Crack Eccentricity Research Articles

Stress Field and Crack Pattern Interpretation by Deep Learning in a 2D Solid

ABSTRACTA nonlinear variational auto‐encoder (NLVAE) is developed to reconstruct the plane strain stress field in a solid with embedded cracks subjected to uniaxial tension, uniaxial compression, and shear loading paths. Latent features are sampled from a skew‐normal distribution, which allows encoding marked variations of the features of the stress field across the load steps. The NLVAE is trained and tested based upon stress maps generated with the finite element method (FEM) with cohesive zone elements (CZEs). The NLVAE successfully captures stress concentrations that develop across the loading steps as a result of crack propagation, especially when enhanced disentanglement is emphasized during training. Some latent variables consistently emerge as significant across various microstructure descriptors and loading paths. Correlations observed between the evolution of fabric descriptors and that of their significant stress latent features indicate that the NLVAE can capture important microstructure transitions during the loading process. Crack connectivity, crack eccentricity, and the distribution of zones of highly connected opened cracks versus zones with no cracks are the fabric descriptors that best explain the sequences of latent features that are the most important for the reconstruction of the stress field. Notably, the distributional shape, tail behavior, and symmetry of microstructure descriptor distributions have more influence on the stress field than basic measures of central tendency and spread.

Stress Intensity Factor (SIF) Solutions and Fatigue Crack Paths in Eccentric Circumferentially Cracked Round Bar (CCRB) in Tension

In this paper, a numerical modeling was developed to study (on the basis of the Paris law) the fatigue propagation paths of eccentric external (outer) cracks in circumferentially cracked round bars (CCRB) subjected to a cyclic type of loading in the form of either remote tensile loading or imposed axial displacement. Results show how the eccentricity (in relation to the wire axis) of the circular resistant ligament increases with the growth of outer circumferential cracks by subcritical fatigue mechanisms. This phenomenon is more pronounced when the solicitation consists of a remote tensile loading than when it is an axial displacement, when the initial eccentricity of the ligament increases (for a given initial diameter), and when the Paris exponent characteristic of the material rises. The paper also analyzes in depth the different situations regarding contact between crack faces during subcritical cyclic fatigue propagation, covering a wide range of cases including no contact, partial contact, and full contact depending on the ligament diameter (during the process of fatigue crack advance) and the relative eccentricity of the annular crack that loses its axial symmetry in relation to the round bar (cylinder) axis. In addition to the fatigue crack path study, closed-form stress intensity factor (SIF) solutions for the considered geometry (a cylinder with an outer annular crack) are provided in the form of third-degree polynomial expressions as a function of the ligament diameter and the crack eccentricity (both in dimensionless terms).

Notch Effects on the Stress Intensity Factor and on the Fatigue Crack Path for Eccentric Circular Internal Cracks in Elliptically Notched Round Bars under Tensile Loading.

In this paper, stress intensity factor (SIF) solutions are numerically obtained for notched bars subjected to tensile loading containing an eccentric circular inner crack located in the cross-section corresponding to the notch root. The finite element method and the J-integral have been used to obtain the SIF and to analyze the effect on it of three elliptical notch geometries (of equal radial depth). The results show how the SIF is greater in the notched bars than in the smooth bar and within the former when the axial semi-axis of the notch rises, its effect being greater as the diameter and eccentricity of the inner crack increase. In addition, the fatigue growth of an eccentric crack induces an increase in such eccentricity, greater as the notch axial semi-axis increases. The cause of these phenomena can be attributed to the constraint loss caused by the notch, which also facilitates bending of the specimen due to the asymmetry generated by the crack eccentricity.

Review and synthesis of stress intensity factor (SIF) solutions for circular inner cracks in round bars under tension loading

In this paper, stress intensity factor (SIF) is calculated in a bar subjected to tensile loading, considering a circular inner crack that exhibits certain eccentricity in relation to the cylinder axis. The computation is made by means of the finite element method (FEM) using a three dimensional (3D) model and the J-integral, the analyzed variables being the diameter and the eccentricity of the circular inner crack. Results show how the SIF is higher at the point of the crack front closest to the bar surface and that an increase of crack eccentricity or of crack diameter raises the difference between the SIF values at the opposite crack points located at minimum and maximum distance from the bar surface.

Experimental and numerical study of compressive buckling stability of plates with off-center crack

One of the criteria in the structural design is the buckling stability of the components. In cracked plates, the buckling phenomenon can be affected by the cracks. Therefore, it is important to investigate the effect of crack length and location on the buckling behavior. In this paper, the buckling stability of plates with different sizes ranging from short to long off-center cracks was studied by using the experimental and numerical methods. For this purpose, the clamped-free plate specimens of 1100 aluminum alloy with a crack in different length and locations were subjected to uniaxial compressive load. The experimental data were complemented with the numerical results obtained from extended finite element analyses, in order to further study the effect of various crack parameters in different types of boundary conditions. The agreement between the test and numerical results was quite satisfactory. Based on the results, the effect of crack eccentricity largely depends on the type of plate supports; and for the plates with two opposite free edges, the larger crack, the lower buckling stability.

Stress intensity factor for an eccentric circular inner crack in a round bar subjected to tensile loading

In this paper, stress intensity factor (SIF) was calculated in a bar subjected to tensile loading, considering a circular inner crack that exhibited certain eccentricity in relation to the cylinder axis. The computation was performed by means of the finite element method (FEM) using a three dimensional (3D) model and the J-integral, the analyzed variables being the diameter and the eccentricity of the circular inner crack. Results show that the SIF is higher at the point of the crack front closest to the bar surface and that an increase of relative crack eccentricity or of relative crack diameter raises the difference between the SIF values at the crack point closest to the bar surface and the crack point furthest from it, thus the existence of eccentricity in the initial crack leads to an increase of such a parameter when fatigue propagation occurs.

The influence of hygrothermal environments on the stress concentration in unidirectional composite lamina

In this paper, the stress analysis of unidirectional composite lamina, containing aligned broken fibers and exposed to hygrothermal conditioning, is investigated. The governing equations are derived based on the modified shear-lag model and a proper micromechanic rule are used to consider the effect of temperature and moisture content on stress concentration factor (SCF) in composite materials. The results show that the SCF has been less affected by low temperature and moisture content while the hot/wet conditions have significant effect on it. At the high operational temperature levels, specifically near to the glass transition temperature and saturation state, it can be observed that the results are in a good agreement with the original shear lag model. The SCF decreases exponentially by increasing the fiber volume fraction in both in dry and hygrothermal conditions. Moreover, the effect of crack eccentricity and crack-tip matrix type on SCF has been evaluated in hygrothermal conditions.

Stress intensity factor for wide-flange steel member with crack surface interference

This paper presents a physically acceptable analysis of stress intensity factor (SIF) for a two-tip web crack in the wide-flange (W shape) steel member widely used in steel construction subjected to the linear distribution loading. The analysis includes the effect of crack surface interference, i.e., crack surfaces are not allowed to overlap, that magnifies the SIF and crack opening displacement (COD) in an opened portion of the crack. For a range of possible web cracks in typical hot-rolled W shapes listed in the AISC Steel Construction Manual, the effective mode-I SIF is a function of applied stress, web crack length, crack eccentricity, and flange-to-web area ratio of the W shape. The depth-to-width ratio of W shape is not a significant parameter in the calculation of SIF. The analysis results show that the conventional (overlapping) solution underestimates the SIF at the tension-side crack tip under bending up to 12%. The effect of crack surface interference only exists between the conditions for complete crack opening and complete crack closure. Both conditions are governed by axial-to-bending stress ratio.

Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria

The presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric fourpoint bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semianalytically using both the maximum tangential stress criterion and the strain energy density criterion (implemented as a procedure within the used finite element computational code) as well as numerically (from verification reasons). Multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series. Recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. It appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.).

Off-set crack propagation analysis under mixed mode loadings

An assessment was carried out herein to study the eccentricity of cracks subjected to mixed-mode loadings. Several loading locations relative to a central line were selected to induce mixed-mode loadings, which were computed using a finite element method. An adaptive meshing technique was adopted during the simulation of crack propagation to ensure the singularity of stress at the tip of the crack. The stress intensity failure criterion was used and programmed, and the node splitting technique was used when the stress intensity factor reached the fracture toughness of the material to simulate crack propagations. It was found that large variations in the stress intensity factor were observed when off-set cracks were used, and that K II decreased when loading distance increased, but increased when the off-set crack distance was increased. Both crack eccentricity and loading distance played important roles in producing mixed-mode loading, compared to the influence of central cracks. Correction factors were introduced to modify the calculation of stress intensity factors under mixed-mode loadings. Simulations of crack propagation were also conducted to study the effects of crack eccentricities and loading distances. It was found that the crack length, the loading distance relative to the central crack and the crack eccentricity dominated calculations of the integrity of cracked structures.