One of the more formidable problems in composite research is the study of delamination and other failure modes in the vicinity of a circular hole in a laminate, e.g., a circular cut-out in a structure. In this problem, the singularity varies around the periphery of the hole as well as through the thickness of the laminate. Under tensile loading, the early failure modes in this problem consist of transverse cracks in various layers, so that delamination occurs only after other damage is precipitated, followed by fiber breakage leading to failure. A literature review of past work clearly shows that mechanical testing with simultaneous AE monitoring is a fruitful technique to study damage accumulation in composite systems. The acoustic-ultrasonic (AU) testing combines the high sensitivity of ultrasonics to internal damage and the method of acoustic emission technique to characterize elastic waves. As damage accumulates in the specimen along the wave path, the net internal damping increases and changes the wave parameters such as peak amplitude, duration, etc. accordingly. Additionally, a range of experimental results over the last decade has further shown that the mechanical deformation and electric resistance of carbon fiber reinforced polymers are coupled, so that the material is inherently a sensor of its own damage state. The monitoring of electric resistance and capacitance changes, linked to the modifications of the conduction paths in the composite, allows the detection of damage growth. It seems logical that a natural extension of these different approaches is the determination of damage mode, e.g., fiber breakage, matrix cracking or delamination, and damage size and position, based on combined measurements from these techniques. These multiple techniques will serve a two-fold purpose, namely, enable comparison as well as complement each other in case of incomplete damage mapping from one set of sensors For this study, we will consider carbon fiber-reinforced toughened bismaleimide, (IM7/5250-4) quasi-isotropic laminate coupons 12” long, 4” wide with hole at the center under tension. Figure 1 shows the damage which occurs around a 0.75” hole in a [45/0/-45/90]s graphite epoxy laminate obtained by radiography after unloading the test specimen from an applied stress of 50 Ksi. The failure stress for this laminate was 56.4 Ksi. Damage in the form of ply cracks in the 90, 45, and −45 plies and delamination around hole edges is clearly evident. The radiograph taken after unloading from a 50 Ksi stress level clearly shows the location and extent of damage, but contains no specific information about the sequence and the timing of damage events. Figure 2 shows stress-strain curves obtained from strain gages mounted at various distances away from the hole edge along with the far-field value. The stress-strain curves provide useful information regarding the initiation as well as the growth of the damage, as evidenced by jump in strain levels and onset of nonlinearity. Damage initiation is first picked up by the strain gage which is mounted closest to the hole edge at a stress level of 21 Ksi. Subsequently, other strain gages begin to sense damage growth as the applied stress level increases. The strain gage data provides useful information regarding initiation, growth and severity of damage, but it is difficult to assign specific damage modes and their location to the measurements. This example clearly demonstrates the needs, with the associated benefits, of the multiple sensor approach. In this work, three different hole sizes (0.25”, 0.5” and 0.75”) will be investigated. This example problem will enable us to examine the combined effects of cut-outs, matrix cracking, delamination and fiber breakage on the ability of various NDE techniques to assess damage. The development and growth of damage in the composite laminate with a hole under compression will be markedly different than in tension. Under compression, the major damage modes are fiber buckling and delamination, and will also be investigated.
Finite element prediction of fatigue damage growth in cancellous bone
