si alloys

The bendability of Al–Mg–Si alloy sheets is a key parameter for their application as skins of automotive body panels. In the present study, the influence of heating rate on the bendability of Al-0.6Mg-1.0Si (in wt%) alloy was investigated using optical microscopy (OM), scanning electron microscopy (SEM), and electron backscatter diffraction (EBSD). The bendability of Al–Mg–Si alloy was found to be significantly dependent on the heating rate of solution treatment. After bending, the rapidly heated specimen exhibited only slight surface undulation, while the slowly heated specimen showed severe surface necking and even micro-cracks. The severe surface necking was caused by intensive shear bands formed during bending, and the micro-cracks were the results of the interaction between the intensive shear bands and coarse second phase particles. Elongated coarse grains were more likely to produce intensive shear bands, and cube-oriented grains impeded the formation of shear bands. The schematics of recrystallization and bending processes for Al-0.6 Mg-1.0 Si alloy considering two different heating rates are proposed.

Influence of texture distribution in magnesium welds on their non-uniform mechanical behavior: A CPFEM study

Recent studies indicate that the texture distribution in friction stir welded (FSW) Mg alloys can be tailored and hence improve the joint performance. In this work, a crystal plasticity finite element modeling (CPFEM) was performed to understand the effects of texture distribution in stir zone (SZ) on the non-uniform plastic deformation and fracture localization. In total, six kinds of observed or purposely tilted texture distributions were modelled. The “concave-convex” appearance, as commonly observed in the tensile sample, was successfully simulated. It reveals that the mirror-symmetrical distribution of basal planes in the region of easy to activate basal slip (EABS) determined the “concave-convex” appearance in SZ-center. The asymmetrical appearance exchanged on plane A and plane B when the directions of basal planes were switched in the two EABS regions. Furthermore, the asymmetrical feature of plastic deformation was changed with varying the texture distribution in SZ. The “embossed” feature became more obvious in SZ-center first, and then gradually weakened with the c-axis rotated away from the weld plate plane. Severe necking was successfully simulated in SZ-center of FSW-H joint and in SZ-side of FSW-L joint. That might determine the observed fracture morphology. We believe that this simulation study is helpful for further improving the performance of FSW Mg joints.

Experimental and Computational Study of Ductile Fracture in Small Punch Tests.

A unified experimental-computational study on ductile fracture initiation and propagation during small punch testing is presented. Tests are carried out at room temperature with unnotched disks of different thicknesses where large-scale yielding prevails. In thinner specimens, the fracture occurs with severe necking under membrane tension, whereas for thicker ones a through thickness shearing mode prevails changing the crack orientation relative to the loading direction. Computational studies involve finite element simulations using a shear modified Gurson-Tvergaard-Needleman porous plasticity model with an integral-type nonlocal formulation. The predicted punch load-displacement curves and deformed profiles are in good agreement with the experimental results.

In Situ Observation of Twin Boundary Sliding in Single Crystalline Cu Nanowires.

Using a homemade, novel, in situ transmission electron microscopy (TEM) double tilt tensile device, plastic behavior of single crystalline Cu nanowires of around 150 nm are studied. Deformation twins occur during the tests as predesigned before the experiments. In situ observation of twin boundary sliding (TBS) caused by full dislocation (extended dislocation) is first revealed at the atomic scale which is confirmed by molecular dynamics (MD) simulation results. Combined with twin boundary migration and multiple dislocations nucleated from surface, TBS causes a superlarge fracture strain which is over 166% and a severe necking which is over 93%, far beyond the typical values for most nanomaterials without twins.

Formation and coalescence of strain localized regions in ferrite phase of DP600 steels under uniaxial tensile deformation

Abstract In this study the key factors in the creation and coalescence of strain localization regions in dual-phase steels were investigated. An in-situ tensile setup was used to follow the microscopic deformation of ferrite phase inside the microstructure of DP600 steel. The test was continued until the specimen was very close to final failure. The captured scanning electron microscopy (SEM) micrographs enabled us to directly observe the evolution of deformation bands as a contour of strain distribution in the ferrite matrix. The image processing method was used to quantify the ferrite microscopic strains; the obtained strain maps were superimposed onto the SEM micrographs. The results revealed important deformational characteristics of the microstructure at the microscopic level. It was observed that despite the formation of slip bands inside the large grains during the early stages of deformation, the large ferrite grains did not contribute to the formation of high-strain bands until the final stages of severe necking. The behavior of voids and initial defects inside the localization bands was also studied. In the final stages of deformation, cracks were observed to preferentially propagate in the direction of local deformation bands and to coalescence with each other to form the final failure lines in the microstructure. It was observed that in the final stages of deformation, the defects or voids outside the deformation bands do not contribute to the final failure mechanisms and could be considered to be of minor importance.

Fracture characterization of high-density polyethylene pipe materials using the $$J$$ J -integral and the essential work of fracture

In this paper, fracture mechanics concepts are reviewed and their relevance to examine the toughness of highly deformable materials such as high-density polyethylene (HDPE) pipe materials is discussed. Using two different specimen configurations (single edge notched bending and compact tension), it was found that the \(J-R\) approach is unable to give pertinent indications on fracture toughness of HDPE. Alternatively, applying the essential work of fracture approach to double edge notched tension specimen, seems a more appropriate way to measure the fracture strength of HDPE and therefore to analyze the fracture process of such materials. Nevertheless, the severe necking occurring at the crack tip and in the plastic zone makes difficult the crack growth measurement, which clearly depends on the strain state and on the stress triaxiality level.

Powder synthesis and aerosol deposition of the BaCe 0.9Y 0.1O 2.95 and SrCe 0.9Y 0.1O 2.95 phases for gas separation membrane application

Mixed-conducting oxide powders, BaCe 0.9Y 0.1O 2.95 (BCY) and SrCe 0.9Y 0.1O 2.95 (SCY), were prepared using a solid-state reaction method. X-ray diffraction patterns of the prepared powders showed the sharp peaks of the BaCe 0.9Y 0.1O 2.95 and SrCe 0.9Y 0.1O 2.95 phases. XRD patterns and FE-SEM morphologies of the oxide powders, fabricated by attrition milling and ball milling, were compared. The oxide powders that were prepared by attrition milling showed rather large particles and severe necking between particles in FE-SEM images as well as residual reactant (BaCO 3) and secondary phases (SrCeO 3 and CeO 2) in XRD patterns. The oxide powders prepared using ball milling showed particles under approximately 500 nm and typical XRD patterns of the BaCe 0.9Y 0.1O 2.95 and SrCe 0.9Y 0.1O 2.95 phases. Ceramic membranes of the BaCe 0.9Y 0.1O 2.95 and SrCe 0.9Y 0.1O 2.95 phases were fabricated by the aerosol deposition method using the oxide powders synthesized. Two fabricated ceramic membranes demonstrated somewhat dense morphologies and relatively fine grains in the FE-SEM surface images.

Structure–function relationships and source-to-ground distance in electrospun polycaprolactone

The strength of electrospun scaffolds has direct relevance to their function within tissue engineering. We characterized the effects of source-to-ground distance on the mechanical properties of electrospun poly(ε-caprolactone) (PCL). Source-to-ground distances of 10, 15 and 20 cm, solids concentrations of 12 and 18 wt.% and mandrel rotation surface speeds of 0–12 m s −1 were utilized. Tensile tests evaluated elastic modulus, tensile strength and elongation at failure. Scanning electron microscopy provided morphology and quantified fiber alignment. Increased source-to-ground distance yielded a microstructure allowing greater fiber rearrangement under load, tripling the observed tensile strength. Increases in rotational speed generally increased fiber alignment and strength at high but not low to moderate speeds. As fiber is quickly pulled out of a comparatively gentle falling process, collision with neighboring fibers moving at different speeds and in different directions can occur. The source-to-ground distance influences these collisions and thus has critical implications for microstructure and biocompatibility. In larger diameter (18 wt.% PCL), heavily point-bonded fibers (produced using a shorter, 10 cm source-to-ground distance), elongation at failure in the aligned direction increases dramatically due to severe localized necking. These specimens show only half of the tensile strength (from 2.6 to 4.5 MPa) and a dramatic increase (from 94% to 503%) in elongation at failure vs. a longer 20 cm source-to-ground distance. Strains of several hundred per cent are accompanied by periodic necking of large-diameter fibers in which microstructural failure appears to occur in a sequential manner involving an equilibrium between localized strain in the tensile direction and anisotropic point bonding that locally resists strain.

Failure analysis of J85 Engine turbine blades

This paper analyzes the cause of the engine damage due to the fracture of the J85 Engine first stage turbine blades. Discoloration due to thermal effect and fine multi-cracks as well as necking at 1/3 of the way down from the tip on the entire first stage turbine blade concave side surface have been noted. Of the first stage blades, nine had fractures 1/3 of the way down from the tip, and at the fractured location more severe necking has been found than blades without fracture. As a result of observing the fine texture of fractured blades and the blades where deformation has occurred, wedge-type intergranular cracks and TCP phase as well as carbide phase have been identified, and γ′ deformation and depletion found around the fracture surface. There were no traces of thermal damage to the first stage vane, no IOD phenomenon has been noted. Analysis of turbine blade deformation and fracture profile and microstructural deformation phenomenon determined that blade fracture was due to high temperature creep rupture.

Fracture behavior under fatigue loading at room temperature and its influence on critical current of Nb–Ti/Cu composite wire

Fracture behavior under fatigue loading at room temperature and its influence on critical superconducting current at 4.2 K were investigated for Nb–Ti/Cu multifilamentary composite wire with a copper ratio of 7.83 and an overall diameter of 0.504 mm in which 24 Nb–Ti filaments were embedded. There was a knee in the relation between the applied maximum stress and the number of cycles to failure ( S– N relations). The fracture mechanism below and above this knee was different. When the maximum stress in the fatigue test was high, extensive multiple necking of the Nb–Ti filament occurred, and this was responsible for the final fracture of the composite wire. On the other hand, when the maximum stress in the fatigue tests was low, the fatigue crack nucleated in the copper, which grew and caused the fracture of the Nb–Ti filaments. The critical current was insensitive to fatigue loading when the maximum stress was low. When the maximum stress was high, the critical current after fatigue loading was lower than that after static loading. This was due to severe multiple necking during fatigue loading. Extracted Nb–Ti filaments were also fatigued using a specially designed fatigue testing machine. The S– N curve of filaments agreed well with the stress component of the filament calculated from the S– N relation of the composite wire.

Fabrication of Cu interconnects of 50 nm linewidth by electron-beam lithography and high-density plasma etching

The feasibility of building Cu interconnects with a linewidth as small as 50 nm embedded in insulating SiO2 has been explored using the damascene process. Fine line test structures, designed for evaluating effects of small linewidth on metal line electric resistivity, were written on a poly(methylmethacrylate) resist layer and then transferred to the underlying SiO2 layer by high-density plasma etching. Using a CHF3 etching gas and an inductive power of 400 W, we were able to produce 50-nm-wide and 150-nm-deep trenches in SiO2. These trenches were then filled with a thin (5–10 nm) TaSiN or TaN liner and a thick Cu layer by the ionized physical vapor deposition technique. The field Cu was removed by a chemical-mechanical polishing process, leaving narrow damascene Cu in the oxide trenches. Direct current resistance measurements have indicated a wide distribution of resistivity in these fine lines. The low end of the distribution is close to the effective resistivity of a perfect Cu line. The high values are indicative of severe necking or other imperfections induced during the fabrication process.

Rigid-plastic and damage behavior in metal forming: Part II—model prediction

Abstract Local sites of material damage by yield intensification and fracture are predicted for a rigid punch deforming a metal sheet in small steps. A modified theory of rigid-plasticity developed in Part I is used in combination with the volume energy density criterion. The condition of perfect elastic rigidity is relaxed in addition to the inclusion of material compressibility and dilatational energy. Compatibility of physical description, numerical computation and damage prediction is emphasized for defining the size of the smallest resolvable detail in an account of the workpiece's structure integrity and configuration tolerance. Computer models are shown to be forgiving when applied to describe global behavior such as punch force/displacement relation, workpiece configuration, etc., but large differences are reflected in the local stress/strain fields and material damage details. Sixteen Gaussian points are required in each of the twelve-node isoparametric elements to achieve sufficient accuracy for determining the maxima and minima of the volume energy density function. Their local and global values are identified with the potential failure sites and stability of the material degradation process. The ability of the workpiece to absorb plastic energy is shown to decrease with increase intensification of yielding and localized necking. A stage would be reached where further energy dissipation takes place in the form of fracture. Progressive cracking is found to be more unstable at the fixed end in contrast to the region under the punch with severe through-thickness necking. These effects are accessed quantitatively by an instability index parameter through which loading rate, workpiece geometry and material type could be optimized as a combination. Predicted fracture path in the necked region of the workpiece is reminiscent to that observed in the ductile failure of a tension specimen. Local description of material damage in metal forming is essential for developing realistic computer models. The DABY program possesses such a capability.

Tensile fracture and fractographic analysis of 1045 spheroidized steel under hydrostatic pressure

Void formation in tensile test under hydrostatic pressure is characterized through quantitative metallography, and the fracture mechanism under pressure is analyzed by fractography. Transition of the fracture surface from the cup-and-cone under atmospheric pressure to a slant structure under high pressure is explained on the basis of the void development leading to fracture and the concomitant change in fracture mechanism. The concept of “shear blocks” is introduced to illustrate the features observed on the fracture surface of specimens tested under high pressure. It is postulated that shear blocks evolve to connect the central crack regions with the shear crack initiated on neck surface due to the severe necking deformation under applied pressure.

Steady-state Eddy-current dominated magnetic domain wall motion with severe bowing and necking

The bowed shape and mobility of domain walls spanning metallic laminations and in steady-state eddy-current-limited motion have been calculated using a linear spline function x w( y), symmetric about the sheet centre plane y = 0, to represent the wall profile without imposing the usual constraint that x w( y) be single valued. Profiles have been calculated for all integral values of the reduced wall speed u up to 51. (Here, u = 8 VM 2 D 2/ π 3 γϱ, V) is the velocity d x/d d of the wall along sheet of thickness D and resistivity ϱ, γ is the specific surface wall energy and 2 M the change in magnetization effected by its passage). For u⩾21, profiles are multivalued with a pinched neck preceding a slightly bulbous tail. Thus, over a range of depths in the lamination, flux is reversed three times by the passage of such a “pinched” wall. The wall profiles vary very smoothly with increasing u with no trace of the oscillations obtained when they were constrained to be single valued. The results suggest that at a finite speed u c > ̆ 50 , the pinched neck ma of drop-like domains may break away from the tail.