Compressive Stress Intensity Research Articles

A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes

This paper introduces a three-dimensional finite element (FE) formulation to accurately model the linear elastic deformation of fractured media under compressive loading. The presented method applies the classic Augmented Lagrangian(AL)-Uzawa method, to evaluate the growth of multiple interacting and intersecting discrete fractures. The volume and surfaces are discretized by unstructured quadratic triangle-tetrahedral meshes; quarter-point triangles and tetrahedra are placed around fracture tips. Frictional contact between crack faces for high contact precisions is modeled using isoparametric integration point-to-integration point contact discretization, and a gap-based augmentation procedure. Contact forces are updated by interpolating tractions over elements that are adjacent to fracture tips, and have boundaries that are excluded from the contact region. Stress intensity factors are computed numerically using the methods of displacement correlation and disk-shaped domain integral. A novel square-root singular variation of the penalty parameter near the crack front is proposed to accurately model the contact tractions near the crack front. Tractions and compressive stress intensity factors are validated against analytical solutions. Numerical examples of cubes containing one, two, twenty four and seventy interacting and intersecting fractures are presented.

Inclined Double Notch Shear Test for Improved Interlaminar Shear Strength Measurements

A novel method to measure interlaminar shear strengths of composites is presented. This method uses the double notch shear (DNS) specimen and modifies the load introduction by use of a fixture. The main concept is to eliminate the compressive stress intensity at the notch roots, arising from the external load, by imposing a counteracting tensile load field there. This field is caused by a bending moment acting over the notched region. Proportional loading is achieved by holding the specimen in an inclined position with supports near its ends and behind the notches. The inclination angle determines the ratio between the compressive normal field and the tensile bending field. The required inclination angle depends on the notch distance, specimen thickness ratio, and to a lesser degree on any material anisotropy. Two test series, with four different notch distances, were carried out to compare the standard DNS test to the new method. The new method produced consistently higher strengths at all notch distances. For the shortest notch distance, which incidentally gives the highest strength values, the measured average interlaminar shear strength was almost doubled with the new method. As with the standard method, the new method still gives lower strength values with increasing notch distances and notable experimental scatter. Causes for this are discussed and some possibilities for improvements are outlined.

Effect of geometry on compressive failure of notched composites

The compressive failure of carbon fibre-epoxy laminates is investigated theoretically and experimentally. Panels with a single edge notch, a central notch or a central hole are considered. The failure mechanism is by microbuckling in the 0° plies and is accompanied by delamination and plastic deformation in the off-axis plies [1]. To predict the critical length of the microbuckle and the failure load, the microbuckle is modelled as a cohesive zone. The magnitude of the normal compressive traction across the microbuckle is assumed to decrease linearly with increasing overlap of material on either side of the microbuckle. The relative effect of the specimen size and a bridging length scale is investigated to illustrate the transition between small-scale and large-scale bridging. If the bridging length scale is small compared with the specimen dimensions, the specimen fails when the stress intensity at the notch tip equals a critical compressive stress intensity factorK IC . When the bridging length scale is not small compared with either the initial defect size or the unnotched ligament length then it is necessary to include the details of the traction across the microbuckle to predict the failure load accurately.

The effects of stress ratio on fatigue threshold

Arising from the fact that there is a reverse compression stress around a fatigue crack, it is supposed that there is an equivalent compressive high-strain area. Based upon the eigenequation of crack growth, the critical value, K th c, of the compressive stress intensity factor is derived. The analytical expression for the change in fatigue threshold with stress ratio is derived from the similarity between the crack closure stress intensity factor and K th c. The fatigue threshold values for some materials are calculated using the results of this paper; it is found that the theoretical values are in good agreement with the experimental results.