Showing papers on "Stress concentration published in 2008"

An interacting micro-crack damage model for failure of brittle materials under compression

Abstract: A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.

Low-speed fracture instabilities in a brittle crystal

Abstract: Multiscale models predict detailed features of surfaces left by crack propagation and rationalize the occurrence of fracture instabilities in a technologically important material, silicon. As a crack propagates along the most stable cleavage plane in silicon at relatively low speeds (800 metres per second), an instability suddenly appears. The authors find that beyond the very tip of the crack, when fracture speed is slow enough, bonds are broken one atomic layer below the fracture plane leading to a systematic downward deflection of the crack. Conversely, deflecting of fracture on another cleavage plane of silicon occur when the fracture speed is very high. Preliminary simulations reveal that similar instabilities could occur in diamond and silicon carbide. When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack1. The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen2. The way the crack propagates, however, is entirely determined by atomic-scale phenomena, because brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front1,3. The physical interplay of multiple length scales makes brittle fracture a complex ‘multi-scale’ phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known1, and significant advances have been made recently in understanding their origin4,5. Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack-tip reconstruction that makes low-speed crack propagation unstable on the (111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto (111) planes, as previously observed experimentally6,7.

Strain controlled cyclic deformation behavior of an extruded magnesium alloy

Abstract: Fatigue properties of an extruded AZ31B magnesium alloy were evaluated using strain-controlled push–pull cyclic tests at different total strain amplitudes at room temperature. The alloy exhibited an asymmetric sigmoidal-shaped hysteresis loop due to twinning in compression during the unloading phase and detwinning during the loading phase. As the total strain amplitude increased, the asymmetry of hysteresis loops, plastic strain amplitude, mean stress, and stress amplitude increased, while the ratcheting strain and pseudoelastic modulus decreased. As the cyclic deformation progressed at a given total strain amplitude (greater than 0.3%), an abrupt increase in the plastic strain amplitude was observed, representing the onset of fatigue crack initiation. The extent of this increase process, which decreased with increasing total strain amplitude, corresponded to the fatigue crack propagation prior to the final fast failure. Fatigue crack initiation was observed to occur at the specimen surface, and fatigue crack propagation was characterized by typical striations. The smaller spacing of fatigue striations and larger fatigue crack propagation zone at the lower total strain amplitude gave rise to a longer fatigue life. The Coffin–Manson and Basquin's relationships can be used to describe the fatigue lifetime of this alloy.

Improving performance of GFRP/aluminum single lap joints using bolted/co-cured hybrid method

Abstract: The present study proposes a bolted/co-cured hybrid joining method, and experimentally investigates the joint strength The bolted/co-cured hybrid joints combine co-cured adhesive joints and bolted joints without damaging reinforcing fibers The method allows for low scatter strength in static and fatigue loading for easily manufactured co-cured joints Testing of the static tensile lap-shear and fatigue strengths is performed using aluminum alloy A5052-F and knit fabric glass epoxy composites The results show that the hybrid joints have 184 times higher maximum shear strength and a quarter of the standard deviation compared with conventional co-cured joints Furthermore, less stress concentration and undamaged glass fibers in the hybrid joints contribute to a much higher fatigue strength than that of the bolted joint

Joint Strength Optimization of Adhesively Bonded Patches

Abstract: Aircraft face damage from impact with objects or birds or due to ageing that leads to fatigue cracks. The conventional methods of repairing aircraft metallic structures generally include the use of a plate joined by screws or rivets. Although these methods are efficient in the short term, they introduce stress concentrations leading to the initiation of new cracks that are difficult or impossible to detect by non-destructive methods. For these reasons, it is necessary to develop new methods to improve the behaviour of the structure (especially for long term) and its manufacture cost. One of the solutions that have been studied by the aeronautical industry is the use of patches bonded with structural adhesives. However, adhesively bonded patches have problems of stress concentration at the edges where crack initiation is prone to occur. This problem can be reduced by the use of a taper and a spew fillet at the end of the patch and by the use of a mixed adhesive technique where a ductile adhesive is placed ...

Influence of restorative technique on the biomechanical behavior of endodontically treated maxillary premolars.: Part II: Strain measurement and stress distribution

Abstract: Statement of problem. Unresolved controversy exists concerning the preferred cavity design and restorative technique used to restore endodontically treated maxillary premolars to minimize strain and improve stress distribution under occlusal load. Purpose. The purpose of this study was to analyze the influence of cavity design and restorative material on strain measurement and stress distribution in maxillary premolars under occlusal loading conditions, and correlate these influences with the failure modes analyzed in Part I. Material and methods. For the strain gauge test, 21 additional specimens were prepared as described in Part 1 of this study (n=3). Two strain gauges were fixed on the buccal (B) and palatal (P) cusps of each specimen with cyanoacrylate adhesive. The specimens were submitted to continuous axial compression loading at a speed of 0.5 mm/min, using a 6-mm sphere, to a maximum limit of 150 N in a universal testing machine. Total strain values were obtained by combining the B and P cusp strain values. These values were submitted to 2-way ANOVA and the Dunnet test (α=.05). For finite element analyses, 7 numerical 2-D models were generated: MODd, direct mesio-occlusal-distal preparation; MODi, indirect mesio-occlusal-distal preparation; AM, MODd restored with amalgam; CR, MODd restored with composite resin; LPR, MODi restored with laboratory-processed composite resin; and LGC, MODi restored with leucite-reinforced glass ceramic; each corresponding to 1 of the experimental groups tested in Part I of this study. The models were analyzed with finite element software, using the von Mises criteria for stress distribution analysis. Results. With the strain gauge test, MODd, MODi, and AM groups showed significantly higher strain values than the CR, LPR, and LGC. Finite element analyses revealed that tooth structure removal and the type of restorative material altered the stress distribution pattern. The MODd, MODi, AM, and LPR models showed higher stress concentration within the tooth structure. Conclusions. The specimens with adhesive restorations were shown to behave in a manner similar to the biomechanical behavior of healthy teeth, while the behavior of those restored with amalgam restorations was more like that observed for teeth with nonrestored cavity preparations. These results directly correlate with the fracture mode results obtained in Part I of this study. (J Prosthet Dent 2008;99:114-122)

Recoverable creep deformation and transient local stress concentration due to heterogeneous grain-boundary diffusion and sliding in polycrystalline solids

Abstract: Numerical simulations are used to investigate the influence of heterogeneity in grain-boundary diffusivity and sliding resistance on the creep response of a polycrystal. We model a polycrystal as a two-dimensional assembly of elastic grains, separated by sharp grain boundaries. The crystal deforms plastically by stress driven mass transport along the grain boundaries, together with grain-boundary sliding. Heterogeneity is idealized by assigning each grain boundary one of two possible values of diffusivity and sliding viscosity. We compute steady state and transient creep rates as functions of the diffusivity mismatch and relative fractions of grain boundaries with fast and slow diffusion. In addition, our results show that under transient conditions, flux divergences develop at the intersection between grain boundaries with fast and slow diffusivity, which generate high local stress concentrations. The stress concentrations develop at a rate determined by the fast diffusion coefficient, and subsequently relax at a rate determined by the slow diffusion coefficient. The influence of the mismatch in diffusion coefficient, loading conditions, and material properties on the magnitude of this stress concentration is investigated in detail using a simple model problem with a planar grain boundary. The strain energy associated with these stress concentrations also makes a small fraction of the plastic strain due to diffusion and sliding recoverable on unloading. We discuss the implications of these results for conventional polycrystalline solids at high temperatures and for nanostructured materials where grain-boundary diffusion becomes one of the primary inelastic deformation mechanisms even at room temperature.

Deformation and fracture during equal channel angular pressing of AZ31 magnesium alloy

Abstract: The deformation and fracture characteristics of AZ31 magnesium alloy during equal channel angular pressing (ECAP) were established. The isothermal behavior of AZ31 magnesium alloy was determined at temperatures between 150 and 250 °C and ram speeds producing average effective strain rates between 0.001 and 0.25 s−1. AZ31 magnesium alloy was particularly susceptible to shear localization during ECAP, uniform flow occurred only at high temperatures and low strain rates. Observations of shear banding and shear fracture were interpreted in terms of the tendency for strain concentration as quantified by the flow localization ‘α’ parameter, or the ratio of the normalized flow softening rate to the strain-rate sensitivity. These understandings of the effect of material properties on flow localization tendency are helpful for the selection of processing parameters with uniform flow during ECAP.

Fracture Toughness, Fracture Strength, and Stress Corrosion Cracking of Silicon Dioxide Thin Films

Abstract: The fracture toughness, fracture strength, and stress corrosion cracking behavior of thin-film amorphous silicon dioxide (SiO2) deposited on silicon wafers via plasma-enhanced chemical vapor deposition have been measured using specimens with length scales comparable to micromachined devices. Clamped-clamped microtensile specimens were fabricated using standard micromachining techniques. These devices exploit residual tensile stresses in the film to create stress intensity factors at precrack tips and stress concentrations at notches, in order to measure fracture toughness and fracture strength, respectively. The fracture toughness of thin-film SiO2 was 0.77 plusmn 0.15 MPa ldr m1/2, and the fracture strength was 0.81 plusmn 0.06 GPa. Stress corrosion cracking (slow crack growth) was also measured in the SiO2 devices with sharp precracks subjected to residual tensile stresses. These data are used to predict lifetimes for a SiO2-based microdevice.

3D Finite-Element Analysis of Substandard RC Columns Strengthened by Fiber-Reinforced Polymer Sheets

Abstract: Numerical analyses are performed to predict the stress–strain behavior of square reinforced concrete columns strengthened by fiber-reinforced polymer (FRP) sheet confinement. The research focuses on the contribution of FRP sheets to the prevention of elastic buckling of longitudinal steel bars under compression, in cases of inadequate stirrup spacing. A new Drucker–Prager-type plasticity model is proposed for confined concrete and is used in constructed finite-element model. Suitable plasticity and elasticity models are used for steel reinforcing bars and fiber-reinforced polymers correspondingly. The finite-element analyses results are compared against published experimental results of columns subjected to axial compression, to validate the proposed finite-element model. Stress concentrations in concrete core and on FRP jacket are investigated considering circular or square sectioned, plain or reinforced concrete columns. Geometry of the section as well as the presence of steel bars and stirrups affect r...

The Modified Wöhler Curve Method applied along with the Theory of Critical Distances to estimate finite life of notched components subjected to complex multiaxial loading paths

Abstract: This paper is concerned with the use of the Modified Wohler Curve Method (MWCM) applied in conjunction with the Theory of Critical Distances (TCD) to estimate fatigue lifetime of mechanical components subjected to multiaxial cyclic loading and experiencing stress concentration phenomena. In more detail, our engineering approach takes as its starting point the idea that accurate estimates can be obtained by simply assuming that the value of the critical length, LM, to be used to evaluate fatigue damage in the medium–cycle multiaxial fatigue regime is a function of the number of cycles to failure, Nf. In other words, the MWCM, which is a bi-parametrical critical plane approach, is suggested here to be applied by directly post-processing the linear-elastic stress state damaging a material point whose distance from the notch tip increases as Nf decreases. According to the main feature of the TCD, the above LM versus Nf relationship is assumed to be a material property to be determined experimentally: such an hypothesis results in a great simplification of the fatigue assessment problem because, for a given material, the same critical length can be used to estimate fatigue damage independent of the considered geometrical feature. The accuracy of the devised approach was checked by analysing about 150 experimental results we generated by testing V-notched cylindrical samples made of a commercial cold-rolled low-carbon steel. The above specimens were tested under in-phase and out-of-phase combined tension and torsion, considering the damaging effect of superimposed static stresses as well. Moreover, in order to better check its accuracy in assessing notched components subjected to complex loading paths, our method was also applied to several data sets taken from the literature. This extensive validation exercise allowed us to prove that the MWCM applied along with the TCD is successful in estimating medium-cycle multiaxial fatigue damage (Nf values in the range 104–106), resulting in predictions falling within the widest scatter band between the two used to calibrate the method itself. Such a high accuracy level is very promising, especially in light of the fact that the proposed approach predicts multiaxial fatigue lifetime by post-processing the linear elastic stress fields in the fatigue process zone: this makes our method suitable for being used to assess real components by performing the stress analysis through simple linear-elastic FE models.