Showing papers on "Stress concentration published in 2014"

Visualization of the complex structure and stress field inside rock by means of 3D printing technology

Abstract: Accurate characterization and visualization of the complex inner structure and stress distribution of rocks are of vital significance to solve a variety of underground engineering problems. In this paper, we incorporate several advanced technologies, such as CT scan, three-dimensional (3D) reconstruction, and 3D printing, to produce a physical model representing the natural coal rock that inherently contains complex fractures or joints. We employ 3D frozen stress and photoelastic technologies to characterize and visualize the stress distribution within the fractured rock under uniaxial compression. The 3D printed model presents the fracture structures identical to those of the natural prototype. The mechanical properties of the printed model, including uniaxial compression strength, elastic modulus, and Poissons ratio, are testified to be similar to those of the prototype coal rock. The frozen stress and photoelastic tests show that the location of stress concentration and the stress gradient around the discontinuous fractures are in good agreement with the numerical predictions of the real coal sample. The proposed method appears to be capable of visually quantifying the influences of discontinuous, irregular fractures on the strength, deformation, and stress concentration of coal rock. The method of incorporating 3D printing and frozen stress technologies shows a promising way to quantify and visualize the complex fracture structures and their influences on 3D stress distribution of underground rocks, which can also be used to verify numerical simulations.

State‐of‐the‐art review on extended stress intensity factor concepts

Abstract: The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V-notches with stress intensities depending on the notch opening angle. The loading-mode-related simple notch stress intensity factors K1, K2 and K3 are introduced. Another extension refers to rounded notches with crack shape or V-notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading-mode-related generalised notch stress intensity factors K1ρ, K2ρ and K3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work-hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K1p, K2p and K3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet-welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V-notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.

Determination of the Effect of Stress State on the Onset of Ductile Fracture Through Tension-Torsion Experiments

Abstract: A tubular tension-torsion specimen is proposed to characterize the onset of ductile fracture in bulk materials at low stress triaxialities. The specimen features a stocky gage section of reduced thickness. The specimen geometry is optimized such that the stress and strain fields within the gage section are approximately uniform prior to necking. The stress state is plane stress while the circumferential strain is approximately zero. By applying different combinations of tension and torsion, the material response can be determined for stress triaxialities ranging from zero (pure shear) to about 0.58 (transverse plane strain tension), and Lode angle parameters ranging from 0 to 1. The relative displacement and rotation of the specimen shoulders as well as the surface strain fields within the gage section are determined through stereo digital image correlation. Multi-axial fracture experiments are performed on a 36NiCrMo16 high strength steel. A finite element model is built to determine the evolution of the local stress and strain fields all the way to fracture. Furthermore, the newly-proposed Hosford-Coulomb fracture initiation model is used to describe the effect of stress state on the onset of fracture.

The strength of the adhesively bonded step-lap joints for different step numbers

Abstract: Peel stresses developing at the edges of the overlap area of the adhesively bonded single lap joints subjected to static tensile loading have a profound effect on the damage of the joint . The reduction in the stress values formed at the edges of the overlap area or the transfer of these stresses to the middle part of the overlap area increase the strength of the joint. In this study, mechanical properties of the single lap joint (SLJ), one step lap joint (OSLJ) and three step lap joint (TSLJ) subjected to tensile loading were examined experimentally and numerically by keeping the bonding area same for all samples examined. In the samples produced for experimental study, AA2024-T3 aluminum alloy was used as adherent, while a flexible adhesive SBT9244 and a stiff adhesive DP460 were applied separately. After experimental studies on the three different joint types were conducted, stress analyses in the joints were performed with a three-dimensional finite element method by considering the geometrical non-linearity and the material non-linearities of the adhesive and adherend. As a result, it was observed that one-step lap geometry reduces the stress concentration developing at the edges of the overlap area while the highest decrease occurred in the three-step lap geometry. Additionally, the amount of reduction in the stress values supports the increase in the experimentally obtained load carrying capacity of the joint.

Gigacycle fatigue properties of Ti–6Al–4V alloy under tensile mean stress

Abstract: The mean stress effects on the gigacycle fatigue properties of three heats of Ti–6Al–4V alloy were investigated by means of ultrasonic and electromagnetic resonance fatigue tests. All heats developed internal fractures under mean stress conditions of R≥0 with negligible frequency effects. The origins of the internal fractures proved not to be inclusions, but clusters of facets. Cross-sectional observations of the internal fractured specimen revealed the facets to have formed in the α-phase in an inclined direction. The gigacycle fatigue strength of the Ti–6Al–4V alloy at R=−1 matched that of quenched and tempered steel, while that under R=0 was clearly lower. Ti–6Al–4V alloy is more prone to internal fracturing under tensile mean stress conditions, resulting in reduced fatigue strength. Its gigacycle fatigue strengths are thus below the modified Goodman line at around R=0. This trend is very dangerous, since the modified Goodman line generally gives predictions with a good margin of safety.

Micromechanics of ITZ–Aggregate Interaction in Concrete Part I: Stress Concentration

Abstract: At the macroscopic scale, concrete appears as a composite made of a cement paste matrix with embedded aggregates. The latter are covered by interfacial transition zones (ITZs) of reduced stiffness and strength. Cracking in the ITZs is probably the key to the nonlinear stress–strain behavior in the prepeak regime. For a deeper understanding of this effect triggered by tensile microstress peaks, we here employ and extend the framework of continuum micromechanics, as to develop analytical solutions relating the macroscopic stresses acting on a piece of concrete, to microtractions at the aggregates' surfaces and to three-dimensional stress states within the ITZs. In the latter context, a new aggregate-to-ITZ stress concentration tensor is derived based on the separation-of-scale principle, which implies that ITZs may be modeled as two-dimensional interfaces at the concrete scale, but as three-dimensional bulk phases at the scale of a few micrometers. Microtensile peaks occur both under uniaxial macroscopic tension and compression. To describe the respective microtraction and microstress fields, it is suitable to define aggregate's “poles” and “equator” by an “axis” through the aggregate center, directed in the uniaxial macroscopic loading direction. Accordingly, tensile microtraction peaks, induced by macro-tension and macro-compression, respectively, occur at the “poles” and at the “equator”, respectively. The largest tensile ITZ-microstresses occur at an offset of about π/8 from the “poles” and the “equator”, respectively. These fields of microtractions and ITZ microstresses are prerequisites for upscaling ITZ-related strength to the macroscopic concrete level, as presented in the companion paper (Part II).

Multiscale fatigue crack growth modelling for welded stiffened panels

Abstract: The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstruc- tural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka-Mura approach for the analysis of the problem. Mode I SIFs, KI, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, Ktot, is derived by a part due to the applied load, Kappl, and by a part due to welding residual stresses, Kres. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.

DEM Simulation of Direct Shear: 1. Rupture Under Constant Normal Stress Boundary Conditions

Abstract: A particle-based distinct element method and its grain-based method are used to generate and simulate a synthetic specimen calibrated to the rupture characteristics of an intact (non-jointed) low-porosity brittle rock deformed in direct shear. The simulations are compared to the laboratory-generated ruptures and used to investigate rupture at various normal stress magnitudes. The fracturing processes leading to shear rupture zone creation and the rupture mechanism are found to be normal stress dependent (progressing from tensile splitting to shear rupture) and show partial confirmation of rupture zone creation in nature and in experiments from other materials. The normal stress dependent change is found to be due to the orientation of the major principal stress and local stress concentrations internal to the synthetic specimens being deformed. The normal stress dependent rupture creation process results in a change to the rupture zone’s geometry, shear stress versus horizontal displacement response, and thus ultimate strength.

Fatigue damage propagation in unidirectional glass fibre reinforced composites made of a non-crimp fabric

Abstract: Damage progression in unidirectional glass fibre reinforced composites manufactured of a non-crimp fabric subjected to tension-tension fatigue is investigated, and a quantitative explanation is given for the experimentally observed stiffness degradation. The underlying damage-mechanisms are examined using three distinct microscopic analyses, and the transverse crack density is measured. It is documented that the stiffness loss in fatigue is directly related to fibre fractures in the load-carrying axial fibre bundles, initialised by interface debonding and cracking in the transverse backing bundles. A simple stiffness spring model validates the stiffness loss observed. A fatigue damage scheme is presented, which suggests that damage initiates due to failure of the backing bundle causing a stress concentration in the axial load-carrying fibres. This stress concentration, along with fretting fatigue, gives rise to axial fibre fractures and a loss of stiffness, eventually leading to final failure. The uniquen...

Characterization of crack tip stress fields in test specimens using mode mixity parameters

Abstract: The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the $$T$$ -stress, elastic–plastic stress fields, integration constant $$I_{n}$$ , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field $$I_{n}$$ and the $$T$$ -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the $$T$$ -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.