Study of Fracture Properties of Composites and Aluminium Alloys Using Size Effect Method

Abstract

The size effect is a problem of scaling, which is central to every physical theory. In fluid mechanics research, the problem of scaling continuously played a prominent role for over a hundred years. In solid mechanics research, though, the attention to scaling had many interruptions and became intense only during the last decade. The question of size effect recently became a crucial consideration in the efforts to use advanced fiber composites and sandwiches for large ship hulls, bulkheads, decks, stacks and masts, as well as for large load-bearing fuselage panels. The scaling problems are even greater in geotechnical engineering, arctic engineering, and geomechanics. In analyzing the safety of an excavation wall or a tunnel, the risk of a mountain slide, the risk of slip of a fault in the earth crust or the force exerted on an oil platform in the Arctic by a moving mile-size ice floe, the scale jump from the laboratory spans many orders of magnitude. In the present investigation, tested 186 specimens made of glass fibre composites with three different widths 30 mm, 40 mm and 50 mm, these composite specimens were tested at four different displacement loading rates to know the effect of displacement loading rate on fracture parameters by using size effect method. The fracture parameters of three different alloys 5052 – H32, 6061 – T6 and 8011 at constant strain rate were determined by using size effect method. The fracture properties of composites and aluminium alloys determined by using linear regression analyis, R-curve approach and work of fracture methods. Size-effect method is used in determining mode-I fracture characteristics of woven fiber glass/epoxy composite laminates for varying loading rates. Tensile testing of geometrically similar single edge notch (SEN) specimens with three widths 30 mm, 40 mm, and 50 mm is carried out for four different displacement loading rates, namely 1, 10, 100, and 500 mm/min. For each width (D) and loading rate, the crack-length (a) is varied as 0.125D, 0.25D, 0.375D, and 0.5D. A total of 186 specimens were tested. The peak stresses (_Nu), the initial Young’s modulus (Exx), and the shear modulus (Gxy) were calculated. The fracture toughness (KIC), critical strain energy release rate (Gf ), and material characteristic length (Cf ) were calculated using linear regression analysis of nonlinear fracture mechanics equations. The values of Gf and Cf first decrease and then increase monotonically as the loading rate changes from 1 to 500 mm/min. This behavior was explained using Bažant size effect equation relating nominal strength and specimen size. The study revealed the change in modes of failure characterized by a jump in brittleness number as loading rate increases from 1 mm/min to 10 mm/min, followed by decrease in brittleness number as loading rate increases from 10 mm/min to 500 mm/min. This conclusion was supported by highly magnified images of failed specimens using scanning electron microscope. A numerical algorithm to determine crack growth resistance curves (R-curves) from peak load is also implemented. The R-curves are geometry as well as loading rate-dependent and give Gf , Cf values which agree qualitatively and to some extent quantitatively with the linear regression approach.Size-effect method is used to determine the fracture properties of three aluminium alloys. Mode-I tensile testing of thin rectangular sheets of aluminium alloys 5052−H32, 6061−T6, and 8011 is carried out. The test specimens are scaled geometrically in the ratio of 1:2:3:4 for a constant length (L) to width (D) ratio (L/D = 4). The notch depth (a) to width (D) ratio is 0.25. The size-dependency of strength is observed. The fracture toughness values and the crack growth resistance curves (R-curves) for these three alloys are determined using the equivalent elastic crack model. The R-curves predict the peak loads accurately with only 0-7% difference from the experimental values. The pre-peak load-deflection curves calculated from the R-curves closely match the experimental curves. Bažant’s size effect law could be used to fit the peak load data. Scaling laws for strains at peak loads are proposed. The transition length (D0) determined for these strain scaling laws differ from those obtained using the size effect law.